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Theories often make predictions about the signs of the effects of economic shocks on observable variables, thus implying inequality constraints on the parameters of a structural vector autoregression (SVAR). We introduce a new Bayesian procedure to evaluate the probabilities of such constraints, and, hence, to validate the theoretically implied economic shocks. We first estimate a SVAR, where the shocks are identified by statistical properties of the data, and subsequently label these statistically identified shocks by the Bayes factors calculated from their probabilities of satisfying given inequality constraints. In contrast to the related sign restriction approach that also makes use of theoretically implied inequality constraints, no restrictions are imposed. Hence, it is possible that only a subset or none of the theoretically implied shocks can be labelled. In the latter case, we conclude that the data do not lend support to the theory implying the signs of the effects in question. We illustrate the method by empirical applications to the crude oil market, and U.S. monetary policy.

We consider estimation of the structural vector autoregression (SVAR) by the generalized method of moments (GMM). Given non-Gaussian errors and a suitable set of moment conditions, the GMM estimato...

We revisit the generalized method of moments (GMM) estimation of the non-Gaussian structural vector autoregressive (SVAR) model. It is shown that in the n-dimensional SVAR model, global and local identification of the contemporaneous impact matrix is achieved with as few as n^2+n(n-1)/2 suitably selected moment conditions, when at least n-1 of the structural errors are all leptokurtic (or platykurtic). The potentially problematic assumption of mutually independent structural errors in part of the previous literature on statistical identification of SVAR models is also relaxed to the requirement that the errors only exhibit no excess co-kurtosis. Moreover, we assume the error term to be only serially uncorrelated, not independent in time, which allows for univariate conditional heteroskedasticity in its components. A small simulation experiment highlights the good properties of the estimator and the proposed moment selection procedure. The use of the methods is illustrated by means of an empirical application to the effect of a tax increase on U.S. gasoline consumption and carbon dioxide emissions.

We study the evolution of U.S. inflation by means of a new noncausal autoregressive model with time-varying parameters that outperforms the corresponding causal and constant-parameter noncausal models in terms of fit and forecast accuracy. Our model also beats the unobserved component stochastic volatility (UCSV) model, one of the best-performing univariate inflation forecasting models, in terms of both point and density forecasts. We also show how the new Keynesian Phillips curve can be estimated based on our noncausal model. Both expected and lagged inflation turn out important, but the former dominates in determining the current inflation.

Summary We consider Bayesian analysis of the noncausal vector autoregressive model that is capable of capturing nonlinearities and effects of missing variables. Specifically, we devise a fast and reliable posterior simulator that yields the predictive distribution as a by-product. We apply the methods to postwar US inflation and GDP growth. The noncausal model is found superior in terms of both in-sample fit and out-of-sample forecasting performance over its conventional causal counterpart. Economic shocks based on the noncausal model turn out to be highly anticipated in advance. We also find the GDP growth to have predictive power for future inflation, but not vice versa. Copyright © 2016 John Wiley & Sons, Ltd.

Franses (Empir Econ, 2018. https://doi.org/10.1007/s00181-018-1417-8 ) criticised the practice in the empirical literature of replacing expected inflation by the sum of realised future inflation and an error in estimating the parameters of the new Keynesian Phillips curve (NKPC). In particular, he argued that this assumption goes against the Wold decomposition theorem and makes the error term in the hybrid NKPC equation correlated with future inflation, invalidating the maximum likelihood (ML) estimator of Lanne and Luoto (J Econ Dyn Control 37:561–570, 2013). We argue that despite the correlation, the Wold theorem is not violated, and the ML estimator is consistent.

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 () 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.

In this paper, Bayesian methods and the Finnish aggregate infrastructure capital series from 1860 to 2003 are used to explore how government infrastructure policy affects long-run output growth. We use Finnish data, since to the best of our knowledge the Finnish land and water construction investments series is the best available sufficiently long time series on aggregate infrastructure investments. The Finnish data provide strong and robust evidence indicating that permanent changes in government infrastructure policy have permanent effects on the growth rate of output.

In this paper, we propose a Bayesian estimation and prediction procedure for noncausal autoregressive (AR) models. Specifically, we derive the joint posterior density of the past and future errors and the parameters, which gives posterior predictive densities as a byproduct. We show that the posterior model probability provides a convenient model selection criterion and yields information on the probabilities of the alternative causal and noncausal specifications. This is particularly useful in assessing economic theories that imply either causal or purely noncausal dynamics. As an empirical application, we consider U.S. inflation dynamics. A purely noncausal AR model gets the strongest support, but there is also substantial evidence in favor of other noncausal AR models allowing for dependence on past inflation. Thus, although U.S. inflation dynamics seem to be dominated by expectations, the backward-looking component is not completely missing. Finally, the noncausal specifications seem to yield inflation forecasts which are superior to those from alternative models especially at longer forecast horizons.

This article uses the Bayesian approach to estimate the parameters of the normalized constant elasticity of substitution (CES) function with factor-augmenting technical progress directly, rather than using derived first-order conditions of profit maximizing behavior. Bayesian estimation is applied because maximum likelihood estimation is sensitive to the starting values of maximization, and the parameters typically fail to converge to the global optimum because of a multimodal likelihood. Thanks to a convenient prior distribution, the posterior simulation of parameters works fairly well. The results indicate that in the long run (over 100 years) the parameters for the elasticity of substitution and capital income share are intimately linked to the shape of capital-augmenting technological progress. In particular, the linear restriction excludes the possibility that the speed of capital-augmenting technological progress converges to zero, which seems to lead to upwardly biased estimates of the elasticity of substitution and income share parameters.

Using GARCH-in-Mean models, we study the robustness of the risk–return relationship in monthly U.S. stock market returns (1928:1–2004:12) with respect to the specification of the conditional mean equation. The issue is important because in this commonly used framework, unnecessarily including an intercept is known to distort conclusions. The existence of the relationship is relatively robust, but its strength depends on the prior belief concerning the intercept. The latter applies in particular to the first half of the sample, where also the coefficient of the relative risk aversion is smaller and the equity premium greater than in the latter half.

We propose an estimation method of the new Keynesian Phillips curve (NKPC) based on a univariate noncausal autoregressive model for the inflation rate. By construction, our approach avoids a number of problems related to the GMM estimation of the NKPC. We estimate the hybrid NKPC with quarterly U.S. data (1955:1–2010:3), and both expected future inflation and lagged inflation are found important in determining the inflation rate, with the former clearly dominating. Moreover, inflation persistence turns out to be intrinsic rather than inherited from a persistent driving process.

We propose a noncausal autoregressive model with time-varying parameters, and apply it to U.S. postwar inflation. The model .fits the data well, and the results suggest that inflation persistence follows from future expectations. Persistence has declined in the early 1980.s and slightly increased again in the late 1990.s. Estimates of the new Keynesian Phillips curve indicate that current inflation also depends on past inflation although future expectations dominate. The implied trend inflation estimate evolves smoothly and is well aligned with survey expectations. There is evidence in favor of the variation of trend inflation following from the underlying marginal cost that drives inflation.

Recently Stock and Watson (2007) showed that since the mid-1980s it has been hard for backward-looking Phillips curve models to improve on simple univariate models in forecasting U.S. inflation. While this indeed is the case when the benchmark is a causal autoregression, little change in forecast accuracy is detected when a noncausal autoregression is taken as the benchmark. In this note, we argue that a noncausal autoregression indeed provides a better characterization of U.S. inflation dynamics than the conventional causal autoregression and it is, therefore, the appropriate univariate benchmark model.

In this paper, we propose a simulation-based method for computing point and density forecasts for univariate noncausal and non-Gaussian autoregressive processes. Numerical methods are needed for forecasting such time series because the prediction problem is generally nonlinear and therefore no analytic solution is available. According to a limited simulation experiment, the use of a correct noncausal model can lead to substantial gains in forecast accuracy over the corresponding causal model. An empirical application to US inflation demonstrates the importance of allowing for noncausality in improving point and density forecasts.

In this article we discuss a few models developed to explain the general public's inflation expectations formation and provide some relevant estimation results. Furthermore, we suggest a simple Bayesian learning model which could explain the expectations formation process on the individual level. When the model is aggregated to the population level it could explain not only the mean values, but also the variance of the public's inflation expectations. The estimation results of the mean and variance equations seem to be consistent with the results of the questionnaire studies in which the respondents were asked to report their thoughts and opinions about inflation.

In this paper, we expand Kleibergen and Zivot's (2003) Bayesian two-stage (B2S) model by allowing for unequal variances. Our choice for modeling heteroscedasticity is a fully Bayesian parametric approach. As an application, we present a cross-country Cobb–Douglas production function estimation.

This paper provides a simple epidemiology model where households, when forming their inflation expectations, rationally adopt the past release of inflation with certain probability rather than the forward-looking newspaper forecast as suggested in Carroll [2003, Macroeconomic Expectations of Households and Professional Forecasters, Quarterly Journal of Economics, 118, 269-298]. The posterior model probabilities based on the Michigan survey data strongly support the proposed model. We also extend the agent-based epidemiology model by deriving for it a simple adaptation, which is suitable for estimation. Our results show that this model is able to capture the heterogeneity in households’ expectations very well.

In this paper we explore how the environment offered by institutions influences long-run growth. In order for the estimation results to be trustworthy we control the reliability of the estimates in several ways. Firstly, we include the lagged level of output per worker in the model to control the effect of conditional convergence. Secondly, we use the production function theory to form an environment of other inputs which may affect the parameter value of institutions and handle the issue of endogeneity using convenient instruments for institutions and other inputs. Thirdly, we use institutional indicator which is built using 18 indicators which all reflect the ability of institutions to create an environment in which the citizens can manage their risks they encounter during their life time. Finally, we study the sensitivity of estimation and control the effect of outliers and bad quality of data using a subsample of 22 industrial countries in addition to the total sample of 86 non-oil countries. Our cross-country analysis - based on Bayesian inference - confirms that the production environment offered by institutions has a significant role on economic growth, but it does not seem as dramatical as some may have expected.