We also estimate the effects on labor force status for veterans between the ages of 60 to 70. We fit the multinomial logistic model in equation (6) below, where \(\text{Ag}e_{a,i}\) are a set of indicator variables that take the value of 1 if the veteran is in age category \(a\), and take the value of zero otherwise. We have grouped the ages between 60 and 70 in 10 categories: 60-61, 62-64, 65-66, 67-68, and 69-70. The outcome variable \(Y_{i}\) contains 7 categories: works full-time, works part-time, unemployed, partly retired, retired, disabled and not-in the labor force.
\begin{equation} Pr\left(Y_{i}=k\right)=\frac{e^{\sum_{a=1}^{A}{\beta_{a,k}\left(UR_{i}\times Age_{a,i}\right)}+\beta_{X,k}X_{i}}}{\sum_{j=1}^{J}e^{\sum_{a=1}^{A}{\beta_{a,j}\left(UR_{i}\times Age_{a,i}\right)}+\beta_{X,j}X_{i}}}\nonumber \\ \end{equation}
The estimation results (marginal effects) are shown in Table 7. A one percentage-point increase in the unemployment rate is associated with a 2.3 percentage-points increase in the probability of working full-time, with a 0.6 percentage-points increase in the probability of working part-time and with a 3.6 percentage-point reduction in the probability of being retired, between the ages of 62 and 64. We also find that a one percentage-point increase in the unemployment rate increases the probability of being partly retired (i.e. reporting being retired but also working part time) by 1.8 percentage points and decreases the probability of being retired by 2.1 percentage points. Thus, our findings indicate that the unemployment rate upon leaving the military have very long-term effects on veterans’ labor force status and on their retirement decisions.
Table : Effect of unemployment rate at time of exit from active service on labor force status between ages 60 and 70.