More importantly, the individual variables, except for age, are interacted with the OAA benefit, which allows the impact of OAA to vary across groups in the population. The interaction terms, which will be analyzed in more detail later, are jointly highly significant and improve the fit of the estimation considerably. With the interaction terms, the coefficient on log benefits in (3) only describes OAA’s effect on individuals with the most common characteristics: eight or fewer years of schooling, married, household head, not living on a farm or in a SMA, native born, and white. Taken together, the estimates imply a slightly smaller effect on participation from the increase in OAA benefits between 1940 and 1950, which suggests that the cross-state variation in demographics is correlated with changes in benefits.

Column (4) adds controls for other state level factors which vary over time and might be related both to participation and benefits. In particular, comprehensive earnings, income, and wealth data is lacking for the sample. State level measures of economic activity can proxy for missing individual data on wages, which should raise participation; and for family income and wealth and the wage available to other family members, which should reduce participation.

Column (4) includes state level economic variables for the manufacturing value added per capita, average farm values, log per capita income, and the unemployment rate. The coefficients on the first three are positive and large and indicate that states with greater gains in economic activity had smaller declines, or greater increases, in participation. For example, manufacturing value added per capita rose by 79% between 1940 and 1950; if it had not risen at all, participation would have fallen to 45.1% in 1950 instead of 48.7%, according to the estimates. It is a key finding that economic growth during the 1940s did not yet produce wealth effects that spurred earlier retirement, but apparently generated substitution effects that raised the rewards to staying in the labor force.

Adding the state level economic variables raises the estimate of OAA’s impact but not significantly, so the measures of economic activity do not appear to be strongly correlated with benefit levels. The estimates in column (4) imply that, if benefits in 1950 had stayed at 1940 levels, labor force participation would have risen from 49.7% in 1940 to 50.1% in 1950. Participation actually dropped to 48.7%, so it would have been 2.9% higher without the increase in OAA benefits. In those states with large increases in benefits – more than 50% in ten states and 33-50% in seven others – the resulting declines in participation are sizable. Therefore, OAA had a substantial impact on retirement, acting as a counterpoint to other economic forces which were encouraging people to work longer.