SEQUENTIAL MONTE CARLO SAMPLING FOR DSGE MODELS

We develop a sequential Monte Carlo (SMC) algorithm for estimating Bayesian dynamic stochastic general equilibrium (DSGE) models; wherein a particle approximation to the posterior is built iteratively through tempering the likelihood. Using two empirical illustrations consisting of the Smets and Wouters model and a larger news shock model we show that the SMC algorithm is better suited for multimodal and irregular posterior distributions than the widely used random walk Metropolis–Hastings algorithm. We find that a more diffuse prior for the Smets and Wouters model improves its marginal data density and that a slight modification of the prior for the news shock model leads to drastic changes in the posterior inference about the importance of news shocks for fluctuations in hours worked. Unlike standard Markov chain Monte Carlo (MCMC) techniques; the SMC algorithm is well suited for parallel computing. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluating DSGE model forecasts of comovements

This paper develops and applies tools to assess multivariate aspects of Bayesian Dynamic Stochastic General Equilibrium (DSGE) model forecasts and their ability to predict comovements among key macroeconomic variables. We construct posterior predictive checks to evaluate conditional and unconditional density forecasts, in addition to checks for root-mean-squared errors and event probabilities associated with these forecasts. The checks are implemented on a three-equation DSGE model as well as the Smets and Wouters (2007) model using real-time data. We find that the additional features incorporated into the Smets–Wouters model do not lead to a uniform improvement in the quality of density forecasts and prediction of comovements of output, inflation, and interest rates.     

RARE SHOCKS,GREAT RECESSIONS

We estimate a DSGE (dynamic stochastic general equilibrium) model where rare large shocks can occur, by replacing the commonly used Gaussian assumption with a Student's t‐distribution. Results from the Smets and Wouters (American Economic Review 2007; 97 : 586–606) model estimated on the usual set of macroeconomic time series over the 1964–2011 period indicate that (i) the Student's t specification is strongly favored by the data even when we allow for low‐frequency variation in the volatility of the shocks, and (ii)) the estimated degrees of freedom are quite low for several shocks that drive US business cycles, implying an important role for rare large shocks. This result holds even if we exclude the Great Recession period from the sample. We also show that inference about low‐frequency changes in volatility—and, in particular, inference about the magnitude of Great Moderation—is different once we allow for fat tails. Copyright © 2014 John Wiley & Sons, Ltd.     

What We can Learn About the Behaviour of Firms from the Average Monthly Frequency of Price‐Changes: An Application to the UK CPI Data

The monthly frequency of price‐changes is a prominent feature of many studies of the CPI micro‐data. In this paper, we see what the frequency implies for the behaviour of price‐setters in terms of the cross‐sectional distribution average of price‐spell durations across firms. We derive a lower bound for the mean duration of price‐spells averaged across firms. We use the UK CPI data at the aggregate and sectoral level and find that the actual mean is about twice the theoretical minimum consistent with the observed frequency. We construct hypothetical Bernoulli–Calvo distributions from the frequency data which we find can result in similar impulse responses to the estimated hazards when used in the Smets–Wouters (2003) model.     

Tests of Predictive Ability for Vector Autoregressions Used for Conditional Forecasting

Many forecasts are conditional in nature. For example, a number of central banks routinely report forecasts conditional on particular paths of policy instruments. Even though conditional forecasting is common, there has been little work on methods for evaluating conditional forecasts. This paper provides analytical, Monte Carlo and empirical evidence on tests of predictive ability for conditional forecasts from estimated models. In the empirical analysis, we examine conditional forecasts obtained with a VAR in the variables included in the DSGE model of Smets and Wouters (American Economic Review 2007; 97 : 586–606). Throughout the analysis, we focus on tests of bias, efficiency and equal accuracy applied to conditional forecasts from VAR models. Copyright © 2016 John Wiley & Sons, Ltd.     

Learning in an estimated medium-scale DSGE model

We evaluate the empirical relevance of learning by private agents in an estimated medium-scale DSGE model. We replace the standard rational expectations assumption in the Smets and Wouters (2007) model by a constant-gain learning mechanism. If agents know the correct structure of the model and only learn about the parameters, both expectation mechanisms produce very similar results, and only the transition dynamics that are generated by specific initial beliefs seem to improve the fit. If, instead, agents use only a reduced information set in forming the perceived law of motion, the implied model dynamics change and, depending on the specification of the initial beliefs, the marginal likelihood of the model can improve significantly. These best-fitting models add additional persistence to the dynamics and this reduces the gap between the IRFs of the DSGE model and the more data-driven DSGE-VAR model. However, the learning dynamics do not systematically alter the estimated structural parameters related to the nominal and real frictions in the DSGE model.     

The implications of financial frictions and imperfect knowledge in the estimated DSGE model of the U.S. economy

In this paper, I study how alternative assumptions about expectation formation can modify the implications of financial frictions for the real economy. I incorporate a financial accelerator mechanism into a version of the Smets and Wouters (2007) DSGE framework and explore the properties of the model assuming, on the one hand, complete rationality of expectations and, alternatively, several learning algorithms that differ in terms of the information set used by agents to produce the forecasts. I show that the implications of the financial accelerator for the business cycle may vary depending on the approach to modeling the expectations. The results suggest that the learning scheme based on small forecasting functions is able to amplify the effects of financial frictions relative to the model with Rational Expectations. Specifically, I show that the dynamics of real variables under learning is driven to a significant extent by the time variation of agents’ beliefs about financial sector variables. During periods when agents perceive asset prices as being relatively more persistent, financial shocks lead to more pronounced macroeconomic outcomes. The amplification effect rises as financial frictions become more severe. At the same time, a learning specification in which agents use more information to generate predictions produces very different asset price and investment dynamics. In such a framework, learning cannot significantly alter the real effects of financial frictions implied by the Rational Expectations model.     

Professional forecasters and real-time forecasting with a DSGE model

This paper analyses the real-time forecasting performance of the New Keynesian DSGE model of Galí, Smets and Wouters (2012), estimated on euro area data. It investigates the extent to which the inclusion of forecasts of inflation, GDP growth and unemployment by professional forecasters improve the forecasting performance. We consider two approaches for conditioning on such information. Under the “noise” approach, the mean professional forecasts are assumed to be noisy indicators of the rational expectations forecasts implied by the DSGE model. Under the “news” approach, it is assumed that the forecasts reveal the presence of expected future structural shocks in line with those estimated in the past. The forecasts of the DSGE model are compared with those from a Bayesian VAR model, an AR(1) model, a sample mean and a random walk.     

Euro area real-time density forecasting with financial or labor market frictions

We compare real-time density forecasts for the euro area using three DSGE models. The benchmark is the Smets and Wouters model, and its forecasts of real GDP growth and inflation are compared with those from two extensions. The first adds financial frictions and expands the observables to include a measure of the external finance premium. The second allows for the extensive labor-market margin and adds the unemployment rate to the observables. The main question that we address is whether these extensions improve the density forecasts of real GDP and inflation and their joint forecasts up to an eight-quarter horizon. We find that adding financial frictions leads to a deterioration in the forecasts, with the exception of longer-term inflation forecasts and the period around the Great Recession. The labor market extension improves the medium- to longer-term real GDP growth and shorter- to medium-term inflation forecasts weakly compared with the benchmark model.     

Assessing DSGE model nonlinearities

We develop a new class of time series models to identify nonlinearities in the data and to evaluate DSGE models. U.S. output growth and the federal funds rate display nonlinear conditional mean dynamics, while inflation and nominal wage growth feature conditional heteroskedasticity. We estimate a DSGE model with asymmetric wage and price adjustment costs and use predictive checks to assess its ability to account for these nonlinearities. While it is able to match the nonlinear inflation and wage dynamics, thanks to the estimated downward wage and price rigidities, these do not spill over to output growth or the interest rate.     

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.     

The Incremental Predictive Information Associated with Using Theoretical New Keynesian DSGE Models vs. Simple Linear Econometric Models*

In this paper we construct output gap and inflation predictions using a variety of dynamic stochastic general equilibrium (DSGE) sticky price models. Predictive density accuracy tests related to the test discussed in Corradi and Swanson [Journal of Econometrics (2005a), forthcoming] as well as predictive accuracy tests due to Diebold and Mariano [Journal of Business and Economic Statistics (1995) , Vol. 13, pp. 253–263]; and West [Econometrica (1996) , Vol. 64, pp. 1067–1084] are used to compare the alternative models. A number of simple time‐series prediction models (such as autoregressive and vector autoregressive (VAR) models) are additionally used as strawman models. Given that DSGE model restrictions are routinely nested within VAR models, the addition of our strawman models allows us to indirectly assess the usefulness of imposing theoretical restrictions implied by DSGE models on unrestricted econometric models. With respect to predictive density evaluation, our results suggest that the standard sticky price model discussed in Calvo [Journal of Monetary Economics (1983), Vol. XII, pp. 383–398] is not outperformed by the same model augmented either with information or indexation, when used to predict the output gap. On the other hand, there are clear gains to using the more recent models when predicting inflation. Results based on mean square forecast error analysis are less clear‐cut, although the standard sticky price model fares best at our longest forecast horizon of 3 years, it performs relatively poorly at shorter horizons. When the strawman time‐series models are added to the picture, we find that the DSGE models still fare very well, often outperforming our forecast competitions, suggesting that theoretical macroeconomic restrictions yield useful additional information for forming macroeconomic forecasts.     

Data‐Driven Identification Constraints for DSGE Models

We propose imposing data‐driven identification constraints to alleviate the multimodality problem arising in the estimation of poorly identified dynamic stochastic general equilibrium models under non‐informative prior distributions. We also devise an iterative procedure based on the posterior density of the parameters for finding these constraints. An empirical application to the Smets and Wouters ( 2007 ) model demonstrates the properties of the estimation method, and shows how the problem of multimodal posterior distributions caused by parameter redundancy is eliminated by identification constraints. Out‐of‐sample forecast comparisons as well as Bayes factors lend support to the constrained model.     

Consumer misperceptions,uncertain fundamentals,and the business cycle

This paper estimates the importance of shocks to consumer misperceptions “noise shocks” for U.S. business cycle fluctuations. I embed imperfect information as in Lorenzoni (2009) into a Smets and Wouters (2007)-type DSGE model. Agents only observe aggregate productivity and a signal about the permanent component contaminated with noise. Based on this information agents form beliefs about the temporary and the permanent component of productivity. Shocks to the signal (noise shocks) trigger aggregate fluctuations unrelated to changes in productivity. Bayesian estimation shows that noise shocks explain up to 14 percent of output and up to 25 percent of consumption fluctuations. Nominal rigidities and the specification of the monetary policy rule are crucial for the importance of noise shocks. These features help to resolve conflicting results in the previous literature.     

Marginalized Predictive Likelihood Comparisons of Linear Gaussian State‐Space Models with Applications to DSGE,DSGE‐VAR,and VAR Models

The predictive likelihood is useful for ranking models in forecast comparison exercises using Bayesian inference. We discuss how it can be estimated, by means of marzginalization, for any subset of the observables in linear Gaussian state‐space models. We compare macroeconomic density forecasts for the euro area of a DSGE model to those of a DSGE‐VAR, a BVAR and a multivariate random walk over 1999:Q1–2011:Q4. While the BVAR generally provides superior forecasts, its performance deteriorates substantially with the onset of the Great Recession. This is particularly notable for longer‐horizon real GDP forecasts, where the DSGE and DSGE‐VAR models perform better. Copyright © 2016 John Wiley & Sons, Ltd.     

Tailored randomized block MCMC methods with application to DSGE models

In this paper we develop new Markov chain Monte Carlo schemes for the estimation of Bayesian models. One key feature of our method, which we call the tailored randomized block Metropolis–Hastings (TaRB-MH) method, is the random clustering of the parameters at every iteration into an arbitrary number of blocks. Then each block is sequentially updated through an M–H step. Another feature is that the proposal density for each block is tailored to the location and curvature of the target density based on the output of simulated annealing, following  and  and Chib and Ergashev (in press). We also provide an extended version of our method for sampling multi-modal distributions in which at a pre-specified mode jumping iteration, a single-block proposal is generated from one of the modal regions using a mixture proposal density, and this proposal is then accepted according to an M–H probability of move. At the non-mode jumping iterations, the draws are obtained by applying the TaRB-MH algorithm. We also discuss how the approaches of Chib (1995) and Chib and Jeliazkov (2001) can be adapted to these sampling schemes for estimating the model marginal likelihood. The methods are illustrated in several problems. In the DSGE model of Smets and Wouters (2007), for example, which involves a 36-dimensional posterior distribution, we show that the autocorrelations of the sampled draws from the TaRB-MH algorithm decay to zero within 30–40 lags for most parameters. In contrast, the sampled draws from the random-walk M–H method, the algorithm that has been used to date in the context of DSGE models, exhibit significant autocorrelations even at lags 2500 and beyond. Additionally, the RW-MH does not explore the same high density regions of the posterior distribution as the TaRB-MH algorithm. Another example concerns the model of An and Schorfheide (2007) where the posterior distribution is multi-modal. While the RW-MH algorithm is unable to jump from the low modal region to the high modal region, and vice-versa, we show that the extended TaRB-MH method explores the posterior distribution globally in an efficient manner.     

The New Keynesian Phillips Curve and staggered price and wage determination in a model with firm-specific labor

We develop a DSGE model with firm-specific labor where wage and price setting are subject to Calvo-type staggering. This is in general an intractable problem due to complicated intertemporal dependencies between price and wage decisions. However, the problem is significantly simplified if we, in line with empirical evidence, assume that prices can be changed whenever wages are. We show that the price- and wage-setting relationships are substantially altered by the introduction of firm-specific labor. Specifically, the inflation response is substantially dampened, whereas the wage inflation response is increased as compared to models with freely mobile labor. These distinctive features of the model with firm-specific labor are supported by empirical evidence from a structural VAR.     

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.     

Public–private wage gap in Latin America (1992–2007): A matching approach

Using matching methods, we estimate the public–private wage gap for urban workers in eleven Latin American countries for the 1992–2007 period. These methods do not require any estimation of earnings equations and hence no validity-out-of-the-support assumptions; furthermore, this approach allows us to estimate not only the average wage gap but also its distribution. Our main findings indicate that the average public sector worker earns more than his/her private counterpart, and that this differential increased over the 1992–2007 period. Important differences along the wage distribution are also shown in the results; in fact, public servants in the highest percentiles of the wage distribution generally earn less than their private sector equivalents. Nonetheless, the percentile at which a positive wage gap becomes a wage penalty shifted over the period as the average wage gap experienced by most countries widened. Still, the most qualified public sector workers do face a wage penalty. Furthermore, indicators of government effectiveness show no relationship with the country ranking according to the public–private wage gap.     

Self/paid-employment, public/private sector selection, and wage differentials

We use Probit models to account for the double selection problem of choice between, on the one hand, self- and paid-employment and, on the other, employment in the public and private sector. These models provide corrections for sample selection in wage equations for paid employees in the public and private sectors. Using a modified version of the Oaxaca and Ransom [J. Econom. 61 (1994) 5] procedure, we decompose the wage gap between the public and private sectors into a portion attributable to differences in characteristics, the public sector advantage, the private sector disadvantage and unobserved selection effects. Rich data for the Republic of Cyprus, a thriving economy with institutional features reminiscent of a developing economy, help determine the choice of type (self/paid) and sector (public/private) of employment. The human capital model describes the wage determination process satisfactorily. The size and distribution of public sector rents between men and women are similar to those in North America and are bracketed by results for developing countries.