A Research Assistant's Guide to Random Coefficients Discrete Choice Models of Demand


Book Description

The study of differentiated-products markets is a central part of empirical industrial organization. Questions regarding market power, mergers, innovation, and valuation of new brands are addressed using cutting-edge econometric methods and relying on economic theory. Unfortunately, difficulty of use and computational costs have limited the scope of application of recent developments in one of the main methods for estimating demand for differentiated products: random coefficients discrete choice models. As our understanding of these models of demand has increased, both the difficulty and costs have been greatly reduced. This paper carefully discusses the latest innovations in these methods with the hope of (1) increasing the understanding, and therefore the trust, among researchers who never used these methods, and (2) reducing the difficulty of use, and therefore aiding in realizing the full potential of these methods.







A Practitioner's Guide to Estimation of Random-Coefficients Logit Models of Demand


Book Description

Estimation of demand is at the heart of many recent studies that examine questions of market power, mergers, innovation, and valuation of new brands in differentiated-products markets. This paper focuses on one of the main methods for estimating demand for differentiated products: random-coefficients logit models. The paper carefully discusses the latest innovations in these methods with the hope of increasing the understanding, and therefore the trust among researchers who have never used them, and reducing the difficulty of their use, thereby aiding in realizing their full potential.




An Optimization-based Econometric Framework for the Evaluation of Monetary Policy


Book Description

This paper considers a simple quantitative model of output, interest rate and inflation determination in the United States, and uses it to evaluate alternative rules by which the Fed may set interest rates. The model is derived from optimizing behavior under rational expectations, both on the part of the purchasers of goods and upon that of the sellers. The model matches the estimates responses to a monetary policy shock quite well and, once due account is taken of other disturbances, can account for our data nearly as well as an unrestricted VAR. The monetary policy rule that most reduces inflation variability (and is best on this account) requires very variable interest rates, which in turn is possible only in the case of a high average inflation rate. But even in the case of a constrained-optimal policy, that takes into account some of the costs of average inflation and constrains the variability of interest rates so as to keep average inflation low, inflation would be stabilized considerably more and output stabilized considerably less than under our estimates of current policy. Moreover, this constrained-optimal policy also allows average inflation to be much smaller. This version contains additional details of our derivations and calculations, including three technical appendices, not included in the version published in NBER Macroeconomics Annual 1997.




Applied Discrete-Choice Modelling


Book Description

Originally published in 1981. Discrete-choice modelling is an area of econometrics where significant advances have been made at the research level. This book presents an overview of these advances, explaining the theory underlying the model, and explores its various applications. It shows how operational choice models can be used, and how they are particularly useful for a better understanding of consumer demand theory. It discusses particular problems connected with the model and its use, and reports on the authors’ own empirical research. This is a comprehensive survey of research developments in discrete choice modelling and its applications.







Predictive Regressions


Book Description

When a rate of return is regressed on a lagged stochastic regressor, such as a dividend yield, the regression disturbance is correlated with the regressor's innovation. The OLS estimator's finite-sample properties, derived here, can depart substantially from the standard regression setting. Bayesian posterior distributions for the regression parameters are obtained under specifications that differ with respect to (i) prior beliefs about the autocorrelation of the regressor and (ii) whether the initial observation of the regressor is specified as fixed or stochastic. The posteriors differ across such specifications asset allocations in the presence of estimation risk exhibit sensitivity to those differences.




Encompassing Tests when No Model is Encompassing


Book Description

This paper considers regression-based tests for encompassing, when none of the models under consideration encompasses all the other models. For both in- and out-of-sample applications, I derive asymptotic distributions and propose feasible procedures to construct confidence intervals and test statistics. Procedures that are asymptotically valid under the null of encompassing (e.g., Davidson and MacKinnon (1981)) can have large asymptotic and finite sample distortions. Simulations indicate that the proposed procedures can work well in samples of size typically available, though the divergence between actual and nominal confidence interval coverage sometimes is large.




Maximum Likelihood Estimation of Discretely Sampled Diffusions


Book Description

When a continuous-time diffusion is observed only at discrete dates, not necessarily close together, the likelihood function of the observations is in most cases not explicitly computable. Researchers have relied on simulations of sample paths in between the observations points, or numerical solutions of partial differential equations, to obtain estimates of the function to be maximized. By contrast, we construct a sequence of fully explicit functions which we show converge under very general conditions, including non-ergodicity, to the true (but unknown) likelihood function of the discretely-sampled diffusion. We document that the rate of convergence of the sequence is extremely fast for a number of examples relevant in finance. We then show that maximizing the sequence instead of the true function results in an estimator which converges to the true maximum-likelihood estimator and shares its asymptotic properties of consistency, asymptotic normality and efficiency. Applications to the valuation of derivative securities are also discussed.




The Bias of the RSR Estimator and the Accuracy of Some Alternatives


Book Description

This paper analyzes the implications of cross-sectional heteroskedasticity in repeat sales regression (RSR). RSR estimators are essentially geometric averages of individual asset returns because of the logarithmic transformation of price relatives. We show that the cross sectional variance of asset returns affects the magnitude of bias in the average return estimate for that period, while reducing the bias for the surrounding periods. It is not easy to use an approximation method to correct the bias problem. We suggest a maximum-likelihood alternative to the RSR that directly estimates index returns that are analogous to the RSR estimators but are arithmetic averages of individual returns. Simulations show that these estimators are robust to time-varying cross-sectional variance and may be more accurate than RSR and some alternative methods of RSR.