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A Bayesian approach to estimating tax and spending multipliers

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  • Matthew Denes
  • Gauti B. Eggertsson

Abstract

This paper outlines a simple Bayesian methodology for estimating tax and spending multipliers in a dynamic stochastic general equilibrium (DSGE) model. After forming priors about the parameters of the model and the relevant shock, we used the model to exactly match only one data point: the trough of the Great Depression, that is, an output collapse of 30 percent, deflation of 10 percent, and a zero short-term nominal interest rate. Because we form our priors as distributions, the key economic inference of our analysis--the multipliers of tax and spending--are well-defined probability distributions derived from the posterior of the model. While the Bayesian methods used are standard, the application is slightly unusual. We conjecture that this methodology can be applied in several different settings with severe data limitations and where more informal calibrations have been the norm. The main advantage over usual calibration exercises is that the posterior of the model offers an interesting way to think about sensitivity analysis and gives researchers a useful way to describe model-based inference. We apply our simple estimation method to the American Recovery and Reinvestment Act (ARRA), passed by Congress as part of the 2009 stimulus plan. The mean of our estimate indicates that ARRA increased output by 3.6 percent in 2009 and 2010. The standard deviation of this estimate is 1 percent.

Suggested Citation

  • Matthew Denes & Gauti B. Eggertsson, 2009. "A Bayesian approach to estimating tax and spending multipliers," Staff Reports 403, Federal Reserve Bank of New York.
  • Handle: RePEc:fip:fednsr:403
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    References listed on IDEAS

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    1. Gauti B. Eggertsson, 2011. "What Fiscal Policy is Effective at Zero Interest Rates?," NBER Chapters,in: NBER Macroeconomics Annual 2010, Volume 25, pages 59-112 National Bureau of Economic Research, Inc.
    2. Gauti B. Eggertsson, 2008. "Great Expectations and the End of the Depression," American Economic Review, American Economic Association, vol. 98(4), pages 1476-1516, September.
    3. Cogan, John F. & Cwik, Tobias & Taylor, John B. & Wieland, Volker, 2010. "New Keynesian versus old Keynesian government spending multipliers," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 281-295, March.
    4. Gauti B. Eggertsson, 2012. "Was the New Deal Contractionary?," American Economic Review, American Economic Association, pages 524-555.
    5. Gauti B. Eggertsson, 2013. "Fiscal Multipliers and Policy Coordination," Central Banking, Analysis, and Economic Policies Book Series,in: Luis Felipe Céspedes & Jordi Galí (ed.), Fiscal Policy and Macroeconomic Performance, edition 1, volume 17, chapter 6, pages 175-234 Central Bank of Chile.
    6. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
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    Cited by:

    1. Lorant Kaszab, 2016. "Rule-of-Thumb Consumers and Labor Tax Cut Policy at the Zero Lower Bound," International Journal of Central Banking, International Journal of Central Banking, vol. 12(3), pages 353-390, September.
    2. Leeper, Eric M. & Walker, Todd B. & Yang, Shu-Chun S., 2010. "Government investment and fiscal stimulus," Journal of Monetary Economics, Elsevier, vol. 57(8), pages 1000-1012, November.
    3. Woodford, Michael, 2010. "Optimal Monetary Stabilization Policy," Handbook of Monetary Economics,in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 14, pages 723-828 Elsevier.
    4. Gauti B. Eggertsson & Kevin B. Proulx, 2016. "Bernanke’s No-Arbitrage Argument Revisited: Can Open Market Operations in Real Assets Eliminate the Liquidity Trap?," Central Banking, Analysis, and Economic Policies Book Series,in: Elías Albagli & Diego Saravia & Michael Woodford (ed.), Monetary Policy through Asset Markets: Lessons from Unconventional Measures and Implications for an Integrated World, edition 1, volume 24, chapter 3, pages 063-104 Central Bank of Chile.
    5. Sanjay Singh & Gauti Eggertsson, 2015. "The non-linear Calvo model at the zero bound: Some analytic solutions and numerical results," 2015 Meeting Papers 1204, Society for Economic Dynamics.
    6. Dupor, Bill & Li, Rong, 2015. "The expected inflation channel of government spending in the postwar U.S," European Economic Review, Elsevier, vol. 74(C), pages 36-56.
    7. Kaszab, Lorant, 2011. "Fiscal Policy Multipliers in a New Keynesian Model under Positive and Zero Nominal Interest Rate," Cardiff Economics Working Papers E2011/11, Cardiff University, Cardiff Business School, Economics Section.
    8. Woodford, Michael, 2010. "Optimal Monetary Stabilization Policy," Handbook of Monetary Economics,in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 14, pages 723-828 Elsevier.

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    Keywords

    Depressions ; Econometric models ; Taxation ; Government spending policy;

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