Mixed hitting-time models

We study a mixed hitting-time (MHT) model that specifies durations as the first time a Levy process - a continuous-time process with stationary and independent increments - crosses a heterogeneous threshold. Such models are of substantial interest because they can be reduced from optimal-stopping models with heterogeneous agents that do not naturally produce a mixed proportional hazards (MPH) structure. We show how strategies for analyzing the MPH model's identifiability can be adapted to prove identifiability of an MHT model with observed regressors and unobserved heterogeneity. We discuss inference from censored data and extensions to time-varying covariates and latent processes with more general time and dependency structures. We conclude by discussing the relative merits of the MHT and MPH models as complementary frameworks for econometric duration analysis.

The Likelihood of Mixed Hitting Times

We present a method for computing the likelihood of a mixed hitting-time model that specifies durations as the first time a latent L\'evy process crosses a heterogeneous threshold. This likelihood is not generally known in closed form, but its Laplace transform is. Our approach to its computation relies on numerical methods for inverting Laplace transforms that exploit special properties of the first passage times of L\'evy processes. We use our method to implement a maximum likelihood estimator of the mixed hitting-time model in MATLAB. We illustrate the application of this estimator with an analysis of Kennan's (1985) strike data.Comment: 35 page

Regular Variation and the Identification of Generalized Accelerated Failure-Time Models

Ridder (1990) provides an identification result for the Generalized Accelerated Failure-Time (GAFT) model. We point out that Ridder's proof of this result is incomplete, and provide an amended proof with an additional necessary and sufficient condition that requires that a function varies regularly at zero and infinity. We also give more readily interpretable sufficient conditions on the tails of the error distribution or the asymptotic behavior of the transformation of the dependent variable. The sufficient conditions are shown to encompass all previous results on the identification of the Mixed Proportional Hazards (MPH) model. Thus, this paper not only clarifies, but also unifies the literature on the non-parametric identification of the GAFT and MPH models.duration analysis;identifiability;Mixed Proportional Hazards model;regular variation

Oligopoly dynamics with barriers to entry

This paper considers the effects of raising the cost of entry for potential competitors on infinite-horizon Markov- perfect industry dynamics with ongoing demand uncertainty. All entrants serving the model industry incur sunk costs, and exit avoids future fixed costs. We focus on the unique equilibrium with last- in first-out expectations: a firm never exits before a younger rival does. When an industry can support at most two firms, we prove that raising barriers to a second producer’s entry increases the probability that some firm will serve the industry and decreases its long-run entry and exit rates. In numerical examples with more than two firms, imposing a barrier to entry stabilizes industry structure.Oligopolies

Better Safe than Sorry? Ex Ante and Ex Post Moral Hazard in Dynamic Insurance Data

This paper empirically analyzes moral hazard in car insurance using a dynamic theory of an insuree's dynamic risk (ex ante moral hazard) and claim (ex post moral hazard) choices and Dutch longitudinal micro data. We use the theory to characterize the heterogeneous dynamic changes in incentives to avoid claims that are generated by the Dutch experience-rating scheme, and their effects on claim times and sizes under moral hazard. We develop tests that exploit these structural implications of moral hazard and experience rating. Unlike much of the earlier literature, we find evidence of moral hazard.insurance;moral hazard;selection;state dependence;event-history analysis

A Structural Empirical Model of Firm Growth, Learning, and Survival

We present a structural model of firm growth, learning, and survival and consider its identification and estimation. In the model, entrepreneurs have private and possibly error-ridden observations of persistent and transitory shocks to profit. We demonstrate that the model's parameters can be recovered from public observations of sales and survival, and we estimate them using monthly data from new bars in Texas. We find that entrepreneurs observe profit's persistent component without error. In this sense, their information is substantially superior to the public's.

Last-in first-out oligopoly dynamics

This paper extends the static analysis of oligopoly structure into an infinite- horizon setting with sunk costs and demand uncertainty. The observation that exit rates decline with firm age motivates the assumption of last-in first- out dynamics: An entrant expects to produce no longer than any incumbent. This selects an essentially unique Markov-perfect equilibrium. With mild restrictions on the demand shocks, a sequence of thresholds describes firms’ equilibrium entry and survival decisions. Bresnahan and Reiss’s (1993) empirical analysis of oligopolists’ entry and exit assumes that such thresholds govern the evolution of the number of competitors. Our analysis provides an infinite-horizon game- theoretic foundation for that structure.Oligopolies

Mixed Hitting-Time Models

We study a mixed hitting-time (MHT) model that specifies durations as the first time a Lévy process - a continuous-time process with stationary and independent increments� crosses a heterogeneous threshold. Such models are of substantial interest because they can be reduced from optimal-stopping models with heterogeneous agents that do not naturally produce a mixed proportional hazards (MPH) structure. We show how strategies for analyzing the MPH model's identifiability can be adapted to prove identifiability of an MHT model with observed regressors and unobserved heterogeneity. We discuss inference from censored data and extensions to time-varying covariates and latent processes with more general time and dependency structures. We conclude by discussing the relative merits of the MHT and MPH models as complementary frameworks for econometric duration analysis

A structural empirical model of firm growth, learning, and survival

In this paper we develop an empirical model of entrepreneurs' business continuation decisions, and we estimate its parameters using a new panel of monthly alcohol tax returns from bars in the state of Texas. In our data, entrepreneurial failure is frequent and predictable. In the first year of life, 20% of our sample's bars exit, and these tend to be smaller than average. In the model, an entrepreneur bases her business continuation decision on potentially noisy signals of her bar's future profits. The presence of noise implies that she should make her decision based on both current and past realizations of the signal. We observe for each bar its sales, which we assume, equals a noisy version of the entrepreneur's signal. That is, the entrepreneur's information about her bar is private. ; The entrepreneur's private information makes the estimation of our model challenging, because we cannot observe the inputs into her decision process. Nevertheless, we are able to recover from our observations the parameters characterizing the entrepreneur's learning process and the noise contaminating publicly available sales observations. The key to our analysis is to note that our ability to forecast the entrepreneur's decisions reveals the amount of noise contaminating publicly available sales observations. We infer that public and private information differ little if we can forecast entrepreneurs' business continuation decisions well. With this information, we can then determine whether the usefulness of past sales observations for forecasting future sales arises only from the noise contaminating public observations or if the observations imply the presence of additional noise contaminating entrepreneurs' observations. ; We estimate our model using observations from the first twelve months of life for approximately 300 Texas bars. We find that entrepreneurs observe the persistent component of profit without error. In this sense, their information is substantially superior to the public's.Business enterprises ; Corporations