Working Paper
Semiparametric Panel Model with Group Heterogeneity
This paper studies a semiparametric partially linear panel model with timevarying
group-level e ects. As a critical feature, the group memberships are unobserved
but time-invariant. The linear coecients estimator is shown asymptotically
normal for inference. For production function estimation, the paper also
considers a two-step problem; the objective (second-step) parameter is identi-
ed by moments, conditional on the partially linear model's potentially in nitedimensional
parameters. The paper proposes a second-step estimator and shows
that it is consistent. The two analyses generically connect to the control function
problem under the presence of time-varying heterogeneity for panel models. With
the two-step solution, the paper extends the proxy variable method, designed for
the simultaneity problem with estimating the rm's production function, by allowing
cross-correlation in rms' productivity. As an empirical application, I
consider four Chilean manufacturing sectors from 1987 to 1996. After accounting
for cross-correlated productivity, I nd larger productivity e ects on output
growth and more heterogeneous productivity among rms.
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group-level e ects. As a critical feature, the group memberships are unobserved
but time-invariant. The linear coecients estimator is shown asymptotically
normal for inference. For production function estimation, the paper also
considers a two-step problem; the objective (second-step) parameter is identi-
ed by moments, conditional on the partially linear model's potentially in nitedimensional
parameters. The paper proposes a second-step estimator and shows
that it is consistent. The two analyses generically connect to the control function
problem under the presence of time-varying heterogeneity for panel models. With
the two-step solution, the paper extends the proxy variable method, designed for
the simultaneity problem with estimating the rm's production function, by allowing
cross-correlation in rms' productivity. As an empirical application, I
consider four Chilean manufacturing sectors from 1987 to 1996. After accounting
for cross-correlated productivity, I nd larger productivity e ects on output
growth and more heterogeneous productivity among rms.
1
Clustering for Multi-Dimensional Heterogeneity
(Joint with Xu Cheng and Frank Schorheide)
This paper provides a new multi-dimensional clustering approach for unobserved heterogeneity in panel data models. Each unit is associated with multiple clusters. For example, a firm can belong to the high productivity group and the low output elasticity group. In contrast, the standard one-dimensional clustering approach would be based on separate groups for each productivity-elasticity pair. Our approach provides substantial gains in estimation accuracy when unobserved features have sparse interactions, e.g., there are only a few firms with high productivity and low output elasticity. We propose an estimator for the unobserved group memberships and the group-specific and common parameters in a nonlinear GMM framework and derive its large sample properties. In particular, we provide the first classification consistency result in a nonlinear GMM setup. We re-evaluate the rise of aggregate markup in De Loecker, Eeckhout, and Unger (2018) by replacing their sector-specific production functions with a cluster-based ones. We find that the upward trajectory persists, but the magnitude is less pronounced after accounting for multi-dimensional heterogeneity.
Matching to Produce Information
(Joint with Ashwin Kambhampati and Carlos Segura-Rodriguez)
In recent decades, research organizations have brought the “market inside the
firm” by allowing workers to sort themselves into teams. How do research teams
form absent a central authority? We introduce a model of team formation in which
workers first match and then non-cooperatively produce correlated signals about an
unknown state. Our analysis identifies matching inefficiencies arising from two channels.
First, productive teams composed of workers producing complementary information
may form at the expense of excluded workers who must form relatively unproductive
teams consisting of workers producing substitutable information. Second,
even when productive teams are efficient, they need not form; a worker in such a team
may prefer to join a less productive team if she can exert less effort in this deviating
team. We discuss the implications of these results for organizational design.
firm” by allowing workers to sort themselves into teams. How do research teams
form absent a central authority? We introduce a model of team formation in which
workers first match and then non-cooperatively produce correlated signals about an
unknown state. Our analysis identifies matching inefficiencies arising from two channels.
First, productive teams composed of workers producing complementary information
may form at the expense of excluded workers who must form relatively unproductive
teams consisting of workers producing substitutable information. Second,
even when productive teams are efficient, they need not form; a worker in such a team
may prefer to join a less productive team if she can exert less effort in this deviating
team. We discuss the implications of these results for organizational design.