Estimating First-Price Auctions with an Unknown Number of Bidders: A Misclassification Approach

In this paper, we consider nonparametric identification and estimation of first-price auction models when N*, the number of potential bidders, is unknown to the researcher, but observed by bidders. Exploiting results from the recent econometric literature on models with misclassification error, we develop a nonparametric procedure for recovering the distribution of bids conditional on the unknown N*. Monte Carlo results illustrate that the procedure works well in practice. We present illustrative evidence from a dataset of procurement auctions, which shows that accounting for the unobservability of N* can lead to economically meaningful differences in the estimates of bidders' profit margins.

Identifying the Returns to Lying 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 returns to lying to be about 7% 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.

Estimating Marginal Treatment Effects in Heterogeneous Populations

This paper proposes a nonparametric method of estimating marginal treatment effects in heterogeneous populations. Building upon an insight of Heckman and Vytlacil, the conventional treatment effects model with heterogeneous effects is shown to imply that outcomes are a nonlinear function of participation probabilities. The degree of this nonlinearity, and hence the shape of the marginal response curve, can be estimated with series methods such as power series or splines. An illustration is provided for the returns to higher education in the U.K, indicating that marginal returns to higher education fall as the proportion of the population with higher education rises, thus providing evidence of heterogeneity in returns.

Dynamic Time Series Binary Choice

This paper considers dynamic time series binary choice models. It proves near epoch dependence and strong mixing for the dynamic binary choice model with correlated errors. Using this result, it shows in a time series setting the validity of the dynamic probit likelihood procedure when lags of the dependent binary variable are used as regressors, and it establishes the asymptotic validity of Horowitz’ smoothed maximum score estimation of dynamic binary choice models with lags of the dependent variable as regressors. For the semiparametric model, the latent error is explicitly allowed to be correlated. It turns out that no long-run variance estimator is needed for the validity of the smoothed maximum score procedure in the dynamic time series framework.

Avoiding Market Dominance: Product Compatibility in Markets with Network Effects

As is well-recognized, market dominance is a typical outcome in markets with network effects. A firm with a larger installed base others a more attractive product which induces more consumers to buy its product which produces a yet bigger installed base advantage. Such a setting is investigated here but with the main difference that firms have the option of making their products compatible. When firms have similar installed bases, they make their products compatible in order to expand the market. Nevertheless, random forces could result in one firm having a bigger installed base in which case the larger firm may make its product incompatible. We find that strategic pricing tends to prevent the installed base differential from expanding to the point that incompatibility occurs. This pricing dynamic is able to neutralize increasing returns and avoid the emergence of market dominance.

Which Nonlinearity in the Phillips Curve? The Absence of Accelerating Deflation in Japan

It is standard to model the output-inflation trade-off as a linear relationship with a time-invariant slope. We assess empirical evidence for three types of nonlinearity in the short-run Phillips curve. At an empirical level, we aim to discover why large negative output gaps in Japan during the period 1998-2002 did not lead to accelerating deflation, but instead coincided with stable, be it moderately negative inflation. We document that this episode is most convincingly interpreted as reflecting a gradual flattening of the Phillips curve. The broader relevance of our analysis lies in its attempt to shed light on the determinants of such time-variation in the Phillips curve slope. Our results suggest that, in any economy where trend inflation is substantially lower (or substantially higher) today than in past decades, time-variation in the slope of the short-run Phillips curve has become too important to ignore.