Working PaPer SerieS
no 1565 / july 2013
riSk, uncertainty
and Monetary Policy
Geert Bekaert, Marie Hoerova
and Marco Lo Duca
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Acknowledgements
We thank the Associate Editor, Refet Gürkaynak, and an anonymous referee for suggestions that signicantly improved the paper. We
are also grateful to Tobias Adrian, Gianni Amisano, David DeJong, Bartosz Mackowiak, Frank Smets, José Valentim and Jonathan
Wright for their very helpful comments on earlier drafts. Falk Bräuning and Carlos Garcia provided excellent research assistance. The
views expressed do not necessarily reect those of the European Central Bank or the Eurosystem. Bekaert gratefully acknowledges
nancial support from Netspar.
Geert Bekaert
Columbia University
Marie Hoerova
European Central Bank; e-mail: [email protected]
Marco Lo Duca
European Central Bank; e-mail: [email protected]
1
ABSTRACT
The VIX, the stock market option-based implied volatility, strongly co-moves with measures of
the monetary policy stance. When decomposing the VIX into two components, a proxy for risk
aversion and expected stock market volatility (“uncertainty”), we find that a lax monetary policy
decreases both risk aversion and uncertainty, with the former effect being stronger. The result
holds in a structural vector autoregressive framework, controlling for business cycle movements
and using a variety of identification schemes for the vector autoregression in general and
monetary policy shocks in particular. The effect of monetary policy on risk aversion is also
apparent in regressions using high frequency data.
JEL Codes: E44, E52, G12, G20, E32
Keywords: Monetary policy, option implied volatility, risk aversion, uncertainty, business
cycle
2
NON-TECHNICAL SUMMARY
A popular indicator of risk aversion in financial markets, the VIX index, strongly co-moves with
measures of the monetary policy stance in the United States. While the current VIX is positively
associated with future (real) Fed funds rates, the relationship turns negative and significant after
13 months: high VIX readings are correlated with expansionary monetary policy in the medium-
run future (see Figure 1).
The strong interaction between the VIX index, known as a “fear index” (Whaley (2000)), and
monetary policy indicators may have important implications for a number of literatures. First,
the recent crisis has rekindled the idea that loose monetary policy may lead to excessive risk-
taking in financial markets. The Federal Reserve’s pattern of providing liquidity to financial
markets following market tensions, which became known as the “Greenspan put,” has been
cited as one of the contributing factors to the build-up of a speculative bubble prior to the 2007-
09 financial crisis.
Second, Bloom (2009) and Bloom, Floetotto and Jaimovich (2009) show that heightened
“economic uncertainty” decreases employment and output. It is therefore conceivable that the
monetary authority responds to uncertainty shocks, in order to affect economic outcomes.
However, the VIX index, used by Bloom (2009) to measure uncertainty, can be decomposed
into a component that reflects actual expected stock market volatility (uncertainty) and a
residual, the so-called variance premium, that reflects risk aversion and other non-linear pricing
effects, perhaps even Knightian uncertainty. Establishing which component drives the strong
co-movements between the monetary policy stance and the VIX is therefore particularly
important.
Third, analyzing the relationship between monetary policy and the VIX and its components may
help clarify the relationship between monetary policy and the stock market, explored in a large
number of empirical papers (Thorbecke (1997), Rigobon and Sack (2004), Bernanke and
Kuttner (2005)). The extant studies all find that expansionary (contractionary) monetary policy
affects the stock market positively (negatively). Interestingly, Bernanke and Kuttner (2005)
ascribe the bulk of the effect to easier monetary policy lowering risk premiums, reflecting both a
reduction in economic and financial volatility and an increase in the capacity of financial
investors to bear risk. By using the VIX and its two components, we test the effect of monetary
policy on stock market risk, but also provide more precise information on the exact channel.
This article characterizes the dynamic links between risk aversion, uncertainty and monetary
policy in a structural vector autoregressive (VAR) framework. Our VARs always include a
business cycle indicator to control for business cycle movements. The main findings are as
3
follows. A lax monetary policy decreases risk aversion in the stock market after about nine
months. This effect is persistent, lasting for more than two years. Moreover, monetary policy
shocks account for a significant proportion of the variance of the risk aversion proxy. Monetary
policy shocks have a significant impact on risk aversion also in regressions using high
frequency data. The effects of monetary policy on uncertainty are similar but somewhat weaker.
On the other hand, periods of both high uncertainty and high risk aversion are followed by a
looser monetary policy stance but these results are less robust and weaker statistically. Finally, it
is the uncertainty component of the VIX that has the statistically stronger effect on the business
cycle, not the risk aversion component.
4
1 INTRODUCTION
A popular indicator of risk aversion in financial markets, the VIX index, shows strong co-
movements with measures of the monetary policy stance. Figure 1 considers the cross-
correlogram between the real interest rate (the Fed funds rate minus inflation), a measure of the
monetary policy stance, and the logarithm of end-of-month readings of the VIX index. The VIX
index essentially measures the “risk-neutral” expected stock market variance for the US
S&P500 index. The correlogram reveals a very strong positive correlation between real interest
rates and future VIX levels. While the current VIX is positively associated with future real rates,
the relationship turns negative and significant after 13 months: high VIX readings are correlated
with expansionary monetary policy in the medium-run future.
- Figure 1 -
The strong interaction between a “fear index” (Whaley (2000)) in the asset markets and
monetary policy indicators may have important implications for a number of literatures. First,
the recent crisis has rekindled the idea that lax monetary policy can be conducive to financial
instability. The Federal Reserve’s pattern of providing liquidity to financial markets following
market tensions, which became known as the “Greenspan put,” has been cited as one of the
contributing factors to the build-up of a speculative bubble prior to the 2007-09 financial crisis.
1
Whereas some rather informal stories have linked monetary policy to risk-taking in financial
markets (Rajan (2006), Adrian and Shin (2008), Borio and Zhu (2008)), it is fair to say that no
extant research establishes a firm empirical link between monetary policy and risk aversion in
asset markets.
2
Second, Bloom (2009) and Bloom, Floetotto and Jaimovich (2009) show that heightened
“economic uncertainty” decreases employment and output. It is therefore conceivable that the
monetary authority responds to uncertainty shocks, in order to affect economic outcomes.
However, the VIX index, used by Bloom (2009) to measure uncertainty, can be decomposed
into a component that reflects actual expected stock market volatility (uncertainty) and a
residual, the so-called variance premium (see, for example, Carr and Wu (2009)), that reflects
risk aversion and other non-linear pricing effects, perhaps even Knightian uncertainty.
Establishing which component drives the strong co-movements between the monetary policy
stance and the VIX is therefore particularly important.
1
Investors increasingly believed that when market conditions were to deteriorate, the Fed would step in and inject liquidity until
the outlook improved. See, for example, “Greenspan Put May be Encouraging Complacency,” Financial Times, December 8,
2000.
2
For recent empirical evidence that monetary policy affects the riskiness of loans granted by banks see, for example, Altunbas,
Gambacorta and Marquéz-Ibañez (2010), Ioannidou, Ongena and Peydró (2009), Jiménez, Ongena, Peydró and Saurina (2009),
and Maddaloni and Peydró (2011).
5
Third, analyzing the relationship between monetary policy and the VIX and its components may
help clarify the relationship between monetary policy and the stock market, explored in a large
number of empirical papers (Thorbecke (1997), Rigobon and Sack (2004), Bernanke and
Kuttner (2005)). The extant studies all find that expansionary (contractionary) monetary policy
affects the stock market positively (negatively). Interestingly, Bernanke and Kuttner (2005)
ascribe the bulk of the effect to easier monetary policy lowering risk premiums, reflecting both a
reduction in economic and financial volatility and an increase in the capacity of financial
investors to bear risk. By using the VIX and its two components, we test the effect of monetary
policy on stock market risk, but also provide more precise information on the exact channel.
This article characterizes the dynamic links between risk aversion, economic uncertainty and
monetary policy in a simple vector-autoregressive (VAR) system. Such analysis faces a number
of difficulties. First, because risk aversion and the stance of monetary policy are jointly
endogenous variables and display strong contemporaneous correlation (see Figure 1), a
structural interpretation of the dynamic effects requires identifying restrictions. Monetary policy
may indeed affect asset prices through its effect on risk aversion, as suggested by the literature
on monetary policy news and the stock market, but monetary policy makers may also react to a
nervous and uncertain market place by loosening monetary policy. In fact, Rigobon and Sack
(2003) find that the Federal Reserve does systematically respond to stock prices.
3
Second, the relationship between risk aversion and monetary policy may also reflect the joint
response to an omitted variable, with business cycle variation being a prime candidate.
Recessions may be associated with high risk aversion (see Campbell and Cochrane (1999) for a
model generating counter-cyclical risk aversion) and at the same time lead to lax monetary
policy. Our VARs always include a business cycle indicator.
Third, measuring the monetary policy stance is the subject of a large literature (see, for example,
Bernanke and Mihov (1998a)); and measuring policy shocks correctly is difficult. Models
featuring time-varying risk aversion and/or uncertainty, such as Bekaert, Engstrom and Xing
(2009), imply an equilibrium contemporaneous link between interest rates and risk aversion and
uncertainty, through precautionary savings effects for example. Such relation should not be
associated with a policy shock. However, our results are robust to alternative measures of the
monetary policy stance and of monetary policy shocks. In particular, the results are robust to
identifying monetary policy shocks using a standard structural VAR, using high frequency Fed
funds futures changes following Gürkaynak, Sack and Swanson (2005), and using the approach
3
Rigobon and Sack (2003, 2004) use an identification scheme based on the heteroskedasticity of stock market returns. Given that
we view economic uncertainty as an important endogenous variable in its own right with links to the real economy and risk
premiums, we cannot use such an identification scheme.
6
in Bernanke and Kuttner (2005), based on the unexpected change in the Fed Funds rate on a
monthly basis.
The remainder of the paper is organized as follows. Section 2 details the measurement of the
key variables in the VAR, including monetary policy indicators, monetary policy shocks and
business cycle indicators. First and foremost, we provide intuition on how the VIX is related to
the actual expected variance of stock returns and to risk preferences. While the literature has
proposed a number of risk appetite measures (see Baker and Wurgler (2007) and Coudert and
Gex (2008)), our measure is monotonically increasing in risk aversion in a variety of realistic
economic settings. This motivates our empirical strategy in which the VIX is split into a pure
volatility component (“uncertainty”) and a residual, which should be more closely associated
with risk aversion. Section 3 analyzes the dynamic relationship between monetary policy and
risk aversion and uncertainty in standard structural VARs. The results are remarkably robust to
a long list of robustness checks with respect to VAR specification, variable definitions and
alternative identification methods. Section 4 employs two alternative methods to identify
monetary policy shocks relying on Fed futures data.
4
Our main findings are as follows. A lax monetary policy decreases risk aversion in the stock
market after about nine months. This effect is persistent, lasting for more than two years.
Moreover, monetary policy shocks account for a significant proportion of the variance of the
risk aversion proxy. Monetary policy shocks have a significant impact on risk aversion also in
regressions using high frequency data. The effects of monetary policy on uncertainty are similar
but somewhat weaker. On the other hand, periods of both high uncertainty and high risk
aversion are followed by a looser monetary policy stance but these results are less robust and
weaker statistically. Finally, it is the uncertainty component of the VIX that has the statistically
stronger effect on the business cycle, not the risk aversion component.
4
The Online Appendix, available at www.mariehoerova.net, contains supplementary material referenced in the article.
7
2 MEASUREMENT
This section details the measurement of the key inputs to our analysis: risk aversion and
uncertainty; the monetary policy stance and monetary policy shocks; and finally, business cycle
variation. Our data start in January 1990 (the start of the model-free VIX series) but our analysis
is performed using two different end-points for the sample: July 2007, yielding a sample that
excludes recent data on the crisis; and August 2010. The crisis period presents special
challenges as stock market volatilities peaked at unprecedented levels and the Fed funds target
rate reached the zero lower bound. Table 1 describes the basic variables used and assigns them a
short-hand label.
- Table 1 –
2.1 MEASURING RISK AVERSION AND UNCERTAINTY
To measure risk aversion and uncertainty, we use a decomposition of the VIX index. The VIX
represents the option-implied expected volatility on the S&P500 index with a horizon of 30
calendar days (22 trading days). This volatility concept is often referred to as “implied
volatility” or “risk-neutral volatility,” as opposed to the actual (or “physical”) expected
volatility. Intuitively, in a discrete state economy, the physical volatility would use the actual
state probabilities to arrive at the physical expected volatility, whereas the risk-neutral volatility
would make use of probabilities that are adjusted for the pricing of risk.
The computation of the actual VIX index relies on theoretical results showing that option prices
can be used to replicate any bounded payoff pattern; in fact, they can be used to replicate
Arrow-Debreu securities (Breeden and Litzenberger (1978), Bakshi and Madan (2000)). Britten-
Jones and Neuberger (2000) and Bakshi, Kapadia and Madan (2003) show how to infer “risk-
neutral” expected volatility for a stock index from option prices. The VIX index measures
implied volatility using a weighted average of European-style S&P500 call and put option
prices that straddle a 30-day maturity and cover a wide range of strikes (see CBOE (2004) for
more details). Importantly, this estimate is model-free and does not rely on an option pricing
model.
While the VIX obviously reflects stock market uncertainty, it conceptually must also harbor
information about risk and risk aversion. Indeed, financial markets often view the VIX as a
measure of risk aversion and fear in the market place. Because there are well-accepted
techniques to measure the physical expected variance, the VIX can be split into a measure of
stock market or economic uncertainty, and a residual that should be more closely associated
with risk aversion. The difference between the squared VIX and an estimate of the conditional
8
variance is typically called the variance premium (see, e.g., Carr and Wu (2009)).
5
The variance
premium is nearly always positive
and displays substantial time-variation. Recent finance
models attribute these facts either to non-Gaussian components in fundamentals and (stochastic)
risk aversion (see, for instance, Bekaert and Engstrom (2013), Bollerslev, Tauchen and Zhou
(2009), Drechsler and Yaron (2011)) or Knightian uncertainty (see Drechsler (2009)). Bekaert
and Hoerova (2013) use a one-period discrete economy with power utility to illustrate the
difference between “risk neutral” and “physical” expected variance and demonstrate that the
variance premium is indeed increasing in risk aversion in a number of realistic calibrated
example economies.
2.1.1 DECOMPOSING THE VIX INDEX
To decompose the VIX index into a risk aversion and an uncertainty component, an estimate of
the expected future realized variance is needed. This estimate is customarily obtained by
projecting future realized monthly variances (computed using squared 5-minute returns) onto a
set of current instruments. We follow this approach using daily data on monthly realized
variances (denoted by RVAR), the squared VIX, the dividend yield and the real three-month T-
bill rate. By using daily data, considerable statistical power is gained relative to the standard
methods employing end-of-month data. For example, forecasting models estimated from daily
data easily “beat” models using only end-of-month data, even for end-of-month samples.
To select a good forecasting model, a horserace is conducted between a total of eight volatility
forecasting models. The first five models use OLS regressions with different predictors: a one-
variable model with either the past realized variance or the squared VIX; a two-variable model
with both the squared VIX and the past realized variance; a three-variable model adding the past
dividend yield; and a four-variable model adding the past real three-month T-bill rate. Three
models that do not require estimation are also considered: half-half weights on the past squared
VIX and past realized variance; the past realized variance; the past squared VIX. Our model
selection criteria are out-of-sample root mean squared error and mean absolute errors, and, for
the estimated models, stability (especially through the crisis period).
This procedure leads us to select a two-variable model where the squared VIX and the past
realized variance are used as predictors. The performance of the three- and four-variable models
is very comparable to this model, but the univariate estimated models and the non-estimated
models perform consistently and significantly worse. Moreover, the selected model is the most
stable of the well-performing forecasting models we considered, with the coefficients
5
In the technical finance literature, the variance premium is actually the negative of the variable that we use. By switching the
sign, our indicator tends to increase with risk aversion, whereas the variance premium becomes more negative with risk aversion.
9
economically and statistically unaltered during the crisis period. The Online Appendix provides
a detailed account of the forecasting horserace. The resulting coefficients from the two-variable
projection are as follows:
6
RVAR
t
=-0.00002 + 0.299 VIX
2
t-22
+ 0.442 RVAR
t-22
+e
t
(1)
(0.00012) (0.067) (0.130)
The standard errors reported in parentheses are corrected for serial correlation using 30 Newey-
West (1987) lags.
The fitted value from the two-variable projection is the estimated conditional variance and our
measure of “uncertainty.” The difference between the squared VIX and the conditional variance
is our measure of “risk aversion.”
2.1.2 RISK AVERSION AND UNCERTAINTY ESTIMATES
Figure 2 plots the risk aversion and uncertainty estimates, along with 90% confidence intervals.
7
To construct the confidence bounds, the coefficients from the forecasting projection together
with their asymptotic covariance matrix are retained. Then, 100 alternative parameter
coefficients from the distribution of these estimates are drawn, which generates alternative risk
aversion and uncertainty estimates. In Section 3.3.4, these bootstrapped series are used to
account for the sampling error in the risk aversion and uncertainty estimates in our VARs.
Throughout our analysis, the logarithms of the risk aversion and uncertainty estimates are used.
They are labeled RA and UC, respectively.
- Figure 2–
2.2 MEASURING MONETARY POLICY
To measure the monetary policy stance, we use the real interest rate (RERA), i.e., the Fed funds
end-of-the-month target rate minus the CPI annual inflation rate. In Section 3.3.1, alternative
measures of the monetary policy stance are considered for robustness. Our first such measure is
the Taylor rule residual, the difference between the nominal Fed funds rate and the Taylor rule
rate (TR rate). The TR rate is estimated as in Taylor (1993):
TR
t
= Inf
t
+ NatRate
t
+ 0.5 (Inf
t
- TargInf) + 0.5 OG
t
(2)
6
This estimation was conducted using a winsorized sample but the estimation results for the non-winsorized sample are in fact very
similar.
7
The estimated uncertainty series is less “jaggedy” than it would be if only the past realized variance would be used to compute it
(as in Bollerslev, Tauchen and Zhou, 2009), which in turn helps smooth the risk aversion process.
10
where Inf is the annual inflation rate, NatRate is the “natural” real Fed funds rate (consistent
with full employment), which Taylor assumed to be 2%, TargInf is a target inflation rate, also
assumed to be 2%, and OG (output gap) is the percentage deviation of real GDP from potential
GDP; with the latter obtained from the Congressional Budget Office. Our other alternative
measures of the monetary policy stance are the nominal Fed funds rate instead of the real rate,
and (the growth rate of) the monetary aggregate M1, which is commonly assumed to be under
tight control of the central bank. M1 (growth) is multiplied by minus one so that a positive
shock to this variable corresponds to monetary policy tightening, in line with all of our other
measures of monetary policy.
Measuring the monetary policy stance is challenging since late 2008, as the Fed funds rate
reached the zero lower bound (the Fed funds target was set in the range 0-0.25% as of
December 2008) and the Federal Reserve turned to unconventional monetary policies, such as
large-scale asset purchases. In the period December 2008 - August 2010, the “true” nominal Fed
funds rate is approximated by taking it to be the minimum between 0.125% (i.e., the mid-point
of the 0-0.25% range) and the TR rate, estimated using equation (2) above. Rudebusch (2009)
has also advocated using the TR rate estimate as a proxy for the “true” Fed funds rate post-2008.
Our analysis in Sections 4.1 and 4.2 uses monetary policy surprises derived from Fed funds
futures data. Section 4.1 relies on monetary policy surprises proposed by Gürkaynak, Sack and
Swanson (2005), henceforth GSS.
8
GSS compute the monetary policy surprises as high-
frequency changes in the futures rate around the FOMC announcements. Their “tight” (“wide”)
window estimates begin ten (fifteen) minutes prior to the monetary policy announcement and
end twenty (forty-five) minutes after the policy announcement, respectively. The data span the
period from January 1990 through June 2008. Section 4.2 uses the unexpected change in the Fed
funds rate on a monthly basis, defined as the average Fed funds target rate in month t minus the
one-month futures rate on the last day of the month t-1. This approach follows Kuttner (2001)
and Bernanke and Kuttner (2005) (henceforth BK), see their equation (5). As pointed out by
BK, rate changes that were unanticipated as of the end of the prior month may well include a
systematic response to economic news, such as employment, output and inflation occurring
during the month. To overcome this problem, “cleansed” monetary surprises that are orthogonal
to a set of economic data releases are used. They are calculated as residuals in a regression of
the “simple” monetary policy surprise, onto the unexpected component of the industrial
production index, the Institute of Supply Management Purchasing Managers Index (the ISM
index), the payroll survey, and unemployment (see Section 2.3 below for a description). Finally,
8
We are very grateful to R. Gürkaynak for sharing the data with us.
11
this regression allows for heterogeneous coefficients before and after 1994, to take into account
a change in the reaction of the Fed to economic data releases, as documented in BK.
To extend the sample of monetary policy surprises until August 2010, we proceed in two steps.
First, data on monetary policy surprises at the zero lower bound are collected from Wright
(2012, Table 5, p. F463). They represent the first principle component of intraday changes in
yields on Treasury futures contracts, taken on days of important policy announcements. The
shocks are positive (negative) when monetary policy is unexpectedly accommodative
(restrictive), and normalized to have a unit standard deviation. For comparability with the GSS
data, Wright’s shocks are rescaled by multiplying them by minus the standard deviation of the
GSS’s shocks, before appending them to the time series of GSS shocks. Second, the gap
between the data from GSS (June 2008) and Wright (November 2008) is filled by calculating
monetary policy surprises using monthly Federal funds futures, following BK.
2.3 MEASURING BUSINESS CYCLE VARIATION
Industrial production is used as our benchmark indicator of business cycle variation at the
monthly frequency. In a robustness exercise in Section 3.3.2, non-farm employment and the
ISM index are considered as alternative business cycle indicators.
Sections 4.1 and 4.2 use data on economic news surprises following the methodology in
Ehrmann and Fratzscher (2004).
9
Our analysis relies on unexpected components of news about
the industrial production index, the ISM index, the payroll survey, and unemployment. The
unexpected component of each news release is calculated as the difference between the released
data and the median expectation according to surveys. The Money Market Survey (MMS) is
used for the period 1990-2001 and Bloomberg for the period 2002-2010. The shocks are
standardized over the sample period.
9
We are very grateful to M. Ehrmann and M. Fratzscher for sharing their dataset with us.
12
3 STRUCTURAL MONETARY VARS
This section follows the identified monetary VAR literature and interprets the shock in the
monetary policy equation as the monetary policy shock. Our benchmark VAR, analyzed in
Section 3.1, consists of four variables: our risk aversion and uncertainty proxies (RA
t
and UC
t
),
the real interest rate as a measure of monetary policy stance (MP
t
), and the log-difference of
industrial production as a business cycle indicator (BC
t
). Alternative VARs are considered as
part of an extensive series of robustness checks discussed in Section 3.3. The business cycle is
the most important control variable as it is conceivable that, for example, news indicating
weaker than expected growth in the economy may simultaneously make a cut in the Fed funds
target rate more likely and cause people to be effectively more risk averse, because their
consumption moves closer to their “habit stock,” or because they fear a more uncertain future.
3.1 STRUCTURAL FOUR-VARIABLE VAR: SET-UP
The four variables of our benchmark VAR are collected in the vector Z
t
= [BC
t
, MP
t
, RA
t
UC
t
]'.
Without loss of generality, constants are ignored. Consider the following structural VAR:
A Z
t
= Φ Z
t-1
+ ε
t
(3)
where A is a 4x4 full-rank matrix and E[ε
t
ε
t
'] = I. Of main interest are the dynamic responses to
the structural shocks ε
t
. Of course, the reduced-form VAR is estimated first:
Z
t
= B Z
t-1
+ C ε
t
(4)
where B denotes A
-1
Φ and C denotes A
-1
. Our estimated VARs include 3 lags, as chosen by the
Akaike criterion.
Six restrictions on the VAR are needed to identify the system. Our first set of restrictions uses a
standard Cholesky decomposition of the estimate of the variance-covariance matrix. The
business cycle variable is ordered first, followed by the real interest rate, with risk aversion and
uncertainty ordered last. This captures the fact that risk aversion and uncertainty, stock market
based variables, respond instantly to monetary policy shocks, while the business cycle variable
is relatively more slow-moving. Effectively, this imposes six exclusion restrictions on the
contemporaneous matrix A, making it lower-triangular.
Our second set of restrictions combines five contemporaneous restrictions (also imposed under
the Cholesky decomposition above) with the assumption that monetary policy has no long-run
effect on the level of industrial production. This long-run restriction is inspired by the literature
13
on long-run money neutrality: money should not have a long run effect on real variables.
10
Following Blanchard and Quah (1989), the model with a long-run restriction (LR) involves a
long-run response matrix, denoted by D:
D ≡ (I - B)
-1
C. (5)
The system with five contemporaneous restrictions and one long-run exclusion restriction
corresponds to setting the [1,2] element in D equal to zero while freeing up the corresponding
element in A.
11
We couch our main results in the form of impulse-response functions (IRFs henceforth),
estimated in the usual way, and focus our discussion on significant responses. Bootstrapped
90% confidence intervals are based on 1000 replications. Our focus is on the pre-crisis sample
because the addition of the crisis period leads to an unstable VAR. The Online Appendix (Table
OA2) provides evidence on the stability of the VAR using a variety of tests. When a standard
Wald test for parameter stability after July 2007 is used, the null hypothesis of stability is
rejected at the 1% significance level for industrial production, the real interest rate and risk
aversion and at the 5% level for uncertainty. When the sup-Wald test of Andrews (1993) is
performed, the procedure finds significant break dates between June 2007 and October 2008,
except for the risk aversion variable where overall stability is rejected at the 10% level but no
significant break date is detected. Finally, the Andrews (2003) test, formally designed for a
break that occurs towards the end of the sample, is also performed. Results are in line with the
other two tests: the null hypothesis of no breakpoint in August 2007 is rejected at the 1%
significance level for all variables with the exception of risk aversion.
3.2 STRUCTURAL FOUR-VARIABLE VAR: RESULTS
Figure 3 graphs the complete results for the pre-crisis sample.
- Figure 3 -
Panels A and B show the interactions between the real rate (RERA) and log risk aversion (RA).
A one standard deviation negative shock to the real rate represents a 34 basis points decrease
under both identification schemes. Laxer monetary policy lowers risk aversion by about 0.032
in both models after 9 months. The impact reaches a maximum of 0.056 after 20 months and
remains significant up and till lag 40. A one standard deviation positive shock to risk aversion,
10
Bernanke and Mihov (1998b) and King and Watson (1992) marshal empirical evidence in favor of money neutrality using data
on money growth and output growth.
11
Both identification schemes satisfy necessary and sufficient conditions for global identification of structural vector
autoregressive systems (see Rubio-Ramírez, Waggoner and Zha (2010)).
14
which is equivalent to 0.347, has a mostly negative impact on the real rate but it is statistically
insignificant in both models.
As Panel C shows, a positive shock to the real rate has an immediate negative impact on
uncertainty. The impact is short-lived and only statistically significant in the model with
contemporaneous restrictions. In the medium run, tighter monetary policy increases uncertainty
in both models (between lags 11 and about 40). The maximum positive impact is about 0.060 at
lag 21 in both models. In the other direction, reported in Panel D, the real rate decreases in the
short-run following a positive one standard deviation shock to uncertainty, which is equivalent
to 0.244. In both models, the impact is (borderline) statistically insignificant.
As for interactions with the business cycle variable (Panels E through J), a contractionary
monetary policy shock leads to a decline in industrial production growth (DIPI) in the medium-
run, but the impact is statistically insignificant in both specifications. In the other direction,
monetary policy reacts as expected to business cycle fluctuations: a one standard deviation
positive shock to industrial production growth, equivalent to 0.005, leads to a higher real rate.
Specifically, in the model with contemporaneous restrictions, the real rate increases by a
maximum of 14 basis points after 6 months, with the impact being significant between lags 1
and 20. The impact is also positive in the model with contemporaneous/long-run restrictions but
it is not statistically significant. Interactions between risk aversion and industrial production
growth are mostly statistically insignificant. Positive uncertainty shocks lower industrial
production growth between lags 6-15, while the impact in the opposite direction is statistically
insignificant. This is consistent with the analysis in Bloom (2009), who found that uncertainty
shocks generate significant business cycle effects, using the VIX as a measure of uncertainty.
12
Finally, increases in risk aversion predict future increases in uncertainty under both
identification schemes (Panel L). Uncertainty has a positive, albeit short-lived effect on risk
aversion (Panel K).
Our main result for the pre-crisis sample is that monetary policy has a medium-run statistically
significant effect on risk aversion. This effect is also economically significant. Figure 4 shows
what fraction of the forecast error variance of the four variables in the VAR is due to monetary
policy shocks at horizons between 1 and 60 months. Monetary policy shocks account for over
20% of the variance of risk aversion at horizons longer than 37 and 29 months in the models
with contemporaneous and contemporaneous/long-run restrictions, respectively. They also
increase uncertainty and Figure 4 shows that they are only marginally less important drivers of
12
Popescu and Smets (2009) analyze the business cycle behavior of measures of perceived uncertainty and financial risk premia in
Germany. They find that financial risk aversion shocks are more important in driving business cycles than uncertainty shocks.
Gilchrist and Zakrajšek (2012) document that innovations to the excess corporate bond premium, a proxy for the time-varying
price of default risk, cause large and persistent contractions in economic activity.
15
the uncertainty variance than they are of the risk aversion variance. Finally, while monetary
policy appears to loosen in response to both risk aversion and uncertainty shocks, these effects
are statistically weaker.
- Figure 4 –
3.3 ROBUSTNESS
In this subsection, six types of robustness checks are considered: 1) measurement of the
monetary policy stance; 2) measurement of the business cycle variable; 3) alternative orderings
of variables; 4) accounting for the sampling error in RA and UC estimates; 5) conducting the
analysis using a six variable monetary VAR with the Fed funds rate and price level measures
CPI and PPI entering as separate variables; and 6) conducting the analysis over the full sample
till August 2010.
13
3.3.1 ALTERNATIVE MONETARY POLICY MEASURES
Three alternative measures of the monetary policy stance are considered: Taylor rule deviations,
nominal Fed funds rate and the growth of the monetary aggregate M1. The results (reported in
the Online Appendix, Table OA3) confirm that a looser monetary policy stance lowers risk
aversion in the short to medium run. This effect is persistent, lasting for about two years. In
some cases, the immediate effect has the reverse sign, however. In the other direction, monetary
policy becomes laxer in response to positive risk aversion shocks but the effect is statistically
significant in less than half the cases. As for the effect of monetary policy on uncertainty,
monetary tightening increases uncertainty in the medium run but this effect is not significant
when using the Fed fund rate. In the other direction, higher uncertainty leads to laxer monetary
policy in all specifications but the effect is only significant when using the Fed fund rate under
contemporaneous identifying restrictions.
3.3.2 ALTERNATIVE BUSINESS CYCLE MEASURES
As alternative business cycle indicators, the log-difference of employment and the log of the
ISM index are considered. Unlike industrial production and employment, the ISM index is a
stationary variable, implying that VAR shocks do not have a long run effect on it. Our long-run
restriction on the effect of monetary policy is thus stronger when applied to the ISM: it restricts
13
Moreover, our results remain robust to the use of both shorter and longer VAR lag-lengths. A VAR with 1 lag, as selected by the
Schwarz criterion, as well as a VAR with 4 lags were estimated (we did not go beyond four lags as otherwise the saturation ratio,
the ratio of data points to parameters, drops below 10). Our results were unaltered.
16
the total effect of monetary policy on the ISM to be zero. Nevertheless, our main results from
Section 3.1 are confirmed for each specification with an alternative business cycle variable.
Figures OA1 and OA2 in the Online Appendix present a full set of IRFs (the equivalent of
Figure 3) for the VARs with the log-difference of employment and the log of the ISM index,
respectively.
3.3.3 ALTERNATIVE ORDERINGS OF VARIABLES
In one alternative ordering, the order of risk aversion and uncertainty in our benchmark VAR is
reversed. In another robustness check, the real interest rate is ordered last, thus allowing it to
respond instantaneously to RA and UC shocks. We consistently find that looser monetary policy
lowers risk aversion and uncertainty in a statistically significant fashion in the medium-run. In
the other direction, the effects are less robust. In the specification with RA and UC reversed,
monetary policy mostly responds to UC shocks, while the response to RA shocks is statistically
insignificant. In the specification with RERA ordered last, monetary policy responds to both
positive RA and UC shocks by loosening its stance, and the effect is statistically significantly
different from zero. Figures OA3 and OA4 in the Online Appendix present a full set of IRFs for
the reversed ordering of RA and UC and for the specification with RERA ordered last,
respectively.
3.3.4 SAMPLING ERROR IN RA AND UC
This subsection verifies that our VAR results are robust to accounting for the sampling error in
the RA and UC estimation. Hundred alternative RA and UC series are drawn from the
distribution of RA and UC estimates (as described in Section 2.1.2) and fed into our
bootstrapped VAR. Per set of alternative RA and UC series, 100 VAR replications are
estimated. Then, the usual 90% confidence bounds are constructed. The results are very similar
to those obtained without taking uncertainty surrounding RA and UC estimates into account,
and are presented in the Online Appendix (Figure OA5).
3.3.5 SIX-VARIABLE MONETARY VAR
We also estimate a six-variable monetary VAR following Christiano, Eichenbaum and Evans
(1999) and featuring the nominal Fed funds rate as the measure of monetary policy stance and
price level measures CPI and PPI as additional variables.
14
To identify monetary policy shocks,
14
The model is estimated with four lags, as suggested by the Akaike criterion. All variables are in logarithms except for the Fed
funds rate. Note that industrial production now enters the VAR in levels.
17
a Cholesky ordering is used with CPI and industrial production ordered first, followed by the
Fed funds rate and PPI, and risk aversion and uncertainty ordered last.
Figure 5 presents impulse-responses to monetary policy shocks. A positive monetary policy
shock corresponds to a 15 basis points increase in the Fed funds rate. A contractionary monetary
shock leads to a statistically significant decrease in the CPI between lags 3 and 23 and in the PPI
between lags 23 and 50. Furthermore, industrial production declines following a monetary
contraction after about 10 months, though the effect is not statistically significant. Importantly,
the reactions of both risk aversion and uncertainty are remarkably similar to those uncovered in
our benchmark four-variable VARs. Looser monetary policy decreases risk aversion by 0.024
after 12 months. The effect reaches a maximum of 0.040 at lag 23, and remains statistically
significant till lag 35. The effects remain economically important as monetary policy shocks
account for over 12% of the variance of risk aversion at horizons longer than 40 months (see
Panel F of Figure 5) but these percentages are nonetheless lower than in our four-variable VAR.
As for uncertainty, a higher Fed funds rate increases uncertainty between lags 12 and 31, with
the maximum impact of 0.040 at lag 23, which is also consistent with our previous findings. In
non-reported results, monetary policy responds to both positive RA and UC shocks by
loosening its stance. The effect is statistically significant between lags 2 and 7 for risk aversion
and between lags 5 and 26 for uncertainty.
- Figure 5–
3.3.6 FULL SAMPLE RESULTS
Despite the instability documented before, we nonetheless repeated our analysis for the full
sample including the crisis period. These results, mimicking Figure 3, can be found in the
Online Appendix (Figure OA6). The full sample results overall confirm our results for the pre-
crisis sample but are somewhat less statistically significant. The results regarding the key
interactions between monetary policy and risk aversion/uncertainty are as follows. The impact
of monetary policy in the full sample is quantitatively weaker, and is only statistically
significant at the 68% confidence level in both 4-variable VARs and the 6-variable VAR. Note
that such tighter confidence bounds are common in the VAR literature (see Christiano,
Eichenbaum, and Evans (1996), Sims and Zha (1999)). Monetary policy’s effect on uncertainty
is significant in the 6-variable VAR but borderline insignificant at the 68% level in the 4-
variable VARs. As to the reverse effect, monetary policy now reacts significantly to uncertainty
in some cases. Given the measurement problems mentioned before, and the rather extreme
volatility the VIX experienced, somewhat weaker statistical power for this sample is not entirely
surprising.
18
4 ALTERNATIVE IDENTIFICATION OF MONETARY
POLICY SHOCKS
In this Section, two alternative methodologies to identify monetary policy shocks are employed:
1) monetary surprises based on high-frequency Fed funds futures and 2) surprises based on the
unexpected change in the Fed Funds rate on a monthly basis. Focus is again on the pre-crisis
sample.
4.1 IDENTIFICATION USING HIGH-FREQUENCY FED FUNDS FUTURES
Our VAR set-up to identify monetary policy shocks and their structural relationship with risk
aversion and uncertainty follows the Sims (1980, 1998) identification tradition. With financial
market values changing continuously during the month, the use of monthly data for this purpose
certainly may cast some doubt on this identification scheme. An alternative identification
methodology that makes use of high frequency data is therefore employed to infer restrictions
on the monthly VAR.
4.1.1 IDENTIFICATION USING HIGH-FREQUENCY FED FUNDS FUTURES: SET-UP
Our approach, inspired by and building on the procedure described in D’Amico and Farka
(2011), consists of three steps. In the first step, the structural monetary policy and business cycle
shocks are measured directly. For monetary policy, we rely on a well-established literature that
uses high frequency changes in Fed funds futures rates to measure monetary policy shocks (see,
for example, Faust, Swanson and Wright, 2004). The measurement was detailed in Section 2.2.
Likewise, for business cycle shocks, news announcements are used. Under certain assumptions,
these shocks can be viewed as measuring the structural shocks ε
t
in the VAR. For monetary
policy shocks, this is plausible because usually only one shock occurs per month, and the use of
high frequency futures data helps ensure that the identified shock is plausibly orthogonal to
other shocks. As to the business cycle shocks, there are a number of potentially important
complicating issues, such as the correlation between the different news announcements and the
structural shock to the actual business cycle variable used in the VAR, and the scale of the
shocks when more than one occurs within a particular month. However, these issues become
moot when business cycle shocks do not generate significant contemporaneous effects on our
financial variables, which ends up being the case.
In the second step, the high frequency effects of monetary policy and economic news surprises
on risk aversion and uncertainty are measured. Daily changes in risk aversion and uncertainty
19
(as proxies for unexpected changes to these variables) are regressed, respectively, on the
monetary policy surprises based on high-frequency futures (using the “tight” window shocks)
15
and the four monthly economic news surprises concerning industrial production (ΔIP), the ISM
index (ΔISM), non-farm payroll and employment (ΔEMP), as described in Section 2.3.
16
The
resulting coefficients (with heteroskedasticity-robust standard errors in brackets) are:
ΔRA
t
= -0.039 + 0.047 ΔMP
t
– 0.005 ΔIP
t
– 0.004 ΔISM
t
– 0.004 ΔEMP
t
(6)
(0.007) (0.020) (0.014) (0.016) (0.017)
ΔUC
t
= -0.009 + 0.013 ΔMP
t
+ 0.002 ΔIP
t
– 0.002 ΔISM
t
– 0.008 ΔEMP
t
(7)
(0.003) (0.010) (0.005) (0.005) (0.011)
The coefficients on the business cycle news surprises are not statistically different from zero and
economically small. However, the responses to the monetary policy surprises are quantitatively
larger and statistically significant at the 5% level for RA and at the 16% level for UC. The
coefficients on ΔMP give us direct evidence on the contemporaneous responses of RA and UC
to structural disturbances in MP. Note that these responses confirm that risk aversion reacts
positively to monetary policy shocks and does so more strongly than uncertainty. By the same
token, we conclude that the contemporaneous responses of RA and UC to a business cycle
shock in our VARs are equal to zero.
In the third step, the estimates of structural responses of RA and UC to monetary policy and
business cycle shocks are used in our VAR analysis. This requires a number of additional
assumptions. In particular, it is assumed that there are no further policy or business cycle shocks
during the month and thus that the monthly shock equals the daily shock identified from high
frequency data. Furthermore, it is assumed that the contemporaneous daily change in risk
aversion and uncertainty identifies the monthly change in unexpected risk aversion and
uncertainty due to these policy and business cycle shocks. Therefore, the high-frequency
regressions effectively yield four coefficients in the A
-1
matrix of our structural VAR. Because
six restrictions in total are needed, two more restrictions are imposed from a Cholesky ordering.
In one identification scheme (Model 1), the imposed restrictions are that both industrial
production and monetary policy do not instantaneously respond to RA; in another scheme, the
same restrictions are imposed on the reaction to UC (Model 2).
17
15
Results for the monetary policy surprises calculated using the “wide” window are very similar.
16
Both the non-farm payroll and the negative of the unemployment surprises are treated as news about employment (ΔEMP) as
they have similar information content. Whenever they come out on the same day (which is mostly the case), they are summed
up.
17
Imposing zero-response restrictions to RA and UC in the BC equation would lead to an under-identified model.
20
4.1.2 IDENTIFICATION USING HIGH-FREQUENCY FED FUNDS FUTURES: RESULTS
Figure 6 presents impulse-responses to monetary policy shocks. Looser monetary policy
(corresponding to a 29 basis points decrease in the real rate) lowers risk aversion on impact and
in the medium run in both models. The maximum impact (at 0.061) is slightly larger and the
duration of the effect (between lags 7 and 17) longer in the model with no contemporaneous
response of the business cycle and monetary policy to UC.
- Figure 6 -
As Panel B shows, a positive shock to the real rate increases uncertainty on impact in the model
with no contemporaneous response of the business cycle and monetary policy to RA. The effect
is positive but not statistically significant in the medium run. In the model with no
contemporaneous response of the business cycle and monetary policy to UC, the positive effect
of the real rate shock on uncertainty is statistically significant on impact and between lags 10-
14, with a maximum impact of 0.059 at lag 14.
Lastly, the impact of monetary policy on industrial production growth is not statistically
significant (Panel C). Note that with different measures for the business cycle, such as
employment, the VAR does produce the expected and statistically significant response of
economic activity to monetary policy.
Because the identifying assumptions on monetary policy shocks have more support in the extant
literature than the assumptions made regarding the business cycle shocks, we also consider a
robustness check in which only the high-frequency responses to monetary policy surprises are
imposed in the monthly VAR. As four additional restrictions are then needed from a Cholesky
ordering to complete identification, the three contemporaneous restrictions in the BC equation
are used (the usual assumption on sluggish adjustment of macro to financial data) and a zero
response by monetary policy to either RA or UC. Results, presented in the Online Appendix
(Figure OA7), confirm that looser monetary policy lowers risk aversion significantly on impact
and in the medium run, with a maximum impact of 0.055 at lag 15 in both models. A positive
shock to the real rate increases uncertainty significantly on impact and between lags 4-36, with a
maximum impact of 0.058 at lag 16 in both models.
Repeating this analysis for the full sample, it is found that all the estimated coefficients in the
second step high frequency regressions are not statistically different from zero, but the effect of
monetary policy shocks on risk aversion is again positive with a t-stat of close to 1. The
21
structural responses from the third step are qualitatively the same but statistically weaker
(Figure OA8 in the Online Appendix).
18
4.2 IDENTIFICATION USING MONTHLY FED FUNDS FUTURES
In this section, the approach of Bernanke and Kuttner (2005) is adopted to study the dynamic
response of risk aversion and uncertainty to monetary policy. The key feature of their approach
is the calculation of a monthly monetary policy surprise using Federal funds futures contracts.
This variable identifies the monetary policy shock and is included in the VAR as an exogenous
variable. The endogenous variables in the VAR are RA, UC and the log difference of industrial
production (DIPI).
Figure 7 presents impulse-responses to “cleansed” monetary policy shocks
19
for the pre-crisis
sample and Figure OA9 in the Online Appendix for the full sample. The results generally
confirm that monetary policy tightening has a positive impact on both risk aversion and
uncertainty, and have the expected negative effect on industrial production. However, the results
are less strong statistically than under our other identification schemes.
- Figure 7 -
A one standard deviation negative shock to the “cleansed” surprise, equivalent to 8.6 basis
points, decreases RA on impact by 0.061 and UC by 0.054. The IRFs are significant on impact
at the 80% confidence level for RA and at the 70% level for UC. These results are robust to the
use of alternative business cycle indicators (non-farm employment and the ISM index).
18
To identify the monthly VAR, the two zero responses to monetary policy surprises from the second step are imposed, plus the
four Cholesky restrictions as described above. Imposing the four zero coefficients from the second step would render the VAR
under-identified.
19
The monetary policy surprise is standardized by subtracting the mean and dividing by the standard deviation.
22
5 CONCLUSIONS
A number of recent studies point at a potential link between loose monetary policy and
excessive risk-taking in financial markets. Rajan (2006) conjectures that in times of ample
liquidity supplied by the central bank, investment managers have a tendency to engage in risky,
correlated investments. To earn excess returns in a low interest rate environment, their
investment strategies may entail risky, tail-risk sensitive and illiquid securities (“search for
yield”). Moreover, a tendency for herding behavior emerges due to the particular structure of
managerial compensation contracts. Managers are evaluated vis-à-vis their peers and by
pursuing strategies similar to others, they can ensure that they do not under perform. This
“behavioral” channel of monetary policy transmission can lead to the formation of asset prices
bubbles and can threaten financial stability. Yet, there is no empirical evidence on the links
between risk aversion in financial markets and monetary policy.
This article has attempted to provide a first characterization of the dynamic links between risk,
uncertainty and monetary policy, using a simple vector-autoregressive framework. Implied
volatility is decomposed into two components, risk aversion and uncertainty, and the
interactions between each of the components and monetary policy are studied under a variety of
identification schemes for monetary policy shocks. It is consistently found that lax monetary
policy increases risk appetite (decreases risk aversion) in the future, with the effect lasting for
more than two years and starting to be significant after about nine months. The effect on
uncertainty is similar but the immediate response of uncertainty to monetary policy shocks in
high frequency regressions is weaker than that of risk aversion. Conversely, high uncertainty
and high risk aversion lead to laxer monetary policy in the near-term future but these effects are
not always statistically significant. These results are robust to controlling for business cycle
movements. Consequently, our VAR analysis provides a clean interpretation of the stylized
facts regarding the dynamic relations between the VIX and the monetary policy stance depicted
in Figure 1. The primary component driving the co-movement between past monetary policy
stance and current VIX levels (first column of Figure 1) is risk aversion but uncertainty also
reacts to monetary policy. Both components of the VIX lie behind the negative relation in the
opposite direction (second column of Figure 1) but statistical confidence in this structural link is
smaller.
We hope that our analysis will inspire further empirical work and research on the exact
theoretical links between monetary policy and risk-taking behavior in asset markets. A recent
literature, mostly focusing on the origins of the financial crisis, has considered a few channels
that deserve further scrutiny. Adrian and Shin (2008) stress the balance sheets of financial
intermediaries and repo growth; Adalid and Detken (2007) and Alessi and Detken (2011) stress
23
the buildup of liquidity through money growth; and Borio and Lowe (2002) emphasize rapid
credit expansion.
20
Recent work in the consumption-based asset pricing literature attempts to
understand the structural sources of the VIX dynamics (see Bekaert and Engstrom (2013),
Bollerslev, Tauchen and Zhou (2009), Drechsler and Yaron (2011)). Yet, none of these models
incorporates monetary policy equations. In macroeconomics, a number of articles have
embedded term structure dynamics into the standard New-Keynesian workhorse model
(Bekaert, Cho, Moreno (2010), Rudebusch and Wu (2008)), but no models accommodate the
dynamic interactions between monetary policy, risk aversion and uncertainty, uncovered in this
article.
The policy implications of our work are also potentially important. Because monetary policy
significantly affects risk aversion and uncertainty and these financial variables may affect the
business cycle, we seem to have uncovered a monetary policy transmission mechanism missing
in extant macroeconomic models. Fed chairman Bernanke (see Bernanke (2002)) interprets his
work on the effect of monetary policy on the stock market (Bernanke and Kuttner (2005)) as
suggesting that monetary policy would not have a sufficiently strong effect on asset markets to
pop a “bubble” (see also Bernanke and Gertler (2001), Gilchrist and Leahy (2002), and
Greenspan (2002)). However, if monetary policy significantly affects risk appetite in asset
markets, this conclusion may not hold. If one channel is that lax monetary policy induces excess
leverage as in Adrian and Shin (2008), perhaps monetary policy is potent enough to weed out
financial excess. Conversely, in times of crisis and heightened risk aversion, monetary policy
can influence risk aversion and uncertainty in the market place, and therefore affect real
outcomes.
20
In fact, the effects of repo, money and credit growth on our results were considered by including them in a four-variable VAR
together with RA, UC, and RERA (replacing the BC variable). We consistently found that the direct effect of monetary policy on
risk aversion and uncertainty we uncovered in our benchmark VARs is preserved.
24
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TABLES AND FIGURES
FIGURE 1: CROSS-CORRELOGRAM LVIX RERA
Notes: The first column presents the (lagged) cross-correlogram between the log of the VIX (LVIX) and past values of the real
interest rate (RERA). The second column presents the (lead) cross-correlogram between LVIX and future values of RERA. Dashed
vertical lines indicate 95% confidence intervals for the cross-correlation. The third column presents the cross-correlation values. The
index i indicates the number of months either lagged or led for the real interest rate variable. The sample period is January 1990 –
July 2007.
29
TABLE 1: DESCRIPTION OF VARIABLES
Name
Label
Description (source)
Conditional variance
Fitted values from the projection in eq. (1)
Consumer price index
CPI
Consumer price index, all items
Dividend yield
Dividend yield of the Standard & Poor 500
index
Fed funds rate
FED
Fed funds target rate
Implied variance VIX
2
Squared implied volatility of options on
the S&P500 index, VIX
2
/ 12
(Log of) Implied volatility (L)VIX
(Log of ) implied volatility of options on
the S&P500 index, (Log) [VIX /
12
]
(Growth of) Industrial production (D)IPI
Log (difference of) total industrial
production index
ISM index
ISM
ISM Purchasing Managers index
M1 money aggregate growth
M1
Month-on-month growth of M1
(Growth of) Non-farm employment
(D)EMP
Log (difference of) non-farm employment
Producer price index PPI
Producer price index for intermediate
materials
Real interest rate
RERA
FED minus annual CPI inflation rate
Realized variance RVAR
Realized variance computed using squared
5-minute returns
Risk aversion RA
Log (implied variance – conditional
variance)
Three-month T-bill
Secondary market yield
Uncertainty (conditional variance)
UC
Log (conditional variance)
Notes: Monthly frequency, end-of-the-month data (seasonally adjusted where applicable). Unless otherwise mentioned in the text,
the data are from Thomson Datastream.
30
FIGURE 2: VIX
2
DECOMPOSITION INTO UNCERTAINTY AND RISK AVERSION
Panel A: Conditional variance (“uncertainty”)
0
20
40
60
80
100
120
140
160
180
1990m1
1991m1
1992m1
1993m1
1994m1
1995m1
1996m1
1997m1
1998m1
1999m1
2000m1
2001m1
2002m1
2003m1
2004m1
2005m1
2006m1
2007m1
2008m1
2009m1
2010m1
Gulf War I
Mexican
Crisis
Asian
Crisis
Russian / LTCM
Crisis
Corporate
Scandals
Low
Uncertainty
Lehman
Aftermath
Euro Area
Debt Crisis
Gulf War I
Mexican
Crisis
Asian
Crisis
Russian / LTCM
Crisis
Corporate
Scandals
Low
Uncertainty
Lehman
Aftermath
Euro Area
Debt Crisis
09/11
Panel B: Difference between implied and conditional variance (“risk aversion”)
0
20
40
60
80
100
120
1990m1
1991m1
1992m1
1993m1
1994m1
1995m1
1996m1
1997m1
1998m1
1999m1
2000m1
2001m1
2002m1
2003m1
2004m1
2005m1
2006m1
2007m1
2008m1
2009m1
2010m1
Gulf War I
Mexican
Crisis
Asian
Crisis
Russian / LTCM
Crisis
Corporate
Scandals
High Risk
Appetite
Lehman
Aftermath
09/11
Euro Area
Debt Crisis
Notes: Figure 2 presents a decomposition of the squared VIX in the two components (in monthly percentages squared, black lines):
the expected stock market variance (our uncertainty proxy, in Panel A) and the residual, the difference between the squared VIX and
uncertainty (our risk aversion proxy, Panel B). The sample period is January 1990 – August 2010. Grey dashed lines are 90%
confidence intervals.
31
FIGURE 3: STRUCTURAL-FORM IRFS FOR THE 4-VARIABLE VAR (DIPI, RERA, RA, UC)
Panel A: Impulse RERA, response RA
Contemporaneous restrictions
Contemporaneous/long-run restrictions
Panel B: Impulse RA, response RERA
Contemporaneous restrictions
Contemporaneous/long-run restrictions
Panel C: Impulse RERA, response UC
Contemporaneous restrictions
Contemporaneous/long-run restrictions
32
Panel D: Impulse UC, response RERA
Contemporaneous restrictions
Contemporaneous/long-run restrictions
Panel E: Impulse RERA, response DIPI
Contemporaneous restrictions
Contemporaneous/long-run restrictions
Panel F: Impulse DIPI, response RERA
Contemporaneous restrictions
Contemporaneous/long-run restrictions
33
Panel G: Impulse RA, response DIPI
Contemporaneous restrictions
Contemporaneous/long-run restrictions
Panel H: Impulse DIPI, response RA
Contemporaneous restrictions
Contemporaneous/long-run restrictions
Panel I: Impulse UC, response DIPI
Contemporaneous restrictions
Contemporaneous/long-run restrictions
34
Panel J: Impulse DIPI, response UC
Contemporaneous restrictions
Contemporaneous/long-run restrictions
Panel K: Impulse RA, response UC
Contemporaneous restrictions
Contemporaneous/long-run restrictions
Panel L: Impulse UC, response RA
Contemporaneous restrictions
Contemporaneous/long-run restrictions
Notes: Estimated structural impulse-response functions (black lines) and 90% bootstrapped confidence intervals (grey dashed lines)
for the 4-variable model (with the log-difference of industrial production (DIPI), real interest rate (RERA), log risk aversion (RA),
and log uncertainty (UC)) with 3 lags (selected by the Akaike criterion), based on 1000 replications. Panels on the left present
results of the model with contemporaneous (Cholesky) restrictions, panels on the right present results of the model with
contemporaneous/long-run restrictions. The sample period is January 1990 – July 2007.
35
FIGURE 4: FORECAST ERROR VARIANCE DECOMPOSITIONS
Impact of the real interest rate (RERA) shocks
Contemporaneous restrictions
Contemporaneous/long-run restrictions
Notes: Fractions of the forecast error variance due to RERA shocks for the four variables: the log-difference of industrial production
(DIPI), real interest rate (RERA), log risk aversion (RA), and log uncertainty (UC) (model with 3 lags, selected by the Akaike
criterion). The panel on the left presents results of the model with contemporaneous restrictions, the panel on the right presents
results of the model with contemporaneous/long-run restrictions. The sample period is January 1990 – July 2007.
36
FIGURE 5: MONETARY POLICY SHOCK IN THE 6-VARIABLE VAR (CPI IPI FED PPI RA UC)
Panel A: Impulse FED, response CPI
Panel B: Impulse FED, response PPI
Panel C: Impulse FED, response RA
Panel D: Impulse FED, response UC
Panel E: Impulse FED, response IPI
Panel F: Forecast error variance
decompositions
Notes: Panels A-E: Estimated structural impulse-responses (black lines) to a monetary policy shock in the 6-variable model (with
log consumer price index (CPI), log industrial production (IPI), Fed Funds rate (FED), log producer price index (PPI), log risk
aversion (RA), and log uncertainty (UC)) and 90% bootstrapped confidence intervals (dashed grey lines), for the model with 4 lags
(selected by the Akaike criterion), based on 1000 replications. Panel F: Fractions of the structural variance due to FED shocks for
the six variables. The sample period is January 1990 – July 2007.
37
FIGURE 6: IDENTIFICATION USING HIGH-FREQUENCY FUTURES AND BUSINESS CYCLE
NEWS ANNOUNCEMENTS
Panel A: Impulse RERA, response RA
Model 1
Model 2
Panel B: Impulse RERA, response UC
Model 1
Model 2
Panel C: Impulse RERA, response DIPI
Model 1
Model 2
Notes: Estimated structural impulse-response functions (black lines) and 90% bootstrapped confidence intervals (grey dashed lines)
for the 4-variable model (with the log-difference of industrial production (DIPI), real interest rate (RERA), log risk aversion (RA),
and log uncertainty (UC)) with 3 lags (selected by the Akaike criterion), based on 1000 replications. Four restrictions are derived
from high-frequency data. Panels on the left present results of Model 1 (DIPI and RERA do not respond instantaneously to RA),
panels on the right present results of Model 2 (DIPI and RERA do not respond instantaneously to UC). The sample period is January
1990 – July 2007.
38
FIGURE 7: IDENTIFICATION USING MONTHLY FUTURES
Panel A: Impulse MP, response RA
Panel B: Impulse MP, response UC
Panel C: Impulse MP, response DIPI
Notes: Estimated impulse-response functions (black lines) of the log risk aversion (RA), log uncertainty (UC) and log-difference of
industrial production (DIPI) to “cleansed” monetary policy (MP) surprises computed using monthly futures following Bernanke and
Kuttner (2005). Grey dashed lines are the 90% bootstrapped confidence intervals. The sample period is January 1990 – July 2007.
