Dynamic Discrete Choice Research Articles

Joint analysis of the discount factor and payoff parameters in dynamic discrete choice models

Most empirical models of dynamic games assume the discount factor to be known and focus on the estimation of the payoff parameters. However, the discount factor can be identifed when the payoffs satisfy parametric or other nonparametric restrictions. We show when the payoffs take the popular linear-in-parameter specification, the joint identification of the discount factor and payoff parameters can be simplified to a one-dimensional model that is easy to analyze. We also show that switching costs (e.g. entry costs) that often feature in empirical work can be identifed in closed-form, independently of the discount factor and other specification of the payoff function. Our identification strategies are constructive. They lead to easy to compute estimands that are global solutions. Estimating the discount factor permits direct inference on borrowing rate. Our estimates of the switching costs can be used for specification testing. We illustrate with a Monte Carlo study and the dataset from Ryan (2012).

Provider Incentives and Healthcare Costs: Evidence from Long-Term Care Hospitals.

We study the design of provider incentives in the post-acute care setting - a high-stakes but under-studied segment of the healthcare system. We focus on long-term care hospitals (LTCHs) and the large (approximately $13,500) jump in Medicare payments they receive when a patient s stay reaches a threshold number of days. Discharges increase substantially after the threshold, with the marginal discharged patient in relatively better health. Despite the large financial incentives and behavioral response in a high mortality population, we are unable to detect any compelling evidence of an impact on patient mortality. To assess provider behavior under counterfactual payment schedules, we estimate a simple dynamic discrete choice model of LTCH discharge decisions. When we conservatively limit ourselves to alternative contracts that hold the LTCH harmless, we find that an alternative contract can generate Medicare savings of about $2,100 per admission, or about 5% of total payments. More aggressive payment reforms can generate substantially greater savings, but the accompanying reduction in LTCH profits has potential out-of-sample consequences. Our results highlight how improved financial incentives may be able to reduce healthcare spending, without negative consequences for industry profits or patient health.

Dynamic discrete choice model for railway ticket cancellation and exchange decisions

The increasing use of internet as a major ticket distribution channel has resulted in passengers becoming more strategic to fare policy. This potentially induces passengers to book the ticket well in advance in order to obtain a lower fare ticket, and later adjust their ticket when they are sure about trip scheduling. This is especially true in flexible refund markets where ticket cancellation and exchange behavior has been recognized as having major impacts on revenues. In this paper, we propose an inter-temporal choice model of ticket cancellation and exchange for railway passengers where customers are assumed to be forward looking agents. A dynamic discrete choice model (DDCM) is applied to predict the timing in which ticket exchange or cancellation occurs in response to fare and trip schedule uncertainty. The problem is formulated as an optimal stopping problem, and a two steps look-ahead policy is adopted to approximate the dynamic programming problem. The approach is applied to real ticket reservation data for intercity railway trips. Estimations results indicate that the DDCM provides more intuitive results when compared to multinomial logit (MNL) models. In addition, validation results show that DDCM has better prediction capability than MNL. The approach developed here in the context of exchange and refund policies for railway revenue management can be extended and applied to other industries that operate under flexible refund policies.

Leaving Your Mamma: Why so Late in Italy?

In Italy, young adults tend to postpone their transition to adulthood and live with their parents until very late compared with other countries. A dynamic discrete choice model is proposed in which agents choose residential arrangements, together with labor supply and marital status, conditional on the economic and institutional framework and on other agents' choices. The model is structurally estimated with the Simulated Method of Moments for nonstudent high-school graduate males and then used to assess, through a variety of counterfactual experiments, the relative importance of factors that are claimed to influence the choice to leave home in the existing literature: labor market conditions, parental resources, housing market conditions and social interaction. Results suggest that Italians choose to remain with their parents due to a combination of poor labor market conditions and high housing costs. The relatively high income of parents could contribute to the patterns observed by acting as an insurance against unemployment. Finally, estimates indicate that individuals tend to conform to a social norm that is influenced by external conditions.

Leaving your mamma: why so late in Italy?

In Italy, young adults tend to postpone their transition to adulthood and live with their parents until very late compared with other countries. A dynamic discrete choice model is proposed in which agents choose residential arrangements, together with labor supply and marital status, conditional on the economic and institutional framework and on other agents’ choices. The model is structurally estimated with the Simulated Method of Moments for non-student high-school graduate males and then used to assess, through a variety of counterfactual experiments, the relative importance of factors that are claimed to influence the choice to leave home in the existing literature: labor market conditions, parental resources, housing market conditions and social interaction. Results suggest that Italians choose to remain with their parents due to a combination of poor labor market conditions and high housing costs. The relatively high income of parents could contribute to the patterns observed by acting as an insurance against unemployment. Finally, estimates indicate that individuals tend to conform to a social norm, especially in the South of the country were family ties and the costs in terms of utility from not complying with expected behaviors appear to be stronger.

Immigration, Wages, and Education: A Labour Market Equilibrium Structural Model

Recent literature analysing wage effects of immigration assumes labour supply is fixed across education-experience cells. This article departs from this assumption estimating a labour market equilibrium dynamic discrete choice model on U.S. micro-data for 1967–2007. Individuals adjust to immigration by changing education, participation, and/or occupation. Adjustments are heterogeneous: 4.2–26.2% of prime-aged native males change their careers; of them, some switch to white-collar careers and increase education by about three years; others reduce labour market attachment and reduce education also by about three years. These adjustments mitigate initial effects on wages and inequality. Natives that are more similar to immigrants are the most affected on impact, but also have a larger margin to adjust and differentiate. Adjustments also produce a self-selection bias in the estimation of wage effects at the lower tail of the distribution, which the model corrects.

Joint Analysis of the Discount Factor and Payoff Parameters in Dynamic Discrete Choice Models

Most empirical and theoretical econometric studies of dynamic discrete choice models assume the discount factor to be known. We show the knowledge of the discount factor is not necessary to identify parts, or all, of the payoff function. We show the discount factor can be generically identified jointly with the payoff parameters. It is known the payoff function cannot non-parametrically identified without any a priori restrictions. Our identification of the discount factor is robust to any normalization choice on the payoff parameters. In IO applications normalizations are usually made on switching costs, such as entry costs and scrap values. We also show that switching costs can be non-parametrically identified, in closed-form, independently of the discount factor and other parts of the payoff function. Our identification strategies are constructive. They lead to easy to compute estimands that are global solutions. We illustrate with a Monte Carlo study and the dataset from Ryan (2012).

Analysis of dynamic decision-making in a bicycle-sharing auction using a dynamic discrete choice model

For clarifying the usefulness and practical issues of a tradable permit system empirically, we implemented a tradable permit system for a bicycle-sharing service in Yokohama city, Japan. We analyzed both travel and transaction behavior within this system. Many activity factors, such as the amount of free time in each day, home location and travel mode to the bicycle port, were shown to affect the transaction of tradable permits. The results of the pilot program indicated that inefficient allocation of tradable permits occurred when participants postponed their decision-making because of uncertainty. To determine the reason for this effect and the contributing factors, we created a dynamic discrete choice model to describe the choice results and timing. The estimation result indicated that the option value of postponing decision-making caused the transactions to be performed at the last minute, and that this effect blocked the liquidity of the permits trade. In addition, because the result reveals that there was heterogeneity in the time discount factor, the initial allocation of permits was found to be important for efficient allocation.

The optimal time to evacuate: A behavioral dynamic model on Louisiana resident data

Understanding what affects the decision process leading to evacuation of a population at risk from the threat of a disaster is of upmost importance to successfully implement emergency planning policies. Literature on this is broad; however, the vast majority of behavioral models is limited to conventional structures, such as aggregate participation rate models or disaggregate multinomial logit models. This research introduces a dynamic discrete choice model that takes into account the threat's characteristics and the population's expectation of them. The proposed framework is estimated using Stated Preference (SP) evacuation data collected from Louisiana residents. The results indicate that the proposed dynamic discrete choice model outperforms sequential logit, excels in incorporating demographic information of respondents, a key input in policy evaluation, and yields significantly more accurate predictions of the decision and timing to evacuate.

Dynamic Random Utility

Under dynamic random utility, an agent (or population of agents) solves a dynamic decision problem subject to evolving private information. We analyze the fully general and non-parametric model, axiomatically characterizing the implied dynamic stochastic choice behavior. A key new feature relative to static or i.i.d. versions of the model is that when private information displays serial correlation, choices appear history dependent: different sequences of past choices reflect different private information of the agent, and hence typically lead to different distributions of current choices. Our axiomatization imposes discipline on the form of history dependence that can arise under arbitrary serial correlation. Dynamic stochastic choice data lets us distinguish central models that coincide in static domains, in particular private information in the form of utility shocks vs. learning, and to study inherently dynamic phenomena such as choice persistence. We relate our model to specifications of utility shocks widely used in empirical work, highlighting new modeling tradeoffs in the dynamic discrete choice literature. Finally, we extend our characterization to allow past consumption to directly affect the agent's utility process, accommodating models of habit formation and experimentation.

A dynamic approach to environmental compliance decisions in U.S. Electricity Market: The Acid Rain Program revisited

The Acid Rain Program (ARP) was implemented in 1995. Since then, coal-fired boilers have had to choose among three main compliance alternatives: purchase pollution permits; switch to an alternative lower-sulfur coal; or adopt a scrubber. This decision problem is driven by the evolution of several economic variables and is revised when significant changes (to prices, quality of inputs, output level, technology, transport costs, regulations, among others) occur. Using a structural dynamic discrete choice model, I recover cost parameters and use them to evaluate two different counterfactual policies. The results confirm there is a trade-off between fuel switching and scrubbing costs (with the latter having a higher investment cost and a lower variable cost), and also the existence of regional heterogeneity. Finally, the ARP implied cost savings of approximately $4.7 billions if compared to a uniform emission rate standard and $14.8 billions if compared to compulsory scrubbing for the 1995–2005 period.

CLOSED-FORM IDENTIFICATION OF DYNAMIC DISCRETE CHOICE MODELS WITH PROXIES FOR UNOBSERVED STATE VARIABLES

Proxies for unobserved skills and technologies are increasingly available in empirical data. For dynamic discrete choice models of forward-looking agents where a continuous state variable is unobserved but its proxy is available, we derive closed-form identification of the structure by explicitly solving integral equations. In the first step, we derive closed-form identification of Markov components, including the conditional choice probabilities and the law of state transition. In the second step, we plug in these first-step identifying formulas to obtain primitive structural parameters of dynamically optimizing agents.

Approximate group context tree

We study a variable length Markov chain model associated with a group of stationary processes that share the same context tree but each process has potentially different conditional probabilities. We propose a new model selection and estimation method which is computationally efficient. We develop oracle and adaptivity inequalities, as well as model selection properties, that hold under continuity of the transition probabilities and polynomial $\beta$-mixing. In particular, model misspecification is allowed. These results are applied to interesting families of processes. For Markov processes, we obtain uniform rate of convergence for the estimation error of transition probabilities as well as perfect model selection results. For chains of infinite order with complete connections, we obtain explicit uniform rates of convergence on the estimation of conditional probabilities, which have an explicit dependence on the processes’ continuity rates. Similar guarantees are also derived for renewal processes. Our results are shown to be applicable to discrete stochastic dynamic programming problems and to dynamic discrete choice models. We also apply our estimator to a linguistic study, based on recent work by Galves et al. [Ann. Appl. Stat. 6 (2012) 186–209], of the rhythmic differences between Brazilian and European Portuguese.

A dynamic programming approach for quickly estimating large network-based MEV models

We propose a way to estimate a family of static Multivariate Extreme Value (MEV) models with large choice sets in short computational time. The resulting model is also straightforward and fast to use for prediction. Following Daly and Bierlaire (2006), the correlation structure is defined by a rooted, directed graph where each node without successor is an alternative. We formulate a family of MEV models as dynamic discrete choice models on graphs of correlation structures and show that the dynamic models are consistent with MEV theory and generalize the network MEV model (Daly and Bierlaire, 2006). Moreover, we show that these models can be estimated quickly using the concept of network flows and the nested fixed point algorithm (Rust, 1987). The main reason for the short computational time is that the new formulation allows to benefit from existing efficient solution algorithms for sparse linear systems of equations.We present numerical results based on simulated data with varying number of alternatives and nesting structures. We estimate large models, for example, a cross-nested model with 200 nests and 500,000 alternatives and 210 parameters that needs between 100–200 iterations to converge (4.3 h on an Intel(R) 3.2 GHz machine using a non-parallelized code). We also show that our approach allows to estimate a cross-nested logit model of 111 nests with a real data set of more than 100,000 observations in 14 h.

Activity Duration Analysis: Discrete-Time Approach for Recurrent Events, Competing Risks, and Multiple States

Most existing activity-based travel demand models are typically implemented on a tour-based microsimulation framework. Two approaches are available to describe people’s daily decision-making processes on activity and travel in the activity-based model framework: rubber banding and growing scheduling. The growing-scheduling approach requires a series of linked dynamic discrete choices of activity episodes, locations, and travel modes to build incrementally an entire day’s activity-travel patterns for individuals in households. To incorporate explicitly time dependencies into activity episode choice and duration, a hazard-based duration model in a discrete-time framework is introduced; this framework is essentially the same as a discrete choice model with temporal dummies as the simplest form of dynamic discrete choice models. In the application of the discrete–time duration model to activity duration analysis, complex situations of activity-travel data are considered; these include multiple states of origin activity, competing risks of destination activity, and a multilevel structure for recurrent activity episodes within individuals. In addition, a circular, or periodic, variable is introduced as a combination of sine and cosine to model time-of-day effects.

CCP Estimation of Dynamic Discrete/Continuous Choice Models with Generalized Finite Dependence and Correlated Unobserved Heterogeneity

This paper investigates conditional choice probability es timation of dynamic structural discrete and continuous choice models. I extend the concept of finite dependence in a way that accommodates non-stationary, irreducible transition probabilities. I show that under this new definition of finite dependence, one-peri od dependence is obtainable in any dynamic structural model. This finite dependence prop erty also provides a convenient and computationally cheap representation of the optimality conditions for the continuous choice variables. I allow for a general form of discrete-valued unobserved heterogeneity in utilities, transition probabilities, an d production functions. The unobserved heterogeneity may be correlated with the observable state variables. I show the estimator is root-n‐asymptotically normal. I develop a new and computationally cheap algorithm to compute the estimator. I apply our method to estimate a model of education and labor supply choices to investigate properties of t he distribution of returns to education, using data from the National Longitudinal Survey of Youth 1979.

A Generalized Dynamic Discrete Choice Model for Green Vehicle Adoption

Abstract: Much is happening in the automotive industry and new models are in the market or are expected to be available soon. At the same time, environmental awareness, new regulations for increased fuel efficiency, and the need to diminish greenhouse gas emissions make small vehicles and alternative fuel vehicles more competitive. As a consequence, vehicle characteristics and consumer decisions will change rapidly in the short and medium run. Accounting for the dynamic of the problem is important to correctly forecast green vehicle acceptance and to evaluate eco-friendly policies. This paper proposes a generalized dynamic discrete choice approach that models purchase behavior and forecasts future preferences in a finite time horizon setting. The framework allows one-time purchases, repeated purchases, univariate and multivariate diffusion processes that capture the evolution of vehicle characteristics and dynamics in the market conditions. The models proposed are estimated using stated preference data collected in Maryland. Results show that the formulation with repeated purchases successfully captures changes in the market shares, and that the multivariate diffusion process adopted to model the evolution of fuel prices further improves both model fit and the ability to recover peaks in demand. The estimated coefficients have been applied to test different policy scenarios, including changes in fuel prices, vehicle purchase prices, and improvements of car characteristics. These policies have a high impact on the adoption of electric cars and on their diffusion in the marketplace.

Identifying the Discount Factor in Dynamic Discrete Choice Models

The identification of the discount factor in dynamic discrete models is important for counterfactual analysis, but hard. Existing approaches either take the discount factor to be known or rely on high level exclusion restrictions that are difficult to interpret and hard to satisfy in applications, in particular in industrial organization. We provide identification results under an exclusion restriction on primitive utility that is more directly useful to applied researchers. We also show that our and existing exclusion restrictions limit the choice and state transition probability data in different ways; that is, they give the model nontrivial and distinct empirical content.

Provider Incentives and Healthcare Costs: Evidence from Long-Term Care Hospitals

We study the design of provider incentives in the post-acute care setting – a high-stakes but under-studied segment of the healthcare system. We focus on long-term care hospitals (LTCHs) and the large (approximately $13,000) jump in Medicare payments they receive when a patient's stay reaches a threshold number of days. The descriptive evidence indicates that discharges increase substantially after the threshold, and that the marginal patient discharged after the threshold is in relatively better health. Despite the large financial incentives and behavioral response in a high mortality population, we are unable to detect any compelling evidence of an impact on patient mortality. To assess provider behavior under counterfactual payment schedules, we estimate a simple dynamic discrete choice model of LTCH discharge decisions. When we conservatively limit ourselves to alternative contracts that hold the LTCH harmless, we find that an alternative contract can generate Medicare savings of about $2,100 per admission, or about 5% of total payments. More aggressive payment reforms can generate substantially greater savings, but the accompanying reduction in LTCH profits has potential out-of-sample consequences. Our results highlight how improved financial incentives may be able to reduce healthcare spending, without negative consequences for industry profits or patient health.

A Study on The Mixture of Exponentiated-Weibull Distribution

Mixtures of measures or distributions occur frequently in the theory and applications of probability and statistics. In the simplest case it may, for example, be reasonable to assume that one is dealing with the mixture in given proportions of a finite number of normal populations with different means or variances. The mixture parameter may also be denumerable infinite, as in the theory of sums of a random number of random variables, or continuous, as in the compound Poisson distribution. The use of finite mixture distributions, to control for unobserved heterogeneity, has become increasingly popular among those estimating dynamic discrete choice models. One of the barriers to using mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive reparability of the log likelihood function. In this thesis, the maximum likelihood estimators have been obtained for the parameters of the mixture of exponentiated Weibull distribution when sample is available from censoring scheme. The maximum likelihood estimators of the parameters and the asymptotic variance covariance matrix have been also obtained. A numerical illustration for these new results is given.