C53 Forecasting and Other Model Applications
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Linear rational-expectations models (LREMs) are conventionally "forwardly" estimated as follows. Structural coefficients are restricted by economic restrictions in terms of deep parameters. For given deep parameters, structural equations are solved for "rational-expectations solution" (RES) equations that determine endogenous variables. For given vector autoregressive (VAR) equations that determine exogenous variables, RES equations reduce to reduced-form VAR equations for endogenous variables with exogenous variables (VARX). The combined endogenous-VARX and exogenous-VAR equations comprise the reduced-form overall VAR (OVAR) equations of all variables in a LREM. The sequence of specified, solved, and combined equations defines a mapping from deep parameters to OVAR coefficients that is used to forwardly estimate a LREM in terms of deep parameters. Forwardly-estimated deep parameters determine forwardly-estimated RES equations that Lucas (1976) advocated for making policy predictions in his critique of policy predictions made with reduced-form equations.
Sims (1980) called economic identifying restrictions on deep parameters of forwardly-estimated LREMs "incredible", because he considered in-sample fits of forwardly-estimated OVAR equations inadequate and out-of-sample policy predictions of forwardly-estimated RES equations inaccurate. Sims (1980, 1986) instead advocated directly estimating OVAR equations restricted by statistical shrinkage restrictions and directly using the directly-estimated OVAR equations to make policy predictions. However, if assumed or predicted out-of-sample policy variables in directly-made policy predictions differ significantly from in-sample values, then, the out-of-sample policy predictions won't satisfy Lucas's critique.
If directly-estimated OVAR equations are reduced-form equations of underlying RES and LREM-structural equations, then, identification 2 derived in the paper can linearly "inversely" estimate the underlying RES equations from the directly-estimated OVAR equations and the inversely-estimated RES equations can be used to make policy predictions that satisfy Lucas's critique. If Sims considered directly-estimated OVAR equations to fit in-sample data adequately (credibly) and their inversely-estimated RES equations to make accurate (credible) out-of-sample policy predictions, then, he should consider the inversely-estimated RES equations to be credible. Thus, inversely-estimated RES equations by identification 2 can reconcile Lucas's advocacy for making policy predictions with RES equations and Sims's advocacy for directly estimating OVAR equations.
The paper also derives identification 1 of structural coefficients from RES coefficients that contributes mainly by showing that directly estimated reduced-form OVAR equations can have underlying LREM-structural equations.
This paper investigates the accuracy of point and density forecasts of four DSGE models for inflation, output growth and the federal funds rate. Model parameters are estimated and forecasts are derived successively from historical U.S. data vintages synchronized with the Fed’s Greenbook projections. Point forecasts of some models are of similar accuracy as the forecasts of nonstructural large dataset methods. Despite their common underlying New Keynesian modeling philosophy, forecasts of different DSGE models turn out to be quite distinct. Weighted forecasts are more precise than forecasts from individual models. The accuracy of a simple average of DSGE model forecasts is comparable to Greenbook projections for medium term horizons. Comparing density forecasts of DSGE models with the actual distribution of observations shows that the models overestimate uncertainty around point forecasts.
This paper investigates the accuracy of point and density forecasts of four DSGE models for inflation, output growth and the federal funds rate. Model parameters are estimated and forecasts are derived successively from historical U.S. data vintages synchronized with the Fed’s Greenbook projections. Point forecasts of some models are of similar accuracy as the forecasts of nonstructural large dataset methods. Despite their common underlying New Keynesian modeling philosophy, forecasts of different DSGE models turn out to be quite distinct. Weighted forecasts are more precise than forecasts from individual models. The accuracy of a simple average of DSGE model forecasts is comparable to Greenbook projections for medium term horizons. Comparing density forecasts of DSGE models with the actual distribution of observations shows that the models overestimate uncertainty around point forecasts.
This paper investigates the accuracy of forecasts from four 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 the model forecasts are dominated by the Greenbook projections. A comparison with forecasts from Bayesian VARs 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.
he predictive likelihood is of particular relevance in a Bayesian setting when the purpose is to rank models in a forecast comparison exercise. This paper discusses how the predictive likelihood can be estimated for any subset of the observable variables in linear Gaussian state-space models with Bayesian methods, and proposes to utilize a missing observations consistent Kalman filter in the process of achieving this objective. As an empirical application, we analyze euro area data and compare the density forecast performance of a DSGE model to DSGE-VARs and reduced-form linear Gaussian models.
This paper contributes a multivariate forecasting comparison between structural models and Machine-Learning-based tools. Specifically, a fully connected feed forward non-linear autoregressive neural network (ANN) is contrasted to a well established dynamic stochastic general equilibrium (DSGE) model, a Bayesian vector autoregression (BVAR) using optimized priors as well as Greenbook and SPF forecasts. Model estimation and forecasting is based on an expanding window scheme using quarterly U.S. real-time data (1964Q2:2020Q3) for 8 macroeconomic time series (GDP, inflation, federal funds rate, spread, consumption, investment, wage, hours worked), allowing for up to 8 quarter ahead forecasts. The results show that the BVAR improves forecasts compared to the DSGE model, however there is evidence for an overall improvement of predictions when relying on ANN, or including them in a weighted average. Especially, ANN-based inflation forecasts improve other predictions by up to 50%. These results indicate that nonlinear data-driven ANNs are a useful method when it comes to macroeconomic forecasting.
In the euro area, monetary policy is conducted by a single central bank for 20 member countries. However, countries are heterogeneous in their economic development, including their inflation rates. This paper combines a New Keynesian model and a neural network to assess whether the European Central Bank (ECB) conducted monetary policy between 2002 and 2022 according to the weighted average of the inflation rates within the European Monetary Union (EMU) or reacted more strongly to the inflation rate developments of certain EMU countries.
The New Keynesian model first generates data which is used to train and evaluate several machine learning algorithms. They authors find that a neural network performs best out-of-sample. They use this algorithm to generally classify historical EMU data, and to determine the exact weight on the inflation rate of EMU members in each quarter of the past two decades. Their findings suggest disproportional emphasis of the ECB on the inflation rates of EMU members that exhibited high inflation rate volatility for the vast majority of the time frame considered (80%), with a median inflation weight of 67% on these countries. They show that these results stem from a tendency of the ECB to react more strongly to countries whose inflation rates exhibit greater deviations from their long-term trend.
The hierarchical feature regression (HFR) is a novel graph-based regularized regression estimator, which mobilizes insights from the domains of machine learning and graph theory to estimate robust parameters for a linear regression. The estimator constructs a supervised feature graph that decomposes parameters along its edges, adjusting first for common variation and successively incorporating idiosyncratic patterns into the fitting process. The graph structure has the effect of shrinking parameters towards group targets, where the extent of shrinkage is governed by a hyperparameter, and group compositions as well as shrinkage targets are determined endogenously. The method offers rich resources for the visual exploration of the latent effect structure in the data, and demonstrates good predictive accuracy and versatility when compared to a panel of commonly used regularization techniques across a range of empirical and simulated regression tasks.
The authors examine the effectiveness of labor cost reductions as a means to stimulate economic activity and assesses the differences which may occur with the prevailing exchange rate regime. They develop a medium-scale three-region DSGE model and show that the impact of a cut in the employers’ social security contributions rate does not vary significantly under different exchange rate regimes. They find that both the interest rate and the exchange rate channel matters. Furthermore, the measure appears to be effective even if it comes along with a consumption tax increase to preserve long-term fiscal sustainability.
Finally, they assess whether obtained theoretical results hold up empirically by applying the local projection method. Regression results suggest that changes in employers’ social security contributions rates have statistically significant real effects – a one percentage point reduction leads to an average cumulative rise in output of around 1.3 percent in the medium term. Moreover, the outcome does not differ significantly across the different exchange rate regimes.