Understanding Gross Workers Flows Across U.S. States

This paper documents and provides an explanation for the main stylized facts about net and gross workers flows across states in the U.S. While it is generally known that gross flows of population across locations are significantly larger in the United States than within most European countries (see Hassler et al., 2005), there is considerable heterogeneity in gross and net flows across locations within the United States itself. The main purpose of the paper is to test whether a simple general equilibrium search model based on Lucas and Prescott (1974)'s island economy can account for the main stylized facts. The paper builds on work by Blanchard and Katz (1992), who focus only on net, rather than gross, flows of workers and on the partial equilibrium analysis of migration decisions by Kennan and Walker (2005). I start by documenting these facts using the decennial Census of the U.S for the post-WWII period. The latter allows one to determine a respondent's state of residence in the Census year as well as five years before the Census year. This information is used to construct state-level aggregate gross and net flow rates of workers. These flows are adjusted to take into account the different demographic and industrial composition of the workforce across states and differences in other state characteristics, such as size. The key stylized facts are as follows. In the cross-sectional dimension: (1) gross inflow rates are more dispersed than net flow rates, which, in turn, are more dispersed than gross outflow rates. (2) Gross inflow and outflow rates are positively correlated. (3) Gross and net inflow rates are highly positively correlated, while net flow rates and gross outflow rates are uncorrelated. These three facts suggest that reallocation of population within the U.S. occurs mainly through variations in gross inflows (large in fast-growing states and small in slow-growing states), rather than in gross outflows. In other words, states that tend to lose population to other states do so by attracting fewer new workers as opposed to losing more local ones. In the time-series dimension, there is a large degree of persistence in both gross and net flow rates across Census years for a given state. Last, there is no significant correlation between average state wages (adjusted by differences in living costs) and gross or net flow rates. In order to explain these facts, I consider a simple search model. The model economy is composed by a set of local labor markets ("islands"), that are hit by idiosyncratic and persistent labor demand shocks. Local wages tend to rise in response to these shocks, but workers' mobility across islands limits the extent to which wages can differ across locations. At a point in time, a location experiences both gross inflows and gross outflows. This is because offered wages in an island, in addition to a location-wide component, also have an idiosyncratic one. The latter gives rise to gross flows. In general equilibrium, the value of migration is pinned down by a zero excess demand condition for aggregate net flows. The model's parameters are estimated using a simulated method of moments. Specifically, estimation occurs in two stages. I first derive the law of motion for net flow rates implied by the model. This is shown to depend on the parameters of the stochastic process for the labor demand shock. The latter are estimated by matching the cross-sectional dispersion of net flow rates and their first and second order autocorrelation coefficients. Second, I feed the estimated process for local labor demand shocks into the model and estimate the remaining parameters by matching the following cross-sectional moments: observed dispersion in average relative wages, average observed wage dispersion within states, the average outflow rate across states, and the fraction of all moves that are motivated by economic factors. At the time of this writing, the estimation of the model is still taking place. Preliminary results based on calibrations of the model are promising. In particular, the model can account for the dispersion in gross flows and the positive cross-sectional correlation between inflows and outflows. The estimated model can be used to assess the quantitative importance of some of the explanations that have been proposed for the lower mobility rates within European countries than in the U.S.: higher compression of European wage distributions, lower dispersion of demand conditions across local labor markets within European countries, etc