Estimating Multi-Product Production Functions: What Can We Learn Without Demand Assumptions?
Abstract: Production functions estimation is widely used to recover markups and total factor productivity, but standard methods cannot be applied to output data as inputs are only observed at the plant level. To recover production functions it is standard to make assumptions on the demand side to back out marginal costs; however, this can lead to large biases when assumptions fail. In this paper, I prove that it is necessary to impose extra assumptions to deal with the unobserved input allocations. I also show that production function parameters are identified without assumptions on demand as long as the productivity distribution is stationary. Using simulations, I show how the moment inequalities perform relative to standard estimators.
Testing for Non-Jointness and Homogeneity with Non-Separable Production Frontiers
Abstract: Production frontiers allow for the flexible estimation of production technologies. To date the focus has been on separable specifications of the frontier; however, while these are easier to estimate, it is well known that they place non-trivial restrictions on the class of non-joint technologies they can accommodate (Cairncross et al., 2025). I show how the cost function approach of Hall (1973) can be adapted to models with adjustment costs and input market power to test for non-joint production. Additionally, when the technology is non-joint, I provide a test of homogeneity by deriving how the degree of homogeneity can be recovered from the production frontier. These results also provide guidance on what non-parametric forms to choose when estimating flexible, non-joint production technologies.
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.
Testing Demand Conduct with Production Data
Abstract: I develop a test for misspecification of the ownership matrix, which can be used to study whether there is collusion in a market. I show that misspecification of the ownership matrix leads to the derived marginal costs being distributed around their true value. However, it is necessary to supplement the input data with a production model as there is zero probability of observing the same inputs twice. The test then compares the estimated marginal costs for similar firms and rejects the ownership matrix whenever the share of marginal costs that disagree with the model are too large.
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.