education and wages

Education and Wages

Pedro Telhado PereiraMay 2004Part 3

Universidade da Madeira 2

We have arrived in part 1 to the following formula – at the time the individual finish his studies

rEdEd eWW

rEdWW

0

0lnln


But the wage profile is


Mincer (1974) suggested

Individuals at time t will devote a certain percentage of his time to acquire human capital – ht

200

0

00

)2/(

)/(

0

xThxhdth

eWW

tThhh

x

t

dthr

Edx

t

x

t


And therefore

2000

))2/((0

))2/((

2lnln

200

200

xT

rhxrhrEWW

eeWW

eWW

dx

xThxhrrEdx

xThxhrEdx


The equation we estimate is

XxxrEW dx2ln

Where:

x – is the work experience after school – generally age-years of education – age of start of education

X – other variables

r - rate of return of Education

To be correct the wage should be a % as individuals are devoting part of their time to acquire human capital.


Problems with the estimation of the equation Problem 1 - Endogeneity of Education Assume that an individual chooses education and maximises a utility

function of the type:

U w E w rE( , ) ln

subject to the individual’s opportunity set summarised by w=g(E),


The first order condition for optimal education requires that:

g E

g Er

' ( )

( )

For the sake of simplicity, it is assumed that the marginal costs are increasing functions of the amount invested in education, and that the marginal returns do not vary with education (the latter assumption is only a matter of simplicity and can be discarded without changing the main implication)


kErr

Eg

Eg

i

i

)(

)('

Since the individual invests in education until the point where marginal costs equal marginal benefits, his optimal amount of education is given by:

Er

kii i*


Integration of the marginal benefits

iEg

Eg )(

)('

leads to a log-linear wage equation for individual i of the type:

lnw a Ei i i i


The model identifies two sources of heterogeneity in the population: variation in marginal rates of return to education at each level of schooling (loosely known as differences in ability) and variation in the marginal costs of investment in schooling (loosely known as differences in access to

funds or tastes for education).


The general econometric problem

0

where

lim

)'1

lim()'1

lim(lim

')'(

1

1

1

X

XXXols

ols

ols

bp

Xn

pXXn

pbp

YXXXb

XY


We have to use instrumental variables

Z – instrumental variables

Z must be correlated with X and

)'1

lim( XZn

p is a full rank matrix

and

0)'1

lim( Zn

p


Instruments used (Harmon, Walker and Westergaard-Nielsen (2001)):

Variation of Compulsory school law Month of birth Years of war – Vietnam, II WW Distance to college Family variables Abolition of fees Age (Barceinas, Oliver, Raymond and

Roig(2001))


In Barceinas, Oliver, Raymond and Roig(2001) paper

“… in the Spanish case the ability bias seems to be not very important and that differences between the OLS and IV estimates do not follow a clearly identifiable pattern…”


The common finding of the literature

The IV estimates are higher than the OLS estimates – Card 1999.

Possible explanation: IV estimators do not represent sample average returns to education but the marginal returns to education of certain subgroups of the population.


The use of fixed effects to handle ability

The problem is that we can not observe a individual with and without education simultaneously as most individuals don’t get more education after they start working.

Use of data on twins (or family members) – the IV estimates are higher than the OLS estimates.


Problem 2 - The return by level of education in Portugal

Graph 5 - Marginal returns to educational levels (per year of schooling)Selected years, Men

0%

5%

10%

15%

20%

25%

1982 1985 1991 1995

Years

Re

turn

d4/d0 d6/d4 d9a/d6 d9t/d6 d11/d9a d14/d11 d17/d11


Graph 6 - Marginal returns to educational levels (per year of schooling)Selected years, Women

0%

5%

10%

15%

20%

25%

1982 1985 1991 1995

Years

Re

turn

d4/d0 d6/d4 d9a/d6 d11/d9a d14/d11 d17/d11


Table 8 - Marginal Returns of Educational Levels, Selected Years

MenLevel Base %dif. (1) %dif. (2) %dif. (1) %dif. (2) %dif. (1) %dif. (2) %dif. (1) %dif. (2)

d4 d0 20% 5% 19% 4% 19% 5% 15% 4%d6 d4 29% 14% 27% 13% 23% 11% 20% 10%d9a d6 37% 11% 31% 10% 31% 9% 29% 9%d9t d9a 0% 0% 8% 8% 19% 19% 19% 19%d9t d6 37% 11% 41% 12% 56% 16% 53% 15%d11 d9a 21% 10% 27% 13% 28% 13% 33% 15%d14 d11 49% 14% 51% 15% 60% 17% 74% 20%d17 d11 77% 12% 89% 14% 103% 15% 125% 18%

WomenLevel Base %dif. (1) %dif. (2) %dif. (1) %dif. (2) %dif. (1) %dif. (2) %dif. (1) %dif. (2)

d4 d0 11% 3% 11% 3% 14% 3% 11% 3%d6 d4 34% 16% 29% 13% 25% 12% 24% 11%d9a d6 44% 13% 42% 12% 38% 11% 35% 10%d9t d6 44% 13% 57% 16% 67% 19% 61% 17%d9t d9a 0% 0% 11% 11% 21% 21% 20% 20%d11 d9a 23% 11% 17% 8% 22% 11% 27% 13%d14 d11 35% 11% 31% 10% 43% 13% 55% 16%d17 d11 55% 9% 111% 16% 134% 19% 147% 20%

Notes: (1) - Comparison drawn in absolute terms. (2) - Comparison per year.

1982 1986 1991 1995

1982 1986 1991 1995


There is not a constant return to education - it depends on the level of education

Similar results were obtained using Spanish data (Barceinas-Paredes, F., J. Oliver-Afonso, J. L. Raymond-Bara, J. L. Roig-Sabaté (2001))


Problem 3 - The OLS assumes a paralel shifting of the distribution

W0 Wed


If there is not a paralel shift

“there may be information gains from estimating and comparing several conditional location measures for the dependent variable, even after controlling for a large set of observed individual and job characteristics” (Hartog, Pereira and Vieira,1999) .


Rates of return to education (%)


This result appears for other european countries and the USA.


Results for European Countries - Martins and Pereira (2004)


Table 1 - Data-sets description

Country Data-set YearN.

Obs.

Austria Mikrozensus 1993 7175

Denmark Longitudinal Labour Market Register 1995 4416

Finland Labour Force Survey 1993 1175

FranceTraining and Professional Qualifications +

Employment Survey 1993 4606

Germany Socio-Economic Panel 1995 ?

Greece Household Budget Survey 1994 2096

Ireland ESRI Household Survey 1994 1903

Italy Survey of Household Income and Wealth 1995 3441

Netherlands Structure of Earnings Survey 1996 49805

Norway Level of Living Survey 1995 870

Portugal Personnel Records 1995 28055

Spain Wage Structure Survey 1995 118005

Sweden Level of Living Surveys 1991 1508

Switzerland Labour Force Survey 1995 6334

UK Family Expenditures Survey 1995 2183

USA Current Population Survey 1995 42347


Table 4 - Summary of results

Country OLS 1st dec. 9th dec. Diff.

Austria 9.7% 7.2% 12.8% 5.6%

Denmark 6.6% 6.3% 7.1% 0.8%

Finland 8.9% 6.8% 10.1% 3.3%

France 7.6% 5.9% 9.3% 3.4%

Germany 8.0% 8.5% 7.5% -1.0%

Greece 6.5% 7.5% 5.6% -1.9%

Italy 6.4% 6.7% 7.1% 0.4%

Ireland 8.9% 7.8% 10.4% 2.6%

Netherlands 7.0% 5.3% 8.3% 3.0%

Norway 6.0% 5.5% 7.5% 2.1%

Portugal 12.6% 6.7% 15.6% 8.9%

Spain 8.6% 6.7% 9.1% 2.4%

Sweden 4.1% 2.4% 6.2% 3.8%

Switzerland 9.5% 8.7% 10.6% 1.9%

UK 8.6% 4.9% 9.7% 4.8%

USA 6.3% 3.9% 7.9% 4.0%

Means 7,9% 6,5% 9,1% 2,7%

St. Dev. 2,0% 1,6% 2,6% 2,7%

Coeff. Var. 0,25 0,24 0,29 1,00


In a graph

Graph 6 - Returns to Education, Western Countries, 1995 (or closest year)

2%

4%

6%

8%

10%

12%

14%


The highest rate is in Portugal – 12.6%

The lowest one is Sweden – 4.1%

The value for Spain is 8.6%


In the majority of countries we observe

The return is higher in the top decile than it is at the lower decile.


Can we say that Portugal has a high rate of return to Education?

We should take, at least, two points in consideration

Support from the State to the Families

Risk of the investment


In Asplund and Pereira (1999) we showed that there is a negative relationship between State Support and Returns to Education


In Pereira and Martins (2002), we showed that there is a negative relationship between return and risk as in all assets.


We used the difference between the coefficient of education at the last decile and the first decile[1] as the measure of the risk [1] The significance of the difference was tested for several countries and it showed to be significantly different from zero, provided the sample was large enough.


we construct dummy variables for years (yeari=1 if year=i, zero otherwise), type of wage (net=1, if net wages were used, zero otherwise). dif stands for the difference in returns between the last and first decile, absdif for its absolute value and ols for the OLS Mincer equation coefficient corrected.


Table 2

Regression with robust standard errors Number of obs = 16 F( 5, 9) = 1957.53 Prob > F = 0.0000 R-squared = 0.9831 Root MSE = 1.3989

| Robust ols | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- net | -.0594735 .4831846 -0.123 0.905 -1.152513 1.033566 dif | .5565127 .169201 3.289 0.009 .1737533 .939272 year91 | 1.985252 .642964 3.088 0.013 .5307662 3.439737 year93 | 6.471456 .9839524 6.577 0.000 4.245601 8.697311 year94 | 7.534957 .2900354 25.979 0.000 6.878851 8.191063 year95 | 6.490306 .7973708 8.140 0.000 4.686527 8.294084 year96 | 5.330462 .5076031 10.501 0.000 4.182184 6.47874


Table 3

Regression with robust standard errors Number of obs = 16 F( 5, 9) = 51.57 Prob > F = 0.0000 R-squared = 0.9818 Root MSE = 1.4512

| Robust ols | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- net | -.5700131 .5674445 -1.005 0.341 -1.853662 .7136356 absdif | .56264 .1762516 3.192 0.011 .1639312 .9613489 year91 | 1.961968 .6697562 2.929 0.017 .446874 3.477062 year93 | 6.616513 .9744813 6.790 0.000 4.412083 8.820943 year94 | 6.719066 .86393 7.777 0.000 4.764721 8.673412 year95 | 6.529603 .7854792 8.313 0.000 4.752726 8.306481 year96 | 5.31208 .5287549 10.046 0.000 4.115953 6.508207


The main finding is the positive relationship between return and risk. There seems to be a positive compensation to “be received” to face the risk of the investment in education.


And what about signalling?

Workers acquire costly education in order to signal their higher ability to employers – who would otherwise know little about their prospective workers skills . Education per se plays no role in enhancing a worker’s productivity and is almost entirely wasteful from the public or social point of view.

One way to test this idea involves comparing the returns to education between employees and the self-employed. The intuition behind this results is whereas the former may benefit from education as a signal, the others will not, given that they are their own employers and have no informational asymmetries problems to deal with. The results for Portugal suggest that returns to education for the self-employed are at least as high as those for employees, therefore there is no sign of signalling.


Barceinas-Paredes, F., J. Oliver-Afonso, J. L. Raymond-Bara, J. L. Roig-Sabaté and A. Skalli (2001)

Use Spanish and French Data Use

– Private and Public Sector• Public sector is more prone to signalling

– No evidence for the screening hypothesis

– Number of years of education and relative position in attainment

• Years=Human Capital, relative position=screening– Education is likely to serve as a signalling device but only

to a rather limited extent.


– Experience eearnings profile of higly educated individuals

• More tenure = less signalling– None of the predictions of the screening hypothesis

could be strongly confirmed

– Sheepskin effects• More years to attain a degree less signal

– Even if the results show that there are many (human capital) reasons to obtain the same result


Their conclusions:

“…our results suggest unanimously that the effect of education is primarily due to its impact in individual’ productivity…”

“… our findings confirm the idea that although there might be some elements of truth in the screening hypothesis, the returns to education are to the greatest extent due to human capital accumulation…”


References Asplund, R. and P. T. Pereira . (1999), ‘Introduction’, in (eds), Returns to human capital in Europe: a

literature review, Helsinki, Finland: ETLA/Taloustieto Oy., pp 259-278. Barceinas-Paredes, F., J. Oliver-Afonso, J. L. Raymond-Bara, J. L. Roig-Sabaté and A. Skalli (2001),

Does Education Improve Productivity or Earnings Only, in: R. Asplund,eds, Education and Earnings – Further Evidence from Europe, ETLA, Helsinki.

Barceinas-Paredes, F., J. Oliver-Afonso, J. L. Raymond-Bara, J. L. Roig-Sabaté (2001), Spain, in: C. Harmon, I. Walker and N. W. Nielsen, eds, Education and Earnings in Europe – a Cross Country Analysis of Returns to Education, Edward Elgar, Cheltenham, UK.

Bosworth, D., P. Dawkins and T. Stromback (1996), The Economics of the Labour Market, Longman, Singapore.

Card, D. (1999), The Causal Impact of Education on Earnings, in: O. Ashenfelter and D. Card, eds, Handbook of Labor Economics, North Holland, Amsterdam and New York.

Harmon C., I. Walker and N. W. Nielsen, (2001), Introduction, in: C. Harmon, I. Walker and N. W. Nielsen, eds, Education and Earnings in Europe – a Cross Country Analysis of Returns to Education , Edward Elgar, Cheltenham, UK.

Hartog, J., P.T. Pereira, J. C. Vieira (1999) "Changing Returns to Education in Portugal During the 1980s and Early 1990s: OLS and Quantile Regression Analysis", Applied Economics, 33/8, 2001, 1021-1037.

Martins, P.S. and P.T. Pereira (2004) "Does Education Reduce Wage Inequality? Quantile Regressions Evidence from Fifteen European Countries and the USA" (forthcoming Labour Economics.

Mincer, J. (1974). Schooling, Experience and Earnings. New York: National Bureau of Economic Research.

Pereira, P. T. and P. S. Martins (2001), Portugal, in: C. Harmon, I. Walker and N. W. Nielsen, eds, Education and Earnings in Europe – a Cross Country Analysis of Returns to Education , Edward Elgar, Cheltenham, UK.

Pereira, P. T. and P. S. Martins (2002), "Is there a Return-Risk Link in Education", Economic Letters, 75, 31-37, (2002).

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