*A Mark Sadowski post*

Most highly publicized academic studies on quantitative easing (QE) seem to come in one of four flavors: 1) event studies on changes in security yields on the days of announcement (e.g. Krishnamurthy and Vissing-Jorgensen, 2011), 2) panel data studies on flow and stock effects of QE on daily security yields during the programs (e.g. D’Amico and King, 2010) , 3) times series studies on the effect of open market operations on security yields during normal times (e.g. Hamilton and Wu, 2011) and 4) studies on the macroeconomic effects of QE using major models calibrated to normal times (e.g. Fuhrer and Olivei 2011). The underlying assumption of nearly all these studies is that the primary channel of the Monetary Transmission Mechanism (MTM) is the Traditional Real Interest Rate Channel, which is almost certainly not the case at the zero lower bound (ZLB) in interest rates.

Notably, there are very few empirical studies on the macroeconomic effects of QE ** during** QE. Indeed, to my knowledge, there are only four: Honda

*et al.*(2007), Girardin and Moussa (2010), Gambacorta

*et al.*(2012) and Behrendt (2013).

What these four studies have in common is that they focus on periods of zero interest rate policy (ZIRP) employing Vector Auto-Regression (VAR) methodology with the monetary base, or bank reserves, as the instrument of monetary policy. The convention in the empirical literature on the transmission of monetary policy is to estimate a VAR with a measure of output, the price level and a short term interest rate (along with other variables). Thus, the principal difference between these four studies, and what is the usual practice, is to substitute the monetary base (or bank reserves) in place of the short term interest rate as the instrument of monetary policy.

Focusing on periods of ZIRP also presents some additional challenges. In particular, instead of having decades of data permitting the use of real GDP (RGDP) and the GDP deflator as the measure of output and price level, there is only a period of years usually necessitating the use of data at monthly frequency, meaning (for example) that the industrial production index may have to be substituted for RGDP, and that a measure of the consumer price level may have to be substituted for the GDP deflator, if a sufficient number of observations is to be available in order for it to be possible to generate statistically significant results.

When constructing a macroeconomic VAR model (as I am about to do), it is especially desirable for the policy variable to Granger cause another variable (or variables) in the model. This is because, if the policy variable Granger causes another variable, then it provides statistically significant information about future values of the other variable. Under those circumstances we might expect shocks to the policy variable in the VAR model to lead to statistically significant changes in the other variable.

To that end, let us consider the relationship between the St. Louis Source Base (SBASENS) and the Consumer Price Index (CPI), the Personal Consumption Expenditures Price Index (PCEPI) and the Industrial Production Index (INDPRO). Here is the natural log of SBASENS and CPI:

the natural log of SBASENS and PCEPI:

and the natural log of SBASENS and INDPRO from December 2008 through May 2015:

The following analysis is performed using a techniques developed by Toda and Yamamato (1995).

Using the Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests I find that the order of integration is one for all four series. I set up three two-equation VARs in the log levels of the data including an intercept for each equation.

Most information criteria suggest a maximum lag length of two for the pair of VARs that include the price level as a variable. The LM test suggests that there is a problem with serial correlation at this lag length, but this problem disappears when the lag length is increased to three in both of these VARs. The AR roots tables suggest that both VARs are dynamically stable at this lag length, and Johansen’s Trace Test and Maximum Eigenvalue Test both indicate the two pairs of series are not cointegrated at this lag length.

Most information criteria suggest a maximum lag length of four for the VAR that includes the industrial production index as a variable. The LM test suggests that there is no problem with serial correlation. The AR roots table suggests that the VAR is dynamically stable, and the Johansen’s Trace Test and Maximum Eigenvalue Test both indicate that the two series ** are** cointegrated at this lag length. This suggests that there must be Granger causality in at least one direction between the monetary base and industrial production.

Then I re-estimated the three level VARs with one extra lag of each variable in each equation. But rather than declare the lag interval for the two endogenous variables to be from 1 to 3, 1 to 4, and 1 to 5 respectively, I left the intervals at 1 to 3, 1 to 3, and 1 to 4, and declared the lag of each variable to be exogenous variables. Here are the Granger causality test results.

Thus, the results are as follows:

- I reject the null that CPI does not Granger cause the monetary base at the 5% significance level, and I reject the null that monetary base does not Granger cause CPI at the 1% significance level.
- I reject the null that PCEPI does not Granger cause monetary base at the 5% significance level, and I reject the null that monetary base does not Granger cause PCEPI at the 1% significance level.
- I reject the null that industrial production does not Granger cause the monetary base at the 5% significance level, and I reject the null that monetary base does not Granger cause industrial production at the 1% significance level.

In other words, there is strong evidence of bidirectional Granger causality between the monetary base and CPI, PCEPI and industrial production from December 2008 through May 2015. Moreover the evidence for Granger causality from the monetary base to CPI, PCEPI and industrial production is slightly stronger than the evidence for Granger causality from CPI, PCEPI and Industrial production to the monetary base.

The next step in this process is to determine the nature of this “correlation”. What does a shock to the monetary base lead to in terms of the price level and output? For example, does a positive shock to the monetary base cause the price level to decline (counterfactually) as the Neo-Fisherites seem to be claiming?

Or might it cause the price level to increase (counterfactually) as Monetarists claim? And what happens to output? In order to determine this we need to estimate properly specified VARs, and then to generate the appropriate Impulse Response Functions (IRFs).

For that, tune in next time.