titative general equilibrium dynamic model with multiple locations around this stylized fact. The
model assumes that in each period, each worker decides where to live given: a) current and future
housing and labor market conditions in an arbitrary number of potential destinations, and b) an
idiosyncratic taste shock. This idiosyncratic taste shock captures taste heterogeneity for mobility
and is drawn from a nested logit distribution. This nesting structure captures the fact that the
home location is special: workers in the model are more reluctant to substitute away the location
where they currently live than to substitute among two potential alternative new destinations.
This assumption on how to model internal mobility allows to decompose the flows of workers
between any two locations between the (endogenous) share of workers who move away from their
original location and, among those, the share who choose each particular destination. This fully
characterizes the entire matrix of flows between locations in an economy. It also makes the home
location a more likely candidate for the following period’s location, something that is crucial in
order to match the empirical regularity that in equilibrium internal migration is relatively low –
only around 5 percent of the population relocates to a different metropolitan area each year. This
modeling choice plays a similar role to the fixed costs of mobility introduced and estimated in
Kennan and Walker (2011) but makes the model very tractable.
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Furthermore, there are a number of features of the model that make it attractive, both for
analytical study and for estimation. First, the population dynamics can be summarized in a very
simple and intuitive equation despite the complexity of having many potential current and future
destinations.
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In each location, the population in the following period is a weighted average between
a) the indirect utility of living in that location relative to all other potential destinations, and b)
the current size of the location. Thus, a simple equation per location fully characterizes (the sticky)
population dynamics of the many locations in the economy and allows for an examination of the
determinants of the speed of convergence to the new steady state. This simple equation allows me
to show that the speed of convergence depends crucially both on the sensitivity of internal migration
and on local congestion forces. The model makes very explicit the idea that reduced migration to
one location is a labor supply shock – or increased competition for housing – in another location,
as discussed in the seminal work of Topel (1986).
Second, the model is particularly suited to studying welfare. Long run changes in the value
across locations can also be summarized in a simple and intuitive equation. The assumptions of
the model imply that the change in the long run value of a location equals the change in the
2
In Appendix D, I compare the model presented in this paper with a model where the idiosyncratic taste shocks
are drawn from a logit distribution and there are fixed costs of moving, showing that differences are small. I also
show how moving costs need to be high to match the findings in this paper. Papers using fixed costs of moving
include the seminal contributions of Kennan and Walker (2011) and Artuc et al. (2010).
3
Given the simplicity of the dynamics generated, this methodological innovation can potentially be used in a
number of different contexts. For example, the model presented in this paper can be used to endogenise the share of
firms that decide to set-up new prices in a sticky price model Calvo (1983). See also Clarida et al. (2000) and Gali
(2015).
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