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A FREQUENCY-DOMAIN APPROACH TO DYNAMIC MACROECONOMIC MODELS

Published online by Cambridge University Press:  10 September 2019

Fei Tan
Fei Tan*
Affiliation:
Saint Louis University Zhejiang University of Finance and Economics
*
Address correspondence to: Fei Tan, Department of Economics, Chaifetz School of Business, Saint Louis University, 3674 Lindell Boulevard, St. Louis, MO 63108-3397, USA. e-mail: tanf@slu.edu. Phone: +1(314)977-2123.
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Abstract

This article proposes a unified framework for solving and estimating linear rational expectations models with a variety of frequency-domain techniques, some established, some new. The solution methodology is applicable to a wide class of models and leads to straightforward construction of the spectral density for performing likelihood-based inference. We also generalize the well-known spectral decomposition of the Gaussian likelihood function to a composite version implied by several competing models. Taken together, these techniques yield fresh insights into the model’s theoretical and empirical implications beyond conventional time-domain approaches can offer. We illustrate the proposed framework using a prototypical new Keynesian model with fiscal details and two determinate monetary–fiscal policy regimes. The model is simple enough to deliver an analytical solution that makes the policy effects transparent under each regime, yet still able to shed light on the empirical interactions between US monetary and fiscal policies along different frequencies.

Keywords

Solution MethodBayesian InferenceSpectral DensityMonetary and Fiscal Policy
Type
Articles
Information
Macroeconomic Dynamics , Volume 25 , Issue 6 , September 2021 , pp. 1381 - 1411
Copyright
© Cambridge University Press 2019

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Footnotes

An earlier draft of this paper was circulated under the title “Testing the fiscal theory in the frequency domain.” I thank Majid Al-Sadoon, Yoosoon Chang, Junjie Guo, Eric Leeper, Laura Liu, Joon Park, David Rapach, Apostolos Serletis (the coeditor), Todd Walker, two anonymous referees, and participants of the 2015 Midwest Econometrics Group Meeting at St. Louis Fed for helpful comments. Financial support from the Chaifetz School of Business summer research grant is also gratefully acknowledged.

References

REFERENCES

Al-Sadoon, M. M. (2018) Linear systems approach to linear rational expectations models. Econometric Theory 34(3), 628–658.CrossRefGoogle Scholar
Altug, S. (1989) Time-to-build and aggregate fluctuations: Some new evidence. International Economic Review 30(4), 889–920.CrossRefGoogle Scholar
Amisano, G. and Geweke, J. (2011) Optimal prediction pools. Journal of Econometrics 164(1), 130–141.Google Scholar
Amisano, G. and Geweke, J. (2017) Prediction using several macroeconomic models. The Review of Economics and Statistics 99(5), 912–925.CrossRefGoogle Scholar
An, S. and Schorfheide, F. (2007) Bayesian analysis of DSGE models. Econometric Reviews 26(2), 113–172.CrossRefGoogle Scholar

Working Paper:

Beaudry, P., Galizia, D. and Portier, F. (2016) Putting the Cycle Back into Business Cycle Analysis. National Bureau of Economic Research. Working Papers: No. 22825.CrossRefGoogle Scholar
Benhabib, J. and Farmer, R. E. A. (1999) Indeterminacy and sunspots in macroeconomics. In: Taylor, J. B. and Woodford, M. (eds.), Handbook of Macroeconomics vol. 1A, pp. 387–448. Amsterdam: North-Holland.CrossRefGoogle Scholar
Berkowitz, J. (2001) Generalized spectral estimation of the consumption-based asset pricing model. Journal of Econometrics 104(2), 269–288.CrossRefGoogle Scholar
Besag, J. E. (1974) Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society, Series B 36, 192–236.Google Scholar
Bhattarai, S., Lee, J. W. and Park, W. Y. (2012) Monetary-fiscal policy interactions and indeterminacy in postwar US data. American Economic Review 102(3), 173–178.CrossRefGoogle Scholar
Blanchard, O. J. and Kahn, C. M. (1980) The solution of linear difference models under rational expectations. Econometrica 48(5), 1305–1311.CrossRefGoogle Scholar
Calvo, G. A. (1983) Staggered prices in a utility maxmizing model. Journal of Monetary Economics 12(3), 383–398.CrossRefGoogle Scholar
Canova, F. and Matthes, C. (2018) A Composite Likelihood Approach for Dynamic Structural Models. Working paper.CrossRefGoogle Scholar
Chen, M.-H. and Shao, Q.-M. (1999) Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics 8(1), 69–92.Google Scholar
Christiano, L. and Vigfusson, R. (2003) Maximum likelihood in the frequency domain: The importance of time-to-plan. Journal of Monetary Economics 50(4), 789–815.CrossRefGoogle Scholar
Clarida, R., Galí, J. and Gertler, M. (2000) Monetary policy rules and macroeconomic stability: Evidence and some theory. Quarterly Journal of Economics 115(1), 147–180.CrossRefGoogle Scholar
Cochrane, J. H. (1998) A frictionless view of U.S. infation. In: Bernanke, B. S. and Rotemberg, J. J. (eds.), NBER Macroeconomics Annual, vol. 14, pp. 323–384. Cambridge, MA: MIT Press.Google Scholar
Cogley, T. (2001) A frequency decomposition of approximation errors in stochastic discount factor models. International Economic Review 42(2), 473–503.CrossRefGoogle Scholar
Davig, T. and Leeper, E. M. (2006) Fluctuating macro policies and the fiscal theory. In: Acemoglu, D., Rogoff, K. and Woodford, M. (eds.), NBER Macroeconomics Annual, vol. 21, pp. 247–298. Cambridge, MA: MIT Press.Google Scholar
Diebold, F. X., Ohanian, L. E. and Berkowitz, J. (1998) Dynamic equilibrium economies: A framework for comparing models and data. The Review of Economic Studies 65(3), 433–451.CrossRefGoogle Scholar
Farmer, R. E. A., Khramov, V. and Nicolò, G. (2015) Solving and estimating indeterminate DSGE models. Journal of Economic Dynamics and Control 54, 17–36.CrossRefGoogle Scholar
Friedman, M. (1970) The Counter-Revolution in Monetary Theory. London: Institute of Economic Affairs.Google Scholar
Galí, J. (2008) Monetary Policy, Inflation, and the Business Cycle. Princeton: Princeton University Press.Google Scholar
Geweke, J. (1992) Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In: Bernando, J. M., Berger, J. O., Dawid, A. P. and Smith, A. F. (eds.), Bayesian Statistics, vol. 4. Oxford, UK: Clarendon Press.Google Scholar
Geweke, J. (1999) Using simulation methods for Bayesian econometric models: Inference, development, and communication. Econometric Reviews 18, 1–73.CrossRefGoogle Scholar
Granger, C. W. J. (1966) The typical spectral shape of an economic variable. Econometrica 34(1), 150–161.CrossRefGoogle Scholar
Hannan, E. J. (1970) Multiple Time Series. New York: A Wiley Publication in Applied Statistics, Wiley.Google Scholar
Hansen, L. P. and Sargent, T. J. (1980) Formulating and estimating dynamic linear rational expectations models. Journal of Economic Dynamics and Control 2, 7–46.CrossRefGoogle Scholar
Hansen, L. P. and Sargent, T. J. (1991) Rational Expectations Econometrics. Boulder, CO: Westview Press.Google Scholar
Hansen, L. P. and Sargent, T. J. (1993) Seasonality and approximation errors in rational expectations models. Journal of Econometrics 55(1), 21–55.CrossRefGoogle Scholar
Harvey, A. C. (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press.Google Scholar
Herbst, E. P. and Schorfheide, F. (2015) Bayesian Estimation of DSGE Models. Princeton and Oxford: Princeton University Press.CrossRefGoogle Scholar
Ireland, P. N. (1997) A small, structural, quarterly model for monetary policy evaluation. Carneige-Rochester Conference Series on Public Policy, 47, 83–108. North-Holland.CrossRefGoogle Scholar
Jeffreys, H. (1961) Theory of Probability. Oxford: Oxford University Press.Google Scholar
Kasa, K. (2000) Forecasting the forecasts of others in the frequency domain. Review of Economic Dynamics 3(4), 726–756.CrossRefGoogle Scholar
Klein, P. (2000): Using the generalized Schur form to solve a multivariate linear rational expectations model. Journal of Economic Dynamics and Control 24(10), 1405–1423.CrossRefGoogle Scholar
Kliem, M., Kriwoluzky, A. and Sarferaz, S. (2016a) Monetary-fiscal policy interaction and fiscal inflation: A tale of three countries. European Economic Review 88, 158–184.CrossRefGoogle Scholar

Journal Article:

Kliem, M., Kriwoluzky, A. and Sarferaz, S. (2016b) On the low-frequency relationship between public deficits and inflation. Journal of Applied Econometrics 31(3), 566–583.CrossRefGoogle Scholar
Leeper, E. M. (1991) Equilibria under ‘active’ and ‘passive’ monetary and fiscal policies. Journal of Monetary Economics 27(1), 129–147.CrossRefGoogle Scholar
Leeper, E. M. and Leith, C. B. (2016) Understanding inflation as a joint monetary-fiscal phenomenon. In: Taylor, J. B. and Uhlig, H. (eds.), Handbook of Macroeconomics, vol. 2. Amsterdam: Elsevier Press.Google Scholar
Leeper, E. M. and Li, B. (2017) Surplus-debt regressions. Economics Letters 151, 10–15.CrossRefGoogle Scholar
Leeper, E. M. and Sims, C. A. (1994) Toward a modern macroeconomic model usable for policy analysis. In: Fischer, S. and Rotemberg, J. J. (eds.), NBER Macroeconomics Annual, pp. 81–118. Cambridge, MA: MIT Press.Google Scholar
Leeper, E. M., Traum, N. and Walker, T. B. (2017) Clearing Up the fiscal multiplier Morass. American Economic Review 107(8), 2409–2454.CrossRefGoogle Scholar
Li, B., Pei, P. and Tan, F. (2018) Credit Risk and Fiscal Inflation. Working Paper.CrossRefGoogle Scholar
Li, B. and Tan, F. (2018) Confronting Monetary-Fiscal Regime Uncertainty. Working Paper.Google Scholar

Journal Article:

Lindsay, B. G. (1988) Composite likelihood methods. Contemporary Mathematics 80, 221–239.CrossRefGoogle Scholar

Journal Article:

Lubik, T. A. and Schorfheide, F. (2003) Computing sunspot equilibria in linear rational expectations models. Journal of Economic Dynamics and Control 28(2), 273–285.CrossRefGoogle Scholar
Lubik, T. A. and Schorfheide, F. (2004) Testing for indeterminacy: An application to U.S. monetary policy. American Economic Review 94(1), 190–217.CrossRefGoogle Scholar
Lucas, R. E. Jr (1976) Econometric policy evaluation: A critique. Carneige-Rochester Conference Series on Public Policy 1, 104–130.Google Scholar
Lucas, R. E. Jr and Sargent, T. J. (1981) Rational Expectations and Econometric Practice. Minneapolis. MN: University of Minnesota Press.Google Scholar
Del Negro, M., Hasegawa, R. B. and Schorfheide, F. (2016) Dynamic prediction pools: An investigation of financial frictions and forecasting performance. Journal of Econometrics 192(2), 391–405.CrossRefGoogle Scholar
Onatski, A. (2006) Winding number criterion for existence and uniqueness of equilibrium in linear rational expectations models. Journal of Economic Dynamics and Control 30(2), 323–345.CrossRefGoogle Scholar
Qu, Z. (2014) Inference in dynamic stochastic general equilibrium models with possible weak identification. Quantitative Economics 5(2), 457–494.CrossRefGoogle Scholar
Qu, Z. (2018) A composite likelihood framework for analyzing singular DSGE models. The Review of Economics and Statistics 100(5), 916–932.CrossRefGoogle Scholar
Qu, Z. and Tkachenko, D. (2012a) Frequency domain analysis of medium scale DSGE models with application to Smets and Wouters (2007). In: Balke, N., Canova, F., Milani, F. and Wynne, M. (eds.) DSGE Models in Macroeconomics: Estimation, Evaluation, and New Developments, pp. 319–385. Bingley: Emerald.Google Scholar
Qu, Z. and Tkachenko, D. (2012b) Identification and frequency domain quasi-maximum likelihood estimation of linearized dynamic stochastic general equilibrium models. Quantitative Economics 3(1), 95–132.CrossRefGoogle Scholar
Rotemberg, J. J. (1982) Sticky prices in the United States. Journal of Political Economy 90, 1187–1211.CrossRefGoogle Scholar
Rothenberg, T. J. (1971) Identification in parametric models. Econometrica 39(3), 577–591.CrossRefGoogle Scholar
Sala, L. (2015) DSGE models in the frequency domains. Journal of Applied Econometrics 30(2), 219–240.CrossRefGoogle Scholar
Sargent, T. J. (1987) Macroeconomic Theory, 2nd ed. San Diego: Academic Press.Google Scholar
Schorfheide, F. (2013) Estimation and evaluation of DSGE models: Progress and challenges. In: Acemoglu, D., Arellano, M. and Dekel, E. (eds.) Econometric Society Monographs, vol. 3, pp. 184–230. Cambridge: Cambridge University Press.Google Scholar
Sims, C. A. (2002) Solving linear rational expectations models. Computational Economics 20(1), 1–20.CrossRefGoogle Scholar
Sims, C. A. (2011) Stepping on a rake: The role of fiscal policy in the inflation of the 1970’s. European Economic Review 55(1), 48–56.CrossRefGoogle Scholar
Sims, C. A. (2012) Modeling the Influence of Fiscal Policy on Inflation. Working Paper.Google Scholar

Journal Article:

Sims, C. A. (2013) Paper money. American Economic Review 103(2), 563–584.CrossRefGoogle Scholar
Smets, F. and Wouters, R. (2007) Shocks and frictions in US business cycles: A Bayesian DSGE approach. American Economic Review 97(3), 586–606.CrossRefGoogle Scholar
Tan, F. (2017) An analytical approach to new Keynesian models under the fiscal theory. Economics Letters 156, 133–137.CrossRefGoogle Scholar
Tan, F. and Walker, T. B. (2015) Solving generalized multivariate linear rational expectations models. Journal of Economic Dynamics and Control 60, 95–111.CrossRefGoogle Scholar
Tanner, M. A. and Wong, W. H. (1987) The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association 82(398), 528–540.CrossRefGoogle Scholar
Traum, N. and Yang, S.-C. S. (2011) Monetary and fiscal policy interactions in the post-war U.S. European Economic Review 55(1), 140–164.CrossRefGoogle Scholar
Uhlig, H. (1999) A toolkit for analyzing nonlinear dynamic stochastic models easily. In: Marimon, R. and Scott, A. (eds.), Computational Methods for the Study of Dynamic Economies, 30–61. Oxford, England: Oxford University Press.Google Scholar
Varin, C., Reid, N. and Firth, D. (2011) An overview of composite likelihood methods. Statistica Sinica 21(1), 5–42.Google Scholar
Waggoner, D. F. and Zha, T. (2012) Confronting model misspecification in macroeconomics. Journal of Econometrics 171(2), 167–184.CrossRefGoogle Scholar
Walker, T. B. (2007) How equilibrium prices reveal information in time series models with disparately informed, competitive traders. Journal of Economic Theory 137(1), 512–537.CrossRefGoogle Scholar
Watson, M. W. (1993) Measures of fit for calibrated models. Journal of Political Economy 101(6), 1011–1041.CrossRefGoogle Scholar
Whiteman, C. (1983) Linear Rational Expectations Models: A User’s Guide. Minneapolis: University of Minnesota Press.CrossRefGoogle Scholar
Woodford, M. (1995) Price-level determinacy without control of a monetary aggregate. Carneige-Rochester Conference Series on Public Policy 43, 1–46.CrossRefGoogle Scholar
Woodford, M. (2003) Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton: Princeton University Press.Google Scholar
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