Essays on Nonseparable Econometric Models
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kono-hkono-phd-econ-2026-thesis.pdf
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Author(s)
Kono, Haruki
Advisor(s)
Abadie, Alberto
Andrews, Isaiah
Mikusheva, Anna
Date Issued
May 2026
Publisher
Massachusetts Institute of Technology
Abstract
This thesis consists of three chapters that study the identification, estimation, and inference of nonseparable econometric models.
The first chapter addresses the issue of shape restriction violations in quantile regression. Standard estimators violate fundamental shape restrictions implied by probability or economic theory, including the non-crossing property of conditional quantile functions, the monotonicity of production output with respect to inputs, and the monotonicity of equilibrium bidding strategies in structural auction models. These violations can produce theoretically inconsistent estimates and undermine downstream analysis. To resolve this, I develop a framework for shape-constrained quantile regression based on a variational formulation. This approach utilizes an infinite-dimensional linear program to characterize the quantile coefficients, enabling the imposition of restrictions such as non-crossing, derivative-based inequalities, and covariate monotonicity. I obtain a computationally feasible estimator via finite-dimensional approximation and establish its asymptotic properties. Monte Carlo simulations demonstrate that the proposed estimator improves upon both classical and existing non-crossing approaches. In an application to U.S. timber auctions, the method yields smooth, theory-consistent estimates of bid distributions, valuation distributions, and bidding strategies, in contrast to conventional methods that violate basic economic restrictions.
The second chapter proposes a novel nonseparable instrumental variable model to address endogeneity in settings with multivariate outcomes. While traditional approaches estimate separate one-dimensional quantile models for each outcome, the inherent correlation among different dimensions invalidates their fundamental assumptions. To overcome this limitation, I jointly model the distribution of multiple outcomes. By specifying the structural function as the gradient of a convex function, the model accommodates flexible dependence across outcome dimensions. I establish the local identification of these structural functions in the presence of discrete treatments and instruments under a completeness-type condition, which reduces to the well-known full-rank condition in one dimension. I introduce a computationally tractable estimator and prove its uniform consistency. Simulation studies confirm the estimator's stable performance in finite samples.
The final chapter investigates the empirical testability of the rationality assumption. Slutsky symmetry and negative semidefiniteness are necessary and sufficient conditions for the rationality of demand functions. While the empirical implications of Slutsky negative semidefiniteness in repeated cross-sectional demand data are well understood, the empirical content of Slutsky symmetry remains unexplored. I take a first step toward addressing this gap. I demonstrate that the average Slutsky matrix is not identified and that its identified set always contains a symmetric matrix. This implies that the symmetry of the average Slutsky matrix is untestable, and that individual Slutsky symmetry cannot be tested through the average. Nevertheless, I show that by imposing bounds on the income elasticity of demand, average Slutsky symmetry yields a set of functional inequality constraints that are empirically testable.
JEL classification codes: C14, C21, C31, C36
MIT Department
Massachusetts Institute of Technology. Department of Economics
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