Modelling multi‐period inflation uncertainty using a panel of density forecasts

This paper examines the determinants of inflation forecast uncertainty using a panel of density forecasts from the Survey of Professional Forecasters (SPF). Based on a dynamic heterogeneous panel data model, we find that the persistence in forecast uncertainty is much less than what the aggregate time series data would suggest. In addition, the strong link between past forecast errors and current forecast uncertainty, as often noted in the ARCH literature, is largely lost in a multi‐period context with varying forecast horizons. We propose a novel way of estimating ‘news’ and its variance using the Kullback‐Leibler information, and show that the latter is an important determinant of forecast uncertainty. Our evidence suggests a strong relationship of forecast uncertainty with level of inflation, but not with forecaster discord or with the volatility of a number of other macroeconomic indicators. Copyright © 2006 John Wiley & Sons, Ltd.     

ARE EMPIRICAL MEASURES OF MACROECONOMIC UNCERTAINTY ALIKE?

Abstract There is a plethora of time series measures of uncertainty for inflation and real output growth in empirical studies but little is known whether they are comparable to the uncertainty measure reported by individual forecasters in the survey of professional forecasters. Are these two measures of uncertainty inherently distinct? This paper shows that, compared with many uncertainty proxies produced by time series models, the use of real‐time data with fixed‐sample recursive estimation of an asymmetric bivariate generalized autoregressive conditional heteroskedasticity model yields inflation uncertainty estimates which resemble the survey measure. There is, however, overwhelming evidence that many of the time series measures of growth uncertainty exceed the level of uncertainty obtained from survey measure. Our results highlight the relative merits of using different methods in modelling macroeconomic uncertainty which are useful for empirical researchers.     

The Measurement and Behavior of Uncertainty: Evidence from the ECB Survey of Professional Forecasters

We examine matched point and density forecasts of output growth, inflation and unemployment from the ECB Survey of Professional Forecasters. We construct measures of uncertainty from individual histograms, and find that the measures display countercyclical behavior and have increased across all forecast horizons since 2007. We also derive measures of forecast dispersion and forecast accuracy, and find that they are not reliable proxies for uncertainty. There is, however, evidence of a meaningful co‐movement between uncertainty and aggregate point predictions for output growth and unemployment. These results are robust to changes in the composition of the survey respondents over time. Copyright © 2015 John Wiley & Sons, Ltd.     

The non-normality of some macroeconomic forecast errors

This paper investigates the distributional properties of individual and consensus time series macroeconomic forecast errors, using data from the Survey of Professional Forecasters. The degree of autocorrelation and the presence of ARCH in the consensus errors is also determined. We find strong evidence of leptokurtic forecast errors as well as evidence of skewness, suggesting that an assumption of error normality is inappropriate; many of the forecast error series are found to have non-zero mean, and we find widespread evidence of consensus error ARCH. Properties of the distribution of cross-sectional forecast errors are also examined.     

Quasi ex-ante inflation forecast uncertainty

We propose a measure of the effects of monetary policy based on an analysis of the distribution of the ex-post inflation forecast uncertainty. We argue that the difference between the distributions of the ex-ante and ex-post uncertainties reflects the impact of monetary policy decisions. Using the theoretical background of the New Keynesian model with imperfect information and a monetary policy rule, we derive a proxy for ex-ante inflation uncertainty called quasi ex-ante forecast uncertainty, which is free to a certain extent of the effects of monetary policy decisions. Furthermore, we introduce the compound strength measure of monetary policy, as well as the uncertainty ratio, which approximates the impact of monetary policy on the reduction of the inflation forecast uncertainty. Our empirical results show that the greatest policy effect in reducing the inflation forecast uncertainty occurs for countries which conduct either a well-established or a relatively pure inflation targeting policy.     

Efficient forecast tests for conditional policy forecasts

Central Banks regularly make forecasts, such as the Fed’s Greenbook forecast, that are conditioned on hypothetical paths for the policy interest rate. While there are good public policy reasons to evaluate the quality of such forecasts, up until now, the most common approach has been to ignore their conditional nature and apply standard forecast efficiency tests. In this paper we derive tests for the efficiency of conditional forecasts. Intuitively, these tests involve implicit estimates of the degree to which the conditioning path is counterfactual and the magnitude of the policy feedback over the forecast horizon. We apply the tests to the Greenbook forecast and the Bank of England’s inflation report forecast, finding some evidence of forecast inefficiency. Nonetheless, we argue that the conditional nature of the forecasts made by central banks represents a substantial impediment to the analysis of their quality—stronger assumptions are needed and forecast inefficiency may go undetected for longer than would be the case if central banks were instead to report unconditional forecasts.     

Combining competing forecasts of inflation using a bivariate arch model

This paper sets out the basic structure of the bivariate generalization of Engle's ARCH model. Conditions which guarantee that the conditional covariance matrix is well defined are summarized, as are estimation and hypothesis testing.The process is used to combine forecasts where the weights are allowed to vary over time. Forecast errors from competing models are treated as a bivariate ARCH process so that the conditional covariance matrix adapts over time. At each point in time these conditional estimates of the variances and covariances are used to construct the optimal weights for combining the forecasts. Consequently, when one model is fitting well, its variance will be reduced and its weight will be increased.Two models of US inflation are constructed; one is a stylized monetarist model while the other is a mark-up model. The forecast errors are modeled as a simple bivariate ARCH process. Diagnostic tests reveal that this has overly restricted the parameterization of the covariance matrix. An approximation to the theoretically anticipated factor structure model is then estimated. The results in both cases show the weights varying over the sample period in moderately interpretable fashion.     

Does global inflation help forecast inflation in industrialized countries?

Ciccarelli and Mojon (CM; Review of Economics and Statistics, 2010, 92(3), 524–535) propose an inflation forecasting model incorporating a global inflation factor and show that it consistently beats several standard forecasting benchmarks. We show that CM's global inflation model does not improve upon the Atkeson and Ohanian (AO; Federal Reserve Bank of Minneapolis Quarterly Review, 2001, 25(1), 2–11) naive benchmark. However, we find that augmenting the AO model with a global inflation factor improves forecast accuracy at longer horizons, supporting CM's claim about the usefulness of global inflation.     

Composite forecasts of inflation: An improvement in forecasting performance

This study investigates the performance of a composite forecast of inflation for the period 1969:I–1992:IV. This composite forecast is generated by combining the forecasts of four methods commonly used to measure expected inflation. Initially, the results of conditional efficiency tests suggest that a composite forecast can improve performance by encompassing a wider information set. The evidence, from the comparison of various forecast series, shows that the composite forecast improves on the performance of the four individual forecasts and an alternative composite forecast in terms of accuracy and rationality criteria.     

Forecasting macroeconomic risks

We construct risks around consensus forecasts of real GDP growth, unemployment, and inflation. We find that risks are time-varying, asymmetric, and partly predictable. Tight financial conditions forecast downside growth risk, upside unemployment risk, and increased uncertainty around the inflation forecast. Growth vulnerability arises as the conditional mean and conditional variance of GDP growth are negatively correlated: downside risks are driven by lower mean and higher variance when financial conditions tighten. Similarly, employment vulnerability arises as the conditional mean and conditional variance of unemployment are positively correlated, with tighter financial conditions corresponding to higher forecasted unemployment and higher variance around the consensus forecast.     

Inflation forecasts and core inflation measures: Where is the information on future inflation?

This paper uses the forecast from a random walk model of inflation as a benchmark to test and compare the forecast performance of several alternatives of future inflation, including the Greenbook forecast by the Fed staff, the Survey of Professional Forecasters median forecast, CPI inflation minus food and energy, CPI weighted median inflation, and CPI trimmed mean inflation. The Greenbook forecast was found in previous literature to be a better forecast than other private sector forecasts. Our results indicate that both the Greenbook and the Survey of Professional Forecasters median forecasts of inflation and core inflation measures may contain better information than forecasts from a random walk model. The Greenbook's superiority appears to have declined against other forecasts and core inflation measures.     

Conditional heteroscedasticity of exchange rates: further results based on the fractionally integrated approach

A recent article (Tse, 1998 ) published in this journal analysed the conditional heteroscedasticity of the yen–dollar exchange rate based on the fractionally integrated asymmetric power ARCH model. In this paper, we present replication results using Tse's ( 1998 ) yen–dollar series. We also examine the robustness of Tse's ( 1998 ) findings across different currencies, sample periods and non‐nested GARCH‐type models. Unlike Tse ( 1998 ), we find some evidence of asymmetric conditional volatility for daily returns of currencies measured against the dollar or the yen. Copyright © 2004 John Wiley & Sons, Ltd.     

A time-varying volatility approach to modeling the phillips curve: A cross-country analysis

This research examines the Phillips curve price adjustment mechanism allowing for the conditional variance of inflation to be time varying. Specifically, we estimate ARCH and GARCH models of inflation for Canada, Japan, and the U.K. The results suggest that an increase in the conditional variability of inflation leads to higher levels of inflation. In addition, inclusion of inflation variability in the Phillips curve model results in a higher weight being attributed to the output gap than in traditional models. (JEF E24)     

A panel data approach to economic forecasting: The bias-corrected average forecast

In this paper, we propose a novel approach to econometric forecasting of stationary and ergodic time series within a panel-data framework. Our key element is to employ the (feasible) bias-corrected average forecast. Using panel-data sequential asymptotics we show that it is potentially superior to other techniques in several contexts. In particular, it is asymptotically equivalent to the conditional expectation, i.e., has an optimal limiting mean-squared error. We also develop a zero-mean test for the average bias and discuss the forecast-combination puzzle in small and large samples. Monte-Carlo simulations are conducted to evaluate the performance of the feasible bias-corrected average forecast in finite samples. An empirical exercise, based upon data from a well known survey is also presented. Overall, these results show promise for the feasible bias-corrected average forecast.     

Evaluating Point and Density Forecasts of DSGE Models

This paper investigates the accuracy of forecasts from four dynamic stochastic general equilibrium (DSGE) models for inflation, output growth and the federal funds rate using a real‐time dataset synchronized with the Fed's Greenbook projections. Conditioning the model forecasts on the Greenbook nowcasts leads to forecasts that are as accurate as the Greenbook projections for output growth and the federal funds rate. Only for inflation are the model forecasts dominated by the Greenbook projections. A comparison with forecasts from Bayesian vector autoregressions shows that the economic structure of the DSGE models which is useful for the interpretation of forecasts does not lower the accuracy of forecasts. Combining forecasts of several DSGE models increases precision in comparison to individual model forecasts. Comparing density forecasts with the actual distribution of observations shows that DSGE models overestimate uncertainty around point forecasts. Copyright © 2013 John Wiley & Sons, Ltd.     

Hard to arbitrage,hard for analysts to forecast

This paper examines whether limits to arbitrage (LA) affect analysts' earnings forecast accuracy. Using the LA index, which is constructed from unique trading constraints in the Chinese stock market and other commonly used measures, we find that forecast accuracy is much lower for stocks with high LA. Moreover, our results are more suited to explanations of cognitive bias that turn to investor sentiment or limited attention and cannot be fully explained by more objective factors, including analyst ability, broker size, broker experience, and commission pressure. We also find that LA amplifies analyst forecast dispersion. Such results indicate that LA distorts analysts’ earnings expectations and provides new insight into how LA affects anomaly returns.     

The effect of parameter uncertainty on forecast variances and confidence intervals for unit root and trend stationary time-series models

In this paper I describe the effect of parameter uncertainty on the way conditional forecast variances grow as the forecast horizon increases. Without parameter uncertainty, forecast variances for the unit root model grow linearly with the forecast horizon while with the trend stationary model they are bounded. With parameter uncertainty, however, I find that for both the unit root and the trend stationary models, forecast variances grow with the square of the forecast horizon so that uncertainty grows at a much faster rate than without parameter uncertainty.     

Combining VAR and DSGE forecast densities

A popular macroeconomic forecasting strategy utilizes many models to hedge against instabilities of unknown timing; see (among others) Stock and Watson (2004), Clark and McCracken (2010), and Jore et al. (2010). Existing studies of this forecasting strategy exclude dynamic stochastic general equilibrium (DSGE) models, despite the widespread use of these models by monetary policymakers. In this paper, we use the linear opinion pool to combine inflation forecast densities from many vector autoregressions (VARs) and a policymaking DSGE model. The DSGE receives a substantial weight in the pool (at short horizons) provided the VAR components exclude structural breaks. In this case, the inflation forecast densities exhibit calibration failure. Allowing for structural breaks in the VARs reduces the weight on the DSGE considerably, but produces well-calibrated forecast densities for inflation.     

Inflation forecast contracts

We introduce a new type of incentive contract for central bankers: inflation forecast contracts, which make central bankers׳ remunerations contingent on the precision of their inflation forecasts. We show that such contracts enable central bankers to influence inflation expectations more effectively, thus facilitating more successful stabilization of current inflation. Inflation forecast contracts improve the accuracy of inflation forecasts, but have adverse consequences for output. On balance, paying central bankers according to their forecasting performance improves welfare. Optimal inflation forecast contracts stipulate high rewards for accurate forecasts.     

Interpreting the skill score form of forecast performance metrics

Performance measures of point forecasts are expressed commonly as skill scores, in which the performance gain from using one forecasting system over another is expressed as a proportion of the gain achieved by forecasting that outcome perfectly. Increasingly, it is common to express scores of probabilistic forecasts in this form; however, this paper presents three criticisms of this approach. Firstly, initial condition uncertainty (which is outside the forecaster’s control) limits the capacity to improve a probabilistic forecast, and thus a ‘perfect’ score is often unattainable. Secondly, the skill score forms of the ignorance and Brier scores are biased. Finally, it is argued that the skill score form of scoring rules destroys the useful interpretation in terms of the relative skill levels of two forecasting systems. Indeed, it is often misleading, and useful information is lost when the skill score form is used in place of the original score.