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

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

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.

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

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

Social experiments and intrumental variables with duration outcomes

This paper examines the empirical analysis of treatment effects on duration outcomes from data that contain instrumental variation. We focus on social experiments in which an intention to treat is randomized and compliance may be imperfect. We distinguish between cases where the treatment starts at the moment of randomization and cases where it starts at a later point in time. We derive exclusion restrictions under various informational and behavioral assumptions and we analyze identifiability under these restrictions. It turns out that randomization (and by implication, instrumental variation) by itself is often insufficient for inference on interesting effects, and needs to be augmented by a semi-parametric structure. We develop corresponding non- and semi-parametric tests and estimation methods.Event-history analysis; intention to treat; non-compliance; policy evaluation; selection

Dynamically assigned treatments: duration models, binary treatment models, and panel data models

Often, the moment of a treatment and the moment at which the outcome of interest occurs are realizations of stochastic processes with dependent unobserved determinants. Notably, both treatment and outcome are characterized by the moment they occur. We compare different methods of inference of the treatment effect, and we argue that the timing of the treatment relative to the outcome conveys useful information on the treatment effect, which is discarded in binary treatment frameworksProgram evaluation; treatment effects; bivariate duration analysis; selection bias; hazard rate; unobserved heterogeneity; fixed effects; random effects

A simple procedure for the evaluation of treatment effects on duration variables

Often, a treatment and the outcome of interest are characterized by the moment they occur, and these moments are realizations of stochastic processes with dependent unobserved determinants. We develop a simple and intuitive method for inference on the treatment effect. The method can be implemented as a graphical procedure or as a straightforward parameter test in an auxiliary univariate single-spell duration model. The method exploits information on the timing of the treatment relative to the outcome that is discarded in binary treatment analyses.Duration analysis; hazard rate; selectivity bias; treatment effect; unobserved heterogeneity