Introducing the Bank of Canada staff economic projections database

We present a new, publicly available database of real-time data and forecasts from the Bank of Canada's staff economic projections, which will be updated on an annual basis. We describe the data construct, its variables, coverage, and frequency. We then provide a forecast evaluation for gross domestic product (GDP) growth, consumer price index (CPI) inflation and the policy rate since 1982: We compare the staff's forecasts with those from commonly used time series models estimated with the real-time data, and with forecasts from other professional forecasters, and provide standard bias tests. Finally, we study changes in predictability of the Canadian economy following the announcement of the inflation-targeting regime in 1991. Our data set is unprecedented outside the USA, and our evidence is particularly interesting, as it covers over 30 years of staff forecasts, two severe recessions, and different monetary policy regimes.     

Rounding behaviour of professional macro-forecasters

The rounding of point forecasts of CPI inflation and the unemployment rate by U.S. Professional Forecasters is modest. There is little evidence that forecasts are rounded to a greater extent in response to higher perceived uncertainty surrounding future outcomes. There is clear evidence that the probability of decline forecasts are rounded: over half of the forecast probabilities of decline in the current quarter are multiples of ten. It is found here that the rounding of these probabilities correlates with worse accuracy, although it is also of note here that worse (less accurate) forecasters might round more as opposed to the degree of rounding per se worsening accuracy. By simulating the loss from rounding for a set of efficient forecasters, it is demonstrated that the explanation that respondents round otherwise efficient forecasts is implausible, and that the contribution of rounding is of minor importance.     

Green shoots and double dips in the euro area: A real time measure

In order to perform real-time business cycle inferences and forecasts of GDP growth rates in the euro area, we use an extension of the Markov-switching dynamic factor models that accounts for the features of the day-to-day monitoring of economic developments, such as ragged edges, mixed frequencies and data revisions. We provide examples that show the nonlinear nature of the relationships between data revisions, point forecasts and forecast uncertainty. Based on our empirical results, we think that the real-time probabilities of recession inferred from the model are an appropriate statistic for capturing what the press call green shoots, and for monitoring double-dip recessions.     

Raiders of the lost high-frequency forecasts: New data and evidence on the efficiency of the Fed's forecasting

We introduce a new dataset of real gross domestic product (GDP) growth and core personal consumption expenditures (PCE) inflation forecasts produced by the staff of the Board of Governors of the Federal Reserve System. In contrast to the eight Greenbook forecasts a year the staff produce for Federal Open Market Committee (FOMC) meetings, our dataset has roughly weekly forecasts. We use these data to study whether the staff forecasts efficiently. Prespecified regressions of forecast errors on forecast revisions show the staff's GDP forecasts exhibit time-varying inefficiency between FOMC meetings, and also show some evidence for inefficient inflation forecasts.     

Bayesian learning and convergence to rational expectations

In this paper the probability distribution of equilibrium outcomes is assumed to be a continuous but unknown function of agents' forecasts (which are probability measures). Agents start with a prior distribution on the set of mappings from forecasts into probabilities on outcomes. This induces an initial forecast. After observing the equilibrium outcome a posterior distribution is computed which induces a new forecast. The main result is that with probability one the forecasts converge to the set of fixed points of the unknown mapping. This can be interpreted as convergence to rational expectations.     

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.     

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.     

Scoring rules and survey density forecasts

This article provides a practical evaluation of some leading density forecast scoring rules in the context of forecast surveys. We analyse the density forecasts of UK inflation obtained from the Bank of England’s Survey of External Forecasters, considering both the survey average forecasts published in the Bank’s quarterly Inflation Report, and the individual survey responses recently made available to researchers by the Bank. The density forecasts are collected in histogram format, and the ranked probability score (RPS) is shown to have clear advantages over other scoring rules. Missing observations are a feature of forecast surveys, and we introduce an adjustment to the RPS, based on the Yates decomposition, to improve its comparative measurement of forecaster performance in the face of differential non-response. The new measure, denoted RPS*, is recommended to analysts of forecast surveys.     

Empirically-transformed linear opinion pools

The linear opinion pool (LOP) produces potentially non-Gaussian combination forecast densities. In this paper, we propose a computationally convenient transformation for the LOP to mirror the non-Gaussianity exhibited by the target variable. Our methodology involves a Smirnov transform to reshape the LOP combination forecasts using the empirical cumulative distribution function. We illustrate our empirically transformed opinion pool (EtLOP) approach with an application examining quarterly real-time forecasts for U.S. inflation evaluated on a sample from 1990:1 to 2020:2. EtLOP improves performance by approximately 10% to 30% in terms of the continuous ranked probability score across forecasting horizons.     

Tests for multiple forecast encompassing

In the evaluation of economic forecasts, it is frequently the case that comparisons are made between a number of competing predictors. A natural question to ask in such contexts is whether one forecast encompasses its competitors, in the sense that they contain no useful information not present in the superior forecast. We develop tests for this notion of multiple forecast encompassing which are robust to properties expected in the forecast errors, and apply the tests to forecasts of UK growth and inflation. Copyright © 2000 John Wiley & Sons, Ltd.     

Evaluating density forecasts: forecast combinations,model mixtures,calibration and sharpness

This paper reviews current density forecast evaluation procedures, and considers a proposal that such procedures be augmented by an assessment of ‘sharpness’. This was motivated by an example in which some standard evaluation procedures using probability integral transforms cannot distinguish the ideal forecast from several competing forecasts. We show that this example has some unrealistic features from a time series forecasting perspective, and so provides insecure foundations for the argument that existing calibration procedures are inadequate in practice. Our alternative, more realistic example shows how relevant statistical methods, including information‐based methods, provide the required discrimination between competing forecasts. We introduce a new test of density forecast efficiency. Copyright © 2010 John Wiley & Sons, Ltd.     

Does Forecast Combination Improve Norges Bank Inflation Forecasts?*

We develop a system that provides model‐based forecasts for inflation in Norway. We recursively evaluate quasi out‐of‐sample forecasts from a large suite of models from 1999 to 2009. The performance of the models are then used to derive quasi real time weights that are used to combine the forecasts. Our results indicate that a combination forecast improves upon the point forecasts from individual models. Furthermore, a combination forecast outperforms Norges Bank's own point forecast for inflation. The beneficial results are obtained using a trimmed weighted average. Some degree of trimming is required for the combination forecasts to outperform the judgmental forecasts from the policymaker.     

Combining probability forecasts

We consider different methods for combining probability forecasts. In empirical exercises, the data generating process of the forecasts and the event being forecast is not known, and therefore the optimal form of combination will also be unknown. We consider the properties of various combination schemes for a number of plausible data generating processes, and indicate which types of combinations are likely to be useful. We also show that whether forecast encompassing is found to hold between two rival sets of forecasts or not may depend on the type of combination adopted. The relative performances of the different combination methods are illustrated, with an application to predicting recession probabilities using leading indicators.     

The comparative forecast performance of univariate and multivariate models: an application to real interest rate forecasting

Does the use of information on the past history of the nominal interest rates and inflation entail improvement in forecasts of the ex ante real interest rate over its forecasts obtained from using just the past history of the realized real interest rates? To answer this question we set up a univariate unobserved components model for the realized real interest rates and a bivariate model for the nominal rate and inflation which imposes cointegration restrictions between them. The two models are estimated under normality with the Kalman filter. It is found that the error-correction model provides more accurate one-period ahead forecasts of the real rate within the estimation sample whereas the unobserved components model yields forecasts with smaller forecast variances. In the post-sample period, the forecasts from the bivariate model are not only more accurate but also have tighter confidence bounds than the forecasts from the unobserved components model.     

The COVID-19 shock and challenges for inflation modelling

We document the impact of COVID-19 on inflation modelling within a vector autoregression (VAR) model and provide guidance for forecasting euro area inflation during the pandemic. We show that estimated parameters are strongly affected, leading to different and sometimes implausible projections. As a solution, we propose to augment the VAR by allowing the residuals to have a fat-tailed distribution instead of a Gaussian one. This also outperforms with respect to unconditional forecasts. Yet, what brings sizeable forecast gains during the pandemic is adding meaningful off-model information, such as that entailed in the Survey of Professional Forecasters. The fat-tailed VAR loses part, but not all of its relative advantage compared to the Gaussian version when producing conditional inflation forecasts in a real-time setup. It is the joint fat-tailed errors and multi-equation modelling that manage to robustify models against extreme observations; in a single-equation model the same solution is less effective.     

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.     

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.     

How reliable are forecasts of GDP growth and inflation for countries with limited coverage?

This paper analyses the performance of GDP growth and inflation forecasts for 25 transition countries between 1994 and 2007, as provided by 13 international institutions, including multilateral, private and academic forecasters. The empirical results show that there is a positive correlation between the number of forecasters covering a given country and the forecast accuracy. Simple combined forecasts are shown to be unbiased and more accurate than most of the individual forecasters, although also inefficient. However, only a few institutions provide efficient and unbiased forecasts, with just one out of 13 forecasters providing both unbiased and efficient forecasts of both GDP growth and inflation in the observed period. The directional analysis shows a correct forecast of the change in the forecast indicator in over two thirds of cases. However, the eventual outcome is within the range of available forecasts in less than half of the cases, with more than 40% of outcomes for GDP growth above the highest forecast. Encouragingly, forecasts are shown to be improving over time and becoming more accurate with the increase in the number of forecasting institutions – forecast accuracy measured by mean absolute error improves by 0.3 percentage points for growth and by 0.2 percentage points for inflation for each additional institution providing forecasts.     

Do precious metal prices help in forecasting South African inflation?

In this paper we test whether the key metals prices of gold and platinum significantly improve inflation forecasts for the South African economy. We also test whether controlling for conditional correlations in a dynamic setup, using bivariate Bayesian-Dynamic Conditional Correlation (B-DCC) models, improves inflation forecasts. To achieve this we compare out-of-sample forecast estimates of the B-DCC model to Random Walk, Autoregressive and Bayesian VAR models. We find that for both the BVAR and BDCC models, improving point forecasts of the Autoregressive model of inflation remains an elusive exercise. This, we argue, is of less importance relative to the more informative density forecasts. For this we find improved forecasts of inflation for the B-DCC models at all forecasting horizons tested. We thus conclude that including metals price series as inputs to inflation models leads to improved density forecasts, while controlling for the dynamic relationship between the included price series and inflation similarly leads to significantly improved density forecasts.     

CONSTRUCTING OPTIMAL DENSITY FORECASTS FROM POINT FORECAST COMBINATIONS

Decision makers often observe point forecasts of the same variable computed, for instance, by commercial banks, IMF and the World Bank, but the econometric models used by such institutions are frequently unknown. This paper shows how to use the information available on point forecasts to compute optimal density forecasts. Our idea builds upon the combination of point forecasts under general loss functions and unknown forecast error distributions. We use real‐time data to forecast the density of US inflation. The results indicate that the proposed method materially improves the real‐time accuracy of density forecasts vis‐à‐vis those from the (unknown) individual econometric models. Copyright © 2013 John Wiley & Sons, Ltd.