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.
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.
Most empirical work in economics has considered only a narrow set of measures as meaningful and useful to characterize individual behavior, a restriction justified by the difficulties in collecting a wider set. However, this approach often forces the use of strong assumptions to estimate the parameters that inform individual behavior and identify causal links. In this paper, we argue that a more flexible and broader approach to measurement could be extremely useful and allow the estimation of richer and more realistic models that rest on weaker identifying assumptions. We argue that the design of measurement tools should interact with, and depend on, the models economists use. Measurement is not a substitute for rigorous theory, it is an important complement to it, and should be developed in parallel to it. We illustrate these arguments with a model of parental behavior estimated on pilot data that combines conventional measures with novel ones.
Interpreting individual heterogeneity in terms of probability theory has proved powerful in connecting behaviour at the individual and aggregate levels. Returning to Ricardo's focus on comparative efficiency as a basis for international trade, much recent quantitative equilibrium modeling of the global economy builds on particular probabilistic assumptions about technology. We review these assumptions and how they deliver a unified framework underlying a wide range of static and dynamic equilibrium models.
This paper develops the nonparametric identification of models with production complementarities, worker-firm specific disutility of labor and search frictions. Mobility in the model is subject to preference shocks, and we assume that firms can write wage contracts. We develop a constructive proof for the nonparametric identification of the model primitives from matched employer-employee data. We use the estimated model to decompose the sources of wage dispersion into worker heterogeneity, compensating differentials, and search frictions that generate between-firm and within-firm dispersion. We find that compensating differentials are substantial on average, but the contribution differs greatly between the lowest and highest types of workers. Finally, we use the model to provide an economic interpretation of several empirical regularities.
We study personalized pricing in a general oligopoly model. The impact of personalized pricing relative to uniform pricing hinges on the degree of market coverage. If market conditions are such that coverage is high (e.g., the production cost is low or the number of firms is high), personalized pricing harms firms and benefits consumers, whereas the opposite is true if coverage is low. When only some firms have data to personalize prices, consumers can be worse off compared to when either all or no firms personalize prices.
Two years prior to elections, two-thirds of Delhi municipal councillors learned they had been randomly chosen for a preelection newspaper report card. Treated councillors in high-slum areas increased pro-poor spending, relative both to control counterparts and treated counterparts from low-slum areas. Treated incumbents ineligible to rerun in home wards because of randomly assigned gender quotas were substantially likelier to run elsewhere only if their report card showed a strong pro-poor spending record. Parties also benefited electorally from councillors' high pro-poor spending. In contrast, in a cross-cut experiment, councillors did not react to actionable information that was not publicly disclosed.
New limit theory is provided for a wide class of sample variance and covariance functionals involving both nonstationary and stationary time series. Sample functionals of this type commonly appear in regression applications and the asymptotics are particularly relevant to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root or fractional processes. The limit theory is unusually general in that it covers both parametric and nonparametric regressions. Self normalized versions of these statistics are considered that are useful in inference. Numerical evidence reveals interesting strong bimodality in the finite sample distributions of conventional self normalized statistics similar to the bimodality that can arise in t-ratio statistics based on heavy tailed data. Bimodal behavior in these statistics is due to the presence of long memory innovations and is shown to persist for very large sample sizes even though the limit theory is Gaussian when the long memory innovations are stationary. Bimodality is shown to occur even in the limit theory when the long memory innovations are nonstationary. To address these complications new self normalized versions of the test statistics are introduced that deliver improved approximations that can be used for inference.
We study dynamic price competition between sellers offering differentiated products with limited capacity and a common sales deadline. In every period, firms simultaneously set prices, and a randomly arriving buyer decides whether to purchase a product or leave the market. Given remaining capacities, firms trade off selling today against shifting demand to competitors to obtain future market power. We provide conditions for the existence and uniqueness of pure-strategy Markov perfect equilibria. In the continuous-time limit, prices solve a system of ordinary differential equations. We derive properties of equilibrium dynamics and show that prices increase the most when the product with the lowest remaining capacity sells. Because firms do not fully internalize the social option value of future sales, equilibrium prices can be inefficiently low such that both firms and consumers would benefit if firms could commit to higher prices. We term this new welfare effect the Bertrand scarcity trap.
In this paper we develop a novel approach to measuring individual welfare within house-holds, recognizing that individuals may have both different preferences (particularly regarding public consumption) and differential access to resources. We construct a money metric mea-sure of welfare that accounts for public goods (by using personalized prices) and the allocation of time. We then use our conceptual framework to analyse intrahousehold inequality in Japan, allowing for the presence of two public goods: expenditures on children and other public goods including housing. We show empirically that women have much stronger preferences for both public goods and this has critical implications for the distribution of welfare in the household.