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on Discrete Choice Models |
| By: | Andrew Chesher; Adam Rosen; Yuanqi Zhang |
| Abstract: | Many structural econometric models include latent variables on whose probability distributions one may wish to place minimal restrictions. Leading examples in panel data models are individual-specific variables sometimes treated as “fixed effects” and, in dynamic models, initial conditions. This paper presents a generally applicable method for characterizing sharp identified sets when models place no restrictions on the probability distribution of certain latent variables and no restrictions on their covariation with other variables. In our analysis latent variables on which restrictions are undesirable are removed, leading to econometric analysis robust to misspecification of restrictions on their distributions which are commonplace in the applied panel data literature. Endogenous explanatory variables are easily accommodated. Examples of application to some static and dynamic binary, ordered and multiple discrete choice and censored panel data models are presented. |
| Date: | 2024–01–08 |
| URL: | http://d.repec.org/n?u=RePEc:azt:cemmap:01/24&r=dcm |
| By: | Narine Yegoryan (HU Berlin); Daniel Guhl (HU Berlin); Friederike Paetz (Clausthal University of Technology) |
| Abstract: | Identifying consumer heterogeneity is a central topic in marketing. While the main focus has been on developing models and estimation procedures that allow uncovering consumer heterogeneity in preferences, a new stream of literature has focused on models that account for consumers’ heterogeneous attribute information usage. These models acknowledge that consumers may ignore subsets of attributes when making decisions, also commonly termed “attribute nonattendance" (ANA). In this paper, we explore the performance of choice models that explicitly account for ANA across ten different applications, which vary in terms of the choice context, the associated financial risk, and the complexity of the purchase decision. We systematically compare five different models that either neglect ANA and preference heterogeneity, account only for one at a time, or account for both across these applications. First, we showcase that ANA occurs across all ten applications. It prevails even in simple settings and high-stakes decisions. Second, we contribute by examining the direction and the magnitude of biases in parameters. We find that the location of zero with regard to the preference distribution affects the expected direction of biases in preference heterogeneity (i.e., variance) parameters. Neglecting ANA when the preference distribution is away from zero, often related to whether the attribute enables vertical differentiation of products, may lead to an overestimation of preference heterogeneity. In contrast, neglecting ANA when the preference distribution spreads on both sides of zero, often related to attributes enabling horizontal differentiation, may lead to an underestimation of preference heterogeneity. Lastly, we present how the empirical results translate into managerial implications and provide guidance to practitioners on when these models are beneficial. |
| Keywords: | choice modeling; preference heterogeneity; attribute non-attendance; inattention; |
| Date: | 2023–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:482&r=dcm |
| By: | William Liu |
| Abstract: | I develop the theory around using control functions to instrument hazard models, allowing the inclusion of endogenous (e.g., mismeasured) regressors. Simple discrete-data hazard models can be expressed as binary choice panel data models, and the widespread Prentice and Gloeckler (1978) discrete-data proportional hazards model can specifically be expressed as a complementary log-log model with time fixed effects. This allows me to recast it as GMM estimation and its instrumented version as sequential GMM estimation in a Z-estimation (non-classical GMM) framework; this framework can then be leveraged to establish asymptotic properties and sufficient conditions. Whilst this paper focuses on the Prentice and Gloeckler (1978) model, the methods and discussion developed here can be applied more generally to other hazard models and binary choice models. I also introduce my Stata command for estimating a complementary log-log model instrumented via control functions (available as ivcloglog on SSC), which allows practitioners to easily instrument the Prentice and Gloeckler (1978) model. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.03165&r=dcm |
| By: | Jos\'e Luis Montiel Olea; Chen Qiu; J\"org Stoye |
| Abstract: | We apply classical statistical decision theory to a large class of treatment choice problems with partial identification, revealing important theoretical and practical challenges but also interesting research opportunities. The challenges are: In a general class of problems with Gaussian likelihood, all decision rules are admissible; it is maximin-welfare optimal to ignore all data; and, for severe enough partial identification, there are infinitely many minimax-regret optimal decision rules, all of which sometimes randomize the policy recommendation. The opportunities are: We introduce a profiled regret criterion that can reveal important differences between rules and render some of them inadmissible; and we uniquely characterize the minimax-regret optimal rule that least frequently randomizes. We apply our results to aggregation of experimental estimates for policy adoption, to extrapolation of Local Average Treatment Effects, and to policy making in the presence of omitted variable bias. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.17623&r=dcm |
| By: | Pesce, Elena; Rapallo, Fabio; Riccomagno, Eva; Wynn, Henry P. |
| Abstract: | After a rich history in medicine, randomized control trials (RCTs), both simple and complex, are in increasing use in other areas, such as web-based A/B testing and planning and design of decisions. A main objective of RCTs is to be able to measure parameters, and contrasts in particular, while guarding against biases from hidden confounders. After careful definitions of classical entities such as contrasts, an algebraic method based on circuits is introduced which gives a wide choice of randomization schemes. |
| Keywords: | A/B testing; algebraic statistics and combinatorics; bias and confounders; big data; design of experiments; AAM requested |
| JEL: | C1 |
| Date: | 2022–12–23 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:118011&r=dcm |
| By: | Sven Neth |
| Abstract: | How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to define or measure subjective probability for partly irrational agents. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.09796&r=dcm |