Appendix

Addressing potential concerns regarding the validity of coefficient estimates from the OLS regression detailed in Table 8, I perform a series of regression diagnostic tests in Stata designed to gauge if the basic assumptions for using OLS are indeed met. This battery of tests includes the following: (1) visual inspection of scatter plots, examination of studentized residuals, examination of levels of leverage, visual inspection of the leverage versus residual squared plot, and calculation of Cook’s D and DFITS, all implemented for detecting issues of outliers or observations that exert large amounts of leverage or influence on the estimation; (2) visual inspection of the kernel density plot of residuals overlaid with a normal density, and visual inspection of comparisons of residuals both to a standardized normal probability and to the quantiles of a normal distribution, all employed to detect issues of non-normality within the residuals (important for validity of hypothesis testing); (3) visual inspection of the plot of residuals versus fitted values, Cameron & Trivedi’s decomposition of IM test, and the Breusch-Pagan/Cook-Weisberg test for heteroskedasticity, all used for highlighting issues of heteroskedasticity of the residuals; (4) calculation of the variance inflation factor, implemented for indicating multicollinearity; (5) visual inspection of scatter plots and kernel density plots, employed for detecting issues of non-linearity; and (6) the link test and omitted variables test, used to test for model misspecification.

Of any concerns resulting from this series of tests, potential heteroskedasticity comes to the forefront given a slightly larger variance in residuals as fitted values increase. However, results from the numerical tests for heteroskedasticity alleviate those concerns, both respective p-values not allowing rejection of the null hypotheses that the variance of residuals is homogenous. Nonetheless, as a step of precaution, I opt to check initial results by using robust standard errors due to the possibility of minor heteroskedasticity. Table 9 reflects the results from this alternative OLS regression, equivalent to those reported in Table 8, however obtained implementing robust standard errors. Huber-White robust standard errors help address any potential minor issues of normality, heteroskedasticity, or observations with large residuals, leverage, or influence. Comparing the standard errors of Table 8 with those of Table 9, differences are minimal; most notably, the slight change in size of standard errors causes the coefficients for both education and marital status to move from being statistically significant to having no statistical significance at the 10% level.