Dynamic Discrete Choice Research Articles

Royal Economic Society Annual Conference 2021 Special Issue on Econometrics of Dynamic Discrete Choice

Royal Economic Society Annual Conference 2021 Special Issue on Econometrics of Dynamic Discrete Choice

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

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.

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%.

Prediction of population behavior in hurricane evacuations

This study advances prediction of population evacuation behavior during hurricanes by comprehensively comparing five different models based on their practical utility for future hurricanes. The models—participation rate (PR-S), logistic regression (LR-S), random parameter logit (RPL), time-dependent Cox (TD-Cox), and dynamic discrete choice (DDC)—were fitted using population survey and hurricane data collected in a consistent format across four different hurricanes (Florence 2018, Michael 2018, Dorian 2019, and Barry 2019). Out-of-sample predictive power was evaluated in terms of prediction of total evacuation rates, spatial distribution of evacuees, evacuation timing, and individual behavior. The final set of predictors can be obtained for a whole region and applied in the future for prediction. The results suggest that if only an estimate of the total evacuation rate for the whole region is required, the LR-S is easiest to implement and provides good predictive power. However, if spatial and/or timing predictions are required, the DDC is recommended. The results suggest that in general, for future hurricanes, the best models currently available can estimate total evacuation rate within one to nine percentage points; evacuation rate for each county within 10 to 15 percentage points; and departure curve within several hours. Results also indicate that errors become smaller as geographic granularity increases.

The Impact of Internship Experience on Schooling and Labour Market Outcomes

Abstract We examine the impact of internship experience during secondary education on students’ schooling and early labour market outcomes by analysing unique, longitudinal data from Belgium. To control for unobservable differences between students with and students without internship experience, we estimate a dynamic discrete choice model. In line with literature on vocational education, we find that internship experience has a positive effect on one’s employment chances up to 5 years after graduation. This positive effect is mainly explained by a positive direct employment effect. Although we also find a positive indirect employment effect through a higher chance to obtain a secondary education qualification, this is largely compensated by negative indirect effects through lower tertiary education attainment. (JEL codes: I21, I26, J21, and J24)

Public-private partnerships: A dynamic discrete choice model for road projects

Public-Private Partnerships (PPPs) are an effective vehicle for delivering critical infrastructure worldwide, particularly road transport assets (e.g., bridges, toll roads and tunnels). However, PPPs have been and continue to be controversial forms of project delivery as there are concerns about their ability to provide taxpayers with value for money (VfM). Current practice to determine VfM focuses on a ‘simplistic’ ex-ante evaluation referred to as the Public Sector Comparator (PSC), aiming to take a life-cycle approach to cost and benefits assessment. However, the complexity of transport projects renders the PSC ineffective and static evaluation of cost and benefits across their life-cycle. Therefore, the PSC cannot accommodate a project's environment's dynamic and changing nature. Acknowledging the limitations of the PSC, we develop and examine a dynamic discrete choice model that can be used to provide a VfM assessment for ‘road projects’. By validating the proposed model using two illustrative cases, the results suggest it can capture a more comprehensive assessment of cost components, functionality, and benefits specific to road projects and quantify the relationship between the consideration of different assessment elements and choice utility. Therefore, utilising the new model to assess VfM can enable policymakers to make more informed decisions about the employment of PPPs.

The influence function of semiparametric estimators

There are many economic parameters that depend on nonparametric first steps. Examples include games, dynamic discrete choice, average exact consumer surplus, and treatment effects. Often estimators of these parameters are asymptotically equivalent to a sample average of an object referred to as the influence function. The influence function is useful in local policy analysis, in evaluating local sensitivity of estimators, and constructing debiased machine learning estimators. We show that the influence function is a Gateaux derivative with respect to a smooth deviation evaluated at a point mass. This result generalizes the classic Von Mises (1947) and Hampel (1974) calculation to estimators that depend on smooth nonparametric first steps. We give explicit influence functions for first steps that satisfy exogenous or endogenous orthogonality conditions. We use these results to generalize the omitted variable bias formula for regression to policy analysis for and sensitivity to structural changes. We apply this analysis and find no sensitivity to endogeneity of average equivalent variation estimates in a gasoline demand application.

Spmv Approaches to Dynamic Discrete Choice Models with Limited Transition

Spmv Approaches to Dynamic Discrete Choice Models with Limited Transition

Locally Robust Semiparametric Estimation

Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where first steps have no effect, locally, on average moment functions. Using these orthogonal moments reduces model selection and regularization bias, as is important in many applications, especially for machine learning first steps. Also, associated standard errors are robust to misspecification when there is the same number of moment functions as parameters of interest. We use these orthogonal moments and cross‐fitting to construct debiased machine learning estimators of functions of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that additional first steps needed for the orthogonal moment functions have no effect, globally, on average orthogonal moment functions. We give a general approach to estimating those additional first steps. We characterize double robustness and give a variety of new doubly robust moment functions. We give general and simple regularity conditions for asymptotic theory.

The whole day path planning problem incorporating mode chains modeling in the era of mobility as a service

The growing popularity of Mobility as a Service (MaaS) has led researchers to realize that it can be used for the optimal management of the transportation system of a city. This study is to solve the whole day multimodal path planning problem considering user-specific modal preference, which can be used on the recommended system of the MaaS platform. The mathematical formulations of the whole day multimodal shortest hyperpath problem are proposed while accounting for individual constraints, such as the time window, multicriteria, and park-and-ride demands, to develop customized travel schemes. The primary obstacle involves consideration of the travelers’ modal preferences to develop an optimal whole day journey. The dynamic discrete choice model (DDCM) that accounts for unobservable heterogeneity is proposed to characterize dynamic mode choice behavior and generate a set of feasible mode chains. The conditional choice probability estimator and expectation–maximization (EM) algorithm are used in conjunction to estimate the dynamic model. In this way, the posterior probability can be adapted to the conditional choice probability estimation. The label correcting concept is used to develop a user-constrained shortest hyperpath algorithm that can solve the multimodal shortest hyperpath problem and calculate the Pareto set of the whole day travel schemes according to the feasible mode chains and different constraints. The proposed techniques are verified by utilizing household travel survey data and multimodal network data in Nanjing (China). Two unobserved states of travelers, namely time- and cost-sensitive, are identified based on the BIC value. The adjusted rho-squared value, accuracies of predicted mode chains, along with the aggregate validation results, confirm the model’s effectiveness. The top two resulting hyperpaths are generated for a randomly chosen traveler on the basis of his or her preferences. This study is an important step toward promoting MaaS and improving the sales of MaaS bundles.

Learning ride-sourcing drivers’ customer-searching behavior: A dynamic discrete choice approach

Ride-sourcing drivers spend a significant portion of their service time being idle, during which they can move freely to search for the next customer. Such customer-searching movements, while not being directly controlled by ride-sourcing platforms, impose great impacts on the service efficiency of ride-sourcing systems and thus need to be better understood. To this purpose, we design a dynamic discrete choice framework by modeling drivers’ customer search as absorbing Markov decision processes. The model enables us to differentiate three latent search movements of idle drivers, as they either remain motionless, cruise around without a target area, or reposition toward specific destinations. Our calibration takes advantage of large-scale empirical datasets from Didi Chuxing, including the transaction information of five million passenger requests and the trajectories of 32,000 affiliated drivers. The calibration results uncover the variations of drivers’ attitudes in customer search across time and space. In general, ride-sourcing drivers do respond actively and positively to the repetitive market variations when idle. They are comparatively more mobile at high-demand hotspots while preferring to stay motionless in areas with long time of waiting being expected. Our results also suggest that drivers’ search movements are not confined to local considerations. Instead, idle drivers show a clear tendency of repositioning toward the faraway hotspots, especially during the evening when the demand cools down in the suburb. The discrepancies between full-time and part-time drivers’ search behavior are also examined quantitatively.

Identification of counterfactuals in dynamic discrete choice models

Dynamic discrete choice (DDC) models are not identified nonparametrically, but the non‐identification of models does not necessarily imply the nonidentification of counterfactuals. We derive novel results for the identification of counterfactuals in DDC models, such as non‐additive changes in payoffs or changes to agents' choice sets. In doing so, we propose a general framework that allows the investigation of the identification of a broad class of counterfactuals (covering virtually any counterfactual encountered in applied work). To illustrate the results, we consider a firm entry/exit problem numerically, as well as an empirical model of agricultural land use. In each case, we provide examples of both identified and nonidentified counterfactuals of interest.

Diamonds in the Rough: Leveraging Click Data to Spotlight Underrated Products

Problem Definition. Inspired by a real data set from the Chinese retailer JD.com, we study the click and purchase behavior of customers in an online retail setting by employing a structural estimation approach. In particular, we aim to understand what characteristics of products drive the click versus purchase decisions of customers.With the boom in e-commerce, which has been further fueled due to the current COVID-19 pandemic, an ever increasing number of customers are shopping online. Such a rapid growth in online shopping provides retailers with abundance of data to study customer shopping behavior. For example, online retailers can benefit from a better understanding of the customer search (click) and purchase behavior to improve their operational decisions such as assortment planning. From an academic standpoint, even though there is an extensive body of work on consumer search models, most prior work do not incorporate search sequences and purchase decisions of customers jointly in their analysis. We, however, combine the click and order data to estimate both the click and purchase behavior of customers.Methodology/Results. Using a large data set from JD.com, we propose a structural model to estimate the click and purchase behavior of customers according to a dynamic discrete choice model. In particular, we assume that the customer's utility from each product has an observed and (pre-click) unobserved part (in addition to a random shock). The observed part of the utility is known to the customer prior to the click; however, the unobserved part of the utility can only be learned after the customer clicks on the product. We assume that the customer solves a dynamic program in order to find the optimal search strategy. Due to the curse of dimensionality, we propose a novel value function approximation scheme inspired by the Conditional Choice Probability approach. This, in turn, reduces the estimation into a computationally tractable two-stage process. By combining the click and order data, our proposed structural framework allows us to disentangle and estimate the observed and unobserved parts of product utilities. Our estimation results show that the value of click for customers can be quite significant. This is evidenced by the fact that the unobserved utilities of products vary significantly across products. Most importantly, we are able to identify underrated products which we call diamonds in the rough: these are products with low “face” values (i.e., low observed utilities), but high total utilities due to their high unobserved utilities. Thus, even though such products have a low chance of being clicked (due to their low observed utilities), they have a high chance of being purchased, if clicked.Managerial Implications. Our structural framework provides an online retailer with new tools and insights to better manage the product assortment based on customer click and purchase behavior. In particular, our structural model allows the retailer to disentangle the observed and unobserved parts of product utilities and identify underrated diamond-in-the-rough products. The online retailer can increase her revenue by bringing such products into the spotlight by promoting them on the search page or using tags such as “spotlight product” (similar to “Amazon's Choice” tags on Amazon.com) to entice customers to click on them.