We examine identification of differentiated products demand when one has “micro data” linking the characteristics and choices of individual consumers. Our model nests standard specifications featuring rich observed and unobserved consumer heterogeneity as well as product/market‐level unobservables that introduce the problem of econometric endogeneity. Previous work establishes identification of such models using market‐level data and instruments for all prices and quantities. Micro data provides a panel structure that facilitates richer demand specifications and reduces requirements on both the number and types of instrumental variables. We address identification of demand in the standard case in which nonprice product characteristics are assumed exogenous, but also cover identification of demand elasticities and other key features when these product characteristics are endogenous and not instrumented. We discuss implications of these results for applied work.
The allocation of decision‐making power is a critical choice that organizations make to mitigate agency problems and information frictions. This paper investigates the role of delegation for organizations where the agency problem is both pervasive and has potentially high welfare consequences: state‐owned enterprises (SOEs). I use a natural experiment in India to uncover the causal effects of granting SOE managers more autonomy over strategic decisions. Managers meaningfully exercise this autonomy, which results in greater value added, but also a reduced emphasis on outcomes valued by the government, such as a reduction in worker amenities (employee housing), and an increase in markups. Returns to autonomy are higher for firms with higher baseline incentive conflict.
The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision‐making. These include a representation of stationary monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries. This extension offers a new perspective on risk attitudes toward time, as well as on the aggregation of multiple discount factors. We also offer a novel class of non‐expected utility preferences over gambles which satisfy invariance to background risk as well as betweenness, but are versatile enough to capture mixed risk attitudes.
A seller trades with q out of n buyers who have valuations a 1 ≥ a 2 ≥ ⋯ ≥ a n > 0 via sequential bilateral bargaining. When q < n , buyer payoffs vary across equilibria in the patient limit, but seller payoffs do not, and converge to max l ≤ q +1 [( a 1 + a 2 +⋯+ a l −1 )/2+ a l +1 +⋯+ a q +1 ]. If l * is the (generically unique) maximizer of this optimization problem, then each buyer i < l * trades with probability 1 at the fair price a i /2, while buyers i ≥ l * are excluded from trade with positive probability. Bargaining with buyers who face the threat of exclusion is driven by a sequential outside option principle : the seller can sequentially exercise the outside option of trading with the extra marginal buyer q + 1, then with the new extra marginal buyer q , and so on, extracting full surplus from each buyer in this sequence and enhancing the outside option at every stage. A seller who can serve all buyers ( q = n ) may benefit from creating scarcity by committing to exclude some remaining buyers as negotiations proceed. An optimal exclusion commitment , within a general class, excludes a single buyer but maintains flexibility about which buyer is excluded. Results apply symmetrically to a buyer bargaining with multiple sellers.
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.