Measuring the Impact of Military Spending: How Far Does a DSGE Model Deviate from Reality?

Abstract

Dunne, Smith, and Willenbockel (2005) argue that the mainstream growth literature has not found military spending to be a significant determinant of economic growth, yet much of the defense economics literature has noted significant effects. This paper revisits this issue by using a DSGE-VAR approach, combining both theoretical and empirical methods. We present that the DSGE approach (estimated with the Bayesian technique) and the Bayesian VAR with the Minnesota Prior both lead to worse in-sample fit than our proposed DSGE-VAR framework. The DSGE-VAR approach reveals that a positive military spending shock boosts the U.S. economy, increasing per capita real GDP growth, consumption, inflation and interest rate. Our results are robust to alternative model specifications. Future investigations such as exploring an optimal military spending policy could adopt the approach in this paper to determine the best model – empirical, theoretical, or a combination of the two.

Keywords:

• U.S. military spending
• DSGE-VAR
• Model misspecifications

JEL Codes:

• E62
• H5

Acknowledgements

The helpful comments from an anonymous referee, David Papier, and Hamid E. Ali are greatly appreciated. Financial support from the National Science Council of Taiwan in the form of grant NSC 102-2410-H-007-011-MY2 is greatly appreciated. All remaining errors are our own.

Notes

¹ The Bayesian approach to DSGE estimation is quite popular today. The basic idea is to construct a state-space system from a DSGE model, estimating it with a Markov Chain Monte Carlo (MCMC) algorithm. See An and Schorfheide (2007) for more details.

² See, for instance, Del Negro et al. (2013) for the DSGE model developed and used at the Federal Reserve Bank of New York.

³ Rubio-Ramírez, Waggoner, and Zha (2010), for example, randomly draw an orthogonal matrix for sign restrictions on impulse response functions (IRFs). The likelihood function, however, is invariant to the selection of such an orthogonal matrix. We are not sure how appropriate such a draw reflects the data, even though IRFs satisfy prior restrictions.

⁴ As mentioned in Waggoner and Zha (2012), the marginal data density used in the macroeconomics literature is the same concept as the marginal likelihood used in the statistics literature – that is, the marginal data density is an integral of the prior density times the likelihood function, with both the prior and the likelihood being proper probability density functions. The marginal data density is capable of detecting which model achieves the best in-sample fit.

⁵ Previous studies tend to focus on fiscal policy in an open economy. For example, please refer to Kim and Roubini (2008), Enders, Müller, and Scholl (2011), and Ravn, Schmitt-Grohé, and Uribe (2012). Theoretically, a positive military spending shock could raise the interest rate and appreciate the real exchange rate, which could affect the effect of military spending on output through the so-called ‘exchange rate channel’. To measure the effect of military spending in a comprehensive way, we adopt an open economy model to study this issue.

⁶ Lubik and Schorfheide (2006) assume that the domestic central bank considers the exchange rate movements in the interest rate setting. We ignore the exchange rate movement in the domestic Taylor rule, because the Fed does not consider such movements for its setting of interest rate. For example, Enders, Müller, and Scholl (2011) do not consider interest rate responses to the exchange rate movements for the specifications of the monetary policy either.

⁷ Some draws are burned for convergence in DSGE-VAR. For a VAR with seven variables, a constant, and four lags, the number of parameters is . It would be too lengthy to show the convergence conditions in all cases. The detailed results are available upon request from the authors.

⁸ The modified version of the Minnesota Prior for the Bayesian VAR is set as follows: the standard deviations of lags shrink as p^d, where d = 0.5, the weight on co-persistence prior dummy observations is , and the weight on own persistence prior dummy observations is μ = 2. See Lubik and Schorfheide (2006) for the details.

⁹ We adopt the Metropolis-Hastings algorithms for the Bayesian estimation of the DSGE model. This approach is widely used for the estimation of the DSGE parameters. See An and Schorfheide (2007) for more details.

¹⁰ As mentioned in Waggoner and Zha (2003), the 50 or 68% error bands are more useful than those with 90 or 95% in terms of characterizing the shape of the likelihood or the posterior distribution.

¹¹ For VAR with nine variables, a constant, and lag order of four, the number of parameters is .

¹² The six countries include Canada, France, Germany, Italy, Japan, and the United Kingdom.

¹³ We thank an anonymous referee for the inspiration of this future direction.