Adrien Bilal


I am an Assistant Professor of Economics at Harvard University.

My research focuses on Macroeconomics, Spatial Economics and Labor Economics. I also have interests in the use of Continuous-Time Methods.

Contact adrienbilal (at) fas (dot) harvard (dot) edu @AdrienBilal Google Scholar

CV You can find my CV here.


Outsourcing, Inequality and Aggregate Output, with H. Lhuillier

NBER Working Paper 29348. 20 minutes podcast by InequaliTalks

Outsourced workers experience large wage declines, yet domestic outsourcing may raise aggregate productivity. To study this equity-efficiency trade-off, we contribute a framework in which multi- worker firms either hire imperfectly substitutable worker types in-house along a wage ladder, or rent labor services from contractors who hire in the same frictional labor markets. Three implications arise. First, selection into outsourcing: more productive firms are more likely to outsource to save on labor costs and higher wage premia. Second, a productivity effect: outsourcing leads firms to raise output and labor demand. Third, an outsourcing wage penalty: contractor firms pay lower wages. We find support for all three implications in French administrative data and rule out alternative explanations. Instrumenting revenue productivity using export demand shocks, we find evidence for selection into outsourcing. Instrumenting outsourcing using variation in occupational exposure, we find evidence for the productivity effect. We confirm the outsourcing wage penalty with a movers design. After structurally estimating the model and validating it against our reduced-form estimates, we find that the rise in outsourcing in France between 1997 and 2016 lowers low skill service worker earnings and welfare by 1.5%. Outsourcing increases labor market sorting, lowers the share of rents going to workers, but raises aggregate output by 6%. A simultaneous 5.5% minimum wage hike stabilizes earnings and maintains employment and output gains.

Solving Heterogeneous Agent Models with the Master Equation (link to slides)

This paper proposes an analytic representation of heterogeneous agent economies with aggregate shocks. Treating the underlying distribution as an explicit state variable, a single value function defined on an infinite-dimensional state space provides a fully recursive representation of the economy: the ‘Master Equation’ introduced in the mathematics mean field games literature. I show that analytic local perturbations of the Master Equation around steady-state deliver dramatic simplifications. The First-order Approximation to the Master Equation (FAME) reduces to a standard Bellman equation for the directional derivatives of the value function with respect to the distribution and aggregate shocks. The FAME has five main advantages: (i) finite dimension; (ii) closed-form mapping to steady-state objects; (iii) applicability when many distributional moments or prices enter individuals’ decision such as dynamic trade, urban or job ladder settings; (iv) block-recursivity bypassing further fixed points; (v) fast implementation using standard numerical methods. The Second-order Approximation to the Master Equation (SAME) shares these properties, making it amenable to settings such as asset pricing. I apply the method to two economies: an incomplete market model with unemployment and a wage ladder, and a discrete choice spatial model with migration.


The Geography of Unemployment

Forthcoming, Quarterly Journal of Economics. NBER Working paper 29269, Response to Kuhn Manovskii Qiu (2021)

Unemployment rates differ widely across local labor markets. I offer new empirical evidence that high local unemployment emerges because of elevated local job losing rates. Local employers, rather than local workers, account for most of spatial gaps in job stability. I then propose a theory in which spatial differences in job loss arise endogenously, due to the spatial sorting of heterogeneous employers across local labor markets. Labor market frictions induce productive employers to over-value locating close to each other. The optimal policy incentivizes them to relocate to areas with high job losing rates, providing a rationale for commonly used place-based policies. I estimate the model using French administrative data. The estimated model accounts for over three fourths of the cross-sectional dispersion in unemployment rates, as well as for the respective contributions of job losing and job finding rates. Employers' inefficient location choices amplify spatial unemployment differentials five-fold. Both real-world and optimal place-based policies can yield sizable local and aggregate welfare gains.

Firm and Worker Dynamics in a Frictional Labor Market, with N. Engbom, S. Mongey and G. Violante

Econometrica, Vol. 90, No. 4 (July 2022), 1425-1462 (link to Online Supplement, Replication Package)

This paper develops a continuous-time random-matching model of a frictional labor market with firm and worker dynamics. Multi-worker firms choose whether to shrink or expand their employment in response to productivity shocks to their decreasing returns to scale technology. Growing entails posting costly vacancies, which are filled either by the unemployed or by employees poached from other firms. Firms also choose optimally when to enter and exit the market. Tractability is obtained by proving that, under a parsimonious set of assumptions, all worker and firm decisions can be characterized by comparisons between marginal surpluses which only depend on firm’s productivity and size. As frictions vanish, the model converges to a standard competitive model of firm dynamics. A parameterized version of the model yields longitudinal and cross-sectional patterns of net poaching in response to productivity shocks that are in line with the data. The model also generates a drop in job-to-job transitions as firm entry declines, offering an interpretation to U.S. labor market dynamics around the Great Recession. All these outcomes are a reflection of the job ladder in marginal surplus that emerges in equilibrium.

Labor Market Dynamics When Ideas are Harder to Find, with N. Engbom, S. Mongey and G. Violante

Forthcoming, in The Economics of Creative Destruction, ed. Akcigit, Van Reenen. NBER Working paper 29479.

This paper evaluates the impact of slowing economic growth on labor market dynamism and misallocation. It provides a model of endogenous growth via imitation in a frictional labor market. The framework accounts for rich data on worker job-to-job transitions as well as stochastic and lifecycle properties of firm growth and job reallocation. High productivity entrants gradually replace obsolescing incumbents by poaching their workers, a process that is intermediated via a frictional labor market. When the likelihood of entrants imitating technologies in the tail of the distribution falls (ideas are harder to find), so does growth. Consistent with US data over the past 30 years, firm entry, incumbents’ employment response to productivity shocks, and job-to-job transitions decline, while the share of old firms increases. With lower imitation, however, there is less misallocation, because the slower rate of obsolescence induces productive growing firms to invest more in costly hiring.

Location as an Asset, with E. Rossi-Hansberg

Econometrica, Vol. 89, No. 5 (September 2021), 2459–2495 (link to Online Supplement)

The location of individuals determines their job opportunities, living amenities, and housing costs. We argue that it is useful to conceptualize the location choice of individuals as a decision to invest in a "location asset". This asset has a cost equal to the location's rent, and a payoff through better job opportunities and, potentially, more human capital for the individual and her children. As with any asset, savers in the location asset transfer resources into the future by going to expensive locations with good future opportunities. In contrast, borrowers transfer resources to the present by going to cheap locations that offer few other advantages. As in a standard portfolio problem, holdings of this asset depend on the comparison of its rate of return with that of other assets. Differently from other assets, the location asset is not subject to borrowing constraints, so it is used by individuals with little or no wealth that want to borrow. We provide an analytical model to make this idea precise and to derive a number of related implications, including an agent's mobility choices after experiencing negative income shocks. The model can rationalize why low wealth individuals locate in low income regions with low opportunities even in the absence of mobility costs. We document the investment dimension of location, and confirm the core predictions of our theory with French individual panel data from tax returns.


Anticipating Climate Change Risk Across the United States, with E. Rossi-Hansberg (link to slides)

This paper evaluates the impact of extreme weather events for the social cost of climate change. To that end we develop a dynamic spatial model of the US economy divided in over 3,000 counties that features risk-averse individuals, forward-looking migration and investment, and idiosyncratic and aggregate climate risk. We achieve tractability by relying on recent methodological advances that leverage analytic perturbations of the Master Equation representation of the economy. We estimate the model on US counties by combining climatic county-level data for weather events such as heat waves, floods and hurricanes over the course of the 20th century with population, migration, investment and income data. We run event studies that trace out the impact of extreme weather events on productivity, amenities, mortality, and capital depreciation. Our findings are twofold. First, climate impacts on capital depreciation and mobility are the main source of climate damages. They substantially magnify the costs of climate change in the business-as-usual warming scenario. Second, adaptation through migration and investment are crucial mitigators of climate damages, without which welfare losses would be much more spatially concentrated.

Asset Pricing According to HANK, with Andreas Schaab