Fitting observed inflation expectations

The paper provides evidence on the extent to which inflation expectations generated by a standard Christiano et al. (2005)/Smets and Wouters (2003)-type DSGE model are in line with what observed in the data. We consider three variants of this model that differ in terms of the behavior of, and the public's information on, the central banks' inflation target, allegedly a key determinant of inflation expectations. We find that (i) time-variation in the inflation target is needed to capture the evolution of expectations during the post-Volcker period; (ii) the variant where agents have Imperfect Information is strongly rejected by the data; (iii) inflation expectations appear to contain information that is not present in the other series used in estimation, and (iv) none of the models fully capture the dynamics of this variable.     

Nonparametric tests for Optimal Predictive Ability

A nonparametric method for comparing multiple forecast models is developed and implemented. The hypothesis of Optimal Predictive Ability generalizes the Superior Predictive Ability hypothesis from a single given loss function to an entire class of loss functions. Distinction is drawn between General Loss functions, Convex Loss functions, and Symmetric Convex Loss functions. The research hypothesis is formulated in terms of moment inequality conditions. The empirical moment conditions are reduced to an exact and finite system of linear inequalities based on piecewise-linear loss functions. The hypothesis can be tested in a statistically consistent way using a blockwise Empirical Likelihood Ratio test statistic. A computationally feasible test procedure computes the test statistic using Convex Optimization methods, and estimates conservative, data-dependent critical values using a majorizing chi-square limit distribution and a moment selection method. An empirical application to inflation forecasting reveals that a very large majority of thousands of forecast models are redundant, leaving predominantly Phillips Curve-type models, when convexity and symmetry are assumed.     

Forecasting crude oil prices with DSGE models

In this study, we conducted an oil prices forecasting competition among a set of structural models, including vector autoregression and dynamic stochastic general equilibrium (DSGE) models. Our results highlight two principles. First, forecasts should exploit the fact that real oil prices are mean reverting over long horizons. Second, models should not replicate the high volatility of the oil prices observed in samples. By following these principles, we show that an oil sector DSGE model performs much better at real oil price forecasting than random walk or vector autoregression.     

On the forecasting performance of a small-scale DSGE model

Dynamic stochastic general equilibrium (DSGE) models have recently become standard tools for policy analysis. Nevertheless, their forecasting properties have still barely been explored. In this article, we address this problem by examining the quality of forecasts of the key U.S. economic variables: the three-month Treasury bill yield, the GDP growth rate and GDP price index inflation, from a small-size DSGE model, trivariate vector autoregression (VAR) models and the Philadelphia Fed Survey of Professional Forecasters (SPF). The ex post forecast errors are evaluated on the basis of the data from the period 1994–2006. We apply the Philadelphia Fed “Real-Time Data Set for Macroeconomists” to ensure that the data used in estimating the DSGE and VAR models was comparable to the information available to the SPF.Overall, the results are mixed. When comparing the root mean squared errors for some forecast horizons, it appears that the DSGE model outperforms the other methods in forecasting the GDP growth rate. However, this characteristic turned out to be statistically insignificant. Most of the SPF's forecasts of GDP price index inflation and the short-term interest rate are better than those from the DSGE and VAR models.     

Evaluating predictive densities of US output growth and inflation in a large macroeconomic data set

We evaluate conditional predictive densities for US output growth and inflation using a number of commonly-used forecasting models that rely on large numbers of macroeconomic predictors. More specifically, we evaluate how well conditional predictive densities based on the commonly-used normality assumption fit actual realizations out-of-sample. Our focus on predictive densities acknowledges the possibility that, although some predictors can cause point forecasts to either improve or deteriorate, they might have the opposite effect on higher moments. We find that normality is rejected for most models in some dimension according to at least one of the tests we use. Interestingly, however, combinations of predictive densities appear to be approximated correctly by a normal density: the simple, equal average when predicting output growth, and the Bayesian model average when predicting inflation.     

The implications of inflation in an estimated new Keynesian model

This paper studies the steady state and dynamic consequences of inflation in an estimated dynamic stochastic general equilibrium model of the U.S. economy. It is found that 10 percentage points of inflation entail a steady state welfare cost as high as 13% of annual consumption. This large cost is mainly driven by staggered price contracts and price indexation. The transition from high to low inflation inflicts a welfare loss equivalent to 0.53% of annual consumption. The role of nominal/real frictions as well as that of parameter uncertainty is also addressed.     

Bayesian prediction with cointegrated vector autoregressions

A complete procedure for calculating the joint predictive distribution of future observations based on the cointegrated vector autoregression is presented. The large degree of uncertainty in the choice of cointegration vectors is incorporated into the analysis via the prior distribution. This prior has the effect of weighing the predictive distributions based on the models with different cointegration vectors into an overall predictive distribution. The ideas of Litterman [Mimeo, Massachusetts Institute of Technology, 1980] are adopted for the prior on the short run dynamics of the process resulting in a prior which only depends on a few hyperparameters. A straightforward numerical evaluation of the predictive distribution based on Gibbs sampling is proposed. The prediction procedure is applied to a seven-variable system with a focus on forecasting Swedish inflation.     

Bayesian inference and prediction in the single server Markovian queue

The use of stochastic models and performance measures for the analysis of real life queuing scenarios are based on the fundamental premise that parameters values are known. This is a rarity since more often than not, parameters are usually unknown and require to be estimated. This paper presents techniques for the same from Bayesian perspective. The queue we intend to deal with is the M/M/1 queuing model. Several closed form expressions on posterior inference and prediction are presented which can be readily implemented using standard spreadsheet tools. Previous work in this direction resulted in non-existence of posterior moments. A way out is suggested. Interval estimates and tests of hypothesis on performance measures are also presented.     

Non-linear DSGE models and the optimized central difference particle filter

We improve the accuracy and speed of particle filtering for non-linear DSGE models with potentially non-normal shocks. This is done by introducing a new proposal distribution which (i) incorporates information from new observables and (ii) has a small optimization step that minimizes the distance to the optimal proposal distribution. A particle filter with this proposal distribution is shown to deliver a high level of accuracy even with relatively few particles, and it is therefore much more efficient than the standard particle filter.     

Bayesian prior elicitation in DSGE models: Macro- vs micropriors

Bayesian approaches to the estimation of DSGE models are becoming increasingly popular. Prior knowledge is normally formalized either directly on deep parameters' values (‘microprior’) or indirectly, on macroeconomic indicators, e.g. moments of observable variables (‘macroprior’). We introduce a non-parametric macroprior which is elicited from impulse response functions and assess its performance in shaping posterior estimates. We find that using a macroprior can lead to substantially different posterior estimates. We probe into the details of our result, showing that model misspecification is likely to be responsible of that. In addition, we assess to what extent the use of macropriors is impaired by the need of calibrating some hyperparameters.     

中国的潜在产出、产出缺口及产量--通货膨胀交替关系--基于"Kalman滤波"方法的研究

本文介绍并运用“Kalman滤波”方法估计1979-2004年间我国的潜在经济增长率和产出缺口,然后根据这些结果检验了我国经济增长与通货膨胀率之间的交替关系、社会的通货膨胀预期对经济的影响、决定产出缺口大小的影响因素等,最后利用研究结果对我国2005年的经济发展进行了预测。     

On some properties of Markov chain Monte Carlo simulation methods based on the particle filter

Andrieu et al. (2010) prove that Markov chain Monte Carlo samplers still converge to the correct posterior distribution of the model parameters when the likelihood estimated by the particle filter (with a finite number of particles) is used instead of the likelihood. A critical issue for performance is the choice of the number of particles. We add the following contributions. First, we provide analytically derived, practical guidelines on the optimal number of particles to use. Second, we show that a fully adapted auxiliary particle filter is unbiased and can drastically decrease computing time compared to a standard particle filter. Third, we introduce a new estimator of the likelihood based on the output of the auxiliary particle filter and use the framework of Del Moral (2004) to provide a direct proof of the unbiasedness of the estimator. Fourth, we show that the results in the article apply more generally to Markov chain Monte Carlo sampling schemes with the likelihood estimated in an unbiased manner.     

Monetary policy trade-offs in an estimated open-economy DSGE model

This paper studies the trade-offs between stabilizing CPI inflation and alternative measures of the output gap in Ramses, the Riksbank׳s estimated dynamic stochastic general equilibrium (DSGE) model of a small open economy. Our main finding is that the trade-off between stabilizing CPI inflation and the output gap strongly depends on which concept of potential output in the output gap between output and potential output is used in the loss function. If potential output is defined as a smooth trend this trade-off is much more pronounced compared to the case when potential output is defined as the output level that would prevail if prices and wages were flexible.     

Open economy forecasting with a DSGE-VAR: Head to head with the RBNZ published forecasts

We construct a DSGE-VAR model for competing head to head with the long history of published forecasts of the Reserve Bank of New Zealand. We also construct a Bayesian VAR model with a Minnesota prior for forecast comparison. The DSGE-VAR model combines a structural DSGE model with a statistical VAR model based on the in-sample fit over the majority of New Zealand’s inflation-targeting period. We evaluate the real-time out-of-sample forecasting performance of the DSGE-VAR model, and show that the forecasts from the DSGE-VAR are competitive with the Reserve Bank of New Zealand’s published, judgmentally-adjusted forecasts. The Bayesian VAR model with a Minnesota prior also provides a competitive forecasting performance, and generally, with a few exceptions, out-performs both the DSGE-VAR and the Reserve Bank’s own forecasts.     

EVALUATING MACROECONOMIC FORECASTS: A CONCISE REVIEW OF SOME RECENT DEVELOPMENTS

Macroeconomic forecasts are frequently produced, widely published, intensively discussed, and comprehensively used. The formal evaluation of such forecasts has a long research history. Recently, a new angle to the evaluation of forecasts has been addressed, and in this review we analyze some recent developments from that perspective. The literature on forecast evaluation predominantly assumes that macroeconomic forecasts are generated from econometric models. In practice, however, most macroeconomic forecasts, such as those from the IMF, World Bank, OECD, Federal Reserve Board, Federal Open Market Committee (FOMC), and the ECB, are typically based on econometric model forecasts jointly with human intuition. This seemingly inevitable combination renders most of these forecasts biased and, as such, their evaluation becomes nonstandard. In this review, we consider the evaluation of two forecasts in which: (i) the two forecasts are generated from two distinct econometric models; (ii) one forecast is generated from an econometric model and the other is obtained as a combination of a model and intuition; and (iii) the two forecasts are generated from two distinct (but unknown) combinations of different models and intuition. It is shown that alternative tools are needed to compare and evaluate the forecasts in each of these three situations. These alternative techniques are illustrated by comparing the forecasts from the (econometric) Staff of the Federal Reserve Board and the FOMC on inflation, unemployment, and real GDP growth. It is shown that the FOMC does not forecast significantly better than the Staff, and that the intuition of the FOMC does not add significantly in forecasting the actual values of the economic fundamentals. This would seem to belie the purported expertise of the FOMC.     

对中国通货膨胀的实证研究——从一般到特殊的建模方法

本文采用从一般到特殊的建模方法,利用PcGets软件,实证考察了1994~2009年中国通货膨胀与货币供应、产出缺口、汇率和国际原油价格之间的联系。研究表明,通货膨胀和货币供应之间存在长期稳定的正相关关系,但通货膨胀并不完全是货币现象。除货币供应外,还有其他更多重要变量共同决定通货膨胀的变化。产出缺口与通货膨胀之间存在显著关系,因而不能忽视汇率因素对通货膨胀的影响等。