aguiar and gopinath (jpe 2007) topic 1: introduction to ... · topic 1: introduction to open...

Topic 1: Introduction to Open Economy Models

• Aguiar and Gopinath (JPE 2007)

• Stochastic Growth Model

• Single-good, single-asset SOE model

• Transitory and trend shocks to productivity.

• Technology: Cobb-Douglas production function, capital, Kt ,and labor, Lt ,

Yt = eztK 1−αt (ΓtLt)α,

α ∈ (0, 1) represents labor’s share of output.

Aguiar and Gopinath JPE 2007

• Parameters zt and Γt represent productivity processes.

zt = ρzzt−1 + εzt (1)

|ρz | < 1, and εzt N(0, σ2z ). i.i.d draws.

Γt = egt Γt−1 = Γ0

t∏s=1

egs

gt = (1− ρg )µg + ρggt−1 + εgt ,

|ρg | < 1 and εgt N(0, σ2g )

• µg :Productivity’s long-run mean growth rate.

Aguiar and Gopinath JPE 2007

• Period utility is Cobb-Douglas,

ut =

(Cγ

t (1− Lt)1−γ)1−σ

1− σ

where 0 < γ < 1.

• Per-period resource constraint:

Ct+Kt+1 = Yt+(1−δ)Kt−φ

2

(Kt+1

Kt− eµg

)2

Kt−Bt+qtBt+1.

(2)

• One-period, risk-free bonds.

• (Closing the model) The price of debt is sensitive to the levelof outstanding debt,

1

qt= 1 + rt = 1 + r∗ + ψ

[e

Bt+1Γt−b − 1

], (3)

• r∗ is the world interest rate

• b represents the steady-state level of normalized debt

• ψ > 0 governs the elasticity of the interest rate to changes inindebtedness.

• Endogenous state variables: K , B

• Exogenous state: z , Γ

• Endogenous variables: C , K , B, L

• Representative agent’s problem can be stated recursively:

V (Kt ,Bt , zt , Γt) = max{Ct ,Lt ,Kt+1,Bt+1}

(Ct

γ (1− Lt)1−γ)1−σ

1− σ+

βE (V (Kt+1,Bt+1, zt+1, Γt+1))

Ct+Kt+1 = Yt+(1−δ)Kt−φ

2

(Kt+1

Kt− eµg

)2

Kt−Bt+qtBt+1.

(4)

Xt = Kt+1 − (1− δ)Kt +φ

2

(Kt+1

Kt− eµg

)2

Kt

• Y ,C ,K ,B are all non-stationary because of the stochastictrend Γ.

• Use hat to denote each variables de-trended counterpart:

xt ≡xt

Γt−1.

• In normalized form:

ut = Γγ(σ−1)

(Cγ

t (1− Lt)1−γ)1−σ

1− σ

s.t. Ct+egt K ′t = Yt+(1−δ)Kt−φ

2

(egt

Kt+1

Kt

− eµg

)2

Kt−Bt+egtqtBt+1.

egt Kt+1 = (1− δ) Kt + Xt −φ

2

(Kt+1

Kt

egt − eµg

)2

Kt .

• Normalized Bellman:

V (Kt , Bt , z , g) = max{C ,L,Kt+1,Bt+1}

(Cγ

t (1− L)1−γ)1−σ

1− σ+ (5)

βegγ(1−σ)Et

(V (Kt+1, Bt+1, zt+1, gt+1

)(6)

• Given an initial capital stock, K0, and debt level, B0, theequilibrium of the economy is characterized by the first-orderconditions of the problem (5), the technology, budgetconstraint, evolution of capital and the transversalityconditions.

• Consumption Euler equation: Bt+1

Ucegtqt + βegtγ(1−σ)Et

(VB(Kt+1, Bt+1, zt+1, gt+1

)= 0

Bt :VB(Kt , Bt , z , g) = −Uc

Uc,t =βegt(γ(1−σ)−1)

qtEtUc,t+1

• For well-behaved consumption of the linearized model in thesteady state we require β(1 + r∗) = eµg (1−γ(1−σ)).

Solow Residual

•srt = zt + αln(Γt)

• Beveridge-Nelson Decomposition

srt = τt + st

τt = limj→∞srt+j

τt = αµg + τt−1 +

(α

1− ρg

)εgt

is a random walk (with drift) and

st = zt −(

αρg

1− ρg

)(gt − µg )

is a stationary series.

Solow Residual

• The random walk component of the Solow residual can beexpressed as ,

σ2∆τ

σ2∆sr

=

α2σ2g

(1−ρg )2[(2

1+ρz

)σ2

z +α2σ2

g

(1−ρ2g )

] . (7)

• Cochrane (1988) that

limK→∞

K−1Var(srt − srt−K ) = σ2∆τ . (8)

• The relative varianceσ2

∆τ

σ2∆SR

can be approximated empirically by

fixing K and calculating the sample variances of (srt − srt−K )and ∆sr .

• Given the (short) length of the time series, most estimationsare inconclusive.

Structural Estimation

• Using GMM: Estimate θ = (σg , σz),m(θ) = [σ(y), σ(c), cov(nx/y , y)].

• Using the volatility of filtered consumption and income

E [m1(θ)2 − y2] = 0

E [m2(θ)2 − c2] = 0

• Using the volatility of filtered income and covariance of filteredincome and (trade balance as a ratio of GDP)

E [m1(θ)2 − y2] = 0

E [m3(θ)2 − nx

y· y ] = 0

Table 3: Benchmark Parameter Values

Time preference rate β 0.98

Consumption Exponent (utility) γ 0.36

Steady-state debt to GDP b 10%

Coefficient on interest rate premium ψ 0.001

Labor Exponent (Production) α 0.68

Risk Aversion σ 2

Depreciation Rate δ 0.05

Capital Adjustment Cost φ 4.0

Notes: Benchmark parameters used in all specifications. Capital adjustment cost parameter is set at 4, except for specification (IV) of Table 4, where it is estimated.

Table 4: Estimated Parameters Mexico Canada

Parameter: (I) (II) (III) (IV) (I) (II) (III) (IV)

σg 2.81 3.06 2.55 2.13 0.88 1.20 0.87 0.47

(0.37) (0.56) (0.52) (0.29) (0.18) (0.32) (0.61) (0.37)

σz 0.48 0.17 0.54 0.53 0.78 0.69 0.78 0.63

(0.27) (0.65) (0.22) (0.34) (0.09) (0.06) (0.08) (0.14)

ρg 0.11 0.00 0.03 0.29

(0.10) (0.05) (0.54) (0.36)

ρz 0.95 0.97

(0.09) (0.02)

µg 0.66 0.73

(0.15) (0.13)

φ 1.37 1.78

(0.39) (0.45)

Random Walk Component 0.96 1.01 1.13 0.88 0.37 0.59 0.38 0.40

(0.07) (0.06) (0.05) (0.11) (0.07) (0.13) (0.29) (0.24)

Moments Used σy, σcσy,

Cov(nx,y) σy, σc,

Cov(c,y) All σy, σcσy,

Cov(nx,y) σy, σc,

Cov(c,y) All

Notes: GMM estimates with standard errors in parentheses. “Moments Used” refer to which empirical moments were matched during estimation. “All” refers to the following eleven moments: the standard deviations of income, consumption, investment, net exports, first-differenced (unfiltered) income; the covariances of income with lagged income, consumption, investment, and net exports; the autcovariance of first-differenced (unfiltered) income; and the mean of first-differenced (unfiltered) income. The “Random Walk Component” is calculated as in equation (14). Standard deviations are reported in percentage terms. All parameters not estimated in each specification were fixed at the benchmark values reported in Table 3. When not estimated, we set ρg=0.01 and ρz=0.95.

Table 5a: Moments for “Emerging Market” (Mexico)

Data (I) (II) (III)

)(yσ 2.40 2.40 2.46 2.13

(0.35) (0.35) (0.31) (0.27)

)( y∆σ 1.52 1.73 1.77 1.42

(0.25) (0.26) (0.22) (0.17)

)()(

ycσ

σ 1.26 1.26 1.33 1.10

(0.08) (0.08) (0.03) (0.05)

( )( )

Iy

σσ 4.15 2.60 2.69 3.83

(0.29) (0.10) (0.04) (0.33)

( )( )

nxy

σσ 0.90 0.71 0.75 0.95

(0.09) (0.04) (0.02) (0.10)

)(yρ 0.83 0.78 0.78 0.82

(0.07) (0.01) (0.002) (0.02)

)( y∆ρ 0.27 0.13 0.14 0.18

(0.09) (0.02) (0.01) (0.08)

),( nxyρ -0.75 -0.66 -0.75 -0.50

(0.08) (0.10) (0.04) (0.06)

),( cyρ 0.92 0.94 0.97 0.91

(0.02) (0.02) (0.01) (0.03)

),( Iyρ 0.91 0.92 0.93 0.80 (0.03) (0.003) (0.002) (0.03)

Notes: Theoretical moments are calculated from the model using the parameters reported in Tables 3 and 4. Columns (I), (II), and (III), use the estimated parameters from Table 4, Columns (I), (II), and (IV), respectively. Standard errors reported in parentheses are calculated from the parameter standard errors reported in Table 4 using the Delta method. Data moments are estimated with GMM. Note that estimation of the autocorrelation of the growth rate of income reduces the sample size by two quarters. We drop the first two quarters for the other moments to maintain a constant number of observations per moment. This truncation implies that the empirical moments above may differ slightly from those reported in Table 2.

Table 5b: Moments for “Developed Market” (Canada) Data (I) (II) (III)

)(yσ 1.55 1.55 1.55 1.24

(0.20) (0.20) (0.20) (0.11)

)( y∆σ 0.80 1.14 1.14 0.82

(0.09) (0.14) (0.15) (0.09)

)()(

ycσ

σ 0.74 0.74 0.91 0.76

(0.05) (0.05) (0.05) (0.07)

( )( )

Iy

σσ 2.67 1.99 2.16 3.14

(0.25) (0.05) (0.05) (0.23)

( )( )

nxy

σσ 0.57 0.41 0.51 0.65

(0.09) (0.03) (0.03) (0.11)

)(yρ 0.93 0.75 0.76 0.81

(0.04) (0.002) (0.002) (0.01)

)( y∆ρ 0.55 0.04 0.06 0.17

(0.10) (0.01) (0.01) (0.04)

),( nxyρ -0.12 0.18 -0.13 -0.15

(0.18) (0.11) (0.08) (0.19)

),( cyρ 0.87 0.87 0.87 0.87

(0.05) (0.01) (0.004) (0.07)

),( Iyρ 0.74 0.94 0.93 0.82 (0.09) (0.004) (0.002) (0.06)

Notes: Theoretical moments are calculated from the model using the parameters reported in Tables 3 and 4. Columns (I), (II), and (III), use the estimated parameters from Table 4, Columns (I), (II), and (IV), respectively. Standard errors reported in parentheses are calculated from the parameter standard errors reported in Table 4 using the Delta method. Data moments are estimated with GMM. Note that estimation of the autocorrelation of the growth rate of income reduces the sample size by two quarters. We drop the first two quarters for the other moments to maintain a constant number of observations per moment. This truncation implies that the empirical moments above may differ slightly from those reported in Table 2.

Table A1: Data Sources

Quarters Source

Emerging Markets

Argentina 1993.1-2002.4 IFS

Brazil 1991.1-2002.1 NP

Ecuador 1991.1-2002.2 IFS

Israel 1980.1-2003.1 IFS

Korea 1979.4-2003.2 OECD

Malaysia 1991.1-2003.1 IFS

Mexico 1980.1-2003.1 OECD

Peru 1990.1-2003.1 IFS

Philippines 1981.1-2003.1 IFS

Slovak Republic 1993.1-2003.2 OECD

South Africa 1980.1-2003.1 IFS

Thailand 1993.1-2003.1 IFS

Turkey 1987.1-2003.2 OECD

Developed Markets

Australia 1979.1-2003.2 OECD

Austria 1988.1-2003.2 OECD

Belgium 1980.1-2003.2 OECD

Canada 1981.1-2003.2 OECD

Denmark 1988.1-2003.1 OECD

Finland 1979.4-2003.2 OECD

Netherlands 1979.4-2003.2 OECD

New Zealand 1987.2-2003.2 OECD

Norway 1979.4-2003.2 OECD

Portugal 1988.1-2001.4 NP

Spain 1980.1-2003.2 OECD

Sweden 1980.1-2003.1 IFS

Switzerland 1980.1-2003.2 OECD See Appendix for discussion of data sources. NP stands for Neumeyer and Perri (2005). NP’s Brazil data are from Instituto Brasileiro de Geografia e Estatística, Novo Sistema de Contas Nacionais (IBGE/SCN novo). NP’s Portugal data are from OECD.

Figure 2: Random Walk Component of Solow Residual

0

0.5

1

1.5

2

2.5

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

K

Rel

ativ

e V

aria

nce

of R

ando

m W

alk

Com

pone

nt

MexicoCanada

Notes: This figure plots σ2

∆τ/σ2sr, where σ2

∆τ is estimated as T/(K(T-K)(T-K+1))Σt=K(yt-yt-K-Kµ)2, where yt is the log Solow residual at time t and µ is the sample average of the growth rate of the Solow residual. Each point corresponds to the choice of K depicted on the horizontal axis. σ2

sr is the value of σ2∆τ when K=1 (i.e., the variance of the first-

difference of log Solow residuals). The solid line depicts Mexico and the dashed line depicts Canada.

Figure 3: Impulse Responses Ratio of Net Exports to GDP

-0.6%

-0.5%

-0.4%

-0.3%

-0.2%

-0.1%

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

g shockz shock

Ratio of Consumption to GDP

-0.8%

-0.6%

-0.4%

-0.2%

0.0%

0.2%

0.4%

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

g shockz shock

Ratio of Investment to GDP

-0.6%

-0.4%

-0.2%

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

g shockz shock

Notes: Impulse response of net exports, consumption, and investment relative to income in response to a one percent shock to εg (“g shock”, solid line) and a one percent shock to εz (“z shock”, dashed line). The values plotted are deviations from steady state. The parameters ρg and ρz are set to 0.01 and 0.95, respectively. All other parameters are as reported in Table 3.

Figure 4: Sensitivity of Moments to the Relative Volatility of Trend Shocks

Relative Volatility of Net Exports, Consumption, and Investment

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

σ_{g}/σ_{z}

σ_{inv}/σ_{y}σ_{c}/σ_{y}σ_{nx}/σ_{y}

Correlations

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

σ_{g}/σ_{z}

ρ(y,y(-1))ρ(∆y,∆y(-1))ρ(nx,y)ρ(c,y)ρ(inv,y)

Notes: The top panel plots the standard deviation of filtered investment, consumption, and net exports relative to the standard deviation of filtered income as a function of alternative σg/σz. The bottom panel plots the autocorrelation of filtered income; the autocorrelation of unfiltered income growth; and the contemporaneous correlations of filtered net exports, consumption, and investment with filtered income; as functions of alternative σg/σz.

Figure 5: Autocovariance Function of Solow Residual: Data and Model

Mexico

-2.E-04

-1.E-04

0.E+00

1.E-04

2.E-04

3.E-04

4.E-04

5.E-04

6.E-04

7.E-04

0 1 2 3 4 5 6 7 8

Lag

Aut

ocov

aria

nce

DataModel-1.5*SE+1.5*SE

Canada

-1.E-04

-5.E-05

0.E+00

5.E-05

1.E-04

2.E-04

0 1 2 3 4 5 6 7 8

Lag

Aut

ocov

aria

nce

DataModel-1.5*SE+1.5*SE

Notes: This figure plots the autocovariance function of filtered log Solow residuals from the data (solid line) and the model (dashed line) for Mexico (top panel) and Canada (bottom panel). The model is generated from parameters reported in Column (IV) of Table 4. The dashed lines represent 1.5 standard error bounds.

Figure 6: Sudden Stop – Mexico Tequila Crisis (1994-1995)

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

1991Q1 1992Q1 1993Q1 1994Q1 1995Q1 1996Q1 1997Q1

Log

Dev

iatio

n fr

om 1

991Q

1

Data NX/Y

Model NX/Y

Notes: Dashed line represents the empirical rartio of net exports to GDP in Mexico. The solid represents the ratio predicted by the model using the observed Solow residuals and the parameters reported in Column (IV) of Table 4. Both series are log deviations from 1991Q1.

Financial Frictions, Financial Accelerator, Real Economy

• Neumeyer and Perri (JME, 2005)

• Firms pay part of the factors of production before productiontakes place, creating a need for working capital.

• Preferences that generate a labor supply that is independentof consumption (GHH)

Neumeyer and Perri (2005)

• The need for working capital to finance the wage bill makesthe demand for labor sensitive to the interest rate.

• Since firms have to borrow to pay for inputs, increases in theinterest rate make their effective labor cost higher and reducetheir labor demand for any given real wage.

• The impact of this fall in labor demand on equilibriumemployment will depend on the nature of the labor supply.

• GHH preferences: labor supply is independent of shocks tointerest rates.

• Declines in labor demand induce a fall in equilibriumemployment

• At business cycle frequencies the capital stock is relativelystable, declines in equilibrium employment translate intooutput declines.

Neumeyer and Perri (2005)

• Data: Measures of expected real interest rate

• For emerging markets use dollar denominated bonds andsubtract expected U.S. inflation.

• Government bonds

• Evidence that interest rates on private corporate andgovernment bonds highly correlated.

Period t

(t-1)+ t- t+

R(st) and A(st) are revealed. Labor and capital are hired.Firms issue bonds at rate R(st-1).

Final good is produced. Bonds issued in (t-1)+

and t- mature. Households buy/issue bonds at rate R(st).Consumption and investment take place.

(t+1)-

Figure 4. Timeline

Neumeyer and Perri (2005)

• To transfer w(st)l(st) to workers that earn w(st) goods perunit of time, firms need to set aside a fraction θ of the wagebill at t− and a fraction (1− θ) at t+. The worker receivesw(st)l(st) at t+.

• An alternative model of the need for working capital wouldhave been to assume some form of limited participation, thatis, that a fraction of the workers are excluded from assetmarkets between t− and t+ but need resources to consume.

• Firms have to borrow θw(st)l(st) (working capital) betweent− and t+ at rate R(st−1)

• The market for the services of capital is frictionless

Neumeyer and Perri (2005)

• Firms and Technology

y(st) = A(st)k(st−1)α((1 + γ)t l(st))1−α

γ: deterministic growth rate of labor-augmentingtechnological change

• Firm’s problem

y(st)− w(st)l(st)− k(st−1)r(st)− [R(st−1)− 1]θw(st)l(st)

• FOC wrt l(st)

w(st)[1 + θR(st−1 − 1)

]= yl(s

t)

Neumeyer and Perri (2005)

• Household’s problem

max∞∑

t=0

∑st

βtπ(st)U(c(st), l(st))

c(st) + x(st) + b(st) + κb(st) = w(st)l(st) + r(st)k(st−1)

+ R(st−1)b(st−1)

κ(.) is a convex function.

x(st) = k(st)− (1− δ)k(st−1) + Φ(k(st−1), k(st))

• Country’s net foreign asset position in period t isb(st−1)− θw(st)l(st)

Neumeyer and Perri (2005)

• Interest Rates

• Loans to the domestic economy are risky assets because therecan be default on payments to foreigners.

• Real interest rates change as the perceived default riskchanges

• Even if the default risk stays constant, interest rates canchange because the preference of international investors forrisky assets change over time.

R(st) = R∗(st)D(st)

• R∗(st): international rate for risky assets (which is notspecific to any emerging economy)

• D(st): country spread over R∗(st) paid by borrowers in aparticular economy

Neumeyer and Perri (2005)

• One asset: all agents (domestic or foreign, borrower or lender)face the same rate of interest R.

• Foreigners lend positive amounts to the domestic economy allalong the equilibrium path.

• What determines D(st)?• Case 1: Exogenous to local productivity shocks• Case 2: D(st) = ηE (A(st+1))

Neumeyer and Perri (2005)

• D(st) = R(st)/R∗(st)

• R(st) : 3-month real yield on Argentine dollar denominatedsovereign bonds

• R∗(st): Redemption real yield on an index of non-investment-grade U.S. domestic bonds.

• Figure 5

• Estimate two independent first order autoregressive processesfor R∗(st) and D(st)

Neumeyer and Perri (2005)

• Calibration:

u(c , l) =1

1− σ

[c − ψ(1 + γ)t lµ

]1−σ

κb(st) = y(st)

(b(s)

y(st)− b

)

Φ =φ

2k(st−1)

(k(st)− k(st−1)(1 + γ)

k(st−1

)2

Neumeyer and Perri (2005)

• Labor markets

−ul

uc= w(st) =

yl(st)

[1 + θR(st−1 − 1)]

• Log linearize with GHH preferences

lt+1 = − 11εs− 1

εd

Rt +α

1εs− 1

εd

kt

Ld(R0)

Ld(R1)

Employment

Real wage

Ld(R0)

Ld(R1)

Employment

Real wage

Ls(c(R1))

Ls(c(R0))

l0 l1l1 l0

GHH preferences Cobb-Douglas preferences

Figure 6. Equilibrium Employment and Interest Rate Shocks (R1 > R0)

Ls

Neumeyer and Perri (2005)

• Linearized first order condition for bonds

ct+1 − c =1

σ

(1− w

ν

)Rt + w (lt+1 − lt)

Ld(R0)

Ld(R1)

Employment

Real wage

Ld(R0)

Ld(R1)

Employment

Real wage

Ls(c(R1))

Ls(c(R0))

l0 l1l1 l0

GHH preferences Cobb-Douglas preferences

Figure 6. Equilibrium Employment and Interest Rate Shocks (R1 > R0)

Ls

Table 2. Baseline parameter values

Shocks

Name Process Parameter ValuesProductivity A

¡st¢= ρA A

¡st−1

¢+ εA

¡st¢

ρA = 0.95 σ(εA) = Varies∗

Intenational rate R∗¡st¢= ρ1R

∗ ¡st−1¢+ εR¡st¢

ρ1 = 0.81 σ(εR) = 0.63%

Country risk (independent) D¡st¢= ρ2D

¡st−1

¢+ εD

¡st¢

ρ2 = 0.78 σ(εD) = 2.59%

Country risk (induced) D¡st¢= −ηEt(A

¡st+1

¢) + εI

¡st¢

η = 1.04 σ(εI) = 1.7%

Preference parameters Value

Name Symbol GHH Cobb DouglasDiscount factor β 0.93 0.98Utility curvature σ 5 5Labor curvature v 1.6 -Labor weight ψ 2.48 -Consumption share µ - 0.24

technology parameters

Name Symbol ValueTechnological progress growth γ 0.62%Capital exponent (production) α 0.38Depreciation rate δ 4.4%% labor income paid in advance θ 1Bond holding cost κ 10−5

Capital adjustment costs φ Varies∗∗ See the notes in table 3 for the value of the parameter in different experiments

Table 3. Simulated and Actual Argentine Business Cycles

% Standard Dev. %Standard Dev. of x%Standard Dev. of GDP

GDP R NX TC INV HRSArgentine Data 4.22 3.87 1.42 1.17 2.95 0.57

(0.36) (0.52) (0.11) (0.03) (0.13) (0.08)No country riska) R∗ shocks 1.24 1.08 1.43 1.12 8.65 1.00b) R∗ and A shocks 4.22 1.08 1.44 0.80 2.95 0.66

Independent country riskc) R∗ and D shocks 2.33 3.87 2.06 1.69 5.26 1.41d) R∗, D and A shocks 4.22 3.87 2.12 1.13 2.95 0.90

Induced country riske) R∗ and A shocks 4.22 3.87 1.95 1.54 2.95 0.89

Correlation of GDP withR NX TC INV HRS

Argentine Data -0.63 -0.89 0.97 0.94 0.52(0.08) (0.02) (0.01) (0.01) (0.11)

No country riska) R∗ shocks -0.36 -0.17 0.82 0.35 0.94b) R∗ and A shocks -0.10 0.03 0.97 0.56 0.98

Independent country riskc) R∗ and D shocks -0.54 -0.48 0.88 0.57 0.97d) R∗, D and A shocks -0.29 -0.08 0.87 0.44 0.90

Induced country riske) R∗ and A shocks -0.54 -0.80 0.97 0.90 0.98

Correlation of R withNX TC INV HRS

Argentine data 0.71 -0.67 -0.59 -0.58(0.06) (0.07) (0.09) (0.12)

No country riska) R∗ shocks 0.96 -0.80 -0.98 -0.66b) R∗ and A shocks 0.95 -0.31 -0.84 -0.27

Independent country riskc) R∗ and D shocks 0.99 -0.86 -0.99 -0.78d) R∗, D and A shocks 0.96 -0.70 -0.97 -0.62

Induced country riske) R∗ and A shocks 0.65 -0.60 -0.66 -0.69

Notes: See the notes in table 1A for a definition of the data series and for a description of how data statistics are computed.

Model series are treated exactly as the data series. Statistics computed on the model series are averages across 500 simulations,

each simulation of same length as the data sample. The capital adjustment cost parameter is φ is set to 8 (models a and b),

25.5 (models c and d), and 40 (model e). The standard deviation of productivity shocks σ(εA) is set to 1.98% (model b),

1.75% (model d), and 1.47% (model e).

Table 4. Sensitivity analysis

PreferencesGHH (ν = 1.2) GHH (Baseline) GHH (v = 4) CD (σ = 5) CD (σ = 50)σ(y)

σ(yDATA)Corr(Y,R)

σ(y)σ(yDATA)

Corr(Y,R)σ(y)

σ(yDATA)Corr(Y,R)

σ(y)σ(yDATA)

Corr(Y,R)σ(y)

σ(yDATA)Corr(Y,R)

θ = 1 -0.57 89% 55% -0.54 22% -0.34 97% 0.86 36% -0.18θ = 1/2 -0.44 52% 34% -0.38 18% -0.16 102% 0.94 26% 0.20θ = 0 0.16 27% 21% 0.14 15% 0.13 112% 0.97 24% 0.69

Notes: The capital adjustment cost parameter φ is set to 25.5 in all experiments. All remaining parameters are set to their

baseline values.

0 0.5 1 1.5 2 2.5 3 3.5 4-4

-3

-2

-1

0

1

2

3Figure 7. Impulse Responses to a Shock in International Interest Rates

Years after shock

Per

cent

dev

iatio

n fro

m s

tead

y st

ate

R

Consumption

Investment

Employment

GDP

NX

Savings

Note: Impulse responses are computed using baseline parameter values and a capital adjustment costs parameter (φ) equal to 25.1.

-4 -3 -2 -1 0 1 2 3 4-1

-0.5

0

0.5Figure 8. Correlation between GDP(t) and R(t+J)

J (Lead/Lag of R)

Cor

rela

tion

Note: The dashed lines are two standard error bands around the cross-correlations in the data.Shocks to international interest rates and to TFP are present in all three models.

Model without Country RiskModel with Independent Country RiskModel with Induced Country RiskData

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

-0.1

-0.05

0

0.05

0.1

Output Cycles in Argentina

Quarters

Dev

iatio

ns fr

om tr

end

of G

DP

DataModel (shocks to international rates and independent country risk)

Figure 9. Business Cycles in Argentina