Sufficient information in structural VARs

We derive necessary and sufficient conditions under which a set of variables is information-ally sufficient, i.e. contains enough information to estimate the structural shocks with a VAR model. Based on such conditions, we provide a procedure to test for informational sufficiency. If sufficiency is rejected, we propose a strategy to amend the VAR. Our method can be applied to FAVAR models and can be used to determine how many factors to include in such models. We apply our procedure to a VAR including TFP, unemployment and per-capita hours worked. We find that the three variables are not informationally sucient. When adding missing information, the effects of technology shocks change dramatically.Structural VAR; non-fundamentalness; information; FAVAR models; technology shocks

How to Advance Theory with Structural VARs: Use the Sims-Cogley-Nason Approach

The common approach to evaluating a model in the structural VAR literature is to compare the impulse responses from structural VARs run on the data to the theoretical impulse responses from the model. The Sims-Cogley-Nason approach instead compares the structural VARs run on the data to identical structural VARs run on data from the model of the same length as the actual data. Chari, Kehoe, and McGrattan (2006) argue that the inappropriate comparison made by the common approach is the root of the problems in the SVAR literature. In practice, the problems can be solved simply. Switching from the common approach to the Sims-Cogley-Nason approach basically involves changing a few lines of computer code and a few lines of text. This switch will vastly increase the value of the structural VAR literature for economic theory.

Testing for Sufficient Information in Structural VARs

We derive necessary and sufficient conditions under which a set of variables is informationally sufficient, i.e. it contains enough information to estimate the structural shocks with a VAR model. Based on such conditions, we suggest a procedure to test for informational sufficiency. Moreover, we show how to amend the VAR if informational sufficiency is rejected. We apply our procedure to a VAR including TFP, unemployment and per-capita hours worked. We find that the three variables are not informationally sufficient. When adding missing information, the effects of technology shocks change dramatically.Structural VAR, non-fundamentalness, information, FAVAR models, technology shocks.

Identification of Technology Shocks in Structural VARs

The usefulness of SVARs for developing empirically plausible models is actually subject to many controversies in quantitative macroeconomics. In this paper, we propose a simple alternative two step SVARs based procedure which consistently identifies and estimates the effect of permanent technology shocks on aggregate variables. Simulation experiments from a standard business cycle model show that our approach outperforms standard SVARs. The two step procedure, when applied to actual data, predicts a significant short-run decrease of hours after a technology improvement followed by a delayed and hump-shaped positive response. Additionally, the rate of inflation and the nominal interest rate displays a significant decrease after a positive technology shock.SVARs, long-run restriction, technology shocks, consumption to output ratio, hours worked

Reduced-Rank Identification of Structural Shocks in VARs

This paper integrates imposing a factor structure on residuals in vector autoregressions (VARs) into structural VAR analysis. Identification, estimation and testing procedures are discussed. The paper applies this approach to the well-known problem of studying the effects of monetary policy in open economy VAR models. The use of factor structure in identifying structural shocks is shown to resolve three long-standing puzzles in VAR literature. First, the price level does not increase in response to a monetary tightening. Second, the exchange rate appreciates on impact and then gradually depreciates. Hence, no price level and exchange rate puzzles are found. Third, monetary policy shocks are much less volatile than suggested by standard VAR identification schemes. In addition, the paper suggests that the apparent weak contemporaneous cross-variable responses and strong own responses in structural VARs can be an artifact of identifying assumptions and vanish after imposing a factor structure on the shocks.Vector autoregressions, identification, factor structure, monetary policy

Monetary policy analysis in a small open economy using Bayesian cointegrated structural VARs

Structural VARs have been extensively used in empirical macroeconomics during the last two decades, particularly in analyses of monetary policy. Existing Bayesian procedures for structural VARs are at best confined to a severly limited handling of cointegration restrictions. This paper extends the Bayesian analysis of structural VARs to cover cointegrated processes with an arbitrary number of cointegrating relations and general linear restrictions on the cointegration space. A reference prior distribution with an optional small open economy effect is proposed and a Gibbs sampler is derived for a straightforward evaluation of the posterior distribution. The methods are used to analyze the effects of monetary policy in Sweden. JEL Classification: C11, C32, E52Counterfactual experiments, Impulse responses, monetary policy, Structural, Vector autoregression

The efficient market hypothesis and identification in structural VARs

Structural vector autoregression (SVAR) models are commonly used to investigate the effect of structural shocks on economic variables. The identifying restrictions imposed in many of these exercises have been criticized in the literature. This paper extends this literature by showing that if the SVAR includes one or more variables that are efficient in the strong form of the efficient market hypothesis, the identifying restrictions frequently imposed in SVARs cannot be satisfied. We argue that our analysis will likely apply to VARs that include variables that are consistent with the weaker form of the efficient market hypothesis, especially when the data are measured at the monthly or quarterly frequencies, as is frequently the case.Macroeconomics ; Econometric models

Structural Factor-Augmented VAR (SFAVAR) and the Effects of Monetary Policy

Factor-augmented VARs (FAVARs) have combined standard VARs with factor analysis to exploit large data sets in the study of monetary policy. FAVARs enjoy a number of advantages over VARs: they allow a better identification of the monetary policy shock; they can avoid the use of a single variable to proxy theoretical constructs, such as the output gap; they allow researchers to compute impulse responses for hundreds of variables. Their shortcoming, however, is that the factors are not identified and, therefore, lack any economic interpretation. This paper seeks to provide an interpretation to the factors. We propose a novel Structural Factor-Augmented VAR (SFAVAR) model, where the factors have a clear meaning: 'Real Activity' factor, 'Price Pressures' factor, 'Financial Market' factor, 'Credit Conditions' factor, 'Expectations' factor, etc. The paper employs a Bayesian approach to extract the factors and jointly estimate the model. This framework is then suited to study the effects on a wide range of macroeconomic variables of monetary policy and non-policy shocks.VAR, Dynamic Factors, Monetary Policy, Structural FAVAR.

The Price Puzzle and Indeterminacy

This paper re-examines the empirical evidence on the price puzzle and proposes a new theoretical interpretation. Using structural VARs and two different identification strategies based on zero restrictions and sign restrictions, we find that the positive response of price to a monetary policy shock is historically limited to the sub-samples associated with a weak central bank response to inflation. These sub-samples correspond to the pre-Volcker period for the US and the pre-inflation targeting regime for the UK. Using a micro-founded DSGE sticky price model of the US economy, we then show that the structural VARs are capable of reproducing the price puzzle on artificial data only when monetary policy is passive and hence multiple equilibria arise. In contrast, the DSGE model never generates on impact a positive inflation response to a policy shock. The omission in the VARs of a variable capturing the high persistence of expected inflation under indeterminacy is found to account for the price puzzle observed on actual data.Price puzzle, DSGE model, Taylor principle, Indeterminacy, SVARs

Opening the black box: structural factor models with large cross-sections

This paper shows how large-dimensional dynamic factor models are suitable for structural analysis. We establish sufficient conditions for identification of the structural shocks and the associated impulse response functions. In particular, we argue that, if the data follow an approximate factor structure, the “problem of fundamentalness”, which is intractable in structural VARs, can be solved provided that the impulse responses are sufficiently heterogeneous. Finally, we propose a consistent method (and n, T rates of convergence) to estimate the impulse-response functions, as well as a bootstrapping procedure for statistical inference. JEL Classification: E0, C1Dynamic Factor Models, fundamentalness, Identification, structural VARs