Open Economies Review

, 20:607 | Cite as

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

Research Article

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.

Keywords

Structural VAR Multivariate GARCH Monetary aggregation 

JEL Classification

C32 E52 E44 

1 Introduction

The early theoretical literature regarding the macroeconomic effects of volatile money growth emphasized the interest rate channel through which money growth volatility affects the level of economic activity. For example, Mascaro and Meltzer (1983) and Evans (1984) argue that money growth volatility increases interest rate volatility and hence the riskiness of bonds. This increase in the risk of holding bonds increases the demand for money and interest rates, and hence reduces investment and output.

There has also been a large number of empirical studies investigating the relationship between money growth volatility and the level of economic activity, many of them mostly being stimulated by the October, 1979 change in operating procedures by the Federal Reserve in the United States. For example, Mascaro and Meltzer (1983), Evans (1984), Belongia (1984), Tatom (1984, 1985), and McMillin (1988), among others, have investigated empirically the effects of volatile money growth on key macroeconomic variables like interest rates and the level of output and report statistically significant effects of money growth volatility on the macroeconomy.

In a more recent paper, Serletis and Shahmoradi (2006) investigate the relationship between the variability of money growth and velocity, using recent advances in the financial econometrics literature. In particular, they specify and estimate a VARMA (vector autoregressive moving average) GARCH-in-mean model of money growth and velocity, and find that VARMA GARCH-M volatility of unanticipated money growth has a more systematic causal relation to the velocity of money than other measures of volatility. In fact, they find evidence of Friedman’s (1983, 1984) hypothesis that the variability of money growth helps predict velocity and that the money/velocity relationship is robust to monetary policy procedures as well as to alternative monetary aggregation methods.

In this paper we extend the work in Serletis and Shahmoradi (2006) by investigating the effects of money growth uncertainty on real economic activity, in the context of Elder’s (2004) multivariate framework in which a structural vector autoregression is modified to accommodate multivariate GARCH-in-Mean errors. 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 (CE) 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.

The paper is organized as follows. Section 2 provides a brief description of the multivariate GARCH-in-Mean VAR and addresses estimation issues. Section 3 presents the data and draws on the empirical literature dealing with identification issues in structural VARs. Section 4 assess the appropriateness of the econometric methodology and presents and discusses the empirical results. Section 5 investigates the robustness of the results and the final section concludes the paper.

2 Econometric methodology

We follow Elder (2004) and use a pth order structural VAR, describing the dynamic interrelations among a set of variables collected in an n × 1 vector, yt, as follows
$$ \text{ {\boldmath$By$}}_{{\kern-1.5pt}t}=\text{ {\boldmath$C$} }+\sum\limits_{j=1}^{p}\mathbf{\Gamma}_{{\kern-1pt}j}\text{ {\boldmath$y$} }_{{\kern-3.5pt} t-j}+\mathbf{\Lambda}\sqrt{\text{ {\boldmath$h$} }_{{\kern-2.5pt}t}}+\text{ {\boldmath$e$} }_{{\kern-2.5pt}t}\text{,}$$
(1)
where B and Γj (j = 1,···,p) are n × n parameter matrices, C is an n × 1 parameter vector, etΩt − 1N (0, Ht), where Ωt − 1 denotes the available information set in period t − 1 and Ht is the conditional variance-covariance matrix, and Λ is an n × n matrix.
We also assume that Ht is diagonal (that is, the structural errors are contemporaneously uncorrelated) and that ht in Eq. 1 is given by
$$\text{ {\boldmath$h$} }_{t}=\text{diag}\left(\text{{\boldmath$H$}}_{{\kern-.5pt}t}\right)=\text{ {\boldmath$C$} }_{v}+\sum\limits_{i=1}^{r}\text{ {\boldmath$F$} }_{i}\,\text{diag}\left(\text{ {\boldmath$e$} }_{{\kern-2.5pt} t-i}\text{ {\boldmath$e$} }_{{\kern-2.5pt}t-i}^{\prime}\right) +\sum\limits_{j=1}^{s}\text{ {\boldmath$G$}}_{{\kern-2pt}j}\,\text{diag}\left( \text{ {\boldmath$H$}}_{{\kern-.5pt} t-j}\right) \text{,}$$
(2)
where Cv is an n × 1 parameter vector and each of F and G are n × n diagonal parameter matrices. The term \(\mathbf{\Lambda} \sqrt{\text{ {\boldmath$h$}}_{{\kern-0.4pt}t}}\) has been included in Eq. 1 to examine the effects of money growth uncertainty on the conditional mean of yt.

To estimate the multivariate GARCH(1,1)-in-Mean VAR, Eqs. 1 and 2, we set r = s = 1 in Eq. 2, consistent with recent empirical evidence regarding the superiority of GARCH(1,1) models—see, for example, Hansen and Lunde (2005). We also set the diagonal elements of B equal to one and impose n(n − 1)/2 exclusion restrictions on B , subject to a rank condition. Finally, we follow Elder (2004) and assume that the structural disturbance vector, et, is conditionally multivariate normally distributed for all t, so that we can express the joint probability density function as a product of the conditional densities — see also Hamilton (1994) for more details. The parameters of the model are estimated by full information maximum likelihood, as discussed in Elder (2004, Appendix).

3 Data and the macroeconomic model

3.1 The data

We use quarterly United States data from the Federal Reserve Economic Database (FRED), maintained by the Federal Reserve Bank of St. Louis, over the period from 1959:1 to 2005:4, on four variables—money (M), real GDP (Y) the GDP deflator (P), and the ‘effective’ federal funds rate (R). We also make comparisons among simple-sum, Divisia, and currency equivalent methods of monetary aggregation at each of the four levels of aggregation—M1, M2, M3, and MZM.

The monetary aggregates currently in use by the Federal Reserve (the Fed) and most central banks around the world are simple-sum indices in which all monetary components are assigned a unitary weight. This index is Mt in
$$M_{{\kern-.7pt}t}=\sum\limits_{j=1}^{n}x_{jt}\text{,}$$
(3)
where xjt is one of the n monetary components of the monetary aggregate Mt. This summation index implies that all monetary components contribute equally to the money total and it views all components as dollar for dollar perfect substitutes.
Although there have been many attempts over the years at properly weighting monetary assets within a monetary aggregate, it was Barnett (1980) that derived the theoretical linkage between monetary theory and aggregation and index number theory. He constructed monetary aggregates based upon Diewert’s (1976) class of superlative quantity index numbers. These aggregates are Divisia quantity indices, defined (in discrete time) as
$$\log M_{{\kern-.7pt}t}^{D}-\log M_{t-1}^{D}=\sum\limits_{j=1}^{n}w_{jt}^{\ast}(\log x_{jt}-\log x_{j,t-1})\text{.}$$
(4)
According to Eq. 4 the growth rate of the aggregate is the weighted average of the growth rates of the component quantities, with the weights being defined as the expenditure shares averaged over the two periods of the change, \(w_{jt}^{\ast}=(1/2)(w_{jt}+w_{j,t-1})\) for j = 1,...,n, where wjt = πjtxjt/ ∑ πktxkt is the expenditure share of asset j during period t, and πjt is the user cost of asset j, derived in Barnett (1978),
$$\pi_{jt}=\dfrac{(R_{t}-r_{jt})}{(1+R_{t})}\text{,}$$
(5)
which is just the opportunity cost of holding a dollar’s worth of the jth asset. In Eq. 5, rjt is the market yield on the jth asset and Rt is the yield available on a ‘benchmark’ asset that is held only to carry wealth between multiperiods—see Barnett et al. (1992), Barnett and Serletis (2000), or Serletis (2007) for more details regarding the Divisia approach to monetary aggregation.
Rotemberg (1991) and Rotemberg et al. (1995) proposed the currency equivalent (CE) index
$$CE=\sum\limits_{j=1}^{n}\dfrac{R_{{\kern-.3pt}t}-r_{jt}}{R_{{\kern-.3pt}t}}x_{jt}\text{.}$$
(6)
In Eq. 6, as long as currency gives no interest, units of currency are added together with a weight of one. Other assets are added to currency but with a weight that declines toward zero as their return increases toward Rt. The difference between Divisia and CE methods of monetary aggregation is that the former measures the flow of monetary services whereas the latter, like simple summation aggregation, measures the stock of monetary assets. The CE aggregates, however, represent a major advance over the official simple-sum aggregates—see Rotemberg (1991) and Barnett (1991) for more details regarding Divisia and CE money measures.
To see the behavior of the different monetary aggregates, Figs. 1, 2, 3, and 4 provide graphical representations of sum, Divisia, and CE money measures for the United States (using monthly data, over the period from 1959:1 to 2006:2) at each of the four levels of monetary aggregation, M1, M2, M3, and MZM. The data were obtained from the Monetary Services Indices project of the Federal Reserve Bank of St. Louis. It is to be noted that we have used the new vintage of the data, documented in detail in Anderson and Buol (2005).
Fig. 1

Sum, Divisia, and CE M1 money measures

Fig. 2

Sum, Divisia, and CE M2 money measures

Fig. 3

Sum, Divisia, and CE M3 money measures

Fig. 4

Sum, Divisia, and CE MZM money measures

3.2 The macroeconomic model

Most of the homoskedastic VARs are estimated in levels. As explained in Hamilton (1994), in the case of homoskedastic VARs, if the true data generating process is the VAR in differences, differencing the variables would improve the small sample properties of the estimates and eliminate some nonstandard asymptotic distributions. However, the asymptotic theory does not apply to the multivariate GARCH-in-Mean model, and in this paper we estimate the multivariate GARCH-in-Mean model using logarithmic first differences of the variables (in fact, the model does not converge when the logged levels of the variables are used). In fact, on the basis of augmented Dickey-Fuller unit root tests—see Dickey and Fuller (1981)—and KPSS level and trend stationarity tests—see Kwiatkowski et al. (1992)—we use growth rates for each of the M, Y, and P variables since the null hypotheses of a unit root cannot be rejected and the null hypotheses of level and trend stationarity can be rejected. We do not difference the short term interest rate, consistent with the monetary VAR literature.

As already noted in Section 2, to identify the VAR, some exclusion restrictions need to be imposed on B. In doing so, we follow a recursive identification scheme. Because data on money, M, is available within a month, we assume that money contemporaneously affects all other variables. The next two equations form a block of equations which determine the level of output and the general price level. Real economic activity responds to Fed policy after only a one-month lag. The federal funds rate equation represents the monetary policy feedback rule and reacts swiftly to innovations in monetary aggregates, output, and inflation. So our B matrix becomes
$$\text{ {\boldmath$B$} }=\left[ \begin{tabular} [c]{cccc} $1$ & $0$ & $0$ & $0$\\ $b_{21}$ & $1$ & $0$ & $0$\\ $b_{31}$ & $b_{32}$ & $1$ & $0$\\ $b_{41}$ & $b_{42}$ & $b_{43}$ & $1$ \end{tabular} \ \right] \text{.} $$
Thus, our recursive factorization scheme imposes six exclusion restrictions on B, satisfying a rank condition. In addition, the diagonal elements of B are normalized to one and there is a restriction that the structural errors are uncorrelated. All these assumptions are sufficient to exactly identify the system.

Our measure of money growth uncertainty is the conditional variance of the ΔlogM shock, denoted h1t. We interpret this uncertainty in a statistical sense and consider a nonlinear relationship, by using \(\sqrt{\text{ {\boldmath$h$} }_{{\kern-.5pt}1t}}\).

4 Empirical results

To estimate the multivariate GARCH(1,1)-in-Mean VAR, we start by first fitting its simplified versions — the homoscedastic VAR, the multivariate ARCH VAR, and the multivariate GARCH VAR. This is required in order to come up with good starting values for the parameters of the multivariate GARCH(1,1)-in-Mean VAR. With our quarterly data, we set p = 3 in Eq. 1, because of degrees of freedom issues; our results, however, are robust to alternative lower lag length specifications. We also add two lags of money growth uncertainty in the output equation; adding only one lag of money growth uncertainty does not make any significant difference in our results. The iteration process is closely monitored in order to find out whether any of the variables has a homoscedastic variance process in which case it is difficult to achieve convergence. Various starting values are attempted to make sure that the global maximum is reached.

In Tables 1, 2, 3, and 4 under the ‘full sample’ (59:1-05:4) columns, we report point estimates of the variance function parameters for sum, Divisia, and CE monetary aggregates at each of the M1, M2, M3, and MZM levels of aggregation. In this multivariate framework, the ARCH and GARCH terms are in general significant (at conventional significance levels) for all the variables in the model. The sum of the ARCH, F, and GARCH, G, terms is close to one in most cases, suggesting that shocks to the variance are strongly persistent. We also test whether the ARCH and GARCH parameters are jointly significant. In doing so, we perform likelihood ratio tests based on the log likelihood of the restricted and unrestricted versions of the model. The likelihood ratio test statistics reject (at conventional significance levels) the null hypotheses of no ARCH \(\left( \text{{\boldmath$F$}}=\mathbf{0}\right)\), no GARCH \(\left( \text{{\boldmath$F$}}=\text{{\boldmath$G$}}=\mathbf{0}\right)\), and no GARCH-in-Mean \(\left( \text{{\boldmath$F$}}=\text{{\boldmath$G$}}=\mathbf{\Lambda}=\mathbf{0}\right)\).
Table 1

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

 

Sum M1

Divisia M1

CE M1

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

Constant (Cv)

  M

0.605 (1.67)

2.425 (0.43)

1.153 (1.35)

0.657 (1.94)

2.137 (0.81)

4.845 ∗ (3.86)

10.103 ∗ (3.27)

11.944 ∗ (1.88)

38.101 (1.23)

  Y

0.020 (0.39)

3.119 ∗ (2.57)

0.286 (1.14)

0.027 (0.70)

3.122 ∗ (3.09)

0.287 (1.13)

0.323 (1.41)

2.378 ∗ (2.36)

0.676 (0.83)

  P

0.024 (1.12)

0.523 ∗ (2.71)

0.055 (0.94)

0.024 (1.17)

0.508 ∗ (3.27)

0.052 (0.91)

0.021 (1.23)

0.703 ∗ (2.96)

0.956 (0.38)

  R

0.076 ∗ (3.78)

0.002 (0.84)

0.017 (1.04)

0.005 (1.09)

0.058 (1.85)

0.020 (1.06)

0.002 (0.35)

0.142 ∗ (2.92)

0.055 ∗ (2.49)

ARCH (F)

  M

0.219 ∗ (2.64)

0.000 (0.00)

0.380 ∗ (2.17)

0.255 ∗ (2.53)

0.000 (0.00)

0.301 (1.32)

0.458 ∗ (2.11)

0.335 (1.44)

0.316 (0.35)

  Y

0.074 ∗ (2.26)

0.479 ∗ (2.24)

0.405 ∗ (2.08)

0.081 ∗ (10.02)

0.471 ∗ (2.35)

0.431 ∗ (2.18)

0.295 ∗ (2.52)

0.638 ∗ (2.78)

0.000 (0.00)

  P

0.114 ∗ (1.98)

0.356 (1.43)

0.385 ∗ (2.26)

0.114 ∗ (2.00)

0.373 (1.71)

0.383 ∗  (2.13)

0.103 ∗ (2.30)

0.173 (0.82)

0.000 (0.00)

  R

1.01 ∗ (31.06)

0.272 ∗ (5.26)

0.385 ∗ (2.47)

0.246 ∗ (4.32)

0.918 ∗ (11.89)

0.431 ∗ (2.51)

0.278 ∗ (5.22)

0.923 ∗ (7.76)

0.966 ∗ (26.42)

GARCH (G)

  M

0.679 ∗ (6.26)

0.062 (0.02)

0.569 ∗ (3.44)

0.604 ∗ (4.70)

0.013 (0.01)

0.000 (0.00)

0.313 ∗ (2.53)

0.483 ∗ (3.04)

0.000 (0.00)

  Y

0.923 ∗ (26.07)

0.000 (0.00)

0.587 ∗ (2.98)

0.916 ∗ (51.09)

0.000 (0.00)

0.558 ∗ (2.75)

0.673 ∗ (5.62)

0.020 (0.16)

0.895 ∗ (10.80)

  P

0.838 ∗ (9.71)

0.000 (0.00)

0.588 ∗ (2.81)

0.838 ∗ (9.97)

0.000 (0.00)

0.594 ∗ (2.78)

0.854 ∗ (13.08)

0.021 (0.08)

0.076 (0.02)

  R

0.000 (0.00)

0.719 ∗ (14.36)

0.612 ∗ (3.87)

0.726 ∗ (11.96)

0.039 (0.64)

0.566 ∗ (3.23)

0.706 ∗ (10.60)

0.000 (0.00)

0.012 (0.58)

Notes: Sample period, monthly data: 1959:1–2006:2. Numbers in parentheses next to the coefficient estimates are t-statistics. An asterisk indicates significance at the 5% level

Table 2

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

 

Sum M2

Divisia M2

CE M2

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

Constant (Cv)

  M

2.864 ∗ (9.45)

1.989 (1.05)

3.031 ∗ (2.42)

0.303 (1.44)

2.461 ∗ (3.44)

0.095 (1.14)

65.192 ∗ (4.02)

45.480 ∗ (2.57)

1.702 (0.21)

  Y

0.062 (0.64)

2.751 ∗ (3.16)

0.610 ∗ (2.07)

0.565 ∗ (2.24)

2.870 ∗ (3.15)

0.299 (0.97)

0.892 (1.73)

2.241 (1.56)

0.443 (1.05)

  P

0.135 ∗ (2.18)

0.015 (0.50)

0.113 (1.20)

0.141 ∗ (2.46)

0.004 ∗ (8.82)

0.141 (1.17)

0.021 (1.59)

0.713 ∗ (3.48)

0.134 (1.36)

  R

0.012 (1.26)

0.003 (0.94)

0.034 ∗ (2.10)

0.080 ∗ (4.98)

0.008 (0.94)

0.020 (1.33)

0.013 ∗ (3.52)

0.048 (1.19)

0.024 ∗ (6.81)

ARCH (F)

  M

0.011 (0.66)

0.000 (0.00)

0.012 (0.66)

0.113 ∗ (2.07)

0.000 (0.00)

0.117 (1.88)

0.624 ∗ (9.28)

0.751 ∗ (6.87)

0.204 ∗ (1.98)

  Y

0.084 (1.64)

0.620 ∗ (2.40)

0.364 ∗ (2.86)

0.447 ∗ (3.32)

0.595 ∗ (2.61)

0.414 (1.72)

0.496 ∗ (3.35)

0.782 (1.72)

0.660 ∗ (2.51)

  P

0.437 ∗ (2.76)

0.087 ∗ (2.01)

0.311 ∗ (1.98)

0.467 ∗ (2.73)

0.000 (0.00)

0.326 ∗ (1.96)

0.108 ∗ (3.20)

0.174 (0.84)

0.352 (1.86)

  R

0.389 ∗ (3.97)

0.250 ∗ (3.26)

0.689 ∗ (5.83)

0.951 ∗ (17.38)

0.277 ∗ (3.18)

0.450 ∗ (3.15)

0.534 ∗ (10.20)

0.840 ∗ (9.56)

0.853 ∗ (18.23)

GARCH (G)

  M

0.000 (0.00)

0.094 (0.10)

0.005 (0.01)

0.780 ∗ (7.90)

0.013 (0.05)

0.872 ∗ (13.38)

0.230 ∗  (4.85)

0.180 ∗ (2.50)

0.794 ∗ (8.75)

  Y

0.905 ∗ (15.35)

0.000 (0.00)

0.452 ∗ (3.28)

0.509 ∗ (3.90)

0.001 (0.01)

0.596 ∗ (2.51)

0.390 ∗ (2.62)

0.000 (0.00)

0.314 (1.03)

  P

0.361 (1.95)

0.889 ∗ (13.82)

0.482 (1.74)

0.330 (1.83)

1.024 ∗ (11.24)

0.425 (1.53)

0.847 ∗  (18.31)

0.000 (0.00)

0.424 (1.90)

  R

0.580 ∗ (5.60)

0.767 ∗ (10.21)

0.305 ∗ (2.55)

0.010 (0.46)

0.691 ∗ (8.41)

0.553 ∗ (3.93)

0.439 ∗ (9.73)

0.121 (1.53)

0.144 ∗ (3.03)

Note: Sample period, quarterly data: 1959:1–2005:4. Numbers in parentheses next to the coefficient estimates are absolute t-statistics. An asterisk indicates significance at the 5% level

Table 3

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

 

Sum M3

Divisia M3

CE M3

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

Constant (Cv)

  M

1.704 ∗ (5.26)

0.222 (0.97)

2.576 (0.87)

0.607 ∗ (2.34)

2.162 ∗ (10.06)

1.667 ∗ (3.80)

73.307 ∗ (3.55)

47.271 ∗ (2.81)

No convergence

  Y

0.184 (1.31)

2.804 ∗ (2.15)

0.235 (1.24)

0.420 (1.64)

3.139 ∗ (8.64)

0.209 (1.13)

0.766 ∗ (2.10)

2.188 ∗ (2.04)

 

  P

0.017 (1.10)

0.517 ∗ (2.84)

0.113 (1.36)

0.019 (1.14)

0.012 (0.37)

0.117 (1.27)

0.021 (1.23)

0.024 (1.87)

 

  R

0.007 (1.36)

0.004 (1.18)

0.032 ∗ (2.12)

0.011 (1.36)

0.003 (0.85)

0.028 (1.67)

0.010 (1.66)

0.003 (0.98)

 

ARCH (F)

  M

0.420 ∗ (2.16)

0.321 ∗ (2.24)

0.166 (0.70)

0.353 ∗ (2.32)

0.000 (0.00)

0.504 ∗ (2.32)

0.687 ∗ (5.29)

0.762 ∗ (6.83)

 

  Y

0.247 ∗ (2.76)

0.503 ∗ (2.31)

0.354 ∗ (3.09)

0.468 ∗ (3.40)

0.507 ∗ (2.41)

0.338 ∗ (2.64)

0.646 ∗ (3.92)

0.708 ∗ (3.24)

 

  P

0.099 ∗ (2.36)

0.365 (1.30)

0.311 ∗ (2.09)

0.105 ∗ (2.31)

0.088 ∗ (2.05)

0.344 ∗ (2.10)

0.108 ∗ (2.25)

0.075 ∗ (2.10)

 

  R

0.334 ∗ (3.54)

0.442 ∗ (4.79)

0.696 ∗ (5.98)

0.339 ∗ (3.57)

0.306 ∗ (4.11)

0.619 ∗ (4.64)

0.482 ∗ (4.25)

0.327 ∗ (3.98)

 

GARCH (G)

  M

0.000 (0.00)

0.626 ∗ (3.73)

0.000 (0.00)

0.453 ∗ (2.86)

0.014 (0.08)

0.000 (0.00)

0.197 ∗ (2.39)

0.164 ∗ (2.39)

 

  Y

0.736 ∗ (7.82)

0.061 (0.23)

0.638 ∗ (4.55)

0.511 ∗ (3.62)

0.008 (0.05)

0.655 ∗ (5.01)

0.366 ∗ (2.22)

0.066 (0.40)

 

  P

0.864 ∗ (14.06)

0.000 (0.00)

0.482 ∗ (2.05)

0.856 ∗ (13.13)

0.892 ∗ (13.75)

0.462 (1.86)

0.848 ∗ (12.30)

0.892 ∗ (22.31)

 

  R

0.640 ∗ (6.68)

0.574 ∗ (6.42)

0.308 ∗ (2.67)

0.628 ∗ (6.29)

0.679 ∗ (9.58)

0.376 ∗ (2.78)

0.496 ∗ (4.41)

0.687 ∗ (8.49)

 

Note: Sample period, quarterly data: 1959:1–2005:4. Numbers in parentheses next to the coefficient estimates are absolute t-statistics. An asterisk indicates significance at the 5% level

Table 4

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

 

Sum MZM

Divisia MZM

CE MZM

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

Constant (Cv)

  M

1.343 ∗ (3.21)

0.952 (1.83)

 

1.079 ∗ (2.31)

1.086 (1.68)

 

43.512 ∗ (3.85)

30.576 ∗ (2.73)

 

  Y

0.059 (0.43)

2.569 ∗ (3.26)

No convergence

0.060 (0.47)

2.675 ∗ (3.31)

No convergence

0.016 (0.32)

2.315 ∗ (2.44)

No convergence

  P

0.023 (1.28)

0.164 ∗ (2.00)

 

0.022 (1.18)

0.004 ∗ (8.89)

 

0.021 (1.21)

0.715 ∗ (3.71)

 

  R

0.004 ∗ (2.03)

0.004 (1.15)

 

0.002 (1.14)

0.005 (0.91)

 

0.012 ∗ (2.11)

0.099 ∗ (2.06)

 

ARCH (F)

  M

0.597 ∗ (10.75)

0.741 ∗ (4.31)

 

0.538 ∗ (3.31)

0.569 (1.92)

 

0.602 ∗ (3.74)

0.992 ∗ (12.04)

 

  Y

0.101 (0.98)

0.676 ∗ (2.87)

 

0.100 (1.02)

0.636 ∗ (2.79)

 

0.068 ∗ (2.41)

0.708 ∗ (3.24)

 

  P

0.108 ∗ (3.89)

0.000 (0.00)

 

0.111 ∗ (2.03)

0.000 (0.00)

 

0.105 ∗ (2.20)

0.144 (0.79)

 

  R

0.304 ∗ (7.15)

0.453 ∗ (3.83)

 

0.313 ∗ (6.56)

0.373 ∗ (4.33)

 

0.547 ∗ (6.92)

0.972 ∗ (14.44)

 

GARCH (G)

  M

0.337 ∗ (5.80)

0.197 (1.24)

 

0.367 ∗ (2.28)

0.292 (1.24)

 

0.218 ∗ (2.49)

0.023 (0.26)

 

  Y

0.893 ∗ (7.79)

0.000 (0.00)

 

0.893 ∗ (8.23)

0.000 (0.00)

 

0.930 ∗ (29.46)

0.028 (0.21)

 

  P

0.846 ∗ (16.60)

0.814 ∗ (21.58)

 

0.844 ∗ (10.80)

1.026 ∗ (10.13)

 

0.850 ∗ (12.21)

0.000 (0.00)

 

  R

0.676 ∗ (14.54)

0562 ∗ (4.84)

 

0.710 ∗ (16.12)

0.608 ∗ (7.34)

 

0.432 ∗ (5.72)

0.042 (0.61)

 

Note: Sample period, quarterly data: 1959:1–2005:4. Numbers in parentheses next to the coefficient estimates are absolute t-statistics. An asterisk indicates significance at the 5% level

We also conduct misspecification tests, based on the standardized residuals,
$$\hat{z}_{jt}=\frac{e_{jt}}{\sqrt{\widehat{h}_{{\kern-1pt}jt}}}\text{,}$$
for j = ΔlogM, ΔlogY, ΔlogP and R. The Ljung-Box Q-statistic for testing residual serial correlation cannot reject (at conventional significance levels) the null of no autocorrelation for the values and the squared values of the standardized residuals, suggesting that there is no evidence of conditional heteroscedasticity. In addition, the test for normality implicitly indicates that the multivariate GARCH(1,1)-in-Mean VAR does not bear significant misspecification error—see, for example, Kroner and Ng (1998).
As can be seen in Tables 5, 6, 7, and 8, under the full sample columns, the model reasonably captures the contemporaneous correlation among the variables in the B matrix. The estimates (with asymptotic absolute t-statistics in parentheses) reveal that there is a negative relationship between money growth and the interest rate. Also monetary policy tightens (i.e., the fed funds rate increases) in response to contemporaneous innovations in each of ΔlogY and ΔlogP—this is consistent with the countercyclical nature of monetary policy.
Table 5

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

 

Sum M1

Divisia M1

CE M1

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

b21

0.042 (0.75)

0.394 ∗ (1.97)

0.060 (1.04)

0.051 (0.97)

0.456 ∗ (3.40)

0.087 (1.24)

−0.010 (0.25)

−0.019 (0.68)

−0.021 (0.28)

b31

0.006 (0.28)

0.109 (1.84)

−0.009 (0.50)

0.011 (0.60)

0.116 (1.77)

−0.008 (0.37)

0.004 (0.37)

0.024 (1.68)

0.034 ∗ (2.31)

b32

−0.031 (1.35)

−0.072 ∗ (1.96)

−0.077 ∗ (2.26)

−0.031 (1.26)

−0.076 ∗ (7.98)

0.077 ∗ (2.28)

−0.031 (1.24)

−0.028 ∗ (0.79)

−0.079 (0.86)

b41

−0.046 ∗ (4.05)

−0.068 ∗ (2.72)

−0.056 ∗ (3.14)

−0.051 ∗ (3.75)

−0.105 ∗  (3.07)

−0.060 ∗ (2.65)

−0.004 (0.83)

−0.001 (0.07)

−0.007 (1.58)

b42

0.035 ∗ (3.41)

0.027 (1.94)

0.041 (1.51)

0.034 ∗ (2.48)

0.050 (1.33)

0.043 (1.61)

0.013 (1.01)

0.013 (0.60)

−0.003 (0.18)

b43

0.070 (1.76)

0.204 ∗ (3.91)

0.160 ∗ (2.21)

0.190 ∗ (4.00)

0.167 ∗ (7.07)

0.155 ∗ (2.14)

0.154 ∗ (3.15)

0.135 ∗ (1.86)

0.253 ∗ (6.65)

α21

0.218 (1.19)

1.047 ∗ (0.09)

−0.031 (0.07)

0.217 (0.98)

1.194 (0.38)

0.047 (0.05)

−0.217(1.49)

−0.374 (1.05)

−0.567 (0.96)

β21

−0.119 (0.29)

1.005 (0.072)

0.212 (0.52)

0.009 (0.58)

1.193 (0.18)

0.456 (0.76)

0.157 (1.02)

0.028 (0.09)

−0.110 (0.23)

γ21

−0.261 (0.75)

−0.174 (0.09)

−0.098 (0.35)

−0.301 (1.11)

−0.420 (0.20)

0.172 (0.30)

0.074 (0.51)

0.339 ∗ (1.71)

0.300 (0.35)

Cum. effect of monetary uncertainty

−0.162

1.878

0.083

−0.075

1.967

0.675

0.014

−0.010

−0.377

χ2(3)

0.745

0.608

0.988

0.836

0.605

0.503

0.688

0.698

0.034

Note: Sample period, quarterly data: 1959:1–2005:4. Numbers in parentheses next to the coefficient estimates are absolute t-statistics. An asterisk indicates significance at the 5% level. Numbers reported for the χ2(3) statistic are p-values—a p-value less than 0.05 rejects the null at the 5% level

Table 6

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

 

Sum M2

Divisia M2

CE M2

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

b21

0.105 (1.44)

0.231 ∗ (2.02)

0.182 ∗ (2.37)

0.112 ∗ (2.41)

0.225 ∗ (4.60)

0.139 (1.75)

0.008 ∗ (2.03)

0.011 (0.68)

0.009 (0.95)

b31

−0.040 (1.65)

−0.086 (1.36)

0.072 ∗ (1.96)

−0.032 (1.55)

−0.060 (1.09)

−0.010 (0.28)

0.003 (1.18)

0.009 (1.55)

0.002 (0.59)

b32

−0.042 (1.83)

−0.037 (1.01)

−0.074 ∗ (2.03)

−0.035 (1.74)

0.000 (0.00)

−0.061 (1.60)

−0.029 (0.91)

−0.024 (0.33)

−0.071 (1.86)

b41

−0.024 (1.41)

−0.145 ∗ (3.34)

0.097 ∗  (5.04)

−0.089 ∗ (4.37)

−0.162 ∗ (3.93)

−0.019 (0.64)

−0.014 ∗ (9.77)

−0.011 ∗ (5.84)

−0.015 ∗ (9.28)

b42

0.022 (1.78)

0.030 (1.89)

0.015 (1.58)

0.041  ∗ (3.87)

0.030 ∗ (2.01)

0.042 (1.52)

0.017 (1.65)

−0.016 (0.85)

0.046  ∗ (2.47)

b43

0.114 ∗ (2.74)

0.223 ∗ (3.03)

−0.003 (0.04)

0.094 ∗  (2.60)

0.216 ∗ (3.53)

0.057 (0.78)

0.116 ∗  (10.46)

0.135 ∗ (3.01)

0.074 (1.66)

α21

−2.267 (0.42)

0.570 (0.98)

−3.261 (0.44)

−2.475 ∗ (2.45)

0.473 (0.28)

−0.630 (0.49)

−0.082  ∗ (3.00)

−0.087 (1.41)

−0.171 (1.15)

β21

−3.106 (0.55)

0.540 (0.27)

−0.306 (0.04)

0.168 (0.69)

0.462 (0.19)

−1.352 (0.87)

−0.033 (1.19)

0.003 (0.04)

0.098 (0.71)

γ21

2.463 (1.54)

0.767 (0.60)

4.115 ∗ (2.77)

1.734 (1.54)

0.962 (1.39)

1.926 (1.27)

0.012 (0.24)

−0.009 (0.28)

0.312 ∗ (2.45)

Cum. effect of monetary uncertainty

−2.910

1.877

0.548

−0.573

1.897

−0.056

−0.103

−0.093

0.239

χ2(3)

0.330

0.751

0.174

0.092

0.656

0.221

0.037

0.010

0.0001

Note: Sample period, quarterly data: 1959:1–2005:4. Numbers in parentheses next to the coefficient estimates are absolute t-statistics. An asterisk indicates significance at the 5% level. Numbers reported for the χ2(3) statistic are p-values—a p-value less than 0.05 rejects the null at the 5% level

Table 7

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

 

Sum M3

Divisia M3

CE M3

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

b21

0.196 ∗ (2.83)

0.227 (1.33)

0.191 ∗ (3.10)

−0.241 ∗ (3.26)

0.236 (1.79)

0.198 ∗ (2.14)

0.005 (0.65)

0.007 (0.33)

 

b31

0.039 (1.09)

−0.094 (1.65)

0.072 ∗ (2.12)

0.040 (1.10)

−0.086 (1.49)

0.042 (1.02)

0.003 (1.02)

0.007 (1.23)

No convergence

b32

−0.041 (1.65)

−0.050 (1.28)

−0.074 ∗ (2.20)

−0.039 (1.18)

−0.036 (1.00)

−0.071 (1.94)

−0.031 (1.29)

−0.026 (0.70)

 

b41

0.020 (1.33)

−0.090 ∗ (4.22)

0.097 ∗  (4.54)

−0.009 (0.62)

−0.110 ∗ (3.76)

0.065 ∗ (2.52)

−0.010 ∗  (5.77)

−0.004 (1.53)

 

b42

0.022 (1.52)

0.016 (1.26)

0.015 (0.45)

0.022 (1.65)

0.030 ∗ (2.03)

0.041 (1.64)

0.016 (1.36)

0.014 ∗ (2.96)

 

b43

0.073 (1.64)

0.175 ∗ (4.19)

−0.002 (0.11)

0.108 ∗ (2.71)

0.215 ∗ (3.84)

−0.011 (0.19)

0.113 ∗ (2.84)

0.152 ∗ (2.45)

 

α21

−1.216 ∗ (2.45)

−1.510 (1.45)

−0.749 (0.77)

−1.789 ∗ (2.67)

0.337 (0.23)

−0.677 (1.63)

−0.061 ∗ (2.21)

−0.065 ∗ (2.73)

 

β21

0.365 (1.13)

2.429 ∗ (1.75)

0.649 (0.37)

1.675 (1.91)

0.327 (0.26)

0.358 (0.81)

−0.040 (1.68)

0.005 (0.04)

 

γ21

−0.299 ∗  (0.98)

−0.842 (0.91)

0.115 (0.02)

−0.780 (1.63)

1.261 (0.65)

−0.335 (0.92)

0.022 (0.97)

−0.009 (0.08)

 

Cum. effect of monetary uncertainty

−1.150

0.077

0.015

−0.894

1.925

−0.654

−0.079

−0.069

 

χ2(3)

0.0003

0.183

0.748

0.0001

0.641

0.333

0.553

0.103

 

Note: Sample period, quarterly data: 1959:1–2005:4. Numbers in parentheses next to the coefficient estimates are absolute t-statistics. An asterisk indicates significance at the 5% level. Numbers reported for the χ2(3) statistic are p-values—a p-value less than 0.05 rejects the null at the 5% level

Table 8

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

 

Sum MZM

Divisia MZM

CE MZM

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

59:1-05:4

59:1-79:3

79:3-05:4

b21

0.030 (0.69)

0.126 (1.34)

 

0.029 (0.66)

0.150 (1.48)

 

−0.001 (0.05)

−0.007 (0.58)

 

b31

−0.012 (0.88)

−0.015 (0.32)

No convergence

−0.009 (0.576)

−0.047 (0.90)

No convergence

0.005 (1.23)

0.011 (1.64)

No convergence

b32

−0.031 (1.34)

−0.021 (0.51)

 

−0.033 (1.40)

0.001 (0.03)

 

−0.029 (1.14)

−0.024 (0.56)

 

b41

−0.051 ∗ (6.23)

−0.108 ∗ (6.47)

 

−0.077 ∗ (6.86)

−0.117 ∗ (6.28)

 

−0.019  ∗ (7.89)

−0.013 (5.25)

 

b42

0.029 ∗ (3.90)

0.023 (1.62)

 

0.032 ∗  (2.76)

0.026 (1.90)

 

0.005 (0.38)

0.003 (0.21)

 

b43

0.133 ∗ (3.33)

0.131 ∗ (2.72)

 

0.146 ∗ (3.75)

0.162 ∗ (3.66)

 

0.126  ∗ (4.31)

0.250 (5.21)

 

α21

0.193 (1.12)

0.204 (0.81)

 

0.231 (1.40)

0.244 (0.66)

 

−0.029 (0.19)

−0.061 ∗ (2.26)

 

β21

−0.089 (0.40)

−0.112 (0.44)

 

−0.062 (0.28)

−0.020 (0.11)

 

−0.003 (0.05)

−0.025 (−0.90)

 

γ21

0.092 (1.73)

0.503 (1.56)

 

0.100 (0.75)

0.670 (1.33)

 

−0.004 (0.20)

0.002 (0.09)

 

Cum. effect of monetary uncertainty

0.196

0.595

 

0.269

0.894

 

−0.036

−0.084

 

χ2(3)

0.043

0.339

 

0.050

0.383

 

0.818

0.041

 

Note: Sample period, quarterly data: 1959:1–2005:4. Numbers in parentheses next to the coefficient estimates are absolute t-statistics. An asterisk indicates significance at the 5% level. Numbers reported for the χ2(3) statistic are p-values—a p-value less than 0.05 rejects the null at the 5% level

In addition to current uncertainty, we incorporate two lags of money growth uncertainty in the ΔlogY equation. The point estimates (with asymptotic absolute t-statistics in parentheses) are reported in Tables 58 under the α21, β21, and γ21 entries. We find that in all cases, money growth uncertainty affects output growth negatively at least in one month and in some cases in two consecutive months. Moreover, the joint null hypothesis that output growth is not affected by money growth uncertainty, H0: α21 = β21 = γ21 = 0, can be rejected with the CE M1, CE M2, Sum M3, Divisia M3, Sum MZM, and Divisia MZM monetary aggregates—this is indicated by the p-values for likelihood ratio test statistics reported in Tables 58, distributed as χ2(3).

Finally, we can quantify the effect of monetary uncertainty on real GDP growth, by using the cumulative effects of monetary uncertainty on real GDP growth, reported in Tables 58. In the case, for example, of the Divisia M3 monetary aggregate, the full sample estimate of the cumulative effect of money growth uncertainty on real GDP growth is − 0.894. The standard deviation of the growth rate of Divisia M3 is 2.442. Hence, the effect of a one standard deviation shock to the growth rate of Divisia M3 on the growth rate of real GDP is − 0.894×2.442 = − 2.183%. This effect is over three quarters, so for the full year the growth rate of real GDP will be reduced by 2.183%×(3/4) = 1.636%.

5 Robustness

The period from 1959 to 2005 covers a lot of significantly different periods of high inflation, low inflation, as well as periods of different Fed chairmen with different approaches to monetary policy. For example, in the 1960s, the Fed targeted on money market conditions, using interest rates as the primary operating instrument. This approach led to procyclical monetary policy. In the 1970s the Fed used monetary aggregates as intermediate targets, but monetary policy continued to be procyclical because the Fed was actually using the federal funds rate as its operating instrument. In the period from October 1979 to October 1982, the Fed de-emphasized the federal funds rate as an operating instrument and nonborrowed reserves became the primary operating instrument. Between October 1982 and the early 1990s, the Fed targeted on borrowed reserves but abandoned monetary aggregates as a guide for monetary policy. Finally, since the early 1990s the Fed has been using the federal funds rate as the primary operating instrument and recently switched to public announcement of the specific target.

Because of nonlinear estimation in the large parameter space and degree of freedom issues (we are estimating 73 parameters), we cannot investigate the relationship between money growth volatility and output growth in the various sub-samples just discussed. However, we investigate the robustness of our results by re-estimating the multivariate GARCH-in-Mean VAR over the pre-October 1979 and post-October 1979 sub-periods, using the same specification as before but with p = 1 in Eq. 1, because of degree of freedom problems. The results are presented in Tables 18 under the ‘pre-1979’ (59:1-79:3) and ‘post-1979’ (79:3-05:4) columns, in the same way as those for the ‘full sample’ (59:1-05:4). As shown in the tables, we have not been able to achieve convergence with the CE M3 and the sum, Divisia, and CE MZM monetary aggregates using the post-1979 sample. Although not strong compared to the full sample, the negative effect of monetary growth uncertainty is still present in a number of cases, including CE M1 for the post-1979 sub-sample, CE M2 for both subsamples, and CE MZM for the pre-1979 sub-sample.

So far, we have considered an identification restriction whereby money comes first in the ordering of the variables in the multivariate GARCH-in-Mean VAR. In practice, however, the Fed expresses monetary policy as targets for short-term nominal interest rates, rather than monetary aggregates. In fact, as already noted, since the early 1990s, the Fed focuses on the federal funds rate, the rate at which financial institutions borrow and lend funds to each other in the federal funds market. Although monetary policy is not expressed in terms of monetary aggregates, the Fed’s adjustments of the federal funds rate nevertheless translate into changes in the monetary aggregates, since an interest rate policy is not distinct from a money supply policy. To investigate the robustness of our results to alternative identification schemes, we put the federal funds rate first, followed by output, inflation, and money—this identification assumes that the interest rate contemporaneously affects all other variables and that money reacts swiftly to innovations in the interest rate, output, and the inflation rate. Our structural multivariate GARCH-in-Mean VAR based on this identification still shows the negative effect of monetary uncertainty on output growth.

We also attempted to include three lags of inflation uncertainty in addition to money growth uncertainty in the output growth equation, in order to investigate whether it is inflation uncertainty or money growth uncertainty that has a negative effect on output growth. We were, however, unable to converge to final parameter estimates, even with the full sample, because of the highly nonlinear structure of the model. Hence, investigating this hypothesis remains an area for potentially productive future research.

Finally, we investigate the robustness of our results to alternative measures of the level of economic activity and to the use of monthly observations. In doing so, we use monthly data from FRED over the 1959:1 to 2006:2 period and measure output (at the monthly frequency) by the industrial production index. We estimate the model with p = 12 in Eq. 1 and report the results in Appendix Tables 9, 10, 11, 12, 13, 14, 15, and 16, in the same fashion as those with the quarterly data in Tables 18. In general, the evidence is consistent with that from the quarterly data. In particular, likelihood ratio test statistics reject the null hypotheses of no ARCH \(\left( \text{ {\boldmath$F$} }=\mathbf{0}\right) \), no GARCH \(\left( \text{ {\boldmath$F$} }=\text{ {\boldmath$G$} }=\mathbf{0}\right) \), and no GARCH-in-Mean \(\left( \text{ {\boldmath$F$} }=\text{ {\boldmath$G$} }=\mathbf{\Lambda}=\mathbf{0}\right) \). Moreover, the joint null hypothesis that industrial production growth is not affected by money growth uncertainty, H0:α21 = β21 = γ21 = 0, can be rejected with the Sum M1, Divisia M2, CE M2, CE M3, Sum MZM, and Divisia MZM monetary aggregates.

6 Conclusion

We have examined the effects of money growth uncertainty on real economic activity using quarterly data for the United States over the period from 1959:1 to 2005:4. In the context of a multivariate framework in which a structural vector autoregression (VAR) is modified to accommodate multivariate GARCH-in-Mean (MGARCH-M) errors, we used a recursive identification scheme and provided 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.

In general, our results indicate that money growth volatility has significant negative effects on the growth rate of real GDP. This result is robust to alternative identification schemes, alternative measures of the level of economic activity, and to the use of monthly data. We thus conclude that macroeconomic policies that reduce money growth uncertainty are, as Elder (2004, p. 926) puts it, “likely to contribute to greater overall economic growth.”

We have also shown that money growth uncertainty has differential effects on output growth depending on how money is measured. This is consistent with the evidence recently reported by Serletis and Uritskaya (2007) who use a statistical physics approach—‘detrended fluctuation analysis’ (DFA), introduced by Peng et al. (1994)—to investigate temporal fractal structure of sum, Divisia, and CE money measures in the United States. Their results suggest that the sum and Divisia monetary aggregates are more appropriate for measuring long-term tendencies in money supply dynamics while the currency equivalent aggregates are more sensitive measures of short-term processes in the economy.

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of CalgaryCalgaryCanada

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