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The Factor-augmented Error-Correction Model (FECM) generalizes the factor-augmented VAR (FAVAR) and the Error-Correction Model (ECM), combining error-correction, cointegration and dynamic factor models. It uses a larger set of variables compared to the ECM and incorporates the long-run information lacking from the FAVAR because of the latter’s specification in differences. In this paper, we review the specification and estimation of the FECM, and illustrate its use for forecasting and structural analysis by means of empirical applications based on Euro Area and US data.

A state space representation of a linearized DSGE model implies a VAR in terms of observable variables. The model is said be non-invertible if there exists no linear rotation of the VAR innovations which can recover the economic shocks. Non-invertibility arises when the observed variables fail to perfectly reveal the state variables of the model. The imperfect observation of the state drives a wedge between the VAR innovations and the deep shocks, potentially invalidating conclusions drawn from structural impulse response analysis in the VAR. The principal contribution of this chapter is to show that non-invertibility should not be thought of as an “either/or” proposition – even when a model has a non-invertibility, the wedge between VAR innovations and economic shocks may be small, and structural VARs may nonetheless perform reliably. As an increasingly popular example, so-called “news shocks” generate foresight about changes in future fundamentals – such as productivity, taxes, or government spending – and lead to an unassailable missing state variable problem and hence non-invertible VAR representations. Simulation evidence from a medium scale DSGE model augmented with news shocks about future productivity reveals that structural VAR methods often perform well in practice, in spite of a known non-invertibility. Impulse responses obtained from VARs closely correspond to the theoretical responses from the model, and the estimated VAR responses are successful in discriminating between alternative, nested specifications of the underlying DSGE model. Since the non-invertibility problem is, at its core, one of missing information, conditioning on more information, for example through factor augmented VARs, is shown to either ameliorate or eliminate invertibility problems altogether.

This chapter contributes to the growing global VAR (GVAR) literature by showing how global and national shocks can be identified within a GVAR framework. The usefulness of the proposed approach is illustrated in an application to the analysis of the interactions between public debt and real output growth in a multicountry setting, and the results are compared to those obtained from standard single country VAR analysis. We find that on average (across countries) global shocks explain about one-third of the long-horizon forecast error variance of output growth, and about one-fifth of the long-run variance of the rate of change of debt-to-GDP. Evidence on the degree of cross-sectional dependence in these variables and their innovations are exploited to identify the global shocks, and priors are used to identify the national shocks within a Bayesian framework. It is found that posterior median debt elasticity with respect to output is much larger when the rise in output is due to a fiscal policy shock, as compared to when the rise in output is due to a positive technology shock. The cross-country average of the median debt elasticity is 1.45 when the rise in output is due to a fiscal expansion as compared to 0.76 when the rise in output follows from a favorable output shock.

The purpose of this paper is to examine the effects of exchange rate shock on the broad spectrum of the US economy using a factor-augmented VAR model (FAVAR).

The authors developed a two-factor FAVAR model and estimated it with the single-step Bayesian likelihood approach using the Gibbs sampling technique. The two factors represented, respectively, the economic activity and price pressures. The exchange rate shock was identified with the Choleski decomposition method for VARs. The authors used the data of 117 time series for the period from 1973:02 to 2007:12. Impulse responses and variance decompositions were computed as the main results.

The authors found that exchange rate shock has pervasive effects on the US economy as the following: depreciation does not appear to help reduce the US trade deficit as both import and export rise with the depreciation shock; in the short run, depreciation appears expansionary as industrial production, manufacturing and employment all increase within a year; in the medium run, depreciation appears inflationary, as consumer price, producer price, import price and export price all increase; and in the medium run, depreciation appears contractionary as personal consumption, consumer confidence, stock price and housing start tend to fall.

Some caveats remain: first, our simple model symmetrically estimates depreciation shock and appreciation shock and, hence, cannot draw inferences for how exchange rate appreciation and depreciation may affect the US economy asymmetrically. Second, the simple model used did not distinguish the different possible sources of exchange rate depreciation shock, the knowledge of which may lead to richer policy implications and is the direction of research for the future.

This research contributes to the literature of whether exchange rate is expansionary or contractionary to the US economy using the FAVAR model. This is the first comprehensive study in the literature studying the pervasive effects of the exchange rate on the broad spectrum of the US economy in one integrated model.

This paper seeks to assess the impact of monetary policy on house price inflation for the nine census divisions of the US economy.

A factor‐augmented VAR (FAVAR) model is estimated using a large data set comprising of 126 quarterly series over the period 1976:01 to 2005:02.

Overall, the results of this investigation show that house price inflation responds negatively to a positive monetary policy shock, suggesting that the framework does not experience the widely observed price puzzle encountered while analyzing monetary policy shocks with standard sized VARs.

The paper only considers house price inflation and ignores other housing market variables. Moreover, given the recent economy‐wide decline in the house price growth rates, it would be worthwhile to update the data set to a more recent period, to capture the possible breakdown in the relationship of house prices with fundamentals driving the market.

The results based on the impulse response functions indicate that, in general, house price inflation responds negatively to monetary policy shock, but the responses are heterogeneous across the census divisions. In addition, the findings suggest, in particular, the importance of South Atlantic, East South Central, West South Central, Mountain and the Pacific divisions in shaping the dynamics of US house price inflation.

To the best of one's knowledge, this is the first paper to analyze the effect of monetary policy on house price inflation in the nine census divisions of the US economy using a FAVAR model.

This chapter investigates the performance of different dimension reduction approaches for large vector autoregressions in multi-step ahead forecasts. The authors consider factor augmented VAR models using principal components and partial least squares, random subset regression, random projection, random compression, and estimation via LASSO and Bayesian VAR. The authors compare the accuracy of iterated and direct multi-step point and density forecasts. The comparison is based on macroeconomic and financial variables from the FRED-MD data base. Our findings suggest that random subspace methods and LASSO estimation deliver the most precise forecasts.

The authors introduce a new approach to estimate high-dimensional factor-augmented vector autoregressive models (FAVAR) where the loadings are subject to idiosyncratic regime-switching dynamics. Our Bayesian estimation method alleviates computational challenges and makes the estimation of high-dimensional FAVAR with heterogeneous regime-switching straightforward to implement. The authors perform extensive simulation experiments to study the finite sample performance of our estimation method, demonstrating its relevance in high-dimensional settings. Next, the authors illustrate the performance of the proposed framework for studying the impact of credit market disruptions on a large set of macroeconomic variables. The results of this study underline the importance of accounting for non-linearities in factor loadings when evaluating the propagation of aggregate shocks.

The study focuses on examining the impact of the supply shock on the Indian macroeconomic variables during the COVID-19 period.

Time-varying factor augmented vector autoregressive model has been employed to study the asymmetry in transmission of supply shock on Indian economy during pre- and post-COVID-19 times.

The authors find that with supply shock, retail food inflation outpaced in COVID-19 times. Production levels reported by IIP fell to abysmally low levels in the post-COVID-19 times when the economy stalled. The liquidity stimulus provided by the central bank led to the negative response of policy rates to the supply shocks during the COVID-19 times.

The study stands novel in examining the impact of COVID-19 pandemic on Indian economy through the lenses of asymmetric transmission of supply shock during pre- and post-COVID-19 times.