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A Discrete Choice Model for Ordered Alternatives

Econometrica 1987 55(2), 409 open access
A generalization of the multinomial logit (MNL) model is developed for cases in which discrete alternatives are ordered so as to induce stochastic correlation among alternatives in close proximity. The model belongs to the Generalized Extreme Value class introduced by McFadden, and is therefore consistent with random utility maximization. If the true model is nearly MNL, iterative estimation on an ordinary MNL computer package provides approximate parameter estimates and a test for the hypothesized failure of the MNL'S "independence from irrelevant alternatives" assumption. A straightforward extension can handle cases where observations have been selected on the basis of a truncated choice set. The model's properties are investigated through a numerical example, and through two empirical applications whose rather unsatisfactory results are very briefly described.

Inferring Labor Income Risk and Partial Insurance From Economic Choices

Econometrica 2014 82(6), 2085-2129 open access
This paper uses the information contained in the joint dynamics of individuals' labor earnings and consumption-choice decisions to quantify both the amount of income risk that individuals face and the extent to which they have access to informal insurance against this risk. We accomplish this task by using indirect inference to estimate a structural consumption–savings model, in which individuals both learn about the nature of their income process and partly insure shocks via informal mechanisms. In this framework, we estimate (i) the degree of partial insurance, (ii) the extent of systematic differences in income growth rates, (iii) the precision with which individuals know their own income growth rates when they begin their working lives, (iv) the persistence of typical labor income shocks, (v) the tightness of borrowing constraints, and (vi) the amount of measurement error in the data. In implementing indirect inference, we find that an auxiliary model that approximates the true structural equations of the model (which are not estimable) works very well, with negligible small sample bias. The main substantive findings are that income shocks are moderately persistent, systematic differences in income growth rates are large, individuals have substantial amounts of information about their income growth rates, and about one-half of income shocks are smoothed via partial insurance. Putting these findings together, the amount of uninsurable lifetime income risk that individuals perceive is substantially smaller than what is typically assumed in calibrated macroeconomic models with incomplete markets.

Pseudo Maximum Likelihood Methods: Theory

Econometrica 1984 52(3), 681 open access
Estimators obtained by maximizing a likelihood function are studied in the case where the true p.d.f. does not necessarily belong to the family chosen for the likelihood function. When such a procedure is applied to the estimation of the parameters of the first order moments, it is possible to prove a necessary and sufficient condition for its consistency. Asymptotic normality is shown as well as the existence of a lower bound for the asymptotic covariance matrix. It is also seen that this bound can be reached if consistent estimates are available for the parameters of the second order moments. Finally, a necessary and sufficient condition for the consistency if the pseudo maximum likelihood estimation of the first and second moments is given.

Identification of Nonparametric Simultaneous Equations Models With a Residual Index Structure

Econometrica 2018 86(1), 289-315 open access
We present new identification results for a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine traditional exclusion restrictions with a requirement that each structural error enter through a “residual index.†Our identification results are constructive and encompass a range of special cases with varying demands on the exogenous variation provided by instruments and the shape of the joint density of the structural errors. The most important results demonstrate identification when instruments have only limited variation. Even when instruments vary only over a small open ball, relatively mild conditions on the joint density suffice. We also show that the primary sufficient conditions for identification are verifiable and that the maintained hypotheses of the model are falsifiable.

Individual Heterogeneity and Average Welfare

Econometrica 2016 84(3), 1225-1248 open access
Individual heterogeneity is an important source of variation in demand. Allow-ing for general heterogeneity is needed for correct welfare comparisons. We consider general heterogenous demand where preferences and linear budget sets are statis-tically independent. Only the marginal distribution of demand for each price and income is identified from cross-section data where only one price and income is observed for each individual. Thus, objects that depend on varying price and/or income for an indiviual are not generally identified, including average exact con-sumer surplus. We use bounds on income effects to derive relatively simple bounds on the average surplus, including for discrete/continous choice. We also sketch an approach to bounding surplus that does not use income effect bounds. We apply the results to gasoline demand. We find tight bounds for average surplus in this application but wider bounds for average deadweight loss.

Experimental Methods of Analyzing Demand for Branded Consumer Goods with Applications to Problems in Marketing Strategy

Econometrica 1964 32(3), 467 open access
Prediction of consumer response to a proposed brand strategy is a major problem in marketing. An increasingly used and highly promising approach to this problem, and one pursued in this book, is to test proposed strategies in a controlled or simulated environment. This is done by placing representative consumers in an experimental environment which is sufficiently realistic to evoke responses similar to those in the marketplace. By manipulating aspects of this environment to reflect different strategies, one can predict with some confidence what will occur if those strategies are used in the market. The author presents an excellent case study in which a simulated market environment provides useful data concerning demand schedules for branded consumer goods and changes in the market share that might result from different brand policies. The book reports on a series of simulated shopping trips for toilet soap and toothpaste. Subjects were shown colored photographs indicating the brands available for each of the two products and asked to indicate the one brand for each they preferred. Prices of the preferred brand and competing brands were varied, with the price of the preferred brand always highest. The number of individuals switching and remaining loyal at different prices and the brands to which they switched were noted. The design of experiments (described in a technical appendix), the data generated and their analysis are more complex and interesting than this brief description might suggest. Chapter 5, "Experimental Results Relating to Brand Loyalty and Brand-Switching Behavior," and Chapter 6, "Models Using Experimental Data to Appraise Marketing Strategy," are the best and most important chap209

Food Policy in a Warming World

Econometrica 2026 94(2), 537-572 open access
This paper studies how governments intervene in agricultural markets to reshape the economic consequences of climate extremes. We construct a global dataset of agricultural policies and extreme heat exposure by country and crop since 1980. Extreme heat shocks to domestic production lead to policies that assist consumers by lowering domestic food prices. This effect is persistent, primarily implemented via border policies, and stronger during election years. Shocks to foreign production induce the opposite response: policies that assist producers by raising prices. These findings can be rationalized by a model in which governments use agricultural policy to redistribute among domestic interest groups. Our estimates imply that policy responses shield domestic consumers, while exacerbating losses for domestic producers and foreign consumers. Policy responses have regressive consequences globally, disproportionately harming poor and heat‐exposed countries.