Measuring the extent to which assortative matching differs between two economies is challenging when the marginal distributions of the characteristic along which sorting takes place (e.g. education) also changes for either or both sexes. Drawing from the statistics literature we define simple conditions that any index has to satisfy to provide a measure of change in sorting that is not distorted by changes in the marginal distributions of the characteristic. While our characterisation of indices of assortativeness is not complete, and hence cannot exclude the possibility of multiple indices providing contradictory results, in an empirical application to US data we find that all indices satisfying our conditions indicate that homogamy by education has increased over time.
We consider a multiproduct monopoly pricing model. We provide sufficient conditions under which the optimal mechanism can be implemented via upgrade pricing—a menu of product bundles that are nested in the strong set order. Our approach exploits duality methods to identify conditions on the distribution of consumer types under which (a)each product is purchased by the same set of buyers as under separate monopoly pricing (though the transfers can be different), and (b) these sets are nested.
We exhibit two distinct sets of sufficient conditions. The first set of conditions weakens the monotonicity requirement of types and virtual values but maintains a regularity assumption, i.e., that the product-by-product revenue curves are single-peaked. The second set of conditions establishes the optimality of upgrade pricing for type spaces with monotone marginal rates of substitution (MRS)—the relative preference ratios for any two products are monotone across types. The monotone MRS condition allows us to relax the earlier regularity assumption.
Under both sets of conditions, we fully characterize the product bundles and prices that form the optimal upgrade pricing menu. Finally, we show that, if the consumer’s types are monotone, the seller can equivalently post a vector of single-item prices: upgrade pricing and separate pricing are equivalent.
We propose an approach to modeling and estimating discrete choice demand that allows for a large number of zero sale observations, rich unobserved heterogeneity, and endogenous prices. We do so by modeling small market sizes through Poisson arrivals. Each of these arriving consumers then solves a standard discrete choice problem. We present a Bayesian IV estimation approach that addresses sampling error in product shares and scales well to rich data environments. The data requirements are traditional market-level data and measures of consumer search intensity. After presenting simulation studies, we consider an empirical application of air travel demand where product-level sales are sparse. We find considerable variation in demand over time. Periods of peak demand feature both larger market sizes and consumers with higher willingness to pay. This amplifies cyclicality. However, observed frequent price and capacity adjustments offset some of this compounding effect.
Firms often involve multiple departments for critical decisions that may result in coordination failures. Using data from a large U.S. airline, we document the presence of important pricing biases that differ significantly from dynamically optimal profit maximization. However, these biases can be rationalized as a “second-best” after accounting for department decision rights. We show that assuming prices are generated through profit maximization biases demand estimates and that second-best prices can persist, even under improvements to pricing algorithm inputs. Our results suggest caution in abstracting from organizational structure and drawing inferences from firms’ pricing decisions alone.
I develop a model of endogenous production network formation between spatially distant firms. Unlike other such models, it is tractable even for very large numbers of firms, that is, it delivers closed-form predictions for firm-to-firm trade, it can be estimated via maximum likelihood, and it can be used for firm-level counterfactual analysis. I exploit novel micro-data on Indian firm-to-firm production networks for estimation. The estimated model implies that upon market integration across Indian states, over half of the variation in changes in firms’ sales to other firms can be explained by endogenous changes in network structure.
Larger Indian firms selling inputs to other firms tend to have more customers, tend to be used more intensively by their customers, and tend to have larger customers. Motivated by these regularities, I propose a novel empirical model of trade featuring endogenous formation of input-output linkages between spatially distant firms. The empirical model consists of (a) a theoretical framework that accommodates first order features of firm-to-firm network data, (b) a maximum likelihood framework for structural estimation that is uninhibited by the scale of data, and (c) a procedure for counterfactual analysis that speaks to the effects of micro- and macro- shocks to the spatial network economy. In the model, firms with low production costs end up larger because they find more customers, are used more intensively by their customers and in turn their customers lower production costs and end up larger themselves.In the model, differences in production costs across firms arise not just from differences in productivity but also from finding the most cost-effective suppliers of intermediate inputs. Firms with low production costs end up larger because they find more customers, are used more intensively by their customers and in turn their customers lower production costs and end up larger themselves. The model is estimated using novel micro-data on firm-to-firm sales between Indian firms. The estimated model implies that a 10% decline in inter-state border frictions in India leads to welfare gains ranging between 1% and 8% across districts. Moreover, over half of the variation in changes in firms’ sales to other firms can be explained by endogenous changes in the network structure.