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MACROECONOMIC MODELS AND THE
TERM STRUCTURE OF INTEREST RATES
Steven Strongin
Working Paper Series
Macro Economic Issues
Research Department
Federal Reserve Bank of Chicago
August, 1990 (WP-90-14)
Macroeconomic Models and the Term Structure
of Interest Rates
Steven Strongin*
This paper examines the relationship between the term structure of interest
rates and the macroeconomy. It does so by examining the ability of the term
structure to forecast various economic variables. In this, it follows Fama
(1990), Mishkin (1990), Hardouvelis (1988), and Bemanke (1990). However,
in those papers the questions about forecasting were asked in a pure
forecasting context, where in this paper the term structure's forecasting ability
is used to analyze the underlying macroeconomic determinants of the term
structure. Thus it attempts to provide some information about how asset
models and macroeconomic models may relate to one another.
The power of the approach in the current application is derived from the fact
that fairly clean hypotheses about what various shapes of the term structure
should forecast can be derived from most macroeconomic models and these
hypotheses fall broadly into three categories: Simple Fisher models with a
constant real interest rate, technology shock models, and models where
monetary policy can temporally distort the real cost of funds. The key point is
that if the term structure is determined in a way consistent with a given type of
model then the forecasting relationships that that class of model predicts for
the term structure will in fact be observed in the data, and conversely if other
factors are the key determinants of the term structure we will observe different
forecasting relationships than those implied by the model.
Clearly, such a methodology requires that the various classes of models give
very different predictions about the relationship of the term spread and
economic observables and that the term-spread in turn has clear and precise
forecasting relationships that are reasonably robust to the inclusion of
additional variables. This is in fact the case. Further, a number of interesting
stylized facts are suggested by the empirical results about the transmission
channels of monetary policy, but these will be addressed later.
*The author wishes to thank Marty Eichenbaum, Ken Kuttner, Bob Laurent, Prakash Loungani,
and Mark Watson for their helpful comments and suggestions. Also Bob King and Surgio Rebelo
for conversations which helped crystalize these ideas.
FRB CHICAGO Working Paper
August 1990, WP-1990-14
I
The issue of the determinants of the yield curve and the resulting
interpretation of the term spread which in this paper is measured as the
difference between the 10 year constant maturity yield to maturity on treasury
bonds and the Federal funds rate, is especially interesting at this time because
of its recent use in forecasting applications by Stock and Watson (1989),
Laurent (1988), and Bemanke (1990) and the attention it has been receiving in
monetary policy debates. The reason for the interest is not mysterious. As
Graph 1 shows, the term-spread's relationship to the real economy is dramatic.
It has inverted before every recession in the last 40 years and gone strongly
positive before every expansion.
F igure 1
Real GNP and the Spread
basis points
billions of dollars
This paper will first examine the three broad classes of models discussed
above to see what they predict about the term-spread's forecasting abilities
and then uses a series of VAR models to look at the actual forecasting
FRB CHICAGO Working Paper
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2
properties of the term-spread and compare the resulting Granger tests, impulse
response functions and decomposition of variances in light of the predictions
of the three types of models.
In general, the results point strongly to the conclusion that while technology
shocks and Fisher type effects cannot be ruled out, it would appear that
monetary policy or some other factor capable of generating short-term
disturbances in the supply of credit, such as innovations in the intermediation
process appears to dominate the term-spread. Thus, the current use of the
term-spread as a measure of monetary policy would appear to be justified and
that pure technology models are unlikely to be able to explain asset price
behavior. In this the results are consistent with Mankiw and Miron (1986),
Mankiw (1986), Strongin and Tarhan (1990) and Tarhan (1990) which all
find clear evidence of Federal Reserve impact on the term structure especially
in the short end.
The paper is in 4 sections. The first is a review of the relevant models and
their predictions. The second examines a set of bivariate VAR results where
the relationship of the term-spread to future economic activity is explored.
The third covers some additional direct tests on the term structure suggested
by the forecast results. The final section examines some additional robustness
tests to understand how sensitive the previous results are to sample choice and
to the presence of an alternative interest rate spread concept.
I. Three classes of macroeconomic models
Constant Real Rate Models
Simple Fisher equation models have the longest history. In these models the
real interest rate is constant and the Fisher equation reduces to a simple
relationship between nominal rates and inflation. This view probably is best
exemplified by Fama (1976) in his work on interest rates as a predictor of
short-run inflation. The cornerstone of these models is their strong
assumption about the time path of real interest rates.
The justification for this assumption normally follows from some combination
of two arguments. First, the variability in the marginal product of capital is
extremely small in comparison with the variability in inflation expectations.
Second, the Federal Reserve cannot affect the real cost of credit because the
markets will arbitrage the excess credit away. With a constant real rate, it
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follows trivially that nominal rates minus a constant are the market’s
expectation of inflation.
The implications for these types of models for the term-spread are quite
simple. A positive term-spread (i.e. when long rates are significantly higher
than short rates) will imply that inflation will be higher in the far future then
in the near future. In the context of a VAR model there are no predictions
about real quantities, but there should be a tight relationship with inflation.
Second, the shape of the impulse response function from the term-spread to
inflation should be rising across time. The model has no implication about the
initial shape of the impulse response function which would depend on the
level of rates relative to current inflation and not on the term-spread.
Real Business Cycle Models
Real business cycle models in their early forms have similar implications for
the forecast relationship of the term-spread to inflation. In Long-Plosser
(1983) for example, real rates are determined by the formula
r = p + ^t-a
( 1)
where p is the discount rate, p is the expected future growth rate and a is a
risk adjustment. The intuition is that agents will equalize the relative
marginal utility of consumption across time based on their internal discount
rate, the growth of future output and a risk factor. Since none of these terms
is time dependent, real rates are constant, reducing to the previous case. This
type of result will hold in any model that either does not have capital or in
which capital adjusts in one period or less.
In more recent models, more interesting time paths for real rates are possible,
producing some potentially useful variance in the term-spread beyond
inflation. In these models, Christiano (1987), for example, the term structure
not only contains information about inflation but also about the marginal
product of capital. In general the intuition works as follows. A permanent
negative productivity shock lowers the equilibrium desired capital stock, this
in turn depresses the desire to invest until the capital stock falls to its new
equilibrium level. This means that the marginal product of capital (the
interest rate) is sharply reduced and then slowly rises to its long-run
equilibrium as the capital stock declines. Consumption is less effected
because part of the adjustment is smoothed by disinvesting. Thus, a positive
FRB CHICAGO Working Paper
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4
spread would be associated with high leisure periods with low investment,
consumption and output.
On the other hand, a temporary shock to productivity would lower
consumption primarily since the long-run value of capital is unaffected
(although there must be some short-run negative effects). In both cases
(transient and permanent shocks), the effect on consumption and investment is
unambiguously negative.
This point is extremely general to the class of neo-classical models in which
there are no credit market imperfections or liquidity constraints. This can be
seen mathematically from a simple example. (The general case is examined
in an appendix). In general, consumption has to follow an Euler equation of
the form:
U'(Ct) i m C t+1) = l+ rt
(2)
where rt is the riskless real interest rate and P is the rate of pure time
preference. If utility is taken as logarithmic of the form
£/ = Z ,
tflo g (C t)
(3)
Ct+ 1! $Ct = l+rt
(4)
then it follows that
Using the fact that log(l+r) approximates r when r is small, it follows that
rt = log( Ct+1) - log( Ct) - log($)
(5)
rt = Sc,+ 1-log($)
(6)
or more simply
where Act+j is the continuously compounded rate growth in consumption in
period t+1 .
Noting that the n period long rate is the average of the n one period rates, it
follows that
FRB CHICAGO Working Paper
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rNt ~ 1IN
Act+ i' l°8($)-
(7)
Thus, it follows that
rN f rl t = l l N f ^ i Act+iJ ' Act+1
(8)
where rjt is the one period rate at time t. This says that if Act+j , next
period's growth, is higher than average future consumption growth there will
be a negative spread. Thus, for any model of this type a negative spread will
be associated with high next period growth in consumption, which would then
fall over time back to equilibrium growth levels. The only conditions in
which this would not be the case is where consumption continued to grow at
ever faster rates (in any damped process the contrary case reverts in short
order as consumption growth nears its peak). Sims (1980) discusses this case
as plausibly holding at a point in time for a two year time span. To avoid
potential problems with this pleasant, but not very realistic possibility, only
very long spreads are examined although the results turn out to be insensitive
to this. (It should also be noted that if this was a significant problem it would
imply impulse response function that sloped upward for significant periods of
time rather than dampening as those estimated later in the paper.)
Thus, in this class of models using the Christiano model as a exemplar, the
term-spread would Granger cause output, consumption and investment. The
association would be that a positive spread would forecast falling growth and
declining investment. Again, it would allow for the inflation effects outlined
in the constant real interest rate case, but would suggest that the inflation
relationship might be considerably looser than would be expected in the
simple Fisher model.
Monetary Distortion Models
The third type of model is the monetary distortion model. In this class of
model the Central bank has the ability to depress the real cost of funds and
thus create a distortion in the term structure away from expectations. ( This
could also be modeled as an innovation process in the financial sector, but
such a distinction is mostly a matter of semantics.) There are a variety of
models of this sort, including a large number of Keynesian (Rotemberg 1987)
and cash-in-advance models (Svensson 1985); however a series of recent
papers, Grossman and Weiss (1983), Rotemberg (1984), Baxter, Fisher, King,
and Rouwenhorst (1990) and Fuerst (1990) provide a very clear notion of the
underlying economics of what makes a monetary distortion model different.
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These models are all cash-in-advance although the specific structure beyond
that differs widely. The commonalty derives from the fact that all of these
models focus on the notion that rigidities create circumstances where an influx
of cash into the economy creates temporarily low interest rates and cheap
goods. Agents arbitrage these conditions by buying goods.
In this class of cash-in-advance model, the central bank is able to create cheap
cash i.e. a temporary reduction in the real rate of interest. But only certain
individuals have access to this cash and are constrained from selling it to other
agents. As a result they can only arbitrage the Central Bank action by buying
goods. Thus, a failure in credit market arbitrage produces arbitrage
possibilities in the goods market. In such models, a positive spread is
associated with positive growth centered in consumption, i.e. temporally
cheap credit causes consumption.
None of these models contain a durable good. Although technically difficult,
adding durable goods would have fairly obvious implications. Durables
would provide a superior method of arbitrage since durable goods would
allow agents to spread the value of cheap cash over a number of periods. This
is a straight forward implication of the permanent income hypothesis. Thus
when applied to data these types of models would predict that a positive
spread would be associated with increased consumption, especially durable
goods consumption. Investment would not be the primary channel of effect
since the long-run marginal product of capital is largely unaffected1.
Thus, if monetary distortion factors are dominate in the formation of the term
structure, Granger tests would show that the term-spread causes GNP and
consumption, with a very sharp positive spike in the impulse response
function for durables goods in response to a positive innovation in the spread
(opposite of the sign for RBC models). There might also be a causal link to
inflation and investment, but with much weaker results than the previous
models would suggest.
Identical results are available from a large class of models, the cited models
provide useful examples because of their focus on the role of the goods
markets to arbitrage market rigidities as opposed to the productivity shock
models where the credit markets simply reflect the time path of the marginal
product of capital. The key point mathematically is that the Euler equations
used above no longer fully describe the agents maximization problem. The
monetary distortion makes goods seem temporarily cheap causing agents to
FRB CHICAGO Working Paper
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shift consumption into the "cheap" period. This follows directly from the first
order conditions
Cf+7 / PQ “ ^ +rt
(9)
If rt is reduced by Federal Reserve action, cash is purchased and then used to
buy goods. The one trick to remember in comparing this to previous models
is that in a cash-in-advance model the asset market opens at the beginning of a
period and then closes and only then does the goods market opens. In the
current context, the dating would be better thought of as the asset market
operating at the end of the period and the goods market the beginning of the
next period. Thus, equation 9 should be rewritten
c t+2 1Pc t+l “ 1^rt
( 10)
A one period drop in rt implies a rise in Ct+j since Ct+2 should be largely
unaffected by a one period drop in interest rates. The only effects on Ct+2
would arise from an increase in the capital stock resulting from lower interest
rates and this, besides being small, would only reinforce the effect on Ct+j.
Thus, as noted before, a Central Bank action which drove rt down would drive
both rt + 1 - rt and Ct+i - Ct up. In some models, of course, the effects would
linger. In any case, the maximum effect on interest rates coincides with the
one period forward maximum effect on consumption, i.e. the cheapest cash
generates the biggest consumption bulge in the subsequent purchase period.
In this class of model, the impulse response path beyond the initial impact
would hinge critically on persistence of the innovation in the term spread, the
more persistent the innovation in the spread the smoother and more prolonged
the consumption response; however, without a precise model of the
determination of the term spread very little can be stated generally about this.
Summary of predictions
Thus, the three classes of models provide significantly different hypotheses
about the relationship of the term-spread to various real and nominal
variables. To summarize, constant real rate models, including some simple
real business cycle models, imply that the term structure should forecast
inflation tightly. More recent productivity shock (real business cycle) models
suggest that the term-spread may be able to forecast GNP, investment, and
consumption, with a positive spread forecasting negative growth in all three.
Monetary distortion models would, on the other hand, imply that a positive
term-spread would forecast rising consumption and GNP, the opposite of the
FRB CHICAGO Working Paper
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real business cycle model, and further that there should be a sharp spike in
consumption, especially durables consumption. No general predictions about
investment are possible beyond the general notion that a reduction in GNP
and consumption is probably bad for investment.
It should be noted that the tests of these hypotheses are not tests of the
models, but tests of what types of factors are influencing the term structure.
Thus, the evidence that follows which suggests that the monetary model is
most consistent with the data should be interpreted as saying that monetary
factors are very important for the term structure not that monetary models are
right and real business cycle models are wrong. By running the tests through
the term-spread's ability to forecast, other channels of impact are ignored.
However, to the extent that the forecasting relationships are significant, it
would also indicate that monetary factors do have some implications for real
activity. Also no implications can be drawn from these results about the
stability the relationship between the term-spread and real output and in fact
given the extremely different implications from the three classes of models
some caution would be indicated.
n. Bivariate results
The definitions of the tested series do not precisely follow normal national
income accounting but are divided by type of decision agent. Thus,
consumption is defined as personal consumption expenditures plus residential
spending. Durables is durables consumed by consumers and is defined as the
sum of durables plus residential housing. Non-durables is non-durables plus
services. Investment is non-residential fixed investment. The definitions are
set up this way to more closely parallel the models discussed above. The CPI,
both complete and less food and energy and the fixed weight GNP deflator are
used to measure inflation. The term spread is defined as the simple difference
between the 10 year constant maturity treasury bond yield and the Federal
Funds rate The ten year bond has the longest continuous history. Laurent
(1989) used a spliced series of 20 and 30 year bond yields; this provides
slightly stronger results than those presented, but the spliced series raises
some questions about comparability across time periods. Alternate definitions
have little impact on the results. The data sample runs from the first quarter
of 1963 to fourth quarter of 1989. All impulse response functions and
decompositions of variances are calculated with the term spread as the last
variable in the ordering. All variables except for the interest rate spreads are
log rates of change.
FRB CHICAGO Working Paper
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Graphs 2-9 show the impulse response functions for each of the bivariate
VARs with 4 lags. Table 1 shows the Granger tests, the
and the
decomposition of variance at lag 4 and 20 for the output or price variable, as
well as the contemporaneous correlation of errors.
At least at this level the results are extremely clear. There is clear evidence
that there is a substantial forecasting relationship between the term-spread and
output and that relationship closely follows the predictions of the monetary
distortion class of models. The effect is focused in consumption and is
sharpest in durables exactly as the monetary distortions models would predict.
In terms of the productivity shock models, the signs are all wrong and
investment effect is relatively weak. In terms of testing the sign of the
impulse response function for statistical significance, the term spread
generates such a simple pattern of impact that a direct test is possible.
Basically all of the explanatorily power in the consumption cases is in the first
lag of the spread which has a t-statistic of at least 4 regardless of lag structure
and specific consumption measure and is positive. In the GNP case the t
bottoms out around 2.5. Single equation term-spread specifications strongly
reinforce this result. This is also consistent with the cross section literature on
Euler equations and consumption, for example, Mankiw, Rotemberg and
Summers (1985).
F igure 2
Plot of Responses of GNP*
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Figure3
Plot of Responses of Consumption*
Figure 4
Plot of Responses of Durables*
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Figure5
Plot of Responses of Nondurables4
F igure 6
Plot of Responses of Investm ent4
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Figure7
Plot of Responses of CPI*
0
2
4
6
8
10
12
14
16
18
*The response to a one standard deviation shock in the labeled variable.
Figure 8
Plot of Responses of CPI Less Food and Energy*
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Figure9
Plot of Responses of GNP Fixed-Weight Deflator*
"The response to a one standard deviation shock in the labeled variable.
The weakness of the inflation forecasts are striking. The term-spread seems to
have much less to do with inflation than standard discussions would suggest
although these results are quite consistent with the literature which has had
some difficulty in pinning down the relationship between interest rates and
inflation. On the other hand, it is only in the price equations that any evidence
of reverse or contemporaneous causation shows up. It would seem that the
Federal Reserve responds to inflation especially to inflation once food and
energy prices have been removed and does so in a manner to control output.
The results are not inconsistent with the Fisher effect, they simply indicate
that the bulk of the variance in the term-spread lies in the real cost of funds.
The results are stable with respect to lag lengths. In fact, the results are even
sharper if the lag length is reduced, but the 4 lag models were presented so
that the more diffuse relationships with prices and investment would also
show through.
FRB CHICAGO Working Paper
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T a b le 1
Bivariate VAR Resuits
Y
G rander F tests
Y -> Spread
Spread -> Y
Term -spread's
Contem porDecom positlon of Y's aneous
forecast variance correlation
Y ’s R2
Lag 4
Lag 20
Y, spread
A GNP
8.5
(0.0000)
1.3
(0.2741)
.34
20.62
29.71
-.11
A Consumption
12.3
(0.0000)
1.5
(0.2211)
.45
37.31
42.32
.03
A Durables
12.9
(0.0000)
2.16
(0.0786)
.40
33.88
36.83
-.00
A Non-durables
4.0
(0.0048)
2.5
(1.2)
.27
13.70
19.23
.00
A Investment
5.2
(0.0007)
0.26
(0.90)
.20
14.53
17.95
-.19
ACPI
2.9
(0.0299)
1.7
(0.1644)
.78
9.65
7.38
-.31
3.2
(0.0148)
2.2
(0.0733)
.74
22.39
27.28
-.43
1.3
(0.2626)
2.3
(0.0630)
.75
5.57
3.96
-.25
A CPI Less Food
& Energy
A FW Deflator
Note: P-value in parentheses
Results on individual sectors and other break-downs of the national income
accounts are consistent, but not presented for brevity's shake.
Thus, it would appear that at least from the bivariate results that monetary
distortions of some type are significant in the determination of the yield
spread.
FRB CHICAGO Working Paper
August 1990, WP-1990-14
15
HI. Some other tests
The above results, if interpreted as indicating that we are observing a
monetary policy transmission process, suggest a number of simple trivariate
tests to explore the nature and usefulness of the term-spread as a measure of
monetary policy.
First, is whether this is purely a consumption based channel. In the above
results, while the investment response was weaker and delayed it is still
significant. However, the investment relationship might be the product of
consumption producing higher cash flows for corporations (Petersen and
Strauss, 1989, Fazzari, Hubbard and Petersen, 1988). If this is the case then a
three variable VAR with consumption, investment and the term-spread would
show that the term-spread has no direct relationship with investment. Table 2
shows the Granger tests and they are consistent with the term-spread acting
entirely through consumption.
The other set of obvious tests is to include money growth and examine if the
term-spread might have any advantages over money as a measure of policy.
These tests are not meant to be complete, but simply to explore if the termspread deserves serious consideration as a measure of monetary policy.
T a b le 2
Trivariate VAR Results
Term -spread's
Contem porDecom position o f
aneous
Y's forecast variance correlation
A Consumption
13.3
(0.0000)
A Investment
1.1
(0.3467)
*
V
■<
Spread -> Y
O
G ranger F tests
Y
NA
NA
4.71
(0.0040)
Y's R2
Lag 4
Lag 20
Y, spread
.46
32.23
37.66
.02
.28
11.08
15.16
-.1 9
Note: P-value in parentheses
FRB CHICAGO Working Paper
August 1990, WP-1990-14
16
Table 3 shows the results for three variable VARs with Ml and M2 paired
with either output or consumption. Graph 10 shows GNP's impulse responses
for the Ml model, other models are largely the same. The results indicate that
the term-spread appears to strongly dominate money in forecasting real
activity. The term-spread retains virtually all of its explanatory power and its
impulse response function is largely unaffected even when placed last in the
orthogonalization. Second, the large difference between contemporaneous
correlations for money and the term-spread in the consumption VARs
indicates that the term-spread may be subject to fewer contemporaneous
correlation problems than money and thus serve as a cleaner policy
instrument. At the very least this suggests that with the data for the 1980s and
new functional forms for interest rates, the Sims (1980) and Litterman and
Wiess (1985) debate may need re-examination.
T a b le 3
Trivariate VAR Results with Money
Test
Granger F-test
M -> Y
Spread -> Y
R2
Decomposition
of Variance for Y
Lag 4, money
Lag 20, money
Lag 4, spread
Lag 20, spread
Contemporaneous
correlations
Money, Y
Spread, Y
GNP, M1
VAR Specification
GNP, M2
C, M1
C, M2
0.6
(0.6128)
6.9
(0.0001)
.35
0.2
(0.92)
6.0
(0.0002)
.34
2.47
(0.0497)
12.7
(0.0000)
.50
1.0
(0.38)
9.4
(0.0000)
.48
2.6
7.7
18.0
25.0
1.4
2.0
20.6
30.7
5.7
13.6
33.9
35.2
3.4
5.0
35.2
41.2
0.00
-0.14
-0.01
-0.11
0.33
0.00
0.26
0.04
Note: P-value in parentheses
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Figure 10
Plot of Responses of GNP*
*The response to a one standard deviation shock in the labeled variable.
IV. Testing robustness
Taken as a pure exercise, it is actually unnecessary to test the robustness of
the bivariate results. The models indicate that there should be a bivariate
relationship between the term-spread and other variables and do not in fact
suggest anything about the stability of the relationship or robustness to the
inclusion of other variables. However, given the strength of the bivariate and
trivariate results and the current use of the term-spread in various forecasting
and policy applications it would seem to be useful to examine a few more
systems and sub-sample stability to get a sense of how robust these results are.
Primarily the worry would be that the term-spread is capturing some type of
market forecast about risk, i.e. it is conceivable that a positive spread means
the current environment is less risky that the future therefore agents might
concentrate activity in the current period. Thus some control for risk
assessment may be in order. Recently, Friedman and Kuttner (1989) have
suggested just such a measure the Public-Private spread which is defined as
the difference between the 6 month commercial paper rate and three month
treasury bill rate.
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The Public-Private spread provides an especially nice test in the current
context because it is also a market spread, but one focused on the market's
assessment of risk as opposed to distortions in the term structure, thus if the
term-spread is somehow picking up some kind of market forecast about future
risk instead of a monetary policy induced distortions then the Public-Private
spread should generate substantial instability in the impulse response
functions and reduce the overall explanatory power of the term-spread
considerably. In fact in Bemanke (1990) the Public-Private spreads seems to
dominate the term-spread to which Bemanke gives the interpretation that the
Public-Private spread is a superior measure of monetary policy.
Table 4 shows the Granger tests and decomposition of variance for systems
where the Public-Private spread is added to the VAR specification and when it
is not. Both the Public-Private spread and the term-spread fair well, although
the term-spread clearly dominates. This would seem to strongly contradict
Bemanke's (1990) result although he did not examine their joint performance.
The impulse response function from the term-spread to output and
consumption is unaffected by the Public-Private spread or money and the
impulse response graphs look just like the previous graphs as is shown in
Graph 11.
Additional tests on larger systems were done and provide
consistent evidence but with reduced power.
T a b le 4
Trivariate VAR Results with Public-Private Spread
Test
GNPwoP-P
GNP w P-P
C wo P-P
Cw P-P
NA
NA
8.5
(0.0000)
.34
2.8
(0.03)
4.9
(0.0013)
.40
NA
NA
12.33
(0.0000)
.45
2.8
(0.0311)
9.4
(0.0000)
.51
NA
NA
20.6
29.7
8.5
10.5
16.2
27.6
NA
NA
37.3
42.3
3.4
5.0
30.8
34.6
NA
-0.11
NA
-0.13
-0.07
-0.23
NA
0.04
NA
-0.15
0.07
-0.25
Granger F-test
>-
A
1
CL
1
CL
T-Spread -> Y
R2
Decomposition
of Variance for Y
Lag 4 P-P
Lag 20 P-P
Lag 4 T-spread
Lag 20 T-spread
Contemporaneous
correlations
P-P, Y
T-Spread, Y
T-Spread, P-P
Note: P-value in parentheses
FRB CHICAGO Working Paper
August 1990, WP-1990-14
19
Figure 11
Plot of Responses of GNP*
Sub-sample tests on parameter stability are presented in Table 5 and show no
evidence of instability. The test are joint F-tests on whether the parameters on
the term-spread would vary in the bivariate case if the sample was broken in
the first quarter of 1976, other break points offer similar evidence of stability.
No formal tests were done on the more complicated VARs, since there are
some well known instabilities in the money-income relationship. A few sub
sample VARs were performed and showed substantial instability, although
this has very little bearing on the present question. There is also some
instability in sub-sample R^s with the later periods showing higher
explanatory power, but this may simply reflect changes in activity of
monetary policy.
FRB CHICAGO Working Paper
August 1990, WP-1990-14
20
T a b le 5
Stability Tests on Term-Spread
Break at 76 q1
Y
A GNP
A Consumption
A Durables
F-test on Term -spread
param eter stability
1.35
(0.2558)
1.32
(0.2665)
0.89
(0.4724)
Note: P-value in parentheses
I should note that the inclusion of an interest rate in levels will have
significant impact, but this really does not provide any information, as it
primarily goes to the issue of functional form, which, at this point, without
substantial theory work directed at the term-spread is difficult to assess.
V. Conclusions
The results in this paper would point strongly to the fact that monetary policy
or some other aspect of supply function of credit needs to be taken seriously
as a determinate of the term structure. Further evidence is developed which
suggests that research into the term-spread as a measure of monetary policy is
not without merit. Lastly, since the goods markets seems to be paying an
important role in arbitraging these distortions it would appear that pure
financial models will have some difficulty accounting for the variance in the
term structure. It is unlikely that agents ability to arbitrage in the goods
market is constant through time.
FRB CHICAGO Working Paper
August 1990, WP-1990-14
21
Notes
1In some ISLM models investment is the primary respondent to interest rate
movements. Although due to the ad hoc nature of such models, it is not easy
to assess the rationale for this. I would argue that in light of recent work on
investment such models are unlikely to be of any practical import.
FRB CHICAGO Working Paper
August 1990, WP-1990-14
22
References
Baxter, Marianne, Stephen Fisher, Robert King, and K. Geert Rouwenhorst,
1990, The liquidity effect in general equilibrium, University of Rochester
Working Paper Series, forthcoming.
Bemanke, Ben S., 1990, On the predictive power of interest rates and interest
rate spreads, Federal Reserve Bank of Boston Review, forthcoming.
Christiano, Lawrence J., 1987, Why is consumption less volatile than
income?, Quarterly Review, Federal Reserve Bank of Minneapolis, Fall, 2-20.
Fama, E.F., 1975. Short term interest rates as predictors of inflation,
American Economic Review 65,269-282.
Fama, E.F., 1976. Forward rates as predictors of future spot rates, Journal of
Financial Economics 3, 361-377.
Fama, E.F., 1990, Term structure forecasts of interest rates, Inflation and real
returns, Journal of Monetary Economics 25, 59-76.
Fazzari, Steven M., R. Glenn Hubbard, and Bruce C. Petersen, 1988,
Financing constraints and corporate investment, Brookings Papers on
Economic Activity 1, 141-195
Friedman, Benjamin and Kenneth Kuttner, 1990, Money, income and prices
after the 1980's, Federal Reserve Bank of Chicago Working Paper, 90-11.
Fuerst, Timothy S., 1990, Liquidity, loanable funds, and real activity,
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Grossman, Sanford, and Laurence Weiss, 1983, A transactions-based model
of the monetary transmission mechanism., The American Economic Review
73, 871-880.
Hardouvelis, Gikas A., 1988, The predictive power of the term structure
during recent monetary regimes, Journal of Finance 43, 339-356.
Laurent, Robert D., 1988, An Interest Rate-Based Predictor of Monetary
Policy. Economic Perspectives, Federal Reserve Bank of Chicago,
January/February, 3-14.
Laurent, Robert D., 1989, Testing the 'Spread', Economic Perspectives,
Federal Reserve Bank of Chicago, July/August, 22-34.
FRB CHICAGO Working Paper
August 1990, WP-1990-14
23
Litterman, Robert B. and Lawrence M. Weiss, 1985, Money, Real Interest
Rates, and Output: A Reinterpretation of Postwar U.S. Data, Econometrica,
January, 129-156.
Long, John B. Jr., and Plosser, Charles I., 1983, Real business cycles, Journal
of Political Economy 91, February: 39-69.
Mankiw, Gregory N., 1986, The Term Structure of Interest Rates Revisited,
Brookings Papers on Economic Activity 1 (Spring), 61-110.
______ and Jeffrey A. Miron, 1986, The Changing Behavior of the Term
Structure of Interest Rates, Quarterly Journal of Economics 101 May, 211-28.
_____ , Julio J Rotemberg, and Lawrence H. Summers, 1985, Intertemporal
Substitution in Macroeconomics, Quarterly Journal of Economics 399
February, 225-251.
Mishkin, F.S., 1990, What does the term structure tell us about future
inflation?, Journal of Monetary Economics 25,77-96.
Petersen, Bruce C. and William A. Strauss, 1989, Investment Cyclicality in
Manufacturing Industries, Economic Perspectives, Federal Reserve Bank of
Chicago, NovemberXDecember, 19-28.
Rotemberg, Julio, 1984, Monetary Equilibrium Model with Transactions
Costs Journal of Political Economy, 92,41-58.
Rotemberg, Julio, 1987, The New Keynesian Microfoundations, NBER
Macroeconomics Annual.
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Monetarism Reconsidered, American Economic Review, May, 250-57.
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FRB CHICAGO Working Paper
August 1990, WP-1990-14
24
Appendix
Using the Euler equation for time separable utility
U'(Ct)/m U '(C t+1) } = l+ r t
(1)
Taking logs and using the approximation that log(l+rt)=rt
logfU'(Ct)Hog®Hog(E{U'(Ct+1)}) = rt
or -Au'(Ct+j h log(b) = rt
(2)
where Au'(Ct+i) is the expected change in the log of expected utility.
This implies that rjqt, the n period rate can be expressed
rNt = -UN { 1 / Au'(Ct+i)} - log®)
(3)
which implies that
rNt - rlt = -1/N
Au'(C[+i) + Au'(Ct+1)
(4)
Thus, if the marginal utihty of consumption is expected to fall more in the
next period then in the average of future periods, the term spread will be
negative. It follows that if there is declining marginal utility of consumption
that a high growth quarter will follow a negative spread.
FRB CHICAGO Working Paper
August 1990, WP-1990-14
25
Research Staff Memoranda, Working Papers and Staff Studies
The following lists papers developed in recent years by the Bank's research
staff. Copies of those materials that are currently available can be obtained by
contacting the Public Information Center (312) 322-5111.
Working Paper Series
A series of research studies on regional economic issues relating to the
Seventh Federal Reserve District, and on financial and economic topics.
REGIONAL ECONOMIC ISSUES
The Effects of Usury Ceilings the Economic Evidence, 1982
*W P-8 2-1
D o n n a C ra ig V an denbrink
Small Issue Industrial Revenue Bond Financing in the
Seventh Federal Reserve District, 1982
**W P-82-2
D a v id R . A lla rd ic e
Natural Gas Policy and the Midwest Region, 1983
WP-83-1
W illiam A . T esta
Taxation of Public Utilities Sales: State Practices
and the Illinois Experience
WP-86-1
D ia n e F . S ieg e l a n d W illiam A. T esta
Measuring Regional High Tech Activity with Occupational Data
W P-87-1
A len ka S. G iese a n d W illiam A. T esta
Alternative Approaches to Analysis of Total Factor Productivity
at the Plant Level
W P-87-2
R o b e rt H . Sch n orbu s a n d P h ilip R . Isra ilev ic h
Industrial R&D An Analysis of the Chicago Area
W P-87-3
A len k a S. G iese a n d W illiam A . T esta
Metro Area Growth from 1976 to 1985: Theory and Evidence
WP-89-1
W illiam A . T esta
Unemployment Insurance: A State Economic Development Perspective
W P-89-2
W illiam A . T esta a n d N a ta lie A . D a v ila
♦Limited quantity available.
♦♦Out of print.
1
W orking p aper series continued
A Window of Opportunity Opens for Regional Economic Analysis:
BEA Release Gross State Product Data
W P-89-3
A len ka S. G iese
Determining Manufacturing Output for States and Regions
W P-89-4
P h ilip R . Isra ile v ic h a n d W illiam A . T esta
The Opening of Midwest Manufacturing to Foreign Companies:
The Influx of Foreign Direct Investment
W P-89-5
A len ka S .G iese
A New Approach to Regional Capital Stock Estimation:
Measurement and Performance
W P-89-6
A len ka S. G iese a n d R o b e rt H . S ch norbu s
Why has Illinois Manufacturing Fallen Behind the Region?
W P-89-7
W illiam A . T esta
Regional Specialization and Technology in Manufacturing
W P-89-8
A len ka S. G iese a n d W illiam A . T esta
Theory and Evidence of Two Competitive Price Mechanisms for Steel
W P-89-9
C h risto p h er E rceg , P h ilip R . Isra ilev ic h a n d R o b e rt H . S ch n orbu s
Regional Energy Costs and Business Siting Decisions:
An Illinois Perspective
W P-89-10
D a v id R . A lla rd ic e a n d W illiam A . T esta
Manufacturing's Changeover to Services in the Great Lakes Economy
W P-89-12
W illiam A . T esta
Construction of Input-Output Coefficients
with Flexible Functional Forms
WP-90-1
P h ilip R . Isra ile v ic h
Regional Regulatory Effects on Bank Efficiency
D o u g la s D . E v a n o ff a n d P h ilip R. Isra ilev ic h
*Limited quantity available.
**Out of print.
W P-90-4
W orking paper series continued
Regional Growth and Development Theory: Summary and Evaluation
W P-90-5
G eoffrey J D . H e w in g s
Institutional Rigidities as Barriers to Regional Growth:
A Midwest Perspective
W P-90-6
M ich a el K en d ix
ISSUES IN FINANCIAL REGULATION
Technical Change, Regulation, and Economies of Scale for Large Commercial
Banks: An Application of a Modified Version of Shepard’s Lemma
WP-89-11
D o u g la s D . E vanoff, P h ilip R . Isra ilev ic h a n d R a n d a ll C. M e rris
Reserve Account Management Behavior: Impact of the Reserve Accounting
Scheme and Carry Forward Provision
W P-89-12
D o u g la s D . E v a n o ff
Are Some Banks too Large to Fail? Myth and Reality
W P-89-14
G eo rg e G. K au fm an
Variability and Stationarity of Term Premia
W P-89-16
R am on P . D e G en n aro a n d J a m e s T. M o se r
A Model of Borrowing and Lending with Fixed and Variable Interest Rates
W P-89-17
T hom as M on d sch ea n
Do "Vulnerable" Economies Need Deposit Insurance?: Lessons from the
U.S. Agricultural Boom and Bust of the 1920s
W P-89-18
C h a rles W. C a lo m iris
The Savings and Loan Rescue of 1989: Causes and Perspective
W P-89-23
G eo rg e G. K au fm an
The Impact of Deposit Insurance on S&L Shareholders’Risk/Retum Trade-offs
W P-89-24
E lija h B r e w e r III
*Limited quantity available.
**Out of print.
3
W orking p aper series continued
Payments System Risk Issues on a Global Economy
W P-90-12
H e rb e rt L . B a e r a n d D o u g la s D . E v a n o ff
MACRO ECONOMIC ISSUES
Back of the G-7 Pack: Public Investment and Productivity
Growth in the Group of Seven
W P-89-13
D a v id A . A sch a u e r
Monetary and Non-Monetary Sources of Inflation: An Error
Correction Analysis
W P-89-15
K en n eth N . K u ttn er
Trade Policy and Union Wage Dynamics
W P -89-19
E llen R . R issm a n
Investment Cyclicality in Manufacturing Industries
W P -89-20
B ru ce C. P e te rse n a n d W illiam A. S tra u ss
Labor Mobility, Unemployment and Sectoral Shifts:
Evidence from Micro Data
W P-89-22
P ra k a sh L o u n gan i, R ic h a rd R o g e rso n a n d Y ang-H oon Sonn
Unit Roots in Real GNP: Do We Know, and Do We Care?
W P-90-2
L a w re n c e J. C h ristia n o a n d M a rtin E ich en bau m
Money Supply Announcements and the Market's Perception
of Federal Reserve Policy
W P-90-3
S teven Stron gin a n d Vefa T arhan
Sectoral Shifts in Interwar Britain
W P-90-7
P ra k a sh L ou n g a n i a n d M a rk R ush
Money, Output, and Inflation: Testing the P-Star Restrictions
W P-90-8
K en n eth N . K u ttn e r
♦Limited quantity available.
♦♦Out of print.
4
Current Real Business Cycle Theories and Aggregate Labor
Market Fluctuations
WP-90-9
L a w re n c e J. C h ristia n o a n d M a rtin E ich en bau m
The Output, Employment, and Interest Rate Effects of
Government Consumption
W P-90-10
S. R a o A iya g a ri, L a w re n c e J. C h ristia n o a n d M a rtin E ich en bau m
Money, Income, Prices and Interest Rates after the 1980s
W P-90-11
B en jam in M . F ried m a n a n d K en n eth N. K u ttn er
Real Business Cycle Theory: Wisdom or Whimsy?
W P-90-13
M a rtin E ich en bau m
Macroeconomic Models and the Term Structure of Interest Rates
W P-90-14
S teven Strongin
^Limited quantity available.
**Out of print.
5
Staff Memoranda
A series of research papers in draft form prepared by members of the
Research Department and distributed to the academic community for review
and comment. (Series discontinued in December, 1988. Later works appear in
working paper series).
Impact of Deregulation on the Mortgage Market, 1981
**SM -81-2
G eo rg e G. K au fm an
An Examination of the Conceptual Issues Involved in Developing Credit
Scoring Models in the Consumer Lending Field,"
**SM -81-3
A lan K . R e ic h e rt
A Critique of the Federal Reserve's New Operating Procedure, 1981
SM -81-4
R o b e rt D . L a u ren t
Banking as a Line of Commerce: The Changing Competitive Evnironment, 1981
" S M -8 1 -5
G eo rg e G. K au fm an
Deposit Strategies of Minimizing the Interest Rate Risk Exposure
of S&Ls, 1982
SM-82-1
H a rv e y R o sen b lu m
Implications of Deregulation for Product Lines and Geographical Markets
of Financial Instititions, 1982
*SM -82-2
G eo rg e K au fm an , L a rry M o te a n d H a rv e y R o sen b lu m
The Fed's Post-October 1979 Technical Operating Procedures:
Reduced Ability to Control Money, 1982
•SM -82-3
G eo rg e G. K au fm an
The Meeting of Passion and Intellect: A History of the term 'Bank'
in the Bank Holding Company Act, 1983
SM-83-1
John J. D i C lem en te
Comparing Alternative Replacements for Lagged Reserves:
Why Settle for a Poor Third Best? 1983
SM -83-2
R o b e r t D . L a u ren t
*Limited quantity available.
**Out of print.
6
S taff m em oranda continued
A Proposal for Federal Deposit Insurance with Risk
Sensitive Premiums, 1983
**SM-83-3
G. O. B ie rw a g a n d G eo rg e G. K au fm an
A Critical Appraisal of McKinnon's World Money Supply Hypothesis, 1983
SM -83-4
H e n ry N . G o ld ste in a n d Steph en E. H a yn es
The Future of Commercial Banks in the Financial
Services Industry, 1983
SM -83-5
G eo rg e G. K au fm an , L a rry M o te a n d H a rv e y R o sen b lu m
Bank Reserve Adjustment Process and the Use of Reserve Carryover Provision
and the Implications of the Proposed Accounting Regime, 1983
SM -83-6
V efa Tarhan
The Inclusion of Thrifts in Bank Merger Analysis, 1983
SM -83-7
John J. D i C lem en te
Financial Services in Transition: The Effects of Nonbank Competitors, 1984
SM-84-1
H a rv e y R o sen b lu m a n d C h ristin e P a v e l
The Securities Activities of Commercial Banks, 1984
SM -84-2
G eo rg e G. K au fm an
Consequences of Deregulation for Commercial Banking
SM -84-3
G eo rg e G. K au fm an, L a rry M o te a n d H a rv e y R o sen b lu m
The Role of Traditional Mortgage Lenders in Future
Mortgage Lending: Problems and Prospects
SM -84-4
G eo rg e G. K au fm an
The Problems of Monetary Control Under
Quasi-Contemporaneous Reserves
SM -84-5
R o b e r t D . L a u ren t
On Banks, Nonbanks, and Overlapping Markets: A Reassessment
of Commercial Banking as a Line of Commerce
SM-85-1
H a rv e y R osen blu m , M . K a th leen 0 B r ie n a n d Joh n J. D i C lem en te
*Limited quantity available.
♦Out of print.
7
S taff m em oranda continued
The Securities Activities of Commercial Banks: A Legal and
Economic Analysis
SM -85-2
T hom as G. F isch er, W illia m H . G ram , G eo rg e G. K au fm an a n d L a rry R. M o te
Implications of Large Bank Problems and Insolvencies for
the Banking System and Economic Policy
SM -85-3
G eo rg e G. K au fm an
The Impact of Deregulation on the True Cost of Savings Deposits:
Evidence From Illinois and Wisconsin Savings & Loan Association
SM -85-4
E lijah B rew e r, III
Financial Darwinism: Nonbanks - and Banks - Are Surviving
SM -85-5
C h ristin e P a v e l a n d H a rv e y R o sen b lu m
Variable-Rate Loan Commitments, Deposit Withdrawal Risk, and
Anticipatory Hedging
G. D . K o p p e n h a v e r
A Note on Managing Deposit Flows with Cash and Futures Market Decisions
G. D . K o p p e n h a v e r
SM -85-6
SM -85-7
Regulating Financial Intermediary Use of Futures and Option
Contracts: Policies and Issues
G. D . K o p p e n h a v e r
SM -85-8
The Impact of Branch Banking on Service Accessibility
SM -85-9
D o u g la s D . E v a n o ff
Risks and Failures in Banking: Overview, History, and Evaluation
SM-86-1
G eo rg e J. B en sto n a n d G eo rg e G. K au fm an
The Equilibrium Approach to Fiscal Policy
SM -86-2
D a v id A la n A sch a u e r
^Limited quantity available.
♦Out of print.
8
S taff m em oranda continued
Banking Risk in Historical Perspective
SM-S6-3
G eo rg e G. K au fm an
The Impact of Market, Industry, and Interest Rate Risks
on Bank Stock Returns
E lija h B r e w e r , III a n d C h en g F e w L e e
Wage Growth and Sectoral Shifts: New Evidence on the
Stability of the Phillips Curve
SM -86-4
SM-87-1
E llen R . R issm an
Testing Stock-Adjustment Specifications and
Other Restrictions on Money Demand Equations
SM -87-2
R a n d a ll C. M e rris
The Truth About Bank Runs
SM -87-3
G eo rg e G. K au fm an
On The Relationship Between Standby Letters of Credit and Bank Capital
SM -87-4
G a ry D . K o p p e n h a v e r a n d R o g e r S to ve r
Alternative Instruments for Hedging Inflation Risk in the
Banking Industry
SM -87-5
G a ry D . K o p p e n h a v e r a n d C h en g F. L e e
The Effects of Regulation on Bank Participation in the Market
SM -87-6
G a ry D . K o p p e n h a v e r
Bank Stock Valuation: Does Maturity Gap Matter?
SM -87-7
V efa T arhan
Finite Horizons, Intertemporal Substitution and Fiscal Policy
SM -87-8
D a v id A lan A sch a u e r
Reevaluation of the Structure-Conduct-Performance
Paradigm in Banking
SM -87-9
D o u g la s D . E v a n o ffa n d D ia n a L. F o rtie r
♦Limited quantity available.
♦♦Out of print.
9
S taff m em oranda continued
Net Private Investment and Public Expenditure in the
United States 1953-1984
SM-87-10
D a v id A la n A sc h a u e r
Risk and Solvency Regulation of Depository Institutions:
Past Policies and Current Options
SM-88-1
G eo rg e J. B en sto n a n d G eo rg e G. K au fm an
Public Spending and the Return to Capital
SM -88-2
D a v id A sch a u e r
Is Government Spending Stimulative?
SM -88-3
D a v id A sch a u e r
Securities Activities of Commercial Banks: The Current
Economic and Legal Environment
SM -88-4
G e o rg e G. K au fm an a n d L a rry R. M o te
A Note on the Relationship Between Bank Holding Company
Risks and Nonbank Activity
SM -88-5
E lija h B re w e r, III
Duration Models: A Taxonomy
SM -88-6
G. 0 . B ie rw a g , G e o rg e G. K au fm an a n d C yn th ia M . L a tta
Durations of Nondefault-Free Securities
G . (9. B ie rw a g a n d G eo rg e G. K au fm an
Is Public Expenditure Productive?
SM -88-7
D a v id A sch a u er
Commercial Bank Capacity to Pay Interest on Demand Deposits:
Evidence from Large Weekly Reporting Banks
SM -88-8
E lija h B re w e r, III a n d T hom as H. M o n d sch ea n
Imperfect Information and the Permanent Income Hypothesis
SM -88-9
A b h ijit V. B a n e rje e a n d K en n eth N . K u ttn er
♦Limited quantity available.
♦♦Out of print.
10
S taff m em oranda continued
Does Public Capital Crowd out Private Capital?
SM-88-1 o
D a v id A sch a u e r
Imports, Trade Policy, and Union Wage Dynamics
SM -88-11
E llen R issm a n
♦Limited quantity available.
♦♦Out of print.
11
Staff Studies
A series of research studies dealing with various economic policy issues on a national level.
Competition in Financial Services: the Impact of Nonbank Entry, 1983
SS-83-1
H a rv e y R o sen b lu m a n d D ia n e S ieg el
Financial Deregulation: Historical Perspective and Impact of the Gam-St
Germain Depository Institutions Act of 1982,1983
**SS-83-2
G illia n G a rc ia
*Limited quantity available.
**Out of print.
12
@FedFRASER