Comparing features of convenient estimators for binary choice models with endogenous regressors

Abstract We discuss the relative advantages and disadvantages of four types of convenient estimators of binary choice models when regressors may be endogenous or mismeasured or when errors are likely to be heteroscedastic. For example, such models arise when treatment is not randomly assigned and outcomes are binary. The estimators we compare are the two‐stage least squares linear probability model, maximum likelihood estimation, control function estimators, and special regressor methods. We specifically focus on models and associated estimators that are easy to implement. Also, for calculating choice probabilities and regressor marginal effects, we propose the average index function (AIF), which, unlike the average structural function (ASF), is always easy to estimate.     

Signs of impact effects in time series regression models

In this paper we consider the problem of interpreting the signs of the estimated coefficients in multivariate time series regressions where the regressors are correlated. Using a continuous time model, we argue that focusing on the signs of individual coefficients in such regressions could be misleading and argue in favour of allowing for the indirect effects that arise due to the historical correlations amongst the regressors. For estimation from discrete time data we show that the sign of the total impact, including the direct and indirect effects, of a regressor can be obtained using a simple regression that only includes the regressor of interest.     

A comparison of bias approximations for the two-stage least squares (2SLS) estimator

We consider the bias of the two-stage least squares (2SLS) estimator in linear instrumental variable regression with only one endogenous regressor. By using asymptotic expansion techniques, we approximate the 2SLS coefficient estimation bias under various scenarios regarding the number and strength of instruments.     

Endogenous regressor binary choice models without instruments,with an application to migration

This paper shows identification of a semiparametric binary choice model containing an endogenous regressor, when no outside instrumental variable is available. A simple estimator, an easy test for endogeneity, and an empirical application to US migration data are provided.     

Trend instrumental variable regression with an application to the US New Keynesian Phillips Curve

When a linear model suffers from endogeneity, a conventional solution is to use external instrumental variables. Sometimes, however, there are either no suitable external IVs or they are of poor quality. This paper constructs an internal instrumental variable from the time trend in the endogenous regressor without using any external IVs. We show that under some mild conditions this new trend IV estimator has desirable asymptotic properties, and also provide a robust Durbin-Wu-Hausman specification test to demonstrate the necessity of the IV method. Monte Carlo simulations show that the estimator and the test have good finite sample performance. In the end, we apply the trend IV estimator to the US New Keynesian Phillips Curve and find that it works as well as the usual external IVs in the literature.     

Large deviations and multinomial probit choice

We consider a discrete choice model in which the payoffs to each of an agent?s n actions are subjected to the average of m i.i.d. shocks, and use tools from large deviations theory to characterize the rate of decay of the probability of choosing a given suboptimal action as m approaches infinity. Our model includes the multinomial probit model of Myatt and Wallace (2003) [5] as a special case. We show that their formula describing the rates of decay of choice probabilities is incorrect, provide the correct formula, and use our large deviations analysis to provide intuition for the difference between the two.     

Returns to Lying? Identifying the Effects of Misreporting When the Truth Is Unobserved

Consider an observed binary regressor D and an unobserved binary variable D?, both of which affect some other variable Y . This paper considers nonparametric identification and estimation of the effect of D on Y , conditioning on D? = 0. For example, suppose Y is a person’s wage, the unobserved D? indicates if the person has been to college, and the observed D indicates whether the individual claims to have been to college. This paper then identifies and estimates the difference in average wages between those who falsely claim college experience versus those who tell the truth about not having college. We estimate this average effect of lying to be about 6% to 20%. Nonparametric identification without observing D? is obtained either by observing a variable V that is roughly analogous to an instrument for ordinary measurement error, or by imposing restrictions on model error moments.     

The dynamic instability of dispersed price equilibria

We adopt an evolutionary framework to explain price dispersion as a time varying phenomenon. By developing a finite strategy analogue of the Burdett and Judd (1983) price dispersion model, we show that all dispersed price equilibria are unstable under the class of perturbed best response dynamics. Instead, numerical simulations using the logit dynamic show that price dispersion manifests itself as a limit cycle. We verify that limit cycles persist even when the finite strategy model approaches the original continuous strategy model. For a particularly simple case of the model, we prove the existence of a limit cycle.     

Coalitional bargaining games with random proposers: Theory and application

We consider a non-cooperative coalitional bargaining game with random proposers in a general situation for which players differ in recognition probability and time preference. We characterize an efficient equilibrium as the generalized Nash bargaining solution that belongs to the core. The model is applied to wage bargaining between an employer and multiple workers. Although involuntary unemployment may occur in equilibrium, full employment emerges as players become sufficiently patient.     

Partial identification in binary response models with nonignorable nonresponses

This study investigates the identification of parameters in semiparametric binary response models of the form y=1(x^′β+v+ε>0)$y=1(x^{\prime }\beta +v+\epsilon >0)$ when there are nonignorable nonresponses. We propose an estimation procedure for the identified set, the set of parameters that are observationally indistinguishable from the true value β$\beta$, based on the special regressor approach of Lewbel (2000). We show that the estimator for the identified set is consistent in the Hausdorff metric.     

The sensitivity of the RESET tests to disturbance autocorrelation in regression analysis

This paper investigates the sensitivity of the RESET tests, proposed by Ramsey (1969) and modified by Thursby and Schmidt (1977), to disturbance autocorrelation in regression analysis. Porter and Kashyap (1984) show that RESET is not robust to autocorrelated disturbance when there is a highly autocorrelated regressor in the model. We show that RESET is sensitive to disturbance autocorrelation even when the regressors are not autocorrelated. We explain the findings of Thursby (1979) and Porter and Kashyap (1984) as well as our result by showing that a spurious correlation between the regressor and the disturbance is responsible for the serious size distortion of the RESET tests. First version received: June 1999/Final version received: November 2000     

Decompositions and potentials for normal form games

A basic model of commitment is to convert a two-player game in strategic form to a “leadership game” with the same payoffs, where one player, the leader, commits to a strategy, to which the second player always chooses a best reply. This paper studies such leadership games for games with convex strategy sets. We apply them to mixed extensions of finite games, which we analyze completely, including nongeneric games. The main result is that leadership is advantageous in the sense that, as a set, the leader's payoffs in equilibrium are at least as high as his Nash and correlated equilibrium payoffs in the simultaneous game. We also consider leadership games with three or more players, where most conclusions no longer hold.     

Let the Data Speak? On the Importance of Theory‐Based Instrumental Variable Estimations

In absence of randomized‐controlled experiments, identification is often aimed via instrumental variable (IV) strategies, typically two‐stage least squares estimations. According to Bayes’ rule, however, under a low ex ante probability that a hypothesis is true (e.g. that an excluded instrument is partially correlated with an endogenous regressor), the interpretation of the estimation results may be fundamentally flawed. This paper argues that rigorous theoretical reasoning is key to design credible identification strategies, the foremost, finding candidates for valid instruments. We discuss prominent IV analyses from the macro‐development literature to illustrate the potential benefit of structurally derived IV approaches.     

The target projection dynamic

We study the target projection dynamic, a model of learning in normal form games. The dynamic is given a microeconomic foundation in terms of myopic optimization under control costs due to a certain status-quo bias. We establish a number of desirable properties of the dynamic: existence, uniqueness and continuity of solution trajectories, Nash stationarity, positive correlation with payoffs, and innovation. Sufficient conditions are provided under which strictly dominated strategies are wiped out. Finally, some stability results are provided for special classes of games.     

Forecasting the volatility of S&P depositary receipts using GARCH-type models under intraday range-based and return-based proxy measures

We employ four various GARCH-type models, incorporating the skewed generalized t (SGT) errors into those returns innovations exhibiting fat-tails, leptokurtosis and skewness to forecast both volatility and value-at-risk (VaR) for Standard & Poor's Depositary Receipts (SPDRs) from 2002 to 2008. Empirical results indicate that the asymmetric EGARCH model is the most preferable according to purely statistical loss functions. However, the mean mixed error criterion suggests that the EGARCH model facilitates option buyers for improving their trading position performance, while option sellers tend to favor the IGARCH/EGARCH model at shorter/longer trading horizon. For VaR calculations, although these GARCH-type models are likely to over-predict SPDRs' volatility, they are, nevertheless, capable of providing adequate VaR forecasts. Thus, a GARCH genre of model with SGT errors remains a useful technique for measuring and managing potential losses on SPDRs under a turbulent market scenario.     

Strategic network formation through peering and service agreements

We introduce a game theoretic model of network formation in an effort to understand the complex system of business relationships between various Internet entities (e.g., Autonomous Systems, enterprise networks, residential customers). In our model we are given a network topology of nodes and links where the nodes act as the players of the game, and links represent potential contracts. Nodes wish to satisfy their demands, which earn potential revenues, but may have to pay their neighbors for links incident to them. We incorporate some of the qualities of Internet business relationships, including customer–provider and peering contracts. We show that every Nash equilibrium can be represented by a circulation flow of utility with certain constraints. This allows us to prove bounds on the prices of anarchy and stability. We also focus on the quality of equilibria achievable through centralized incentives.     

Robust monopoly pricing

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the pricing policies under two distinct decision criteria with multiple priors: (i) maximin utility and (ii) minimax regret. The equilibrium price under either criterion is lower then in the absence of uncertainty. The concern for robustness leads the seller to concede a larger information rent to all buyers with values below the optimal price without uncertainty.     

ESTIMATION WITH CENSORED REGRESSORS: BASIC ISSUES*

We study issues that arise for estimation of a linear model when a regressor is censored. We discuss the efficiency losses from dropping censored observations, and illustrate the losses for bound censoring. We show that the common practice of introducing a dummy variable to “correct for” censoring does not correct bias or improve estimation. We show how censored observations generally have zero semiparametric information, and we discuss implications for estimation. We derive the likelihood function for a parametric model of mixed bound‐independent censoring, and apply that model to the estimation of wealth effects on consumption.     

Cost performance of Brazilian soccer clubs: A Bayesian varying efficiency distribution model

This paper analyzes the cost efficiency of Brazilian first league soccer clubs using a Bayesian Varying Efficiency Distribution (VED) model. We confirm that the model fits the data well with all coefficients correctly signed and in line with the theoretical requirements. From the efficiency results, it was clear that the Brazilian soccer league operates at a lower performance in comparison to other international soccer leagues. Factors which contributed to this finding as well as other policy implications are provided.