Exogenous uncertainty and the identification of Structural Vector Autoregressions with external instruments

Angelini, Giovanni and Fanelli, Luca (2018): Exogenous uncertainty and the identification of Structural Vector Autoregressions with external instruments.

Abstract

We provide necessary and sufficient conditions for the identification of Structural Vector Autoregressions (SVARs) with external instruments, considering the case in which r instruments are used to identify g structural shocks of interest, r>=g>=1. Novel frequentist estimation methods are discussed by considering both a partial shocks identification strategy, where only g structural shocks are of interest and are instrumented, and in a full shocks identification strategy, where despite g structural shocks are instrumented, all n structural shocks of the system can be identified under certain conditions. The suggested approach is applied to empirically investigate whether financial and macroeconomic uncertainty can be approximated as exogenous drivers of U.S. real economic activity, or rather as endogenous responses to first moment shocks, or both. We analyze whether the dynamic causal effects of non-uncertainty shocks on macroeconomic and financial uncertainty are signicant in the period after the Global Financial Crisis.

• Item Type: MPRA Paper
• Language: English
• Keywords: Exogenous Uncertainty, External Instruments, Identification, proxy-SVAR, SVAR.
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E44 - Financial Markets and the Macroeconomy; G - Financial Economics > G1 - General Financial Markets > G10 - General

References

Amisano, G. and Giannini, C. (1997). Topics in Structural VAR Econometrics, 2nd edn, Springer, Berlin.

Angelini, G., Bacchiocchi, E., Caggiano, G., and Fanelli, L. (2019), Uncertainty across volatility regimes, Journal of Applied Econometrics 34, 437-455.

Arias, J. E., Rubio-Ramirez, J. F. and Waggoner, D. F. (2018a), Inference based on Structural Vector Autoregressions identified with sign and zero restrictions, Econometrica 86, 685-720.

Arias, J. E., Rubio-Ramirez, J. F. and Waggoner, D. F. (2018b), Inference in Bayesian SVARs identified with external instruments, Working Paper, Federal Reserve, version dated October 2018.

Baker, S.R., Bloom, N. and Davis, S.J. (2016), Measuring economic policy uncertainty, Quarterly Journal of Economics 131, 1593-1636.

Basu, S. and Bundik, B. (2015), Endogenous volatility at the Zero Lower Bound: Implications for stabilization policy, NBER Working Paper No. 21838.

Bloom, N. (2009), The impact of uncertainty shocks, Econometrica 77, 623-685.

Brüggemann, R., Jentsch, C. and Trenkler, C. (2016), Inference in VARs with conditional volatility of unknown form, Journal of Econometrics 191, 69-85.

Caggiano, G., E. Castelnuovo, and Pellegrino, G. (2017), Estimating the real effects of uncertainty shocks at the Zero Lower Bound, European Economic Review 100, 257-272.

Caldara, D. and Herbst, E. (2019), Monetary policy, real activity, and credit spreads: evidence from Bayesian proxy SVARs, American Economic Journal: Macroeconomics 11, 157-192.

Caldara, D. and Kamps, C. (2017), The analytics of SVARs: A unified framework to measure fiscal multipliers, Review of Economic Studies 84, 1015-1040.

Carriero, A., Mumatz, H., Theodoritis, K. and Theophilopoulou, A. (2015), The impact of uncertainty shocks under measurement error: A proxy SVAR approach, Journal of Money, Credit, and Banking 47, 1223-1238.

Carriero, A., Clark, T. E. and Marcellino, M. (2018), Endogenous uncertainty?, Federal Reserve Bank of Cleveland, Working Paper No. 18-05.

Christiano, J.C., Motto, R. and Rostagno, M. (2014), Risk shocks, American Economic Review 104, 27-65.

Gertler, M. and Karadi, P. (2015), Monetary policy surprises, credit costs, and economic activity, American Economic Journal: Macroeconomics 7, 44-76.

Jentsch, C. and Lunsford, K.C. (2016), Proxy VARs: Asymptotic theory, bootstrap inference and the effects of income tax changes in the united states, Federal Reserve Bank of Cleveland, Working Paper No. 16-19.

Jentsch, C. and Lunsford, K. (2019), The dynamic effects of personal and corporate income tax changes in the United States: Comment, American Economic Review, forthcoming.

Jurado, K., Ludvigson, S.C. and Ng, S. (2015), Measuring uncertainty, American Economic Review 105(3), 1177-1216.

Kilian, L. (2009), Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market, American Economic Review 99, 1053-1069.

Kilian, L. and Lütkepohl, H. (2017), Structural Vector Autoregressive Analysis, Cambridge University Press.

Ludvigson, S.C., Ma, S. and Ng, S. (2018), Uncertainty and business cycles: exogenous impulse or endogenous response? Working Paper, draft dated November 19, 2018.

Lunsford, K. G. (2015), Identifying Structural VARs with a proxy variable and a test for a weak proxy, Federal Reserve Bank of Cleveland, Working Paper No. 15-28.

Lütkepohl, H. (2005), New introduction to multiple time series analysis, Springer-Verlag, Berlin.

Magnus, J.R. and Neudecker, H. (1999), Matrix differential calculus with applications in Statistics and Econometrics, Wiley & Sons, 2nd edition.

Mertens, K. and Montiel Olea, J.L. (2018), Marginal tax rates and income: New time series evidence, Quarterly Journal of Economics 133, 1803-1884.

Mertens, K. and Ravn, M. (2013), The dynamic effects of personal and corporate income tax changes in the United States, American Economic Review 103, 1212-1247.

Mertens, K. and Ravn, M. (2014), A reconciliation of SVAR and narrative estimates of tax multipliers, Journal of Monetary Economics 68, S1-S19.

Mertens, K. and Ravn, M. (2019), The dynamic effects of personal and corporate income tax changes in the United States: Reply to Jentsch and Lunsford, American Economic Review, forthcoming.

Montiel Olea, J.L., Plagborg-Møller, M. (2019), Simultaneous confidence bands: Theory, implementation, and an application to SVARs, Journal of Applied Econometrics 34, 1-17.

Montiel Olea, J.L., Stock, J.H. and Watson, M.W. (2018), Inference in SVARs identified with an external instrument, Working Paper, version dated November 2018.

Newey, W.K and D. McFadden (1994), Large sample estimation and hypothesis testing, Handbook of Econometrics, R.F. Engle and D.L. McFadden (eds.), Vol. IV, Chap. 36.

Pellegrino, G. (2017), Uncertainty and monetary policy in the US: A journay into a non-linear territory, Melbourne Institute Working Paper No. 6/17.

Plagborg-Møller, M. and Wolf, C.K. (2018), Instrumental variable identification of dynamic variance decompositions, Working Paper, Princetonn University, version dated November 24, 2018.

Plante, M., Richter, W.A. and Throckmorton, N.A. (2018), The Zero Lower Bound and endogenous uncertainty, The Economic Journal 128, 1730-1757.

Ramey, V. (2016), Macroeconomic shocks and their propagation, Handbook of Macroeconomics Vol. 2, 71-162.

Rogers, J.H,. Scotti, C. and Wright, J.H. (2018), Unconventional monetary policy and international risk premia, Journal of Money, Credit and Banking 50, 1827-1850.

Rothenberg, T.J. (1971), Identication in parametric models, Econometrica 39, 577-591.

Rubio-Ramírez, J. F., Waggoner, D.F. and Zha, T. (2010), Structural Vector Autoregressions and algorithms for inference, Review of Economic Studies 77, 665-696.

Stock, J.H and Watson, M.W. (2012), Disentangling the channels of the 2007-2009 recession, Brooking Panel of Economic Activity, Conference Paper March 22-23.

Stock, J.H., & Watson, M.W. (2018). Identification and estimation of dynamic causal effects in macroeconomics using external instruments. The Economic Journal 128, 917-948.

Wu, J. C. and Xia, F.D. (2016), Measuring the macroeconomic impact of monetary policy at the zero lower bound, Journal of Money, Credit, and Banking 48, 253-291.