The Proportional Hazard Model: Estimation and Testing using Price Change and Labor Market Data

We use labor market data and data on price changes to examine the role of structural duration dependence and heterogeneity in shaping aggregate hazard rates. In line with an extensive literature, we examine this question through the lens of the proportional hazard model. We focus on environments where we observe two observations per individual, as this not only allows us to estimate the model non-parametrically, but also to test whether the true data-generating process is likely to have a structure imposed by a proportional hazard model. Formally, we can reject the null hypothesis that the proportional hazard model is the data generating process, but this is not surprising given the size of our data sets. We also estimate the model and find that the estimates are sensitive to assumptions on the distribution of unobserved heterogeneity. In addition, we show that, if the true data generating process for our labor market data is given by a structural stopping time model, estimates that impose the proportional hazard assumption understate the importance of heterogeneity in the economy.