THE EFFECT OF DEFENSE SPENDING ON US OUTPUT: A FACTOR AUGMENTED VECTOR AUTOREGRESSION (FAVAR) APPROACH

Abstract

Empirical evidence on the effect of defense spending on US output is at best mixed. Against this backdrop, this paper assesses the impact of a positive defense spending shock on the growth rate of real GNP using a Factor Augmented Vector Autoregressive (FAVAR) model estimated with 116 variables spanning the quarterly period of 1976:01 to 2005:02. Overall, the results show that a positive shock to the growth rate of the real defense spending translates to a positive short‐run effect on the growth rate of real GNP lasting up to ten quarters, but the effect is significant only for two quarters. Beyond the tenth quarter, the effect becomes negative and shows signs of slow reversal at around the 17th quarter. Our results tend to indicate that the mixed empirical evidence, based on small‐scale Vector Autoregressive (VAR) and Vector Error Correction (VEC) models, could be a result of a small information set not capturing the true theoretical relationships between the two variables of interest.

Keywords:

• Defense spending
• Output
• FAVAR

JEL Codes:

• C32
• C52
• E27
• H41

ACKNOWLEDGMENT

The authors would like to thank an anonymous referee for many helpful comments.

Notes

¹ Refer to Atesoglu (2009) for an excellent literature review on the effect of defense expenditure on output.

² This section relies heavily on the discussion available in Chapter 12 of Barro (1997).

³ Refer to Figure 12.5 in Barro (1997: 460) for further details.

⁴ Note, in an infinitely‐live representative agent model – the framework we use for our theoretical analysis – the assumption that the timing of taxes does not matter under the Ricardian equivalence only holds under the existence of a natural borrowing limit. The natural borrowing limit is defined as the limit that allows the households to borrow up to the capitalized value of their endowment sequences (Ljungqvist and Sargent, 2000: 219).

⁵ This paper follows the econometric framework of the FAVAR model described in Bernanke et al. (2005).

⁶ Given that only quarterly data are available for the two key variables of interest, namely GNP and defense spending, the 111 monthly macroeconomic variables taken from the Boivin et al. (2008) data set were converted to their quarterly values by calculating averages of the monthly data.

⁷ Please refer to Boivin et al. (2008) for further information on the 111 macroeconomic variables. The source of data for the five additional variables is the FRED database of, the Federal Reserve Bank of St. Louis. Real defense spending is measured by the national defense consumption expenditures and gross investment deflated by the implicit GNP deflator, real non‐defense government spending is equal to the real Government Consumption Expenditures & Gross Investment less real defense, and real public debt is the total outstanding national debt deflated by the implicit GNP deflator.

⁸ The claim is based on historical budget data as of 2008, obtained from the Office of Management and Budget of the Congressional Budget Office. The Tables are available for download from: http://www.cbo.gov/budget/data/historical.pdf.

⁹ Following Atesoglu (2009) the VAR is estimated with four lags and is found to be stable with no roots lying outside the unit circle. To be consistent with the FAVAR model, the growth rate of defense spending is ordered last. Alternative ordering schemes, however, do not affect the nature of the impact of the growth rate of real defense expenditure on the growth rate of output.

¹⁰ Note that if A _t+n denotes the actual value of a specific variable in period t + n and _t F _t+n is the forecast made in period t for t + n, the RMSE statistic can be defined as: . For n = 1, the summation runs from 2001:01 to 2005:02, and for n = 2, the same covers the period of 2001:02 to 2005:02, and so on.

¹¹ As is standard in forecasting with the FAVAR models, it included the five factors and the seven variables of the VAR. Note that both the FAVAR and the VAR were estimated based on four lags over an in‐sample period of 1976:01 to 2000:04 and then recursively over the out‐of‐sample horizon of 2001:01 to 2005:02.

¹² The choice of the out‐of‐sample horizon is based on the fact that the level of real defense spending increased continuously, while its growth rate became more volatile, beyond the year 2000.