Bayesian Model Averaging in the Instrumental Variable Regression Model

This paper considers the instrumental variable regression model when there is uncertainty about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainty can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very exible and can be easily adapted to analyze any of the di¤erent priors that have been proposed in the Bayesian instrumental variables literature. We show how to calculate the probability of any relevant restriction (e.g. the posterior probability that over-identifying restrictions hold) and discuss diagnostic checking using the posterior distribution of discrepancy vectors. We illustrate our methods in a returns-to-schooling application.

Stochastic Search Variable Selection in Vector Error Correction Models with an Application to a Model of the UK Macroeconomy

This paper develops methods for Stochastic Search Variable Selection (currently popular with regression and Vector Autoregressive models) for Vector Error Correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK macroeconomic model.

What Belongs Where? Variable Selection for Zero-Inflated Count Models with an Application to the Demand for Health Care

This paper develops stochastic search variable selection (SSVS) for zero-inflated count models which are commonly used in health economics. This allows for either model averaging or model selection in situations with many potential regressors. The proposed techniques are applied to a data set from Germany considering the demand for health care. A package for the free statistical software environment R is provided.

Inverted Haavelmo Effects in a General Equilibrium Analysis of the Impact of Implementing the Scottish Variable Rate of Income Tax.

The Scottish Parliament has the authority to make a balanced-budget expansion or contraction in public expenditure, funded by corresponding local changes in the basic rate of income tax of up to 3p in the pound. This fiscal adjustment is known as the Scottish Variable Rate of income tax, though it has never, as yet, been used. In this paper we attempt to identify the impact on aggregate economic activity in Scotland of implementing these devolved fiscal powers. This is achieved through theoretical analysis and simulation using a Computable General Equilibrium (CGE) model for Scotland. This analysis generalises the conventional Keynesian model so that negative balanced-budget multipliers values are possible, reflecting a regional “inverted Haavelmo effect”. Key parameters determining the aggregate economic impact are the extent to which the Scottish Government create local amenities valuable to the Scottish population and the extent to which this is incorporated into local wage bargaining.

The Role of Institutions in Cross-Section Income and Panel Data Growth Models: A Deeper Investigation on the Weakness and Proliferation of Instruments

This paper investigates the role of institutions in determining per capita income levels and growth. It contributes to the empirical literature by using different variables as proxies for institutions and by developing a deeper analysis of the issues arising from the use of weak and too many instruments in per capita income and growth regressions. The cross-section estimation suggests that institutions seem to matter, regardless if they are the only explanatory variable or are combined with geographical and integration variables, although most models suffer from the issue of weak instruments. The results from the growth models provides some interesting results: there is mixed evidence on the role of institutions and such evidence is more likely to be associated with law and order and investment profile; government spending is an important policy variable; collapsing the number of instruments results in fewer significant coefficients for institutions.

Model Switching and Model Averaging in Time- Varying Parameter Regression Models

This paper investigates the usefulness of switching Gaussian state space models as a tool for implementing dynamic model selecting (DMS) or averaging (DMA) in time-varying parameter regression models. DMS methods allow for model switching, where a different model can be chosen at each point in time. Thus, they allow for the explanatory variables in the time-varying parameter regression model to change over time. DMA will carry out model averaging in a time-varying manner. We compare our exact approach to DMA/DMS to a popular existing procedure which relies on the use of forgetting factor approximations. In an application, we use DMS to select different predictors in an in ation forecasting application. We also compare different ways of implementing DMA/DMS and investigate whether they lead to similar results.

Okun’s law – A meta analysis

This paper seeks to identify whether there is a representative empirical Okun’s Law coefficient (OLC) and to measure its size. We carry out a meta regression analysis on a sample of 269 estimates of the OLC to uncover reasons for differences in empirical results and to estimate the ‘true’ OLC. On statistical (and other) grounds, we find it appropriate to investigate two separate subsamples, using respectively (some measure of) unemployment or output as dependent variable. Our results can be summarized as follows. First, there is evidence of type II publication bias in both sub-samples, but a type I bias is present only among the papers using some measure of unemployment as the dependent variable. Second, after correction for publication bias, authentic and statistically significant OLC effects are present in both sub-samples. Third, bias-corrected estimated true OLCs are significantly lower (in absolute value) with models using some measure of unemployment as the dependent variable. Using a bivariate MRA approach, the estimated true effects are -0.25 for the unemployment sub-sample and -0.61 for the output-sub sample; with a multivariate MRA methodology, the estimated true effects are -0.40 and -1.02 for the unemployment and the output-sub samples respectively.

Quantile forecasts of inflation under model uncertainty

Bayesian model averaging (BMA) methods are regularly used to deal with model uncertainty in regression models. This paper shows how to introduce Bayesian model averaging methods in quantile regressions, and allow for different predictors to affect different quantiles of the dependent variable. I show that quantile regression BMA methods can help reduce uncertainty regarding outcomes of future inflation by providing superior predictive densities compared to mean regression models with and without BMA.