We explore the deliberate infusion of ambiguity into the design of contracts. We show that when the agent is ambiguity‐averse and hence chooses an action that maximizes their minimum utility, the principal can strictly gain from using an ambiguous contract, and this gain can be arbitrarily high. We characterize the structure of optimal ambiguous contracts, showing that ambiguity drives optimal contracts toward simplicity. We also provide a characterization of ambiguity‐proof classes of contracts, where the principal cannot gain by infusing ambiguity. Finally, we show that when the agent can engage in mixed actions, the advantages of ambiguous contracts disappear.
This paper studies how social media affects the dynamics of protests and strikes in China during 2009–2017. Based on 13.2 billion microblog posts, we use tweets and retweets to measure social media communication across cities and exploit its rapid expansion for identification. We find that, despite strict government censorship, Chinese social media has a sizeable effect on the geographical spread of protests and strikes. Furthermore, social media communication considerably expands the scope of protests by spreading events across different causes (e.g., from anticorruption protests to environmental protests) and dramatically increases the probability of far‐reaching protest waves with simultaneous events occurring in many cities. These effects arise even though Chinese social media barely circulates content that explicitly helps organize protests.
The maximum‐likelihood estimator of nonlinear panel data models with fixed effects is asymptotically biased under rectangular‐array asymptotics. The literature has devoted substantial effort to devising methods that correct for this bias as a means to salvage standard inferential procedures. The chief purpose of this paper is to show that the (recursive, parametric) bootstrap replicates the asymptotic distribution of the (uncorrected) maximum‐likelihood estimator and of the likelihood‐ratio statistic. This justifies the use of confidence sets and decision rules for hypothesis testing constructed via conventional bootstrap methods. No modification for the presence of bias needs to be made.
Climate change is increasing the frequency of extreme weather events, with low‐income countries being disproportionately impacted. However, these countries often face market frictions that hinder their ability to adopt effective adaptation strategies. In this paper, I explore the role of credit market failures in limiting adaptation. To achieve this, I collaborate with a large microfinance institution and offer a randomly selected group of farmers access to guaranteed credit through an “Emergency Loan” following a negative climate shock. I document three key results. First, farmers who have access to the emergency loan make less costly adaptation choices and are less severely affected when a flood occurs. Second, I find no evidence of adverse spillover effects on households that did not receive the Emergency Loan. Finally, I demonstrate that providing the Emergency Loan is profitable for the microfinance institution, making it a viable tool for the private sector to employ in similar circumstances.
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.