resource-based fdi and expropriation in developing economies

Journal of International Economics 92 (2014) 124–146

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Journal of International Economics

j ourna l homepage: www.e lsev ie r .com/ locate / j i e

Resource-based FDI and expropriation in developing economies

Christopher Hajzler 1

Department of Economics, University of Otago, PO Box 56, Dunedin 9054, New Zealand

E-mail address: [email protected] Tel.: +64 3 479 7387.2 This includes risk associated with corruption, war, an

survey conducted by the IMF CMCG (2003), most manaFDI rank access to the legal system and the enforceabilitthe political risks associated with investing. See Albu(2008), Geiger (1989), Jensen (2006) and Wei (2000) foverse impact of political risk on FDI.

0022-1996/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.jinteco.2013.10.004

a b s t r a c t
a r t i c l e i n f o
Article history:Received 21 September 2010Received in revised form 18 October 2013Accepted 18 October 2013Available online 28 October 2013

Keywords:ExpropriationForeign direct investmentNatural resources

Globally, foreign direct investment (FDI) assets are expropriated more in resource extraction industries com-pared to other sectors. Despite the higher apparent risk of expropriation in resources, countriesmore likely to ex-propriate also have a larger share of FDI in the resource sector. An incomplete markets model of FDI is developedto account for this puzzle. The type of government regime is stochastic, with low penalty regimes facing a rela-tively low, exogenous cost of expropriating FDI, and country risk ismeasuredby the variation in these costs acrossdifferent regimes. The key innovation of the model is that the government, before the regime type is known, isable to charge different prices to domestic and foreign investors for mineral rights. Granting cheap access in-creases FDI and reduces the country's share of resource rents, increasing the temptation to expropriate in a rel-atively low penalty regime. In very high-risk countries, subsidizing resource FDI increases the total value ofoutput by raising investment, and the net gains from expropriating in a low penalty regime outweigh the rentsforegone under a high penalty one. However, a stochastic resource output price results in relatively low-riskcountries restricting FDI inflows to the resource sector instead— “windfall profits” in this sector raise incentivesto expropriate when prices are high, yet minimization of the ex ante risk of expropriation is preferred owing tothe relatively high penalty for expropriating. These results imply a higher average share of resource-based FDI incountriesmost likely to expropriate, while resources account for a high share of expropriated assets compared tothe sector's global share of FDI. We show that the model is able to reconcile observed patterns of foreign invest-ment and expropriation for a sample of 38 developing and emerging economies.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Political risk is frequently cited as an important determinant offoreign direct investment (FDI) in developing countries.2 A relativelyextreme but not uncommon form of political risk is expropriation,where a host-country government seizes company assets without faircompensation. This risk is particularly acute in resource-based sectors.Compared to the relative importance of these sectors in aggregate in-vestment and output, foreign investment is expropriated more in min-ing and petroleum than in other industries. Hajzler (2012) examinesthe sectoral distributions of expropriation over the 1990–2006 periodaccording to both number of foreign affiliated firms and the estimatedvalue of assets seized, which are reproduced in Table 1. The proportionof all foreign affiliates having had assets seized between 1990 and 2006that operated in extractive industries is 47%. In terms of the proportionof total FDI assets seized during this period, the resource sector shareis even higher (almost 60%). These shares are high compared to the

d expropriation. According to agers of companies engaged iny of contracts first in assessingquerque (2003), Alfaro et al.r empirical evidence of the ad-

ghts reserved.

average developing country resource production shares (about 22%),with the bulk of expropriation in mining and petroleum. Truitt (1970),Kobrin (1984), and Jones (1993) examine evidence for this sectoralpattern over the 1960s and 1970s, employing variousmeasures of expro-priation.3 This observation has motivated several authors to examineindustry-specific factors that increase the likelihood of expropriation inresources. The factors proposed include the prevalence of sunk costs inresources and mineral price volatility (Nellor, 1987; Monaldi, 2001;Engel and Fischer, 2010), varying uncertainty over project returns atdifferent phases of production (Kobrin, 1980), and issues related to na-tional economic security and strategic political objectives (Kobrin,1980; Shafer, 2009).

Much less attention has been given to the apparent willingnessof foreign investors to continue investing in resource extraction inseveral high-risk countries. In Bolivia, Ecuador, Russia, and Venezuela,for instance, large amounts of FDI are currently being expropriated inmining and petroleum, the same industries which had been national-ized in these countries several times during the past half-century. Re-peating cycles of foreign investment and expropriation, particularly in

3 Kobrin's (1984) expropriation data, which is also extended by Hajzler (2012) for the1993–2006 period, is a frequency-based measure he refers to as an expropriation “act.”Although a similar sector pattern of expropriation emerges using each of these measuresof expropriation intensity, we focus on the distribution over the value of assets seizedbecause this measure maps more naturally into our model's predictions.

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Table 2Sector FDI and output: expropriators vs non-expropriators.a

Non-expropriators Expropriators

Average N Average N

FDI (% total)Primaries 15.9 39 34.5 9Manufacturing 35.4 39 24.6 9Services 48.7 39 40.9 9

Value added (% total)Primaries 21.8 39 16.5 9Manufacturing 17.9 39 17.9 9Services 60.3 39 65.7 9

a Source: Hajzler (2012).

Table 1Sector expropriation shares: firms and FDI assets (1990–2006).⁎

1990–2006 period % of all firmsexpropriateda

% of all FDIassets seizedb

Primaries 47.1 58.3Agriculture 7.4 0.4Mining 17.6 16.2Petroleum 22.1 41.6

Manufacturing 17.6 9.4Services 35.3 32.3

a Excludes the 50 Dutch-owned farms estimated to have been expropriated inZimbabwe in 2005.

b Excludes Bolivia's Petrobas and Russia's Shakalin petroleum projects.⁎ Source: Hajzler (2012).

125C. Hajzler / Journal of International Economics 92 (2014) 124–146

extractive industries, have been well documented.4 There is alsocounter-intuitive evidence suggesting that developing countries thatare more likely to expropriate do better in attracting resource-based FDIrelative to the other sectors. Hajzler (2012) compares sector FDI and pro-duction shares across expropriating and non-expropriating countriesover 1990–2006 and finds that the resource FDI share is significantlyhigher among expropriating countries compared to non-expropriatingcountries, even though sector value-added shares differ little betweencountry groups. Specifically, the average share of resources in the totalstock of FDI is 35% in countries that have expropriated and only 16% inthose that have not (Table 2). What makes this observation is puzzlingis that expropriating countries do not appear more highly resource-dependent. If anything, expropriating countries appear slightly lessresource reliant.5 The relatively high resource-based FDI in countriesthat are likely to expropriate may help to explain why expropriationof resource-based FDI is relatively common and is a recurrent event inmany countries. Yet there is still a challenge in explaining what makesresource-based FDI relatively attractive in these countries. One possibleinterpretation is that governments offer incentives to foreign investorsin the form of low royalty rates in risky investment climates. However,under what circumstances this arrangement would be desirable fromthe host country's perspective, and what the implications are for foreigninvestment patterns, remain unclear.6

This paper formally examines the impact of expropriation riskon sectoral patterns of FDI, focussing on the role of governments in man-aging the economy's stock of mineral wealth. Host country governmentstypically decide how mineral rights are allocated and under what terms,and they can exercise a special influence over FDI in this sector that isnot paralleled in other sectors.7 The question we ask is this: under what

4 Hajzler (2012) notes that many of the countries expropriating during the 1990–2006period have also nationalized theMining and Petroleum sector atmultiple points over thepast century – Argentina (1963, 1974), Bolivia (1937, 1952, 1969, 2006), the DemocraticRepublic of Congo (1976, 1993), Ecuador (1969–1979, 2006), Indonesia (1960, 1965),Russia (1918, 2006) and Venezuela (1975, 2005)– as well as in the utilities sector —

Indonesia (1966, 1976, 1998) and Venezuela (1963, 1969). Other historical examples of“serial expropriators” are discussed in Gadano (2010) and Hogan et al. (2010). The latternote that host-countries, having felt the negative consequences of expropriation, will of-ten offer very favorable deals to investors to entice them back: “Then the cycle may startagain, with similar costs to both parties as before” (p.3).

5 It would be less surprising if these expropriating countries were also found to be par-ticularly resource-dependent. In this case, one explanation would be that sectoral FDI pat-terns are driven primarily by a country's comparative advantage, and that countrieswith acomparative advantage in the relatively risky resource sectors, in turn, have a higher pro-pensity to expropriate. However, a comparison of sector output shares does not revealsubstantial differences between the two groups.

6 Hajzler (2012) discusses evidence of this from published investor surveys, as well asother anecdotal evidence. Alternatively, it could also be argued that offering such incen-tives to foreign investors does not usually benefit the host country. Rather, the lack oftransparency and accountability in many countries can allow corrupt governments to selloff mineral rights cheaply and to pocket much of the gains.

7 Historically, utilities and banking have also been relatively vulnerable to expropria-tion. The utilities and banking sectors appear to share this feature of extractive industriesinsofar as governments can regulate market entry and offer companies monopoly profits,and the theoretical framework considered in this paper could potentially offer insight intoexpropriation in these sectors.

circumstances would governments want to partially offset the negativeimpact of political risk on FDI by offering mineral-rights more cheaplyto foreign investors? The idea that governments are able to offset expro-priation risk by providing “sweet deals” to foreign investors in the re-source sector is not a new one (see, for example, Monaldi, 2001). Incountries where a relatively low capital stock is a primary motivationfor attracting FDI, cheap mineral rights may be an attractive substitutefor direct subsidies. (Subsidies necessarily drawon already scarce domes-tic capital, which may be difficult financially and politically for many de-veloping country governments.) We ask whether or not a host countrybenefits from offering more favorable terms to foreign investors in re-sources when country risk is high, and whether this can provide insightinto the relatively large resource-based FDI in expropriating countries.

The two-sector environment that we consider builds on the single-sector, incomplete markets models of Eaton and Gersovitz (1984) andCole and English (1991). These papers consider a capital poor countrythat benefits from capital inflows, or FDI, but where aggregate invest-ment remains inefficiently low due to expropriation risk. There areno enforceable international regulations to protect investors, and ahost country government that maximizes domestic welfare (or perhapseven its own coffers) is tempted to take these investments when theirvalue is high. The payments the government collects from investorscan not be conditioned (fully) on the current and future profitabilityof the investment or on the costs of expropriating.8 The novel approachtaken in this paper is to examine the role of the host country mineralcontract in determining the patterns of foreign investment and expro-priation at the sector level. The government's optimal allocation andpricing ofmineral rights, aswell as required investments in the resourcesector, are evaluated at different levels of political risk. Of particularinterest are the implications for FDI at the sector level.

We focus on two sources of uncertainty: stochastic resource outputprices and a random external penalty to host country income if it expro-priates. Changes in the expropriation penalty can represent variation inthe external sanctions foreign investors (or their governments) canimpose on the host country, or may capture shifts in domestic politicalattitudes towards foreign investment. Political risk is then measured asthe spread between the size of the expropriation penalty in the highestpenalty regime – representing a governmentwith a high disincentive toexpropriate – and the size of the penalty of the lowest penalty regime.A relatively low risk country is one in which the expropriation penaltyis similarly high for all regimes, whereas a relatively high risk countryis characterized by large swings in the incentive to expropriate acrossthe different regimes.

We find that the model generates a positive relationship betweencountry risk and the share of FDI in resources, and this relationship is

8 This assumption also implies that expropriation can occur in equilibrium, which isconsistent with observation. For an analysis of the effects of expropriation risk on patternsof FDIwhen contracts are complete, see Thomas andWorrall (1994). Here, the equilibriumcontract delivers a positive share of the returns to the host-country only as necessary todeter expropriation— this allows the investor to recover its sunk investment costs soonerso that investment can be raised towards the efficient level, and expropriation neveroccurs.

126 C. Hajzler / Journal of International Economics 92 (2014) 124–146

attributed to two sources of asymmetry between the resource and non-resource sectors. First, we assume that the host country government caninfluence investment intensity in the resource sector as part of theminer-al contract, whereas it does not directly influence investment in the non-resource sector.9When a country is sufficiently high risk, the host countrygovernment expropriates in the lowest penalty regime (independent ofthe resource output price); in this case the optimal investment levels ex-ceed the competitive investment levels given the positive probability ofexpropriation, and offering mineral rights cheaply to foreign investorsamounts to shifting FDI out of the sectorwhere optimal investment levelscannot be attained to the sectorwhere they can.10 Although this asymme-try is sufficient to generate relatively high resource FDI shares in very highrisk countries, the second source of sector asymmetry we consider – rel-atively volatile resource output prices – results in a more subtle relation-ship between country risk and the optimal resource FDI share amongrelatively low risk countries. For low risk countries, where expropriatingis always costly, the optimal way to maximize FDI is to minimize thetemptation to ever expropriate at given levels of aggregate investment.Expropriation occurs when the aggregate ex post value of foreign assetsexceeds the expropriation penalty. This condition, along with the desireto keep the temptation to expropriate low, partitions the parameterspace into two sub-regions of country risk, each associatedwith a distinctcorner solution with respect to the optimal allocation of FDI between thetwo sectors. For the lower risk category, the ex post return per unit of in-vestment in the resource sector, which depends positively on theresource output price, can exceed that of the non-resource sector. Thisis because the threshold price below which expropriation never occursis high, allowing for potential “windfall” resource sector profits. Herethe temptation to expropriate in the low penalty regime is minimizedby allocating all mineral rights to domestic investors and shifting all FDIto the non-resource sector. For relatively high risk category, by contrast,ex post return in the resource sector never exceeds that of the othersector in a lowpenalty regimewithout all foreign assets being expropriat-ed. This implies that the temptation to ever expropriate is reduced asmore of the country's FDI is allocated to the resource sector.

We calibrate the model and simulate sector FDI shares and expropri-ation probabilities for a sample of 38 developing and emerging econo-mies. Predicted investment patterns and expropriation risk are broadlyconsistent with the data. Countries predicted to fall in the lowest riskcategory have expropriatedmuch less, on average, compared to countriesclassified as moderate or high risk, and they are also predicted to havemuch lower shares of FDI located in the resource sector compared to rel-atively high risk countries. These results imply that the volume of foreignassets seized will be biased towards resources relative to the sector'saverage importance in GDP. Moreover, for each country in the sample,we compare both the predicted and the empirical FDI shares to that ofstandard models. Our model predicts an adjustment in FDI shares in adirection of the empirical shares for 80% of the countries in the sample.Finally, the timing of expropriation in natural resource sectors often coin-cides with above average commodity prices both in the model and inthe data. As we might expect, host-country governments are more likelyto expropriate when the value of assets is high, whether they seek tomaximize host-country welfare or to line their own pockets. (This is akey feature of the models of expropriation developed by Eaton andGersovitz (1984), Cole and English (1991) – for certain host-countrywelfare functions – and Thomas and Worrall (1994)). The empiricaltendency for governments to expropriate or raise tax and royalty rates

9 This appears to be a standard feature of most mining contracts where investment ispartially determined, for example, by specifying minimum exploration requirements orby permissible cost-recovery deductions, which are discussed briefly in the next section.10 In relatively low risk countries, by contrast, where even the lowest penalty for expro-priating is high, the optimal level of FDI is associated with a zero probability of expropria-tion and this the optimal investment intensities in each sector do not differ from thecompetitive solution.

when the mineral price is above trend is documented in Duncan (2005)and Hajzler (2012).

This paper complements a number of recent theoretical investigationsof expropriation of foreign investment in natural resource sectors. Hoganet al. (2010), Engel and Fischer (2010), and Guriev et al. (2009) each ex-amine resource sector contracts in the presence of expropriation risk.They note that, historically, investors' returns in this sector tend to belower than what is stipulated in their contracts when prices are high(due to expropriation), yet they are offered very favorable concessionswhen prices are low (which are not likely to be honored in the longrun). Engel and Fischer (2010) show that deviations fromafixedpaymentschedule such as this can be an optimal response to expropriation risk inindustries with large sunk investments. In their model, however, theprobability of expropriation is an exogenous, positive function of projectreturn and all investment is sunk investment. These assumptions allowthe authors to focus on the effects of risk on the optimal allocation ofreturns in the resource contract. The analysis of this paper instead focuseson the relationship between country risk and sectoral patterns of expro-priation and FDI. In Guriev et al. (2009), simple resource sector contractsare considered and expropriation is also endogenous, but they focus ex-clusively on the effects of output prices and institutional quality (whichthey represent by a high, constant cost of expropriating) on foreign in-vestment and expropriation within a single sector.

Ourmodel also provides a rationale for cycles of particularly favorableresource FDI incentives interrupted by expropriation that have been ob-served in several countries, which relates to the recent literature on en-dogenous cycles of expropriation and privatization in natural resources.The dynamic, political economy model of Chang et al. (2010) explainsthese cycles by focusing on the links between private ownership, the evo-lution of income inequality, and the government's desire to redistributewealth. Opp (2012) develops a model with stochastic government re-gimes but where the productivity gap between foreign and state-operated projects differs across industries. He shows that cycles ofexpropriation and privatization are more likely in industries where thegap is not so large that it is never worthwhile to expropriate but not solow to discourage investment. Gadano (2010) provides a theory for cyclesof privatization attempts and reversals in Argentina's petroleum sector.He describes efforts to draw foreign capital as urgent responses to statesofmacroeconomic emergency, but observes thatmost instances of privat-ization have required government leaders to go back on campaign prom-ises, arguing that these betrayals render the resulting private contractspolitically untenable. Our analysis, in contrast, suggests that high levelsof political instabilitymay induce host country governments to offermin-eral rights cheaply to attract more FDI, which in turn increases the likeli-hood of expropriating in the future.

The rest of the paper is organized as follows. Section 2 and presentsthe basic model environment and defines the equilibrium strategies ofinvestors and the host country government. In Section 3, a simplifiedversion of the model with no resource output price uncertainty and asimple resource contract is used to emphasize main intuition for whyvery high-risk countries offermineral rights cheaply to foreign investorsto maximize FDI in this sector. Section 4 considers equilibrium with astochastic resource output price, and demonstrates the additionalimplications of price volatility on the optimal choice of resource con-tract at different levels of country risk. The model's key results are gen-eralized for a broader range of resource contracts, including ad valoremroyalty-based payments, in Section 5. Section 6 presents the empiricalresults for the calibrated model, and compares differences in the pre-dicted host country shares of resource sector returns and welfareunder various contract types. Section 7 concludes.

2. The model

Having reviewed the empirical facts and related literature,we presenta static, two-sectormodel of foreign investment and expropriation that isbroadly consistent with these facts.

12 Important exceptions may arise in industries where the government can guarantee


2.1. Basic environment

The basic environment consists of a large number of foreign inves-tors that compete for a limited number of projects in each of two sectorsof the host country. The host-country is capital poor and is unable to fi-nance all of these projects itself. Domestic and foreign capital are perfectsubstitutes in production, and the relatively high returns to capital inthe host country provide a motivation for foreign investors to invest.For simplicity, it is assumed that there is no foreign borrowing, so allcapital inflows take the form of FDI.11 We also assume that all FDIprojects are financed using foreign capital and do not use any domesticcapital. Therefore the source of capital determines project ownership/control.

In addition to domestic or foreign capital, production in each sectorrequires a sector-specific domestic input. In the resource sector, thisinput is a mineral right. In the non-resource sector, domestic labor isemployed. Output in each sector is produced using twice-differentiable,linear-homogenous production functions:

X j ¼ FðKXj; LjÞRj ¼ GðKRj;MjÞ

where Rj is the quantity of resource-sector output produced by firmsof type j and Xj is the quantity of non-resource output by firms of typej: either foreign (j = f) or domestic (j = h).Mj is the quantity of themin-eral rights leased by firms of type j. Similarly, Lj denotes labor employedby each firm type, and Kij is investment in sector i. Aggregate stocksof labor L and mineral rights M, as well as the total stock of domesticcapital K, are fixed, and the stock of labor is normalized to 1. We alsoassume F(0,∙) = G(0,∙) = 0, and

limKX→0

FK KX ; �ð Þ ¼ limKR→0

GK KR; �ð Þ ¼ ∞

where FK(∙) = ∂F / ∂K and GK(∙) = ∂G / ∂K.In the non-resource sector (henceforth “manufacturing”), both

foreign and domestic firms compete for access to domestic laborand face a common labor price w. In the resource sector, by contrast,the mineral rights are allocated by the government in the form of re-source contracts. The choice of resource contract is the main policytool available to the government, and the contract stipulates trans-fers to the government as well as the investment obligations of thefirm. One way to interpret the standard resource contract is as fol-lows. For each concession and corresponding investment amount,domestic and foreign investors compete by offering payments τhand τf resulting in schedules [KRj,τj] for j = h,f. The governmentchooses the preferred contracts among foreign and domestic biddersand allocates mineral rights accordingly. We begin by assuming thepayment schedule is independent of the state of nature. (This as-sumption is relaxed in Section 5.)

Under this resource contract the host-country government exercisesa significant influence over investment levels in this sector that it doesnot have in the other sector. This assumption is motivated by the obser-vation that, in practice, the government exercises significant controlover the supply and price of an essential input in production in resource

11 Albuquerque (2003) considers both FDI and foreign borrowing in an imperfect con-tract enforcement environment, where the value of borrowed capital is fully appropriablewhenever default occurs but only a fraction of the value of FDI can be appropriated. (Thiscaptures the notion that FDI is often accompanied byfirm-specificmanagerial or organiza-tional expertise that is costly or impossible for the host country to acquire.) In his analysis,FDI and borrowed or equity capital occur in distinct sectors and are therefore imperfectsubstitutes. In the context of industries where FDI and equity capital are substitutes, how-ever, the idea that it is relatively costly for the host country to appropriate FDI implies thatthis form of foreign investment is superior in the presence of expropriation risk, providinga rationale for focusing on FDI and abstracting from other types of capital inflows. I amgrateful to one of the referees for pointing out this connection.

extraction as well as contract terms, but typically does not in othersectors.12 Specific terms of mining contracts will typically jointly deter-mine the quantity and form of payment for the mineral concession andthe quantity of investment per concession. In the extreme, the entire setof investment obligations of each contracting party will be explicitlynegotiated. More often, however, only part of the investment willbe specified, as in the case of minimum investment requirements orwhen the development of specific infrastructure such as roads or portsis included in the contract, leaving the remaining capital investmentsup to the investor. A range of other contractual elements also influenceinvestment intensity, such as cost-recovery limits, the pooling of pro-duction and exploration expenses for tax purposes, and environmentalregulations (for instance, clean-up and restoration of the site at the endof production).13

Investment is risky – there is a positive probability that foreign capitaland derived output are seized by the host country government. That is,once the successful bidders for the resource contract as well as investorsin the non-resource sector have invested and output is produced, thegovernment may decide it is worthwhile to expropriate foreign investorassets. However, the relative costs and benefits to the host country fromexpropriating are unknown to both investors and the government at thetime that investments are made. Specifically, agents face an uncertainrelative mineral output price p∈P as well as a random penalty a∈Aincurred by the host country if the government decides to expropriate.We also assume that foreign firm payments are paid after revenues arereceived and only in the event their assets are not expropriated. A partic-ular state {a,p} is denoteds∈S ¼ A×P. The timingof themodel is summa-rized as follows:

Government announces resource contracts↓

KR; f ;KX; f ;KR;h; and KX;h are invested and output is produced↓

s∈S is realized↓

Government decides whether or not to expropriate↓

Investors pay τ f M f ; τhMh;wLf and wLh if not expropriated

��

��

2.2. Host country objective

The host-country government is altruistic and chooses a resourcecontracts that maximize what we refer to as host-country income. Theobjective function is a linear aggregator that takes into account the ex-pected penalty incurred from expropriation.

If the government does not expropriate, the host country receivesthe value of domestic firm production plus the revenues from leasingthe sector specific inputs to foreign firms, τfMf and wLf. If, on the otherhand, the government expropriates, the host country claims the entirevalue of output of both sectors. The country also incurs penalty a and

market power, such as telecommunications and public works. Here the essential input ismarket access itself, and it is reasonable to think that governments should exercise a com-mensurate degree of influence in these industries as well. Specified investment amountsare also common in the utilities sector and for build-to-operate contracts in otherindustries.13 Raising cost-recovery limits, which cap the amount of investment expenditures thatcan be deducted from taxable income,makes investmentmore attractive. Thismechanismis especially effective when decided in conjunction with the size and configuration of theexploration territory that forms the basis for the tax and exemptions. If the areas are largeand contain “frontier” regions that require considerable exploration expense, relaxingcost-recovery limits can raise the amount of exploration (and future development of wellsor mines) that takes place when exploration costs can be deducted from the income gen-erated on themore profitable tracts. A thorough comparison of different types of contractsin the petroleum production sector is provided by Johnston (2007).


forgoes domestic factor payments from investors whose assets havebeen seized.14

For ease of exposition, it is useful to define the vector of joint deci-sions taken prior to the expropriation decision as

θ ¼ Mf ;Mh;KRf ;KRh;KXf ;KXh; τ f ; τh; L f ; Lh� �

and to defineD⊂S ¼ A×P as the set (possibly empty) of states in whichthe government expropriates, which depends on θ. We refer to D as the“default set”.

Given any realization of a particular state, if the government doesnot expropriate, expected national income is

YN p; θð Þ ¼ F KXh; Lhð Þ þ pG KRh;Mhð Þ þw θð ÞL f þ τ f M f

where w(θ) represents the equilibrium price of labor given θ. If insteadthe government chooses to expropriate, income is

YE p; θð Þ−a ¼Xj¼h; f

ðFðKXj; L jÞ þ pGðKRj;MjÞÞ−a

Ex ante host-country income is

V θð Þ ¼Z

s∈D θð ÞYE p; θð Þ−a� �

h sð ÞdsþZ

s∉D θð ÞYN p; θð Þh sð Þds ð1Þ

where h(∙) is the joint probability density function over A×P.This treatment of the expropriation penalty as a deadweight loss is

most closely related to the approach of Eaton and Gersovitz (1984)who consider a host country government that can expropriate foreigncapital but is constrained from appropriating foreign managerial exper-tise, and where the domestic supply of managers is uncertain at thetime of investment. (A country with a higher expected managerialcapacity receives a comparatively low amount of FDI because the outputloss associated with expropriation is relatively low.) In the dynamicmodels of expropriation considered by Cole and English (1991), Thomasand Worrall (1994) and Albuquerque (2003), the threat of being cut offfrom future foreign investment is a sufficient penalty to prevent thehost country from finding it optimal to expropriate in all states, provid-ed the government's discount factor is not too low. Unlike thesemodels,future investment decisions are not relevant in the static environmentthat we consider here. However, the common feature with these dy-namic frameworks is a stochastic marginal utility of current consump-tion relative to the marginal utility of future consumption conditionalon the decision to expropriate.15

Note that the penalty is independent of the value of output andinvestment seized. Hence there is no incentive for the government topartially expropriate foreign assets once this penalty is incurred.

2.3. Investor returns

Foreign firms are assumed to fully commit to paying domesticfactors conditional on their assets not being expropriated, and candelay payments until payments for production are received. Denotingby π = Prob(s ∈ D) the ex ante probability that expropriation occurs,

14 In the manufacturing sector, we assume that the government pays all workers fromthe revenues of its newly acquired state enterprise.15 What is essential for FDI is that there is some positive, exogenous cost component as-sociated with expropriation. Whether this is interpreted as a loss in output, as in the caseof externally imposed sanctions, or as a lack of political support for such actions, does notmatter. In the former case, the government objective function is expectednational income,and in the latter case it is instead a government utility function that is linear over expectednational income and the expected default penalty.

expected returns to the representative foreign investor in themanufacturing sector is given by

E ΠXf

h i¼ 1−πð Þ FðKXf ; L f Þ−wLf

� �− 1þ rð ÞKXf ð2Þ

where r is the world risk-free rate of return on capital. (Without loss ofgenerality, capital is assumed to fully depreciate.) Domestic investorsdo not face risk of expropriation, but must pay domestic capital rh, anddomestic investor returns are

E ΠXh½ � ¼ F KXh; Lhð Þ−wLh− 1þ rh� �

KXh: ð3Þ

Resource sector contracts deliver the following returns to foreignand domestic investors:

E ΠRf

h i¼ 1−πð Þ E p½ js∉Dð �GðKRf ;Mf Þ−τ f M f Þ− 1þ rð ÞKRf ð4Þ

E ΠRh½ � ¼ E p½ �G KRh;Mhð Þ−τhMh− 1þ rh� �

KRh ð5Þ

where E[p|s ∉ D] is the expected price of the resource good given that ex-propriation has not occurred and E[p] is the unconditional expected price.

2.4. Equilibrium

With the above definitions of production, resource contracts, inves-tor returns, and host country income, we can define an open-economyequilibrium with foreign investment.

Definition 2.1. An open-economy equilibrium is a vector

θ ¼ Mf ;Mh;KRf ;KRh;KXf ;KXh; τ f ; τh; L f ; Lh� �

as well as prices w and rh, default set D and a probability of expropriation πsatisfying the following:

(i) Givenw, π and rh, foreign and domestic manufacturing firms choose{KXf,Lf} and {KXh,Lh}, respectively, to maximize Eqs. (2) and (3).

(ii) The host country government chooses contracts [KRf,τf] and [KRh,τh]and allocates Mf and Mh to maximize Eq. (1) subject to the partici-pation constraints of foreign and domestic firms, Eq. (4) ≥ 0 andEq. (5) ≥ 0, taking into account the optimal responses of firms inthe manufacturing sector and corresponding changes in D.

(iii) Given θ, w, rh, and realization of s∈A×P , expropriation occurswhenever the resulting net gain in host-country income exceedsthe penalty a:

s∈D ⇔ abYE p; θð Þ−YN p; θð Þ:

(iv) Given θ and joint distribution h(∙) overA×P, the ex ante probabilityof expropriation is

π ¼Z

s∈Dh sð Þds:

(v) The domestic resource constraints are satisfied:

M f þMh ¼ MLf þ Lh ¼ 1KXh þ KRh ¼ K:

Section 3 characterizes the equilibrium in the special case of aconstant resource output price. This provides the benchmark for consid-ering the importance of stochastic resource output price in Section 4.Several general properties of the equilibrium are described beforeconsidering these separate cases.

KX

0

YE - YN - a

),( 2πxX kΠ ),( 1πxX kΠ

XK )( 1πXK

Fig. 1. Investor strategy in the non-resource sector.


Equilibrium conditions (iii) and (iv) define mappings from the vec-tor θ to the default set and probability of expropriation, respectively,D(θ) and π(θ). Observing θ and taking w(θ) and π(θ) as given, if thereis positive foreign investment in the manufacturing sector, competitiveforeign investors pay a wage to labor Lf that satisfies their zero profitcondition. The assumed homogeneity of production implies

w θð Þ ¼ FðkXf ;1Þ−1þ r

1−π θð Þ� �

kXf ð6Þ

where kXf = KXf / Lf. Conditional on positive foreign investment in thissector, the foreign investor capital–labor ratio in manufacturing deter-mines the equilibrium price of laborw(θ). If domestic investors operatein this sector, they payw(θ) per unit of labor and choose kXh = KXh / Lhto satisfy

w θð Þ ¼ F kXh;1ð Þ−FK kXh;1ð ÞkXf

where FK(⋅) = ∂F/∂Kh.If π(θ) is continuous (or constant) around equilibrium θ, the foreign

investment in manufacturing solves FK(kX(θ),1) = (1 + r) / (1 −π(θ)). However, if π(θ) is discontinuous in the region of optimal foreigninvestment, where an incremental increase in KXf implies a discretechange in the default set D(θ), it is possible for a single investor to gofrom strictly positive to strictly negative expected returns by increasingKXf beyond some threshold KXf θð Þ≤KXf θð Þ. In this situation no investorwould choose higher investment than KXf θð Þ , even though they maybe earning positive expected profits. This scenario is depicted in Fig. 1.For clarity, the resource output price is assumed to be constant in thisexample. The figure plots the expected profit functions E[ΠXf] for therepresentative foreign firm corresponding to two different expropria-tion probabilities, π1 b π2. In the event that the representative firmwas able to take probability π1 as given (hence facing profit functionΠX(Kx,π1)), the profit maximizing level of investment is K .16 Contrastthis with the casewhere increasingKX past K results in a discrete changein the default set. In the figure, this threshold is marked by a change inYE − YN − a from a negative to a positive value for some penaltya ∈ S. In other words, for values of KX below K, the net gain from expro-priating when penalty a is realized is negative and therefore a is not in-cluded in the default set. For values of KX above K, however, a enters thedefault set and the probability of expropriation rises to π2. Taking intoaccount the expropriation decision of the government, then, the actualprofit function of the firm is the solid curve, with the dashed portionscorresponding to infeasible default sets. From this function it is clearthat, if the jump in probability is large enough to result in negativeexpected profits for all foreign firms in the resource sector, no firm iswilling to invest beyond K .

More formally, consider any KXf1 (and corresponding default set

D(θ1)) such that, for some (ai,pj) ∉ D(θ1),

ai ¼ YEðpj; θ1Þ−YN pj; θ1� �

:

Given θ and p, an increase inKXfholding other elements of θ constantincreases YE(p,θ) − YN(p,θ). Consider θ2, the initial vector of actions θ1but with an arbitrarily small increase in KXf. Then {ai,pj} ∈ D(θ2). If K

1Xfb

KXf θ2ð Þ, then all firms are still earning positive expected returns after avery small increase in investment, and it is optimal to raise KXf. Other-wise, increasing KXf results in negative expected returns and optimalinvestment is KXf

1 .

16 In equilibrium, labor is paid its marginal product, shifting this curve downward suchthat profits are zero at this level of investment.

Equilibria with positive foreign and domestic investment inmanufacturing are also characterized by kXf = kXh = kX(θ).17 ThereforekX(θ) is also aggregate capital invested in themanufacturing sector, andkX(θ) = K − kRh(M − Mf) (kRh = KRh/(M − Mf)). Hence kX(θ) pinsdown Lf(θ) and Lh(θ) given kRh and Mf:

L f θð Þ ¼ 1−Lh θð Þ ¼kX θð Þ− K−kRh M−Mf

� �� kX θð Þ :

Finally, FK(kX(θ), 1) = 1 + rh(θ), implying 1 + rh(θ) = (1 + r)/(1 − π(θ)).

Successful bidders for the resource-sector contracts simply carry outthe investment and payments specified in the contract chosen by thegovernment (since all contracts deliver non-negative expected profits).This results in a schedule τf(θ) for foreign investors (and an analogousschedule for domestic investors). This schedule leaves the foreign inves-tor with zero expected profits:

τ f θð Þ ¼ E p½ js∉D θð Þ�GðkRf ;1Þ−1þ r

1−π θð Þ� �

kRf : ð7Þ

Given the payments made to labor and for access to mineral rightssummarized by Eqs. (6) and (7), it is straightforward to verify thatexpected host country income given by expression (1) is equal to:

V θð Þ ¼ F KXh; Lhð Þ þ FðKXf ; L f Þ þ E p½ �G KRh;Mhð Þ þ E p½ �GðKRf ;Mf Þ− 1þ rð Þ KXf þ KRf

h i−π θð ÞE a½ js∈D θð Þ�: ð8Þ

where E[p] is theunconditional averagemineral output price.Moreover,substituting Eqs. (6) and (7) into YE(p,θ) − YN(p,θ), D(θ) and π(θ) areimplicitly defined by

s∈D θð Þ ⇔ ab p−E p½ js∉D θð Þð �ÞGðKRf ;Mf Þ þ1þ rð Þ KXf þ KRf

� �1−π θð Þ : ð9Þ

17 Given that F kXf ;1� �

− 1þr1−π θð Þ

� �kXf and F(kXh,1) − FK(kXh,1)kXh are strictly concave, equal

to zero at kXj = 0, and given F(kXh,1) − FK(kXh,1)kXh is strictly increasing, equalitybetween these functions to w(θ) implies that kXf = kXh = kX(θ) in equilibrium at either0 or FK(kX,1) = (1 + r)/(1 − π(θ)), and the latter is satisfied if there is positive produc-tion in the manufacturing sector.


The equilibrium can be solved in two stages by backward inductionwhere, in the second stage of the game, foreign and domestic firmsadopt the optimal production and investment decisions just describedconditional on the resource sector contracts, equilibrium prices, andthe probability of expropriation. In the first stage of the game, the gov-ernment chooses resource contracts that maximize Eq. (8), taking intoaccount the optimal responses of firms and the corresponding effectson prices and the probability of expropriation. Given Eq. (7), this firststage collapses to a simultaneous decision over (KRf, KRh, Mf).

3. Equilibrium with a Constant Mineral Price

In this section, we examine the relationship between country riskand sectoral patterns of FDI using a stylized example with a constantmineral output price and two potential expropriation penalties facedby the host-country government:

A ¼ al; ahf ge πl;1−πlf g:

Differences in country risk are considered by varying the distributionover these direct costs of expropriation. Specifically, political risk ismeasured as the difference in the size of expropriation penalty in thehigh penalty regime, ah, representing a government with a high disin-centive to expropriate, and the size of the low penalty, al.18 Withoutloss of generality, we fix ah at a value just above the level such that itcould never be optimal for the government to expropriate such that alas an inversemeasure of country risk. In otherwords, a is high for all po-litical regimes in a relatively low risk country, whereas a relatively highrisk country is characterized by large swings in the expropriation incen-tives of the different regimes.19

Depending on the equilibrium levels of foreign investment in bothsectors, the probability of expropriation occurring is either zero orthe probability of the low penalty regime, πl. With a constant mineralprice p0, condition (9) implies that expropriation occurs with probabil-ity zero if and only if:

al≥ 1þ rð Þ KXf þ KRf

� �¼ 1þ rð Þ kXf L f þ kRfM f

� �ðNEÞ

and expropriation occurs whenever al is realized and π(θ) = πl. Werefer to (NE) as the no-expropriation constraint. We assume that

0≤alba ¼ 1þ rð Þ kFBX þ kFBR M−K� �

where kiFB is the efficient capital ratio in sector i. This ensures that expro-priation risk matters for investment decisions (the interesting case)since it implies that efficient levels of investment in both sectors arenot feasible.

Wefind that, for relatively high values of al (a relatively low risk coun-try), (NE) binds, expropriation never occurs and the optimal resourcecontract corresponds to a continuous range of foreign mineral rights

18 This notion of country risk is similar in spirit to that adopted by Cole et al. (1995) intheir analysis of sovereign default, where a government transits through different politicalstates that affect its valuation of future investments.19 An alternative approach would be to vary both ah and al such that the expected valueof a is unchanged across different risk groups. This alternative approach would result inqualitatively identical results in terms of sectoral foreign investment patterns, which isthe main focus of this analysis, and merely influences the threshold value of al belowwhich expropriation occurswith positive probability. The reason is that it is never optimalfor foreign investor to invest beyond the point at which it is also optimal to expropriate inboth states and, as we will demonstrate, optimal foreign investment only exceeds thethreshold for which expropriation occurs in the low penalty state when the difference be-tween al and ah is large. Conversely, holding the difference between ah and al constant butvarying the expected value of the penalty is yet another way to conceive differences incountry risk. It is not clear that the implications of the model are identical when countryrisk is modeled in this particular way. For the purposes of this analysis, however, our pri-mary interest is the variation in the support of a, and for simplicity we focus on the size ofal.

allocations Mf. This implies that the resource sector FDI share is notuniquely determined. Moreover, the “average” share of FDI in the re-source sector, defined as the median share across the set of all possibleequilibria, may be increasing or decreasing over a range of al dependingon a country's relative factor abundance and properties of the productionfunctions. For relatively low values of al, by contrast, the government al-ways expropriates in this state and the optimal resource contract resultsin no foreign investment in themanufacturing sector, while positivemin-eral rights are allocated to foreign investors to achieve the efficient invest-ment level in the resource sector. This implies that resources FDI makesup 100% of all FDI. The efficient investment level in resources is achieveddespite a positive probability of expropriation by offering lower mineralconcession prices, which are paid in the event expropriation does notoccur. These findings are summarized by the following propositions.

Proposition 3.1. For all al∈ 0; a½ Þ , kRh = kRf = kR and kXh = kXf = kX.Furthermore, provided K is not too low, there exists a′∈ 0; að Þ such that

1. for al ∈ [0,a′), kR = kRFB, kX = kX

FB, and Mf = min{M,M − (K − kXFBL)/

kRFB} and Lf = 0; expropriation occurs if and only if a = al.

2. for al∈ a′; a �

, kR b kRFB, kX b kX

FB and the host-country government isindifferent towards the allocation of Mf and corresponding equilibriumLf that are consistent with sector investment kXL and kRM; expropriationnever occurs.

Proof. See the Mathematical Appendix. □The optimal resource contracts for a relatively high risk country

allocate a relatively large share of the stock of mineral rights to foreigninvestors, which increases domestic capital available for investment inthe other sector and raises the wage rate. This renders foreign invest-ment in this sector unprofitable given the positive probability of expro-priation. Efficient levels of investment are achieved in both sectors. Forthe relatively high risk group, ex post host-country income is unambig-uously higher in the event that a = al (and expropriation occurs) com-pared to the income it would receive if investment were chosen tosatisfy (NE). However, this benefit is at the cost of lower payments formineral rights and income in the event expropriation does not occur.When country risk is low, al is sufficiently high that the expected directcost of expropriating exceeds the cost of lower aggregate FDI comparedto the casewhere (NE) does not bind. However, the allocation of miner-al rights between domestic and foreign investors is not uniquely deter-mined for this low risk group. Consequently, the model does not implyany specific relationship between exogenous country risk and the re-source FDI share within this high risk group when the mineral outputprice is constant. However, even in this simple example, the resource“average” FDI share is unambiguously higher in the case of high risk((NE) does not bind) compared to the casewhere (NE) binds. A full char-acterization of variation in the share of FDI in resources at different levelsof risk is provided in the following proposition.

Proposition 3.2. If K N 0, the “average” share of FDI in the resource sectorσR ¼ med kRfM f = kXf L f þ kRfM f

� �� across the set of all equilibria, is strictly

higher for a relatively high-risk country (al ∈ [0,a′)) compared to low-risk country (al∈ a′; a

�). Moreover, if K ≥ max{kXFBL, kRFBM}, σR is non-

increasing over both [0,a′) and a′; a� �

. If K b max{kXFBL, kRFBM} and theelasticity of manufacturing sector investment to an increase in al is at leastas high as the resource sector investment elasticity, σR is non-increasingover [0,a′) and a′; a

� �provided K/M is not too low.

Proof. See the Mathematical Appendix. □Although the correlation between sector FDI shares and country risk

implied by Proposition 3.2 is ambiguous within risk categories due to amultiplicity of equilibria, Propositions 3.1 and 3.2 have a clear implicationfor the probability of expropriation between risk categories. Specifically,in a sample of randomly chosen equilibria across the different risk catego-ries, the average resource FDI sharewill be strictly higher in countries that

20 According to this model, provided there are no constraints on the pricing of mineralconcessions, there is no benefit to the host country from introducing direct subsidies. Inpractice, direct subsidies may even be more politically controversial than discounting re-source concession payments, in provides one justification for focusing exclusively on theoptimal resource contract.


have expropriated compared to countries that have not. Comparing a veryhigh risk country such as Bolivia to a very low risk country such asMalaysia, our results imply that the resource contract in the high riskcountrywill tend to offermineral rightsmore cheaply to foreign investorsand is expected to have a larger proportion of aggregate FDI located in theresource sector.

This contrasts the equilibrium patterns that are predicted under a re-source pricing scheme where the government does not influence invest-ment intensity and domestic factors are paid their marginal products.Denoting the profit-maximizing capital ratios in each sector by kR andkX (which would be identical in this case given 1 + rh = (1 + r)/(1 − π(θ)), Eq. (8) can be expressed as:

V θð Þ ¼ F kX θð Þ;1ð Þ þ E p½ �G kR θð Þ;1ð ÞM− 1þ rð Þ kX θð Þ þ kR θð ÞM−K½ �−π θð ÞE a½ js∈D θð Þ�:

Therefore V(θ) does not depend on the allocation of labor ormineralrights between domestic and foreign firms. In particular, when (NE)does not bind and π = πl, the host-country is indifferent in allocatingM, and a range of possible equilibria exist with the bounds of “average”resource FDI share in Proposition 3.2 determined in the same way forrelatively high risk and low risk group.

The above analysis does not take into account the possibility of thehost country government offering direct investment subsidies to foreigninvestors in themanufacturing sector. The assumption that a capital poorcountry is too cash constrained to offer direct investment subsidies in allsectors simultaneously is perhaps uncontroversial. Yet it is still possiblefor the host country government to finance foreign investment subsidiesin manufacturing out of foreign resource concession payments. We referto a national subsidy-payment scheme as “self-financing” if ϕKXf ≤ τfMf,where ϕ is the subsidy per unit of manufacturing FDI. We can show thatthemain result of Proposition 3.1 – that all FDI is located in resources in asufficiently high risk country – no longer holds under such a scheme.However, this option to directly subsidize manufacturing FDI does notimprove upon host country welfare.

To see why, define kX(θ,ϕ) to be the competitive manufacturing cap-ital to labor ratio given subsidy per unit invested, ϕ, which is implicitlydefined by

F ′K kX θ;ϕð Þ;1ð Þ ¼ 1þ r1−π θð Þ−ϕ:

Host country income when expropriation does not occur becomes

YN p; θð Þ ¼ F kX θ;ϕð Þ;1ð Þ 1−L f

� �þ pG KRh;Mhð Þ þw θð ÞL f

þ τ f M f−ϕkX θ;ϕð ÞL f

whereas income when expropriating, YE(p, θ), is unchanged. It isstraightforward to verify that the only difference implied by the subsidyto the host country income in Eq. (8) and the decision to expropriategiven by Eq. (9) is that foreign and domestic investment inmanufactur-ing can be expressed by kX(θ,ϕ)Lf and kX(θ,ϕ)(1 − Lf).

The solution to the government's problemwhen (NE) binds does notchange with the manufacturing subsidy. However, the government'soptimal choice of subsidy when (NE) does not bind satisfies the follow-ing first order condition:

F ′K kX θ;ϕð Þ;1ð Þ ∂kX θ;ϕð Þ∂ϕ − 1þ rð Þ ∂kX θ;ϕð Þ

∂ϕ ¼ 0 ⇒ kX θ;ϕð Þ ¼ kFBX :

Therefore the efficient level of investment is attained inmanufactur-ing, with the corresponding optimal subsidy rate ϕ∗ = πl(1 + r)/(1 − πl). Because the optimal decisions over {KRf,Khf,Mf} imply kRf =kRh = kR

FB, as in the case with no subsidy, the efficient level of invest-ment is attained in both sectors even if KXf N 0. This implies that, withan optimal subsidy ϕ∗, host country income is maximized for any

allocation of Mf and corresponding labor allocation LF. Ensuring thatthe optimal subsidy-payment scheme is also self-financingmay restrictthe feasible range for Mf, but it is no longer necessary that the optimalresource contract and mineral rights allocation results in strictly higherresource FDI shareswhen (NE) is not binding compared towhen it doesbind. Nevertheless, the optimal subsidy does not increase expectedhost country income.20 When there are no restrictions on the mineralconcession payments charged, there is no advantage offered by theadditional policy instrument. In the next section stochastic resourceoutput prices are added to themodel. This leads to a secondmotivationformaximizingmineral rights allocated to foreign investors for relative-ly high risk countries, and motivating restrictions on FDI in resourcesamong low risk countries. This mechanism, by contrast, does not de-pend on the existence of direct investment subsidies.

4. Equilibrium with Price Uncertainty

So far we have not considered variation in resource output prices.In this section we introduce random resource output prices and re-examine the average relationship between FDI and risk. Price uncertain-ty has substantive implications for the optimal resource contract inmoderate risk countries. Governments in countries in the moderate tolow risk category aim to minimize the ex ante risk of expropriationby limiting FDI to the resource sector and maximizing non-resourceFDI, while countries in the moderate to high risk group minimize thelikelihood of expropriation by maximizing FDI in resources instead.Proposition 3.2 still serves to illustrate the key predictions for resourcecontracts in very high risk countries. In addition, introducing mineraloutput price variability allows us to consider the positive correlationbetween mineral prices and the likelihood of expropriation observedin the data.

For simplicity, the cumulative distribution function for mineraloutput prices is assumed to be continuous and twice differentiableover a bounded (non-negative) interval:

peZ p;ph i

and a and p are assumed to be independent.The key implication of random prices in terms of player strategies is

that the government's expropriation decision can be summarized by achoice of cutoff values for resource price, one for each penalty state a,above which it is optimal to expropriate. This implies that the expropria-tion set is described by

D p�l θð Þ;p�h θð Þ� � ¼ p�l θð Þ; p� ; p�h θð Þ; p� � �

where pk∗(θ) is the cutoff resource price whenever expropriation penalty

ak is realized. So, for instance, if the government strategy is to neverexpropriate when facing the high penalty, but to expropriate when thepenalty is low and the price is above some pl

∗, p∗h θð Þ ¼ p, the expropria-tion set is simply D p∗l θð Þ;p∗h θð Þð Þ ¼ p∗l θð Þ; pð �f g. If, in addition, p∗l θð Þ ¼ p,this signifies that expropriation is never optimal and D(pl∗(θ), ph∗(θ)) isempty. The threshold values pk∗(θ) (k = l, h), are defined by the follow-ing system of equations: for each k,

p�k θð Þ ¼ p if ak≥YE p; θð Þ−YN p; θð Þp if akbY

Eðp; θÞ−YNðp; θÞ

(


and for all other θ, pk∗(θ) is implicitly defined by

ak ¼ YE p�k; θ� �

−YN p�k; θ� � ð10Þ

where the explicit expression for YE(p,θ) − YN(p,θ) is Eq. (9). The host-country government's objective function is Eq. (8) as before, and theprobability of expropriation can be expressed as

π θð Þ ¼ π p�l θð Þ;p�h θð Þ� � ¼ πl

Z p

p�l θð Þz pð Þdpþ 1−πlð Þ

Z p

p�h θð Þz pð Þdp ð11Þ

where z(p) = ∂Z(p)/∂p. In this environment with a continuum of ran-dom prices, very small changes in FDI have a negligible effect the expro-priation probability defined by Eqs. (9) and (11), conditional on positiveforeign investment in the resource sector. When there is foreign invest-ment in resources, the competitive foreign investment decision inmanufacturing satisfies FK(kX(θ), 1) = (1 + r)/(1 − π(θ)).

Introducing price uncertainty does not have any impact on the equi-librium for the very high risk group, as these countries still expropriatewhenever the lowpenalty is realized (regardless of the price). However,for the more moderate risk group, price uncertainty has an importanteffect on equilibrium outcomes. The main difference is that, whenthere is positive FDI in the resource sector, the potential for foreign in-vestors to earn positive (ex post) rents in this sector when their assetsare not expropriated (above what is earned by manufacturing firms)makes expropriating particularly attractive in some states. Specifically,the direct gain from expropriating is increasing in the difference be-tween the realized price of resource output and the effective marginalrevenues received by foreign investors, p − E[p|s ∉ D(pl∗(θ), ph∗(θ))].The effective marginal product determines the price paid for each re-source concession, and hence also the share of resource rents going tothe host-country. Because these payments are not contingent on theprice of output, investors earn high profits ex post when the price ishigh and assets are not expropriated. This results in a greater tempta-tion to expropriate in high-price states, and this temptation increasesin the amount of resource-based FDI.21

For those countries that anticipate relatively high expropriationpenalties, reducing the temptation to expropriate in a low penalty re-gime (which is costly) is the preferred strategy. For the lowest level ofcountry risk, this is achieved by funneling all domestic capital into theresource sector. For higher risk countries (yet not so risky that the gov-ernment subsidizes resource FDI), concentrating FDI in the resource-sector lowers the temptation to expropriate, allowing for higher overallforeign investment. The reason is that foreign firms in this sector, condi-tional on not being expropriated, earn lowor negative returns in the lowpenalty regime compared to foreign firms in the non-resource sector.Increasing FDI in resources therefore raises the probability of expropri-ation by less than an equal increase in non-resource FDI.

To provide a sharper illustration of these relationships, considerthe case where it is never optimal to expropriate when sanctions arehigh (p∗h θð Þ ¼ p).22 For this case, the characteristics of the equilibriumsolutions across varying levels of country risk al are summarized bythe following proposition:

21 A positive difference p − E[p|s ∉ D(pl∗(θ), ph∗(θ))] is related to “windfall” profits in thesense that it captures the returns per unit of output in excess of what is received in themanufacturing sector (when expropriation does not occur). The average windfall profitscould be reduced by setting a concession payment schedule that varies positively withthe resource output price, thoughwe demonstrate in the next section that ad valorempay-ments are not sufficient to have any qualitative effect on these findings. What is requiredto prevent expropriation are resource sector payments that contingent on both prices andon the penalty regime. Equilibrium in this complete contracts framework is considered inSection 5.22 When only two possible penalties are assumed, this becomes the relevant case to con-sider. In our calibrated numerical exercise, p∗h θð Þbp occurs only when ah is sufficiently lowand very close to al, and where there is a very large variance in the resource output price.

Proposition 4.1. For all al∈ 0; a½ Þ, kXh = kXf = kX in equilibrium. ProvidedK is not too low and under certain conditions on F(⋅), G(⋅), and Z(⋅)guaranteeing a unique solution to Definition 2.1, the interval 0; a½ Þ can bepartitioned into continuous subintervals AL, AM and AU such that

1. for al∈AL, kRh = kRf = kRFB, kX = kX

FB, Mf = min{M, M − (K − kXFBL)/

kRFB} and Lf = 0; expropriation occurs if and only if a = al.

2. foral∈AM, kRh b kRf b kRFB, kX b kX

FB, Mf = min{M, M − (K − kXL)/kRf}

and Lf ≥ 0; expropriation occurs if a = al and p N pl0 for somep∗l ¼ p0l ∈

p; ph �

.

3. for al∈AU , kRf b kRh b kRFB, kX b kX

FB, Mf = max{0, M − K/kRh} and

Lf N 0. If Mf N 0, expropriation occurs if a = al and p N pl1 for some p∗l¼

p1l ∈ p;p� i

. Otherwise expropriation never occurs.

Moreover, ifAM is non-empty,ALbAMbAL (that is supAL ¼ infAM andsupAM ¼ infAU) and pl

0 b pl1. If insteadAM is empty,ALbAU and supAL ¼

infAU.

Proof. See the Mathematical Appendix. □Although a detailed proof is provided in the appendix, we provide

some additional intuition here. For sufficiently low al (al∈AL), the equi-librium is as described in Proposition 3.1 but where p0 = E[p]. In thiscase it is always optimal to expropriate when a = al, resource-basedFDI is maximized and manufacturing FDI is zero (in the absence of thedirect subsidies to manufacturing FDI discussed in Section 3).

At more moderate risk levels, the government expropriates onlywhen a = al and themineral output price exceeds a particular thresholdprice, conditional on positive FDI in the resource sector. (With noresource-based FDI, manufacturing FDI is determined by the (NE)constraint, expropriation never occurs and, equivalently, p∗l ¼ p .) Howthe optimal resource contract varies across levels of al for thismoremod-erate risk group can be interpreted as follows. Consider reallocations ofdomestic capital and foreign investment across sectors that leave totalFDI unchanged (such that only the foreign ownership shares of a givencapital stock in each sector change). When expropriation occurs, thehost-country seizes the entire value of output but incurs the penaltyand forgoes the contracted payments from foreign investors. In a rela-tively low risk country, a relatively high cost of expropriating in thelow penalty regime implies that, for a given foreign ownership share inthe resource sector, the threshold resource output price for which thegovernment is indifferent between expropriating and not will be highcompared to a relatively high risk country. Therefore in the relativelylow risk country, the threshold price pl

∗ is sufficiently high that, for reali-zations of p equal to the threshold pl

∗, foreign investors in resources walkaway with higher ex post profits compared to foreign investors in thenon-resource sector. This implies that, if the share of foreign investmentin resources is increased and the share in the other sector is decreased,the total ex post value of assets under the contract increases at thisthreshold price. It follows that, in the low penalty regime, host-countryincome conditional onnot expropriating decreases relative to the incomeit would receive from expropriating, and therefore the government iswilling to expropriate at this original threshold price. The thresholdprice above which expropriation occurs is therefore decreasing as theforeign investment share increases in resources, increasing the ex anteprobability of expropriation, and therefore the total amount of FDI thatcan be attained is decreasing as this FDI is shifted to resources. The oppo-site is true in a relatively high risk countrywith a sufficiently low thresh-old price pl

∗ such that, conditional on not being expropriated in the lowpenalty regime, foreign investors in the resource sector always walkaway with relatively low ex post returns compared to foreign investorsin the non-resource sector. In this case an increase in the foreign owner-ship share in resources decreases the total rents accruing to foreign inves-tors whenever this threshold price is realized, which implies that the


threshold price is increasing (and the temptation to expropriate is de-creasing) as FDI is shifted towards resources.

More formally, it is useful to define Q xð Þ ¼ x−E p½ js∉D x;pð Þ�, where

Q(x) is strictly increasing in x for x∈ p; ph i

given Z, andQ pð ÞN0. Examin-

ing Eq. (9)which implicitly defines the price abovewhich expropriationoccurs in the low penalty regime, if al is relatively high (al∈AU) then forany amount of resource FDI, kRfMf,there is a unique p∗l Np satisfying thisequality (taking into account the effects of pl

∗ on the probability ofexpropriation and manufacturing sector foreign investment) such thatQ(pl∗) ≥ 0. In this case it is optimal to lowerMf (to zero, if the domesticcapital stock is sufficient to attain desired investment in this sector),because this permits a rise in pl

∗ for a given quantity of aggregate FDI,and therefore raises total FDI and V(θ). Expropriation risk is minimized,and the probability of expropriating is even zero if there is sufficient do-mestic capital to optimally allocate all mineral rights to domestic inves-tors. This policy is reversedwhenever al is sufficiently low thatQ(pl∗) b 0(al∈AM). In this case raisingMf is optimal because any “windfall profits”in the high-price, low penalty states are entirely appropriated by thehost country in the low penalty regime when expropriation occurs.When a = al (i.e. p b pl

∗), the ex post foreign asset value in the resourcesector are therefore below that in the non-resource sector. Shifting FDIfrom the non-resource sector to the resource sector makes expropria-tion less attractive in the low penalty regime, for a given level of aggre-gate FDI.23 IncreasingMf therefore increases the amount of total FDI.

The implied expropriation pattern for countries in themoderate riskgroup (al∈AM) generates a positive relationship between resource out-put prices and the timing of expropriation. For this group, when a lowpenalty regime is realized, the host-country government expropriatesif and only if the price exceeds the threshold price because this givesthe host country higher ex post income/consumption given the size ofthe penalty compared to not expropriating. In this static environment,this result requires only that the objective function be strictly increasingin consumption/output. In a dynamic context where investors canthreaten to cut off future investment if expropriation occurs, however,whether or not the host-country government in this group would bemore tempted to expropriate when the resource output price is highorwhen it is lowwill also depend on the degree of risk aversion impliedby the objective function, as shown in Cole and English (1991). In partic-ular, in their dynamic one-sector model of expropriation where therelative value of domestic consumption and the continuation values ofconsumption under the contract is stochastic, sufficient concavity ofthe objective function in consumption/output implies that it is optimalto expropriate whenever the value of today's consumption is relativelylow. This is because the increased marginal utility of not-expropriatingwhen the value of output is low is high relative to the loss in future con-sumption from reduced foreign investment. Therefore in a dynamic envi-ronment, the prediction that expropriation tends to coincide withrelatively high priced sates will depend on the government's degree ofrisk aversion as well as the type of research contract.24

5. Ad valorem Payments and Other Contracts

In this section we consider a generalized version the resourcecontract of the previous section. This class of contracts includes a taxon the value of resource-sector output (rather than simply charging

23 For some functional forms and parameter values it is possible that the threshold levelof al for which it is always optimal to expropriate in this state (supAL) is higher than thethreshold level of al such that Q(pl∗) b 0 at the corresponding levels of investment, inwhich case all countries would be classified in either the very high risk or very low riskgroups (supAL = infAU).24 Specifically, in addition to concavity of the objective function, whether or not expro-priation is predicted to occur in high or low price states should also depend on how thehost-country's share of current period returns relative to future expected returns variesaccording to the resource output price.

foreign investors a fixed price per unit of mineral concessions). Thistype of payment arrangement is common under standard royalty con-tracts. We are interested in such resource contracts because when re-source output prices are variable it is conceivable that the fixedpayment schedule assumed in the previous examples exaggerates therisk associated with resource FDI compared to a royalty contract. Apure ad valorem royalty payment is perfectly correlated with the re-source output price. This implies that the temptation of governmentsin moderate risk countries to expropriate when the price is high is, atleast partially, reduced. We establish sufficient conditions on the struc-ture of optimal contracts to generate the same equilibrium relationshipsbetween country risk, allocation of mineral rights between foreign anddomestic investors, and expropriation established by Proposition 4.1.Moreover, we show that this condition is satisfied by all resource con-tracts that include any combination of ad valorem royalty paymentsand fixed payments per unit of mineral concessions.

Denoting the total optimal resource sector tax payment for therepresentative foreign firm by C(KRf,Mf,p), the optimal contract rendersthe foreign investor indifferent between investing and not investing:

E ΠRf

h i¼ 1−π θð Þð ÞE p½ js∉D θð Þ�GðKRf ;Mf Þ− 1þ rð ÞKRf

− 1−π θð Þð ÞE CðKRf ;Mf ; pÞh ��s∉D θð Þ� ¼ 0

ð12Þ

whereD(θ) and π(θ) are determined by price cutoff rule pl∗ following thelogic of the previous section. This resource payment is more generalbecause it may now depend on p. For example, an ad valorem royaltyρf satisfying Eq. (12):

E ΠRf

h i¼ 1−π θð Þð Þ 1−ρ f

� �E p½ js∉D θð Þ�GðKRf ;Mf Þ− 1þ rð ÞKRf ¼ 0

results in the following ex post royalty paymentwhich increases propor-tionately with realizations of p:

C KRf ;Mf ; p� �

¼ ρ f θð Þ � pGðKRf ;Mf Þ

¼ p GðKRf ;Mf Þ−1þ r

1−π θð Þ� �

KRf

E p½ js∉D θð Þ��

:

Note that the conditional expectation E[C(KRf,Mf,p)|s ∉ D(θ)] isequal to expected payment under the contract of the previous section,τf(θ)Mf, defined by Eq. (7). In fact, any resource contract satisfyingEq. (12) corresponds to identical ex ante expected share of resource sec-tor returns for the host country and foreign investors:

E CðKRf ;Mf ;pÞh ��s∉D θð Þ

i¼ E p½ js∉D θð Þ�GðKRf ;Mf Þ−

1þ rð ÞKRf

1−π θð Þ :

Therefore host-country income is given by Eq. (8) for any resourcecontract satisfying Eq. (12), and the host-country government problemdiffers across contracts only in terms of the ex post expropriation deci-sion, which in turn defines the cutoff rule pl∗. The general form of condi-tion (10) defining cutoff p∗l∈ p; p

� �is

1þ rð ÞKXf

1−π θð Þ þ p�l GðKRf ;Mf Þ−CðKRf ;Mf ; p�l Þ−al ¼ 0: ð13Þ

It is possible to derive conditions on the resource contract thatnecessarily imply the same relationship between country risk, expropri-ation price thresholds, and mineral rights allocation that are alreadysummarized by Proposition 4.1, assuming the contract satisfies theconditions for a unique solution to the government problem. A suffi-cient condition is established in the following proposition:

Proposition 5.1. A continuous, differentiable payment schedule C(KRf,Mf,p) that satisfies Eq. (12), such that the representative foreign investorin the resource sector pays this amount in the event it is not expropriated,


produces the equilibrium relationships between al, Mf, KX, KRf, KRh andthreshold resource price pl

∗ summarized by Proposition 4.1 whenever itsatisfies the following requirements:

p�l NE p½ js∈D θð Þ�⇔p�l GK KRf ;Mf

� �−CK KRf ;Mf ;p

�l

� �N

1þ r1−π θð Þ

andp�l NE p½ js∉D θð Þ�⇒p�l GM KRf ;Mf

� �−CM KRf ;Mf ;p

�l

� �≥0

p�l bE p½ js∉D θð Þ�⇒p�l GM KRf ;Mf

� �−CM KRf ;Mf ;p

�l

� �≤0

where, for J = {K,M},

C J KRf ;Mf ;p�l

� �¼

∂C KRf ;Mf ;p� �

∂ J jp¼p�l

:

Moreover, a resource contract consisting of an ad valorem royalty, a fixedpayment per unit of resource concessions, or a mixture of both that satisfiesEq. (12) will also satisfy these requirements.

Proof. See the Mathematical Appendix. □

Proposition 5.1 demonstrates that the equilibrium relationshipsoutlined in the previous section correspond to a wide variety of resourcesector contracts, including combinations of ad valorem royalties and fixedpayments per concession typically observed in standardmining contracts.Specifically, under this broad class of conditional payments for mineralconcessions, pl∗(θ) is decreasing and π(θ) is increasing in country riskand, whenever pl∗ N E[p|s ∉ D(θ)], the optimal policy is to lower Mf to-wards zero (until all domestic capital is located in the resource sector).When the opposite inequality holds, but pl∗ is above the threshold corre-sponding to the highest risk category, the optimal policy is to raiseMf to-wardsM until all manufacturing sector investment is domestic capital. Asa result, both the share of FDI in resources and the probability of expropri-ation are increasing in country risk for all such contracts, though invest-ment and output levels may vary under the different types of contract.25

It is also instructive to briefly consider resource sector contracts forwhich the equilibrium sectoral foreign investments are not necessarilyrelated to country risk according to the pattern described in the previ-ous section. A natural benchmark is the constrained efficient contract,where payments for resource rights can be conditioned on the expro-priation penalty/regime such that the contract is self-enforcing andexpropriation never occurs. Specifically, we consider complete state-contingent resource and wage contracts, specifying investments, min-eral rights, and payments τ(θ,s) per mineral right and w(θ,s) per unitof labor in every state s, respectively, that maximize host country wel-fare, offer non-negative expected profits to foreign investors, and satisfya series of no-expropriation constraints for every state of the world,

∀s∈S; a≥YE θ; sð Þ−YN θ; sð Þ;

or equivalently,

∀s∈S; a≥pGðKRf ;Mf Þ−τðθ; sÞMf þ FðKXf ; L f Þ−wðθ; sÞL f : ð14Þ

Because any contract satisfying Eq. (14) is self-enforcing, π(θ) = 0and the set D(θ) is empty. The corresponding non-negative profitconstraints, or foreign investor participation constraints, are therefore

E τ θ; sð ÞMf

h i≤E p½ �GðKRf ;Mf Þ− 1þ rð ÞKRf ; ð15Þ

and E w θ; sð ÞL f

h i≤ FðKXf ; Lf Þ− 1þ rð ÞKXf : ð16Þ

25 This suggests there are potential welfare implications from a choice over the type ofresource payment at different levels of country risk a model of expropriation such as thisone. See Engel and Fischer (2010) for a theoretical analysis along these lines.

Finally, the contracts should be feasible in the sense that paymentsmade by foreign investors in each sector should not exceed the totalvalue of output in any state:

∀s∈S; τ θ; sð ÞMf ≤pGðKRf ;Mf Þ; and ð17Þ

∀s∈S; w θ; sð ÞL f ≤ FðKXf ; L f Þ: ð18Þ

Properties of constrained efficient contracts have been analyzedby Kehoe and Levine (1993) and Kocherlakota (1996) in the contextof dynamic risk-sharing arrangements and stochastic endowments.Our environment with production and one-sided commitment ismost similar to Tomz and Wright (2010), however, who analyzeself-enforcing optimal debt/investment contracts for a general classof host-country welfare functions. Interestingly, we find that whenthe host country maximizes expected output (i.e. the social welfarefunction is linear), the no-expropriation constraints always bindunder the constrained optimal contracts (provided first-best invest-ment levels are not attainable). This contrasts the case of concavehost country utility, where this constraint only binds when the out-put price is above a certain threshold. The reason is that the risk-averse host-country prefers to smooth consumption over states.This is possible only when the value of output – and hence the temp-tation to expropriate – is relatively low, and the host-country is will-ing to accept lower average consumption in exchange for a steadyconsumption portfolio across low price states. (See Tomz andWright, 2010, pp. 91–93 for a complete analysis and discussion.)However, when the host-country is risk neutral, there is no desireto smooth consumption and instead the no-expropriation con-straints are equally binding across all states by the desire tomaximize inflows of foreign capital inflows. We summarize theproperties of the constrained optimal contracts in the followingproposition:

Proposition 5.2. The constrained optimal payment schedules τ∗(θ,s)Mf

and w∗(θ,s) and allocation {KRh∗ ,KRf

∗ ,KXf∗ ,Lf∗,Mf

∗} that maximize

V θ; sð Þ ¼ E p½ �GðKRh;Mf Þ þ FðK−KRh; L−L f Þ−τ θ; sð ÞMf−w θ; sð ÞLf ð19Þ

subject to Eqs. (14)–(18), satisfy

FK k�Xh;1� � ¼ E p½ �G k�Rh;1

� �where kXh

∗ = (K − KRh∗ )/(L − Lf

∗) and kRh∗ = (KRh

∗ )/(M − Mf∗). Further-

more, the optimal allocations of mineral rights and labor between domesticand foreign investors, Mf

∗ and Lf∗, are not uniquely determined, and kXf

∗ =KXf∗ /Lf∗ = kXh

∗ and kRf∗ = KRf

∗ /Mf∗ = kRh

∗ . Moreover, if a first-best efficientallocation is unattainable, the constrained optimal contracts satisfyEqs. (14)–(16) with strict equality, and

K�Rf þ K�

Xf ¼E a½ �1þ r

: ð20Þ

where E[a] is the unconditional expectation of a.

Proof. See the Mathematical Appendix. □Proposition 5.2 demonstrates that under constrained optimal

contracts, capital per unit of labor and per mineral right are equalbetween foreign and domestic investors in each sector, and the hostcountry is indifferent between allocating mineral rights to foreign ordomestic investors. However, if the first best investment levels are notattainable, total FDI equals E[a]/(1 + r)— total FDI decreases monoton-ically with country risk.

The no-expropriation constraints are binding when the first best isnot attainable, but with two complete state-contingent contracts, onefor each sector, the constraints do not uniquely identify the payment

27 The sample of countries is limited predominantly by the availability of data on sectorFDI stocks.28 The annual coefficient of variationover 1990–2006 for themetal price index after remov-ing the linear trend is 0.31 and the corresponding value for petroleum is 0.36. The standard

deviation in prices corresponding to a uniform distribution isσp ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip−p� �2

=12

r, implying

a coefficient of variation equal to cv ¼ σp=E p½ � ¼ p−p� �

=ffiffiffi3

ppþ p� �

. For E[p] = 1, it is

straightforward to verify that p ¼ 2−p and p ¼ 1−ffiffiffi3

pcv. Assuming a value of cv = 0.35,

the support of the resource output price is approximately [0.4,1.6].29 Based on the full century of expropriation data of Tomz and Wright (2010), Kobrin(1984), Minor (1994) and Hajzler (2012), the average duration between expropriation


schedules for foreign investors in each sector.26 However, to facilitatecomparison of a constrained optimal resource contract with theresource sector contracts already considered, it is useful to considerthe special case of non state-contingentwage contracts, and for simplicityassume that the feasibility constraints never bind. Specifically, considera fixed wage satisfying w(θ,s)Lf = F(KXf,Lf) − (1 + r)KXf for all s ∈ S.Given Eq. (14) always binds, the corresponding (unique) self-enforcingresource contract is

τ θ; sð Þ ¼ pGðKRf ;Mf Þ þ 1þ rð ÞKXf−a:

Using Proposition 5.2, we can express the self-enforcing contract as

C�ðKRf ;Mf ;p; aÞ ¼ pGðKRf ;Mf Þ− 1þ rð ÞKRf þ E a½ �−að Þ

which is differentiable in KRf and Mf. It is straightforward to verify that

plGKðKRf ;Mf Þ−C�KðKRf ;Mf ;p

�l ; aÞ ¼ 1þ rð Þ

for all p ∈ P. Since, by definition, p∗l ¼ pNE p½ � under a constrained effi-cient contract, the contract will not satisfy the first requirement ofProposition 5.1. This is not surprising given Proposition 5.2, whichdemonstrates that the relationship between equilibrium sector invest-ment and country risk under such contracts need not correspond withthe patterns outlined in the previous section.

However, the constrained efficient contract is not the only type ofresource contract that may yield different sectoral FDI patterns. An ex-ample of a resource contract where payments are not conditioned onthe expropriation penalty, but which nevertheless produces differentsectoral investment patterns, is one where the entire ex post value of re-source sector production accrues to the host country, but where foreigninvestors deduct the risk-adjusted value of their capital investments.Specifically, foreign investors pay, conditional on not being expropriated,

CðKRf ;Mf ; pÞ ¼ pGðKRf ;Mf Þ−1þ r

1−π θð Þ� �

KRf

for all p ∈ P. This payment schedule satisfies Eq. (12): ex post foreigninvestor profits in the resource sector equal π(θ)(1 + r)KRf/(1 − π(θ))when expropriation does not occur, and equal− (1 + r)KRfwhen expro-priation does occur.

Note that for any value of p,

pGK ðKRf ;Mf Þ−CKðKRf ;Mf Þ ¼1þ r

1−π θð Þ

and pGM(KRf,Mf) − CM(KRf,Mf,p) = 0, and therefore only one of the tworequirements for the condition outlined in Proposition 5.1 is satisfied.The reason is that, under such a contract, expropriation either alwaysoccurs in the low penalty regime or else never occurs:

YE−YN−al ¼1þ r

1−π θð Þ� �

KXf þ KRf

� �−al:

In otherwords, eitherp∗l ¼ p (and (1 + r)[KXf + KRf] N (1 − πl)al) orp∗l ¼ p (and (1 + r)[KXf + KRf] ≤ al), as in the case with no resource–output price uncertainty.

26 More precisely, in states where the feasibility constraints do not bind, for given levelsof foreign investment, different combinations of τ(θ,s) andw(θ,s) in these states satisfy theno-expropriation constraint and the firm participation constraints. Given that expropria-tion affects foreign investments in both sectors simultaneously, there is a sense in whicha complete state-contingent contract in a single sector can be self-enforcing, at least tothe extent that the feasibility constraints never bind under the contract in this sector.

6. Numerical Results

We illustrate the predicted relationships between country risk, sec-tor production and FDI shares, and the probability of expropriationusing a calibrated numerical example based on data for a sample of 38developing and emerging economies over the period 1990–2006.27

We are interested in the extent to which this simple, stylized modelmay be able capture a number of characteristics in cross-country datain comparison to standard models. We also use the calibrated modelto examine how the host-country's expected return from its stock ofminerals and expected income vary under the various types of resourcecontracts considered in the previous section.

For this exercise, we assume that aggregate output in each sector isproduced using Cobb–Douglas production functions:

GðKRj;MjÞ ¼ KαRjM

1−αj α∈ 0;1ð Þ

FðKXj; L jÞ ¼ KγXj ALj

� �1−γγ∈ 0;1ð Þ

where A is a labor-augmenting productivity parameter. For simplicity, itis also assumed that prices are uniformly distributed over the interval

p;ph i

, implying the following simple expression for the probability of

expropriation:

π θð Þ ¼ p−πlp�l θð Þ− 1−πlð Þp�h θð Þ

p−p:

Finally, we also maintain the simplifying assumption that ah is al-ways sufficiently high thatp∗h θð Þ ¼ p. As discussed above, the qualitativeresults do not depend on changes in this assumption.

Technology parameters are chosenbased on standard estimates in theliterature, while country specific labor productivity, domestic capitalstocks and resource stocks are chosen to match aggregate capital andFDI stocks and sector production shares in the data. Unless otherwisestated, all parameter estimates correspond to averages over 1990–2006in the data. A government stability index is used to construct a measureof country risk, summarized by penalty parameter al. The simulated sec-tor FDI shares for each country are then compared to empirical FDI sharesestimates, and the predicted probabilities of expropriation among differ-ent country risk groups are compared to the corresponding country ex-propriation frequencies observed.

In order to calibrate resource output price volatility, r, and πl, we takea “period” to be one year. The average resource output price, E[p], is nor-malized to 1 and the support of resource output prices chosen to matchthe coefficient of variation on detrended petroleum and metals priceindices from the IMF's International Financial Statistics.28 The annualrisk-free interest rate r is set to 0.05, and πl is also set to 0.05. The latterimplies countries that are most likely to expropriate will expropriatewith a 50% probability over a 17-year period.29 We assume γ is equal

acts among the ten countries that have expropriated FDI at least three times over the1900–2006 is 15.5 years, with approximately half of the expropriation intervals between5 and 15 years. (Expropriation acts within a five-year period are treated as a single eventin these calculations.) Assuming this sample of serial expropriators represents countriesmost likely to expropriate, πl = 0.05 provides a good approximation of observed expro-priation frequencies. However, the qualitative results are not highly sensitive to thischoice.

Table 3Numerical example: parameter values.

Parameter Value Parameter Value

r 0.05 πl 0.05α 0.42 γ 0.33p 0.4 p 1.6

31 Itmay appear that this strategy for estimating al is overlyflexible in terms of the abilityto match country risk levels and therefore resource FDI shares, the main variable of inter-est. However, provided v2 N 0, themodel predictions are disciplinedby the ordinal rankingof countries according to the stability index used, and the choice of v1 and v2 simultaneous-ly influences the predicted expropriation thresholds for all countries in the sample.32 For Singapore, the calibrated parameters did not satisfy the sufficient conditions for aunique equilibrium outlined in Proposition 4.1 and the solution algorithm in the case ofSingapore did not converge. Therefore comparisons for Singapore have been excluded.The algorithm converges for all other countries.33 To compute the constrained efficient contract, it is necessary to specify one additionalparameter: ah, the expropriation penalty in the high penalty state. Higher values of ah im-ply that the efficient investment levels are more easily attained by trading off sufficientlylow payments from foreign investors when the expropriation penalty is low for higherpaymentswhen the penalty is high (subject to the feasibility conditions). For this exercise,


to 0.33 based on the non-resource (manufacturing and services) capitalincome shares estimated by Valentinyi and Herrendorf (2008) for theUS economy. The authors do not estimate a separate capital incomeshare for all primaries production, but their estimated share for Agricul-tural production is 0.54, which excludesmining and energy sectors. Wetherefore assume a resource sector capital income share of 0.42, approx-imately equal to the average of the corresponding shares of agricultureand manufacturing. The resultant set of parameter estimates are listedin Table 3.

In calibrating the remaining country-specific parameters,A, K,M andal, we normalize L = 1and employ data onper capita sector production,capital stocks, and sector FDI stocks, as well as an index of governmentstability, for a sample of 38 developing and emerging economies. Totaleconomy-wide capital is estimated from Penn World Tables (constantdollar) per capita gross capital formation data using the perpetual in-ventory method and assuming a geometric rate of depreciation equalto 0.06. With this estimated total capital stock, KPCAP = K + FDI, wechoose A andM to match predicted sector production with average an-nual sector value added data obtained from theUnited Nations'NationalAccounts Statistics: Main Aggregates and Detailed Tables.30 The sector-specific FDI stocks (as well as the aggregate FDI stock) used to evaluatethe model's predicted foreign investment patterns are from Hajzler(2012).

The penalty parameter al is a more challenging parameter to esti-mate given that there is no direct counterpart in the data. In the contextof the model, the discrepancy between al and ah (relative to optimalaggregate FDI) represents the magnitude in the shift in policy ideologybetween government regimes, at least with respect to foreign invest-ment. The strategy we adopt is to estimate al from an index of govern-ment stability (GOVSTAB) for each country in the sample using thefollowing formula:

alFDI�

¼ ν1 þ ν2 GOVSTABð Þ

where FDI∗ represents the efficient level of aggregate foreign investmentimplied by the model given K, GOVSTAB ∈ [0,1], and ν2 N 0. Whenν1 ≥ 0 and ν2 = 1, for example, this mapping implies the countrywith the highest stability index is able to achieve the efficient level of in-vestment without incurring any penalty in the model of Section 4(al ≥ FDI∗), while countries with a lower index will face lower overallinvestment or a positive penalty. The stability index is taken from thePolitical Risk Services' International Country Risk Guide. This index is ascore based on the level of a country's (i) government unity, (ii) legisla-tive strength, and (ii) popular support. We normalize the index to takevalues between 0 and 1 based on themaximumandminimumvalues in

30 Specifically,we calibrate themodel tomatch aggregate sector production shareswhencapital stocks are equal to investors' profit-maximizing investment for a given domesticinterest rate rh(θ) and expropriation probability π(θ). This strategy involves guessingrh(θ) (and hence π(θ)), estimating domestic capital as the difference between the estimat-ed capital stock per person and FDI per person, and setting A and M to match estimatedvalue added per person in each sector. The model is then solved for sector capital stocks(which in our model need not equal the approximated levels implied by profit-maximizing investment) and thedomestic interest rate implied by themodel. This processis repeated until convergence in the predicted interest rate is achieved. Using this proce-durewe are able tomatch the empirical sector production shareswith a high degree accu-racy (±1 percentage point for all countries in the sample). The resulting matched sectorproduction shares and aggregate capital stock per capita (given estimated values for al,whichwe discuss below) are provided in Table 6 of Appendix B. The remaining parameterestimates, A, M, and K are listed in Table 7.

our sample. Themodel is simulated for several different values of v1 andv2, and we present the results for the values that produce the closest fitwith the data in terms of matching predicted expropriation frequencieswithin each of the three risk categories of Proposition 4.1 (v1 = 0.2 andv2 = 0.5).31

The predicted and empirical sector foreign investment shares aswellas the predicted probabilities of expropriation are compared for allcountries in Table 4.32 Statistics are grouped according to country riskcategories: π(θ) = 0 (al ∈ AU), π(θ) ∈ (0,πl) (al ∈ AM) and π(θ) = πl(al ∈ AL). The first column reports the empirical resources FDI sharefor each country. The second column reports aggregate resource-sector investment share under the constrained efficient contract consid-ered in the previous section.33 These shares are equivalent to thosepredicted by a two-sectormodelwith competitively determined invest-ment in both sectors— that is, when investors choose investment inde-pendent of the resource payment.34 The allocation of mineral rightsbetween domestic and foreign investors is not uniquely determinedunder these contract types — therefore the aggregate resource invest-ment share corresponds to the expected resources FDI share, providinga natural benchmark against which to contrast the predictions of themodel. The third column reports the resource FDI share predictedby our calibrated model. The fourth column contains the predictedprobability of expropriating at least once over the entire seventeenyear period,35 and the final column contains an indicator variable thatequals 1 if the country has in fact expropriated at least once between1990 and 2006.

Comparing the first and second columns, we observe lower resourceFDI shares in the data compared to the investment shares implied by thestandard models on average for countries in the top portion of the table(π(θ) = 0), and higher resource shares compared to those implied bythe standard model on average for countries in the lower portions ofthe table (π(θ) N 0). Specifically, the empirical resource FDI share forcountries in the relatively low risk category is below the investmentshare predicted by standard models for 20 of the 23 countries in thisgroup (87% of countries). The average discrepancy between predictedaggregate sector investment shares and estimated shares that is observedfor relatively high risk countries is the opposite sign. Among countrieswith a positive predicted probability of expropriating in the model, theresource FDI share observed in the data exceeds the share predicted bythe standard models for 10 of the 14 countries (71%). The bottom threerows of Table 4 report the average country shares for the three risk

we set ah for each country such that it is never optimal to expropriate under the contract ofour model, for any output price realization and foreign investment34 Specifically, investments that satisfy

FK kXh;1ð Þ ¼ E p½ �GK kRh;1ð Þ

and satisfy the zero profit conditions of all investors imply the following relationship be-tween sector production and sector investment shares for Cobb–Douglas technology:

KR

KX þ KR¼ αE p½ �R

αE p½ �Rþ γX:

where R = Rh + Rf and X = Xh + Xf.35 This is given by 1 − (1 − π(θ))17.

36 More precisely, it may be the case that available technologies or expertise applicableto any single sector are limited to the extent that, if investment in that sector consisted en-tirely of domestic firms, the returns to the economy's fixed factors of productionwould besignificantly lower than the case of positive foreign investment in this sector.37 In the case of the fixed payment τf per mineral right given by Eq. (7), the ad valoremequivalent payment is

eρ f θð Þ ¼ τ f θð ÞMf

E pjs∉D θð Þ½ �G KRf ;Mf

� � ¼ 1− 1þ r1−π θð Þ� �

kRf

E pjs∉D θð Þ½ �G kRf ;1� � :

where kRf = KRf/Mf. This expression is identical to the optimal royalty rate implied by themodel, but the equilibrium foreign investment ratio and expropriation probability will, ingeneral, differ between the two types of contract. The ad valorempayments under compet-itive investment and constrained efficient contract are similarly defined. However, underthe constrained optimal contract this is the expected payment, as the royalty rate variesacross states, and π(θ) = 0, E[p|s ∉ D(θ)] = E[p] = 1.

Table 4Predicted resource FDI shares and exprop. Probability (v1 = 0.2, v2 = 0.6).

Country Data Resource FDI shares Prob. of exprop.(model)

Exprop. = 1(1990–2006)

Constrainedefficient

Model (fixedpayment)

BGR 0.015 0.215 0 0 0BRA 0.016 0.105 0 0 0CHL 0.375 0.150 0 0 0DOM 0.009 0.127 0 0 1HND 0.207 0.246 0 0 0HRV 0.031 0.117 0 0 0IND 0.078 0.337 0 0 0KOR 0.009 0.069 0 0 0LTU 0.013 0.117 0 0 0MEX 0.020 0.076 0 0 0MOR 0.174 0.220 0 0 0MOZ 0.357 0.330 0 0 0MYS 0.025 0.227 0 0 0PAK 0.141 0.335 0 0 0PHL 0.104 0.212 0 0 0RUS 0.162 0.163 0 0 1SVK 0.008 0.074 0 0 0THA 0.042 0.155 0 0 0TUN 0.478 0.205 0 0 0TUR 0.025 0.188 0 0 0UGA 0.044 0.444 0 0 0UKR 0.050 0.263 0 0 0ZAF 0.063 0.134 0 0 0ARG 0.249 0.091 0.429 0.560 1BOL 0.422 0.260 0.995 0.421 1BWA 0.561 0.464 0.846 0.032 0CRI 0.224 0.133 0.626 0.560 0GUY 0.692 0.617 0.883 0.432 0IDN 0.560 0.293 0.892 0.416 1TTO 0.264 0.207 0.682 0.458 0COL 0.197 0.218 1.000 0.560 0ECU 0.671 0.305 1.000 0.560 1PER 0.160 0.169 1.000 0.560 0PNG 0.901 0.583 1.000 0.560 0POL 0.006 0.085 0.620 0.560 0SLV 0.009 0.145 0.906 0.560 0VEN 0.405 0.237 1.000 0.560 1

Category Averages:π(θ) = 0 0.106 0.196 0.000 0.00 0.09π(θ) ∈ (0, πl) 0.425 0.295 0.765 0.41 0.43π(θ) = πl 0.336 0.249 0.932 0.56 0.29


categories. The average empirical relationship between country risk andresources FDI is not monotonic across the three groups (the averageshare for the highest risk group is slightly below that of the moderaterisk group). This is explained by the relatively high resource productionshares among the intermediate country risk group in our sample, whichis also reflected in relatively large calibrated stocks of resource rights Mrelative to effective labor A and domestic capital K. (See Tables 6 and 7in Appendix B.)

Comparing the third column of the table to both the empirical re-source FDI shares and those predicted by standard models illustratesthe extent towhich ourmodel helps to explain thedata. For the relative-ly low risk (politically stable) group, no mineral rights are allocated toforeign investors (and the probability of expropriation is zero). For therelatively high risk countries, the expropriation probability is positiveand the share of mineral rights allocated to foreign investors is maxi-mized. As a result, the model provides a rationale for the tendency forresource-based FDI shares to be significantly lower among relativelylow risk countries compared to high risk countries, even though produc-tion shares between the two groups are comparatively small (seeTable 6). This coincides with the empirical evidence documented inHajzler (2012).

The model also provides a rationale for the large discrepancies be-tween the resource FDI shares predicted by standard models and the

data for many countries, particularly countries in the relatively lowrisk group. Quantitatively, however, the predicted shares for individualcountries do not generally improve upon those implied by standardmodels, tending to predict shares that are either much lower or muchhigher than those observed, but in the opposite direction. Thereforewe view the model as providing only a partial account of mineral rightsallocations and sector FDI patterns. Specifically, we propose a few im-portant determinants of FDI outside of our simple model that couldbring predicted sector FDI shares closer in line with the data. For exam-ple, FDI is often accompanied by specialized technology and appropriatemanagerial expertise that domestic investors or the governmentmaybeunable to provide.36 In such cases it would be efficient for foreign inves-tors to invest in a given sector of the economy, independent of risk cat-egory, whenever the surplus benefit from foreign technology outweighsthe cost of increased expropriation risk. Amodelwith this featurewouldpredict less extreme average aggregate investment shares. Moreover, ahigher average risk of expropriation in resources, attributed to variouspotential factors considered in the expropriation literature (Kobrin,1980; Shafer, 2009; Nellor, 1987; Monaldi, 2001; Engel and Fischer,2010), would tend to lower resource sector FDI shares compared tothose predicted by our model among relatively high-risk countries.

In terms of predicted expropriation frequencies across country riskcategories, however, ourmodel performs quite well. Only 9% of countriesin our predicted sample of relatively low risk countries have actually ex-propriated during the period under examination, while approximately36% of countries in themediumandhigh risk countries have. The predict-ed probabilities of expropriation across risk categories do not differ sub-stantially from these frequencies. The government stability index, in thecontext of our model, provides additional insight into the determinantsof expropriation risk across countries. A final empirical prediction of themodel is between the resource output price and the timing of expropri-ation. This positive relationship is driven by the expropriation strategiesof governments in moderate risk countries. When expropriation doesoccur, the resource output price tends to be above average. For thehighest risk group, there is no relationship between expropriation andthe resource output price because expropriation always occurs in alow penalty regime.

Our calibrated model enables us to examine how foreign investorpayments for mineral rights and corresponding host country incomevary under the different types resource sector contracts considered inSection 5. Of particular interest is howmuch lower the expected royaltypayments are in our model compared to the constrained efficient con-tract and the casewhere resource sector investment is determined com-petitively. Expected foreign investor payments in the resource sector(conditional on not being expropriated) are calculated as a percentageof the expected value of foreign-owned production. That is, expected re-source sector payments under the alternative contracts are converted toad valorem royalty equivalents. The corresponding payments under theconstrained efficient contract, the benchmark fixed payments contract,the ad valorem royalty contract, and the competitive investment scenar-io are compared in Table 5.37

Table 5Expected resource payments: share of production value.

Country Constrainedefficient

Fixedpayment

Ad valoremroyalty

Competitiveinvestment

ARG 0.607 0.558 0.558 0.580BOL 0.606 0.564 0.558 0.580BWA 0.602 0.566 – 0.580CRI 0.605 0.558 0.558 0.580GUY 0.599 0.564 0.558 0.580IDN 0.595 0.565 – 0.580TTO 0.624 0.563 0.558 0.580COL 0.593 0.558 0.558 0.580ECU 0.595 0.558 0.558 0.580PER 0.594 0.558 0.558 0.580PNG 0.606 0.558 0.558 0.580POL 0.596 0.558 0.558 0.580SLV 0.595 0.558 0.558 0.580VEN 0.593 0.558 0.558 0.580

Category averages:π(θ) ∈ (0, πl) 0.605 0.562 0.558 0.580π(θ) = πl 0.596 0.558 0.558 0.580


As our model predicts no foreign investments and payments in re-sources for the lowest risk category, Table 5 does not include comparisonsfor this group. For this group, our model predicts that domestic invest-ment in resources equals the competitively determined level. When re-source sector investment is determined competitively, the optimalroyalty rate equals 1 − α (column 4), including at the unconstrained ef-ficient solution, providing a natural benchmark for comparing optimalroyalty rates for the relatively high risk categories. Royalty paymentsunder the constrained efficient contract (column 1) are consistentlyhigher than the competitive rate. Although the constrained efficient con-tract is associated with comparatively high investment per mineral rightwhich requires, ceteris paribus, a lower ad valorem payment, expropria-tion risk is sufficiently reduced compared to the competitive investmentsolution to command higher payments. By contrast, the ad valoremequivalent of the fixed payment contract in our model (column 2) isconsistently lower than both the constrained efficient and the competi-tive rates. The royalty rates are lowest for the highest risk group(π(θ) = πl), illustrating the extent to which optimal discounting of min-eral rights among relatively high risk countries is implied by our model.The percentage difference in the implied royalty rates range from 2.5–4% when compared to the competitive investment model and 5–11%when compared to the constrained efficient contract.

For the optimal, pure royalty contract (column 3), our calibrated pa-rameters imply that all countries either join the high risk group(π(θ) = πl) or relatively low risk group (π(θ) = πl). In other words,the range of values for al that correspond to the intermediate risk cate-gory, where π(θ) ∈ (0,πl), becomes more narrow under an ad valoremroyalty compared to the fixed payment contract. Intuitively, owing tothe positive correlation with the resource output price, the ad valorempayment relaxes the no-expropriation constraint (13) relative to afixed payment whenever the realized price is above average (i.e.when-ever foreign investors in resources earn high ex post returns relative to themanufacturing sector) by allocating a greater share of the ex post returnsto the host country, and tightens it whenever the price is below average.This implies that, for a given country risk level, the threshold output pricebelowwhich it is never optimal to expropriate is lower in the case of thead valorem royalty. Countries in the intermediate risk category near thethreshold of the lowest risk group, Botswana and Indonesia, transit tothe latter group under the ad valorem royalty contract.38 For all othercountries in the intermediate risk category, the no-expropriation

38 Threshold levels of country risk demarcating risk categories depend not only on thegovernment stability index but also on other model parameters such as the stocks of min-erals and domestic capital, and therefore these thresholds are country specific.

constraint is tightened under the ad valorem royalty conditional onnot expropriating, implying lower aggregate FDI and host-country util-ity relative to the highest risk group, which expropriate whenevera = al. This implies that countries on the threshold of belonging tothe highest risk group under the fixed payment contract transit to thisgroup under the ad valorem payment. Although the range of penaltyvalues that correspond to the intermediate risk category is reduced(or even eliminated) under the royalty contract for the calibrated pa-rameters, themagnitudes of ex post foreign payment discounts are sim-ilar to those under a fixed payment among the relatively high riskcountries.

Expected host country income under the optimal fixed payment andad valorem royalty contracts is strictly higher than host country incomeunder competitive investment and, for most countries, is remarkablyclose to the first best, zero risk level. (See Table 8). Host country incomeunder the constrained efficient contract comes even closer to first bestincome than the optimal fixed payment or royalty contacts for a largemajority of countries. For countries in the lowest risk category, wherecontracts are self-enforcing, the constrained efficient contract mustdeliver higher host country income. However, it is interesting to notethat for some countries in the high risk group (Argentina, Costa Rica,Trinidad & Tobago, and Papua New Guinea), by allowing expropriationto occur when the penalty is low, optimal fixed payment and royaltycontracts deliver higher host country income relative to the constrainedefficient contract. Even though the contained efficient contract offersflexibility in that it allows agents to condition payments on governmentregime, some countries in the relatively high risk group do better byexpropriating in some states.

It would be interesting to compare differences in the host countryshare of resource sector income in Table 5 to observeddifferences acrosscountries, and to examine to what extent observed differences can beattributed to country risk. This is difficult, however, due to both therelative complexity of resource contracts in practice and the limiteddata available. Resource contracts often include combinations of varioustypes of payments, from ad valorem royalties (sometimes administeredon a sliding scale) to export, income, asset, and windfall profits taxes aswell as fixed payments per mineral concession (sometimes in the formof initial contract bids), and may also include incentives such as taxholidays and deductions for exploration and other expenditures.Because attributes of the typical contract can vary substantially acrosscountries, and indeed across contracts within countries, comparisonacross thesemanydimensions is not straightforward (and data is not al-ways available on government or official web-sites). Ad valorem royal-ties and corporate income taxes are accessible for most countries andminerals, and are perhaps themost common sources of government rev-enues from such contracts. Nevertheless, focusing exclusively on thesepayment types may not accurately reflect differences in the host countryshare of resource sector revenues. For such comparisons, the ideal mea-sure of the host country share is total government take as a share oftotal income less operating costs in the sector. Although these data existfor large country samples – for example, estimates of government takecompiled from BEA data on U.S. affiliate operations in Mcmillan andWaxman (2007) – access to these data even at the country level is gener-ally restricted for confidentiality reasons. Moreover, it is important toconsider government take or royalty data over a sufficiently long timehorizon given that periodic hikes in royalty rates often accompany,or are tantamount to, resource sector expropriation. For example, inBolivia, Ecuador, and Venezuela, petroleum royalty rates were lessthan 17% prior to 2001. (For some contracts these rates were as low as1% in Venezuela.) These rates have since been raised to 30% inVenezuela in 2001 and to 50% in Ecuador and Bolivia in 2006. Thissuggests that relatively volatility of government take may be moreinformative about the effects of country risk than a snapshot of relativeincome shares at a particular point in time.

Without access to country level time series on government take inresources, we do not attempt to explore these relationships empirically.


Nevertheless, this would be an interesting avenue for future research.Anecdotal evidence suggests that cheap access to minerals is an impor-tant draw for investors in countries considered to be high risk; a surveyconducted by the IMF CMCG (2003) indicates that tax incentives play animportant role in attracting FDI in the extractive sectors where the fixedcosts are high and investments are generally front-loaded. (Foreigninvestors operating in Africa additionally reported that they tended toonly invest in the extractive industries of higher risk countries becauseit was here that opportunities in for taking advantage of natural re-source availability were sufficient to offset legal problems and politicalrisks.) However, Mcmillan and Waxman (2007) is the only work weare aware of that attempts to quantify the effects of political risk onthe host country share of resource rents. They show that differences inthe average share of government take across regions are substantial —the developed economy share in 1999 is 0.33 compared to 0.27 inLatin America as well as North Africa and the Middle East, 0.17 inSubsaharan Africa and 0.10 in emerging economies of Europe andCentral Asia.39 Regressing host country's resource income share on anindex for institutional quality, they find that an increase in institutionalquality from the lowest to the highest score raises the host country'sresource income share by 10 percentage points, suggesting that institu-tional quality has the potential to account for a substantial portionof cross-country variation. Their focus is on the roles of democraticaccountability and corruption, and further research is needed to quanti-fy the effects of government stability and expropriation risk on the hostcountry shares of resource sector returns.

7. Conclusions

By focusing on government choice of mineral contract in the contextof a small, two-sector open economy where FDI is risky and the futurecosts and benefits of expropriating are unknown, this paper provides a ra-tionale for relatively high extractive industry FDI shares in countriesmostlikely to expropriate. Specifically, the predictions of the incomplete mar-kets model of FDI and expropriation considered in this paper reconcile anumber of stylized facts. These are (i) a high global share of resource sec-tor FDI in total expropriation compared to the sector's average productionshare; (ii) a positive relationship between mineral output prices and thetiming of resource-sector expropriation; and (iii) an average share of pri-maries in total FDI that is higher in expropriating countries compared tonon-expropriating countries, particularly in mining and petroleum,even though on average these country groups do not differ significantlyin terms of sector production shares. The first two facts are well-documented in the literature, and have been used to support and/or mo-tivate explanations forwhy FDI in extractive sectors ismore vulnerable toexpropriation. The third fact presents somewhat of a puzzle if expropriat-ing countries are perceived by foreign investors as more likely to expro-priate, and if resource-based FDI is particularly risky.

We argue that the capacity (and incentive) for governments to offermineral rights to foreign investors cheaply in countries characterized bya high degree political risk can help explain this puzzle. Specifically, ourtheory suggests that countries in the highest risk category benefit frompromoting FDI in the resource sector (and by lowering the cost of min-eral rights) because, although this raises the likelihood that a future gov-ernment will choose to expropriate and lowers FDI in the non-resourcesector, the expected value of expropriated assets more than compen-sates for this loss. Governments in low and moderate risk countries in-stead aim to minimize the probability of expropriation for given levelsof aggregate FDI. For the lower risk countries, this is accomplished byrestricting resource-sector FDI because higher-than-average prices re-sult in “windfall profits,” and the temptation for a low penalty regimeto expropriate in these states. In contrast, governments of moderaterisk countries manage risk by concentrating FDI in resources — in

39 The standard deviation across all countries and time periods considered is 0.27.

the lowpenalty regime, when the government ismost tempted to expro-priate, resource sector firms earn below-average returns on their invest-ments (conditional on not being expropriated), and the governmentis less likely to expropriate as FDI is concentrated in resources. Thesepatterns are robust to alternative types of resource contract (such as astandard royalty payment) provided investment levels are also specifiedand contracts are incomplete.

These predictions for government policy towards resource-based FDIimply a positive relationship between resource FDI shares and the prob-ability of expropriation among countries of similar resource wealth anddomestic capital stocks. This relative concentration of FDI in resourcesamong countries most likely to expropriate implies that the total shareof resource-based FDI in total assets expropriated globally will be higherthan the average share of this sector in GDP. Quantitatively, the theoryalso helps to explain deviations in observed country sector FDI patternsfrom those predicted by a standard, competitive two-sector model.

Finally, the findings suggest that countries that have a poor record ofexpropriation, such as Bolivia, Ecuador, andVenezuela,mayfind that pro-moting relatively large amounts of FDI in resources is desirable and, for aslong as default risk in these countries remains high, this suggests that acycle of privatization and nationalization will persist. Moreover, becausethis implies that mineral rights should be offered to foreign investors onvery favorable terms, this paper offers a novel perspective for the lowgovernment take in resources that has been documented in many coun-tries. That foreign investorsmust be compensated for political risk if theyare willing to invest is evident. However, this paper emphasizes that(i) subsidies to foreign investment will be most effective in resource sec-tors, where governmentsmanage a key factor input and influence invest-ment, and (ii) this policy is not likely to produce desirable results forcountries at all levels of political risk. In particular, very high risk countriesare expected to benefit from subsidizing resource FDI, while countriescharacterized by relatively low default risk do not. Governments ofrelatively low risk countries have a stronger incentive to minimize theex ante risk of expropriating by restricting FDI in the resource sector ifthey anticipate the costs of expropriating will be high ex post.

Acknowledgements

I thank my advisors James MacGee and Igor Livshits for their in-valuable guidance. I also thank Martin Gervais, Guy Holburn, HiroKasahara, Timothy Kehoe, Steffen Lippert, Dorian Owen, JonathanRosborough, Claudiu Tunea, Martijn van Hasselt, Mark Wright, andtwo anonymous referees for many helpful insights and suggestions, aswell as participants of the Money/Macro seminar at the University ofWestern Ontario, the Department of Finance, Canada, the University ofAuckland, the University of Otago, and Massey University, NewZealand for useful comments. All errors are mine.

A. Mathematical Appendix

A.A. Proof of Proposition 3.1

The proof proceeds by describing the optimal investment and re-source contract decisions when the no-expropriation binds (π(θ) = 0)and when this constraint is violated (π(θ) = πl). These cases areshown to correspond to two distinct regions of country risk, definedover values of al, and the implied relationship between country riskand the (expected) share of FDI located in the resource sector is consid-ered in Proposition 3.2.

NE binds and π(θ) = 0: Consider first the case where (NE) binds,and assume KXf N 0 and Lf N 0. From the no-expropriation constraint,kX θð Þ ¼ KXf

L f¼ al= 1þrð Þ−KRf

L f. Similarly, the resource constraint for domestic

capital implies kX θð Þ ¼ KXhLh

¼ K−KRhLh

. Together, these conditions imply

kX θð Þ ¼al1þr þ K−KRf−KRh

L


Substituting into expression (8) and setting E[p] = p0, homogeneityof F(⋅) implies that we can express the host country decision overresource contracts as

maxKRf ;KRh ;M ff g

V ¼ Fal

1þ rþ K−KRf−KRh; L

� �þ p0G KRh;M−Mf

� �þp0G KRf ;Mf

� �−al

V is strictly concave in each of the arguments, and the solution satisfies

FK kX :1ð Þ ¼ p0GK kRh;1ð ÞFK kX :1ð Þ ¼ p0GKðkRf ;1ÞGM kRf :1� �

¼ GM kRh;1ð Þ:

The first two conditions imply kRh = kRf = kR. The last condition istherefore redundant, and Mf is not uniquely determined.

If instead KXf = Lf = 0, kX = kXh does not depend on optimal foreigninvestment, and the decision over resource contracts is instead:

maxKRh ;M ff g

V ¼ F K−KRh; Lð Þ þ p0GðKRh;M−Mf Þ þ p0Gal

1þ r;Mf

� �−al

and the solution satisfies FK(kX,1) = p0GK(kRh,1) and GM(kRf,1) =GM(kRh,1), again implying kRh = kRf = kR.

In both cases, host country income can be expressed as

VNE ¼ F kX ;1ð ÞLþ p0G kR;1ð ÞM−al:

Themarginal conditions indicate that aggregate investment and total sec-tor specific factors of production, which are equal in both cases, are allo-cated in the same proportions, resulting in identical values of kX and kR.Therefore the maximized values of V are also equal and KXf = Lf = 0 ismerely a special case of the general problem KXf, Lf ≥ 0. It follows thatMf and Lf are not uniquely determined, and equilibrium kR and kX satisfy

kXLþ kRM ¼ al1þ r

þ K ¼ FDIþ K

and

FK kX :1ð Þ ¼ p0GK kRh;1ð Þ:

NE does not bind and π(θ) = πl: Now consider the casewhere (NE)is violated, and assume KXf, Lf N 0. Foreign and domestic investors opti-mally choose KXj and Lj to satisfy FK(kXj,1) = (1 + r)/(1 − πl), and thecorresponding capital to labor ratio in this sector kXc b kX

FB is determinedby r and πl. The distribution of labor between domestic and foreignfirms, in turn, depends on kX

c and the resource contracts:

Lh ¼ KXh

kcX¼ K−KRh

kcX; Lf ¼ L−KXh

kcX¼ kcXLþ KRh−K

kcX:

Using kXh = kXf = kXc and the resource constraints, the host country

decision over resource contracts can be expressed as

maxKRf ;KRh ;M ff g

V ¼ F kcX ;1� �

− 1þ rð ÞkcX� �

Lþ p0GðKRh;M−Mf Þ

þp0GðKRf ;Mf Þ þ 1þ rð Þ K−KRh−KRf

� �−πlal

The optimal contracts satisfy p0GK(kRh,1) = p0GK(kRf,1) = 1 + rwhich implies kRh = kRf = kR

FB. The additional optimality conditionGM(kRf.1) = GM(kRh,1) is therefore redundant, andMf is not uniquelydetermined.

If instead KXf = Lf = 0, kX = kXh, kX is determined by the resourcecontract, and the government problem is

maxKRf ;KRh ;M ff g

V ¼ F K−KRh; Lð Þ þ p0GðKRh;M−Mf Þ þ p0GðKRf ;Mf Þ− 1þ rð ÞKRf−πlal:

The solution satisfies FK(kX.1) = p0GK(kRh,1) and GM(kRf.1) =GM(kRh,1), again implying kRh = kRf = kR. Finally, p0GK(kRf.1) = 1 + r,implying FK(kX.1) = 1 + r. Therefore kX = kX

FB and kR = kRFB, and opti-

mal Mf is unique: Mf = min{M, M − (K − kXFBL)/kRFB}.

In both cases, expected host country income can be expressed as

Vπl¼ F kX ;1ð Þ− 1þ rð ÞkXð ÞLþ p0G kR;1ð Þ− 1þ rð ÞkRð ÞM

þ 1þ rð ÞK−πlal:

Note F(kX,1) − (1 + r)kX and p0G(kR,1) − (1 + r)kR are increasing forkX ≤ kX

FB and kR ≤ kRFB. Because kX

c b kXFB, maximum expected host-

country income corresponds to KXf = Lf = 0 as long as domestic capitalK exceeds kX

cL. Below this threshold, restricting Lf = 0 results in sub-optimally low investment in the manufacturing sector and the optimalcontract instead results in positive foreign investment in this sectorwith kX(θ) = kX

c .Two regions of country risk: [0,a′) & a′; a

�: Consider al ¼ a−�a

for �a ≈ 0. Then there exist �x and �r satisfying al = (1 + r)(kXFBL −�xL + kR

FBM − �rM − K) such that

V � ¼ F kFBX −�x;1� �

Lþ p0G kFBR −�r ;1� �

M

− 1þ rð Þ kFBX −�x

� �Lþ kFBR −�r

� �M−K

� �N F kFBX ;1� �

Lþ p0G kFBR ;1� �

M− 1þ rð Þ kFBX Lþ kFBR M−K� �

−πlal¼ Vπl

where Vπlis the income attainable when (NE) is violated. Therefore for

sufficiently high al, the optimal resource constraint satisfies (NE).Now consider some alba and the corresponding optimal capital to

labor ratiosekX andekR satisfying (NE). DenoteΔkX ¼ kFBX −ekX,ΔkR ¼ kFBR −ekR,ΔX ¼ F kFBX ;1� �

−F ekX ;1� �� L andΔR ¼ p0 G kFBR ;1

� �−G ekR;1� ��

M.

Then

Vπl−VNE ¼ ΔX þ ΔRþ 1−πlð Þal−a

¼ ΔX þ ΔR− 1þ rð Þ ΔkXLþ ΔkRMð Þ−πlal

Strict concavity of F(⋅) and G(⋅) implies that ΔX −(1+r) ΔkXL andΔR −(1+r)ΔkRM are strictly positive and decreasing over ekX and ekR for ekXbkFBXand ekRbkFBR . This implies that, for penalties al below some thresholda′ N 0,Vπl−VNE N0. □

A.B. Proof of Proposition 3.2

When al∈½a′; aÞ, (NE) binds, π(θ) = 0 andMf is not uniquely deter-mined. If K is sufficiently large to cover optimal aggregate investment ineither sector given kX and kR (K ≥ K∗ = max{kXL, kRM}), the optimalrange for Mf is [0,M]. This implies that the share of FDI located in theresource sector, σR = kRMf/(kRMf + kXLf), lies within the range [0.1].We refer to the “average” resource FDI share as the midpoint of thisrange: σR ¼ 0:5. When al ∈ [0, a′), (NE) does not bind and π(θ) = πl.In this case Lf = 0 and therefore σR ¼ σR ¼ 1. Therefore σR is strictlygreater for al ∈ [0, a′) compared to al∈½a′; aÞ, conditional on K N K∗.

However, if al∈½a′; aÞ but K b kRM, the lower bound on Mf given kR

and kX is M ¼ M 1− KkRM

� �(since domestic capital stock is insufficient

to cover all desired investment in resources) and the correspondinglower bound on σR is σ R ¼ al− 1þ rð Þ kXL½ �ð Þ=alN0. If K b kXL, kXLf =kXL − K N 0 and the upper bound on σR is σR ¼ 1þ rð Þ kRM½ �=alb1. Itis possible to show that σ R is strictly increasing and σR is strictly

40 When KRf = 0, either π(θ) = 0 or π(θ) = πl and (NE) does not bind, and the equilib-rium is as described in Proposition 3.1.


decreasing over a′; a �

when these internal bounds are binding. This im-plies that themedian share σR may be increasing or decreasing depend-ing onwhich is binding, and this in turn depends on relative values ofM,L, and K. If both are binding, whether σR is increasing or decreasing de-pends on the relative elasticities of kRM and kXL, which in turn dependson relative capital intensities of production in each sector. In general,therefore, the relationship between σR and al may be increasing,decreasing, or may even change sign over a′; a

�.

The derivatives of the lower and upper boundswith respect to al canbe expressed as

∂σ R

∂al¼ 1þ rð ÞkXL

a2l1−μXð Þ; ∂σR

∂al¼ 1þ rð ÞkRM

a2lμR−1ð Þ

where μX = (∂kXL/∂al)(al/(kXL)) and μR = (∂kRM/∂al)(al/(kRM)) are theelasticities of total sectoral investment in response to an increase in al.This suggests the lower bound is increasing and the upper bound isdecreasing if these elasticities are less than 1. Total differentiation of(NE) yields

μXkXLþ μRkRM ¼ al1þ r

:

From the definition of (NE) it is straightforward to verify thatμX + μR b 1, and therefore 0 b μX, μR b 1 is guaranteed if aggregate in-vestment in both sectors increases with a relaxation in this constraint.Because this increasing lower bound will bind when M is high relativeto K (otherwise the lower bound is constant at zero), whereas the de-creasing upper bound binds when L is high relative to K, this impliesthat aR is increasing in especially resource-abundant countries (highM and low L) and decreasing in especially labor-abundant countries(low M and high L). When both M and L are sufficiently high relativeto K, both inner bounds will bind, and σR is increasing over a′; a

�if

and only if

∂ σ R þ σRð Þ∂al

N0 ⇔ μRN1−12

KkRM

� �:

Whether or not this condition is satisfied will depend on propertiesof F(⋅) and G(⋅), as well as K/M. However, because kRM N K, σR is strictlydecreasing for μR b 0.5, and a sufficient condition is μR ≤ μX. □

A.C. Proof of Proposition 4.1

The proof proceeds by describing the optimal investment andresource contract decisions when (pl∗ − E[p|s ∉ D(θ)]) ≥ 0 and when(pl∗ − E[p|s ∉ D(θ)]) b 0 where pl

∗ is implicitly defined by

1−π θð ÞÞ p�l −E½p� ��s∉D θð Þ�� GðKRf ;Mf Þ þ 1þ rð Þ KXf þ KRf

� �− 1−π θð Þð Þal ¼ 0

ð21Þ

in conjunctionwith thedefinition ofπ θð Þ ¼ π p∗l ;pð Þ in Eq. (11).We showthat (1 − π(θ))(pl∗ − E[p|s ∉ D(θ)]) is strictly increasing in pl

∗ and that

Eq. (21) implies that pl∗ is strictly decreasing in al forp∗l∈ p;p� �

, and there-

fore (pl∗ − E[p|s ∉ D(θ)]) ≥ 0 and (pl∗ − E[p|s ∉ D(θ)]) b 0 correspondto two categories of country risk, al ≥ a″ and al b a″. Properties of equilib-rium in each case are then discussed, assuming conditions for uniquenessare satisfied. It follows fromProposition 3.1 that, for sufficiently low al, theequilibrium is as described in Proposition 3.1.1 but where p0 = E[p]. Thethreshold level of country risk a′ below which this describes the equilib-rium, however, does not necessarily exceed a″. This implies that it ispossible for there to be only be two relevant categories of country risk,(pl∗ − E[p|s ∉ D(θ)]) ≥ 0 and p∗l ¼ p . However, provided that a″ N a′,then (pl∗ − E[p|s ∉ D(θ)]) b 0 corresponds to a third, intermediate riskcategory. Whether there are two or three relevant categories of

country risk, the share of resource FDI is increasing in country risk(and strictly increasing between risk categories). Finally, sufficientconditions for uniqueness of equilibrium at each level of countryrisk are established.

At the optimal contract, pl∗ is strictly decreasing in al if KRf, Mf N 0:Consider the case where KRf N 0 and Mf N 0, implying that kX(θ) isimplicitly defined by (1 − π(θ))FK(kX,1) = 1 + r and foreign anddomestic firms employ identical capital to labor ratios.40 Aggregatemanufacturing sector production is F(KXf + K − KRh, L), manufacturingFDI is

KXf θð Þ ¼ Γ θð Þ− K−KRhð Þ

where Γ θð Þ ¼ F−1K

1þr1−π θð Þ

� �. The government problem can be expressed as

maxKRf ;KRh ;M ff g

V ¼ F Γ θð Þ; Lð Þ þ E½p� GðKRh;M−Mf Þ þ GðKRf ;Mf Þ� �

− 1þ rð Þ KRf þ Γ θð Þ− K−KRhð Þ� �

−π θð Þal:

subject to the usual non-negativity/resource constraints, (21) and (11).Assume for the moment an interior solution for both optimal KRf andKRh. Taking into account the effects of the choice of resource contractson pl

∗, π(θ) and KXf(θ), the first-order conditions for the governmentproblem are

∂V∂KRf

¼ E p½ �GKðkRf ;1Þ− 1þ rð Þ−ΨKRf ¼ 0 ð22Þ

∂V∂KRh

¼ E p½ �GK kRh;1ð Þ− 1þ rð Þ−ΨKRh ¼ 0 ð23Þ

∂V∂Mf

¼ E p½ � GMðkRf ;1Þ−GM kRh;1ð Þ� �

−ΨM f þ λ0−λ1ð Þ ¼ 0 ð24Þ

where

ΨX ¼ ∂π θð Þ∂p�l

∂p�l∂X

!al− FK Γ θð Þ; Lð Þ− 1þ rð Þð ÞΓπð Þ

and where Γπ = ∂Γ(θ)/∂π b 0. λ0 ≥ 0 and λ1 ≥ 0 are the multiplierson constraints Mf ≥M and Mf ≤M respectively, where M ¼ max

0;M−K=kRhf g and M ¼ min M;M K−kXLð Þ=kRfn o

. (These upper and

lower bounds on Mf are defined by Proposition 3.1. For simplicity, wecarry out the analysis taking these bounds as given, and ignore anyeffect of government decision over KRf and KRh on V as a result of the

potential effect on these bounds.) Complementary slackness implies λ0

Mf−M� �

¼ 0 and λ1 M−Mf

� �¼ 0 . From Eq. (11), ∂π(θ)/

∂pl∗ = − πlz(pl∗) b 0 (given the assumption p∗h ¼ p). Implicitly differen-tiating Eq. (21), we obtain the partial derivative of pl∗ with respect toeach choice variable:

∂p�l∂KRf

¼ −ð1−π θð ÞÞ p�l −E pjs∉D½ ��

GKðkRf ;1Þ þ ð1þ rÞΩ

;

∂p�l∂KRh

¼ − 1þ rð ÞΩ

;∂p�l∂Mf

¼ −ð1−π θð ÞÞ p�l −E pjs∉D½ ��

GMðkRf ;1ÞΩ

;


where

Ω ¼ 1−π θð Þð ÞGðKRf ;Mf Þ−πlz p�l� �

al þ 1þ rð ÞΓπð Þ

is the slope of Eq. (21) with respect to pl∗, given that

∂∂p�l

1−π θð Þð Þ p�l −E pjs∉D½ �� ¼ 1−π θð Þ:

In the neighborhood of an equilibrium solution Ω N 0, implyingthat pl

∗ decreases, and hence π(θ) increases, as manufacturing sectorFDI increases. This implies that ∂pl∗/∂KRh b 0, since KXf is increasing inKRh given aggregate investment. Intuitively, at the equilibrium level ofmanufacturing FDI, additional foreign investment in this sector mustraise the benefit of expropriation relative to the cost. (This condition isautomatically satisfied if, for instance, FK(KX,L)KX is strictly increasing.)Hence ΨKRh N0. We can also verify that ∂pl∗/∂KRf b 0 in equilibrium. Tosee why, consider a capital to labor ratio kRf b kR

FB in the neighborhoodof the foreign firm's profit maximizing level, such that 1 + r ≈(1 − π(θ))E[p|s ∉ D]GK(kRf,1). Evidently, ∂pl∗/∂KRf is strictly negative,approximately equaling:

−p�l 1−π θð Þð ÞGKðkRf ;1Þ

Ωb0

and only for kRf sufficiently below this ratio would there be a reversal insign. However, given that kX ≤ kX

FB,

Φ ¼ − ∂π θð Þ∂p�l

!�al− FK Γ θð Þ; Lð Þ− 1þ rð Þð ÞΓπ

�N0:

Therefore ∂pl∗/∂KRf N 0 would imply that ΨKRf ¼ − ∂p∗l =∂KRf� �

Φ=Ωb0 ,and condition (22) in turn implies kRf N kR

FB, a contradiction. Hence ∂pl∗/∂KRf b 0 andΨKRf N0.

That Eq. (21) is strictly increasing in pl∗ implies that pl∗ is increasing

and π(θ) is decreasing in al.Three categories of country risk: The first order conditions also

imply that either Mf ¼ M or Mf ¼ M (λ0 N 0 or λ1 N 0). To see this,note that

∂p�l∂Mf

¼ GMðkRf ;1ÞGKðkRf ;1Þ

∂p�l∂KRf

− ∂p�l∂KRh

" #:

Moreover, the conditions (22)–(23) imply

∂p�l∂KRf

− ∂p�l∂KRh

¼ ∂π θð Þ∂p�l

�al− FK Γ θð Þ; Lð Þ− 1þ rð Þð ÞΓπ

� !−1

�

GKðkRf ;1Þ−GK kRh;1ð Þ� �

:

Substituting these expressions for ∂pl∗/∂Mf in Eq. (24) and simplify-ing yields

GK kRh;1ð ÞGKðkRf ;1Þ

−GMðkRh;1ÞGMðkRf ;1Þ

¼ λ1−λ0

GMðkRf ;1Þ:

This equation implies that if kRh ≥ kRf then λ1 − λ0 b 0 and henceλ0 N 0 andMf ¼ M. If kRh b kRf thenMf ¼ M. Whether kRh N kRf dependson pl

∗. Specifically,ΨKRf N0 andΨKRh N0 are strictly decreasing in ∂pl∗/∂KRf

and ∂pl∗/∂KRh. Given (1 − π(θ))(pl∗ − E[p|s ∉ D]) is strictly increasing inpl∗ and non-negative if and only if pl∗ ≥ E[p|s ∉ D],

p�l ≥E pjs∉D½ � ⇔ ΨKRf ≥ΨKRh ⇔ kRf ≤kRh:

This implies that Mf ¼ M when pl∗ ≥ E[p|s ∉ D] and Mf ¼ M when

pl∗ b E[p|s ∉ D], conditional on optimal p∗l Np . Because pl

∗ is strictly

decreasing in al over the range ðp;pÞ, these two scenarios correspondto two categories of country risk, where al

0 ∈ AU and al1 ∈ AM implies

al0 N al

1.Note that if eitherM ¼ 0 orM ¼ M then KRf = 0 or KRh = 0. For the

former case, pl∗ is no longer implicitly defined by Eq. (21), and insteadthe equilibrium is described by the previously considered case withno-price uncertainty when (NE) binds, but where KRf = Mf = 0.(In this case expropriation never occurs.) When KRf N 0, however,pl∗ satisfies Eq. (21) and expropriation occurs whenever a = al and

p N pl∗. Therefore when al ∈ AM and Mf ¼ M , expropriation occurs

with positive probability. For sufficiently low al, it is optimal to expro-priate for any resource output price p and equilibrium is described byProposition 3.1.1, providing a third category of country risk suchthat a0l ∈AL and a1l ∈AM implies al1 N al

0. This will be true at a penaltylevel al∗ above that for which p∗l ¼ p satisfies Eq. (21). Thereforeit is possible that AM is empty, where supAL ¼ infAU . Otherwise,supAL ¼ infAM and supAM ¼ infAU .

Sufficient conditions for a unique solution to the governmentproblem: We now describe sufficient conditions under which the firstorder conditions correspond to a unique solution. Specifically, sufficientconditions for strict concavity of V are derived. These sufficient condi-tions for a unique solution are not necessary conditions, and a uniquesolution may still exist when they are violated. However, second ordernecessary conditions are not reducible to expressions that are easy tointerpret, and we therefore consider sufficient conditions instead.

V is strictly concave in KRf if Eq. (22) is strictly decreasing in KRf. It isconvenient to rewrite Eq. (22) as

χGK ðkRf ;1Þ− 1þ rð Þ 1þΦΩ

� �¼ 0

where

χ ¼ E p½ �− ΦΩ

� �1−π θð Þð Þ p�l −E pjs∉D½ ��

:

The derivative of Eq. (22) with respect to KRf. ∂2V/∂KRf2 , is

χGKK ðKRf ;Mf Þ−2∂p�l∂KRf

�ΦΩ

!1−π θð Þð ÞGK ðkRf ;1Þ−

∂p�l∂KRf

!2ΦΩ

� ��

� πlz p�l� �

GðKRf ;Mf Þ−πlzp p�l� �

al þ 1þ rð ÞΓπð Þ þ πlz p�l� �� 2 1þ rð ÞΓππ

−Ωzp p�lð Þz p�l� � !þ πlz p�l

� �� 2 ∂p�l∂KRf

!2

FK Γ θð Þ; Lð Þ− 1þ rð Þð ÞΓππ

þ πlz p�l� �� 2 ∂p�l

∂KRf

!2

FKK Γ θð Þð Þ Γπð Þ2

ð25Þ

where GKK(KRf,Mf) = ∂2G(KRf,Mf)/∂KRf2 , Γππ = ∂2Γ(θ)/∂π2 and zp(pl∗) =

∂z(pl∗)/∂pl∗. Given Γπ b 0 and Γππ N 0, the above expression is negativeprovided πlz(pl∗) = − ∂π(θ)/∂pl∗ is not too large and Γ(θ) is not toosmall. To see why, first observe that provided πlz(pl∗) is not too large,χ N 0. For kRf ≤ kRf

FB, E[p] ≥ (1 + r)/GK(kRf,1), χ is bounded below by

1þ r

GK kRf ;1� �− Φ

Ω

� �1−π θð Þð Þ p�l −E pjs∉D½ ��

:

Using the derived expression for ∂pl∗/∂KRf, it is straightforward to verifythat this expression is strictly positive if

∂p�l∂KRf

N− 1þ rð Þ 1þ ΩΦ

� �ð26Þ


where

ΩΦ

¼1−π θð ÞÞGðKRf ;Mf Þ−πlz p�lð Þðal þ 1þ rð ÞΓπ� �

πlz p�l� �

al− FK Γ θð Þ; Lð Þ− 1þ rð Þð ÞΓπð Þ :

Because al − (FK(Γ(θ), L) − (1 + r))Γπ ≥ 0 and (1 − π(θ))G(KRf,Mf) b 0, Ω/Φ is strictly decreasing in πlz(pl∗), and therefore the lowerπlz(pl∗) the more likely (A.C) is satisfied. Evidently, as πlz(pl∗) becomessmall,Φ/Ω is also reduced and χGKK(KRf,Mf) b 0 in Eq. (25) must eventu-ally dominate the sum of the remaining terms in this expression render-ing the entire expression negative. However, even where πlz(pl∗) exceedsthis threshold level, a sufficient condition for Eq. (25) to be negative is

−πlz p�l� � ∂p�l

∂KRf1−

1−π θð ÞÞzpðp�l� �

πlz p�l� �2

0@ 1AGðKRf ;Mf Þ þ πlz p�l� ��

1þ rð ÞΓππ

0@ 1A− Ω

Φ

� �πlz p�l� �� 2 Fk Γ θð Þð Þ− 1þ rð Þð ÞΓππ þ FKK Γ θð Þð Þ Γπð Þ2

� �N2 1−π θð Þð ÞGKðkRf ;1Þ

When zp(pl∗) ≈ 0 and πlz(pl∗)Γππ ≈ 0, this condition is satisfied if

∂p�l∂KRf

b−2 1−π θð Þð ÞGKðkRf ;1Þπlz p�l� �

GðKRf ;Mf Þ:

The derivative of Eq. (23) with respect to KRh, ∂2V/∂KRh2 , is

E p½ �GKKðKRh;Mf Þ−∂p�l∂KRh

� �2 ΦΩ

� �� πlz p�l� �

GðKRf ;Mf Þ

−πlzp p�l� �

al þ 1þ rð ÞΓπð Þ þ πlz p�l� �� 2 1þ rð ÞΓππ−Ω

zp p�lð Þz p�l� � !


∂KRh

� �2

FK Γ θð Þ; Lð Þ− 1þ rð Þð ÞΓππ þ FKK Γ θð Þð Þ Γπð Þ2� �

:

ð27Þ

Because the first term in this expression is negative for all parametervalues, for sufficiently low value of πlz(pl∗) this expression is negative.Moreover, evenwhere πlz(pl∗) exceeds this threshold level, it is straight-forward to verify that zp(pl∗) ≈ 0 and πlz(pl∗)Γππ ≈ 0 are also sufficientto ensure this expression is negative.

Finally, the derivative of Eq. (24) with respect toMf. ∂2V/∂Mf2, is

χGMMðKRf ;Mf Þ þ E½p�GMMðKRh;M−Mf Þ

−2∂p�l∂Mf

�ΦΩ

!1−π θð Þð ÞGMðkRf ;1Þ−

∂p�l∂Mf

!2ΦΩ

� ��

� πlz p�l� �

GðKRf ;Mf Þ−πlzp p�l� �

al þ 1þ rð ÞΓπð Þ

þ πlz p�l� �� 2 1þ rð ÞΓππ−Ω

zp p�lð Þz p�l� � !


∂Mf

!2

FK Γ θð Þ; Lð Þ− 1þ rð Þð ÞΓππ þ FKK Γ θð Þð Þ Γπð Þ2� �

:

ð28Þ

Sufficient conditions for this expression to be negative are analogousto the conditions derived for Eq. (25) b 0; note however that theconditions for Eq. (28) b 0 are not as strict given that the secondterm, E[p]GMM(KRh, M − Mf), is strictly negative for all parametervalues. □

A.D. Proof of Proposition 5.1

Equilibrium properties of a general class of payment schedules:Host-country income V(θ) is given by Eq. (8) for any resource contract

corresponding to a payment schedule C(KRf,Mf,p) satisfying Eq. (12), asin the case of the specific resource contract considered in Section 4,and pl

∗ is implicitly defined by Eq. (10) (for p∗l∈ðp:pÞ ) and π(θ) isdefined by Eq. (11). This implies that the first-order necessaryconditions corresponding to the government problem are identicalto Eqs. (22)–(24) of Proposition 4.1, given ∂pl∗/∂X, X = {KRf,KRh,Mf}.However, the general expression for Eq. (10) is given by Eq. (13),which produces the following expressions for ∂pl∗/∂X:

∂p�l∂KRf

¼ −ð1−π θð ÞÞðp�l GK ðkRf ;1Þ−CKðKRf ;Mf ;p

�l ÞÞ

Ω;

∂p�l∂KRh

¼ − 1þ rð ÞΩ

;

∂p�l∂Mf

¼ −ð1−π θð ÞÞðp�l GMðkRf ;1Þ−CMðKRf ;Mf ; p

�l ÞÞ

Ω;

where

Ω ¼ 1−π θð Þ þ πlz p�l� ��

GðKRf ;Mf Þ−πlz p�l� �

al þ 1þ rð ÞΓπð Þþπlz p�l

� �CðKRf ;Mf ; p

�l Þ− 1−π θð Þð ÞCpðKRf ;Mf ;p

�l Þ

and where ∂pl∗/∂KRh b 0 implies Ω N 0.Suppose for the moment that the resource contract satisfies the

requirement pl∗ N E[p|s ∉ D(θ)] if and only if

ð1−π θð ÞÞ p�l GKðkRf ;1Þ−CKðKRf ;Mf ; p�l Þ

� �Nð1þ rÞ

in equilibrium. This would imply pl∗ N E[p|s ∉ D(θ)] if and only if− ∂pl∗/∂KRf N − ∂pl∗/∂KRh, and given equilibrium conditions (22)–(23):

p�l NE pjs∉D θð Þ½ � ⇔ kRf bkRh: ð29Þ

Inspection of condition (24) reveals that kRf b kRh implies

λ0−λ1ð Þ−ΨM f N0

where λ0 and λ1 are the multipliers on the lower and upper bounds ofMf, and where

ΨM f ¼ ∂π θð Þ∂p�l

∂p�l∂Mf

!al− FK Γ θð Þ; Lð Þ− 1þ rð Þð ÞΓπð Þ ¼ −Φ

Ω∂p�l∂Mf

;

withΦ N 0. Therefore if, in addition to Eq. (29), pl∗ N E[p|s ∉ D(θ)] shouldimply ∂pl∗/∂Mf ≤ 0 and pl

∗ b E[p|s ∉ D(θ)] should imply ∂pl∗/∂Mf ≥ 0 isalso a requirement satisfied by payment schedule C(KRf,Mf,p), thenλ0 N 0 and Mf ¼ M whenever pl

∗ N E[p|s ∉ D(θ)] and λ1 N 0 and Mf

¼ M whenever pl∗ b E[p|s ∉ D(θ)]. This second requirement reduces to

p�l NE½pjs∉D θð Þ� ⇒ p�l GM kRf ;1� �

−CM KRf ;Mf ;p�l

� �≥0

p�l bE½pjs∉D θð Þ� ⇒ p�l GM kRf ;1� �

−CM KRf ;Mf ;p�l

� �≤0:

ð30Þ

Taken together, these two requirements on the resource contract aresufficient to generate the equilibrium relationships summarized byProposition 4.1.

Equilibrium properties of mixed ad valorem royalty and perconcession payments: We demonstrate that a payment schedulebased oneither a percentage of the value of output or per unit ofmineralconcessions employed, or any mixture of each, satisfies the abovesufficient condition, implying that these payment schedules produce

Table 6Matched moments in country data (v1 = 0.2, v2 = 0.5).

Country Res. valueadded

DataGOVSTAB

Capital perworker

Res. valueadded

Modelal/FDI∗

K + FDI

BGR 0.177 0.20 9812 0.18 0.31 9798BRA 0.084 0.23 11406 0.09 0.33 11420CHL 0.121 0.60 16289 0.13 0.50 16132DOM 0.103 0.32 6910 0.10 0.37 6908HND 0.204 0.30 3796 0.21 0.36 3800HRV 0.095 0.64 16706 0.10 0.52 16694IND 0.285 0.18 1446 0.28 0.30 1447KOR 0.055 0.38 47402 0.05 0.40 47466LTU 0.094 0.46 18896 0.09 0.44 18889MEX 0.061 0.29 20175 0.06 0.36 20161MOR 0.182 0.87 4929 0.18 0.63 4924MOZ 0.279 0.46 542 0.28 0.44 542MYS 0.188 0.89 16538 0.19 0.64 16530PAK 0.283 0.39 1366 0.28 0.40 1365PHL 0.175 0.29 2868 0.18 0.36 2869RUS 0.133 0.60 18614 0.13 0.50 18627


the equilibrium relationships summarized in Proposition (3.1), whenthe equilibrium described is unique. Consider the payment schedule

CðKRf ;Mf ;pÞ ¼ ρ f pGðKRf ;Mf Þ þ τ f M f

for any τf ≥ 0 and ρf ∈ [0, 1) that also satisfy the investors' zero profitcondition, given KRf and Mf:

1−ρ f

� �E pjs∉D θð Þ½ �GðKRf ;Mf Þ−τ f M f−

1þ r1−π θð ÞKRf ¼ 0:

Using this restriction to express τfMf in terms of ρf and substituting forτfMf in C(KRf,Mf,p), we can express the payment schedule as

CðKRf ;Mf ; pÞ ¼ E½pjs∉D θð Þ�GðKRf ;Mf Þ−1þ r

1−π θð ÞKRf

þρ f p−E½pjs∉D θð Þ�ð ÞGðKRf ;Mf Þ:

Therefore

1−π θð Þð Þðp�l GKðKRf ;Mf Þ−CKðKRf ;Mf ;p�l ÞÞ

¼ 1−ρ f

� �1−π θð Þð Þ

�p�l −E½pjs∉D θð Þ�

�GK KRf ;Mf

� �þ 1þ rð Þ:

For ρf ∈ [0, 1), this expression is strictly greater than (1 + r) if and onlyif pl∗ N E[p|s ∉ D(θ)], satisfying the first requirement of the above condi-tion. Moreover,

p�l GKðKRf ;Mf Þ−CKðKRf ;Mf ; p�l Þ ¼ 1−ρ f

� �p�l −E pjs∉D θð Þ½ ��

GMðKRf ;Mf Þ

which is strictly positive when pl∗ N E[p|s ∉ D(θ)] and strictly negative

when pl∗ b E[p|s ∉ D(θ)], satisfying the second requirement. □

A.E. Proof of Proposition 5.2

Denoting the multipliers on Eqs. (14), (15), (16), (17), and (18)by μ(s)h(s), λR, λX, ψR(s)h(s), and ψX(s)h(s), respectively, andthe multipliers on the non-negativity constraints for Mf and Lf byϕM and ϕL, the first order necessary conditions to the constrainedoptimization problem with respect to KRh, KRf, KXf, Mf, w(θ,s) and τ(θ,s)are:

FK kXh;1ð Þ ¼ E p½ �GK kRh;1ð Þ ð31Þ

GKðkRf ;1Þ λRE p½ �−Z

Sμ sð Þ−ψR sð Þð Þph sð Þds

� �¼ λR 1þ rð Þ ð32Þ

FK ðkXf ;1Þ λX−Z

Sμ sð Þ−ψX sð Þð Þh sð Þds

� �¼ λX 1þ rð Þ ð33Þ

FLðkXf ;1Þ λX−Z

Sμ sð Þ−ψX sð Þð Þh sð Þds

� �−FL kXh;1ð Þ

¼ λX−1ð ÞE½w θ; sð Þ�−Z

Sμ sð Þ−ψX sð Þð Þw θ; sð Þh sð Þds−ϕL

ð34Þ

E p½ �GMðkRf ;1Þ λR−Z

Sμ sð Þ−ψR sð Þð Þph sð Þds

� �−E½p�GL kRh;1ð Þ

¼ λR−1ð ÞE½τ θ; sð Þ�−Z

Sμ sð Þ−ψR sð Þð Þτ θ; sð Þh sð Þds−ϕM

ð35Þ

L f 1−λXð Þ þ μ sð Þ−ψX sð Þð ÞL f ¼ 0 ð36Þ

Mf 1−λRð Þ þ μ sð Þ−ψR sð Þð ÞMf ¼ 0: ð37Þ

Conditions (36) and (37) imply ψR(s) = (λX − λR) + ψX(s), andtherefore ψR(s) and ψX(s) are perfectly correlated. That is, for any state

in which the feasibility constraint binds in one sector, the feasibilityconstraint also binds in the other sector. In addition, because theremust be states s′ forwhich the feasibility constraints do not bind (other-wise the contracts would not satisfy the foreign firm participationconstraints), ψR s′

� � ¼ ψX s′� � ¼ ψ s′

� � ¼ 0 , and therefore λR ¼ λX ¼ λ .But then ψR s″

� � ¼ ψX s″� � ¼ ψ s″

� �N0 in states s″ where the feasibility

constraints do bind.Therefore λ ¼ 1þ μ sð Þ−ψ sð Þ for all s ∈ S. Solving and substituting for

μ(s) into Eqs. (32) and (33), these conditions imply that either the foreignfirm participation constraints bind (λN1, implying the first best invest-ment level in both sectors is not attainable) and μ(s) N 0 for all s (theno-expropriation constraints always bind), or else the first best invest-ment levels are unattainable and the no-expropriation constraintsnever bind (μ(s) = 0 and λ ¼ 1). Moreover, these conditions also imply

FK ðkXf ;1Þ ¼ E p½ �GK ðkRf ;1Þ: ð38Þ

Substituting for μ sð Þ ¼ λ−1 into Eqs. (34) and (35), we find thatkXh = kXf and kRh = kRf and the non-negativity constraints on Lf andMf never bind. Suppose to the contrary that ϕL N 0 implying FL(kXf,1) b

FL(kXh,1) and kXf b kXf. Then Eqs. (38) and (31) imply E[p]GK(kRf,1) N

E[p]GK(kRh,1) and kRf b kRh. But then Eq. (35) impliesϕM N 0, and there-fore ϕL N 0 implies ϕM N 0. Analogously, ϕM N 0 implies ϕL N 0. But ifboth non-negativity constraints bind, the host country desires zeroforeign investment under the constrained optimal contracts for anylevel of domestic capital, a contradiction. Therefore it must be the casethat ϕL = ϕM = 0, and hence kXh = kXf and kRh = kRf.

If the foreign firmparticipation constraints and the no-expropriationconstraints do not bind, then these investment levels are equal to thefirst best levels. If instead the first best investment levels are not attain-able, these constraints all bind, and therefore

E τ θ; sð Þ½ �MF ¼ E p½ �GðKRf ;Mf Þ− 1þ rð ÞKRf ; ð39Þ

E w θ; sð Þ½ �LF ¼ FðKXf ; L f Þ− 1þ rð ÞKXf ; and ð40Þ

E τ θ; sð Þ½ �MF þ E w θ; sð Þ½ �LF ¼ E p½ �GðKRf ;Mf Þ þ FðKXf ; Lf Þ−E a½ �: ð41Þ

Together these conditions imply

KRf þ KXf ¼E a½ �1þ r

:

B. Numerical results tables

Table 6 (continued)

Country Res. valueadded

DataGOVSTAB

Capital perworker

Res. valueadded

Modelal/FDI∗

K + FDI

SVK 0.059 0.28 28991 0.06 0.35 29033THA 0.126 0.42 8716 0.13 0.41 8717TUN 0.168 0.84 7437 0.17 0.61 7429TUR 0.154 0.39 12341 0.15 0.40 12341UGA 0.386 0.55 436 0.39 0.48 435UKR 0.219 0.36 7877 0.22 0.39 7878ZAF 0.109 0.57 11330 0.11 0.49 11321ARG 0.073 0.34 10949 0.07 0.38 11966BOL 0.213 0.33 2082 0.22 0.37 2104BWA 0.401 0.73 13487 0.41 0.56 14310CRI 0.107 0.26 8597 0.11 0.34 9392GUY 0.553 0.34 4165 0.56 0.38 4276IDN 0.242 0.35 3645 0.25 0.39 3705TTO 0.167 0.32 22126 0.17 0.37 22355COL 0.180 0.17 6953 0.18 0.30 7595ECU 0.257 0.13 6643 0.26 0.28 7260PER 0.138 0.06 7456 0.14 0.25 8149PNG 0.523 0.00 2459 0.52 0.22 2687POL 0.068 0.17 17846 0.07 0.30 19493SLV 0.118 0.26 4733 0.12 0.34 5169VEN 0.196 0.28 16058 0.20 0.35 17533

Category averages:π(θ) = 0 0.163 0.456 11949 0.163 0.434 11945π(θ) ∈ (0, πl) 0.251 0.382 9293 0.254 0.399 9730π(θ) = πl 0.211 0.154 8878 0.211 0.291 9698

Table 7Calibrated model parameters (v1 = 0.2, v2 = 0.5).

Country M A K FDI

BGR 8951 41528 9544 254BRA 4943 53612 11131 289CHL 10563 76381 14501 1630DOM 3673 32101 6656 252HND 3942 15339 3710 90HRV 8081 77254 15820 874IND 2018 5058 1443 4KOR 12820 221797 46937 529LTU 8929 85918 18425 463MEX 6435 99845 19271 890MOR 4428 19944 4777 147MOZ 748 1935 535 7MYS 15258 66062 16185 346PAK 1943 4913 1336 29PHL 2574 12158 2783 85RUS 12080 78897 18521 106SVK 8646 138590 28379 653THA 5604 38878 8425 292TUN 6181 30595 7220 209TUR 9365 51382 12232 109UGA 894 1423 399 36UKR 8446 30097 7841 37ZAF 6091 49987 11122 200ARG 4229 53855 9934 2032BOL 2284 8430 1695 409BWA 29002 43295 10618 3692CRI 4891 40696 7782 1610GUY 11870 9586 3585 690IDN 4564 14289 3310 395TTO 19175 95657 16623 5732COL 6628 30240 6701 895ECU 9051 26188 6299 961PER 5457 34099 7193 956PNG 6824 6221 2123 564POL 6462 88156 17345 2148SLV 2953 22137 4497 671VEN 16676 68432 15282 2252

Category averages:π(θ) = 0 6635 53639 11617 327π(θ) ∈ (0, πl) 10859 37972 7650 2080π(θ) = πl 7722 39353 8491 1207

Table 8Expected host country income under alternative contracts (v1 = 0.2, v2 = 0.5).

Country VFB Percent Deviations from First Best

Constrainedefficient

Fixedpayment

Ad valoremroyalty

Competitiveinvestment

BGR 32243 0.017 0.044 0.044 0.076BRA 37496 0.015 0.037 0.037 0.069CHL 52875 0.119 0.138 0.138 0.293DOM 22642 0.021 0.052 0.052 0.102HND 12312 0.010 0.024 0.024 0.049HRV 53647 0.016 0.033 0.033 0.097IND 4649 0.000 0.001 0.001 0.001KOR 152041 0.002 0.004 0.004 0.009LTU 60810 0.006 0.014 0.014 0.035MEX 66441 0.073 0.084 0.084 0.162MOR 15679 0.002 0.005 0.005 0.023MOZ 1737 0.002 0.004 0.004 0.012MYS 52451 0.001 0.002 0.002 0.012PAK 4430 0.006 0.014 0.014 0.034PHL 9413 0.016 0.039 0.039 0.075RUS 59350 0.000 0.000 0.000 0.002SVK 94070 0.011 0.024 0.024 0.047THA 28169 0.013 0.031 0.031 0.070TUN 23674 0.002 0.005 0.005 0.022TUR 39589 0.001 0.002 0.002 0.006UGA 1418 0.046 0.110 0.110 0.176UKR 25140 0.000 0.001 0.001 0.002ZAF 36231 0.002 0.005 0.005 0.015ARG 35155 0.161 0.138 0.138 0.237BOL 6447 0.151 0.165 0.192 0.294BWA 42622 0.117 0.263 0.263 0.334CRI 27436 0.134 0.127 0.127 0.225GUY 13108 0.082 0.130 0.156 0.180IDN 11697 0.048 0.113 0.119 0.176TTO 67223 0.468 0.238 0.250 0.354COL 22992 0.037 0.074 0.074 0.141ECU 21879 0.049 0.079 0.079 0.154PER 24688 0.041 0.061 0.061 0.152PNG 7880 0.152 0.100 0.100 0.171POL 59151 0.058 0.069 0.069 0.141SLV 15583 0.049 0.094 0.094 0.176VEN 53009 0.039 0.095 0.095 0.155

Category averages:π(θ) = 0 38544 0.017 0.029 0.029 0.060π(θ) ∈ (0, πl) 29098 0.166 0.168 0.178 0.257π(θ) = πl 29312 0.061 0.082 0.082 0.156


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