Write new appendix where commuting shares are endogeneous

[santiagohermo]

In this issue we will

• revise our discussion in the model about people moving within and across
• if accepted to the AEJ, add a new appendix, in the spirit of Appendix A, where commuting shares respond to the MW.

Extract from cover letter for AEJ submission

3. Comments related to the model in Section 2.

• R3's first comment argues that assuming perfectly flexible adjustments in the intensive margin of housing demand (as we do) seems contradictory with the “short-run” nature of the analysis where commuting shares are fixed. R3 also points out that the counterfactual policy evaluation would be invalid unless this issue is addressed.

  • In our static model, people are allowed to move within a ZIP code as long as commuting shares don't change. Appendix A presents an extension with a time dimension and people signing new contracts every 12 months where this dynamic is modelled explicitly.We emphasize that, as long as workers can in principle move, prices will respond even if they decide to stay in the same housing unit. Proposition 2 would also hold in a model where workers are allowed to move to different locations but the commuting shares do not change as a result. We will revise the text in Section 2 to make these points more salient.

  • We do observe changes in commuting shares annually, and use time-varying commuting shares to construct our workplace MW measure in Panel B of Table 3, finding very similar results. The difference between the time-varying shares workplace MW and the fixed-shares one in months with some MW change is very small, and is centered around zero (the 95% confidence interval ranges from approximatelly -0.005 to 0.005). As a result, we think that changes in commuting shares are not playing a large role.

  • We will add another extension to the model, in the spirit of Appendix A, with endogenous commuting shares, and show why our estimating equation can be taken as an approximation to the equilibrium in the extended model.

• R3's second comment is that we over-emphasize the theoretical novelty of our model. We will revise the text to frame the model as a tool for interpreting the empirical analysis and will moderate our claims of novelty.

• R3 also points to an imprecision in the proof of Proposition 1. We will of course fix this.

[santiagohermo]

Something I wrote on the whiteboard

Looks like the effect of changing commuting shares would go inside the workplace MW.

[santiagohermo]

Opening comment updated to focus more broadly on commuting shares in the model and not only in new appendix.

[santiagohermo]

This task was implemented in #267, see in particular https://github.com/diegogentilepassaro/min_wage_rent/commit/96a9c33b46729aee46956ea0d3e217e72a744ede