A Study Tried to Find the Determinants of the Increase

Essay

A study tried to find the determinants of the increase in the number of households headed
by a female.Using 1940 and 1960 historical census data, a logit model was estimated to
predict whether a woman is the head of a household (living on her own)or whether she is
living within another's household.The limited dependent variable takes on a value of one
if the female lives on her own and is zero if she shares housing.The results for 1960
using 6,051 observations on prime-age whites and 1,294 on nonwhites were as shown in
the table: $\begin{array}{|c|c|c|}\hline \text { Regression } & \text { (1) White } & \text { (2) Nonwhite } \\\hline \text { Regression model } & \text { Logit } & \text { Logit } \\\hline \text { Constant } & 1.459 & -2.874 \\& (0.685) & (1.423) \\\hline \text { Age } & -0.275 & 0.084 \\& (0.037) & (0.068) \\\hline \text { age squared } & 0.00463 & 0.00021 \\& (0.00044) & (0.00081) \\\hline \text { Education } & -0.171 & -0.127 \\& (0.026) & (0.038) \\\hline \text { farm status } & -0.687 & -0.498 \\& (0.173) & (0.346) \\\hline \text { South } & 0.376 & -0.520 \\& (0.098) & (0.180) \\\hline \text { expected family } & 0.0018 & 0.0011 \\\text { earnings } & (0.00019) & (0.00024) \\\hline \text { family composition } & 4.123 & 2.751 \\& (0.294) & (0.345) \\\hline \text { Pseudo- } \text {R }^{2} & 0.266 & 0.189 \\\hline \text { Percent Correctly } & 82.0 & 83.4 \\\text { Predicted } & & \\\hline\end{array}$
where age is measured in years, education is years of schooling of the family head, farm
status is a binary variable taking the value of one if the family head lived on a farm, south
is a binary variable for living in a certain region of the country, expected family earnings
was generated from a separate OLS regression to predict earnings from a set of
regressors, and family composition refers to the number of family members under the age
of 18 divided by the total number in the family.
The mean values for the variables were as shown in the table. $$\begin{array} { | c | c | c | } \hline \text { Variable } & \text { (1) White mean } & \text { (2) Nonwhite mean } \\\hline \text { age } & 46.1 & 42.9 \\\hline \text { age squared } & 2,263.5 & 1,965.6 \\\hline \text { education } & 12.6 & 10.4 \\\hline \text { farm status } & 0.03 & 0.02 \\\hline \text { south } & 0.3 & 0.5 \\\hline \text { expected family earnings } & 2,336.4 & 1,507.3 \\\hline \text { family composition } & 0.2 & 0.3 \\\hline\end{array}$$ (a)Interpret the results.Do the coefficients have the expected signs? Why do you think age
was entered both in levels and in squares?