NONPARAMETRIC CONTINUOUS/DISCRETE CHOICE MODELS*

Modeling choices that are both discrete and continuous is important in several settings. The purpose of this article is to explore formulation and identification of such models when indirect utility functions are specified nonparametrically. Here we consider general nonseparable disturbances. We give identification results for nonseparable sample selection models and use these to analyze identification of discrete/continuous choice models.     

A NOTE ON SEMIPARAMETRIC ESTIMATION OF FINITE MIXTURES OF DISCRETE CHOICE MODELS WITH APPLICATION TO GAME THEORETIC MODELS*

We view a game abstractly as a semiparametric mixture distribution and study the semiparametric efficiency bound of this model. Our results suggest that a key issue for inference is the number of equilibria compared to the number of outcomes. If the number of equilibria is sufficiently large compared to the number of outcomes, root‐n consistent estimation of the model will not be possible. We also provide a simple estimator in the case when the efficiency bound is strictly above zero.     

A COMPUTATIONALLY PRACTICAL SIMULATION ESTIMATION ALGORITHM FOR DYNAMIC PANEL DATA MODELS WITH UNOBSERVED ENDOGENOUS STATE VARIABLES*

This article develops a simulation estimation algorithm that is particularly useful for estimating dynamic panel data models with unobserved endogenous state variables. Repeated sampling experiments on dynamic probit models with serially correlated errors indicate the estimator has good small sample properties. We apply the estimator to a model of female labor supply and show that the rarely used Polya model fits the data substantially better than the popular Markov model. The Polya model also produces far less state dependence and many fewer race effects and much stronger effects of education, young children, and husband's income on female labor supply decisions.     

THE IDENTIFICATION AND ECONOMIC CONTENT OF ORDERED CHOICE MODELS WITH STOCHASTIC THRESHOLDS*

This article extends the widely used ordered choice model by introducing stochastic thresholds and interval‐specific outcomes. The model can be interpreted as a generalization of the GAFT (MPH) framework for discrete duration data that jointly models durations and outcomes associated with different stopping times. We establish conditions for nonparametric identification. We interpret the ordered choice model as a special case of a general discrete choice model and as a special case of a dynamic discrete choice model.     

PRIOR ELICITATION IN MULTIPLE CHANGE‐POINT MODELS*

This article discusses Bayesian inference in change‐point models. The main existing approaches treat all change‐points equally, a priori, using either a Uniform prior or an informative hierarchical prior. Both approaches assume a known number of change‐points. Some undesirable properties of these approaches are discussed. We develop a new Uniform prior that allows some of the change‐points to occur out of sample. This prior has desirable properties, can be interpreted as “noninformative,” and treats the number of change‐points as unknown. Artificial and real data exercises show how these different priors can have a substantial impact on estimation and prediction.     

INCOMPLETE INFORMATION GAMES WITH MULTIPLE PRIORS*

We present a model of incomplete information games, where each player is endowed with a set of priors. Upon arrival of private information, it is assumed that each player “updates” his set of priors to a set of posterior beliefs, and then evaluates his actions by the most pessimistic posterior beliefs. So each player's preferences may exhibit aversion to ambiguity or uncertainty. We define a couple of equilibrium concepts, establish existence results for them, and demonstrate by examples how players’ views on uncertainty about the environment affect the strategic outcomes.     

COMPLEMENTS VERSUS SUBSTITUTES AND TRENDS IN FERTILITY CHOICE IN DYNASTIC MODELS*

Demographers emphasize decreased mortality and “economic development” as the main contributors generating the demographic transition. Contrary to previous findings, we show that simple dynastic models à la Barro–Becker can reproduce observed changes in fertility in response to decreased mortality and increased productivity growth if the intertemporal elasticity of substitution is low enough. We show that this is largely due to number and welfare of children being substitutes in the utility of parents in this case. We find that with an IES of one‐third, model predictions of changes in fertility amount to two‐thirds of those observed in U.S. data since 1800.     

IDENTIFICATION AND ESTIMATION OF AUCTION MODEL WITH TWO‐DIMENSIONAL UNOBSERVED HETEROGENEITY*

This article investigates the empirical importance of allowing for multidimensional sources of unobserved heterogeneity in auction models with private information. It develops the estimation procedure to recover the distribution of private information in the presence of two sources of unobserved heterogeneity. It is shown that this estimation procedure identifies components of the model and produces uniformly consistent estimators of these components. The results of the estimation with highway procurement data indicate that allowing for two‐dimensional unobserved heterogeneity may significantly affect the results of estimation as well as policy‐relevant instruments derived from the estimated distributions of bidders’ costs.     

A HYBRID DISCRETE CHOICE MODEL OF DIFFERENTIATED PRODUCT DEMAND WITH AN APPLICATION TO PERSONAL COMPUTERS

In this article, I consider a new discrete choice model of differentiated product demand that distinguishes a brand‐level differentiation from a product‐level differentiation. The model is a hybrid of the random coefficient logit model of Berry et al. (Econometrica 63 (1995), 841–90) and the pure characteristics model of Berry and Pakes (International Economic Review 48 (2007), 1193–1225) and describes markets where firms offer multiple products of different qualities under the same brand name. I compare the hybrid model with existing models using data on personal computers. Using the estimates of the hybrid model, I also provide empirical evidence that firms reposition their brands in a postmerger market.     

PANEL DATA ANALYSIS OF JAPANESE RESIDENTIAL WATER DEMAND USING A DISCRETE/CONTINUOUS CHOICE APPROACH*

Block rate pricing is often applied to income taxation, telecommunication services, and brand marketing, in addition to its best‐known application in public utility services. Under block rate pricing, consumers face piecewise‐linear budget constraints. A discrete/continuous choice approach is usually used to account for piecewise‐linear budget constraints in demand and price endogeneity. A recent study proposed a method to incorporate a separability condition ignored by previous studies, by implementing a Markov chain Monte Carlo simulation based on a hierarchical Bayesian approach. To extend this approach to panel data, our study proposes Bayesian hierarchical models incorporating random and fixed individual effects.     

PRODUCTION FUNCTION ESTIMATION WITH UNOBSERVED INPUT PRICE DISPERSION

We propose a method to consistently estimate production functions in the presence of input price dispersion when intermediate input quantities are not observed. We find that the traditional approach to dealing with unobserved input quantities—using deflated expenditure as a proxy—substantially biases the production estimates. In contrast, our method controls for heterogeneous input prices by exploiting the first‐order conditions of the firm's profit maximization problem and consistently recovers the production function parameters. Using our preferred method, we provide empirical evidence of significant input price dispersion and even wider productivity dispersion than is estimated using proxy methods.     

USING ELICITED CHOICE PROBABILITIES TO ESTIMATE RANDOM UTILITY MODELS: PREFERENCES FOR ELECTRICITY RELIABILITY*

When choice data are not available, researchers studying preferences sometimes ask respondents to state the actions they would choose in choice scenarios. Data on stated choices are then used to estimate random utility models, as if they are data on actual choices. Stated and actual choices may differ because researchers typically provide respondents less information than they would have in actuality. Elicitation of choice probabilities overcomes this problem by permitting respondents to express uncertainty about behavior. This article shows how to use elicited choice probabilities to estimate random utility models and reports estimates of preferences for electricity reliability.     

SIMULTANEOUS MEASUREMENT OF TIME AND RISK PREFERENCES: STATED PREFERENCE DISCRETE CHOICE MODELING ANALYSIS DEPENDING ON SMOKING BEHAVIOR*

Measuring time and risk preferences and relating them to economic behaviors are important topics in behavioral economics. We developed a new method to simultaneously measure the rate of time preference and the coefficient of risk aversion. Analyzing the individual‐level relationships between preference parameters and cigarette smoking, we conclude that current smokers are more impatient and risk‐prone than nonsmokers. Heavy smokers are the most impatient and risk‐prone, whereas ex‐smokers are the most patient and risk‐averse. Among nonsmokers, neither age‐related nor gender‐related differences were found. On the other hand, risk and time preferences are significantly different according to age and gender for smokers.     

A DYNAMIC DISCRETE CHOICE MODEL OF REVERSE MORTGAGE BORROWER BEHAVIOR

Using unique data on reverse mortgage borrowers in the Home Equity Conversion Mortgage (HECM) program, we semiparametrically estimate a dynamic discrete choice model of borrower behavior. Our estimator is based on a new identification result we develop for models with multiple terminating actions. We show that the per-period utility functions and discount factor are identified without restrictive, ad hoc identifying restrictions that lead to incorrect counterfactual implications. Our estimates provide insights about factors that influence HECM refinance, default, and termination decisions and allow us to quantify the trade-offs involved for proposed program modifications, such as income and credit requirements.     

VOLATILITY MODELS*

Models for estimating the volatility of financial assets are reviewed in this paper. The volatility can be estimated by the univariate GARCH family of models, or stochastic volatility models. These univariate models are developed intomultivariate models. Finally, the search for an adequate framework for the estimation has led to the analysis of high frequency intraday data. The variance over a fixed interval can be estimated accurately as the sum of squared realizations, provided the data are available at sufficiently high sampling frequencies. The future of this new area is wide open for theoretical developments and for applied studies.     

IDENTIFICATION AND ESTIMATION OF EXCHANGE RATE MODELS WITH UNOBSERVABLE FUNDAMENTALS*

This article is concerned with issues of model specification, identification, and estimation in exchange rate models with unobservable fundamentals. We show that the continuous‐time model proposed by Gardeazabal, Regúlez, and Vázquez (International Economic Review 38 (1997), 389–404) is not identified and that this property is characteristic of the discrete‐time representation of the model that they used as the basis for estimation by simulated method of moments. We briefly discuss the implications of this result in the context of the asset‐market model of exchange rates with unobservable fundamentals.     

DISCRETE CHOICE AND RATIONAL INATTENTION: A GENERAL EQUIVALENCE RESULT

This article establishes a general equivalence between discrete choice and rational inattention models. Matějka and McKay (2015) showed that when information costs are modeled using the Shannon entropy, the choice probabilities in the rational inattention (RI) model take the multinomial logit form. We show that, for one given prior over states, RI choice probabilities may take the form of any additive random utility discrete choice model (ARUM) when the information cost is a Bregman information, a class defined in this article. The prior information of the rationally inattentive agent is summarized in a constant vector of utilities in the corresponding ARUM.