Parametric and nonparametric inference in equilibrium job search models

Equilibrium job search models allow for labor markets with homogeneous workers and firms to yield nondegenerate wage densities. However, the resulting wage densities do not accord well with empirical regularities. Accordingly, many extensions to the basic equilibrium search model have been considered (e.g., heterogeneity in productivity, heterogeneity in the value of leisure, etc.). It is increasingly common to use nonparametric forms for these extensions and, hence, researchers can obtain a perfect fit (in a kernel smoothed sense) between theoretical and empirical wage densities. This makes it difficult to carry out model comparison of different model extensions. In this paper, we first develop Bayesian parametric and nonparametric methods which are comparable to the existing non-Bayesian literature. We then show how Bayesian methods can be used to compare various nonparametric equilibrium search models in a statistically rigorous sense

Using VARs and TVP-VARs with many macroeconomic variables

This paper discusses the challenges faced by the empirical macroeconomist and methods for surmounting them. These challenges arise due to the fact that macroeconometric models potentially include a large number of variables and allow for time variation in parameters. These considerations lead to models which have a large number of parameters to estimate relative to the number of observations. A wide range of approaches are surveyed which aim to overcome the resulting problems. We stress the related themes of prior shrinkage, model averaging and model selection. Subsequently, we consider a particular modelling approach in detail. This involves the use of dynamic model selection methods with large TVP-VARs. A forecasting exercise involving a large US macroeconomic data set illustrates the practicality and empirical success of our approach

Time varying VARs with inequality restrictions

In many applications involving time-varying parameter VARs, it is desirable to restrict the VAR coe¢ cients at each point in time to be non-explosive. This is an example of a problem where inequality restrictions are imposed on states in a state space model. In this paper, we describe how existing MCMC algorithms for imposing such inequality restrictions can work poorly (or not at all) and suggest alternative algorithms which exhibit better performance. Furthermore, previous algorithms involve an approximation relating to a key integrating constant. Our algorithms are exact, not involving this approximation. In an application involving a commonly-used U.S. data set, we show how this approximation can be a poor one and present evidence that the algorithms proposed in this paper work well

The vector floor and ceiling model

This paper motivates and develops a nonlinear extension of the Vector Autoregressive model which we call the Vector Floor and Ceiling model. Bayesian and classical methods for estimation and testing are developed and compared in the context of an application involving U.S. macroeconomic data. In terms of statistical significance both classical and Bayesian methods indicate that the (Gaussian) linear model is inadequate. Using impulse response functions we investigate the economic significance of the statistical analysis. We find evidence of strong nonlinearities in the contemporaneous relationships between the variables and milder evidence of nonlinearity in the conditional mean

A new index of financial conditions

We use factor augmented vector autoregressive models with time-varying coefficients and stochastic volatility to construct a financial conditions index that can accurately track expectations about growth in key US macroeconomic variables. Time-variation in the model’s parameters allows for the weights attached to each financial variable in the index to evolve over time. Furthermore, we develop methods for dynamic model averaging or selection which allow the financial variables entering into the financial conditions index to change over time. We discuss why such extensions of the existing literature are important and show them to be so in an empirical application involving a wide range of financial variables

Semiparametric Bayesian inference in smooth coefficient models

We describe procedures for Bayesian estimation and testing in both cross sectional and longitudinal data smooth coefficient models (with and without endogeneity problems). The smooth coefficient model is a generalization of the partially linear or additive model wherein coefficients on linear explanatory variables are treated as unknown functions of an observable covariate. In the approach we describe, points on the regression lines are regarded as unknown parameters and priors are placed on differences between adjacent points to introduce the potential for smoothing the curves. The algorithms we describe are quite simple to implement - estimation, testing and smoothing parameter selection can be carried out analytically in the cross-sectional smooth coefficient model, and estimation in the hierarchical models only involves simulation from standard distributions. We apply our methods by fitting several hierarchical models using data from the National Longitudinal Survey of Youth (NLSY). We explore the relationship between ability and log wages and flexibly model how returns to schooling vary with measured cognitive ability. In a generalization of this model, we also permit endogeneity of schooling and describe simulation-based methods for inference in the presence of the endogeneity problem. We find returns to schooling are approximately constant throughout the ability support and that simpler (and often used) parametric specifications provide an adequate description of these relationships.

Prior elicitation in multiple change-point models

This paper discusses Bayesian inference in change-point models. Existing approaches involve placing a (possibly hierarchical) prior over a known number of change-points. We show how two popular priors have some potentially undesirable properties (e.g. allocating excessive prior weight to change-points near the end of the sample) and discuss how these properties relate to imposing a fixed number of changepoints in-sample. We develop a new hierarchical approach which allows some of of change-points to occur out-of sample. We show that this prior has desirable properties and handles the case where the number of change-points is unknown. Our hierarchical approach can be shown to nest a wide variety of change-point models, from timevarying parameter models to those with few (or no) breaks. Since our prior is hierarchical, data-based learning about the parameter which controls this variety occurs

An Investigation of Thresholds in Air Pollution-Mortality Effects

In this paper we introduce and implement new techniques to investigate threshold effects in air pollution-mortality relationships. Our key interest is in measuring the dose-response relationship above and below a given threshold level where we allow for a large number of potential explanatory variables to trigger the threshold effect. This is in contrast to existing approaches that usually focus on a single threshold trigger. We allow for a myriad of threshold effects within a Bayesian statistical framework that accounts for model uncertainty (i.e. uncertainty about which threshold trigger and explanatory variables are appropriate). We apply these techniques in an empirical exercise using daily data from Toronto for 1992-1997. We investigate the existence and nature of threshold effects in the relationship between mortality and ozone (O3), total particulate matter (PM) and an index of other conventionally occurring air pollutants. In general, we find the effects of our considered pollutants on mortality to be statistically indistinguishable from zero with no evidence of thresholds. The one exception is ozone, for which results present an ambiguous picture. Ozone has no significant effect on mortality when we exclude threshold effects from the analysis. Allowing for thresholds we find a positive and significant effect for this pollutant when the threshold trigger is the average change in ozone two days ago. However, this significant effect is not observed after controlling for PM.Threshold-air pollution mortality effects; Bayesian model; averaging; PM; O3