Information criteria for impulse response function matching estimation of DSGE models

We propose new information criteria for impulse response function matching estimators (IRFMEs). These estimators yield sampling distributions of the structural parameters of dynamic stochastic general equilibrium (DSGE) models by minimizing the distance between sample and theoretical impulse responses. First, we propose an information criterion to select only the responses that produce consistent estimates of the true but unknown structural parameters: the Valid Impulse Response Selection Criterion (VIRSC). The criterion is especially useful for mis-specified models. Second, we propose a criterion to select the impulse responses that are most informative about DSGE model parameters: the Relevant Impulse Response Selection Criterion (RIRSC). These criteria can be used in combination to select the subset of valid impulse response functions with minimal dimension that yields asymptotically efficient estimators. The criteria are general enough to apply to impulse responses estimated by VARs, local projections, and simulation methods. We show that the use of our criteria significantly affects estimates and inference about key parameters of two well-known new Keynesian DSGE models. Monte Carlo evidence indicates that the criteria yield gains in terms of finite sample bias as well as offering tests statistics whose behavior is better approximated by the first order asymptotic theory. Thus, our criteria improve existing methods used to implement IRFMEs.     

DSGE Models in the Frequency Domains

We use frequency domain techniques to estimate a medium‐scale dynamic stochastic general equilibrium (DSGE) model on different frequency bands. We show that goodness of fit, forecasting performance and parameter estimates vary substantially with the frequency bands over which the model is estimated. Estimates obtained using subsets of frequencies are characterized by significantly different parameters, an indication that the model cannot match all frequencies with one set of parameters. In particular, we find that: (i) the low‐frequency properties of the data strongly affect parameter estimates obtained in the time domain; (ii) the importance of economic frictions in the model changes when different subsets of frequencies are used in estimation. This is particularly true for the investment adjustment cost and habit persistence: when low frequencies are present in the estimation, the investment adjustment cost and habit persistence are estimated to be higher than when low frequencies are absent. Copyright © 2014 John Wiley & Sons, Ltd.     

Aggregation is not the solution: the PPP puzzle strikes back

Recently, Imbs, Mumtaz, Ravn and Rey (2005, hereinafter IMRR) have argued that much of the purchasing power parity (PPP) puzzle is due to upwardly biased estimates of persistence. According to them, the source of the bias is the existence of heterogeneous price adjustment dynamics at the sectoral level that established time series or panel data methods fail to control for. This paper re‐examines this claim in two steps. Firstly, we demonstrate that IMRR's measures of sectoral persistence are systematically downwardly biased because they are based on an inaccurate definition of the ‘average’ impulse response function (IRF). We then show that standard estimates of shock persistence are recovered after this bias is corrected. Secondly, building on the results in Mayoral (2008), which prove that aggregate and micro models induce the same shock persistence behavior, we show that estimates based on aggregate and sectoral exchange rates are, in fact, highly consistent. Thus, aggregation is not the solution to the PPP puzzle. Copyright © 2009 John Wiley & Sons, Ltd.     

A Note on the Identification of Dynamic Economic Models with Generalized Shock Processes

Dynamic stochastic general equilibrium (DSGE) models with generalized shock processes, such as shock processes which follow a vector autoregression (VAR), have been an active area of research in recent years. Unfortunately, the structural parameters governing DSGE models are not identified when the driving process behind the model follows an unrestricted VAR. This finding implies that parameter estimates derived from recent attempts to estimate DSGE models with generalized driving processes should be treated with caution, and that there always exists a tradeoff between identification and the risk of model misspecification. However, these results also make it easier to address the issue of model misspecification by making it computationally easier to check the validity of cross‐equation restrictions.     

Selecting structural innovations in DSGE models

Dynamic stochastic general equilibrium (DSGE) models are typically estimated assuming the existence of certain structural shocks that drive macroeconomic fluctuations. We analyze the consequences of estimating shocks that are “nonexistent” and propose a method to select the economic shocks driving macroeconomic uncertainty. Forcing these nonexisting shocks in estimation produces a downward bias in the estimated internal persistence of the model. We show how these distortions can be reduced by using priors for standard deviations whose support includes zero. The method allows us to accurately select shocks and estimate model parameters with high precision. We revisit the empirical evidence on an industry standard medium‐scale DSGE model and find that government and price markup shocks are innovations that do not generate statistically significant dynamics.     

Fixed effects estimation of structural parameters and marginal effects in panel probit models

Fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper, I characterize the leading term of a large-T expansion of the bias of the MLE and estimators of average marginal effects in parametric fixed effects panel binary choice models. For probit index coefficients, the former term is proportional to the true value of the coefficients being estimated. This result allows me to derive a lower bound for the bias of the MLE. I then show that the resulting fixed effects estimates of ratios of coefficients and average marginal effects exhibit no bias in the absence of heterogeneity and negligible bias for a wide variety of distributions of regressors and individual effects in the presence of heterogeneity. I subsequently propose new bias-corrected estimators of index coefficients and marginal effects with improved finite sample properties for linear and nonlinear models with predetermined regressors.     

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.     

PRACTICAL TOOLS FOR POLICY ANALYSIS IN DSGE MODELS WITH MISSING SHOCKS

In this paper we analyze the propagation of shocks originating in sectors that are not present in a baseline dynamic stochastic general equilibrium (DSGE) model. Specifically, we proxy the missing sector through a small set of factors that feed into the structural shocks of the DSGE model to create correlated disturbances. We estimate the factor structure by either matching impulse responses of the augmented DSGE model to those generated by an auxiliary model or by using Bayesian techniques. We apply this methodology to track the effects of oil shocks and housing demand shocks in models without energy or housing sectors. Copyright © 2014 John Wiley & Sons, Ltd.     

Technical change in the U.S. primary metals industry

A dual cost function embodying biased technical change is estimated for the postwar primary metals industry. The identifying restriction of constant rates of factor augmentation is used to derive significant estimates of rates of biased technical change which are consistent with the induced innovation hypothesis. Also, the bias in elasticity estimates which results from ignoring biased technical change is shown to be serious.     

Estimating substitution elasticities with the Fourier cost function: Some Monte Carlo results

The Fourier flexible form possesses desirable asymptotic properties that are not shared by other flexible forms such as the translog, generalized Leontief, and generalized Box-Cox. One of them is that an elasticity of substitution can be estimated with negligible bias in sufficiently large samples regardless of what the true form actually is, save that it be smooth enough. This article reports the results of an experiment designed to determine whether or not this property obtains in samples of the sizes customarily encountered in practice. A three-input, homothetic version of the generalized Box-Cox cost function was used to generate technologies that were oriented in a two-dimensional design space according to a central composite rotatable design; the two factors of the design were the Box-Cox parameter and a measure of the dispersion of the substitution matrix. The Fourier cost function was used to estimate the substitution elasticities at each design point, and the bias at each point was estimated using the Monte Carlo method. A response surface over the entire design space was fitted to these estimates. An examination of the surface reveals that the bias is small over the entire design space. Roughly speaking, the estimates of elasticities of substitution are unbiased to three significant digits using the Fourier flexible form no matter what the true technology. Our conclusion is that the small bias property of the Fourier form does obtain in samples of reasonable size; this claim must be tampered by the usual caveats associated with inductive inference.     

The zero lower bound,the dual mandate,and unconventional dynamics

This paper examines monetary policy when it is constrained by the zero lower bound (ZLB) on the nominal interest rate. Our analysis uses a nonlinear New Keynesian model with technology and discount factor shocks. Specifically, we investigate why technology shocks may have unconventional effects at the ZLB, what factors affect the likelihood of hitting the ZLB, and the implications of alternative monetary policy rules. We initially focus on a New Keynesian model without capital (Model 1) and then study that model with capital (Model 2). The advantage of including capital is that it introduces another mechanism for intertemporal substitution that strengthens the expectational effects of the ZLB. Four main findings emerge: (1) In Model 1, the choice of output target in the Taylor rule may reverse the effects of technology shocks when the ZLB binds; (2) When the central bank targets steady-state output in Model 2, a positive technology shock at the ZLB leads to more pronounced unconventional dynamics than in Model 1; (3) The presence of capital changes the qualitative effects of demand shocks and alters the impact of a monetary policy rule that emphasizes output stability; and (4) In Model 1, the constrained linear solution is a decent approximation of the nonlinear solution, but meaningful differences exist between the solutions in Model 2.     

A count-amount model with endogenous recording of observations

This paper discusses some of the problems which are encountered if an event ? is only recorded if its value satisfies a recording criterion A. It follows that we get an incorrect idea of the frequency of the events and of its true distribution. In order to solve these problems, an econometric model has been constructed by means of which consistent estimation of the true parameters is possible. The model is estimated on consumer purchases, where the number of purchases is assumed to be NEGBIN-distributed and the purchase amounts obey a lognormal distribution. Purchases are only recorded if their value exceeds Dfl. 10. It is shown that ignoring the recording condition will result in biased estimates and invalid predictions. Apart from this, the model is, among others, relevant for insurance problems, marketing surveys and criminological and epidemiological phenomena.     

Estimates of the return to schooling in Sweden from a large sample of twins

A large sample of twins was used to examine whether conventional estimates of the return to schooling in Sweden are biased because ability is omitted from the earnings–schooling relationship. Ignoring measurement error, the results indicate that omitting ability from the earnings–schooling relationship leads to estimates that are positively biased. However, reasonable estimates of the measurement-error-adjusted returns are both above and below the unadjusted estimates, showing that the results depend crucially on a parameter not known at this time. However, an estimate of the reliability ratio was obtained using two measures on educational attainment. With this estimate of the reliability ratio, the measurement-error-adjusted estimate of the return to schooling in the sample of identical twins indicates that there is at most a slight ability bias in the conventional estimates of the return to schooling. The fundamental assumption of this kind of study is that within-pair differences in educational attainment are randomly determined. This assumption was also tested, but no strong evidence to reject it was found.     

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.     

Spatial Vector Autoregressions

Abstract

A spatial vector autoregressive model (SpVAR) is defined as a VAR which includes spatial as well as temporal lags among a vector of stationary state variables. SpVARs may contain disturbances that are spatially as well as temporally correlated. Although the structural parameters are not fully identified in SpVARs, contemporaneous spatial lag coefficients may be identified by weakly exogenous state variables. Dynamic spatial panel data econometrics is used to estimate SpVARs. The incidental parameter problem is handled by bias correction rather than more popular alternatives such as generalised methods of moments (GMM). The interaction between temporal and spatial stationarity is discussed. The impulse responses for SpVARs are derived, which naturally depend upon the temporal and spatial dynamics of the model. We provide an empirical illustration using annual spatial panel data for Israel. The estimated SpVAR is used to calculate impulse responses between variables, over time, and across space. Finally, weakly exogenous instrumental variables are used to identify contemporaneous spatial lag coefficients.     

What (really) accounts for the fall in hours after a technology shock?

The paper asks how state of the art DSGE models that account for the conditional response of hours following a positive neutral technology shock compare in a marginal likelihood race. To that end we construct and estimate several competing small-scale DSGE models that extend the standard real business cycle model. In particular, we identify from the literature six different hypotheses that generate the empirically observed decline in hours worked after a positive technology shock. These models alternatively exhibit (i) sticky prices; (ii) firm entry and exit with time to build; (iii) habit in consumption and costly adjustment of investment; (iv) persistence in the permanent technology shocks; (v) labor market friction with procyclical hiring costs; and (vi) Leontief production function with labor-saving technology shocks. In terms of model posterior probabilities, impulse responses, and autocorrelations, the model favored is the one that exhibits habit formation in consumption and investment adjustment costs. A robustness test shows that the sticky price model becomes as competitive as the habit formation and costly adjustment of investment model when sticky wages are included.     

A finite sample correction for the variance of linear efficient two-step GMM estimators

Monte Carlo studies have shown that estimated asymptotic standard errors of the efficient two-step generalized method of moments (GMM) estimator can be severely downward biased in small samples. The weight matrix used in the calculation of the efficient two-step GMM estimator is based on initial consistent parameter estimates. In this paper it is shown that the extra variation due to the presence of these estimated parameters in the weight matrix accounts for much of the difference between the finite sample and the usual asymptotic variance of the two-step GMM estimator, when the moment conditions used are linear in the parameters. This difference can be estimated, resulting in a finite sample corrected estimate of the variance. In a Monte Carlo study of a panel data model it is shown that the corrected variance estimate approximates the finite sample variance well, leading to more accurate inference.     

In Search of the Transmission Mechanism of Fiscal Policy in the Euro Area

This paper applies the DSGE‐VAR methodology to assess the size of fiscal multipliers in the data and the relative contributions of two transmission mechanisms of government spending shocks, namely hand‐to‐mouth consumers and Edgeworth complementarity. Econometric experiments show that a DSGE model with Edgeworth complementarity is a better representation of the transmission mechanism of fiscal policy as it yields dynamic responses close to those obtained with the flexible DSGE‐VAR model (i.e. an impact output multiplier larger than one and a crowding‐in of private consumption). The estimated share of hand‐to‐mouth consumers is too small to replicate the positive response of private consumption. Copyright © 2016 John Wiley & Sons, Ltd.     

Estimating the economic return to educational levels using data on twins

This paper relaxes some restrictions of previous twin‐based estimates of the effects of education on earnings. First, it estimates the earnings premiums associated with different educational levels. Second, it estimates a piecewise linear relationship between the natural logarithm of annual earnings and years of schooling. Third, the measurement error corrections are based on a less restrictive, ‘non‐classical’, measurement error model. The estimation strategy implies that ability bias can be investigated separately in different parts of the educational distribution. The linear relationship between the logarithm of annual earnings and years of schooling is rejected. Furthermore, the results in the sample of identical (MZ) twins indicated both that the ability bias could be of different signs and of different magnitudes in different parts of the educational distribution. The twin‐based estimates in the sample of fraternal (DZ) twins did not display any marked differences as compared to the cross‐sectional estimates. Finally, the results indicated that the error‐corrected twin‐based estimates of the average return to years of schooling that rely on a classical measurement error model are upwards biased by approximately 30%. Copyright © 2004 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.