The Output Effects of Money Growth Uncertainty: Evidence from a Multivariate GARCH-in-Mean VAR

Abstract

In this paper we extend the work in Serletis and Shahmoradi (Macroecon Dyn 10:652–666, 2006) by investigating the effects of money growth uncertainty on real economic activity, in the context of a multivariate framework in which a structural vector autoregression is modified to accommodate multivariate GARCH-in-Mean errors, as in Elder (J Money, Credit Bank 36:912–928, 2004). The model uses a recursive identification scheme, takes into account the possible interaction between conditional means and variances, isolates the effects of money growth volatility on output growth, and is able to explicitly model heteroskedasticity. We use quarterly data for the United States over the period from 1959:1 to 2005:4, provide a comparison among simple-sum, Divisia, and currency equivalent monetary aggregation procedures at each of the four levels of monetary aggregation—M1, M2, M3, and MZM—and find evidence that money growth volatility has significant negative effects on output growth. Issues of structural stability are addressed and sub-sample analysis is performed. Moreover, the robustness of the results to alternative identification schemes, alternative measures of the level of economic activity, and to the use of monthly observations is also investigated.

Appendix

Table 9 Estimates of C _v , F, and ${\boldsymbol G}{\rm~diag}({\boldsymbol H}_t) = {\boldsymbol C}_v + {\boldsymbol F}{\rm diag} ({\boldsymbol e}_{t-1} {\boldsymbol e}^\prime_{t-1}) + {\boldsymbol G}{\rm~diag} ({\boldsymbol H}_{t-1})$

Table 10 Estimates of C _v , F, and ${\boldsymbol G}{\rm~diag}({\boldsymbol H}_t) = {\boldsymbol C}_v + {\boldsymbol F}{\rm diag} ({\boldsymbol e}_{t-1} {\boldsymbol e}^\prime_{t-1}) + {\boldsymbol G}{\rm~diag} ({\boldsymbol H}_{t-1})$

Table 11 Estimates of C _v , F, and ${\boldsymbol G}{\rm~diag}({\boldsymbol H}_t) = {\boldsymbol C}_v + {\boldsymbol F}{\rm diag} ({\boldsymbol e}_{t-1} {\boldsymbol e}^\prime_{t-1}) + {\boldsymbol G}{\rm~diag} ({\boldsymbol H}_{t-1})$

Table 12 Estimates of C _v , F, and ${\boldsymbol G}{\rm~diag}({\boldsymbol H}_t) = {\boldsymbol C}_v + {\boldsymbol F}{\rm diag} ({\boldsymbol e}_{t-1} {\boldsymbol e}^\prime_{t-1}) + {\boldsymbol G}{\rm~diag} ({\boldsymbol H}_{t-1})$

Table 13 Structural and in-mean coefficient estimates ${\boldsymbol{By}}_t = {\boldsymbol C} + \Gamma_1 {\boldsymbol y}_{t-1} + \Gamma_2 {\boldsymbol y}_{t-2} + \ldots + \Gamma_p {\boldsymbol y}_{t-p} + \alpha \sqrt{{\boldsymbol h}_t} + \beta \sqrt{{\boldsymbol h}_{t-1}}+ \gamma \sqrt{{\boldsymbol h}_{t-2}}+ {\boldsymbol e}_t$

Table 14 Structural and in-mean coefficient estimates ${\boldsymbol{By}}_t = {\boldsymbol C} + \Gamma_1 {\boldsymbol y}_{t-1} + \Gamma_2 {\boldsymbol y}_{t-2} + \ldots + \Gamma_p {\boldsymbol y}_{t-p} + \alpha \sqrt{{\boldsymbol h}_t} + \beta \sqrt{{\boldsymbol h}_{t-1}}+ \gamma \sqrt{{\boldsymbol h}_{t-2}}+ {\boldsymbol e}_t$

Table 15 Structural and in-mean coefficient estimates ${\boldsymbol{By}}_t = {\boldsymbol C} + \Gamma_1 {\boldsymbol y}_{t-1} + \Gamma_2 {\boldsymbol y}_{t-2} + \ldots + \Gamma_p {\boldsymbol y}_{t-p} + \alpha \sqrt{{\boldsymbol h}_t} + \beta \sqrt{{\boldsymbol h}_{t-1}}+ \gamma \sqrt{{\boldsymbol h}_{t-2}}+ {\boldsymbol e}_t$

Table 16 Structural and in-mean coefficient estimates ${\boldsymbol{By}}_t = {\boldsymbol C} + \Gamma_1 {\boldsymbol y}_{t-1} + \Gamma_2 {\boldsymbol y}_{t-2} + \ldots + \Gamma_p {\boldsymbol y}_{t-p} + \alpha \sqrt{{\boldsymbol h}_t} + \beta \sqrt{{\boldsymbol h}_{t-1}}+ \gamma \sqrt{{\boldsymbol h}_{t-2}}+ {\boldsymbol e}_t$