Knowledge that Transforms

Consider a bipartite network where N consumers choose to buy or not to buy M different products. This paper considers the properties of the logit fit of the N × M array of “ i ‐buys‐ j ” purchase decisions, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="bold">Y</a:mi> <a:mo>=</a:mo> <a:msub> <a:mrow> <a:mo stretchy="false">[</a:mo> <a:msub> <a:mrow> <a:mi>Y</a:mi> </a:mrow> <a:mrow> <a:mi>i</a:mi> <a:mi>j</a:mi> </a:mrow> </a:msub> <a:mo stretchy="false">]</a:mo> </a:mrow> <a:mrow> <a:mn>1</a:mn> <a:mo>≤</a:mo> <a:mi>i</a:mi> <a:mo>≤</a:mo> <a:mi>N</a:mi> <a:mo>,</a:mo> <a:mn>1</a:mn> <a:mo>≤</a:mo> <a:mi>j</a:mi> <a:mo>≤</a:mo> <a:mi>M</a:mi> </a:mrow> </a:msub> </a:math>, onto a vector of known functions of consumer and product attributes under asymptotic sequences where (i) both N and M grow large, (ii) the average number of products purchased per consumer is finite in the limit, (iii) there exists dependence across elements in the same row or same column of Y (i.e., dyadic dependence), and (iv) the true conditional probability of making a purchase may, or may not, take the assumed logit form. Condition (ii) implies that the limiting network of purchases is sparse : only a vanishing fraction of all possible purchases are actually made. Under sparse network asymptotics, I show that the parameter indexing the logit approximation solves a particular Kullback–Leibler Information Criterion (KLIC) minimization problem (defined with respect to a certain Poisson population). This finding provides a simple characterization of the logit pseudo‐true parameter under general misspecification (analogous to a (mean squared error (MSE) minimizing) linear predictor approximation of a general conditional expectation function (CEF)). With respect to sampling theory, sparseness implies that the first and last terms in an extended Hoeffding‐type variance decomposition of the score of the logit pseudo composite log‐likelihood are of equal order. In contrast, under dense network asymptotics, the last term is asymptotically negligible. Asymptotic normality of the logistic regression coefficients is shown using a martingale central limit theorem (CLT) for triangular arrays. Unlike in the dense case, the normality result derived here also holds under degeneracy of the network graphon. Relatedly, when there “happens to be” no dyadic dependence in the data set in hand, it specializes to recently derived results on the behavior of logistic regression with rare events and i.i.d. data. Simulation results suggest that sparse network asymptotics better approximate the finite network distribution of the logit estimator. A short empirical illustration, and additional calibrated Monte Carlo experiments, further illustrate the main theoretical ideas.

This paper proposes a model for, and investigates the consequences of, strong spatial dependence in economic variables. Our findings echo those of the corresponding “unit root” time series literature: Spatial unit root processes induce spuriously significant regression results, even with clustered standard errors or spatial HAC corrections. We develop large‐sample valid unit root and stationarity tests that can detect such strong spatial dependence. Finally, we use simulations to study strategies for valid inference in regressions with persistent spatial data, such as spatial analogues of first‐differencing transformations. Regressions from Chetty, Hendren, Kline, and Saez (2014) are used to illustrate the issues and methods.

There is substantial empirical evidence showing that peer effects matter in many activities. The workhorse model in empirical work on peer effects is the linear‐in‐means (LIM) model, whereby it is assumed that agents are linearly affected by the mean action of their peers. We develop a new general model of peer effects that relaxes the linear assumption of the best‐reply functions and the mean peer behavior and that encompasses the spillover, conformist model, and LIM model as special cases. Then, using data on adolescent activities in the United States, we structurally estimate this model. We find that for many activities, individuals do not behave according to the LIM model. We run some counterfactual policies and show that imposing the mean action as an individual social norm is misleading and leads to incorrect policy implications.

This paper studies certification design and its implications for information disclosure. Our model features a profit‐maximizing certifier and the seller of a good of unknown quality. We allow for common values as the seller's opportunity cost may depend on the quality of the good. We compare certifier‐optimal with transparency‐maximizing certification design. Certifier‐optimal certification design implements the evidence structure of Dye (1985)—a fraction of sellers acquire information while the remaining sellers are uninformed—and results in partial disclosure to the market. A transparency‐maximizing regulator prefers a less precise signal, which conveys more information to the market through a higher rate of certification and unraveling (Grossman (1981), Milgrom (1981)) at the disclosure stage.

Oil and gas leases between mineral owners and extraction firms typically specify a date by which the firm must either drill a well or lose the lease. These deadlines are known as primary terms. Using data from the Louisiana shale boom, we first show that well drilling is substantially bunched just before the primary term deadline. This bunching is not necessarily surplus‐reducing: using an estimated model of firms' drilling and input choices, we show that primary terms can increase total surplus by countering the effects of leases' royalties, as royalties are a tax on revenue and delay drilling. These benefits are reduced, however, when production outcomes are sensitive to drilling inputs and when drilling one well indefinitely extends the period of time during which additional wells may be drilled. We enrich the model to consider mineral owners' lease offers and find small effects of primary terms on owners' revenue.

This paper develops a sufficient statistics framework for analyzing the welfare effects of disability insurance (DI). We derive social‐optimality conditions for the two main DI policy parameters: (i) eligibility rules and (ii) benefit levels. Applying this framework to two restrictive DI reforms in Austria, we find that tighter DI eligibility rules triggered higher fiscal cost savings and lower insurance losses. Hence, tighter DI eligibility rules dominate DI benefit reductions in scaling back the Austrian DI system.

We formulate an order over constraint sets <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>A</mi> <mo>⊆</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>ℓ</mi> </mrow> </msup> </math>, called the parallelogram order , which guarantees that argmin p ⋅ x : x ∈ A increases in the product order as A increases in the parallelogram order, for any vector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mi>p</mi> <mo>∈</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>ℓ</mi> </mrow> </msup> </math>. Using this result, we characterize the utility/production functions that lead to normal demand as well as the closely related class of production functions with marginal costs that increase with factor prices. By generalizing the concept of supermodularity, we also characterize the class of production functions for which factors are complements. In the context of decision‐making under uncertainty, our new set order leads to natural generalizations of first‐order stochastic dominance in multi‐prior models.

In a setting of many‐to‐one two‐sided matching with nontransferable utilities, for example, college admissions, we study conditions under which preferences of both sides are identified with data on one single market. Regardless of whether the market is centralized or decentralized, assuming that the observed matching is stable, we show nonparametric identification of preferences of both sides under certain exclusion restrictions. To take our results to the data, we use Monte Carlo simulations to evaluate different estimators, including the ones that are directly constructed from the identification. We find that a parametric Bayesian approach with a Gibbs sampler works well in realistically sized problems. Finally, we illustrate our methodology in decentralized admissions to public and private schools in Chile and conduct a counterfactual analysis of an affirmative action policy.

We study the design of optimal mechanisms when the designer is uncertain both about the form of information held by the agents and also about which equilibrium will be played. The guarantee of a mechanism is its worst performance across all information structures and equilibria. The potential of an information structure is its best performance across all mechanisms and equilibria. We formulate a pair of linear programs, one of which is a lower bound on the maximum guarantee across all mechanisms, and the other of which is an upper bound on the minimum potential across all information structures. In applications to public expenditure, bilateral trade, and optimal auctions, we use the bounding programs to characterize guarantee‐maximizing mechanisms and potential‐minimizing information structures and show that the max guarantee is equal to the min potential.

This paper introduces and analyzes sequentially stable outcomes in extensive‐form games. An outcome ω is sequentially stable if, for any ε > 0 and any small enough perturbation of the players' behavior, there is an ε ‐perturbation of the players' payoffs and a corresponding equilibrium with outcome close to ω . Sequentially stable outcomes exist for all finite games and are outcomes of sequential equilibria. They are closely related to stable sets of equilibria and satisfy versions of forward induction, iterated strict equilibrium dominance, and invariance to simultaneous moves. In signaling games, sequentially stable outcomes pass the standard selection criteria, and when payoffs are generic, they coincide with outcomes of stable sets of equilibria.