Mothers’ Involuntary Job Loss and Children’s Academic Achievement

Abstract

Using matched mother-child data from the National Longitudinal Survey of Youth, I examine the impact of mothers’ involuntary job loss on children’s academic achievement. Single mothers’ job displacement affects children’s math and reading test scores negatively and statistically significantly in the short run. Displacement of married mothers has no impact on their children’s test scores. The decline in income and a worsening of child’s behavioral problems are two channels through which single mothers’ job loss impacts test scores.

Appendices

Appendix 1

Summary of the Strategy Introduced by Oster 2015:

$A=\omega D+{X}_1+{X}_2$ where $A$ is the test outcome, child’s test score, $D$ is mother’s job displacement, ${X}_1$ is the set of observables and ${X}_2$ is the set of unobservable variables. Oster (2015) defines the proportional selection assumption as $\frac{cov\left(D,{X}_2\right)}{var\left({X}_2\right)}=\delta \frac{cov\left(D,{X}_1\right)}{var\left({X}_1\right)}$ where $\delta$ is the degree of proportionality. When the model has an error term included, there are two components for $\delta$. The first component, $\overset{\sim }{\delta }$, is the proportional selection between ${X}_1$, observable variables, and the unobservable variables related to $D$. It captures how much of $D$ is explained by observables and how much is explained by unobservable variables. The second component is, ${R}_{max}$, the full regression R-Squared in which $D$, ${X}_1$ and ${X}_2$ are controlled for. Once we have values for ${R}_{max}$ and $\overset{\sim }{\delta }$, an identified set for the treatment effect can be calculated. The identified set is: $\overset{\sim }{\delta}\in \left[0,1\right]\; and\;{R}_{max}\in \left[\overset{\sim }{R}, \min \left\{\mu \overset{\sim }{R},1\right\}\right]$ where $\overset{\sim }{R}$ is the R-squared from estimating equation with observable variables ($D$ and ${X}_1$) and $\mu$ is a parameter taking different values. The question is what values to set for $\overset{\sim }{\delta }$ and ${R}_{max}$. Note that the cutoff value for ${R}_{max}$ varies with the value of $\mu$. By utilizing nature of randomized data, Oster (2015) defines a bounding value for ${R}_{max}$ with which a result can be considered as robust. This value is obtained by $\mu =2.2$. in a second robustness standard, she checks whether the bounds of the identified set falls within +/−2.8 standard errors of the controlled estimate. The cut-off value generated by the randomized data is determined by $\mu =1.5$

The steps in the procedure are as follows.

• 1. Estimate $A$ on $D$, obtain baseline coefficient on $D$ and R-squared

• 2. Estimate $A$ on $D$ and ${X}_1$, obtain controlled effect coefficient on $D$ and R-square

• 3. Assume $\overset{\sim }{\delta }=1$, which means observable variables are at least as important as the unobservable variables and calculate identified set with $\mu =1.5$ and $\mu =2.2$.

• 4. Analyze if the set excludes zero.

Appendix 2

Table 8 Definitions of the variables

Table 9 Exogeneity test

Table 10 The impact of the mother’s job displacement on PIAT scores fixed effects estimates

Table 11 Coefficients of ‘Mother’s Job Displacement’ in the baseline and controlled estimation equations and identified sets - The treatment variable: mother’s job displacement

Table 12 BPI subscale questions