Monetary Shock Measurement and Stock Markets

by

Arabinda Basistha

(West Virginia University)

and

Richard Startz*

(University of California, Santa Barbara)

March 2020

Abstract:

The narrative approach based measurement of monetary shocks suggests infrequent shocks are

crucial for understanding the impact of monetary policy shocks on the economy. However, the

narrative approach is dependent on costly data collection process, researcher judgment, and is

prone to delays due to official document release. We present a stock market based regime

switching unobserved components model to estimate the monetary shocks while preserving the

key feature of infrequent shocks. Our estimated shocks are large and comparable to Romer and

Romer (2004) shocks. The impulse responses to our estimated monetary policy shocks suggest

that a one percent contractionary shock leads to two percent long term decline in industrial

production with a peak effect of 3.5 percent decline and more than one percent long term decline

in CPI.

JEL Code: E52, E58, E32, E31.

Keywords: Monetary policy; Monetary Shock; Stock market, regime switching; unobserved

components model.

* Contact author: Arabinda Basistha, Box 6025, Department of Economics, West Virginia

University, Morgantown, WV – 26506. Email: arbasistha@mail.wvu.edu. Richard Startz,

Department of Economics, University of California, Santa Barbara, Santa Barbara, CA - 93106-

9210. Email: startz@ucsb.edu. Authors would like to thank the editor Pok-Sang Lam, the

referee, the participants of Midwest Econometrics Group 2017 meeting, EcoSta 2018 conference,

Money, Macro and Finance 2018 conference, Society for Nonlinear Dynamics and Econometrics

2019 conference, Georgetown Center for Economic Research 2019 conference, North American

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Summer Meeting of the Econometric Society 2019, American University of Beirut, and the

UCSB Econometrics Working Group for comments and suggestions. Alex Kurov kindly

provided the federal funds futures shocks data. The authors assume the responsibility for all

errors and omissions.

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1. Introduction

Estimation of monetary policy shocks is a crucial issue in understanding the effects of monetary

policy on the economy. For our purposes we take the “gold standard” to be the narrative based

approach to measuring monetary policy shocks, starting with Romer and Romer (1989) and

further developed by Romer and Romer (2004), which relies on Federal Reserve economic

forecasts based on official documents. While we regard this work as the gold standard, using

narratives relies on expert judgement; thus it may be difficult to implement. Data collection often

comes with substantial lags due to timing of release of official documents. In the case of

countries with less clear historical evidence, the narrative approach may be infeasible.

The primary contribution of our paper is to offer a time series econometric method to

estimate shocks that matches well with the findings from the narrative approach in Romer and

Romer (2004) without explicitly using the narrative approach based data collection. Central to

matching well is the idea that monetary shocks are relatively infrequent. Our econometric model

uses a two-step approach. In the first step, we estimate the reduced form residuals from a

standard VAR based on stock market data, federal funds rate data and other standard indicators

of economy. Novelty lies in our second step, in which we develop a Markov-switching, state-

space model that explicitly allows for a “no shock” regime. This allows for monetary shocks to

be infrequent, without forcing the “infrequent” property on the data. This second step is similar

to the heteroskedasticity based identification proposed by Rigobon (2003) although we estimate

the no-shock regimes instead of pre-identifying them. We use a simple bivariate model in the

second step although the model can be easily generalized further to use more information.

Our estimated infrequent monetary shocks are large in size and similar to Romer and

Romer (2004). The estimates are robust to the use of different VAR lags, shadow federal funds

rate in the zero lower bound period, and the possibility of stock market feedback effects to the

federal funds rate. The estimated regime probabilities show a long period of no large monetary

shocks during the 1990s and early 2000s, supporting the evidence on increasing transparency and

information disclosure efforts by the Federal Reserve. The dynamic responses of output to the

shocks show large and persistent effects similar in size to the Romer and Romer (2004) study.

The price effects show a similarly declining pattern but are smaller in size. The standard VAR

based approach to estimating monetary shocks using regularly spaced time series, as followed by

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Leeper, Sims and Zha (1996), Bernanke, Gertler and Watson (1997), Bernanke and Mihov

(1998), Bernanke, Boivin and Eliasz (2005), finds small effects of monetary policy shocks on

output.1 The advantage of this approach is easy availability of the data used, both domestic and

international, making it simpler to compare across countries and the ease with which one can

integrate additional channels of transmission and modeling features in the analysis.2 The shocks

themselves are estimated to be moderately sized. As a practical matter, the VAR approach

estimates shocks from a continuous distribution occurring at whatever frequency is used in the

VAR.

Measurement of infrequent monetary shocks has taken two approaches. The first is the

Romer and Romer methodology. (See also Monnet (2014) for an interesting example of this

approach using historical data from France.) The crucial outcome of this approach is large output

effects. Monetary shocks of early 1980s play a major role in this approach. The second approach

to measure infrequent monetary shocks is to use the daily or high-frequency federal funds futures

data pioneered by Kuttner (2001). A primary appeal of Kuttner’s approach is the use of precisely

measured (in real time) financial data that can help in measuring the current monetary shocks.

The shocks are estimated to be moderately sized in this approach. However, a limitation of this

approach is the availability of futures data that dates back to only late 1980s. This issue makes it

impossible to analyze the events of early 1980s using this method.

A brief reminder of the Romer and Romer (2004) procedure may be helpful. The authors

employed a two-step procedure. In the first step they identified monetary policy shocks to the

federal funds rate as the change in the expected funds rate before and after FOMC meetings by

reading the Fed’s Record of Policy Actions of the Federal Open Market Committee, Minutes of

the FOMC, and Transcripts of the FOMC. The authors then applied expert judgment to make

adjustments to the initial data, in particular in regard to situations where the FOMC signaled a

future change without making a current change. After reading the narrative record and applying

1 The above referenced studies are selective examples chosen to highlight the issue. For a complete

reference of other important studies using this approach and the related issues, please refer to Ramey

(2016) and Stock and Watson (2016). 2 Jarocinski (2010) is an example of international comparison of effects of monetary shocks between EU

New Member States and other EU members using standard time series data and integrating a hierarchical

linear model in a structural VAR.

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their best judgement, in their second step Romer and Romer ran their series against Greenbook

forecasts to purge the measured shocks of endogeneity with regard to forecast future economic

developments. The correlation of Romer and Romer shocks with shocks using Kuttner’s

approach with daily data is 0.67 in the limited sample of approximately three years of

overlapping data. The correlation of the Romer and Romer shocks with a Christiano,

Eichenbaum and Evans (1999) structural VAR based federal funds shock (our estimation) is

0.37.

Our two-step statistical model recreates the essence of Romer and Romer’s two steps.

Romer and Romer first pulled changes in the expected funds rate out of the written record. This

gives a series in which monetary shocks are infrequent, since the expected funds rate frequently

didn’t change. In our first step we initially identify shocks as the errors in a standard VAR,

which gives “shocks” that come from a continuous distribution. Romer and Romer’s second

stage filters out the information in Greenbook forecasts. Such a filter can turn first-step zeros into

small, continuously distributed final shock estimates. In our second stage, we use an unobserved-

components state-space model to account for endogeneity using the assumption that information

about the future is incorporated in stock prices.3 The state-space model incorporates a discrete,

Markov-switching model which allows shocks to be infrequent since the continuous part of the

shock estimate is multiplied by a state that takes on the values 0 or 1. Because states are

estimated rather than observed, our final shock estimates—like Romer and Romer’s—also have

introduced small, continuous values. The question then is whether our approach comes close to

identifying the shocks reported by Romer and Romer. The answer is that it does rather well, and

particularly does an excellent job of identifying the small number of really large shocks, which

are presumably those of particular interest. The remainder of the paper is arranged in the

following order: In section 2 we lay out our basic empirical model, data sources and features, and

estimation details. In section 3, we discuss the estimated monetary shocks, the shock

3 This strategy of using additional financial market information in the reduced form errors to isolate the

monetary policy shocks was also used in the Bernanke and Mihov (1998) study. They used the total

reserves and non-borrowed reserves data to extract the exogenous component of federal funds rate

shocks, but they do not use stock prices. We do not use the reserves data or explicitly allow for the non-

borrowed reserve targeting regime change as in Bernanke and Mihov (1998). Our regime switching

framework focuses on identifying the no-shock regimes to isolate the large shocks that are also reflected

in stock prices.

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probabilities, and the cumulative impulse responses of output and price to the estimated

monetary shocks. We present multiple model and lag structure sensitivity analyses along with a

special restricted model in section 4. We conclude in section 5.

2. The Monetary Shock Estimation Process and the Data

2a. The Monetary Shock Estimation Process

We use a two-step process for estimation of monetary shocks. In the first step, we use a reduced

form VAR to extract the estimated residuals. In the next step, we use the reduced form VAR

residuals from the stock returns and federal funds rate equations to estimate a regime switching

model such that monetary shocks are specified to be occurring infrequently. Let 𝑦𝑡 denote our set

of variables in the following reduced form VAR:

𝑦𝑡 = 𝑐 + ∑ 𝐴𝑖𝑦𝑡−𝑖 + 𝑒𝑡𝑘𝑖=1 (1)

We use a five variable VAR with S&P 500 returns, federal funds rate, industrial production

growth, Consumer Price Index inflation rate and the unemployment rate. Beyond the stock market

variable, the selection of the other variables follows Coibion (2012) that builds on previous studies

such as Leeper, Sims and Zha (1996). Let 𝑒1 and 𝑒2 denote the estimated reduced form residuals

from the S&P 500 (used in the next step to filter for endogeneity) and federal funds rate (the shock

of interest) equations respectively.

Extracting the reduced form residuals from the first step, we then specify the following

bivariate measurement equation with a regime-switching unobserved components model to

estimate the unobserved monetary shocks:

𝑒1,𝑡 = 𝑢1,𝑡 + 𝑎13 ∗ 𝑆𝑡 ∗ 𝑢3,𝑡

𝑒2,𝑡 = 𝑢2,𝑡 + 𝑆𝑡 ∗ 𝑢3,𝑡 (2)

In the above model the 𝑢′𝑠 are unobserved state variables: 𝑢1 is a S&P 500 specific

shock, 𝑢2 is a federal funds rate specific shock, and 𝑢3 is the monetary shock estimated in terms

of the federal funds rate and allowed to affect S&P 500 returns. The variables 𝑢1, 𝑢2, and 𝑢3 are

assumed to be Gaussian and mutually and serially uncorrelated. The implicit unit coefficient in

federal funds shock equation identifies 𝑢3 as the monetary shock and 𝑎13 serves as a scaling

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factor. The variable 𝑆𝑡 is the unobserved, discrete, state variable following the regime switching

process specified below:

𝑆𝑡 = 0, 1

𝑃(𝑆𝑡 = 0|𝑆𝑡−1 = 0) = 𝑝

𝑃(𝑆𝑡 = 1|𝑆𝑡−1 = 1) = 𝑞 (3)

where the transition probability parameters 𝑝 and 𝑞 allow for persistent regimes and are

estimated in our models.

While we estimate 𝑢3 as a shock in each period, all that really matters is 𝑆𝑡 ∗ 𝑢3,𝑡. So if

𝑆𝑡 = 1 is a low probability event, then effectively monetary shocks are relatively infrequent.

The measurement equations (2) can also be written in the compact form:

[𝑒1,𝑡

𝑒2,𝑡] = 𝐻𝑆𝑡

∗ 𝑢3,𝑡 + [𝑢1,𝑡

𝑢2,𝑡] (4)

The matrix 𝐻 in equation (4) is specified as

𝐻0 = [00

] if 𝑆𝑡 = 0 and 𝐻1 = [𝑎13

1] if 𝑆𝑡 = 1. This implies when 𝑆𝑡 = 0, the unobserved

monetary shock common to both stock market residuals and Federal Funds rate residuals is not

present, thereby making it the no monetary shock regime.

2b. Data Description and Estimation Details

Monthly data on seasonally adjusted industrial productions, seasonally adjusted consumer price

index, seasonally adjusted civilian unemployment rate and effective federal funds rate were

obtained from the Federal Reserve Bank of St. Louis’ Fred database. We computed the monthly

(annualized) growth rate of real industrial production and the monthly (annualized) inflation rate.

Daily S&P 500 data was obtained from Yahoo Finance web site and monthly returns were

computed using monthly close prices. To address the issue of zero lower bound of Federal Funds

rate from December, 2008, we use the Wu-Xia shadow federal funds rate made available by the

authors. Wu and Xia (2016) use a non-linear term structure model to estimate a shadow federal

funds rate during the zero lower bound regime. They keep the shadow rate equal to the effective

federal funds rate outside the zero lower bound period of January 2009 to November 2015.

Descriptive statistics of the variables used are reported in Table 1.

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Our estimation full sample is from July 1955 to December 2016. The starting date is

chosen to allow for all estimated models to have the same starting point. The number of lags

used in the VAR is five, as selected by AIC. All other information criterion chose shorter lags.

We use two ending points as our samples for comparison: one ending in December 2008 and the

other ending in December 2016. The samples using December 2016 as the ending date use Wu-

Xia shadow rate for the zero lower bound period. The maximum likelihood estimation of the

regime switching models based on equations (2) and (3) were done using the approximate

maximum likelihood methods outlined in Kim and Nelson (1999).

3. The Estimation Results and Dynamic Effects on Output and Price

3a. The Estimation Results from the Regime Switching Models

In this section we present two sets of estimation results of monetary shocks. The benchmark

model uses a five lag VAR residuals for the sample ending in December 2008. Our second set of

results differs from the benchmark model only in that we use the Wu-Xia shadow rates to expand

our sample till December 2016. The estimated parameters from the benchmark model with the

Federal Funds rate and the Wu-Xia Funds rate are reported in Table 2. The first column reports

the parameter estimates of the benchmark model with the Federal Funds rate. All the parameters

are fairly precisely estimated. As expected, the stock market shocks are most volatile. The no

shock regime is highly persistent. Interestingly, the stock market reaction to a contractionary

monetary shock is estimated to be around negative 1.0 percent; a correct sign but a lower number

than the Bernanke and Kuttner (2005) estimates of around five percent.

Figures 1-3 present various estimates of the probability weighted monetary shocks,

Pr(𝑆𝑡 = 1) ∗ 𝑢3,𝑡 as well as the filtered probability that 𝑢3,𝑡 affected the market4. The estimated

monetary shocks illustrated in the top panel of Figure 1 use filtered probabilities along with

Romer and Romer (2004) monetary shocks for comparison. The estimated monetary shocks

illustrated in the bottom panel of Figure 1 use smoothed probabilities. In the common sample,

4 The alternative to using the filtered estimates of the shocks is to use the smoothed estimates of the

shocks. We illustrate our results in the appendix with smoothed shocks. The results are similar. The

estimated 𝑢3 shocks are also serially uncorrelated as specified in the model.

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the big events match quite well with Romer and Romer (2004). The difference in the estimates of

monetary shocks due to using either filtered or smoothed probabilities is extremely small. We

will use only filtered probability based analysis from here onwards. The major contractionary

shocks of early 1980s show similar signs. We estimate a 2.6 percent shock in March 1980

whereas Romer and Romer (2004) report 1.4 percent. In May 1981 we estimate a shock

magnitude of 2.1 percent compared to the Romer and Romer (2005) estimates of 1.5 percent. In

a very interesting case, we estimate the May 1980 shock to be negative and large 5.4 percent but

Romer and Romer (2004) report it to be only negative 0.78. However, they report the April, 1980

shock to be negative 3.2 percent whereas we do not estimate that as a shock month. In most cases

the two shocks are similar with a positive correlation of 0.4 in the Romer and Romer (2004)

sample period. The correlation of our shocks with Christiano, Eichenbaum and Evans (1999)

structural VAR shock with Cholesky identification (our estimates with monthly data and twelve

lags) is 0.77.

The estimated filtered probabilities of the monetary shock states in the benchmark model

are reported in Figure 2. The model estimates two shocks closely related to the historical

narrative of monetary and credit episodes in Bordo and Haubrich (2010); a big advantage of our

approach in enabling us to go beyond the sample period covered by Romer and Romer (2004).

Bordo and Haubrich (2010) discussed two episodes of persistent Fed tightening in 1957 and

1960 leading to credit crunches and recessions. These two episodes are not documented in

Romer and Romer (1989) but a closely related contractionary episode in March 1959 is

documented in Romer and Romer (1993). Our filtered probabilities pick up two shocks in

August 1958 and February 1961. The first among them is a reversal in the direction of the federal

funds rate by about 100 basis points that is also present in Chart 2 in Romer and Romer (1993)

leading to a long rise in the interest rates. Romer and Romer (1993) identify roughly the middle

of this long rise to be the contractionary episode. We estimate this shock to be approximately a

90 basis point rise. The second shock is also a reversal in the federal funds rate with some initial

volatility that we estimate to be a contractionary shock of about 125 basis points. In this episode,

the S&P 500 return declined from an approximately 5 percent return in the previous three

months to 2.6 percent along with low inflation, negative industrial production growth and rising

unemployment rate in the same three months.

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The big jumps in monetary shock estimates are in early and mid-1970s, and early-1980s.

This is followed by a December 1984 jump that is estimated to be an expansionary 1 percent

shock. Romer and Romer (2004) estimate the November 1984 shock to be expansionary 55 basis

points followed by another 14 basis points in December 1984. This is related to the fall in the

effective federal funds rate from 9.43 percent in November to 8.38 percent in December. We

have no further shock state probabilities that exceed fifty percent in the 1990s and early 2000s.

The parameter estimates from the full sample Wu-Xia Funds rate are in the second

column of Table 2. The estimated monetary shocks and the filtered shock probabilities are

illustrated in Figure 3. The pattern of the parameter estimates are similar in magnitude to the

previous estimates. The no-shock regimes are persistent and the stock market shock is much

more volatile than the other shocks. The filtered probabilities are similar in the pre-2009 sample.

There is also a long stretch of no shocks from late 1980s consistent with the ‘great moderation’

phase of the US economy as analyzed by Kim and Nelson (1999), McConnell and Perez-Quiros

(2000), and Stock and Watson (2002). Primiceri (2005) found a similar result by estimating the

time varying standard deviation of the monetary policy shocks. The estimated standard deviation

was not statistically different from zero in most periods after 1984. Additionally, we offer

estimated monetary shocks in the post-2008 period. In January, 2009 the filtered probability of a

monetary shock is about 99 percent. Interestingly, it is estimated to be a contractionary shock of

one percent, which is consistent with the Wu and Xia (2016) shadow rate estimates. This is right

after the beginning of the zero lower bound period but before the quantitative easing events. Wu

and Xia (2016) estimate a rise in the shadow federal funds rate in that month to 0.61 percent

continuing to February to a peak of 0.87 percent.

Romer and Romer’s estimates of monetary shocks suggest a large number of small

shocks and a small number of large shocks. Half the estimated shocks are under 10 basis points

(in absolute value). Seven percent of shocks are 50 basis points or more and one-and-a-half

percent of shocks are more than 100 basis points. For many purposes, identifying large shocks is

of particular interest. The discrete state-switching model we present does an excellent job of

identifying large shocks, albeit at the cost of doing little to identify small shocks. For the shocks

greater than 100 basis points, the correlation between our estimates and the Romer and Romer

estimates is 0.90. For shocks between 50 and 100 basis points, the correlation is 0.24. For shocks

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between 10 and 50 basis points the correlation is 0.29 and for shocks below 10 basis points the

series are essentially uncorrelated, with a correlation of only -0.04.

3b. The Dynamic Effects of Monetary Shocks on Output and Price

We estimate the dynamic response of output and price to the estimated monetary shocks using

the same autoregressive distributed lag empirical framework as used by Romer and Romer

(2004). Specifically, we use the following model, where Ω𝑡 indicates the information set

available through date 𝑡:

𝑦𝑖𝑡 = 𝛼𝑖 + ∑ 𝛽𝑖,𝑗𝑦𝑖,𝑡−𝑗 + ∑ 𝜃𝑖,𝑘�̂�3,𝑡−𝑘 + 휀𝑖,𝑡𝑛𝑘=1

𝑚𝑗=1 (5)

where �̂�3,𝑡 = 𝑃(𝑆𝑡 = 1|Ω𝑡) ∗ 𝑢3,𝑡|Ω𝑡+ 𝑃(𝑆𝑡 = 0|Ω𝑡) ∗ 0 (6)

We use seasonally adjusted industrial production as our measure of output and seasonally

adjusted consumer price index as our measure of price. Beyond the 24 autoregressive lags for

both output growth and inflation, we use 36 lags of monetary shocks for the industrial production

and 48 lags of monetary shocks for CPI as in Romer and Romer (2004). We do not include

seasonal dummies in the estimating equations as our data is already seasonally adjusted. The

contemporaneous effects are assumed to be zero in the two equations. The accumulated impulse

responses using the two sets of estimated monetary shocks are illustrated in Figures 4 and 5. In

the top panel of each graph, we show the response of industrial production and in the bottom

panel we show the accumulated impulse response of CPI to one percent shock in federal funds

rate.

Note that the estimated responses have the generated regressor issue, as outlined in Pagan

(1984), since our monetary shocks are estimated. We use a Monte Carlo based approach to

account for that issue in constructing the confidence intervals. We first draw from a multivariate

normal distribution of estimated parameters of the reduced form VAR with their variance

covariance matrix. For each draw, we estimate the reduced form shocks, use them in our regime

switching procedure to re-estimate a new set of monetary shocks. Additionally, we draw a shock

from a zero mean normal distribution with the standard error of the estimated autoregressive

distributed lag regression as the standard deviation. We reconstruct the endogenous variable of

the autoregressive distributed lag with these two draws together and the estimated parameters

with original data. We then re-estimate the autoregressive distributed lag model and construct the

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impulse responses. We do 1000 replications of this process. The 90 percent confidence intervals

of the impulse responses are shown in the two figures as dotted lines.

In Figure 4, we show the responses using the benchmark model monetary shocks. The

responses of the industrial production show a slow decline to a peak effect of -3.7 percent after

25 months and then gradually recovering to about -2.0 to -2.3 percent after five years. These

numbers are very similar to the Romer and Romer (2004) estimates of -4.3 percent peak effect

and -1.7 percent effect after four years. Our estimates are also higher than the structural VAR

based estimates reported in Christiano, Eichenbaum and Evans (1999), Coibion (2012), and

Ramey (2016), which usually show output effects below one percent. The CPI response show a

similar dynamic pattern as Romer and Romer (2004) but the long-term effect is a smaller decline

of about 1.8 percent.5 We do note a slightly stronger price puzzle in the CPI responses than

reported in Romer and Romer (2004) but their maximum impact response of 0.3 percentage is

within our 90 percent confidence interval.

The results from the full sample Wu-Xia Funds rate monetary shocks are shown in Figure

5. The peak effect is a little lower at -3.4 percent and the five year effect is around -2.2 percent.

These estimates are still higher than structural VAR estimates including estimates from Bernanke

and Mihov (1998) who show a peak effect of approximately 0.2 percentage of GDP for an

expansionary 25 basis point federal funds rate shock. The long term price responses are around -

1.1 percent. The confidence intervals for the output responses are wide but still show mostly

negative response, even in the long run. The confidence intervals for the price responses are also

wide but mostly includes zeros in the long term response. Overall, we find a similar set of

cumulative impulse responses of output and price to our estimated monetary shocks for both

samples. The responses are comparable to Romer and Romer (2004) magnitudes and dynamics,

especially for output.

4. Model Sensitivity Analyses

In this section, we perform five sets of model sensitivity analyses of our primary results. All of

the analyses highlight how our model and sample features affect the estimation of monetary

5 In this study, we use the five year accumulated response as the ‘long-term’ or ‘long-run’ effect.

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shocks or the dynamic effects on industrial production and CPI. The first set allows for further

generalization of our benchmark model in section 2 to examine potentially restrictive

misspecification on estimation of monetary shocks. In the first set we allow for a stock market

feedback effect. We also allow for longer VAR lags in this set. In the second set, we restrict the

lag structures of the autoregressive distributed lag models. This is to examine the issue of long

lag structure in the ARDL equation, as highlighted by Coibion (2012), on the dynamic effects of

the shocks. In the third set, we allow for the three additional reduced form shocks as controls in

the regime switching estimation step. This is a robustness check for omitted variables. In the

fourth set, we restrict the monetary shock state transition probability to zero thereby not allowing

it to be persistent. This set highlights a further restriction one can put in on our benchmark model

without seriously affecting the outcomes. In the fifth set, we re-estimate our benchmark model

limiting the sample to 1987 through 2008 and compare the shock regimes with the large shocks

documented in Kuttner (2001). Overall, the analyses help us to understand how different features

of our benchmark model shaped the primary results.

We start out with relaxing the potentially restrictive zero stock market feedback

assumption. We now allow for a potential stock market feedback to federal funds rate as stressed

in Rigobon and Sack (2003) and Bjornland and Leitemo (2009). However, both studies found

this feedback effect to be relatively small. Additionally, in an estimated Markov-switching

DSGE model, Hur (2017) also found the feedback effect to be weak and driven by 1990s sample.

In our benchmark model, we assume this feedback to be zero. Here we relax this assumption. We

use the following bivariate measurement equation with a regime switching unobserved

components model to estimate the unobserved monetary shocks:

𝑒1,𝑡 = 𝑢1,𝑡 + 𝑎13 ∗ 𝑆𝑡 ∗ 𝑢3,𝑡

𝑒2,𝑡 = 𝑢2,𝑡 + 𝑎21 ∗ 𝑢1,𝑡 + 𝑆𝑡 ∗ 𝑢3,𝑡 (7)

The parameter estimates after allowing for stock market feedback effect using the full

sample are in the first column of Table 3. We assume and impose a feedback effect of 𝑎21 =

0.01 on the federal funds rate equation. The number 0.01 is lower than the Rigobon and Sack

(2003) and the Bjornland and Leitemo (2009) estimates of 4-5 basis points in response to a one

percent rise in stock prices. However, when we tried to estimate a non-negative feedback effect,

the maximum likelihood estimate converged to zero; effectively the full sample benchmark

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model outcome is consistent with Crowder (2006) and Hur (2017) results. The log likelihood in

the column reports a lower number than the Table 2 log likelihood for the full sample and can be

rejected at 1 percent level by the likelihood ratio test. The log likelihood substantially worsened

when we tried imposing 2 basis points as the feedback effect on 𝑎21. Most of the other parameter

estimates are not sensitive to this issue. The estimated monetary shocks and the filtered shock

probabilities are comparable to the full sample benchmark shocks and shock probabilities. In

other words, the evidence is against a feedback effect, but the results are robust against an

imposed moderately-sized feedback.

We proceed with our second sensitivity check using residuals from a longer lag length 12

lag VAR model using the full sample and the benchmark regime switching model. We denote

this model as 12 lag VAR model using equations (2) – (4) for the regime switching framework.

The parameter estimates from the 12 lag VAR model are in the last column of Table 3. The

pattern of the parameter estimates are similar to the previous estimates although the point

estimates of the standard deviation of the shocks are slightly smaller. The estimated monetary

shocks and the filtered shock probabilities are extremely similar to the benchmark model.6 The

impulse responses for both models using the autoregressive distributed lag model in equation (5)

are illustrated in Figure 6. The solid lines show the impulse responses using the stock market

feedback model and the dashed lines show the impulse responses using the 12 lag VAR model.

The industrial productions responses are a little lower for the 12 lag VAR model although both

models show the same pattern of responses. The long term price responses range from negative

1.5 to 1.9 percent.

Our next set of sensitivity analyses is driven by the issue of long lags in the

autoregressive distributed lag model as highlighted by Coibion (2012) in table 2, panel A of that

study. We first use 12 autoregressive lags for both industrial productions and consumer price

index equations. We allow for 12 lags of estimated monetary shocks for the industrial

productions equation and 39 lags of monetary shocks for the consumer price index equation as

specified by Coibion (2012). Additionally, we also use six month shorter lags than our

benchmark results in both autoregressive lags and distributed lags. This helps us to understand

6 We report the estimated monetary shocks and the filtered shock probabilities from the stock market

feedback model and the 12 lag VAR model in the appendix.

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how the magnitudes and the shapes of the impulse responses change as we go from shorter to

longer lags. We use Wu-Xia Funds rate shocks using the full sample. The impulse response

results are in Figure 6. Lines with solid dots show the responses from the shorter lags models and

the lines with checks show the responses from the relatively longer lags models. As Coibion

(2012) claims, the output effects are smaller for the shorter lags model. The long term output

effects are still around -1.9 percent but there is not much difference between the peak effect and

the long-term effect. More interestingly, in the longer lags model the peak effect is bigger, -3.7

percent, happens later around 2.5 years, but the response still flattens out after that. The

differences in the magnitudes and the shape show how the middle lags (18 – 26) drive the

magnitude differences and the late lags (30 – 36) drive the differences between the peak effect

and the long term effect in the output responses. The long term price effects are zero to -1.2

percent but the dynamics is similar to our previous results. Overall, the differences in magnitude

and shapes of the output effect show how long lag structures are critical for the Romer and

Romer (2004) outcomes even in our much longer sample.

Our next two sets of sensitivity analyses examine expansion and restriction of our

benchmark regime switching model in equation (2). We start out with the expanded model that

allows for controlling the effects of the remaining three reduced form shocks while estimating

the monetary shocks. This is effectively ordering the federal funds rate last in a recursively

identified structural VAR model as the linear combination of the structural shocks will be

represented by the reduced form shocks. Augmenting our regime-switching framework with the

three shocks address the issue of potential bias due to omitted contemporaneous effects in

estimating the monetary shocks. Additionally, we also allow the three shocks to influence S&P

500 residuals. (Note that data for output, prices and labor markets are released with a lag.) In the

specification below 𝑒3, 𝑒4 and 𝑒5 represent reduced form residuals from inflation, industrial

production growth and unemployment equations respectively:

𝑒1,𝑡 = 𝑢1,𝑡 + 𝑎13 ∗ 𝑆𝑡 ∗ 𝑢3,𝑡 + ∑ 𝛾𝑗𝑒𝑗,𝑡5𝑗=3

𝑒2,𝑡 = 𝑢2,𝑡 + 𝑆𝑡 ∗ 𝑢3,𝑡 + ∑ 𝛿𝑘𝑒𝑘,𝑡5𝑘=3

(8)

We estimate the extended model twice with our two samples and the parameter estimates

are reported in the first and second columns of Table 4. The coefficients in stock market equation

are statistically imprecise. While most other effects are small, the unemployment residual does

15

show correct sign in the federal funds rate equation in both samples. In the top panel Figure 7 we

show the estimated monetary shocks and the probabilities of the shocks states for the full

sample.7 The results are similar to our benchmark results. The impulse responses (reported in the

appendix), using the lag structure of our primary results in Section 3, show similar outcomes to

those reported in Figures 4 and 5. Although this extended model is primarily a robustness

analysis, the model and the outcomes highlight how one fit in a partially recursive structure in

the model and isolate the potentially important additional information.

Our fourth set of sensitivity analysis restricts the transition probability 𝑞 in equation (3)

to zero. Setting 𝑃(𝑆𝑡|𝑆𝑡−1) = 0 may be thought of as a strong identification restriction of what it

means to be a “shock” with an expected duration of one period. This is the model with least

number of parameters. We then re-estimate the two step model with our two samples; one ending

in December 2008 with the regular Federal Funds rate and the other ending in 2016 with the Wu-

Xia Funds rate. The estimated parameters are reported in the two columns of Table 5. Both

columns show larger monetary shocks and higher response of the stock market than our

benchmark results. The estimated shocks and the shock probabilities from the full sample are

shown in the bottom panel of Figure 7. The shocks are also relatively less frequent when

compared to our benchmark model estimates in Figure 3. We estimate the probability of a shock

to be over 50 percent approximately 14 percent of the time in the benchmark model but only

about 4 percent of the time in here. The impulse responses (reported in the appendix), using the

lag structure of our primary results in Section 3, are quite similar in size and dynamics when

compared to the comparable cases in Figures 4 and 5 with long term output effects around -2

percent. This restricted model helps us to understand the relatively important shocks driving our

primary results.8

The last set of sensitivity analysis reestimates our benchmark model for a restricted

sample starting in 1987 and ending in 2008. The parameter estimates are reported in Table 6. The

changes to note are a sharp drop in the size of the monetary shock to about 19 basis points and a

7 To avoid unnecessary repetition, we do not show the 1955:7 to 2008:12 estimated monetary shocks and

shock probabilities for these two sets of sensitivity analyses. The results are similar and available upon

request. 8 We also experimented with estimating the impulse responses with randomly drawn false shocks. As

expected, the outcomes are close to zero and do not show any pattern.

16

rise in the response of the stock prices to negative four percentage points. The drop in the

volatility of the federal funds rate around this time was also noted in Basistha and Startz (2004).

The response of the stock market is now much closer to Bernanke and Kuttner (2005) since the

sample considered is also closer. Our estimated probabilities of monetary shock regimes are

illustrated in Figure 8. They pick up the large shocks of Kuttner (2001)9 quite nicely. Our

estimated filtered shocks have correlation of 0.41 with the Kuttner shocks, but for shocks with

more than 10 basis points in size the correlation is 0.65. There are 95 months of zero Kuttner

shocks in our sample. Our average estimated monetary shocks for those months is less than

(negative) one-half basis point. Finally, in one case in January, 2008 with two FOMC meetings

and the last being on 30th January, our estimated monetary shock picks up February, 2008 as the

shock month. Overall, this sample relates to the long no monetary shock span in our earlier

analysis and shows that there were shocks in this period but of much smaller size relative to pre-

1987 period.

5. Conclusion

Narrative approach based measurement of monetary shocks suggests infrequent shocks are

crucial for understanding the impact of monetary policy shocks on the economy. However, the

narrative approach is also dependent on a costly data collection process, researcher judgment and

prone to delays due to official document release. In this study, we present a time series based

empirical model using stock market data to estimate monetary shocks while preserving the key

feature of infrequent shocks. We use easily available monthly data and a two-step estimation

process to compute the shocks. Our estimated monetary shocks are large in size and are

comparable to Romer and Romer (2004) shocks. The estimated cumulative impulse responses

suggest that our estimated contractionary shocks lead to two percent long term decline in

industrial production with a peak effect of more than three percent decline. We estimate a more

than one percent long term decline in CPI.

9 These shocks are based on daily federal funds futures data on FOMC event days. There are five months

in our sample with multiple FOMC meetings. For those months, we show the average of the daily shocks.

17

References:

Bagliano, Fabio C., and Carlo A. Favero (1999). “Information from Financial Markets and VAR

Measures of Monetary Policy”, European Economic Review, 43 (4–6): 825–37.

Basistha, Arabinda, and Richard Startz (2004). “Why were Changes in the Federal Funds Rate

Smaller in the 1990s?”, Journal of Applied Econometrics, 19 (3), 339-354.

Bernanke, Ben S., Mark Gertler, and Mark Watson (1997). “Systematic Monetary Policy and the

Effects of Oil price Shocks.” Brookings Papers on Economic Activity 1, 91–142.

Bernanke, Ben S., Jean Boivin, and Piotr Eliasz. (2005), “Measuring the Effects of Monetary

Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach.” Quarterly

Journal of Economics, 120 (1), 387-422.

Bernanke, Ben S., and Ilian Mihov (1998). “Measuring Monetary Policy.” Quarterly Journal of

Economics, 113 (3), 869-902.

Bernanke, Ben S., and K. Kuttner (2005). “What Explains the Stock Market’s Reaction to

Federal Reserve Policy?” Journal of Finance, 60, 1221–1257.

Bjornland, H. C., and Kai Leitemo (2009). “Identifying the Interdependence between US

Monetary Policy and the Stock Market”, Journal of Monetary Economics, 56, 275-282.

Bordo, M. D., and J. G. Haubrich (2010). “Credit Crises, Money and Contractions: An Historical

View”, Journal of Monetary Economics, 57 (1), 1-18.

Gertler, M., and P. Karadi (2015). “Monetary Policy Surprises, Credit Costs, and Economic

Activity”, American Economic Journal: Macroeconomics, 7 (1), 44-76.

Christiano, L. J., M. Eichenbaum, and C. L. Evans (1999). “Monetary Policy Shocks: What have

We Learned and to What End?”, Handbook of Macroeconomics, 1, Elsevier, 65-148.

Coibion, Olivier (2012). “Are the Effects of Monetary Policy Shocks Big or Small?” American

Economic Journal: Macroeconomics, 4 (2), 1-32.

Cook, T., and T. Hahn (1989). “The Effect of Changes in the Federal Funds Rate Target on

Market Interest Rates in 1970s”, Journal of Monetary Economics, 24, 331-35.

18

Crowder, W. (2006). “The Interaction of Monetary Policy and Stock Returns”, Journal of

Financial Research, 29 (4), 523–535.

D’Amico, S., and M. Farka (2011). “The Fed and the Stock Market: An Identification Based on

Intraday Futures Data”, Journal of Business and Economic Statistics, 29 (1), 126-137.

Hur, Joonyoung (2017), “Monetary Policy and Asset Prices: A Markov-Switching DSGE

Approach”, Journal of Applied Econometrics, 32 (5), 965-982.

Inoue, A. and B. Rossi (2018), “The Effects of Conventional and Unconventional Monetary

Policy: A New Approach”, Working Paper.

Jarociński, Marek (2010). “Responses to monetary policy shocks in the east and the west of

Europe: a comparison”, Journal of Applied Econometrics, 25 (5), 833 – 868.

Kilian, L., (2009). “Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply

Shocks in the Crude Oil Market”, American Economic Review, 99 (3), 1053-69.

Kim, Chang-Jin, and C. R. Nelson (1999). “State-Space Models with Regime Switching”. MIT

Press, Cambridge, MA.

Kim, C.L. and C. R. Nelson (1999). “Has the US Economy Become More Stable? A Bayesian

Approach Based On A Markov-Switching Model of the Business Cycle”, The Review of

Economics and Statistics, 81(4), 608-616.

Kuttner, K.N. (2001). “Monetary Policy Surprises and Interest Rates: Evidence from the Fed

Funds Future Market”, Journal of Monetary Economics, 47, 523-544.

Leeper, E., C. Sims, and T. Zha (1996). “What does monetary policy do?” Brookings Papers on

Economic Activity, 2, 1–63.

McConnell, M., and Gabriel Perez-Quiros (2000). “Output Fluctuations in the United States:

What Has Changed since the Early 1980s?” American Economic Review, 90, 1464-76.

Monnet, Eric (2014). “Monetary Policy without Interest Rates: Evidence from France's Golden

Age (1948 to 1973) Using a Narrative Approach”, American Economic Journal:

Macroeconomics, 6 (4), 137-69.

19

Pagan, Adrian (1984). “Econometric Issues in the Analysis of Regressions with Generated

Regressors”, International Economic Review, 25 (1), 221-247.

Primiceri, G. E. (2005). “Time varying Structural Vector Autoregressions and Monetary Policy”,

The Review of Economic Studies, 72 (3), 821-52.

Ramey, V. A. (2016). “Macroeconomic Shocks and their Propagation”, Handbook of

Macroeconomics, 2, 71-162.

Rigobon, R. (2003). “Identification through Heteroskedasticity”, The Review of Economics and

Statistics, 85 (4), 777–792.

Rigobon, R., and B. Sack (2003). “Measuring the Reaction of Monetary Policy to the Stock

Market”, Quarterly Journal of Economics, 118, 639–669.

Romer, Christina D. and David H. Romer (1989). “Does Monetary Policy Matter? A New Test

in the Spirit of Friedman and Schwartz”, NBER Macroeconomics Annual, MIT Press.

Romer, Christina D. and David H. Romer (1993). “Credit Channel or Credit Actions? An

Interpretation of the Postwar Traansmission Mechanism”, Proceedings – Economic

Policy Symposium – Jackson Hole, Federal Reserve Bank of Kansas City, 71-149.

Romer, Christina D. and David H. Romer (2004). “A New Measure of Monetary Policy Shocks:

Derivation and Implications”, American Economic Review, 94 (4), 1055-84.

Stock, James H. and Mark W. Watson (2002). “Has the Business Cycle Changed and Why?” in

Mark Gertler and Kenneth Rogoff, eds., NBER Macroeconomics Annual, Cambridge,

MA: MIT Press, 159-218.

Stock, James H., and Mark W. Watson (2012). “Disentangling the Channels of the 2007-09

Recession”, Brookings Papers on Economic Activity, Spring, 81-156.

Stock, James H., and Mark W. Watson (2016). “Dynamic Factor Models, Factor-Augmented

Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics”,

Handbook of Macroeconomics, 2, Elsevier, 415-525.

20

Wu, Jing Cynthia and Fan D. Xia (2016). “Measuring the Macroeconomic Impact of Monetary

Policy at the Zero Lower Bound”, Journal of Money, Credit, and Banking, 48 (2-3), 253-

291.

21

Table 1: Descriptive Statistics of Key Variables

Variables Mean Median Std. Deviation

S&P 500 Return 0.54 0.91 4.21

Federal Funds Rate 5.70 5.25 3.31

Wu-Xia Funds Rate 4.83 4.76 3.84

Industrial Production Growth 2.58 3.04 10.37

CPI Inflation 3.58 3.07 3.73

Unemployment Rate 6.00 5.70 1.58

Source and Description

S&P 500 S&P 500, not seasonally adjusted, Yahoo Finance, ^GSPC.

Federal Funds Rate Effective Federal Funds Rate, not seasonally adjusted, FRED

database, FEDFUNDS.

Wu-Xia Funds Rate Wu-Xia shadow rates,

https://sites.google.com/site/jingcynthiawu/home/wu-xia-

shadow-rates

Industrial Production The Industrial Production Index, seasonally adjusted, FRED

database, INDPRO.

Consumer Price Index Consumer Price Index for All Urban Consumers: All Items,

seasonally adjusted, FRED database, CPIAUCSL.

Unemployment Rate Civilian unemployment rate, seasonally adjusted, FRED

database, LNS14000000.

Note: The sample for monthly S&P 500 return is 1955:07 to 2016:12. The sample for Federal

Funds Rate is 1955:07 to 2008:12. The sample for Wu-Xia Funds Rate is 1955:07 to 2016:12 but

from 1955:07 to 2008:12 and 2015:12 to 2016:12 the series is the effective Federal Funds Rate.

The sample for annualized industrial production growth is 1955:07 to 2016:12. The sample for

annualized CPI inflation is 1955:07 to 2016:12. The sample for unemployment rate is 1955:07 to

2016:12.

22

Table 2: Parameter Estimates for the Benchmark Model

Parameters Federal Funds Rate Wu-Xia Rate

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟏) 4.091 (0.11) 4.084 (0.11)

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟐) 0.215 (0.01) 0.209 (0.01)

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟑) 1.003 (0.08) 1.001 (0.03)

𝒑 0.978 (0.01) 0.979 (0.01)

𝒒 0.890 (0.03) 0.881 (0.04)

𝒂𝟏𝟑 -1.019 (0.41) -1.028 (0.40)

Log L -1963.875 -2218.346

N 642 738

Note: The estimation samples are 1955:07 to 2008:12 and 1955:07 to 2016:12. The terms

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝒊) denote the standard deviations of the shock 𝑢𝑖 where 𝑖 = 1, 2, 3, and estimated as

parameters of the model. Standard errors are reported in the parentheses. The log likelihoods in

the two columns are not comparable as they are defined over different dataset lengths for the

estimation of the parameters.

23

Table 3: Further Parameter Estimates for Sensitivity Analysis

Parameters Stock Market Feedback Model 12 lag VAR Model

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟏) 4.070 (0.11) 3.960 (0.10)

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟐) 0.214 (0.01) 0.191 (0.01)

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟑) 0.990 (0.05) 0.815 (0.07)

𝒑 0.978 (0.01) 0.975 (0.01)

𝒒 0.878 (0.04) 0.899 (0.03)

𝒂𝟏𝟑 -1.353 (0.41) -0.803 (0.42)

𝒂𝟐𝟏 0.01* -

Log L -2234.888 -2173.517

N 738 738

Note: The estimation sample is 1955:07 to 2016:12. The terms 𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝒊) denote the

standard deviations of the shock 𝑢𝑖 where 𝑖 = 1, 2, 3, and estimated as parameters of the model.

Standard errors are reported in the parentheses. The log likelihoods in the two columns are not

comparable as they are defined over different datasets for the estimation of the parameters. *

indicates that the coefficient for 𝑎21 in the Stock Market Feedback Model is imposed, not

estimated.

24

Table 4: Parameter Estimates from the Expanded Model

Parameters Federal Funds Rate Wu-Xia Funds Rate

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟏) 4.083 (0.11) 4.079 (0.11)

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟐) 0.207 (0.01) 0.202 (0.01)

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟑) 0.975 (0.12) 0.974 (0.06)

𝒑 0.975 (0.01) 0.976 (0.01)

𝒒 0.882 (0.04) 0.873 (0.04)

𝒂𝟏𝟑 -0.998 (0.42) -1.002 (0.40)

𝜸𝟑 -0.076 (0.06) -0.065 (0.06)

𝜸𝟒 0.007 (0.02) 0.002 (0.02)

𝜸𝟓 1.108 (1.10) 0.660 (1.13)

𝜹𝟑 0.010 (0.00) 0.010 (0.00)

𝜹𝟒 0.001 (0.00) 0.002 (0.00)

𝜹𝟓 -0.220 (0.06) -0.150 (0.06)

Log L -1950.560 -2206.601

N 642 738

Note: The estimation sample is 1955:07 to 2008:12 for the second column and 1955:07 to

2016:12 for the last column. The terms 𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝒊) denote the standard deviations of the

shock 𝑢𝑖 where 𝑖 = 1, 2, 3, and estimated as parameters of the model. Standard errors are

reported in the parentheses. The log likelihoods in the two columns are not comparable as they

are defined over different dataset horizons for the estimation of the parameters.

25

Table 5: Parameter Estimates from the Restricted Model

Parameters Federal Funds Rate Wu-Xia Funds Rate

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟏) 4.086 (0.11) 4.076 (0.11)

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟐) 0.312 (0.01) 0.296 (0.01)

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟑) 1.656 (0.28) 1.583 (0.24)

𝒑 0.955 (0.01) 0.955 (0.01)

𝒒 0* 0*

𝒂𝟏𝟑 -1.346 (0.50) -1.436 (0.50)

Log L -2085.487 -2360.1422

N 642 738

Note: The estimation sample is 1955:07 to 2008:12 for the second column and 1955:07 to

2016:12 for the last column. The terms 𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝒊) denote the standard deviations of the

shock 𝑢𝑖 where 𝑖 = 1, 2, 3, and estimated as parameters of the model. Standard errors are

reported in the parentheses. The log likelihoods in the two columns are not comparable as they

are defined over different dataset horizons for the estimation of the parameters. * indicates that

the coefficient for 𝑞 in the two restricted models is imposed, not estimated.

26

Table 6: Parameter Estimates for the Benchmark Model with 1987-2008 Sample

Parameters Federal Funds Rate

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟏) 4.173 (0.18)

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟐) 0.105 (0.02)

𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝟑) 0.189 (0.02)

𝒑 0.947 (0.04)

𝒒 0.924 (0.06)

𝒂𝟏𝟑 -4.108 (2.96)

Log L -622.091

N 264

Note: The estimation samples are 1987:01 to 2008:12. The terms 𝑺𝒕𝒅. 𝑫𝒆𝒗(𝒖𝒊) denote the

standard deviations of the shock 𝑢𝑖 where 𝑖 = 1, 2, 3, and estimated as parameters of the model.

Standard errors are reported in the parentheses.

27

Figure 1: Estimated Monetary Shocks using the Federal Funds Rate

-6

-4

-2

0

2 -4

-3

-2

-1

0

1

2

60 65 70 75 80 85 90 95 00 05

Estimated Monetary Shocks, Filtered

Romer and Romer (2004) Shocks

-6

-4

-2

0

2 -4

-3

-2

-1

0

1

2

60 65 70 75 80 85 90 95 00 05

Estimated Monetary Shocks, Smoothed

Romer and Romer (2004) Shocks

Note: The horizontal axis represents months from July, 1955 to December, 2008. The left vertical axis

represents percentages for the estimated monetary shocks. The right vertical axis represents percentages

for Romer and Romer (2004) shocks.

28

Figure 2: Estimated Shock Probabilities using the Federal Funds Rate

0.0

0.2

0.4

0.6

0.8

1.0

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Estimated Probability of a Monetary Shock

Note: The horizontal axis represents months from July, 1955 to December, 2008. The vertical axis

represents probabilities.

29

Figure 3: Estimated Monetary Shocks and Probabilities using Wu-Xia Funds Rate

-6

-4

-2

0

2 0.0

0.2

0.4

0.6

0.8

1.0

60 65 70 75 80 85 90 95 00 05 10 15

Estimated Monetary Shocks

Estimated Probabilities of a Monetary Shock

Note: The horizontal axis represents months from July, 1955 to December, 2016. The left vertical axis

represents percentages. The right vertical axis represents probabilities.

30

Figure 4: Dynamic Effects of Monetary Shocks using the Federal Funds Rate

-6

-5

-4

-3

-2

-1

0

1

2

5 10 15 20 25 30 35 40 45 50 55 60

Industrial Production Response

-5

-4

-3

-2

-1

0

1

2

3

5 10 15 20 25 30 35 40 45 50 55 60

Consumer Price Index Response

Note: The horizontal axes represents monthly time periods. The vertical axes represents percentages. The

solid lines show cumulative responses in percentages. The dotted lines show 90 percent confidence

interval using 1000 Monte Carlo repetitions after accounting for the generated regressor problem.

31

Figure 5: Dynamic Effects of Monetary Shocks using Wu-Xia Funds Rate

-6

-5

-4

-3

-2

-1

0

1

2

5 10 15 20 25 30 35 40 45 50 55 60

Industrial Production Response

-5

-4

-3

-2

-1

0

1

2

3

5 10 15 20 25 30 35 40 45 50 55 60

Consumer Price Index Response

Note: The horizontal axes represents monthly time periods. The vertical axes represents percentages. The

solid lines show cumulative responses in percentages. The dotted lines show 90 percent confidence

interval using 1000 Monte Carlo repetitions after accounting for the generated regressor problem.

32

Figure 6: Model and Lag Sensitivity Analysis of Dynamic Effects using Monetary Shocks

-6

-5

-4

-3

-2

-1

0

1

2

5 10 15 20 25 30 35 40 45 50 55 60

Stock Market Feedback 12 Lag VAR

ARDL 12, 12 ARDL 18, 30

-5

-4

-3

-2

-1

0

1

2

3

5 10 15 20 25 30 35 40 45 50 55 60

Stock Market Feedback 12 Lag VAR

ARDL 12, 39 ARDL 18, 42

Note: The horizontal axes represent monthly time periods. The vertical axes represent percentages. The

graphs show cumulative responses in percentages. The top panel shows the effects on industrial

production and the bottom panel shows the effects on Consumer Price Index.

33

Figure 7: Monetary Shocks and Probabilities from Expanded and Restricted Models

-6

-4

-2

0

2 0.0

0.2

0.4

0.6

0.8

1.0

60 65 70 75 80 85 90 95 00 05 10 15

-6

-4

-2

0

2

0.0

0.2

0.4

0.6

0.8

1.0

60 65 70 75 80 85 90 95 00 05 10 15

Estimated Monetary Shocks

Estimated Probabilities of a Monetary Shock

Note: The horizontal axis represents months from July, 1955 to December, 2016. The left vertical axes

represent percentages. The right vertical axes represent probabilities. The top panel shows the estimates

from the expanded model while the bottom panel shows the estimates from the restricted model.

34

Figure 8: Estimated Shock Probabilities and Kuttner (2001) Shocks

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

Estimated Probabilities of a Monetary Shock

Kuttner (2001) Shock

Note: The horizontal axis represents months from January, 1987 to December, 2008. The left

vertical axes represent percentages. The Kuttner (2001) shocks start in February, 1994.

35

Appendix:

Figure A1: Shock Probabilities and Effects of Shocks using the Federal Funds Rate

0.0

0.2

0.4

0.6

0.8

1.0

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Filtered Probability Smoothed Probability

-6

-5

-4

-3

-2

-1

0

1

2

5 10 15 20 25 30 35 40 45 50 55 60

IP Filtered IP Smoothed

-5

-4

-3

-2

-1

0

1

2

3

5 10 15 20 25 30 35 40 45 50 55 60

CPI Filtered CPI Smoothed

Explanation: The above three panels compare the outcomes between the filtered probabilities and

the smoothed probabilities for the benchmark model using sample till 2008:12.

36

Figure A2: Shock Probabilities and Effects of Shocks using the Wu-Xia Funds Rate

0.0

0.2

0.4

0.6

0.8

1.0

60 65 70 75 80 85 90 95 00 05 10 15

Filtered Probability Smoothed Probability

-6

-5

-4

-3

-2

-1

0

1

2

5 10 15 20 25 30 35 40 45 50 55 60

IP Filtered IP Smoothed

-5

-4

-3

-2

-1

0

1

2

3

5 10 15 20 25 30 35 40 45 50 55 60

CPI Filtered CPI Smoothed

Explanation: The above three panels compare the outcomes between the filtered probabilities and

the smoothed probabilities for the full sample model using Wu-Xia Funds rate.

37

Figure A3: Estimated Monetary Shocks and Probabilities with Stock Market Feedback

-6

-4

-2

0

2 0.0

0.2

0.4

0.6

0.8

1.0

60 65 70 75 80 85 90 95 00 05 10 15

Estimated Monetary Shocks

Estimated Probabilities of a Monetary Shock

Note: The horizontal axis represents months from July, 1955 to December, 2016. The left vertical axis

represents percentages. The right vertical axis represents probabilities.

Explanation: The solid line shows the estimated monetary shocks and the dashed line shows the

filtered probabilities of a monetary shock. Both are estimated from the stock market feedback

model. The results are similar to those reported in Figure 3.

38

Figure A4: Estimated Monetary Shocks and Probabilities with 12 Lag VAR Model

-6

-4

-2

0

2 0.0

0.2

0.4

0.6

0.8

1.0

60 65 70 75 80 85 90 95 00 05 10 15

Estimated Monetary Shocks

Estimated Probabilities of a Monetary Shock

Note: The horizontal axis represents months from July, 1955 to December, 2016. The left vertical axis

represents percentages. The right vertical axis represents probabilities.

Explanation: The solid line shows the estimated monetary shocks and the dashed line shows the

filtered probabilities of a monetary shock. Both are estimated from 12 lag VAR model. The

results are similar to those reported in Figure 3.

39

Figure A5: Dynamic Effects from Expanded and Restricted Models

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-5

-4

-3

-2

-1

0

1

2

5 10 15 20 25 30 35 40 45 50 55 60

Expanded Model 2008 Expanded Model 2016

Restricted Model 2008 Restricted Model 2016

-5

-4

-3

-2

-1

0

1

2

3

5 10 15 20 25 30 35 40 45 50 55 60

Expanded Model 2008 Expanded Model 2016

Restricted Model 2008 Restricted Model 2016

Note: The horizontal axes represent monthly time periods. The vertical axes represent percentages. The

graphs show cumulative responses in percentages. The top panel shows the effects on industrial

production and the bottom panel shows the effects on Consumer Price Index.

40

Explanation: The impulse responses reported in Figure A5 use the lag structure of our primary

results in Section 3. The solid lines show the impulse responses from the expanded model using

the sample till 2008. The dashed lines show the impulse responses from the expanded model

using the full sample. The outcomes are similar to those reported in Figures 4 and 5. The solid

dotted and dashed lines show the impulse responses from the restricted model using the sample

till 2008 and the lines with checks show the impulse responses from the restricted model using

the full sample.

41

Figure A6: Comparison of Price Puzzle with Romer and Romer (2004) sample

-5

-4

-3

-2

-1

0

1

2

3

5 10 15 20 25 30 35 40 45 50 55 60

Consumer Price Index Response

Consumer Price Index Romer and Romer sample

Romer and Romer maximum impact

Explanation: The above figure compares the CPI response reported in bottom panel of Figure 4

with a similarly estimated CPI response based on Romer and Romer (2004) sample of 1969 -

1996. The estimated responses are a little higher than our original sample but within our previous

90 percent confidence interval. Additionally, we also show the maximum price puzzle impact of

0.3 percent stated in Romer and Romer (2004) (page 1073). That also lies within our 90 percent

confidence interval. Overall, while our point estimates of price puzzle is higher than reported in

Romer and Romer (2004) and shows some sample sensitivity but the 90 percent confidence

interval includes most of the estimates.

42

Figure A7: Comparison of Output Response with Cholesky Identification

-6

-5

-4

-3

-2

-1

0

1

2

5 10 15 20 25 30 35 40 45 50 55 60

Industrial Production Response Cholesky Identification

Industrial Production Response

Explanation: The above figure compares the industrial production response reported in top panel

of Figure 4 with a Christiano, Eichenbaum and Evans (1998) (hereafter CEE) based 100 basis

point federal funds rate shock. Following CEE we used log industrial production, log CPI, log

PPI commodity, federal funds rate, log total reserves, log nonborrowed reserves and log M1. We

used the Cholesky identification in that order. We use monthly data (not quarterly as reported in

CEE) for close comparison with our monthly results. The data is from 1959:1 – 2007:12 and we

use 12 lags (CEE use four quarters). The end of our sample is driven by negative nonborrowed

reserves numbers in 2008. The correlation between Cholesky based federal funds rate shocks and

our baseline shocks is 0.77 in the common sample.