Equilibrium policy simulations with random utility models of labour supply

Many microeconometric models of discrete labour supply include alternative-specific constants meant to account for (possibly besides other factors) the density or accessibility of particular types of jobs (e.g. parttime jobs vs. full-time jobs). The most common use of these models is the simulation of tax-transfer reforms. The simulation is usually interpreted as a comparative static exercise, i.e. the comparison of different equilibria induced by different policy regimes. The simulation procedure, however, typically keeps fixed the estimated alternative-specific constants. In this note we argue that this procedure is not consistent with the comparative statics interpretation. Equilibrium means that the number of people willing to work on the various job types must be equal to the number of available jobs. Since the constants reflect the number of jobs and since the number of people willing to work change as a response to the change in tax-transfer regime, it follows that the constants should also change. A structural interpretation of the alternative-specific constants leads to the development of a simulation procedure consistent with the comparative static interpretation. The procedure is illustrated with an empirical example.