Dynamic Discrete Choice Model Research Articles

Network-based representations and dynamic discrete choice models for multiple discrete choice analysis

In many choice modeling applications, consumer demand is frequently characterized as multiple discrete, which means that consumer choose multiple items simultaneously. The analysis and prediction of consumer behavior in multiple discrete choice situations pose several challenges. In this paper, to address this, we propose a random utility maximization (RUM) based model that considers each subset of choice alternatives as a composite alternative, where individuals choose a subset according to the RUM framework. While this approach offers a natural and intuitive modeling approach for multiple-choice analysis, the large number of subsets of choices in the formulation makes its estimation and application intractable. To overcome this challenge, we introduce directed acyclic graph (DAG) based representations of choices where each node of the DAG is associated with an elemental alternative and additional information such as the number of selected elemental alternatives. Our innovation is to show that the multi-choice model is equivalent to a recursive route choice model on the DAG, leading to the development of new efficient estimation algorithms based on dynamic programming. In addition, the DAG representations enable us to bring some advanced route choice models to capture the correlation between subset choice alternatives. Numerical experiments based on synthetic and real datasets show many advantages of our modeling approach and the proposed estimation algorithms.

Human capital and migration: A cautionary tale

We analyze the impact that the option of migration might have on human capital accumulation. We show that, when the return to education for migrants is lower in the destination than in the origin, the overall incentive to accumulate human capital is reduced as restrictions on migration are relaxed. We use panel data from the Chinese Household Income Project to document that the return to education for rural individuals is lower in urban areas than in rural areas. We then use a difference-in-differences design to show that the 1983 reform that eliminated the strong restriction that existed for rural–urban migration resulted in a reduction of 0.4 years of schooling for rural people in China. Guided by these results, we estimate a life-cycle dynamic discrete choice model of education decisions and circular rural–urban migration in which individuals differ in observable characteristics and unobservable cognitive and non-cognitive skills. We validate the model by showing it is able to replicate the impact estimates from the difference-in-differences specification. Our simulations show that, while it would take a small subsidy (conditional on staying in school) to undo about 40% of the negative effects of the 1983 policy on rural education, the annual subsidy would need to be half of annual earnings to undo the effects entirely.

Semiparametric Bayesian estimation of dynamic discrete choice models

We propose a tractable semiparametric estimation method for structural dynamic discrete choice models. The distribution of additive utility shocks in the proposed framework is modeled by location-scale mixtures of extreme value distributions with varying numbers of mixture components. Our approach exploits the analytical tractability of extreme value distributions in the multinomial choice settings and the flexibility of the location-scale mixtures. We implement the Bayesian approach to inference using Hamiltonian Monte Carlo and an approximately optimal reversible jump algorithm. In our simulation experiments, we show that the standard dynamic logit model can deliver misleading results, especially about counterfactuals, when the shocks are not extreme value distributed. Our semiparametric approach delivers reliable inference in these settings. We develop theoretical results on approximations by location-scale mixtures in an appropriate distance and posterior concentration of the set identified utility parameters and the distribution of shocks in the model.

Dynamic discrete choice model and its estimation algorithm with dynamic inconsistent expected utility in an uncertain situation

Decision making in terms of travel behavior is always dynamic; however, the future behavior of an individual is often inconsistent with their present plan. Therefore, this study aims to incorporate dynamic inconsistency into the expected utility of dynamic sequential choices with a novel structural estimation approach. The incorporation of dynamic heterogeneity into expected utility enables the illustrative modeling of more types of decision making because decision making often involves dynamic inconsistent expected utilities. However, the existing approaches for dynamic discrete choice suppose an equilibrium situation and cannot evaluate these dynamic inconsistent situations. In this study, we propose a novel dynamic discrete choice model with dynamic inconsistency in its expected utility and an empirical algorithm for parameter estimation. We formulate a heterogeneous expected utility as a range constraint near the dynamic consistent expected utility for model identification. Our algorithm, which applies a mathematical program to inequality constraints, enables parameter estimation with dynamic heterogeneity. The proposed model and algorithm were applied to the problem of evacuation departure choice in the city of Rikuzentakata during the Great East Japan Earthquake and Tsunami of 2011. The case study demonstrated the validity of introducing dynamic heterogeneity via likelihood comparisons; it was also found that dynamic heterogeneity is distributed around the dynamic consistent expected utility.

Positive Spillovers from Infrastructure Investment: How Pipeline Expansions Encourage Fuel Switching

Abstract This paper studies the role of the U.S. pipeline infrastructure in the country's transition from coal to natural gas energy. I leverage the Environmental Protection Agency's Mercury and Air Toxics Standards as a plausibly exogenous intervention, which encouraged many coal plants to convert to natural gas. Combining this quasi-experimental variation with a plant's preexisting proximity to the pipeline network, I isolate implied pipeline connection costs within a dynamic discrete choice model of plant conversions. Key model results indicate that infrastructure-related costs prevent $9 billion in emissions reductions from taking place, suggesting a $2.4 million per mile external benefit of pipeline expansions.

Nested Pseudo likelihood estimation of continuous-time dynamic discrete games

We introduce a sequential estimator for continuous time dynamic discrete choice models (single-agent models and games) by adapting the nested pseudo likelihood (NPL) estimator of Aguirregabiria and Mira (2002, 2007), developed for discrete time models with discrete time data, to the continuous time case with data sampled either discretely (i.e., uniformly-spaced snapshot data) or continuously. We establish conditions for consistency and asymptotic normality of the estimator, a local convergence condition, and, for single agent models, a zero Jacobian property assuring local convergence. We carry out a series of Monte Carlo experiments using an entry-exit game with five heterogeneous firms to confirm the large-sample properties and demonstrate finite-sample bias reduction via iteration. In our simulations we show that the convergence issues documented for the NPL estimator in discrete time models are less likely to affect comparable continuous-time models. We also show that there can be large bias in economically-relevant parameters, such as the competitive effect and entry cost, from estimating a misspecified discrete time model when in fact the data generating process is a continuous time model.

Threshold-based incentives for ride-sourcing drivers: Implications on supply management and welfare effects

Ride-sourcing companies have been widely using threshold-based incentive programs to encourage drivers to extend their work hours. In such programs, a driver receives a certain amount of monetary reward if she completes a given supply task within a predetermined time window. However, despite the popularity of these incentives, little is known about how drivers respond to them in practice, and currently, there are no means to comprehensively evaluate and optimize their designs. To fill the void, we develop a dynamic discrete choice model that formulates ride-sourcing drivers’ working decisions influenced by threshold-based incentives and then calibrate it using real-world data from a ride-sourcing company. Our results provide fresh insights into the market and welfare effects of the threshold-based incentive and its various designs. It is found that the threshold-based incentive could increase welfare significantly for full-time drivers but marginally for part-time drivers. In contrast, involving part-time drivers in the incentive programs generally can yield higher profits for the platform, while incentivizing full-time drivers is mostly unprofitable. On incentive design, the incentive threshold and reward must be closely paired for different driver groups to avoid inferior consequences for the platform and drivers. In addition, switching from threshold-based incentives to direct wage increments may benefit both full-time drivers and the ride-sourcing company.

Role of next generation access networks on COVID-19 propagation: Empirical assessment with a dynamic multinomial discrete choice model framework

Through the application of discrete choice and machine learning models, the primary objective of this study is to assess the impact of NGA networks coverage on reducing the risk of contagion during the first wave of COVID-19 across 278 municipalities in mainland Portugal, while controlling for other domains under the tutelage of the local public administration. Benchmark estimations reveal that, while holding everything else constant, each spatial unit is 2.4 p.p. more likely to become a high-risk municipality with additional 10 ​000 cabled houses with NGA networks. In a multinomial discrete choice model setting, the technical novelty of this study lies in providing graphical visualization and economic interpretation of coefficients and average marginal effects as a function of the number of classes used to define the dependent variable, while ensuring the satisfaction of the IIA assumption. The positive and significant coefficients of NGA indicate that additional coverage of NGA networks increases the likelihood of municipalities becoming high-risk for increasing number of spatial units not belonging to the low-risk efficiency frontier. The significant, negative, and decreasing average marginal effects of NGA suggest that the ability to remain a low-risk municipality diminishes with increasing NGA networks coverage as the number of municipalities belonging to the low-risk efficiency frontier decreases. The analysis also confirms that the effect of NGA networks coverage on COVID-19 is statistically significant in the indirect channel. This impact persists due to the mediation of population density, which is directly influenced by NGA networks coverage. All these findings can be explained by the fact that benefits related to productive activities do not outweigh costs associated with leisure time. Hence, this research emphasizes the need for a normative discussion on the intended purpose of digital technologies built on top of NGA networks to ensure a level playing field in the post-pandemic era.

Dynamic discrete choice models with incomplete data: Sharp identification

In many empirical studies, those states that are relevant for forward-looking economic agents to make decisions may not be included in the data to which researchers have access. This problem often arises in the context of declining/booming industries. In this paper, we develop the sharp identified sets of structural parameters and counterfactuals for dynamic discrete choice models when empirical data do not cover realizations of relevant future states. Applying the proposed method to the annual Toyo Keizai database, we study the behaviors of Japanese firms on foreign direct investments in China without observing the future states after Chinese economy slows down.

Estimating a model of forward-looking behavior with discrete choice experiments: The case of lifetime hunting license demand

Sales of deer licenses, one of the most important revenue sources for wildlife management at the Indiana Department of Natural Resources (IDNR), have been declining for a decade. To increase its revenue, the IDNR is considering introducing a new lifetime deer license for sale. This license would allow hunters to harvest deer (and possibly other species) each year for the rest of their lives in exchange for a relatively large up-front fee. The forward-looking nature of the decision to buy a lifetime license means hunters' choice behavior is necessarily dynamic. Prior work estimates preferences for long-lived, durable goods using standard discrete choice experiments underpinned by static models. We derive a dynamic discrete choice model of lifetime license purchases. Our model informs the design of a novel, dynamic discrete choice experiment, generating data that allows us to consistently estimate individuals’ forward-looking preferences for lifetime hunting licenses. We use our model to estimate the price of lifetime licenses that maximizes IDNR revenues.

Online and In-Store Shopping Behavior during the COVID-19 Pandemic: Lessons Learned from a Panel Survey in New York City

This paper presents a study of various factors that influenced online and in-store shopping behaviors in New York City during the COVID-19 pandemic. It uses panel data collected by the New York City Department of Transportation for May, July, and October 2020. In the survey, 696 respondents consistently responded in all three months and, therefore, this group was used for analysis. The study adopts random effect ordered probit models with marginal effects and dynamic discrete choice models to understand the factors that influenced online and in-store shopping during the pandemic. The models reveal that increased subway usage was correlated with in-store shopping during the pandemic. Income also played a part in shopping behavior: higher-income individuals were less likely to shop in store, whereas lower-income individuals (more likely to ride the subway or bus) were more likely to shop in store. Contrary to previous research, age did not appear to have an impact on online and in-store shopping behaviors. Finally, this study discovered that online and in-store shopping are not necessarily indirectly proportional, which was unexpected. This means an increase in online shopping does not necessarily lead directly to a decrease in in-store shopping. By understanding how individuals reacted to the pandemic, proper policies—especially from a transportation aspect—can be developed in advance to prepare for future pandemic threats.

Counterfactual Sensitivity and Robustness

We propose a framework for analyzing the sensitivity of counterfactuals to parametric assumptions about the distribution of latent variables in structural models. In particular, we derive bounds on counterfactuals as the distribution of latent variables spans nonparametric neighborhoods of a given parametric specification while other “structural” features of the model are maintained. Our approach recasts the infinite‐dimensional problem of optimizing the counterfactual with respect to the distribution of latent variables (subject to model constraints) as a finite‐dimensional convex program. We also develop an MPEC version of our method to further simplify computation in models with endogenous parameters (e.g., value functions) defined by equilibrium constraints. We propose plug‐in estimators of the bounds and two methods for inference. We also show that our bounds converge to the sharp nonparametric bounds on counterfactuals as the neighborhood size becomes large. To illustrate the broad applicability of our procedure, we present empirical applications to matching models with transferable utility and dynamic discrete choice models.

Dynamic Spatial General Equilibrium

We incorporate forward‐looking capital accumulation into a dynamic discrete choice model of migration. We characterize the steady‐state equilibrium; generalize existing dynamic exact‐hat algebra techniques to incorporate investment; and linearize the model to provide an analytical characterization of the economy's transition path using spectral analysis. We show that capital and labor dynamics interact to shape the economy's speed of adjustment toward steady state. We implement our quantitative analysis using data on capital stocks, populations, and bilateral trade and migration flows for U.S. states from 1965–2015. We show that this interaction between capital and labor dynamics plays a central role in explaining the observed decline in the rate of income convergence across U.S. states and the persistent and heterogeneous impact of local shocks.

A Recursive Partitioning Approach for Dynamic Discrete Choice Models in High-Dimensional Settings

A Recursive Partitioning Approach for Dynamic Discrete Choice Models in High-Dimensional Settings

Identification of Dynamic Discrete Choice Models with Hyperbolic Discounting Using a Terminating Action

Identification of Dynamic Discrete Choice Models with Hyperbolic Discounting Using a Terminating Action

Job prospects and labour mobility in China

China's structural changes have brought new challenges to its regional employment structures, entailing labour redistribution. Until now, Chinese migration research with a forward-looking perspective and on bilateral longitudinal determinants at the prefecture city level is almost non-existent. This paper investigates the effects of job prospects on individual migration decisions across prefecture boundaries. To this end, we created proxy variables for wage and employment prospects, introduced reference-dependence to a dynamic discrete choice model, and estimated corresponding empirical specifications with a unique quasi-panel of 66,427 individuals from 283 cities during 1997–2017. To address multilateral resistance to migration resulting from the future attractiveness, we exploited various monadic and dyadic fixed effects. Multilevel logit models and two-step system GMM estimation were adopted for the robustness check. Our primary findings are that a 10% increase in the ratio of sector-based employment prospects in cities of destination to cities of origin raises the probability of migration by 1.281–2.185 percentage points, and the effects tend to be stronger when the scale of the ratio is larger. Having a family migration network causes an increase of approximately 6 percentage points in migratory probabilities. Further, labour migrants are more likely to be male, unmarried, younger, or more educated. Our results suggest that the ongoing industrial reform in China influences labour mobility between cities, providing important insights for regional policymakers to prevent brain drain and to attract relevant talent.

Understanding the Effects of Workfare Policies on Child Human Capital

Workfare can impact child development by inducing parents to spend less time at home. I study the mechanisms by which workfare policies affect children using the New Hope workfare experiment. The program randomly assigned individuals to a policy bundle including income and childcare subsidies conditional on full-time work. For families with young children, the program had positive effects on child academic performance and classroom behavior. Counterfactual experiments from a dynamic discrete choice model indicate that most of the effect of New Hope on young children is explained by parents enrolling their children in center-based childcare.

Modeling activity-travel behavior under a dynamic discrete choice framework with unobserved heterogeneity

The major challenges in dynamic activity-based models include predicting activity-related choices and understanding inherent heterogeneous preferences. The dynamic discrete choice model (DDCM) has been used for daily activity-travel planning. However, ignoring unobservable heterogeneity can bias the estimation and prediction results. To solve this problem, we propose a DDCM that accounts for unobserved heterogeneity to capture useful hidden information on travelers’ characteristics. The conditional choice probability estimator and expectation–maximization (EM) algorithm are used in conjunction to estimate the dynamic model. The algorithm iteration depends mainly on the mapping relationship between posterior distributions and conditional choice probabilities. Meanwhile, a less complex log-likelihood function is proposed in the maximization step to estimate two types of parameters simultaneously. The proposed techniques are verified using household travel survey data from Chongqing (China). Two unobserved types of travelers, time and cost sensitivity, are identified based on the Bayesian information criterion (BIC) value. Time- and segment-varying sensitivity analyses are conducted to present choice probability differences of mode and activity scheduling under a one-unit increase in the number of schoolchildren and cars. Different impacts on activity-travel patterns, such as trip frequency, mode share, and activity schedule, generated by changes in auto ownership, are analyzed. Finally, the adjusted rho-squared value, BIC values compared with other single-effect models, and aggregate validation results demonstrate the exceptional performance of the proposed model.

Dynamic demand for differentiated products with fixed-effects unobserved heterogeneity

Summary This paper studies identification and estimation of a dynamic discrete choice model of demand for differentiated product using consumer-level panel data with few purchase events per consumer (i.e., short panel). Consumers are forward-looking and their preferences incorporate two sources of dynamics: last choice dependence due to habits and switching costs, and duration dependence due to inventory, depreciation, or learning. A key distinguishing feature of the model is that consumer unobserved heterogeneity has a Fixed Effects structure; that is, its probability distribution conditional on the initial values of endogenous state variables is unrestricted. I apply and extend recent results to establish the identification of all the structural parameters as long as the dataset includes four or more purchase events per household. The parameters can be estimated using a sufficient statistic—conditional maximum likelihood (CML) method. An attractive feature of CML in this model is that the sufficient statistic controls for the forward-looking value of the consumer’s decision problem, such that the method does not require solving dynamic programming problems or calculating expected present values.

“It's Not You, It's Me”: Prices, Quality, and Switching in U.S.-China Trade Relationships

Abstract Costs from switching suppliers can affect prices by discouraging buyer movements from high- to low-cost sellers. This paper uses confidential data on U.S. importers and their Chinese exporters to investigate these costs. I find barriers to supplier adjustments: nearly half of importers keep their partner over time. Importers switch less if their supplier offers higher quality or provides lower prices. I propose and structurally estimate a dynamic discrete choice model to compute switching costs. Cost estimates are large, heterogeneous across products, and matter for trade prices: halving switching costs reduces the U.S.-China Import Price Index by 7.6%.