Working Paper Series 

Congressional Budget Office 

Washington, DC 

ARE MARRIED WOMEN SECONDARY WORKERS? 

THE EVOLUTION OF MARRIED WOMEN'S LABOR SUPPLY 

IN THE U.S. FROM 1983 TO 2000 

Kyoo-il Kim 

Department of Economics 

University of California, Los Angeles 

E-mail: kyookim@ucla.edu 

José Carlos Rodríguez-Pueblita 

Department of Economics 

University of Pennsylvania 

E-mail: joserp@econ.upenn.edu 

December 2005 

2005-11 

The authors served as interns at CBO when they performed the analysis for this paper. 

Working papers in this series are preliminary and are circulated to stimulate discussion 

and critical comment. These papers are not subject to CBO’s formal review and editing 

processes. The analysis and conclusions expressed in them are those of the authors and 

should not be interpreted as those of the Congressional Budget Office. References in 

publications should be cleared with the authors. Papers in this series can be obtained at 

www.cbo.gov (select Publications then Working and Technical Papers).
Abstract 

Applying several estimation procedures to the Panel Study of Income Dynamics, we find that 

labor supply elasticities with respect to own wages and to other household members’ income for 

married white women have decreased significantly in absolute terms during the 1983-2000 

period. The elasticities with respect to after-tax wages are statistically either not different from 

zero or negative, while the elasticities with respect to other household members’ income are 

negative, significant, and relatively stable for much of the period. Our results are robust and 

consistent across models and specifications. These findings suggest an important change in the 

labor supply behavior of married women, revealing that younger females today are not behaving 

like younger females in the past. We informally explore several possible explanations to this 

phenomenon: changes in the intrahousehold resource allocation and in turnover rates for younger 

cohorts. These institutional adjustments, together with the increasing portion of younger females 

in the labor force pool, might explain the empirical findings of our study. 
1

1. Introduction1

A conventional view of labor supply in the United States highlights the differences between men 

and women. However, women have changed their labor market behavior over time, prompting 

Heckman’s (1993) empirical question: “Has the consensus view of the 1960s of high labor 

supply elasticities for married women and low labor supply elasticities for married men held 

up?” 

Many early papers (Heckman (1974), Mroz (1987), Cogan (1980)) as well as relatively recent 

ones (Zabel (1993), Blundell, et al. (1998), Angrist (1991), Eissa (1995)) found relatively high 

labor supply elasticities with respect to wages for married women, in contrast to those for their 

partners. For instance, Eissa (1995) estimates an uncompensated elasticity of 0.6 using a 

difference-in-difference approach with data from the 1986 to 1988 and 1990 to 1992 March 

Current Population Surveys (CPS). Zabel (1993) reports an estimate of 0.197 using data from 

the 1987 Panel Study of Income Dynamics (PSID) and a Tobit-type model. The widely accepted 

conclusion of these studies is that secondary workers are, in comparison with primary workers, 

significantly more responsive to wage and income variations.2

To analyze the evolution of the behavior of married women’s labor supply, we estimate laborsupply elasticities with respect to their own wages and to all other household income (“non-labor 

income” from now on) with data from the PSID for the period from 1983 to 2000. We check the 

 1

We thank the Congressional Budget Office for the opportunity to work on this project as members of its Summer 

Internship Program. We also thank David Brauer, Eva De Francisco, Tom DeLeire, Ufuk Demiroglu, Bob Dennis, Doug 

Hamilton, Joe Kile, Kim Kowalewski, Rob McClellan, Ben Page, and Frank Russek, as well as other participants of the CBO 

seminar series, for their useful comments. 

2

 Possible explanations for the difference include the responsibility for child care and cultural elements. In this paper, 

married women are classified as “secondary workers” when their husbands are working and receiving a paycheck. 
2

robustness of our estimates by using the simultaneous equations method and the two-step 

estimation method of Vella (1993), both with two models from Zabel (1993), and the differencein-differences (DID) approach with instrumental variables used by Blundell, et al. (1998). 

Our main findings from all three approaches are that the wage elasticity has trended down over 

time and is now zero or even negative, while the non-labor income elasticities are always 

significantly negative and fairly stable for much of the period. Compensated wage elasticities 

under different hypotheses of intra-family resource allocation also are not significantly different 

from zero in recent years. Our results are similar to those of Heim (2004), who found that the 

uncompensated wage elasticity of married women has shrunk dramatically over time using the 

CPS data from 1979 to 2003, a decrease mainly caused by a drop in the estimated wage and 

income coefficients of the labor supply regressions. 

The remainder of the paper is organized in four sections. Section 2 explains the estimation 

methods we use. Data analysis and estimation results are presented in Section 3. Section 4 

suggests possible explanations on what we found in this study. We conclude in Section 5. 

2. Estimation Methods

Several econometric methods have been used to estimate workers’ wage and non-labor income 

elasticities. Some of them focus on controlling for the endogeneity caused by the nonlinear 

budget set resulting from the tax system (see Triest (1990) and Heim and Meyer (2003)). Others, 

including Mroz’s (1987) seminal paper, deal with other sources of endogeneity such as wage 

rates, non-labor incomes, the presence of children in the household, labor market experience, and 
3

self-selection into the labor force. Among these potential sources of endogeneity, this study 

mainly considers wage rates and labor force participation for both the cross-sectional and the 

repeated cross-section analyses, although we also address potential simultaneity problems caused 

by other types of income and children in the household. 

For the cross-section data, we adopt two models used by Zabel (1993). Zabel studies four 

models: 1) a simplified Tobit-type version of the Heckman (1974) model, 2) the fixed cost 

model, 3) the minimum hours constraint model, and 4) the generalized labor supply model. 

However, we only use two--the Heckman model and the generalized Tobit-type labor supply 

model–because Zabel’s findings show that estimated labor supply elasticities are quite similar in 

their magnitudes and signs for all of the models except Heckman’s. We estimate the two models 

using the maximum likelihood (ML) simultaneous-equations approach. We also use the twostep estimation procedure of Vella (1993) to check the robustness of our ML estimates because 

ML estimates can be numerically inaccurate for high dimensional density functions (see Mroz 

(1997)). 

For the repeated cross-section study, we use the DID approach proposed by Blundell, et al. 

(1998), which includes a “control function” method to eliminate the potential biases induced by 

the wage rate, other income, participation to the labor force, and data selection away from the 

kink in the after-tax budget constraint. However, we do not consider the endogeneity from the 

kink in the budget set for two reasons. First, it is unlikely that there are significant kinks in the 

U.S. tax system for many people given its complicated structure.3

 Second, even for the case of a 

 3

Blundell, et al. (1998) did not find strong arguments to support bunching around the kink in the UK, a country where the 

tax system is far less complicated (only two well identified brackets) than the US tax system in terms of number of brackets, and 
4

significant kink in the U.K., Blundell, et al. (1998) conclude that the kink has very little effect on 

the estimated elasticities. Therefore, we only control for the possible endogeneity from the wage 

rate, other income, and participation in the labor force.4

2.1. The Simultaneous Equations Approach

The simplified Heckman model and the generalized labor supply model used by Zabel (1993) 

consist of two equations: one characterizing desired hours of work, and another for latent wages. 

The main difference between the two models is that the generalized labor supply model allows 

for separate equations for labor force participation (LFP) and hours of work. 

Zabel (1993) specifies the hours-of-work and wage equations as: 

 Hi

* = β1 lnWi* + β2NIi + Xi'

β3 + u1i (1) 

and 

 lnWi

* = Yi'

α + u2i , (2) 

where Hi

* is the latent value for desired hours of work, lnWi*

 is the latent value for the natural 

logarithm of hourly wages, NIi is income other than the wife’s labor income, Xi and Yi are 

vectors of individual characteristics, and u1i and u2i are jointly normal errors with zero mean 

and covariance matrix Σ12 = σ1

2 σ12

σ 2

2

⎛

⎝

⎜

⎞

⎠

⎟ . 

 thus, number of kinks. Moreover, the U.S. tax system has been subject recently to multiple changes in a relatively short period of 

time; a fact that we believe can deter individuals from deciding their hours of work based on current tax rates. 

 

4

In an earlier version of this paper, we also treated children variables as endogenous. 
5

2.1.1. Tobit-type Model 

Individuals participate in the labor force when desired hours of work are greater than zero, while 

they do not work otherwise. That is: 

work if Hi

* > 0 , 

do not work if Hi

* ≤ 0 →

u1i + β1u2i

σ

≤ −ti , 

where 

ti = β1

Yiα + β2NIi + Xi

'

β3

σ

and 

σ = std dev(u1i + β1u2i) = (σ1

2 + β12

σ 2

2 + 2β1

σ12 )

1/2 . 

Thus, the corresponding log-likelihood function for this model is written as: 

log L = log Φ −t ⎡ ( i) ⎣ ⎤

⎦

0

∑ + log b u1i ,u2i ⎡ ( ;Σ12 ) ⎣ ⎤

⎦

1

∑ , 

where Φ is the standard normal cumulative density function and b v( ,w;Σ) is the bivariate 

normal density with the covariance matrix Σ . 

 

2.1.2. Generalized Tobit-type Model 

The second labor supply model generalizes the Tobit-type model in two ways. First, the 

parameters of the LFP equation are not restricted to be proportional to the parameters in the 

hours-of-work equation. Second, the regressors in the LFP equation are not necessary identical to 

those in the reduced form hours-of-work equation. We characterize the LFP as: 

work if LFPi

* > 0 , 
6

do not work if LFPi

* ≤ 0 → u3gi ≤ −Zi'

π , 

where LFPi

* = Zi'

π + u3gi is a latent tendency to work. Again, we assume that the three error 

terms follow a joint normal distribution with zero mean and covariance matrix as: 

Σ123g =

σ1

2 σ12 σ13g

σ 2

2 σ 23g

1

⎛

⎝

⎜

⎜

⎜

⎞

⎠

⎟

⎟

⎟

. 

We perform the ML estimation based on the log-likelihood function: 

 

log L = log Φ −Zi

' ⎡ ( π ) ⎣ ⎤

⎦

0

∑ +

log Φ Zi

'

π u1i ( ) ,u2i ⎡

⎣ ⎤⎦ + log b u1i ,u2i ( ) ;Σ12 ⎡

⎣ ⎤ { }⎦ . 1

∑ (3) 

The first term in (3) is the probability of not working. The second term is the probability of 

working conditional on the error terms from the wage and hours of work equations. This term 

would be zero under the restrictions made in the simple Tobit-type model. The last expression is 

the density associated with the hours-of-work decision. 

We estimate both the Tobit-type model and the generalized labor supply model using the PSID 

data for every available year in the 1983 to 2000 period.5

 The logarithm of wages, non-labor 

income, age, education, and variables related to the number of children and health status of the 

household head are included in the hours-of-work equation. The wage equation contains age and 

education variables up to cubic terms, health, a variable indicating residence in a SMSA 

(standard metropolitan statistical area), parents’ education, regional dummies, and the local labor 

 5

 We estimate the two models using both before- and after-tax wages and incomes. It turns out that accounting for taxes 

makes little difference to the estimates. 
7

market variables. Finally, the union of the variables in the hours-of-work and wage equations are 

used for the LFP equation in the generalized labor supply model. The estimation results are 

discussed in Section 3. 

We encountered several problems using maximum likelihood. For some years, we had difficulty 

obtaining convergence of the estimates because the likelihood surface was relatively flat, a 

common problem of estimating labor supply models. The sign of the wage elasticity was 

counterintuitive (i.e., negative). In addition, the wage parameters were not often significant. We 

overcame the first problem by using different initial values for certain years, which gave us 

consistent estimates across years.6

 Nevertheless, given the counterintuitive signs and lack of 

significance of the ML estimates, we decided to use a more robust two-step method in hopes of 

obtaining better estimates. 

2.2. Two-Step Approach 

The two-step approach, widely used in the labor economics literature among other fields, has 

several virtues. Most importantly, it can deal with selection bias and other simultaneity problems 

in a rather simple manner as suggested by Vella (1993), and its results are numerically robust. 

Moreover, it relaxes some of the strong distributional assumptions and tends to impose fewer 

computational burdens than ML estimation. The main drawbacks of this approach are a loss of 

efficiency as compared with ML and a lack of flexibility. Nevertheless, we used this two-step 

methodology in order to overcome potential problems as mentioned in Mroz (1997) of 

numerically inaccurate estimates in our ML estimations. 

 6

 We used both OLS and IV estimates for each year as initial values following Mroz (1987). 
8

In the first step, we estimate two reduced-form equations using the probit estimator: one for labor 

force participation and the other for wages. In the second step, we use ordinary least squares 

(OLS) on the hours-of-work equation with the inverse Mill’s ratio constructed from the firststage probit estimation and the residuals from the estimated wage equation as additional 

regressors. To be more precise, we estimate the following bias-corrected, hours-of-work equation 

using OLS: 

Hi = α + β1 lnWi + β 2NIi + Xi

'

β3 + δ wυ

$

i

w

+ δ Pυ

$

i

P

+ ε i , 

where Xit includes age, education, children variables, and health, lnWi and NIi stand for the 

logarithm of wage and other income, respectively. 

^

w υi denotes the estimated residual from the 

wage equation estimation and 

^

P υi is the inverse Mill’s ratio obtained from the first-stage probit 

estimation. In the first-stage, reduced-form estimations, the wage equation contains age and 

education variables up to cubic terms, health, a SMSA dummy, parents’ education, regional 

dummies, and the local market variables. The union of the variables in the hours-of-work and 

wage equations are used for the probit estimation. A detailed description of the variables used 

and the estimation results will be presented in Section 3. 

Our findings from the generalized Tobit-type estimation and the 2-step estimation suggest that 

our ML estimates have the wrong sign and are not very precise for certain years. The former 

suggests a possible misspecification of the model and the later might reflect the numerical 

inaccuracy of the ML estimates. Consequently, we implement the DID approach of Blundell, et 

al. (1998), which may produce more reasonable estimates. 
9

2.3. Difference-in-Differences Approach 

A DID approach is commonly used to measure the effect of a certain treatment on a group by 

comparing the behaviors of the treated group and the untreated group before and after the 

treatment. The difference in behavior (before and after the treatment) of the treated group will 

contain two factors: the effect of the treatment and a common shock (macro shock or time 

effect). The difference in behavior of the untreated group will contain only the common shock. 

Subtracting the two differences in behavior (difference in differences) eliminates the common 

shock, leaving the true effect of the treatment. 

In our DID approach, we treat tax reforms natural experiments. The idea is that if two different 

cohort groups are affected differently by tax reforms, the difference of the responses by two 

different groups to the tax reforms will identify the labor supply responses. The main advantage 

of this DID approach is that we can use exogenous experiments (tax reforms) and can combine 

several years of data. We used the four major tax reforms in 1986, 1990, 1993, and 1997 during 

the 1983-2000 period. Our main identification assumption is that these exogenous changes had 

different effects on different groups of individuals, namely birth cohort and education level. We 

used those groups because they are likely to be affected differently by the tax reforms. 

Cohort/experience effects on wage and non-labor income as well as changes in returns to 

education across time suggest that wage and other income distributions are different across these 

groups. Moreover, birth cohort and educational attainment are exogenous to the labor supply 

decision at the time these women were analyzed, making them reasonable instrumental variables. 
10

Although one might be tempted to split the sample up into groups based on tax status, that 

approach is invalid for the purposes of this paper. In contrast with the U.K. system studied by 

Blundell, et al., there is no salient kink or discontinuity in the United States tax system. All 

individuals in the U.K. have a tax allowance on earnings, regardless of the total level of 

household income or consumption. About 30 percent of working married women are exempt 

from tax under this allowance, which enables researchers to divide them into two groups as ‘nontaxpayers’ and ‘taxpayers’. Another factor that creates a discontinuity in the budget constraint 

under the U.K. tax system is the national insurance system (NI). Contributions to the system are 

paid on the entire income between the lower earning limit and upper earnings limit. Interestingly, 

the NI kink (in the lower limit) and the tax kink are very close each other, creating a unique 

salient kink in the budget set in practice. By contrast, the U.S. tax system has several tax credits 

and tax brackets, but the after-tax budget set is relatively linear. A second reason for not using 

tax status as a grouping criterion is that even if there is one salient kink in the budget set, the 

composition of the groups defined by tax status will change over time in a nonrandom way, as 

argued in Blundell, et al. (1998). 

Average federal tax rates across cohorts and education levels do not show any unusual patterns 

over the period (see Table 1). The tax rates are calculated for every married woman in the PSID 

using the NBER’s TAXSIM tax calculator. On average, income tax rates faced by one cohort (or 

education level) differ consistently from those faced by any other cohort (or educational level). 

The income tax rates of people born in 1940s, for example, were always higher than those of 

people born in 1930s for comparable years on average. The same is true for the 1950s cohort as 

compared with the 1960s cohort for comparable years. Finally, higher education groups always 
11

1920s 1930s 1940s 1950s 1960s 1970s Weighted 

Average

1983 26.35 24.66 26.63 25.11 - - 25.75

1984 24.10 25.44 25.95 24.88 - - 25.30

1985 24.46 24.94 25.53 25.03 - - 25.13

1986 22.79 23.10 26.19 24.14 - - 24.54

1987 25.70 23.35 25.63 23.58 - - 24.30

1988 21.85 21.16 23.10 21.65 - - 22.04

1989 21.00 21.50 23.64 22.26 - - 22.56

1990 - 19.09 21.11 20.94 18.79 - 20.58

1991 - 16.66 21.29 20.97 19.45 - 20.31

1992 - 19.45 22.35 21.44 19.69 - 21.20

1993 - - 24.04 23.09 21.62 - 22.94

1994 - - 24.44 22.98 21.45 - 22.85

1995 - - 23.12 23.46 22.30 - 22.95

1996 - - 23.05 24.09 22.89 - 23.33

1998 - - 24.52 23.59 22.11 - 23.15

2000 - - 24.10 24.72 23.40 21.97 23.98

Weighted 

Average 24.43 21.64 23.79 22.85 21.84 21.97

1983 25.40 23.38 24.86 23.98 - - 24.34

1984 22.97 23.68 24.34 23.02 - - 23.64

1985 23.45 22.73 22.94 23.05 - - 22.99

1986 21.90 21.00 23.74 22.38 - - 22.42

1987 25.14 20.77 23.68 21.22 - - 22.13

1988 19.88 20.04 21.19 20.39 - - 20.55

1989 20.80 19.48 21.20 20.44 - - 20.47

1990 - 17.50 19.60 19.11 16.08 - 18.77

1991 - 15.32 19.39 19.76 17.75 - 18.66

1992 - 18.10 20.15 19.86 17.62 - 19.38

1993 - 19.96 22.60 21.60 19.52 - 21.38

1994 - 20.97 23.40 22.21 19.58 - 21.79

1995 - 19.84 21.06 22.15 20.58 - 21.33

1996 - 18.17 21.11 22.65 21.01 - 21.60

1998 - 21.50 23.03 22.45 20.10 - 21.66

2000 - - 22.45 23.16 21.83 20.15 22.43

Weighted 

Average 23.40 19.97 21.85 21.29 19.86 20.15

1983 29.02 28.86 28.87 26.20 - - 27.98

1984 27.94 30.57 28.39 26.86 - - 28.08

1985 27.71 29.79 28.31 26.85 - - 27.87

1986 24.90 28.31 28.82 25.67 - - 27.08

1987 26.79 29.17 27.85 25.58 - - 26.80

1988 28.53 23.69 25.17 22.71 - - 23.71

1989 21.50 27.15 25.92 23.68 - - 24.63

1990 - 23.85 23.38 23.01 22.46 - 23.16

1991 - 20.73 23.88 22.23 21.08 - 22.41

1992 - 23.28 25.43 23.12 21.77 - 23.47

1993 - 25.81 25.64 24.48 23.17 - 24.48

1994 - 22.79 25.59 23.69 23.03 - 23.89

1995 - 26.73 25.47 24.72 23.69 - 24.57

1996 - 23.53 25.12 25.50 24.34 - 24.96

1998 - - 25.80 24.46 23.66 - 24.32

2000 - - 25.19 25.89 24.57 22.63 25.06

Weighted 

Average 27.37 26.20 26.06 24.32 23.47 22.63

Table 1. Marginal Federal Tax Rates by Cohort and Education Level

Source: Authors using PSID and NBER's TAXSIM tax calculator.

All Individuals

Up to High School

More Than High School
12

face higher income tax rates than lower education groups for all cohorts and comparable years on 

average. Table 1 highlights the non-randomness of tax rates as well as the power of the cohort 

instrumental variable as an identification tool. 

We use 8 groups in all. We used 4 birth cohorts and and 2 levels of education, both interacted 

with the tax year. The four birth cohorts are: (i) those who were born before-1940; (ii) those born 

from 1940 to 1949; (iii) those born from 1950 to 1959; and (iv) those born in 1960 and 

thereafter. The 2 education groups are high school or less, and more than high school.7

 Our main 

identifying assumption is the same as that of Blundell, et al. (1998) -- average differences in 

labor supply between groups are constant over time, after conditioning on the wage, other 

income, and demographic characteristics. In practical terms, that assumption means that while 

the full set of time and group effects are included in the hours-of-work equation, the time-group 

interactions can be ignored. That enables us to identify the parameters in the labor supply 

equation. 

Suppose that we are interested in estimating the following labor supply equation (assuming, for 

simplicity, that there is no covariate and the logarithm of wage is exogenous): 

hit = a + blnwit + uit , 

where individual i can be categorized in one of several demographic groups g = {g1,g2 ,KgG}, 

each sampled for a least two time periods. Define for a variable x : 

Dx

gt = E(xit | Pit , g,t) − E(xit | Pit , g) − E(xit | Pit ,t) , 

 7

This is a standard cut-off, although alternatives could be used. Given the importance of a college degree in the labor 

market, this cut-off is useful for identifying differences in individuals’ labor supply behavior. 
13

where Pit is an indicator for an individual’s working status at time t . Blundell, et al. (1998) 

assume that: 

Assumption A1: E(uit | Pit ,g,t) = ag + mt

Assumption A2: E[(Dw

gt)

2

] ≠ 0 . 

Assumption A1 implies that the unobserved differences in average labor supply across groups 

can be explained by a group effect ( ag ) plus an additive time effect ( mt ) without interaction 

terms, which creates exclusion restrictions for identification. Another implicit restriction of 

Assumption A1 is that we do not allow E(uit | Pit ,g,t) to vary over time. More specifically, that 

restriction implies that labor participation ( Pit ) is completely explained by time and group effects 

without interaction terms, which is too restrictive (athough the data might show this is the case). 

Assumption A2 requires that after taking away time and group effects, wages still have some 

variation, excluding the possible multicollinearity of the wage variable with time and group 

dummies. In that sense, it is a usual rank condition for identification. Blundell, et al. (1998) relax 

the two assumptions presented above, but still allow exclusion restrictions for the interacting 

dummies: 

Assumption B1: E(uit | Pit ,g,t) = ag + mt + ρλ gt

Assumption B2: E[(Dw

gt − ρ wλ

gt)

2

] ≠ 0 and E[(Dλ

gt)2

] ≠ 0 , 

where λ

gt

 is the inverse Mill’s ratio evaluated at Φ−1(L

gt) with Φ−1

 being the inverse function 

of the standard normal distribution, and L

gt being the proportion of group g working in period t. 

ρ w is naturally defined as the population partial regression coefficient 

ρ w = E[Dw

gtDλ

gt] / E[(Dλgt)2

] . Assumption B2 is the same rank condition with Assumption A2. If 
14

indeed E[(Dλ

gt)2

] = 0 , we can disregard the selection bias caused by ρλ gt in the estimation of the 

wage coefficient. 

2.3.1. Implementation of the DID Estimator 

We implement the difference-in-differences estimator using a regression approach, controlling 

for several endogeneities using the control functions, similar to the two-step method. The 

potential endogenous variables are the wage rate, other income, participation in the labor market, 

and children variables. However, we ignore the potential endogeneity of the children variables 

for several reasons. First, we could not find any significant differences between treating children 

variables as endogenous or exogenous. Secondly, most of the studies, including Zabel (1993), 

Triest (1990), and Blundell, et al. (1998), that estimate intensive margins in married women 

labor supply treat children variables as exogenous. The last reason is a technical one regarding 

difficulties raised when treating dummy endogenous variables in the estimation.8

We first estimate the reduced-form equations for each of endogenous regressors. Right-hand side 

variables include a complete set of group and time dummies and their interactions along with 

several other demographic variables including regional variables, health, and parents’ education. 

The equation for the logarithm of wages was estimated using data for those employed; the other 

income equation and the participation probit were estimated with the entire sample. 

In the second step, we estimate the hours-of-work equation using ordinary least squares. The 

 8

 We could estimate reduced-form equations for the children dummy variables using a probability index model such as 

a probit. However, the treatment of dummy endogenous variables in a censored equation is beyond the scope of this paper. See 

Heckman (1978) and Kim (2004) for a discussion of the issue. 
15

basic equation without the children dummy variable interactions is: 

 Hit = ag + mt + β1 lnWit + β 2NIit + Xit

'

β3 + δ wυ

$

it

w

+ δ NIυ

$

it

NI

+ δ Pυ

$ it

P

+ ε it , (4) 

where ag are the group dummies, mt are time dummies, Xit are the children dummy variables 

and the health variable, lnWit and NIit are the logarithm of the individual i’s after-tax wage and 

her level of other income, respectively. Children dummy variables include a dummy for no 

children under seventeen in the household, a dummy for the youngest child under six years old, 

and a dummy indicating the youngest child between six to seventeen years old. The υˆ ’s 

variables are the residuals from the reduced-form estimations that control for the endogeneity of 

wages (υˆit

w ), other income (υˆitNI ), and participation (υˆitP , inverse Mill’s ratio). One of the virtues 

of this control function approach is that we can directly test the exogeneity of every possible 

endogenous variable using t-statistics for the δ parameters (Smith and Blundell (1986)). In 

equation (4), we exclude all interactions of the group and time dummies, which is justified under 

Assumption A1 or Assumption B1 conditional on the wage, other income, demographic, and 

health variables. From these exclusions, we can identify this structural equation. Also note that in 

the reduced-form estimation, we drop the interacting time and group dummies if the cells 

associated with these interacting dummies have less than 45 observations. In addition, some of 

the interacting dummies are dropped to avoid multicollinearities, including the exact ones. The 

asymptotic covariance matrix accounts for the generated regressors used in the second step and 

heteroskedasticity as noted by Blundell, et al. (1998). A detailed description of the calculation of 

the standard errors is presented in Appendix F. 

Finally, although equation (4) is a cross-sectional, marginal-rate-of-substitution equation with a 

full set of time dummies, it differs from an intertemporal Euler equation with a common real 
16

interest rate because it excludes the average group interest rate which is assumed to vary over 

time and across groups. Such variation in the interest rate could arise from the tax system or 

liquidity constraints.

3. Empirical Results 

3.1. The Data 

The raw data used for this analysis are the annual interviews from the PSID longitudinal data set 

for the period 1983 to 2001. Data from two consecutive years were merged to create a consistent 

data set. The data for interview year t includes actual information on wages, income, and hours 

of work for year t-1, while data from the interview year t-1 contains the actual individual and 

family information for t-1. Thus, individual and family data from interview year t-1 were merged 

with labor supply and income related information of the interview year t, for every possible t and 

t-1, for those individuals who are present in both samples. We did not perform this merge for the 

last two interview years (1999 and 2001), because the PSID is produced every other year from 

1997 on. Consequently, we decided to use labor and income data from the 1999 and 2001 

interview years directly. We ended up with 16 cross-section data sets, which are named 

according to the date of the labor and income information they contain: yearly from 1983 to 

1996; 1998, and 2000. 

Our analysis is limited to white, married women with the following characteristics: (i) they are 

30-60 years of age whose husbands earned labor income that year; (ii) they do not belong to the 

low-income sample in the PSID; (iii) their spouses are present and there was no change in 

household status for head and spouse; and (iv) they were neither retired nor students at the time 
17

of the survey. We also dropped those individuals who met one or more of the following 

conditions: (i) the unemployment rate in their county of residence was above 50%; (ii) they 

belonged to the top 2.5% of the non-labor income distribution and such income was more than 

$150,000 in 1990 dollars;9

 (iii) their reported annual hours of work were greater than 4,000 

hours; 10 (iv) their computed marginal tax rate was negative; and (v) there was missing 

information for any variable used in the estimations.11 The resulting data set contains a total of 

16,385 observations (see Table 2). 

 9

 This limit makes the nonlabor income distribution in our 1986 sample more similar to that in Zabel’s (1993) sample. 

10 This upper bound is the total number of hours for a person who works two 8-hour jobs per day, 5 days a week with no 

vacations. 

11 The number of individuals deleted for the first four criteria never exceeded 5% of observations for any criterion in any 

year. 

Year Observations 

(Women) Working Not Working

Percent 

Working

1983 620 449 171 72%

1984 856 627 229 73%

1985 858 632 226 74%

1986 852 654 198 77%

1987 923 719 204 78%

1988 810 643 167 79%

1989 842 686 156 81%

1990 1,428 1,104 324 77%

1991 1,506 1,218 288 81%

1992 1,518 1,168 350 77%

1993 927 747 180 81%

1994 908 759 149 84%

1995 1,179 957 222 81%

1996 1,188 966 222 81%

1998 952 814 138 86%

2000 1,018 853 165 84%

Total 16,385 12,996 3,389 79%

Table 2. Sample Sizes by Year

Source: Authors.

Note: The analysis could not be done in 1997 and 1999.
18

Exogenous methodological variations in the PSID sampling process account for the differences 

in sample size across years.12 We assume that the changes in sample size are on average neutral 

across all types of individuals. This assumption is supported by the lack of sudden jumps in the 

female labor force participation rate shown in Table 2 and in the descriptive statistics for each 

year shown in Appendix C and by the findings of other studies using the PSID data set, such as 

Gouskova and Schoeni (2002). 

3.1.1. Construction of the Hours, Wage, and Income Variables 

Hours of work are defined as “aggregated hours of work in all jobs.” “Wage rate” is used for the 

years where this variable is available (1993 to 2000). In the years where pre-tax wage rates are 

not explicitly asked in the questionnaire, we constructed them by dividing “yearly income from 

work” by “aggregated hours in all jobs.” Non-labor income is constructed by summing the 

taxable income of all other family members.

After-tax wages were calculated by using liabilities and tax rates of “secondary earners” in the 

TAXSIM (Internet TAXSIM version 5.1) software provided by the NBER. We used those 

imputed liabilities and tax rates because we wanted to get an overall effective tax rate and thus 

minimize possible measurement errors in the data caused by individuals’ imprecise answers 

 12 For instance, (i) there was a change from pencil and paper to computer-assisted telephone interview in 1994; (ii) after 

1996, about 2,000 low-income families were dropped from the sample; (iii) a sample of families who immigrated to the U.S. 

since 1968 was added in 1997; and (iv) the length of the interview was doubled from 1995 to 1999. See Gouskova and Schoeni 

(2002) for more details on the reliability of income data from the PSID and their remarkable similarity to the March Current 

Population Survey. 
19

about their tax burden and status. 13 We were able to compute federal, state, and FICA tax rates 

accurately because the PSID has most of the necessary information (i.e., disaggregation by 

incomes and expenditures) to compute them via TAXSIM.14

3.1.2. Hours, Wages, and Participation in the PSID

From 1983 to 2000, the sample of married women in the PSID has increased its labor force 

participation and hours of work, and has earned greater after-tax wages. Figure 1 shows that 

both average yearly hours of work and the participation rate have trended up over time. Figure 2 

indicates that real, after-tax wages for married women and their non-labor income also have 

trended up. Both income variables fell significantly at the beginning of the 1990s, however, 

possibly due in part to the rise in tax rates in the 1990 tax reform and the economic downturn of 

1990-1991. 

Although Figures 1 and 2 suggest a positive relationship between hours of work and real wages, 

that inference is not necessarily valid because we still have to control for the possible 

endogeneity problems and potential cohort/education effects. 

Figures 3 and 4 show participation rates and average yearly hours by cohort for certain years. 

Those figures illustrate the marked differences in labor-market behavior across cohorts, 

consistent with their positions in their life cycles. 

 13The overall tax rate includes federal, state and FICA taxes. City tax rates cannot be computed because individuals’ city 

of residency is unavailable. 

14We compared the tax data returned by this software with tax data reported by individuals in the survey for comparable 

years and we did not find significant differences. Nevertheless, we used TAXSIM data because we think it provides a relevant 

overall effective tax rate. 
20

Figure 1. Women's Average Hours of Work per Year and Labor Force Participation, 

1983-2000 

Figure 2. Average After-Tax, Non-Labor Incomes and Wages of Married Women 

in Real Terms, 1983-2000

1,000

1,050

1,100

1,150

1,200

1,250

1,300

1,350

1,400

1,450

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1998 2000

Average Hours

70%

72%

74%

76%

78%

80%

82%

84%

86%

Participation Rate

Average Hours

Participation

Source: Authors using the PSID.

20

22

24

26

28

30

32

34

36

38

40

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1998 2000

Thousands of constant dollars

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

Logarithm of Wage (1982=100)

After-tax Non-Labor Income

After-tax Log Wage

Source: Authors using the PSID.
21

Figure 3. Participation by Cohort 

Figure 4. Hours-of-Work by Cohort 

0%

10%

20%

30%

40%

50%

60%

1986 1988 1991 1994 1998 2000

Rate

1939 and before

1940-1949

1950-1959

1960 and after

Source: Authors using the PSID.

1,450

1,500

1,550

1,600

1,650

1,700

1,750

1986 1988 1991 1994 1998 2000

Average Hours of Work per Year

1939 and before

1940-1949

1950-1959

1960 and after

Source: Authors using the PSID.
22

3.2. Estimation Results

3.2.1. Simultaneous Equation Approach 

The estimation results using the after-tax variables are presented in Tables 3 and 4, where we 

report coefficients and elasticities from the hours-of-work equations. 15 (Figures 5 and 6 show the 

elasticities over time.) 

 15 Additional estimation results are in Appendix A. Appendix B shows that the estimation results from the generalized 

Tobit-type model using before-tax variables are very similar to those using after-tax wage and income. 

Parameter Elastictity Parameter Elastictity

1983 668.64 *** 0.63 -25.57 * -0.57

1984 617.39 0.57 -24.88 * -0.57

1985 1406.57 * 1.29 -22.91 * -0.54

1986 436.23 0.37 -21.58 * -0.48

1987 952.49 ** 0.78 -19.84 * -0.47

1988 -947.21 ** -0.81 -6.50 * -0.23

1989 -308.85 -0.25 -13.31 * -0.33

1990 -491.17 ** -0.40 -8.18 * -0.26

1991 -449.34 ** -0.35 -15.29 * -0.35

1992 -730.76 * -0.60 -7.32 * -0.26

1993 -2138.98 * -1.63 -8.88 * -0.30

1994 -1122.27 * -0.70 -11.60 * -0.31

1995 -2607.21 * -1.99 -9.31 * -0.33

1996 -2267.39 * -1.72 -10.80 * -0.38

1998 -2744.35 * -1.96 -6.15 * -0.25

2000 -1550.71 * -1.11 -6.13 * -0.27

After-tax log wage

Table 3. Cross-Section Elasticities by Tobit-Type Model

Year

After-tax non-labor 

income

* Significant at 90% of confidence or more.

** Significant at 85% of confidence.

*** Significant at 80% of confidence.

Source: Authors.
23

The wage elasticities are quite surprising: they are all negative after 1987 in both models and 

generally significant in the later years. Moreover, the elasticities appear to fall over time for 

much of the sample period, particularly for the Tobit-type estimates. The elasticities with respect 

to after-tax non-labor income are negative as expected and mostly significant in both models; the 

estimates show much less variation over time than the wage elasticities, particularly after 1987. 

The elasticities from the Tobit-type model are usually larger in absolute value than those from 

the generalized Tobit-type model, also noted by Zabel (1993), because the standard labor supply 

elasticities for the Tobit-type model compound both the intensive margin and the extensive 

margin (participation effect). Given that the income elasticities are smaller in absolute value than 

Parameter Elastictity Parameter Elastictity

1983 -1658.44 -1.56 -11.89 * -0.26

1984 n.d. n.d. n.d. n.d.

1985 494.19 * 0.45 -6.88 * -0.16

1986 209.13 0.18 -6.15 * -0.14

1987 -148.80 -0.12 -8.51 * -0.20

1988 -146.57 -0.12 -3.35 * -0.12

1989 -1072.43 * -0.87 -6.09 * -0.15

1990 -444.96 *** -0.36 -4.42 * -0.14

1991 -58.12 -0.05 -5.97 * -0.13

1992 -269.50 *** -0.22 -1.21 *** -0.04

1993 -802.23 * -0.61 -2.12 * -0.07

1994 -1142.91 * -0.71 -4.91 * -0.13

1995 n.d. n.d. n.d. n.d.

1996 -1408.95 * -1.07 -5.98 * -0.21

1998 -1337.33 * -0.95 -3.02 * -0.12

2000 -809.40 * -0.58 -4.45 * -0.20

*** Significant at 80% of confidence.

n.d. We do not report estimates given convergence problems.

Table 4. Cross-section Elasticities by Generalized Tobit-type Model

Source: Authors.

* Significant at 90% of confidence or more.

After-tax log wage

Year

After-tax non-labor 

income

** Significant at 85% of confidence.
24

the wage elasticities, the compensated wage elasticities are negative in both models, contrary to 

expectations.16

Figure 5. Trends in Wage Elasticities over Time 

To confirm that our estimation procedure was correct, we estimated before-tax elasticities for the 

year 1986 using both the Tobit-type and the generalized models in order to compare our results 

to those of Zabel (1993). For the Tobit-type model, Zabel reported 0.554 for the before-tax wage 

elasticity and -0.322 for the before-tax non-labor income elasticity, and our results are very 

close: 0.426 and -0.333, respectively. In the case of the generalized Tobit-type model, we have 

0.186 for the before-tax wage elasticity and -0.102 for before-tax non-labor income elasticity, 

also close to Zabel’s estimates of 0.197 and -0.115, respectively. 

 16 The upper bound of compensated wage elasticities can be obtained by subtracting the income elasticities (adjusted by a 

factor smaller or equal to one) from the uncompensated wage elasticities. 

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1998 2000

Tobit

Generalized Tobit

Two-Step
25

Figure 6. Trends in Non-Labor Income Elasticities over Time 

The initial values for those ML estimations were obtained from OLS and instrumental variable 

(IV) approaches employed by Mroz (1987). After 1986, the IV estimates of the wage coefficients 

are negative, though they are smaller in absolute value than the ML estimates in many cases. The 

signs of the wage coefficients in the OLS hours-of-work equations after 1986 have positive 

signs, which are exactly opposite signs of the IV and the ML estimates for those years. Previous 

studies have shown that OLS produces negative signs for the wage coefficients, while IV 

estimates are positive. We observe exactly the opposite switch of signs, suggesting that 

endogeneity of wage is still a driving force of the sign switch of these parameter estimates. 

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1998 2000

Tobit

Generalized Tobit

Two-Step
26

The surprising values of the wage parameters obtained and their low significance in some years 

when using the simultaneous equations methods (Tobit-type and generalized Tobit), altogether 

with the similarity of the maximum log-likelihood values across models, suggests that we might 

have an identification problem caused by either a misspecification of the model or poor fitness of 

the data.17 As mentioned in an earlier version of this paper, our model specification has been 

widely used in the labor economics literature for estimating women’s labor supply.18 So, in the 

first hand, we do not believe the misspecification is the source of the problem but we rather think 

 17 See Appendix A. 

18 Kim and Rodríguez-Pueblita (2004). 

Parameter Elastictity Parameter Elastictity

1983 302.95 0.29 -27.49 * -0.61

1984 -211.44 -0.19 -12.39 * -0.28

1985 489.03 * 0.45 -8.91 * -0.21

1986 189.81 * 0.16 -11.93 * -0.26

1987 -47.53 -0.04 -11.57 * -0.28

1988 -65.99 -0.06 -4.09 * -0.14

1989 -212.68 *** -0.17 -11.20 * -0.28

1990 -281.70 * -0.23 -4.90 * -0.15

1991 -119.28 -0.09 -11.17 * -0.25

1992 -371.61 * -0.30 -3.37 * -0.12

1993 -560.97 * -0.43 -0.98 * -0.03

1994 -288.38 ** -0.18 -7.09 * -0.19

1995 -81.10 -2.64 -2.64 * -0.09

1996 -489.81 * -0.37 -4.45 * -0.16

1998 -384.66 *** -0.27 -3.64 * -0.15

2000 -500.38 * -0.36 -3.10 * -0.14

* Significant at 90% of confidence or more.

** Significant at 85% of confidence.

Source: Authors.

*** Significant at 80% of confidence.

After-tax lnwage

Table 5. Cross-Section Elasticities by Two-Step Model

Year

After-tax non-labor 

income
27

the estimation method we use creates the problem. Thus, we rely on a more robust method such 

as the two-step estimation proposed by Vella (1993) to investigate if our belief is correct. 

3.2.2. Two-Step Method with Correction of Wage Endogeneity 

The two-step method estimation correcting for wage endogeneity produces estimates that are 

similar to the ML estimations in sign, magnitude, and significance (see Figures 5 and 6 and 

Tables 5 and 6). The wage elasticities are still negative after 1986, but they are smaller in 

magnitude than the ML estimates. The income elasticities are the same order of magnitude as 

the ML estimates and appear to trend up over time. 

We take three conclusions from these cross-section results. First, the driving force of our results 

is not the methodology but the specified model, which was used by others for estimating married 

women’s labor behavior. Second, estimates of the wage elasticity for married women appear to 

have fallen over time, while estimates of the non-labor income elasticity from the Tobit model 

and the 2-step estimation have fallen in absolute terms. Third, the estimation results by Zabel 

(1993) appear to be very particular to the year 1986, and may not be applicable to later years. 

The following section attempts to solve for the model specification problem with a difference-indifferences approach used by Blundell et al (1998). 

3.2.3. Difference-in-Differences Results 

Like our previous models, our DID approach with interaction terms on the children dummy 

variables produces a significant decline in the after-tax wage elasticity over time.19 The

 19Appendix E presents reduced-form estimates of the wage, non-labor income, and participation equations. 
28

elasticities are shown in Table 7, and the underlying parameters in Table 8. The estimated wage 

elasticities are negative using the whole sample, but positive when using just years 1983 to 1989. 

Older cohorts (born before 1950) show positive wage elasticities, while younger cohorts (born in 

1950 or later) exhibit negative wage elasticities. Noting that the data from the years 1983 to 1989 

do not include individuals born after 1960 and that the estimation with years 1990 to 2000 

includes a greater percentage of younger cohorts, those results suggest that the younger cohorts 

of married women behave differently than the older cohorts. The elasticities on other income, 

however, are significant and negative in all cases.

Table 7 also reports compensated wage elasticities. In the column labeled ‘compensated 

wage(a)’, we use the income share of wives (Share1 = Wage/(Wage+Nonlabor income)), and in 

the column labeled ‘compensated wage(b)’ we use an income share of one, 

After-tax 

log wage

After-tax 

non-labor 

income

After-tax 

log wage

After-tax 

non-labor 

income

After-tax 

log wage

After-tax 

non-labor 

income

1983 0.63 *** -0.57 * -1.56 -0.26 * 0.29 -0.61 *

1984 0.57 -0.57 * n.d. n.d. -0.19 -0.28 *

1985 1.29 * -0.54 * 0.45 * -0.16 * 0.45 * -0.21 *

1986 0.37 -0.48 * 0.18 -0.14 * 0.16 * -0.26 *

1987 0.78 ** -0.47 * -0.12 -0.20 * -0.04 -0.28 *

1988 -0.81 ** -0.23 * -0.12 -0.12 * -0.06 -0.14 *

1989 -0.25 -0.33 * -0.87 * -0.15 * -0.17 *** -0.28 *

1990 -0.40 ** -0.26 * -0.36 *** -0.14 * -0.23 * -0.15 *

1991 -0.35 ** -0.35 * -0.05 -0.13 * -0.09 -0.25 *

1992 -0.60 * -0.26 * -0.22 *** -0.04 *** -0.30 * -0.12 *

1993 -1.63 * -0.30 * -0.61 * -0.07 * -0.43 * -0.03 *

1994 -0.70 * -0.31 * -0.71 * -0.13 * -0.18 ** -0.19 *

1995 -1.99 * -0.33 * n.d. n.d. -0.06 -0.09 *

1996 -1.72 * -0.38 * -1.07 * -0.21 * -0.37 * -0.16 *

1998 -1.96 * -0.25 * -0.95 * -0.12 * -0.27 *** -0.15 *

2000 -1.11 * -0.27 * -0.58 * -0.20 * -0.36 * -0.14 *

Source: Authors.

*** Significant at 80% of confidence.

** Significant at 85% of confidence.

* Significant at 90% of confidence.

Tobit Two-step

Table 6. Cross-Section Elasticities by Different Models

Year

Generalized Tobit
29

Share2=Wage/Wage=1. In other words, Share1 stands for the families where their members 

share their resources fully (i.e., they pool their resources), while Share2 is applicable to families 

where each member lives on only their own income (i.e., purely individualistic resource 

allocation). Thus, we informally suggest that ‘compensated wage(a)’ is the lower bound of the 

compensated wage elasticity and ‘compensated wage(b)’ is the upper bound of the elasticity. We 

will revisit the issue of intrahousehold allocation in section 4. 

The estimation using only data of the younger cohorts shows that the upper bounds of the 

compensated wage elasticities is negative for all three groups defined by children dummy 

variables, which contradicts economic theory. For the other cases, the upper bounds of the 

compensated wage elasticities are positive except for the “no children under seventeen years old” 

groups for the 1983-2000 and 1990-2000 panels. It is worthwhile mentioning that, even for 

negative values, we cannot reject the hypothesis that the compensated wage elasticity is zero for 

a moderate range of standard errors.20

 20 Assuming the covariance between the wage elasticity and the income elasticity is positive, the range of standard errors 

is 0.074 to 0.104 for the ‘no children’ case in the 1983-2000 panel and 0.098 to 0.138 for the ‘no children’ case in the 1990-2000 

panel. 
30

Wage

Compensated 

Wage (a)

Compensated 

Wage (b)

Other 

Income Hours Wage Income

No Children -0.119 -0.096 -0.005 -0.114 1722 1.85 42.95

0.051 0.043

Youngest Child 0-6 -0.156 -0.115 0.081 -0.237 1375 1.87 42.23

0.065 0.053

Youngest Child 6-17 -0.108 -0.077 0.069 -0.178 1594 1.76 43.01

0.056 0.046

No Children 0.084 0.134 0.315 -0.231 1645 1.64 30.34

0.105 0.083

Youngest Child 0-6 0.101 0.185 0.552 -0.451 1243 1.68 29.29

0.141 0.107

Youngest Child 6-17 0.077 0.135 0.363 -0.286 1553 1.53 28.52

0.113 0.081

No Children -0.168 -0.142 -0.042 -0.126 1759 1.96 49.40

0.064 0.057

Youngest Child 0-6 -0.227 -0.180 0.043 -0.269 1440 1.96 49.17

0.079 0.071

Youngest Child 6-17 -0.147 -0.113 0.050 -0.197 1615 1.87 50.35

0.070 0.063

No Children 0.120 0.150 0.275 -0.155 1654 1.77 41.08

0.076 0.064

Youngest Child 0-6 0.166 0.215 0.424 -0.258 1378 1.77 33.97

0.100 0.073

Youngest Child 6-17 0.157 0.197 0.381 -0.224 1544 1.69 39.04

0.083 0.065

No Children -0.206 -0.183 -0.106 -0.100 1844 2.01 46.93

0.063 0.057

Youngest Child 0-6 -0.277 -0.238 -0.053 -0.223 1375 1.88 43.22

0.083 0.071

Youngest Child 6-17 -0.210 -0.182 -0.051 -0.159 1620 1.79 45.23

0.071 0.062

 Compensated Wage (a) is the lower-bound estimate and Compensated Wage (b) is the upper-bound estimate.

Source: Authors.

Notes: Asymptotic standard errors in italics.

 All wages and incomes are after-tax.

Elasticities Group Means

Table 7. Wage and Income Elasticities with the Chldren Interactions

1983-2000

1983-1989

1990-2000

Older Cohorts (30s, 40s)

Younger Cohorts (50s, 60s)
31

In Tables 9 and 10, we report the same set of experiments but excluding the children dummy 

variable interactions. The overall results are quite similar to those using interaction terms as 

shown in Tables 7 and 8. 

1983 to 

1989

1990 to 

2000

1983 to 

2000

Older 

Cohorts 

(30s, 40s)

Constant 1775.562 2475.879 2132.065 1204.487

251.937 155.008 135.465 189.233

Youngest Child 0-6 -163.212 -73.202 -161.608 -272.150

136.534 85.713 70.664 183.272

Youngest Child 6-17 -8.864 -205.468 -139.720 -73.802

94.637 70.955 53.889 73.662

Health -121.163 -137.373 -118.118 -219.407

180.280 129.135 98.004 136.992

No Children 138.297 -294.739 -205.731 198.578

180.280 129.135 98.004 136.992

Youngest Child 0-6 124.998 -326.347 -214.750 228.338

182.122 129.254 98.737 153.275

Youngest Child 6-17 120.311 -237.192 -172.915 243.122

181.263 129.500 98.620 137.922

No Children -12.525 -4.477 -4.585 -6.232

4.608 2.298 1.880 2.725

Youngest Child 0-6 -19.141 -7.882 -7.720 -10.482

4.712 2.361 1.923 3.152

Youngest Child 6-17 -15.575 -6.307 -6.590 -8.847

4.583 2.298 1.872 2.685

Wage -62.417 374.373 283.825 -132.768

179.230 127.943 97.246 135.938

Other Income 7.425 3.261 2.387 3.936

4.555 2.287 1.868 2.723

Participation -253.594 -340.706 -397.135 306.341

226.613 134.061 122.306 212.558

Source: Authors.

Notes: Asymptotic standard errors in italics.

 All wages and incomes are after-tax.

1.937

2.448

-232.828

152.518

-5.695

2.459

449.801

124.107

-3.923

2.470

-7.106

2.490

-380.196

125.414

-340.817

126.464

-175.524

126.246

-379.690

126.246

2341.079

180.481

-264.322

94.864

Table 8. Parameter Estimates for Hours-of-Work Equation With the Children Interactions

Wage Effects

Other Income Effects

Residuals

Younger 

Cohorts (50s, 

60s)

-245.868

85.032
32

Wage

Compensated 

Wage (a)

Compensated 

Wage (b)

Other 

Income Hours Wage Income

1983-2000 -0.126 -0.095 0.041 -0.167 1588 1.82 42.80

0.062 0.052

1983-1989 0.111 0.176 0.428 -0.317 1513 1.60 29.34

0.118 0.088

1990-2000 -0.188 -0.155 -0.008 -0.180 1625 1.92 49.73

0.079 0.070

Older Cohorts (30s, 40s) 0.153 0.191 0.357 -0.204 1597 1.74 39.89

0.085 0.067

Younger Cohorts (50s, 60s) -0.249 -0.220 -0.094 -0.155 1583 1.87 44.80

0.079 0.069

Table 9. Wage and Income Elasticities Without the Children Interactions

 All wages and incomes are after-tax.

Elasticities Group Means

Notes: Asymptotic standard errors in italics.

Source: Authors.

1983 to 

1989

1990 to 

2000

1983 to 

2000

Older 

Cohorts 

(30s, 40s)

Younger 

Cohorts 

(50s, 60s)

Constant 1778.239 2530.792 2150.677 1220.095 2434.088

249.951 153.142 131.289 187.800 173.081

Youngest Child 0-6 -394.357 -302.786 -320.429 -366.097 -412.947

74.037 36.392 33.966 63.382 46.151

Youngest Child 6-17 -124.751 -193.626 -172.412 -101.129 -262.887

35.820 25.238 19.618 23.933 31.555

Health -132.688 -142.806 -127.581 -210.861 -184.932

178.519 128.475 98.350 135.609 124.600

Log Wage 168.419 -305.328 -200.578 243.820 -394.692

178.519 128.475 98.350 135.609 124.600

Other Income -16.326 -5.868 -6.205 -8.165 -5.489

4.527 2.288 1.948 2.663 2.448

Wage -101.664 398.313 288.899 -155.642 480.068

179.232 128.867 98.678 136.082 124.686

Other Income 8.552 3.197 2.546 4.744 1.712

4.547 2.300 1.961 2.709 2.463

Participation -153.193 -324.715 -351.655 276.029 -199.734

223.690 134.916 120.123 210.700 153.126

 All wages and incomes are after-tax.

Residuals

Source: Authors.

Notes: Asymptotic standard errors in italics.

Table 10. Parameter Estimates for Hours-of-Work Equation Without the Children Interactions
33

Table 11 presents the parameter estimates for a number of different specifications using the data 

for all the years. In column (1), we correct for the endogeneity of the wage rate, non-labor 

income, and labor force participation. In columns (3) and (4), we drop the corrections for nonlabor income and for participation, respectively. As in Blundell, et al. (1998), the results in these 

(1) (2) (3) (4) (5)

Constant 2132.065 1862.607 2169.103 1919.643 1477.919

120.754 87.204 117.861 105.500 44.226

Youngest Child 0-6 -161.608 -137.532 -179.174 -262.994 -255.158

58.819 58.365 57.484 51.707 51.634

Youngest Child 6-17 -139.720 -110.983 -151.069 -157.451 -131.840

45.575 44.712 44.859 45.331 44.592

Health -118.118 -96.246 -127.220 -191.623 -160.255

87.992 17.227 63.379 87.055 17.203

No Children -205.731 72.526 -291.712 -252.970 65.881

87.992 17.227 63.379 87.055 17.203

Youngest Child 0-6 -214.750 64.869 -300.586 -259.213 62.865

88.787 19.085 64.575 87.970 19.088

Youngest Child 6-17 -172.915 108.589 -259.630 -219.754 103.720

88.673 15.562 63.821 87.760 15.550

No Children -4.585 -8.384 -2.241 -2.590 -2.384

1.709 1.239 0.390 1.618 0.390

Youngest Child 0-6 -7.720 -11.534 -5.392 -5.577 -5.509

1.730 1.264 0.513 1.626 0.509

Youngest Child 6-17 -6.590 -10.373 -4.272 -4.570 -4.439

1.689 1.216 0.380 1.594 0.379

Wage 283.825 - 370.260 330.051 -

88.017 - 63.101 87.122 -

Other Income 2.387 6.197 - 0.348 -

1.695 1.215 - 1.598 -

Participation -397.135 -448.734 -345.510 - -

109.999 108.869 103.717 - -

Wage Effects

Residuals

Table 11. Various Specifications of the Model for the 1983 to 2000 Period

Source: Authors.

Notes: Asymptotic standard errors in italics.

 All wages and incomes are after-tax.

Other Income Effects
34

three columns are quite similar because the changes in those endogenous variables can be 

controlled by the group and time effects without the correction terms. In column (2), we do not 

include the correction term for the wage rate, observing an important difference from the 

corrected model of column (1), suggesting that what really matters is the correction for the 

endogeneity of the wage rate. Moreover, column (2) provides quite similar estimates to the OLS 

results of column (5), which has a positive sign for the wage coefficient. The positive signs of 

the OLS estimate for the wage rate (expected from the relationship between the hours of work 

and the wage rate depicted in Figures 1 and 2) and the estimate in column 2 confirms the idea 

that wages are the main source of endogeneity in this model. 

Job 

Stability

Job 

Variation

Job 

Stability

Job 

Variation

All 45.22% -28.50% 58.47% -20.30%

19-24 25.44% -25.73% 30.33% -16.89%

25-34 23.23% -43.78% 54.53% -29.70%

35-44 78.67% -8.55% 52.18% -8.85%

45-54 144.08% 13.57% 190.11% -19.10%

High School Dropouts 23.40% -18.40% 69.39% -5.28%

High School 59.50% -28.00% 67.71% -21.72%

Some College 47.21% -40.55% 47.59% -26.71%

College Graduates 35.52% -21.42% 41.83% -34.57%

White 43.62% -29.48% 48.41% -22.28%

Nonwhite 61.71% -22.38% 146.64% -12.53%

Married-Spouse Present 50.56% -25.50% 61.01% -26.98%

Other 34.82% -23.52% 52.52% -14.12%

Education

Race

Martial Status

Table 12. Variations in Job Stability and Job Security, 1975 versus 2000 

(as a percentage of 1975 transition rates)

Source: Table 2, Stewart (2002).

Men Women

Age
35

4. Possible Explanation of Our Findings 

Our empirical analysis shows that the wage elasticity for married women has been decreasing 

across time regardless of methodology and model specification. There are two compelling 

arguments for that result. One, there have been important changes in the intrahousehold resource 

allocation that have affected women’s labor supply behavior. Two, women have raised their 

turnover rates that in turn generates the negative wage estimates. 

Support for the first potential explanation comes from Browning, et al. (1994) who study a 

sample of Canadian couples with no children and find that relative incomes between partners are 

one of the main factors determining the final allocations of expenditures on each partner. If this 

is a current driving factor of labor behavior, then a married woman cannot be treated as a 

‘secondary worker’ anymore, because informally speaking, she lives on her own income, which 

implies she is a separate “primary worker.” Thus, when younger cohorts make up a higher 

percentage of working women, aggregate behavior changes. 

Our second probable explanation relies on the fact that younger generations change their careers 

and jobs more often than do older cohorts. This phenomenon might have become more important 

as women had gained more access to the labor market, allowing them to switch jobs more easily 

than before. According to empirical evidence, it is indeed unlikely for a woman of a younger 

generation to stay in a single firm during her whole career. Evidence of this trend can be found in 

Stewart (2002), who reports that job stability has fallen for married couples, while job security 

has increased in the March CPS data over the period from 1975-76 to 2000-2001. Stewart notes 

that there has been a dramatic increase in employment-to-employment transitions for those job 
36

changes with two or fewer weeks of unemployment (58.47% for all women and 61.01% for 

married women as a percentage of 1975 as shown in Table 13), indicating that it has become 

easier to change employers than before. These trends are consistent with findings from the PSID 

(see Rose (1995) and Marcotte (1996)). 21

One of the reasons why women move to a new job may be that they can earn more total income 

than in their previous job with the same or fewer hours of work. If so, that creates a selection 

problem in the estimation, or at least makes statistical inference difficult if movements from job 

to job are frequent enough. This phenomenon, if it is significant, can make the estimated wage 

elasticities negative. Therefore, the higher portion of younger cohorts we have in our sample, the 

more salient negative wage elasticities will result from the estimation. 

5. Conclusion 

The aim of this paper was to estimate the responsiveness of secondary workers to changes in 

their wages and other income in a world where average hours-of-work of these individuals, as 

well as their participation rates, have increased substantially over the last two decades. 

Implementing several econometric methodologies and using PSID for the period of 1983-2000, 

we found that the wage elasticity for white, married women has decreased significantly in 

magnitude, while their elasticity with respect to other income has remained relatively constant 

for much of the period. In particular, the secondary workers’ labor supply elasticities with 

respect to their after-tax wages are either not different from zero or negative across 

methodologies and several specifications, while their elasticities with respect to non-labor 

 21 We should note that there are several other papers reporting little or no changes in job stability including Farber (1998), 

Diebold, Neumark, and Polsky (1997), and Jaeger and Stevens (1999). 
37

income are negative, statistically significant and stable or shrinking in absolute value over the 

years depending on the estimation approach. These findings might imply that our conventional 

models of married women labor behavior are not powerful anymore. Another possible important 

implication is that married women’s elasticity is not a good reference any more when talking 

about the most sensitive group of individuals to changes in wage rates. Therefore, younger 

cohorts of married women do not fit the “secondary worker” definition anymore compared to 

several decades ago, confirming the saying that the labor supply behavior gap between women 

and men is indeed shrinking. In that sense, our study partially answers the original question 

raised by Heckman (1993): “Has the consensus view of the 1960s of high labor supply 

elasticities for married women and low labor supply elasticities for married men held up?” Our 

answer is “no.” Our results are robust and consistent across models and specifications in the 

sense that all of them show declining wage elasticities over the time span studied. 

Interestingly, when we use the difference-in-differences approach, the only case where our IV 

estimates of wage coefficients show a significant difference between the bias-corrected and 

uncorrected models is when the endogeneity of the wage rate is addressed. Moreover, when we 

do not control for this endogeneity bias, our estimates are quite similar to the OLS results, 

suggesting that the wage is the main source of endogeneity in our model. 

Finally, the cross-section results suggest that in recent years the non-labor income elasticities are 

smaller in magnitude than the wage elasticities, resulting in negative compensated wage 

elasticities, contradicting theory. One way to reconcile our empirical findings with theory is by 

arguing changes in the intrahousehold resource allocation pattern for younger cohorts, a 
38

phenomenon with interesting social implications that has not been taken into account explicitly 

in the labor model of secondary workers. Additionally, changing patterns in younger cohorts on 

turnover rates, together with their increasing portion in the pool of the labor force, can help us to 

understand our results. Future research in these hypotheses is required in order to find a solution 

to this puzzle. 
39

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42

Appendix A 

Estimations using After-Tax Wages and Non-Labor Income Year After-tax lnwage After-tax non- labor income Age Education Number of kids 0 to 6 years old Number of kids 6 to 17 years old Number of kids 0 to 17 years old Whether kids younger than 6 years old Health Constant σ1 σ2 ρ12 Log likelihood 1983 668.64 -25.57 -8.14 36.37 -556.00 -60.57 - - -672.64 640.36 1091.71 0.54 -0.35 -4265.56 534.21 2.96 7.08 43.26 87.46 50.17 - - 265.35 597.22 110.93 0.02 0.47 - 1984 617.39 -24.88 -13.13 18.37 -462.66 -56.15 - - -244.58 1196.04 1043.02 0.51 -0.21 -5917.46 * 2.50 5.57 18.25 68.51 40.31 - - 163.71 369.44 35.07 0.01 0.24 - 1985 1406.57 -22.91 -17.20 -22.55 -560.36 -104.69 - - -545.09 749.62 1176.29 0.48 -0.55 -5889.93 458.64 2.44 6.25 43.52 66.98 39.62 - - 198.68 463.60 131.49 0.01 0.32 - 1986 436.23 -21.58 -26.76 33.51 -550.90 -132.51 - - 38.00 1882.70 995.64 0.48 -0.17 -6255.35 806.89 2.41 5.51 67.49 62.56 36.97 - - 126.62 444.99 69.36 0.01 0.62 - 1987 952.49 -19.84 -29.46 -8.68 -631.77 -122.45 - - -232.74 1771.67 1117.45 0.52 -0.52 -6708.41 649.15 2.06 6.02 59.37 60.18 36.35 - - 128.63 450.37 179.26 0.01 0.41 - 1988 -947.21 -6.50 -26.68 150.12 -608.35 -132.06 - - -505.06 2368.82 1150.70 0.56 0.48 -6434.16 641.32 1.41 6.67 66.87 63.92 38.13 - - 183.37 404.43 177.71 0.02 0.44 - 1989 -308.85 -13.31 -16.52 95.24 -442.33 -70.87 - - -429.37 1746.10 942.53 0.54 0.20 -6380.96 369.48 1.86 5.64 45.63 60.18 34.26 - - 119.80 336.58 49.17 0.01 0.46 - 1990 -491.17 -8.18 -23.20 96.37 -365.18 -64.08 - - -596.02 2218.90 1130.38 0.52 0.42 -10427.07 318.98 1.23 4.60 26.99 50.32 28.04 - - 119.52 324.68 75.67 0.01 0.33 - 1991 -449.34 -15.29 -14.41 119.01 -378.84 -107.80 - - -122.62 1689.63 1049.60 0.53 0.30 -11680.71 306.25 1.41 4.23 32.04 46.65 26.23 - - 88.76 266.94 54.97 0.01 0.37 - 1992 -730.76 -7.32 -18.50 116.63 -421.55 -128.47 - - -697.99 2415.06 1083.75 0.60 0.26 -11342.08 247.22 1.13 4.77 19.29 50.89 28.12 - - 99.21 346.94 47.99 0.01 0.36 - 1993 -2138.98 -8.88 0.04 275.97 - - -101.23 -169.37 -572.07 2414.06 1448.45 0.53 0.74 -7074.11 777.62 1.40 8.60 84.99 - - 94.40 34.25 201.13 602.91 308.56 0.01 0.25 - 1994 -1122.27 -11.60 3.21 195.67 - - -286.72 -59.11 -143.83 1287.19 1181.72 0.58 0.59 -7183.40 574.31 1.70 7.59 64.96 - - 89.07 32.53 140.16 410.50 202.11 0.02 0.35 -

1995 -2607.21 -9.31 -12.09 405.63 - - -388.89 -1.78 -749.20 1756.93 1895.76 0.55 0.87 -9041.93

1520.54 1.11 9.34 192.87 - - 79.81 29.10 222.49 687.93 729.12 0.01 0.16 -

1996 -2267.39 -10.80 -24.02 338.85 - - -429.56 -25.32 -750.13 2719.95 1763.45 0.56 0.85 -9121.31

959.56 1.13 8.23 111.12 - - 79.81 29.56 188.70 671.38 463.58 0.01 0.16 -

1998 -2744.35 -6.15 -5.86 354.66 - - -607.78 -111.04 -1031.12 3021.66 1892.88 0.55 0.88 -7767.41

1738.02 1.00 10.03 200.48 - - 89.42 32.52 292.19 974.45 848.25 0.01 0.16 -

2000 -1550.71 -6.13 -10.04 218.96 - - -498.70 -150.08 -751.46 2762.13 1361.36 0.56 0.72 -8347.07

594.93 0.84 7.52 68.51 - - 94.95 32.54 149.61 494.35 242.82 0.01 0.24 -

Table A1. Estimates from Unrestricted Tobit-Type Model

Source: Authors.Notes: Estimates were computed both with and without initial values. The estimates shown in this table are those with the sma where the unrestricted parameter was negative.

llest standard errors.

 No restrictions were imposed on the wage parameter. When it was restricted to be nonnegative, convergence was achi* There are no standard errors for the wage estimate in 1984 given convergence problems.

eved with values very close to zero in those years 

 Standard errors are in italics.
43

Year

After-tax 

lnwage

After-tax nonlabor income Age Education

Number of 

kids 0 to 6 

years old

Number of 

kids 6 to 17 

years old

Number of 

kids 0 to 17 

years old

Whether 

kids 

younger 

than 6 years 

old Health Constant σ1 σ2 ρ12 ρ13 ρ23

Log 

likelihood

1983 -1658.44 -11.89 -8.99 119.81 -309.90 -56.78 - - -893.73 3073.16 1129.20 0.55 0.82 0.18 0.07 -4218.4

1511.92 3.01 7.35 104.71 80.42 36.91 - - 489.86 1121.37 681.08 1.04 0.28 0.43 0.41 -

1984* n.d. n.d. n.d. n.d. n.d. n.d. - - n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d.

n.d. n.d. n.d. n.d. n.d. n.d. - - n.d. n.d. n.d. n.d. n.d. n.d. n.d. -

1985 494.19 -6.88 -4.20 -51.20 -179.94 -90.11 - - -156.24 2000.07 711.15 0.51 -0.22 -0.36 -0.55 -5857.3

252.52 2.45 4.33 21.91 59.73 30.15 - - 141.58 329.13 36.10 1.04 0.44 0.40 0.31 -

1986 209.13 -6.15 -1.96 -36.26 -208.73 -68.69 - - -90.75 2189.97 696.92 0.54 0.08 -0.57 -0.80 -6173.8

297.15 1.91 4.48 23.24 49.99 28.10 - - 94.05 299.14 27.88 1.04 0.49 0.36 0.12 -

1987 -148.80 -8.51 -5.73 3.69 -258.27 -76.44 - - -161.98 2475.00 655.11 0.54 0.15 -0.33 -0.49 -6629.9

283.39 2.19 4.59 25.06 63.65 27.07 - - 79.24 283.19 37.04 1.04 0.50 0.51 0.35 -

1988 -146.57 -3.35 -13.91 18.73 -361.36 -111.19 - - -104.96 2417.13 677.25 0.56 0.12 0.09 -0.22 -6375.8

450.63 1.20 4.91 47.76 64.67 27.67 - - 124.18 266.23 36.92 1.03 0.62 0.55 0.48 -

1989 -1072.43 -6.09 4.84 93.34 -268.47 -109.51 - - 13.72 2584.91 1006.44 0.63 0.77 -0.81 -0.75 -6337.2

460.38 1.44 7.18 53.15 46.49 25.90 - - 151.59 352.07 223.94 1.04 0.22 0.16 0.16 -

1990 -444.96 -4.42 -16.60 31.10 -303.24 -115.18 - - -369.99 2973.22 743.28 0.56 0.38 0.28 -0.19 -10901.6

192.86 0.98 3.57 17.63 39.33 20.00 - - 86.75 233.22 48.06 1.02 0.34 0.40 0.40 -

1991 -58.12 -5.97 0.24 -12.41 -135.89 -80.73 - - -12.21 2305.32 714.07 0.59 0.26 -0.63 -0.74 -11713.2

156.39 1.12 3.20 13.51 36.67 19.18 - - 64.16 207.87 30.72 1.03 0.34 0.24 0.13 -

1992 -269.50 -1.21 -0.37 -3.70 -141.33 -93.16 - - -24.08 2588.69 768.74 0.67 0.34 -0.78 -0.65 -11320.8

151.19 0.90 3.57 11.98 39.20 20.80 - - 75.82 252.85 39.95 1.03 0.33 0.16 0.16 -

1993 -802.23 -2.12 2.71 60.08 - - -86.83 -47.68 78.41 2716.92 884.00 0.61 0.62 -0.81 -0.72 -7168.5

243.70 1.11 5.17 27.55 - - 25.37 67.21 107.45 345.10 94.21 1.03 0.26 0.13 0.15 -

1994 -1142.91 -4.91 13.56 108.22 - - -51.32 40.52 13.99 2348.50 1060.64 0.63 0.77 -0.83 -0.77 -7065.7

552.82 1.36 7.01 53.92 - - 24.97 67.34 127.65 466.64 269.58 1.03 0.24 0.13 0.13 -

1995* n.d. n.d. n.d. n.d. - - n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d.

n.d. n.d. n.d. n.d. - - n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. -

1996 -1408.95 -5.98 -7.14 168.59 - - -38.12 -223.91 -308.12 2733.57 1112.09 0.56 0.80 0.22 0.00 -9099.6

518.40 1.38 5.97 60.50 - - 22.26 76.58 142.36 441.88 239.21 1.02 0.19 0.46 0.33 -

1998 -1337.33 -3.02 -7.63 160.12 - - -79.07 -370.40 -398.34 2892.12 1030.30 0.55 0.79 0.12 0.08 -7700.0

755.32 0.87 5.87 86.34 - - 25.39 75.84 147.06 525.22 332.18 1.03 0.24 0.37 0.42 -

2000 -809.40 -4.45 -9.77 98.29 - - -117.37 -335.14 -286.24 3017.30 841.86 0.60 0.57 -0.17 -0.69 -8325.4

259.29 0.80 4.82 32.40 - - 27.22 78.19 109.19 321.11 87.45 1.04 0.28 0.51 0.25 -

 No restrictions were imposed on the wage parameter. When it was restricted to be nonnegative, convergence was achieved with values very close to zero in those years where the unrestricted parameter was negative.

Table A2. Estimates from the Generalized Tobit-Type Model

Source: Authors.Notes: Estimates were computed both with and without initial values. The estimates shown in this table are those with the sma* There were convergence problems in 1984 and 1995.

llest standard errors.

 Standard errors are in italics.
44

 

Year

After-tax 

lnwage

After-tax 

non-labor 

income Age Education

Number of 

kids 0 to 6 

years old

Number of 

kids 6 to 17 

years old

Number of 

kids 0 to 17 

years old

Whether 

kids 

younger 

than 6 

years old Health Residuals Mills Ratio Constant

1983 302.95 -27.49 -8.71 60.24 -614.39 -65.25 - - -871.47 -327.74 1378.48 895.74

264.20 5.01 4.73 29.43 109.65 35.77 - - 231.82 272.87 391.68 485.25

1984 -211.44 -12.39 -0.69 20.66 -234.77 -90.26 - - -3.95 301.04 -65.10 2020.23

356.68 3.40 4.03 28.27 68.27 28.44 - - 127.48 362.00 268.31 419.58

1985 489.03 -8.91 -4.92 -45.06 -214.65 -98.48 - - -190.67 -459.52 -243.68 2001.40

210.27 2.94 4.46 23.09 75.43 29.25 - - 139.82 218.64 232.52 318.99

1986 189.81 -11.93 -9.09 -10.16 -334.13 -100.56 - - -64.69 -123.89 81.55 2179.87

221.13 2.52 5.14 24.34 71.06 29.98 - - 88.18 227.53 260.34 263.84

1987 -47.53 -11.57 -10.89 13.03 -350.45 -92.78 - - -205.08 10.34 174.74 2395.49

219.45 2.37 4.93 22.41 73.57 27.73 - - 80.43 224.48 231.46 261.06

1988 -65.99 -4.09 -17.14 18.94 -419.74 -116.41 - - -136.55 71.42 333.54 2374.70

199.76 1.25 4.87 25.47 72.90 27.58 - - 102.34 204.47 244.02 254.49

1989 -212.68 -11.20 -10.74 48.11 -403.19 -93.80 - - -270.13 244.62 578.35 2102.87

161.76 1.93 4.58 26.74 56.51 24.79 - - 98.03 167.75 268.17 277.36

1990 -281.70 -4.90 -19.13 25.61 -332.04 -131.54 - - -346.44 369.38 550.82 2838.51

132.68 0.99 3.82 16.32 44.29 20.76 - - 79.85 137.35 234.92 206.95

1991 -119.28 -11.17 -6.72 32.98 -267.38 -107.64 - - -55.42 192.50 459.91 2039.88

129.71 1.43 3.26 16.40 43.56 19.29 - - 61.25 134.17 196.91 194.13

1992 -371.61 -3.37 -6.71 32.89 -258.60 -122.22 - - -252.54 281.84 129.68 2477.26

134.55 0.97 3.62 15.92 47.54 20.36 - - 92.11 138.54 197.74 212.87

1993 -560.97 -0.98 3.53 27.36 - - -72.25 -32.07 111.35 462.86 -764.13 2604.08

206.49 1.45 4.39 28.83 - - 27.99 67.92 107.51 210.81 270.43 281.79

1994 -288.38 -7.09 5.69 53.12 - - -68.22 -47.86 -20.75 288.40 150.44 1610.38

180.90 1.70 4.40 25.50 - - 24.49 75.87 87.27 186.68 254.55 275.69

1995 -81.10 -2.64 3.50 11.03 - - -55.49 -62.46 -178.95 179.23 -549.95 1902.23

219.68 1.37 3.85 29.93 - - 21.26 86.96 99.02 222.73 272.21 258.49

1996 -489.81 -4.45 -2.88 52.69 - - -28.11 -175.17 -199.33 651.05 -138.95 2338.96

204.81 1.50 4.49 30.06 - - 21.34 85.08 101.79 208.42 269.85 249.96

1998 -384.66 -3.64 -7.47 59.09 - - -89.75 -418.77 -383.04 502.51 258.92 2318.12

297.60 0.98 4.09 35.80 - - 25.16 92.76 117.07 300.42 249.05 282.44

2000 -500.38 -3.10 -7.89 46.56 - - -74.62 -284.83 -115.97 568.90 -458.79 3000.85

177.74 0.85 4.34 25.40 - - 30.91 75.46 104.60 182.09 321.06 269.42

Source: Authors.

Note: Standard errors are in italics.

Table A3. Estimates from the Two-Step Method
45

Figure A1. Maximum Log-likelihood Values with 

Tobit-type and Generalized Tobit-type Models 

-12,000

-11,000

-10,000

-9,000

-8,000

-7,000

-6,000

-5,000

-4,000

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1998 2000

Tobit

Generalized Tobit
46

Appendix B 

Variable Definitions 

Variable Definition 

age Age at the time of the interview. 

atnonlinc (husband's total taxable income + other family members' taxable 

income - wife's labor income - household's total tax)/1000 

basiceduc 1 if elementary school degree 

educ Years of education. 

fedrate Federal income tax marginal rate 

fedtax Federal income tax payable 

feduccol 1 if father attended to college 

feduchs 1 if father attended to college 

fica Contribution to federal insurance 

ficarate Contribution marginal rate to federal insurance 

h Annual hours of work 

lfp Labor force participation 

lkaw 1 if there was a health condition that limited working (a lot, 

somewhat or just a little). 

lnatwageafta

x 

ln(labor income/h)*(1-mgtotal)) or lnatwage = ln(wage rate(1-

mgtotal)) 

lnunskll ln(Unskilled worker wage rate). 

lnwage Logarithm of wage 

matj 1 if negative local labor market situation (more applicants than jobs 

and many more applicants than jobs) 

meduccol 1 if mother attended to college. 

meduchs 1 if mother attended to high school. 

mgtotal (Federal marginal rate+State marginal rate+(FICA marginal 

rate)/2)/100 

nkid0t17 Number of children 17 years old or younger present in the 

household. 

nkid6t17 Number of children 7 to 17 years old present in the household. 

nkidlt6 Number of children 6 years old and younger present in the 

household. 

nonlinc Income from other family members 

northcen 1 if region is North Central. 

northest 1 if region is Northwest. 

smsa 1 if standard metropolitan statistical area. 

south 1 if region South. 

unemprate County’s unemployment rate 

west 1 if region West. 

whkidt6 Whether there are children 6 years old or younger present in the 

household. 
47

Appendix C 

Estimations using Before-tax Wages and Non-Labor Incomes 

Variable definitions are in Appendix B. 

1986 1988 1991 1994 1999 2001

lnwage 280.37 -249.79 -74.57 -522.90 -1175.63 -716.00

223.71 258.00 160.08 257.25 658.94 239.65

nonlinc -4.05 -2.35 -4.01 -4.35 -1.81 -2.84

1.43 0.97 1.02 1.25 0.73 0.63

age -3.96 -12.52 0.22 5.33 -3.99 -6.58

4.49 4.61 3.37 4.41 6.06 4.49

educ -41.59 33.00 -7.10 88.21 158.45 87.38

17.77 31.63 14.55 38.67 86.83 32.15

nkid1t6 -225.06 -360.60 -125.83 - - -

50.10 61.03 37.84 - - -

nkid6t17 -65.21 -109.61 -76.08 - - -

27.69 27.41 19.27 - - -

nkid0t17 - - - -79.60 -76.53 -97.59

- - - 21.30 25.00 24.26

whkidt6 - - - -69.36 -362.41 -300.36

- - - - 74.55 71.36

lkaw -81.45 -134.13 8.15 -13.61 -432.81 -301.37

89.11 110.57 65.99 93.07 159.14 102.23

cons 2074.83 2412.38 2267.08 1743.31 2892.38 3035.95

276.85 284.70 238.54 261.03 515.41 323.12

sigma1 687.38 697.85 729.65 771.73 1011.30 834.69

134.98 180.81 175.55 254.46 558.00 262.35

sigma2 0.68 0.59 0.69 0.62 0.59 0.57

0.13 0.11 0.11 0.11 0.10 0.09

rho12 0.10 0.27 0.34 0.49 0.78 0.59

0.18 0.20 0.12 0.13 0.06 0.07

rho13 -0.47 0.11 -0.59 0.11 0.19 -0.09

0.14 0.27 0.08 0.25 0.13 0.20

rho23 -0.88 -0.18 -0.86 0.17 0.27 -0.04

0.01 0.27 0.01 0.36 0.14 0.24

Table C1. Estimates of the Generalized Labor Supply Model for Selected Years

Source: Authors.
48

Year

Wage 

Coefficient

Wage 

Elasticity

Nonlabor 

Income 

Coefficient

Nonlabor 

Income 

Elasticity

1986 280.367 0.186 -4.045 -0.102

1988 -249.788 -0.164 -2.347 -0.067

1991 -74.575 -0.046 -4.008 -0.094

1994 -522.902 -0.324 -4.348 -0.122

1999 -1175.626 -0.703 -1.813 -0.065

2001 -716.000 -0.425 -2.163 -0.084

Table C2. Estimated Wage and Nonlabor Income Elasticities 

Source: Authors.
49

 Appendix D 

Descriptive Statistics for the Whole Sample and for Each Year 

Variable definitions are in Appendix B. 

Variable Mean Std. Dev. Min Max

age 40.99 7.88 30 60

atnonlinc* 42.81 26.61 -42 188

basiceduc 0.53 0.50 0 1

educ 13.21 2.43 1 21

fedrate** 22.85 8.17 -40 52

fedtax* 8.49 8.12 -4 102

feduccol 0.12 0.33 0 1

fica* 7.26 3.84 0 29

ficarate** 14.70 2.01 0 15

h 1258.59 878.10 0 4000

lfp 0.79 0.41 0 1

lkaw 0.11 0.31 0 1

lnatwage 1.44 0.92 -2 5

lnwage 1.90 1.11 -1 5

meduccol 0.08 0.27 0 1

meduchs 0.46 0.50 0 1

nkid1t6 0.34 0.65 0 4

nkid6t17 0.97 1.07 0 6

nonlinc* 47.07 27.07 0 150

northcen 0.30 0.46 0 1

northest 0.22 0.41 0 1

south 0.30 0.46 0 1

unemprate (%) 5.82 2.30 1 31

west 0.18 0.38 0 1

1920s 0.04 0.20 0 1

1930s 0.12 0.32 0 1

1940s 0.27 0.45 0 1

1950s 0.44 0.50 0 1

1960s 0.23 0.42 0 1

1970s 0.06 0.23 0 1

Table D1. Summary Statistics: Aggregate Data 1983 to 2000

Source: Authors.

* Thousands of dollars.

** Effective imputed rate.
50

Table D2. Summary Statistics by Year 

Variable Mean Std. Dev. Min Max Variable Mean Std. Dev. Min Max

lfp 0.724 0.447 0.0 1.0 lfp 0.732 0.443 0.0 1.0

h 1062.365 879.284 0.0 3606.0 h 1089.875 874.848 0.0 3232.0

lnatwage 1.076 0.827 0.0 4.3 lnatwage 1.070 0.796 0.0 3.4

atnonlinc 23.632 15.911 0.1 107.0 atnonlinc 24.719 15.551 0.1 105.8

age 40.994 8.715 30.0 60.0 age 40.991 8.866 30.0 60.0

educ 12.955 2.151 3.0 17.0 educ 12.937 2.215 3.0 17.0

lkaw 0.052 0.221 0.0 1.0 lkaw 0.062 0.241 0.0 1.0

nkid1t6 0.340 0.627 0.0 3.0 nkid1t6 0.353 0.659 0.0 3.0

nkid6t17 0.927 1.001 0.0 4.0 nkid6t17 0.937 1.053 0.0 5.0

northest 0.198 0.399 0.0 1.0 northest 0.246 0.431 0.0 1.0

northcen 0.294 0.456 0.0 1.0 northcen 0.304 0.460 0.0 1.0

south 0.260 0.439 0.0 1.0 south 0.318 0.466 0.0 1.0

west 0.245 0.431 0.0 1.0 west 0.129 0.335 0.0 1.0

meduchs 0.469 0.499 0.0 1.0 meduchs 0.479 0.500 0.0 1.0

educ 12.955 2.15128 3.0 17.0 educ 12.937 2.215468 3.0 17.0

meduccol 0.071 0.257 0.0 1.0 meduccol 0.070 0.255 0.0 1.0

feduccol 0.118 0.323 0.0 1.0 feduccol 0.105 0.307 0.0 1.0

fedtax 7298.255 7818.725 -500.0 89379.0 fedtax 7360.409 6847.630 -500.0 69550.0

fica 4249.053 1979.896 0.0 9567.0 fica 4726.790 2108.172 0.0 10584.0

fedrate 25.725 9.373 0.0 44.0 fedrate 25.283 8.447 0.0 45.6

ficarate 13.314 1.074 0.0 13.4 ficarate 13.918 1.067 0.0 14.0

Variable Mean Std. Dev. Min Max Variable Mean Std. Dev. Min Max

lfp 0.735 0.441 0.0 1.0 lfp 0.768 0.423 0.0 1.0

h 1085.957 872.566 0.0 3430.0 h 1178.306 879.733 0.0 3568.0

lnatwage 1.118 0.809 0.0 4.3 lnatwage 1.211 0.809 0.0 3.3

atnonlinc 25.625 15.924 0.1 103.2 atnonlinc 26.081 15.948 0.0 98.3

age 40.753 8.764 30.0 60.0 age 40.590 8.464 30.0 60.0

educ 13.111 2.239 3.0 17.0 educ 13.336 2.361 5.0 21.0

lkaw 0.068 0.251 0.0 1.0 lkaw 0.094 0.292 0.0 1.0

nkid1t6 0.351 0.664 0.0 4.0 nkid1t6 0.370 0.695 0.0 4.0

nkid6t17 0.967 1.045 0.0 5.0 nkid6t17 0.941 1.039 0.0 5.0

northest 0.245 0.430 0.0 1.0 northest 0.184 0.388 0.0 1.0

northcen 0.333 0.472 0.0 1.0 northcen 0.345 0.476 0.0 1.0

south 0.298 0.458 0.0 1.0 south 0.271 0.445 0.0 1.0

west 0.117 0.321 0.0 1.0 west 0.197 0.398 0.0 1.0

meduchs 0.487 0.500 0.0 1.0 meduchs 0.516 0.500 0.0 1.0

educ 13.111 2.239062 3.0 17.0 educ 13.336 2.361062 5.0 21.0

meduccol 0.080 0.272 0.0 1.0 meduccol 0.092 0.289 0.0 1.0

feduccol 0.106 0.308 0.0 1.0 feduccol 0.137 0.344 0.0 1.0

fedtax 7606.915 7123.363 -512.0 59725.0 fedtax 7900.812 7289.652 0.0 66679.0

fica 4855.936 2306.297 0.0 11167.0 fica 5274.962 2503.109 0.0 12012.0

fedrate 24.854 9.113 0.0 45.9 fedrate 24.536 9.685 -10.0 46.8

ficarate 14.018 1.074 0.0 14.1 ficarate 14.199 1.196 0.0 14.3

Variable Mean Std. Dev. Min Max Variable Mean Std. Dev. Min Max

lfp 0.779 0.415 0.0 1.0 lfp 0.794 0.405 0.0 1.0

h 1222.205 878.525 0.0 3556.0 h 1219.559 873.583 0.0 3710.0

lnatwage 1.296 0.852 0.0 4.1 lnatwage 1.331 0.879 0.0 4.0

atnonlinc 29.125 17.366 0.4 108.8 atnonlinc 43.437 21.652 0.3 138.8

age 40.606 8.159 30.0 60.0 age 40.853 8.145 30.0 60.0

educ 13.271 2.207 5.0 17.0 educ 13.391 2.388 5.0 21.0

lkaw 0.143 0.350 0.0 1.0 lkaw 0.136 0.343 0.0 1.0

nkid1t6 0.353 0.668 0.0 3.0 nkid1t6 0.330 0.634 0.0 3.0

nkid6t17 0.960 1.041 0.0 5.0 nkid6t17 0.933 1.068 0.0 5.0

northest 0.237 0.426 0.0 1.0 northest 0.298 0.457 0.0 1.0

northcen 0.355 0.479 0.0 1.0 northcen 0.262 0.440 0.0 1.0

south 0.220 0.414 0.0 1.0 south 0.248 0.432 0.0 1.0

west 0.185 0.389 0.0 1.0 west 0.189 0.392 0.0 1.0

meduchs 0.525 0.500 0.0 1.0 meduchs 0.532 0.499 0.0 1.0

educ 13.271 2.207335 5.0 17.0 educ 13.391 2.388409 5.0 21.0

meduccol 0.093 0.291 0.0 1.0 meduccol 0.095 0.293 0.0 1.0

feduccol 0.132 0.339 0.0 1.0 feduccol 0.131 0.337 0.0 1.0

fedtax 7566.868 7335.532 -820.0 45584.0 fedtax 7285.477 6882.240 -874.0 44859.0

fica 5741.359 2522.265 0.0 12526.0 fica 6124.515 2809.093 0.0 13517.0

fedrate 24.018 9.323 0.0 39.3 fedrate 22.043 8.031 0.0 33.0

ficarate 14.161 1.406 0.0 14.3 ficarate 14.872 1.486 0.0 15.0

1988

1985 1986

1987

1983 1984
51

Variable Mean Std. Dev. Min Max Variable Mean Std. Dev. Min Max

lfp 0.815 0.389 0.0 1.0 lfp 0.773 0.419 0.0 1.0

h 1233.151 846.065 0.0 3840.0 h 1236.875 896.367 0.0 4000.0

lnatwage 1.448 0.886 0.0 4.0 lnatwage 1.323 0.876 0.0 3.8

atnonlinc 30.665 18.906 0.4 106.1 atnonlinc 48.632 30.283 0.1 188.3

age 40.232 7.821 30.0 60.0 age 41.008 8.147 30.0 60.0

educ 13.378 2.173 5.0 17.0 educ 12.552 3.153 1.0 21.0

lkaw 0.100 0.300 0.0 1.0 lkaw 0.122 0.327 0.0 1.0

nkid1t6 0.337 0.643 0.0 3.0 nkid1t6 0.344 0.645 0.0 3.0

nkid6t17 0.969 1.057 0.0 5.0 nkid6t17 1.020 1.129 0.0 6.0

northest 0.298 0.458 0.0 1.0 northest 0.172 0.378 0.0 1.0

northcen 0.287 0.453 0.0 1.0 northcen 0.250 0.433 0.0 1.0

south 0.242 0.429 0.0 1.0 south 0.363 0.481 0.0 1.0

west 0.167 0.374 0.0 1.0 west 0.214 0.410 0.0 1.0

meduchs 0.555 0.497 0.0 1.0 meduchs 0.460 0.499 0.0 1.0

educ 13.378 2.17266 5.0 17.0 educ 12.552 3.152642 1.0 21.0

meduccol 0.097 0.297 0.0 1.0 meduccol 0.078 0.268 0.0 1.0

feduccol 0.135 0.342 0.0 1.0 feduccol 0.119 0.324 0.0 1.0

fedtax 7636.119 7310.315 -910.0 52912.0 fedtax 6562.172 6824.522 -953.0 57074.0

fica 6376.342 3005.572 0.0 14419.0 fica 6193.675 3238.133 0.0 15697.0

fedrate 22.213 7.994 0.0 33.0 fedrate 20.576 7.964 0.0 33.0

ficarate 11.791 6.174 0.0 15.0 ficarate 15.204 1.211 0.0 15.3

Variable Mean Std. Dev. Min Max Variable Mean Std. Dev. Min Max

lfp 0.809 0.393 0.0 1.0 lfp 0.769 0.421 0.0 1.0

h 1308.296 879.471 0.0 3984.0 h 1225.528 898.435 0.0 3765.0

lnatwage 1.458 0.888 0.0 4.4 lnatwage 1.463 0.981 0.0 4.5

atnonlinc 29.005 19.692 -42.1 108.6 atnonlinc 46.672 24.445 0.4 166.4

age 40.898 8.045 30.0 60.0 age 40.901 7.741 30.0 60.0

educ 12.964 2.707 5.0 21.0 educ 12.845 2.999 1.0 21.0

lkaw 0.107 0.309 0.0 1.0 lkaw 0.113 0.316 0.0 1.0

nkid1t6 0.323 0.638 0.0 4.0 nkid1t6 0.360 0.662 0.0 4.0

nkid6t17 0.972 1.083 0.0 6.0 nkid6t17 1.033 1.112 0.0 6.0

northest 0.189 0.392 0.0 1.0 northest 0.190 0.392 0.0 1.0

northcen 0.260 0.439 0.0 1.0 northcen 0.260 0.439 0.0 1.0

south 0.349 0.477 0.0 1.0 south 0.346 0.476 0.0 1.0

west 0.199 0.399 0.0 1.0 west 0.205 0.404 0.0 1.0

meduchs 0.492 0.500 0.0 1.0 meduchs 0.501 0.500 0.0 1.0

educ 12.964 2.707448 5.0 21.0 educ 12.845 2.999375 1.0 21.0

meduccol 0.086 0.280 0.0 1.0 meduccol 0.090 0.287 0.0 1.0

feduccol 0.131 0.338 0.0 1.0 feduccol 0.135 0.342 0.0 1.0

fedtax 6664.983 6929.807 -1235.0 61549.0 fedtax 7901.779 7793.148 -1384.0 72696.0

fica 6789.175 3553.104 0.0 19080.0 fica 7476.242 3623.971 15.0 20491.0

fedrate 20.303 8.182 0.0 36.7 fedrate 21.196 7.487 0.0 31.9

ficarate 15.193 1.147 2.9 15.3 ficarate 15.177 1.227 2.9 15.3

Variable Mean Std. Dev. Min Max Variable Mean Std. Dev. Min Max

lfp 0.806 0.396 0.0 1.0 lfp 0.836 0.371 0.0 1.0

h 1301.162 864.112 0.0 3854.0 h 1337.704 838.554 0.0 3822.0

lnatwage 1.583 0.940 0.0 4.3 lnatwage 1.615 0.919 -0.4 4.6

atnonlinc 49.360 23.133 0.7 143.2 atnonlinc 58.000 27.828 1.3 146.7

age 40.098 6.949 30.0 60.0 age 40.303 7.195 30.0 60.0

educ 13.472 2.171 5.0 21.0 educ 13.417 2.083 5.0 18.0

lkaw 0.106 0.308 0.0 1.0 lkaw 0.096 0.294 0.0 1.0

whkidt6 0.268 0.443 0.0 1.0 whkidt6 0.256 0.436 0.0 1.0

nkid0t17 1.389 1.180 0.0 5.0 nkid0t17 1.356 1.194 0.0 6.0

northest 0.200 0.400 0.0 1.0 northest 0.193 0.395 0.0 1.0

northcen 0.313 0.464 0.0 1.0 northcen 0.334 0.472 0.0 1.0

south 0.297 0.457 0.0 1.0 south 0.284 0.451 0.0 1.0

west 0.191 0.393 0.0 1.0 west 0.157 0.364 0.0 1.0

meduchs 0.600 0.490 0.0 1.0 meduchs 0.589 0.492 0.0 1.0

educ 13.472 2.170649 5.0 21.0 educ 13.417 2.083379 5.0 18.0

meduccol 0.104 0.305 0.0 1.0 meduccol 0.116 0.320 0.0 1.0

feduccol 0.164 0.370 0.0 1.0 feduccol 0.169 0.375 0.0 1.0

fedtax 9660.294 8915.409 -1511.0 60373.0 fedtax 9378.040 8000.635 -2528.0 59926.0

fica 8310.889 3468.592 76.0 20084.0 fica 8575.335 3607.615 687.0 20829.0

fedrate 22.941 7.290 0.0 44.1 fedrate 22.851 6.948 0.0 44.2

ficarate 15.180 1.217 2.9 15.3 ficarate 15.204 1.085 2.9 15.3

1994

1989 1990

1991 1992

1993
52

Variable Mean Std. Dev. Min Max Variable Mean Std. Dev. Min Max

lfp 0.812 0.391 0.0 1.0 lfp 0.813 0.390 0.0 1.0

h 1318.374 850.871 0.0 3950.0 h 1327.015 880.307 0.0 3920.0

lnatwage 1.558 0.922 0.0 4.1 lnatwage 1.605 0.944 0.0 4.3

atnonlinc 50.846 24.644 0.6 161.7 atnonlinc 52.319 24.701 1.5 152.0

age 40.584 7.180 30.0 60.0 age 40.853 7.356 30.0 60.0

educ 13.331 2.052 5.0 17.0 educ 13.429 2.118 5.0 17.0

lkaw 0.119 0.324 0.0 1.0 lkaw 0.122 0.327 0.0 1.0

whkidt6 0.255 0.436 0.0 1.0 whkidt6 0.246 0.431 0.0 1.0

nkid0t17 1.320 1.182 0.0 6.0 nkid0t17 1.258 1.161 0.0 6.0

northest 0.209 0.407 0.0 1.0 northest 0.210 0.407 0.0 1.0

northcen 0.330 0.470 0.0 1.0 northcen 0.315 0.465 0.0 1.0

south 0.287 0.452 0.0 1.0 south 0.300 0.458 0.0 1.0

west 0.174 0.379 0.0 1.0 west 0.176 0.381 0.0 1.0

meduchs 0.010 0.100 0.0 1.0 meduchs 0.013 0.115 0.0 1.0

educ 13.331 2.051748 5.0 17.0 educ 13.429 2.117656 5.0 17.0

meduccol 0.002 0.041 0.0 1.0 meduccol 0.005 0.071 0.0 1.0

feduccol 0.005 0.071 0.0 1.0 feduccol 0.008 0.087 0.0 1.0

fedtax 9755.809 9189.152 -2968.0 62655.0 fedtax 10238.230 9111.899 -3556.0 58243.0

fica 8573.605 3845.917 260.0 21122.0 fica 8909.821 3905.548 91.0 21349.0

fedrate 22.951 7.295 0.0 42.6 fedrate 23.330 7.355 0.0 41.9

ficarate 15.205 1.080 2.9 15.3 ficarate 15.23737 0.8793717 2.9 15.3

Variable Mean Std. Dev. Min Max Variable Mean Std. Dev. Min Max

lfp 0.842 0.365 0.0 1.0 lfp 0.838 0.369 0.0 1.0

h 1407.417 855.874 0.0 3904.0 h 1413.684 869.846 0.0 4000.0

lnatwage 1.721 0.923 -0.2 3.6 lnatwage 1.809 0.964 -1.5 4.1

atnonlinc 60.828 26.847 6.4 164.8 atnonlinc 64.527 28.209 7.5 167.6

age 42.372 7.035 30.0 60.0 age 43.265 7.248 30.0 60.0

educ 13.634 2.052 5.0 17.0 educ 13.723 2.051 8.0 17.0

lkaw 0.135 0.342 0.0 1.0 lkaw 0.130 0.336 0.0 1.0

whkidt6 0.214 0.410 0.0 1.0 whkidt6 0.184 0.387 0.0 1.0

nkid0t17 1.204 1.141 0.0 6.0 nkid0t17 1.137 1.144 0.0 7.0

northest 0.191 0.394 0.0 1.0 northest 0.195 0.397 0.0 1.0

northcen 0.359 0.480 0.0 1.0 northcen 0.345 0.476 0.0 1.0

south 0.283 0.451 0.0 1.0 south 0.278 0.448 0.0 1.0

west 0.164 0.371 0.0 1.0 west 0.180 0.384 0.0 1.0

meduchs 0.690 0.463 0.0 1.0 meduchs 0.679 0.467 0.0 1.0

educ 13.634 2.052219 5.0 17.0 educ 13.723 2.051424 8.0 17.0

meduccol 0.092 0.289 0.0 1.0 meduccol 0.104 0.306 0.0 1.0

feduccol 0.134 0.341 0.0 1.0 feduccol 0.141 0.349 0.0 1.0

fedtax 10619.130 8498.126 -3756.0 66801.0 fedtax 11969.060 10005.250 -3888.0 101645.0

fica 10064.530 4083.007 0.0 22473.0 fica 10946.590 4656.959 918.0 28612.0

fedrate 23.151 8.041 -40.0 39.2 fedrate 23.976 6.879 0.0 51.8

ficarate 15.210 1.052 2.9 15.3 ficarate 15.117 1.495 2.9 15.3

2000

1996

1998

1995
53

Appendix E 

Reduced-Form Estimation 

This appendix presents reduced-form estimates for the difference-in-differences approach. The 

first row in each table shows the group effect, defined by cohort and education level, while the 

first column illustrates the time effect. Each cell represents the interaction effect of the 

corresponding group and year. Some of cells are empty because of multicollinearity or because 

the number of observations in those cells is too small (i.e. less than 45). The base year is 1983. 

Demographic variables such as health, parents’ education, regional dummies, children dummy 

variables, and local unemployment rates are included in each reduced-form estimation. Tables 

E1 to E3 display results for all years and all cohort groups. Estimation results for subsamples 

(1983-1989 only, 1990-2000 only, younger cohorts only, and older cohorts only) will be 

provided upon request. 

The strength of the instruments is a relevant question here. The problem of weak instruments has 

been treated in theoretical and empirical work, including the well-known Angrist and Krueger 

(1991) study of the returns to schooling using quarter of birth as an instrument (the problem of 

their instruments was raised by Bound, et al. (1996)). Standard asymptotic theory can be 

misleading when the instruments are weak as pointed by Nelson and Startz (1990a, b) and 

Staiger and Stock (1997) among others. 

The results presented here suggest that all of the first-stage estimations are statistically valid. All 

of the regressions show high R2 values of over 80 percent, much greater than the guideline 

commonly used, as suggested by Staiger and Stock (1997). 
54

Time 

Effects <1940 1940-1949 1950-1959 1960+ <1940 1940-1949 1950-1959 1960+

Group Effects 1.439 1.510 1.439 1.340 1.661 1.686 1.676 1.642

0.054 0.064 0.080 0.132 0.065 0.062 0.081 0.190

year=84 0.079 -0.148 -0.140 - - -0.143 -0.048 -0.138 -

0.094 0.116 0.120 - - 0.133 0.122 0.134 -

year=85 -0.025 0.004 0.100 0.071 - -0.023 0.045 - -

0.093 0.119 0.123 0.132 - 0.134 0.121 - -

year=86 -0.018 0.150 0.066 0.120 - 0.038 0.176 - -

0.089 0.116 0.118 0.126 - 0.133 0.117 - -

year=87 0.162 0.027 -0.090 0.043 - - -0.011 -0.029 -

0.101 0.124 0.128 0.135 - - 0.119 0.134 -

year=88 0.239 -0.130 -0.159 -0.141 - - - -0.078 -

0.067 0.102 0.104 0.110 - -- 0.110 -

year=89 0.313 -0.121 -0.180 -0.113 - - 0.040 -0.055 -

0.131 0.155 0.155 0.158 - - 0.146 0.157 -

year=90 0.110 0.065 0.052 0.090 - 0.106 0.220 0.145 -

0.161 0.166 0.176 0.180 - 0.185 0.174 0.181 -

year=91 0.514 -0.325 -0.247 -0.247 -0.369 - -0.112 -0.143 -0.182

0.105 0.124 0.127 0.133 0.174 - 0.120 0.133 0.219

year=92 0.612 -0.335 -0.219 -0.222 -0.191 - -0.124 -0.205 -0.172

0.116 0.137 0.136 0.142 0.177 - 0.129 0.142 0.222

year=93 0.400 - 0.002 0.047 - - 0.064 0.093 0.102

0.109 - 0.136 0.139 - - 0.132 0.139 0.164

year=94 0.362 - 0.003 0.087 -0.061 - 0.126 0.096 0.075

0.114 - 0.140 0.143 0.172 - 0.137 0.142 0.218

year=95 0.395 - -0.025 0.061 0.033 - 0.109 0.142 0.228

0.109 - 0.135 0.138 0.165 - 0.132 0.138 0.213

year=96 0.477 - -0.113 -0.009 0.069 - 0.065 0.115 0.162

0.132 - 0.157 0.157 0.181 - 0.150 0.157 0.225

year=98 1.172 - -0.840 -0.663 -0.644 - -0.696 -0.639 -0.629

0.560 - 0.567 0.567 0.573 - 0.566 0.566 0.589

year=00 0.583 - -0.025 - 0.031 - 0.037 0.066 0.031

0.088 - 0.133 - 0.163 - 0.121 0.122 0.211

health -0.093

0.017

Regional Dummies Parents' Education

northest 0.074 meduchs 0.051

0.016 0.014

northcen -0.090 feduchs 0.055

0.015 0.013

south -0.043 meduccol 0.088

0.015 0.023

unemprate -0.008 feduccol 0.121

0.003 0.020

Youngest Child <6 -0.031

0.016

Youngest Child 6-17 -0.099

0.013

Table E1. Estimates of the Reduced-Form Wage Equation

Source: Authors.

Other Coefficients

 Missing cells are due to multicollinearity and a small number of observations (< 45).

Notes: The adjusted R-squared is 0.916.

Up to High School More than High School
55

Time 

Effects <1940 1940-1949 1950-1959 1960+ <1940 1940-1949 1950-1959 1960+

Group Effects 26.083 19.804 17.255 14.839 28.087 22.566 16.792 29.713

1.776 2.125 2.672 4.428 2.268 2.158 2.656 6.483

year=84 -0.183 0.204 3.875 - - 1.009 0.498 1.194 -

3.138 3.820 4.019 4.606 4.194 4.436

year=85 2.691 -0.588 0.996 -2.103 - -0.522 -2.148 - -

3.050 3.830 4.055 4.370 4.568 4.099

year=86 3.785 -3.074 -0.083 -2.228 - -0.783 -2.294 - -

2.941 3.778 3.949 4.228 4.546 3.985

year=87 5.775 -1.556 3.184 -3.643 - - 0.600 0.587 -

3.550 4.162 4.408 4.644 4.203 4.574

year=88 23.953 -10.785 -2.656 -9.871 - - - -1.118 -

2.358 3.395 3.559 3.803 3.716

year=89 8.591 -4.304 1.282 -4.603 - - 0.720 -1.030 -

4.519 5.212 5.322 5.410 5.083 5.333

year=90 16.202 0.109 12.498 4.443 - 12.882 19.759 18.972 -

5.308 5.415 5.799 5.979 6.176 5.817 5.975

year=91 5.917 -1.715 5.477 0.016 -0.164 - 3.938 4.032 -13.957

3.743 4.265 4.439 4.643 5.960 4.269 4.624 7.594

year=92 29.681 -16.238 -2.889 -7.983 -10.579 - 4.300 3.572 -17.214

3.944 4.531 4.610 4.810 5.922 4.456 4.794 7.583

year=93 19.123 - 10.012 5.762 - - 11.178 15.883 -6.373

3.579 4.507 4.611 4.471 4.573 5.701

year=94 27.033 - 11.251 6.590 1.571 - 12.587 14.889 -3.569

3.647 4.616 4.682 5.693 4.577 4.639 7.357

year=95 16.882 - 13.168 14.240 7.499 - 23.428 25.642 7.043

3.463 4.385 4.476 5.439 4.371 4.451 7.176

year=96 14.140 - 14.070 19.701 14.562 - 22.795 29.579 13.344

3.907 4.759 4.838 5.704 4.704 4.817 7.375

year=98 18.861 - 18.890 17.531 7.967 - 23.355 28.082 8.356

15.514 15.819 15.797 16.062 15.782 15.772 16.724

year=00 38.321 - 0.678 - -6.739 - 6.560 13.076 -8.319

3.016 4.483 5.496 4.198 4.119 7.197

health -3.798

0.558

Regional Dummies Parents' Education

northest 5.425 meduchs 2.547

0.554 0.484

northcen 0.298 feduchs 3.638

0.518 0.473

south -2.122 meduccol 5.126

0.517 0.827

feduccol 7.109

unemprate -0.489 0.703

0.087

Youngest Child <6 1.902

0.557

Youngest Child 6-17 1.789

0.457

 Missing cells are due to multicollinearity and a small number of observations (< 45).

Up to High School More than High School

Table E2. Estimates of the Reduced-Form for Non-Labor Income

Source: Authors.

Other Coefficients

Notes: The adjusted R-squared is 0.916.
56

Time 

Effects <1940 1940-1949 1950-1959 1960+ <1940 1940-1949 1950-1959 1960+

Group Effects 0.617 0.851 1.050 1.187 1.114 1.232 0.996 1.904

0.109 0.132 0.168 0.277 0.152 0.144 0.164 0.435

year=84 -0.002 -0.105 0.101 - - -0.016 0.005 0.058 -

0.196 0.235 0.250 0.303 0.273 0.274

year=85 0.058 -0.233 -0.042 -0.116 - -0.140 0.058 - -

0.187 0.233 0.250 0.271 0.295 0.268

year=86 0.348 -0.409 -0.183 -0.182 - -0.476 -0.364 - -

0.185 0.233 0.249 0.268 0.295 0.261

year=87 -0.171 0.011 0.307 0.412 - - 0.243 0.364 -

0.232 0.265 0.285 0.302 0.283 0.294

year=88 -0.029 -0.023 0.093 0.384 - - - 0.295 -

0.160 0.216 0.231 0.253 0.241

year=89 -0.336 0.210 0.460 0.480 - - 0.652 0.684 -

0.289 0.327 0.340 0.345 0.345 0.340

year=90 -0.241 0.094 0.194 0.429 - -0.073 0.140 0.658 -

0.326 0.331 0.357 0.370 0.384 0.365 0.369

year=91 0.040 -0.043 0.004 0.276 -0.133 - 0.020 0.416 -0.384

0.255 0.281 0.295 0.309 0.384 0.293 0.307 0.518

year=92 -0.273 0.161 0.278 0.458 -0.062 - 0.273 0.584 -0.209

0.253 0.284 0.293 0.307 0.372 0.291 0.305 0.504

year=93 0.006 - 0.072 0.133 - - 0.049 0.258 -0.642

0.218 0.278 0.286 0.289 0.282 0.394

year=94 -0.130 - 0.392 0.292 0.214 - 0.155 0.651 -0.525

0.220 0.288 0.290 0.355 0.296 0.290 0.484

year=95 -0.170 - 0.246 0.314 0.246 - 0.248 0.535 -0.342

0.207 0.267 0.274 0.336 0.280 0.272 0.473

year=96 -0.365 - 0.107 0.482 0.504 - 0.500 0.845 -0.071

0.237 0.288 0.298 0.354 0.304 0.298 0.485

year=98 -0.390 - 0.365 0.781 0.395 - 0.413 0.897 -0.291

0.931 0.951 0.953 0.968 0.954 0.950 1.022

year=00 0.144 - -0.299 - -0.138 - -0.297 0.201 -0.883

0.197 0.284 0.351 0.281 0.269 0.480

health -0.442

0.035

Regional Dummies Parents' Education

northest 0.037 meduchs 0.081

0.037 0.032

northcen 0.105 feduchs 0.029

0.035 0.032

south 0.033 meduccol 0.048

0.034 0.057

unemprate -0.029 feduccol 0.040

0.006 0.048

Youngest Child <6 -0.526

0.038

Youngest Child 6-17 -0.067

0.032

 Missing cells are due to multicollinearity and a small number of observations (< 45).

Up to High School More than High School

Table E3. Estimates of the Reduced-Form of the Participation Probit

Source: Authors.

Other Coefficients

Notes: The adjusted R-squared is 0.916.
57

Appendix F 

Computation of the Standard Errors 

The model we consider for the two-step method and difference-in-difference estimation has the 

form: 

1

'

K k

i ii k i

k

yx z β δ υ

=

= + + ∑ $ , 

where i denotes individuals (with the sample size n ), i x contains all the regressors of the model 

including the time and the group dummies for the difference-in-difference estimation, and 

1

( )'

K

zz z ii i = $$ $ K is the vector of estimated residuals and/or the inverse Mill’s ratio used as 

correction terms. Let the k-th estimated correction term be defined as $ ( ')

k k

i k i k z sm = γ $ for a 

smooth function of ( ) k s ⋅ and $

k γ be the 1 k q × vector of coefficients in the k-th reduced form. 

Finally, denote ˆ ( ' ')' i Qxz i i = $ and ( ' ')' Qxz i ii = , where i z represents the residuals evaluated 

at the true parameter estimates, thus we can write ( ' ) k k

i kik z sm = γ . 

Here we assume: 

Assumption F1: k

k

n

p

n

→ with 0 1 k < < p as k n → ∞ and n → ∞ for 1, , k K = K . 

Assumption F2: 

1 1

1 1 ˆ ˆ lim ' lim '

n n

ii ii n n i i

p QQ p QQ →∞ →∞ n n = =

∑ ∑ = and 

1 1

1 1 ˆ ˆ lim ' lim '

n n k k

ii ii n n i i

p Qp Q →∞ →∞ n n = =

∑ ∑ Γ = Γ , 1, , k K = K . 

Assumption F3: $ 2 2

1

1 ˆ ˆ lim ' '

n

i ii i ii n i

p QQ E QQ

n

υ υ →∞ =

= ⎡ ⎤ ∑ ⎣ ⎦ and ( )< ∞

2

E υiQi . 

Assumption F4: $

( ) (0, ) d

kk k k n N γ γ − ⎯⎯→ Ω and ˆ (1) k kp Ω =Ω + o , 
58

where ˆ k Γi ( k Γi ) denotes the derivative of $ ( ') k

k i k s m γ ( ( ') k

kik s m γ ) with respect to k γ , 

respectively. 

Assumption F1 is clearly satisfied in our model. Assumption F2 through F4 can be justified 

under some regularity conditions as usual. Now let Qˆ represent the entire sample for the x and 

zˆ variables and define ˆ k Γ to be the k n q × matrix whose i-th row is given by the derivative of 

$ ( ') k

k i k s m γ with respect to ' k γ . Finally, let 1 ( ' )' θ = βδ δ K K and then given Assumptions 

F1-F4, we can estimate the asymptotic covariance of $

θ as: 

 $ $ $ 2 2 1 1

1 1

ˆ ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ ˆ ˆ () ( ' ) ' ' ' ( ' )

n K

k k k

i k i i

i k k

V Q Q QQ Q Q Q Q

n

θ υδ − −

= =

⎡ ⎤ Ω = + ΓΓ ⎢ ⎥ ⎣ ⎦ ∑ ∑ , (FE1) 

where ˆ k

k n

Ω is the asymptotic variance of $

k γ . 

Here, we note that the covariance matrix is robust to possible heteroskedasticity and corrects for 

the effects of estimated correction terms. In this formula, we ignore the covariance of the 

reduced form coefficients $

k γ across the 1, , k K = K reduced forms, for computational simplicity, 

as Blundell et al. (1998) did. We also note that if the absolute values of $

δ k ’s are small, then the 

usual standard errors formula without correction will give us very similar results with the 

corrected standard errors based on (FE1). 

 Practically we can decompose (FE1) into two parts: 
59

$ $

2 1 1

1

1

ˆ ˆ ˆˆ ˆ ˆ () ( ' ) '( ' )

n

i i i

i

V Q Q QQ Q Q θ υ − −

=

⎡ ⎤ = ⎢ ⎥ ⎣ ⎦ ∑ and 

$ $

2 1 1

2

1

ˆ ˆˆ ˆ ˆ ˆˆ ˆ ˆ () ( ' ) ' ' ( ' )

K

k k k

k

k k

V QQ Q Q QQ

n

θ δ − −

=

⎡ ⎤ Ω = ΓΓ ⎢ ⎥ ⎣ ⎦ ∑ . 

$

1 V ( ) θ is the covariance matrix that one will obtain using “robust” option in STATA. $ 2 V ( ) θ

requires a separate STATA programming, which could be cumbersome. Thanks to Hardin (2002) 

we can overcome this computational burden. The authors would like to thank James W. Hardin 

for providing us a copy of his paper, Hardin (2002). 

Table F1 illustrates how much a usual inference without correction for the estimated 

residuals and estimated inverse Mill’s ratio underestimates the standard errors. For comparison, 

we present three alternative standard errors for the models considered in Table 9; under 

homoskedasticity assumption (HOM S.E.), heteroskedasticity robust ones (HET S.E.), and twostep estimation robust ones (TSE S.E.) based on (FE1). For example, in the subsample estimation 

of 1983-1989, standard errors of wage effects are underestimated around 4 percent under the 

homoskedasticity assumption without correction, if compared to the corrected ones; while in the 

subsample of 1990-2000, standard errors of wage effects are underestimated around 14 percent. 
60

COEF. HOM S.E. HET S.E. TSE S.E. COEF. HOM S.E. HET S.E. TSE S.E. COEF. HOM S.E. HET S.E. TSE S.E. COEF. HOM S.E. HET S.E. TSE S.E. COEF. HOM S.E. HET S.E. TSE S.E.

1940s and Basic Educ 60.540 60.243 61.376 63.498 121.343 47.663 51.490 55.624 54.905 35.051 35.966 38.724 166.096 48.020 48.368 50.400 - - - -1950s and Basic Educ -14.273 92.864 95.379 98.532 138.588 62.458 66.234 71.505 41.578 50.221 51.909 55.670 - - - - - - - -1960s+ and Basic Educ - - - - -12.547 65.854 70.644 76.209 -88.439 57.364 60.235 64.547 - - - - -161.987 29.977 30.512 52.942<1940 and Higher Educ 15.827 72.548 74.200 76.755 185.069 80.634 84.566 91.817 49.235 49.352 50.844 54.784 112.105 68.355 69.173 72.146 - - - -1940s and Higher Educ -31.451 100.042 99.749 103.332 161.529 71.248 74.359 80.562 31.273 55.211 55.924 60.229 133.329 86.405 85.663 89.365 - - - -1950s and Higher Educ -57.189 103.072 104.091 107.693 183.692 75.997 79.194 85.794 42.252 57.804 59.019 63.482 - - - - 51.134 31.499 30.582 51.7181960s+ and Higher Educ - - - - 195.416 79.905 83.936 90.852 82.322 64.869 66.479 71.475 - - - - 74.347 38.543 38.334 57.760year=84 48.256 41.037 41.040 42.573 - - - - 26.619 40.389 41.166 44.521 47.807 47.190 48.750 50.873 49.585 78.008 78.168 85.286year=85 49.038 41.982 42.263 43.811 - - - - 29.860 41.049 41.740 45.136 25.606 48.540 49.775 51.957 66.370 76.915 77.610 84.569year=86 93.105 41.867 41.843 43.379 - - - - 79.958 40.390 41.241 44.543 57.319 49.384 50.301 52.531 144.757 75.353 76.817 83.498year=87 158.879 46.195 45.379 47.106 - - - - 138.261 41.407 41.765 45.173 120.721 51.322 50.227 52.607 221.736 76.187 78.220 84.866year=88 357.757 84.628 85.886 88.940 - - - - 197.588 47.121 48.951 52.718 179.669 63.315 65.055 67.879 288.464 80.299 82.393 89.409year=89 128.995 53.047 52.536 54.517 - - - - 111.329 44.468 44.775 48.404 77.315 59.530 59.751 62.419 211.104 77.588 77.930 84.876year=90 - - - - - - - - 317.372 50.273 51.344 55.427 217.501 73.190 74.599 77.828 439.205 81.946 82.439 89.855year=91 - - - - -98.543 56.198 57.734 62.786 205.487 41.967 42.419 45.858 125.360 56.453 57.958 60.468 322.787 75.352 75.684 82.366year=92 - - - - 37.915 34.936 35.909 39.067 342.481 48.075 49.553 53.416 202.281 68.496 71.056 74.064 467.767 79.233 80.670 87.699year=93 - - - - 80.191 39.847 40.042 43.707 380.766 51.795 52.599 56.812 266.549 73.577 72.733 76.104 521.840 83.447 84.871 92.273year=94 - - - - 91.215 34.285 34.392 37.556 391.618 58.351 59.633 64.333 314.023 84.671 85.362 89.168 530.595 91.143 92.195 100.363year=95 - - - - 89.989 34.028 33.103 36.322 393.120 52.328 53.126 57.388 257.614 74.973 74.248 77.697 541.478 84.238 85.248 92.785year=96 - - - - 110.404 35.794 36.015 39.300 408.986 53.938 54.845 59.214 117.675 78.194 79.506 82.931 593.868 87.132 87.768 95.606year=98 - - - - 189.639 38.265 37.998 41.513 480.836 61.647 62.617 67.582 359.739 95.666 94.835 99.175 643.581 95.038 96.101 104.536year=00 - - - - 257.312 42.882 43.152 47.085 541.940 65.638 66.769 72.051 218.169 104.227 107.942 112.479 727.828 98.659 99.690 108.476

Youngest Child 0-6 -163.212 115.569 135.008 136.534 -73.202 70.686 84.242 85.713 -161.608 58.819 69.238 70.664 -272.150 137.666 182.110 183.272 -264.322 80.810 92.952 94.864Youngest Child 6-17 -8.864 80.020 94.015 94.637 -205.468 60.010 70.087 70.955 -139.720 45.575 53.205 53.889 -73.802 61.834 73.199 73.662 -245.868 73.114 84.007 85.032

Health -121.163 49.063 52.282 53.926 -137.373 34.454 36.239 39.292 -118.118 28.977 30.579 32.811 -219.407 50.146 50.986 53.081 -175.524 37.752 40.026 43.175

No Children 138.297 173.441 174.018 180.280 -294.739 113.207 119.350 129.135 -205.731 87.992 91.269 98.004 198.578 126.072 131.676 136.992 -379.690 115.483 116.440 126.246

Youngest Child 0-6 124.998 175.154 175.899 182.122 -326.347 113.852 119.507 129.254 -214.750 88.787 92.057 98.737 228.338 137.560 148.578 153.275 -380.196 114.190 115.552 125.414

Youngest Child 6-17 120.311 175.048 175.041 181.263 -237.192 113.728 119.766 129.500 -172.915 88.673 91.940 98.620 243.122 128.461 132.645 137.922 -340.817 114.748 116.683 126.464

No Children -12.525 4.504 4.449 4.608 -4.477 2.035 2.125 2.298 -4.585 1.709 1.751 1.880 -6.232 2.586 2.616 2.725 -3.923 2.255 2.283 2.470Youngest Child 0-6 -19.141 4.495 4.555 4.712 -7.882 2.071 2.191 2.361 -7.720 1.730 1.795 1.923 -10.482 2.944 3.056 3.152 -7.106 2.244 2.303 2.490Youngest Child 6-17 -15.575 4.401 4.423 4.583 -6.307 2.021 2.125 2.298 -6.590 1.689 1.743 1.872 -8.847 2.553 2.574 2.685 -5.695 2.221 2.271 2.459Wage -62.417 173.792 172.928 179.230 374.373 113.024 118.083 127.943 283.825 88.017 90.463 97.246 -132.768 127.051 130.585 135.938 449.801 114.028 114.129 124.107

Other Income 7.425 4.435 4.394 4.555 3.261 2.022 2.112 2.287 2.387 1.695 1.738 1.868 3.936 2.576 2.614 2.723 1.937 2.222 2.259 2.448Participation -253.594 210.589 219.780 226.613 -340.706 120.872 123.633 134.061 -397.135 109.999 114.110 122.306 306.341 202.123 204.188 212.558 -232.828 135.196 140.942 152.518Constant 1775.562 233.383 244.122 251.937 2475.879 138.485 143.158 155.008 2132.065 120.754 126.495 135.465 1204.487 172.907 182.108 189.233 2341.079 164.734 166.729 180.481

Children and Health

Wage Effects

Other Income Effects

Residuals

Source: Authors.

Younger Cohorts (50s, 60s)

Table F1. Comparison of Standard Errors

Group Dummies

Time Dummies

1983-1989 1990-2000 1983-2000 Older Cohorts (30s, 40s)