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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 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.

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.

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.

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.

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.

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.

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.