Shaun P. Vahey

Real-Time Prediction With U.K. Monetary Aggregates in the Presence of Model Uncertainty

A popular account for the demise of the U.K.’s monetary targeting regime in the 1980s blames the fluctuating predictive relationships between broad money and inflation and real output growth. Yet ex post policy analysis based on heavily revised data suggests no fluctuations in the predictive content of money. In this paper, we investigate the predictive relationships for inflation and output growth using both real-time and heavily revised data. We consider a large set of recursively estimated vector autoregressive (VAR) and vector error correction models (VECM). These models differ in terms of lag length and the number of cointegrating relationships. We use Bayesian model averaging (BMA) to demonstrate that real-time monetary policymakers faced considerable model uncertainty. The in-sample predictive content of money fluctuated during the 1980s as a result of data revisions in the presence of model uncertainty. This feature is only apparent with real-time data as heavily revised data obscure these fluctuations. Out-of-sample predictive evaluations rarely suggest that money matters for either inflation or real output. We conclude that both data revisions and model uncertainty contributed to the demise of the U.K.’s monetary targeting regime.

UK Real-time Macro Data Characteristics

We characterise the relationships between preliminary and subsequent measurements for 16 commonly-used UK macroeconomic indicators drawn from two existing real-time data sets and a new nominal variable database. Most preliminary measurements are biased predictors of subsequent measurements, with some revision series affected by multiple structural breaks. To illustrate how these findings facilitate real-time forecasting, we use a vector autoregresion to generate real-time one-step-ahead probability event forecasts for 1990Q1 to 1999Q2. Ignoring the predictability in initial measurements understates considerably the probability of above trend output growth

Forecast densities for economic aggregates from disaggregate ensembles

Abstract We extend the “bottom up” approach for forecasting economic aggregates with disaggregates to probability forecasting. Our methodology utilises a linear opinion pool to combine the forecast densities from many disaggregate forecasting specifications, using weights based on the continuous ranked probability score. We also adopt a post-processing step prior to forecast combination. These methods are adapted from the meteorology literature. In our application, we use our approach to forecast US Personal Consumption Expenditure inflation from 1990q1 to 2009q4. Our ensemble combining the evidence from 16 disaggregate PCE series outperforms an integrated moving average specification for aggregate inflation in terms of density forecasting.

RBCs and DSGEs: The Computational Approach to Business Cycle Theory and Evidence

Real business cycle (RBC) and dynamic stochastic general equilibrium (DSGE) methods have become essential components of the macroeconomists toolkit. This literature review stresses recently developed techniques for computation and inference, providing a supplement to the Romer textbook, which stresses theoretical issues. Many computational aspects are illustrated with reference to the simple divisible labor RBC model. Code and US data to replicate the computations are provided on the internet, together with a number of appendices providing background details.

Forecasting Substantial Data Revisions in the Presence of Model Uncertainty

A recent revision to the preliminary measurement of GDP(E) growth for 2003Q2 caused considerable press attention, provoked a public enquiry and prompted a number of reforms to UK statistical reporting procedures. In this article, we compute the probability of ‘substantial revisions’ that are greater (in absolute value) than the controversial 2003 revision. The predictive densities are derived from Bayesian model averaging over a wide set of forecasting models including linear, structural break and regime-switching models with and without heteroscedasticity. Ignoring the nonlinearities and model uncertainty yields misleading predictives and obscures recent improvements in the quality of preliminary UK macroeconomic measurements.

Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this article, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial dependence. The copula parameter matrix is given by the correlation matrix of a latent stationary and Markov vector autoregression (VAR). We show that the likelihood can be evaluated efficiently using the unique partial correlations, and estimate the copula using Bayesian methods. We examine the forecasting performance of the model for four U.S. macroeconomic variables between 1975:Q1 and 2011:Q2 using quarterly real-time data. We find that the point and density forecasts from the copula model are competitive with those from a Bayesian VAR. During the recent recession the forecast densities exhibit substantial asymmetry, avoiding some of the pitfalls of the symmetric forecast densities from the Bayesian VAR. We show that the asymmetries in the predictive distributions of GDP growth and inflation are similar to those found in the probabilistic forecasts from the Survey of Professional Forecasters. Last, we find that unlike the linear VAR model, our fitted Gaussian copula models exhibit nonlinear dependencies between some macroeconomic variables. This article has online supplementary material.

A Real Time Tax Smoothing Based Fiscal Policy Rule

In this paper we consider the real-time implementation of a fiscal policy rule based on tax smoothing (Barro (1979) and Bohn (1998)). We show that the tax smoothing approach, augmented by fiscal habit considerations, provides a surprisingly accurate description of US budget surplus movements. In order to investigate the robustness of the policy implications of the rule, we construct a real-time US fiscal data set, complementing the data documented by Croushore and Stark (2001). For each variable we record the different vintages, reflecting the remeasurements that occur over time. We demonstrate that the easily constructed rule provided a useful benchmark for policy analysis that is robust to real-time remeasurements.

Interwar U.K. Unemployment: The Benjamin and Kochin Hypothesis or the Legacy of 'Just' Taxes?

Benjamin and Kochin (1979, Journal of Political Economy) present regression estimates to support their hypothesis that larger unemployment benefits increased U.K. unemployment post?World War I (WWI). The Benjamin-Kochin (BK) regression is easy to replicate. When the replication is widened to include income tax rates and WWI observations using Bayesian Monte Carlo methods, the evidence moves against the BK hypothesis and in favor of regressions that include the capital income tax rate. We explain these results with Daunton (2002, Just Taxes). He argues that U.K. tax rates were set during WWI and the interwar period to achieve an equitable, or ?just,? mix of taxes and debt. Neoclassical theory suggests that capital income tax rates fluctuations created inefficient factor input allocations that drove up interwar U.K. unemployment.

Real-Time Probability Forecasts of UK Macroeconomic Events

An overview is provided of the issues raised in the recent literature on the use of real-time data in the context of nowcasting and forecasting UK macroeconomic events. The ideas are illustrated through two specific applications using UK real-time data available over 1961-2006 and providing probability forecasts that could have been produced in real time over the past twenty years. In the first, we consider the reliability of first-release data on the components of UK aggregate demand by looking at forecasts of the probability of substantial data revisions. In the second, we consider the estimation of the output gap, illustrating the uncertainty surrounding its measurement through density forecasts and focusing on its interpretation in terms of inflationary pressure through an event probability forecast.

The McKenna Rule and U.K. World War I Finance

The United Kingdom employed the McKenna rule to conduct fiscal policy during World War I (WWI) and the interwar period. Named for Reginald McKenna, Chancellor of the Exchequer (1915?16), the McKenna rule committed the United Kingdom to a path of debt retirement, which we show was forward-looking and smoothed in response to shocks to the real economy and tax rates. The McKenna rule was in the tradition of the ?English method? of war finance because the United Kingdom taxed capital to finance WWI. Higher rates of capital taxation also paid for debt retirement during and subsequent to WWI. The United Kingdom was motivated to implement the McKenna rule because of a desire to achieve a balance between fairness and equity. However, the McKenna rule adversely affected the real economy, according to a permanent income model. WWI and interwar U.K. data support the prediction that real activity is lower in response to higher past debt retirement rates.