ABSTRACT
The theoretical framework for inferring the determinants of local population follows Haurin (1980) and Rappaport (2004a,b). The world is assumed to comprise a large number of “localities.” These are fixed geographic areas where people both live and
work and across which there is at least moderate factor mobility. Localities exogenously differ with respect to some attributes that affect local quality of life and local productivity. Local attributes that affect quality of life enter directly as arguments in individuals’ utility functions; those that affect productivity enter directly as arguments in firms’ profit functions. Equivalently, quality of life attributes shift individuals’ indifference curves over wages and prices. Productivity attributes shift firms’ iso-profit curves over wages and other input prices. In a long-run steady state, population density is an increasing function of local quality of life and local productivity. Individuals are willing to endure greater crowdedness and the associated higher price of housing in order to directly enjoy higher quality of life and to indirectly enjoy higher productivity via the higher wages it affords. Indeed, varying local population density is the primary mechanism by which local wages and house prices adjust to equate utility and profits across localities. The setup might suggest that a “level” regression of population density on exogenous attributes can identify their contributions to quality of life and productivity. But this is unlikely: factor mobility is not perfect, and both productivity and quality of life also depend on endogenous attributes. Imperfect factor mobility implies that current population density may differ substantially from steady-state population density. Even relatively small frictions to labor and capital mobility can cause population to require several decades to transition from one steady state to another (Rappaport, 2004a). Hence a positive partial correlation between current population density and an exogenous attribute may reflect a past rather than a present contribution to quality of life and productivity. The partial dependence of quality of life and productivity on endogenous attributes introduces an additional difficulty: such endogenous attributes are likely to be correlated with the exogenous ones. Substantial research suggests that quality of life and productivity themselves depend on population size and density. Size and density may increase quality of life by allowing for increased social interaction and product variety (e.g., Glaeser et al., 2001; Fujita and Thisse, 2002; Compton and Pollak, 2004). And they may increase productivity via local scale economies (e.g., Henderson et al., 1995; Ciccone and Hall, 1996; Henderson, 2003). An exogenous attribute that increased quality of life and productivity in the past may no longer do so in the present. But the high population density caused by the past contribution may cause steady-state population density to remain correlated with the attribute via a “lock-in effect” from self-reinforcing agglomeration forces (Fujita and Mori, 1996). Interpreting partial correlations between population growth and exogenous attributes is more straightforward. Regardless of factor mobility, an exogenous attribute that is partially correlated with long-run population growth will be partially correlated with a change in steady-state density. Imperfect factor mobility simply implies that the change may have occurred substantially before the period over which population growth is being measured. One possible cause of a change in steady-state density is a change in the contribution from the exogenous
attribute to quality of life and productivity. Another is a change in the contribution to these from an endogenous attribute that is correlated with the exogenous attribute. To rule out the latter possibility, regressions can include controls for predetermined endogenous attributes.
