Quantifying QE

QE – Why $85 Billion per Month? Why Not $170 or $42 -1/2 Billion?

by Paul Kasriel, The Econtrarian

Author’s warning: If you should choose to read this commentary, I recommend that you have ready a pot of coffee or your chosen type of cognitive stimulant. The commentary is lengthy and geeky.

Am I the only one who wondered how the Federal Reserve arrived at a figure of $85 billion as the amount of longer-maturity securities it planned to purchase per month in its third round of quantitative easing (QE)? Why not double that amount? Why not half that amount? How will the Fed know when it is time to “taper” its securities purchases? How will the Fed know by how much to taper? Inquiring minds want to know.

According to conventional wisdom, the rationale for QE is to bring down bond yields in order to stimulate the aggregate demand for goods and services, which, in turn, will bring down the unemployment rate. Implicit in this rationale for QE is the assumption that there is a negative relationship between the behavior of bond yields and the behavior of aggregate demand. That is, there is an assumption that a decrease in bond yields is associated with an increase in the growth of aggregate demand.

Because QE involves the Federal Reserve purchase of longer-maturity securities, also implicit in the rationale for QE is that the behavior of bond yields has a larger negative impact on the behavior of aggregate demand for goods and services than does the behavior of money market yields.

Before even getting into the issue of the amount of longer-maturity securities the Fed would need to purchase in the open market in order to reduce the Treasury bond yield or the conventional 30-year fixed mortgage rate by one basis point, let’s first check to see if the conventional-wisdom implicit assumptions behind QE are validated empirically. Namely, let’s check to see if, in fact, the behavior of bond yields has a greater influence on the behavior of aggregate demand than does the behavior of money market rates and that there is, in fact, a negative relationship between the behavior of bond yields and the behavior of aggregate demand.

Chart 1 shows that there is a high positive correlation, 0.89 out of a maximum possible 1.00, between the levels of the Treasury 10-year security yield and the overnight federal funds rate. So, in order to discern whether the behavior of bond yields has a greater effect on the behavior of aggregate demand than does the behavior of money market rates, we need some technique to disentangle the independent effects of the behavior of the interest rate on these two types of securities with different maturities. Fortunately, multivariate regression analysis provides such a technique. It enables us to test for the effect of the level of a bond yield on the behavior of aggregate demand independent of the effect of the level of a money market rate and the effect of a money market rate on the behavior of aggregate demand independent of the effect of the level of the bond yield.

Chart 1

The results of such a regression are presented in the table below. The dependent variable, RDOMPURCHYY, is the year-over-year percent change in real gross domestic purchases. The measure of real gross domestic purchases is the volume of currently-produced goods and services purchased by U.S. residents. This measure makes no distinction as to where the goods and services purchased were produced, domestically or abroad.

The two key independent variables, the variables upon which the behavior of changes in real gross domestic purchases depends are FFMOVAV4 (-1), the four-quarter moving average of the level of the federal funds rate, lagged one quarter and T10MOVAV4 (-1), the four-quarter moving average of the level of the Treasury 10-year security yield, lagged one quarter.

Because there is a lot of trend, or serial correlation, in the behavior of the year-over-year percent changes in real gross domestic purchases and this trend can distort the “true” value of the effects of the independent variables, the level of the federal funds rate and the Treasury bond yield, a correction for this trend (serial correlation) has been made and is represented by the AR(1) and AR(2) variables.

Let’s go through some of the results that bear on the implicit premises underlying Federal Reserve purchases of longer-maturity securities in executing QE. Firstly, notice the signs on the coefficients of the independent variables, the federal funds rate and the Treasury 10-year security yield. The sign on the coefficient of the federal funds rate is negative, indicating that there is a negative relationship between the level of the federal funds rate and percentage changes in real gross domestic purchases. Thus, after accounting for the effect of the Treasury 10-year security yield, a decrease in the level of the federal funds rate is associated with an increase in the percentage change in real gross domestic purchases. Nothing at odds with conventional wisdom in this result. But the sign on the coefficient of the Treasury 10-year security is positive, indicating that after accounting for the effect of the federal funds rate, a decrease in the level of the Treasury 10-year yield is associated with a decrease in the percentage change in real gross domestic purchases.

Uh oh. This is 180 degrees at odds with the conventional wisdom underlying the rationale for the Federal Reserve’s current purchases of longer-maturity securities. But how much confidence should we place in these findings? Statistically speaking, quite a lot. The far right column in the table with the heading “Prob.” presents the statistical probability that a coefficient is zero. Thus, the statistical probability that the coefficients on the federal funds rate and the Treasury 10-year security yield are zero are 0.00% and 1.16%, respectively.

Conversely, then, there is a high statistical probability that the federal funds rate and the Treasury 10-year security yield have an effect on real gross domestic purchases as indicated by their respective coefficients. The adjusted R-squared of 0.85 (rounded) indicates that 85% of the variance of the percentage changes in real gross domestic purchases is accounted for by the independent variables of the federal funds rate, the Treasury 10-year security yield, the constant term (C) and the two AR (serial correction) terms.

In my July 22nd commentary, “If the Fed Wants to Lower Bond Yields, Perhaps It Should Switch to QT”, I showed that since the Fed had begun engaging in QE, there had been a tendency for bond yields to rise, not fall. In this commentary, I have shown that rising bond yields are associated with faster growth in aggregate demand for goods and services. I would conclude from this that if QE works to stimulate aggregate demand, it works differently than the conventional-wisdom explanation.

In previous commentaries I have argued that QE can stimulate aggregate spending and explained how with an explanation that differs greatly from the conventional-wisdom explanation. Let me briefly re-iterate. The essence of QE can be found in its name – quantitative easing. The quantity referred to is the quantity of credit created figuratively out of “thin air”. Credit created out of thin air enables the borrower to increase his current spending whilst not requiring anyone else to simultaneously to decrease his current spending. Thus, an increase in credit created out of thin air would likely result in a net increase in nominal spending in an economy.

If you recall your undergraduate Money & Banking course, you were taught that in a fractional-reserve banking system, the banking system can create an amount of credit (loans and securities on its balance sheet) and simultaneously an amount of liabilities (deposits and other liabilities) that are some multiple of the amount of new “seed money” (cash reserves) created by the central bank (the Federal Reserve in the U.S.). Both the new seed money introduced by the central bank and the new credit extended by the banking system are created out of thin air. Hence, I have defined total thin-air credit as the sum of depository institution (commercial banks, S&Ls and credit unions) system credit and central bank credit.

My explanation of how QE works is that increases in Federal Reserve created thin-air credit augment depository institution system thin-air credit. Following the bursting of asset-price bubbles, depository institutions experience extraordinary loan losses that, in turn, greatly reduce their capital. The loss of capital prohibits depository institutions from creating normal amounts of thin-air credit. As a result, nominal aggregate spending in the economy contracts or remains weak.

If the central bank steps in to create more thin-air credit on its own to partially or wholly make up for the shortfall of normal thin-air credit creation by depository institutions, then aggregate nominal spending will be boosted. In my explanation of QE, the maturity of securities purchased by the central bank is, at best, of only secondary import. What is of primary importance to the effectiveness of QE in stimulating nominal aggregate spending is the quantity of thin-air credit created by the central bank.

Let’s look at some empirical evidence related to my unconventional explanation as to how QE works. Plotted in Chart 2 are year-over-year percent changes in quarterly observations of nominal gross domestic purchases, credit created by depository institutions (DIs) and the sum of DI credit and securities holdings by the Federal Reserve (including the securities held via repurchase agreements). Both DI credit and the credit sum are lagged one quarter.

Correlation coefficients (r) between pairs of the variables are reported in the bottom portion of the chart. The highest correlation coefficients between nominal gross domestic purchases and the credit aggregates were obtained with the credit aggregates lagged one quarter. This is prima facie evidence that the behavior of these credit aggregates leads the behavior of nominal gross domestic purchases. There is not much difference in magnitude of the correlation coefficients of the two credit aggregates with respect to nominal gross domestic purchases, 0.64 for depository institution credit and 0.65 for the sum of depository institution credit and Fed securities holdings. But we would not expect much difference in these respective correlation coefficients inasmuch as the correlation coefficient between the two credit aggregates is 0.92.

Notice that the behavior of the two credit aggregates only differ significantly after the onset of the recent financial crisis. Of course, this was the first time in the post-WWII era in which QE was used. The fact that the credit sum has generally grown faster than depository institution credit alone starting in mid 2009 likely accounts for the marginally-higher correlation coefficient between nominal gross domestic purchases and the credit sum.

Chart 2

Another way to examine the effect of QE on aggregate demand is to run two separate linear regressions with the behavior of nominal gross domestic purchases as the dependent variable and the behavior of depository institution credit alone as the independent variable in one regression and the behavior of the sum of depository institution credit and Fed securities holdings as the independent variable in the second regression. Then we want to examine the residuals – the actual year-over-year percent change in nominal gross domestic purchases minus the year-over-year percent change in nominal gross domestic purchases predicted by each credit aggregate. Residuals from both of these regressions are plotted in Chart 3.

Chart 3

Not surprisingly, for reasons given above in the discussion of the correlation coefficients, the residuals from both of these regressions are very similar in direction and magnitude up until about the beginning of 2010. Starting in 2010 through Q1:2012, the residuals for the regression with depository institution credit are consistently positive, meaning that the actual changes in nominal gross domestic purchases consistently exceed the changes predicted by the behavior of depository institution credit. There was less consistency in the sign of the residuals in the regression with the sum of depository institution credit and Federal Reserve holdings of securities as the independent variable.

From Q1:2010 through Q1:2013, the average value of the residual for the regression using depository institution credit as the independent variable was plus 1.32 percentage points, meaning that, on average, the actual change in nominal gross domestic purchases was 1.32 percentage points above what was predicted by the behavior of depository institution credit alone. Thus, from Q1:2010 through Q1:2013, percentage changes in depository institution credit tended to underpredict percentage changes in nominal gross domestic purchases, indicating that the behavior of aggregate demand was being affected by something other than the weak growth in depository institution credit.

In contrast, during this same time period, the average value of the residual for the regression using the sum of depository institution credit and Federal Reserve holdings of securities as the independent variable was minus 0.38 percentage points, meaning that, on average, percentage changes in the sum of DI credit and Fed holdings of securities tended to overpredict changes in nominal gross domestic purchases by 0.38 percentage points.

But the underprediction of aggregate demand growth by the growth (or lack thereof) in depository institution credit was 3.5 times as large as the overprediction by the growth in the sum of DI credit and Fed holdings of securities.

From Q1:2010 through Q1:2013, the average absolute value of the residual in the regression with depository institution credit alone as the independent variable was 1.95 percentage points. For this same period, the average absolute value of the residual in the regression with the sum of depository institution credit and Federal Reserve holdings of securities as the independent variable was only 0.75 percentage points. Thus, during this period of on-again and off-again QE, the prediction errors of depository institution credit growth alone with respect to aggregate demand growth were 2.6 times larger than the prediction errors of the sum of DI credit and Fed holdings of securities. Thus, the behavior of the sum of depository institution credit and Fed holdings of securities does a 2.6 times better job of predicting the behavior of gross domestic purchases than does the behavior of depository institution credit alone during this period of on-again and off-again QE.

The relatively high correlation between changes in aggregate demand and lagged changes in the sum of depository institution credit and Fed credit from the second half of 1953 through early 2013 and, in particular, the behavior of the residuals from early 2010 through early 2013 in the regression with sum of depository institution credit and Federal Reserve securities holdings strongly suggest that QE not only works, but works via the total quantity of thin-air credit.

Now, what is the subject of this commentary? Oh yes. The next time you encounter a Fed official, ask him/her how he/she decided on $85 billion per month as the quantity of securities to purchase per month.

If you don’t happen to encounter a Fed official but me instead, here is how I would answer you. Given that historically there has been a relatively close and robust positive relationship between lagged growth in the sum of depository institution credit and Fed holdings of securities, including those securities obtained via repurchase agreements, and growth in nominal domestic purchases of goods and services, I would humbly suggest to the Fed that it vary its securities purchases in accordance with trying to hit some target rate of growth in the aforementioned credit sum. When the credit sum is growing below its targeted rate, the Fed should step up its securities purchases by the amount of the target shortfall. When the credit sum is growing above its targeted rate, the Fed should cut back on its purchases of securities or sell securities by the amount of the target overshoot.

What should be the target rate of growth in the sum of depository institution and Fed credit? Chairman Bernanke could put his stable of crack economists to work on answering this question. But for starters, I can tell them that from Q2:1953 through Q1:2013, both the average and median year-over-year percent change in quarterly observations of the sum of depository institution credit and Fed holdings of securities has been 7.3%.  In Q1:2013 vs. Q1:2012, this credit aggregate was up by 5.15%.

One last comment. On Wednesday, July 31st, the Commerce Department will rewrite economic history by releasing revised estimates of gross domestic product and related series back to 1929. From press reports, these revisions will be significant. So, I guess I will have to redo all of the empirical tests conducted in this commentary. Oh well, I am almost finished watching the first season of “Orange Is the New Black”. So, I will have the time.