Part IISecond-Generation Studies

of Labor Supply• 1) Introduction• 2) Wage equation• 3) Analysis of labor force participation decision• 4) Comparing conditional OLS and Tobit estimates

of labor supply• 5) Heckman two-stage method

1) Introduction

• Major shortcoming of first-generation studies of labor supply: neglecting the selectivity bias (focus on working cohort only)

• Data: US, 1975, women

Variables• WHRS…...labor supply….. hours worked per year in 1975

• WA………..age

• WE………...education in years

• WW………..wage………….hourly wage rate

• KL6………number of children less than 6 years old

• K618 ……..number of children more than 6 years old and less than 18 years old

• LWW = ln(WW)

• LWHRS = ln(WHRS)

• WA2=(WA^2)/100

• AX……….labor market experience in years

• CIT……….dummy variable, =1 if live in large city

2) Wage equationLn(wage)=0+1WA+2(WA)2+3WE+4AX+5CIT

. reg lww wa wa2 we ax cit if lfp==1

Source | SS df MS Number of obs = 412---------+------------------------------ F( 5, 406) = 15.48 Model | 29.0635943 5 5.81271886 Prob > F = 0.0000Residual | 152.426739 406 .375435319 R-squared = 0.1601---------+------------------------------ Adj R-squared = 0.1498 Total | 181.490334 411 .441582321 Root MSE = .61273

------------------------------------------------------------------------------ lww | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- wa | .0817128 .043384 1.883 0.060 -.0035724 .1669981 wa2 | -.1013208 .0506685 -2.000 0.046 -.2009261 -.0017156 we | .0948108 .0136498 6.946 0.000 .0679777 .1216438 ax | .021488 .0043347 4.957 0.000 .0129667 .0300093 cit | .0306213 .0636208 0.481 0.631 -.094446 .1556885 _cons | -1.947883 .930407 -2.094 0.037 -3.776899 -.1188661

2) Wage equationLn(wage)=0+1WA+2(WA)2+3WE+4AX

. reg lww wa wa2 we ax if lfp==1

Source | SS df MS Number of obs = 412---------+------------------------------ F( 4, 407) = 19.33 Model | 28.9766214 4 7.24415535 Prob > F = 0.0000Residual | 152.513712 407 .374726566 R-squared = 0.1597---------+------------------------------ Adj R-squared = 0.1514 Total | 181.490334 411 .441582321 Root MSE = .61215

------------------------------------------------------------------------------ lww | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- wa | .0823313 .043324 1.900 0.058 -.0028353 .167498 wa2 | -.1017366 .0506133 -2.010 0.045 -.2012326 -.0022405 we | .0957238 .0135045 7.088 0.000 .0691764 .1222711 ax | .0214121 .0043278 4.948 0.000 .0129045 .0299197 _cons | -1.957437 .9293168 -2.106 0.036 -3.784297 -.1305774

Wages of workers vs. non-workers

. sum lww

Variable | Obs Mean Std. Dev. Min Max---------+----------------------------------------------------- lww | 412 1.129844 .6645166 -2.054164 2.295873

. sum lwwn

Variable | Obs Mean Std. Dev. Min Max---------+----------------------------------------------------- lwwn | 325 .9164476 .2690776 -.0913529 1.731436

3) Analysis of labor force participation decision: OLS

. reg lfp lwwall kl6 k618 wa we

Source | SS df MS Number of obs = 737---------+------------------------------ F( 5, 731) = 22.38 Model | 24.1240676 5 4.82481351 Prob > F = 0.0000Residual | 157.558429 731 .215538207 R-squared = 0.1328---------+------------------------------ Adj R-squared = 0.1268 Total | 181.682497 736 .246851218 Root MSE = .46426

------------------------------------------------------------------------------ lfp | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- lwwall | .1202237 .0352973 3.406 0.001 .0509275 .1895199 kl6 | -.2996388 .0364913 -8.211 0.000 -.3712791 -.2279985 k618 | -.0164462 .0142628 -1.153 0.249 -.0444471 .0115547 wa | -.0135461 .0025879 -5.234 0.000 -.0186267 -.0084654 we | .0281336 .008534 3.297 0.001 .0113795 .0448878 _cons | .7610717 .1634964 4.655 0.000 .4400932 1.08205

3) Analysis of labor force participation decision: OLS

. reg lfp lwwall kl6 wa we

Source | SS df MS Number of obs = 737---------+------------------------------ F( 4, 732) = 27.64 Model | 23.8374882 4 5.95937205 Prob > F = 0.0000Residual | 157.845008 732 .215635257 R-squared = 0.1312---------+------------------------------ Adj R-squared = 0.1265 Total | 181.682497 736 .246851218 Root MSE = .46437

------------------------------------------------------------------------------ lfp | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- lwwall | .1227266 .0352384 3.483 0.001 .0535462 .1919071 kl6 | -.2950878 .0362854 -8.132 0.000 -.3663236 -.2238519 wa | -.0123327 .0023649 -5.215 0.000 -.0169755 -.00769 we | .0286843 .0085226 3.366 0.001 .0119527 .045416 _cons | .6766642 .1462266 4.628 0.000 .3895906 .9637377

Problem with OLS:values of LFP outside the range [0,1]

. predict olsp

. sum olsp

Variable | Obs Mean Std. Dev. Min Max---------+----------------------------------------------------- olsp | 737 .5590231 .1799664 -.1660837 1.033887

3) Analysis of labor force participation decision: PROBIT

Probit Estimates Number of obs = 737 chi2(4) = 103.70 Prob > chi2 = 0.0000Log Likelihood = -453.85482 Pseudo R2 = 0.1025

------------------------------------------------------------------------------ lfp | Coef. Std. Err. z P>|z| [95% Conf. Interval]---------+-------------------------------------------------------------------- lwwall | .3414153 .0975097 3.501 0.000 .1502999 .5325307 kl6 | -.8461751 .1120412 -7.552 0.000 -1.065772 -.6265783 wa | -.034834 .006805 -5.119 0.000 -.0481716 -.0214965 we | .0836028 .0244023 3.426 0.001 .0357751 .1314305 _cons | .4715593 .4166221 1.132 0.258 -.3450051 1.288124------------------------------------------------------------------------------

3) Analysis of labor force participation decision: PROBIT

predicted values = probability to work

. predict probp

. sum probp

Variable | Obs Mean Std. Dev. Min Max---------+----------------------------------------------------- probp | 737 .5609 .1796111 .0275137 .9348859

3) Analysis of labor force participation decision: PROBITMarginal effects = change in probability to work due to a

marginal increase in explanatory variablesProbit Estimates Number of obs = 737 chi2(4) = 103.70 Prob > chi2 = 0.0000Log Likelihood = -453.85482 Pseudo R2 = 0.1025

------------------------------------------------------------------------------ lfp | dF/dx Std. Err. z P>|z| x-bar [ 95% C.I. ]---------+-------------------------------------------------------------------- lwwall | .1344203 .0383353 3.50 0.000 1.03574 .059284 .209556 kl6 | -.3331518 .0442183 -7.55 0.000 .240163 -.419818 -.246486 wa | -.0137147 .0026783 -5.12 0.000 42.5495 -.018964 -.008465 we | .0329157 .0096114 3.43 0.001 12.232 .014078 .051754---------+-------------------------------------------------------------------- obs. P | .5590231 pred. P | .5645112 (at x-bar)------------------------------------------------------------------------------ z and P>|z| are the test of the underlying coefficient being 0

3) Analysis of labor force participation decision: LOGIT

Logit Estimates Number of obs = 737 chi2(4) = 103.96 Prob > chi2 = 0.0000Log Likelihood = -453.72489 Pseudo R2 = 0.1028

------------------------------------------------------------------------------ lfp | Coef. Std. Err. z P>|z| [95% Conf. Interval]---------+-------------------------------------------------------------------- lwwall | .5771894 .1690888 3.414 0.001 .2457813 .9085974 kl6 | -1.403624 .1931729 -7.266 0.000 -1.782236 -1.025013 wa | -.0573988 .0112889 -5.085 0.000 -.0795246 -.0352729 we | .1369775 .0411124 3.332 0.001 .0563988 .2175563 _cons | .7613688 .6843124 1.113 0.266 -.5798588 2.102596

LOGIT marginal effects

E s t i m a t e d t h e c o e f f i c i e n t s f r o m t h e l o g i t m o d e l a n d c a l c u l a t e

a t m e a n v a l u e s o f x v a r i a b l e s .

T h e n c a l c u l a t e t h e m a r g i n a l e f f e c t s o f i n d i v i d u a l e x p l a n a t o r y v a r i a b l e s :

V a r i a b l e M a r g i n a l e f f e c tL w w a l . 1 4 1 9 7 1 2K l l 6 - . 3 4 5 2 4 9 3W a - . 0 1 4 1 1 8 4W e . 0 3 3 6 9 2 3

)(1

1Pr ''

'

xe

eYob

xb

x

xxx

xyE '' 1

0.5634828)( ' x

4) Comparing conditional OLS and Tobit estimates

of labor supply

• Avg.hours(US)<Avg.hours(CZ)

• Higher corr(wage,edu) in the US (see next slides)

OLS for working women

. reg lwhrs lww we kl6 k618 if lfp==1

Source | SS df MS Number of obs = 412---------+------------------------------ F( 4, 407) = 11.02 Model | 35.1553278 4 8.78883196 Prob > F = 0.0000Residual | 324.518108 407 .797341788 R-squared = 0.0977---------+------------------------------ Adj R-squared = 0.0889 Total | 359.673436 411 .875117848 Root MSE = .89294

------------------------------------------------------------------------------ lwhrs | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- lww | .1820677 .0703565 2.588 0.010 .0437601 .3203752 we | -.055888 .0210205 -2.659 0.008 -.0972103 -.0145658 kl6 | -.4997141 .1136211 -4.398 0.000 -.7230717 -.2763566 k618 | -.08619 .033777 -2.552 0.011 -.1525891 -.019791 _cons | 7.582763 .260332 29.127 0.000 7.071 8.094526------------------------------------------------------------------------------

OLS for the whole sample (constructed wages)

. reg lwhrs lwwall we kl6 k618

Source | SS df MS Number of obs = 737---------+------------------------------ F( 4, 732) = 22.48 Model | 985.213477 4 246.303369 Prob > F = 0.0000Residual | 8019.24109 732 10.9552474 R-squared = 0.1094---------+------------------------------ Adj R-squared = 0.1045 Total | 9004.45456 736 12.2343133 Root MSE = 3.3099

------------------------------------------------------------------------------ lwhrs | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- lwwall | 1.052204 .2515781 4.182 0.000 .5583033 1.546104 we | .1758487 .0606386 2.900 0.004 .0568024 .294895 kl6 | -1.641327 .2345313 -6.998 0.000 -2.101761 -1.180893 k618 | .0460325 .0928994 0.496 0.620 -.1363485 .2284135 _cons | .9469223 .6957805 1.361 0.174 -.4190411 2.312886

TOBIT (censored point = 0)

tobit lwhrs lwwall we kl6, ll

Tobit Estimates Number of obs = 737 chi2(3) = 85.14 Prob > chi2 = 0.0000Log Likelihood = -1539.8361 Pseudo R2 = 0.0269

------------------------------------------------------------------------------ lwhrs | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- lwwall | 1.495446 .4170418 3.586 0.000 .6767087 2.314183 we | .366786 .10701 3.428 0.001 .1567039 .5768682 kl6 | -3.221031 .4734994 -6.803 0.000 -4.150605 -2.291456 _cons | -3.15548 1.236986 -2.551 0.011 -5.583932 -.7270272---------+-------------------------------------------------------------------- _se | 5.438618 .2156116 (Ancillary parameter)------------------------------------------------------------------------------

Obs. summary: 325 left-censored observations at lwhrs<=0 412 uncensored observations

5) Heckman two-stage method

1) Estimate probit lfp = lwwall kl6 wa we

for the whole sample of working and not-working women, and calculate inverse Millsration for women who work

2) use this ratio as an additional explanatory variable in OLS estimation model of laborsupply:

)(

)(

xF

xf

5) Heckman two-stage method reg lwhrs lwwall we kl6 k618 lamb

Source | SS df MS Number of obs = 412---------+------------------------------ F( 5, 406) = 9.38 Model | 37.2510751 5 7.45021503 Prob > F = 0.0000Residual | 322.422361 406 .794143745 R-squared = 0.1036---------+------------------------------ Adj R-squared = 0.0925 Total | 359.673436 411 .875117848 Root MSE = .89115

------------------------------------------------------------------------------ lwhrs | Coef. Std. Err. t P>|t| [95% Conf. Interval]---------+-------------------------------------------------------------------- lwwall | .0806484 .0939565 0.858 0.391 -.1040535 .2653503 we | -.0810441 .0260746 -3.108 0.002 -.1323023 -.029786 kl6 | -.2962574 .1689488 -1.754 0.080 -.628381 .0358662 k618 | -.110411 .0368593 -2.995 0.003 -.1828699 -.0379521 lamb | -1.759013 1.082802 -1.625 0.105 -3.887612 .3695858 _cons | 8.815867 .8022987 10.988 0.000 7.238689 10.39305------------------------------------------------------------------------------