Estimating Multi-Product Production Functions: What Can We Learn Without Demand Assumptions? [paper]
Abstract: I prove that, when the demand side is unrestricted, production functions for multi-product firms are unidentified, except in population if the conditional time- series variance of inputs is unbounded. I develop a novel identification strategy that does not rely on demand-side assumptions. Instead, by imposing the weaker assumption that the productivity distribution is in a stationary equilibrium, I show that the production function parameters are set-identified. Using simulations, I show that the estimator is robust to non-stationarity of the productivity processes in short panels and provide evidence that the identified set is highly informative about the data-generating parameters. My approach avoids the need for instruments or numerical solvers, providing a widely applicable method for estimation.
Testing for Non-Jointness and Homogeneity with Non-Separable Production Frontiers
Abstract: I show that, by inferring the firm's perceived input prices from its marginal rate of technical substitution, the cost function approach of Hall (1973) can be adapted to test for non-jointness of the production technology when firms face adjustment costs or have input market power. Additionally, for a firm with a two-output, non-joint technology the returns to scale for a given product is the ratio of the change in the product’s aggregate input elasticity to the concurrent change in the output transformation elasticity along the production frontier. These results can be used to test for homogeneity of the technology and provide guidance on what non-parametric forms to choose when estimating flexible non-joint production frontiers.
Partition Dependent Expected Utility (joint with Agustin Troccoli-Moretti)
Abstract: In this paper, we study choice under objective risk where the primitive is enriched to include an exogenous equivalence relation on the space of lotteries. We seek conditions on this enlarged primitive ensuring the existence of an expected utility representation in which the Bernoulli utility index may depend on the partition generated by the equivalence relation. We term this model the Partition Dependent Expected Utility (PDEU) and show examples of recent choice models in the literature on non-expected utility that fall into this class. We prove representation theorems characterizing PDEU preferences when the partition generates convex cells, and under different continuity assumptions. Our theorems address partitions with both countable and uncountable elements, with cells that can be lower-dimensional, fully dimensional, or a combination of both. We show that for fully dimensional cells, the parameters of the representation are suitably unique, but this is not the case for lower-dimensional cells. We conclude with a discussion of the technical challenges that may arise when studying partitions with non-convex cells.
State of UK Competition Report 2024 (joint with Amanda Ereyi, Fizza Jabbar, Joel Kariel, Luke McWatters, Rajssa Mechelli, Max Read, and Jakob Schneebacher) CMA Microeconomics Unit Report, 2024.
Competition and Market Power in UK Labour Markets (joint with Joel Kariel, Renisha Rana, Max Read, Ana Rincon Aznar, and Jakob Schneebacher) CMA Microeconomics Unit Report, 2024.