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 the aggregate hazard rates. In line with an extensive literature we examine this question through the lens of a mixed proportional hazard model. While we think that this model is a convenient representation of the data, we recognize that its structure can be too restrictive. 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 test whether the true data-generating process is likely to have a structure imposed by a mixed proportional hazard model. We reject that this is the case both for the price change data and labor market data. We then turn to data simulated from reasonable structural models, none of which can be represented as a mixed proportional hazard model, to examine implications of estimating a misspecified mixed proportional hazard model. We use a ``CalvoPlus'' model for price changes, while for the labor market data, we assume that individual durations follow an inverse Gaussian distribution. We find that, in fact, the mixed proportional hazard model is a good approximation of the CalvoPlus model and therefore the estimated baseline hazard rate is very similar to the true structural hazard rate. This is not the case for the inverse Gaussian model for the labor market where the mixed proportional hazard model cannot be viewed as a good approximation. As a consequence, fitting a mixed proportional hazard model to these data vastly understate the importance of heterogeneity in the economy.