Peter E. Rossi

Bayesian Analysis of Stochastic Volatility Models

New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain coverage in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance states is a by-product of our Markov-chain method. In addition, multistep-ahead predictive densities can be constructed that reflect both inherent model variability and parameter uncertainty. We illustrate our method by analyzing both daily and weekly data on stock returns and exchange rates. Sampling experiments are conducted to compare the performance of Bayes estimators to method of moments and quasi-maximum likelihood estimators proposed in the literature. In both parameter estimation and filtering, the Bayes estimators outperform these other approaches.

Optimal Taxation in Models of Endogenous Growth

We study the problem of optimal taxation in three infinite-horizon, representative-agent endogenous growth models. The first model is a convex model in which physical and human capital are perfectly symmetric. Our second model incorporates elastic labor supply through a Lucas-style technology. Analysis of these two models points out the danger of assuming that government expenditures are exogenous. In our third model, we include government expenditures as a productive input in capital formation, showing that the limiting tax rate on capital is no longer zero. In numerical simulations, we find similar effects on growth and welfare in all three models.

Marketing models of consumer heterogeneity

The distribution of consumer preferences plays a central role in many marketing activities. Pricing and product design decisions, for example, are based on an understanding of the differences among consumers in price sensitivity and valuation of product attributes. In addition, marketing activities which target specific households require household level parameter estimates. Thus, the modeling of consumer heterogeneity is the central focus of many statistical marketing applications. In contrast, heterogeneity is often regarded as an ancillary nuisance problem in much of the applied econometrics literature which must be dealt with but is not the focus of the investigation. The focus is instead on estimating average effects of policy variables. In this paper, we discuss various approaches to modeling consumer heterogeneity and evaluate the utility of these approaches for marketing applications.

An exact likelihood analysis of the multinomial probit model

Abstract We develop new methods for conducting a finite sample, likelihood-based analysis of the multinomial probit model. Using a variant of the Gibbs sampler, an algorithm is developed to draw from the exact posterior of the multinomial probit model with correlated errors. This approach avoids direct evaluation of the likelihood and, thus, avoids the problems associated with calculating choice probabilities which affect both the standard likelihood and method of simulated moments approaches. Both simulated and actual consumer panel data are used to fit six-dimensional choice models. We also develop methods for analyzing random coefficient and multiperiod probit models.

Response Modeling with Nonrandom Marketing-Mix Variables

Sales response models are widely used as the basis for optimizing the marketing mix. Response models condition on the observed marketing-mix variables and focus on the specification of the distribution of observed sales given marketing-mix activities. The models usually fail to recognize that the levels of the marketing-mix variables are often chosen with at least partial knowledge of the response parameters in the conditional model. This means that contrary to standard assumptions, the marginal distribution of the marketing-mix variables is not independent of response parameters. The authors expand on the standard conditional model to include a model for the determination of the marketing-mix variables. They apply this modeling approach to the problem of gauging the effectiveness of sales calls (details) to induce greater prescribing of drugs by individual physicians. They do not assume a priori that details are set optimally, but instead they infer the extent to which sales force managers have knowledge of responsiveness, and they use this knowledge to set the level of sales force contact. The authors find that their modeling approach improves the precision of the physician-specific response parameters significantly. They also find that physicians are not detailed optimally; high-volume physicians are detailed to a greater extent than low-volume physicians without regard to responsiveness to detailing. It appears that unresponsive but high-volume physicians are detailed the most. Finally, the authors illustrate how their approach provides a general framework.

A Bayesian analysis of the multinomial probit model with fully identified parameters

We present a new prior and corresponding algorithm for Bayesian analysis of the multinomial probit model. Our new approach places a prior directly on the identified parameter space. The key is the specification of a prior on the covariance matrix so that the (1,1) element if fixed at 1 and it is possible to draw from the posterior using standard distributions. Analytical results are derived which can be used to aid in assessment of the prior.

Overcoming Scale Usage Heterogeneity: A Bayesian Hierarchical Approach

Questions that use a discrete ratings scale are commonplace in survey research. Examples in marketing include customer satisfaction measurement and purchase intention. Survey research practitioners have long commented that respondents vary in their usage of the scale: Common patterns include using only the middle of the scale or using the upper or lower end. These differences in scale usage can impart biases to correlation and regression analyses. To capture scale usage differences, we developed a new model with individual scale and location effects and a discrete outcome variable. We model the joint distribution of all ratings scale responses rather than specific univariate conditional distributions as in the ordinal probit model. We apply our model to a customer satisfaction survey and show that the correlation inferences are much different once proper adjustments are made for the discreteness of the data and scale usage. We also show that our adjusted or latent ratings scale is more closely related to actual purchase behavior.

Do Switching Costs Make Markets Less Competitive

The conventional wisdom in economic theory holds that switching costs make markets less competitive. This article challenges this claim. The authors formulate an empirically realistic model of dynamic price competition that allows for differentiated products and imperfect lock-in. They calibrate this model with data from frequently purchased packaged goods markets. These data are ideal in the sense that they have the necessary variation to identify switching costs separately from consumer heterogeneity. Equally important, consumers exhibit inertia in their brand choices, a form of psychological switching cost. This makes the results applicable to the broad range of products that are distinctly identified (i.e., branded) rather than just to products for which there is a product adoption cost or explicit switching fee. In the simulations, prices are as much as 18% lower with than without switching costs. More important, equilibrium prices do not increase even in the presence of switching costs that are of the same order of magnitude as product price.

Body time and social time: Mood patterns by menstrual cycle phase and day of the week

Multiple regression analysis traces the effects of two time dimensions (body time as indexed by the female menstrual cycle, and social time as indexed by the calendar week) upon moods, in a prospective study of daily moods over a 40-day period. Positive moods peaked in the ovulatory phase and on weekends, while negative moods peaked in the luteal phase of the menstrual cycle. An individual difference analysis showed that women whose moods are responsive to the menstrual cycle are physically active, socially assertive, sexually orgasmic women for whom the maternal role is important.

Invited Paper-Even the Rich Can Make Themselves Poor: A Critical Examination of IV Methods in Marketing Applications

Marketing is a field that is rich in data. Our data is of high quality, often at a highly disaggregate level, and there is considerable variation in the key variables for which estimates of effects on outcomes such as sales and profits are desired. The recognition that, in some general sense, marketing variables are set by firms on the basis of information not always observable by the researcher has led to concerns regarding endogeneity and widespread pressure to implement instrumental variables methods in marketing problems. The instruments used in our empirical literature are rarely valid and the IV methods used can have poor sampling properties, including substantial finite sample bias and large sampling errors. Given the problems with IV methods, a convincing argument must be made that there is a first order endogeneity problem and that we have strong and valid instruments before these methods should be used. If strong and valid instruments are not available, then researchers need to look toward supplementing the information available to them. For example, if there are concerns about unobservable advertising or promotional variables, then the researcher is much better off measuring these variables rather than using instruments such as lagged marketing variables that are clearly invalid. Ultimately, only randomized variation in marketing variables with proper implementation and large samples can be argued to be a valid instrument without further assumptions.