Is there a male marital wage premium?
Causal and Spurious Effects of Marriage on Wage
Figure 1. Causal and Spurious Effects of Marital Wage Premium
Causal Effects
What are the causal effects of marriage? What do they look like?
The specialization hypothesis provides one explanation. Husbands specialize in breadwinning, and wives take care of housework and childcare. Husbands invest more in their human capital than unmarried men, which yields faster wage growth not immediately but in the long run. The long-dashed line in the left figure illustrates the causal effect of specialization.
Causal effects can also be immediate and time-constant, as shown in the short-dashed line in the left figure. The work effort hypothesis states that husbands immediately devote more time to work and work harder. Employers may favor married men and believe they are more productive workers than unmarried men, deserving more money to meet families’ financial needs.
Spurious Effects
What are the spurious effects of marriage? What do they look like?
Selection on wage level indicates that men with higher wages are more likely to get married. They are more attractive candidates in the marriage market. They may possess unobservable time-constant traits that reward them in the labor market: health, personality, social skills, etc. The short-dashed line in the figure on the right side shows the selection on wage level.
The long-dashed line shows selection on wage potential and growth, another spurious effect. Women may prefer to marry men on a steep career trajectory since they are more promising in the future.
To debunk marital wage premiums, we need statistical tools to control for the spurious effects. What remains, if significant, are the causal effects.
Analytical Strategies
Pooled OLS Model (POLS)
$$\ln w_{it} = \alpha_{2} exp_{it} + \beta m_{it} + \alpha_{1} + \varepsilon_{it}$$
In this model, the dependent variable is the log-transformed wage of the person $i$ at time $t$. $\alpha_{2}$ captures the percent of wage increase with one additional year of work experience $exp$. $\beta$ is the key coefficient of interest: the percentage of wage premium after marriage. $\alpha_{1}$ is the intercept that applies to all individuals. All other variables, observable or unobservable, are captured by the error term $\varepsilon_{it}$.
The POLS model assumes a common intercept for all individuals and does not account for unobservable between-individual differences. Previous literature using POLS found substantial marital wage premiums, 16% in Dougherty (2006) and 17.5% in Ahituv and Lerman's (2007).
Standard Fixed-Effect Models (FE)
Standard fixed-effect models differ from OLS models by considering individual-specific intercepts:
$$\ln w_{it} = \alpha_{2}exp_{it} + \beta m_{it} + \alpha_{1i} + \varepsilon_{it}$$
Now the wage level $\alpha_{1i}$ is a constant allowed to vary across individuals. The individual intercept subsumes all time-constant variables, whether observable or unobservable, such as one’s capability, personality, and social skills. We use the de-meaning approach: subtracting the person-specific mean from the actual values. Therefore, since selection on wage levels is time-constant, it will not affect the estimate of marriage premiums.
The FE models reveal a smaller but significant marital wage premium compared to POLS models, 6% in Dougherty (2006), 7% in Killewald and Gough (2013), and 8% in Ahituv and Lerman's (2007).
Fixed-Effect Models with Group-Specific Slopes (FEGS)
FEGS models allow for differences in outcome growth between treatment groups:
$$\ln w_{it} = \alpha_{20}exp_{it} + \alpha_{21} treat_{i} \times exp_{it} + \beta m_{it} + \alpha_{1i} + \varepsilon_{it}$$
$treat_{i}$ is a time-constant dummy variable indicating whether a man eventually marries. Thus, $\alpha_{20}$ is the coefficient of the work experience of men who do not marry, the sum of $\alpha_{20}$ and $\alpha_{21}$ is the steepness of the wage profile of men who marry.
The FEGS assumes common trends in the two treatment groups. However, it does not consider marriage timing within the ever-married group. Men with higher wage growth may marry earlier.
Fixed-Effect Models with Individual-Specific Slopes (FEIS)
Consider the model:
$$\ln w_{it} = \alpha_{2i}exp_{it} + \beta m_{it} + \alpha_{1i} + \varepsilon_{it}$$
It differs from Equation 2 in that the slopes of wage trajectories $\alpha_{2i}$ varies across individuals. It removes the bias of selection based on wage level and wage growth.
Results and Findings
library(plm) #FE and FEGS library(feisr) #FEIS library(texreg) #output data(mwp) head(mwp) #> id year lnw exp expq marry evermarry enrol yeduc age cohort #>1 1 1981 1.934358 1.076923 1.159763 0 1 1 11 18 1963 #>2 1 1983 2.468140 3.019231 9.115755 0 1 1 12 20 1963 #>3 1 1984 2.162480 4.038462 16.309174 0 1 1 12 21 1963 #>4 1 1985 1.746280 5.076923 25.775146 0 1 0 12 22 1963 #>5 1 1986 2.527840 6.096154 37.163090 0 1 1 13 23 1963 #>6 1 1987 2.365361 7.500000 56.250000 0 1 1 13 24 1963 #> yeargr yeargr1 yeargr2 yeargr3 yeargr4 yeargr5 #>1 2 0 1 0 0 0 #>2 2 0 1 0 0 0 #>3 2 0 1 0 0 0 #>4 2 0 1 0 0 0 #>5 3 0 0 1 0 0 #>6 3 0 0 1 0 0
Now let’s estimate the four different models.
#POLS
wages.pols <- lm(lnw ~ marry + enrol + yeduc + as.factor(yeargr)
+ exp + I(exp^2),
data = mwp)
#FE
wages.fe <- plm(lnw ~ marry + enrol + yeduc + as.factor(yeargr)
+ exp + I(exp^2),
data = mwp,
index = c("id", "year"),
model = "within",
effect = "individual")
#FEGS
wages.fegs <- plm(lnw ~ marry + enrol + yeduc + as.factor(yeargr)
+ exp + I(exp^2) + evermarry*exp + evermarry*I(exp^2),
data = mwp,
index = c("id", "year"),
model = "within",
effect = "individual")
#FEIS
wages.feis <- feis(lnw ~ marry + enrol + yeduc + as.factor(yeargr)
| exp + I(exp^2),
data = mwp,
id = "id")Summarize the results in a table.
#Print results
screenreg(list(wages.pols, wages.fe, wages.fegs, wages.feis),
digits = 3,
custom.model.names = c("POLS", "FE", "FEGS", "FEIS"))
#>==========================================================================
#> POLS FE FEGS FEIS
#>--------------------------------------------------------------------------
#>(Intercept) 1.443 ***
#> (0.049)
#>marry 0.161 *** 0.078 *** 0.041 0.013
#> (0.020) (0.022) (0.024) (0.027)
#>enrol -0.219 *** -0.208 *** -0.205 *** -0.118 ***
#> (0.023) (0.023) (0.023) (0.023)
#>yeduc 0.076 *** 0.056 *** 0.056 *** -0.002
#> (0.004) (0.007) (0.007) (0.014)
#>as.factor(yeargr)2 -0.203 *** -0.141 *** -0.136 *** -0.046
#> (0.035) (0.030) (0.030) (0.035)
#>as.factor(yeargr)3 -0.284 *** -0.165 *** -0.156 *** -0.019
#> (0.046) (0.047) (0.047) (0.051)
#>as.factor(yeargr)4 -0.424 *** -0.276 *** -0.262 *** -0.136 *
#> (0.055) (0.062) (0.062) (0.062)
#>as.factor(yeargr)5 -0.481 *** -0.298 *** -0.267 *** -0.187 *
#> (0.066) (0.079) (0.080) (0.077)
#>exp 0.072 *** 0.073 *** 0.055 ***
#> (0.009) (0.009) (0.012)
#>exp^2 -0.001 ** -0.001 *** -0.001
#> (0.000) (0.000) (0.001)
#>exp:evermarry 0.027 *
#> (0.011)
#>exp^2:evermarry -0.001
#> (0.001)
#>--------------------------------------------------------------------------
#>R^2 0.378 0.414 0.417 0.025
#>Adj. R^2 0.376 0.357 0.359 0.022
#>Num. obs. 3100 3100 3100 3100
#>Num. groups: id 268
#>RMSE 0.285
#>==========================================================================
#>*** p < 0.001; ** p < 0.01; * p < 0.05
In the POLS model, we found a 16% increase in wages due to marriage, close to what Dougherty (2006) and Ahituv and Lerman (2007) found. In the standard FE model, the marital wage premium is 7.8% percent, very close to 0.073 reported by Killewald and Gough (2013). In the FEGS model, marital wage premium shrinks to 4.1%, marginally significant at the significance level of 0.1. The interaction term indicates that the wage slope differs significantly between the never-married and the ever-married groups. Finally, in the FEIS model, marital wage premium is not significant.
Figure 2. Comparison of Marital Wage Premiums Across Four Modeling Approaches
In summary, selection on wage growth fully accounts for the remaining marriage premium in the FE model.
Discussion
The FEIS model has its drawbacks.
The FEIS model is data-hungry. It requires at least $j+1$ person-years per individual, where $j$ is the number of individual-specific slope parameters plus the individual intercept. We allowed work experience, the square term of work experience, and the intercept to vary across individuals. Therefore, we need at least four observations per person. Panel datasets are often not long enough.
It requires you to identify the most relevant variable for the outcome growth. Work experience is most pertinent to wage growth. For other outcomes, it might not be so straightforward.
I hope this blog introduced some new methodologies and helped you understand how the advancement of statistical models challenged previous conclusions.
Reference
Ahituv, A., & Lerman, R. I. (2007). How do marital status, work effort, and wage rates interact? Demography, 44(3), 623–647.
Dougherty, C. (2006). The Marriage Earnings Premium as a Distributed Fixed Effect. Journal of Human Resources, XLI(2), 433–443.
Killewald, A., & Gough, M. (2013). Does Specialization Explain Marriage Penalties and Premiums? American Sociological Review, 78(3), 477–502.
Ludwig, V., & Brüderl, J. (2018). Is There a Male Marital Wage Premium? New Evidence from the United States. American Sociological Review, 83(4), 744–770.