INSTRUMENTAL-VARIABLES FRACTIONAL PROBIT MODEL IN ACTION!
We want to study 401(k) participation rate (prate). We believe that corporate employment size (ltotemp) and its square are determinants of participation rates, as are an indicator of whether the 401(k) is the sole pension plan (sole) and the plan matching rate (mrate). We believe, however, that the plan matching rate is endogenous. In other words, there are unobserved determinants of participation rates that also affect the plan matching rate. For instance, matching rate and participation rate might be associated with industry practices and regional practices not observable in the data. To address endogeneity, we instrument matching rate using the age of the plan (age) and its square.
. ivfprobit prate c.ltotemp##c.ltotemp i.sole (mrate = c.age##c.age)
Inside the parentheses is the endogenous variable along with the instrumental variables we used to model it. Outside the parentheses are the exogenous variables, that affect prate directly. We get
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We find a positive effect of the matching rate on the participation rate. Additionally, we see that the estimated correlation between the unobservables, corr(e.mrate, e.prate), is different from zero. This means there is evidence to support our endogeneity conjecture.