July 30, 2013
QE – Why $85 Billion per Month? Why Not $170 or
$42 -1/2 Billion?
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.
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Dependent Variable: RDOMPURCHYY
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Method: Least Squares
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Sample (adjusted):
1955Q1 2012Q1
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Included observations:
229 after adjustments
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Convergence achieved
after 12 iterations
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Variable
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Coefficient
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Std. Error
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t-Statistic
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Prob.
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FFMOVAV4(-1)
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-0.865007
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0.202015
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-4.281906
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0.0000
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T10MOVAV4(-1)
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0.704561
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0.276920
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2.544281
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0.0116
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C
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3.133550
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1.333620
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2.349657
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0.0197
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AR(1)
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1.225264
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0.063347
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19.34222
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0.0000
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AR(2)
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-0.334641
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0.063349
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-5.282516
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0.0000
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R-squared
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0.856139
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Mean dependent var
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3.054274
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Adjusted R-squared
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0.853570
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S.D. dependent var
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2.372628
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S.E. of regression
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0.907913
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Durbin-Watson stat
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2.068330
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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.
Paul
L. Kasriel
Econtrarian,
LLC
http://www.the-econtrarian.blogspot.comSenior
Economic and Investment Advisor
Legacy
Private Trust Co. of Neenah, Wisconsin
1-920-818-0236
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