Discussion Papers In Economics
And Business

Has the effect of monetary policy changed
during 1990s?:
An Application of Identified Markov Switching Vector Autoregression to the
Impulse Response Analysis When the Nominal Interest Rate is Almost Zero

Ippei Fujiwara

Discussion Paper 03-08

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANHas the effect of monetary policy changed
during 1990s?:
An Application of Identified Markov Switching Vector Autoregression to the
Impulse Response Analysis When the Nominal Interest Rate is Almost Zero

Ippei Fujiwara

Discussion Paper 03-08

April 2003

この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANHas the effect of monetary policy changed
during 1990s?:
An Application of Identified Markov Switching Vector Autoregression to the
Impulse Response Analysis When the Nominal Interest Rate is Almost Zero

Ippei Fujiwara∗†
Bank of Japan and Osaka University
Preliminary Version, April 2003

Abstract
I study whether the effect of monetary policy has changed during 1990s
and the zero bound of nominal interest rate may have some distortional
effect on macroeconomic dynamics. In order to check the existence ofstructural change without any prior knowledge on break point and to beable to compare the effect of monetary policy before and after the breakwithout any distortion from the difference in degrees of freedom causedby the different estimated periods, the identified Markov switching vector
autoregression model is estimated.
The result shows that there is a structural change in 1990s and theeffect of monetary policy has become weaker since then. As obvious,
traditional interest rate channel is not functioning and therefore the roleof monetary expansion is limited now.
Another intriguing by-product is that the conventional puzzles withidentified VAR, namely price puzzle and liquidity puzzle, are often resolved in one regime, but not in the whole sample. This finding may havesome implication for the cause of those puzzles, the coexistence of equilibrium dynamics and disequilibrium dynamics in economic time series.

JEL Classification: C33; E50.
Key words: Markov Switching Model; VAR; Monetary Policy;
Price Puzzle; Liquidity Puzzle; Bootstrapping;Zero Bound of Nominal Interest Rate
∗ Author’s correspondence: ippei.fujiwara@boj.or.jp† The author would like to thank Michael Ehrmann (European Central Bank) for valuablecomments and sharing the code for the impulse responses from Markov switching model
written by Ox. Further, I appreciate the helpful comments from Kosuke Aoki (Universitat
Pompeu Fabra), Kanemi Ban (Osaka University), Shigeru Fujita (University of California,
San Diego), Yutaka Soejima (Bank of Japan) and seminar participants at Osaka university.
Importantly, the view in this paper should not be taken as those of the Bank of Japan nor
any of its respective monetary policy or other decision making bodies. Further, any errors is
my responsibilibily alone.

1

1

Introduction

It is often argued that the effect of monetary policy has significantly weakened
during 1990s. Looking at the Japanese macroeconomy since 1990 carefully,indeed, monetary policy does not seem to have obvious stimulating effect onthe ”lost decade.”1 Several preceding research such as Miyao (2000) points out
three reasons for this event; ”(i) the yen appreciation to over 80 yen per dollar,(ii) the Bank of Japan’s actions to lower the official discount rate or the call rate
to a record low below 1%, and (iii) the series of bank failures that disclosed theserious bad loan problem in Japan’s financial sector.” Moreover, as mentioned
in Kimura, Kobayashi, Muranaga and Ugai (2002), the introduction of the zeronominal interest rate should have made the effect of monetary policy further lesseffective as there has been less room to ease from interest rate policy, namely due
to the lack of traditional interest rate channel of monetary policy transmission.
The principal aim of this paper is to check whether there was a structuralchange in monetary policy effect on real economy during 1990s due to the backgrounds as mentioned above and if so, to understand the current state of relationship between monetary instruments and other economic variables especiallywhen the nominal interest rate is almost zero.
The easiest way to test the structural break is perhaps to conduct a conventional break point test and compare the impulse responses before and after the
break separately. However, the degree of freedom usually differs between two
periods due to the difference in estimated periods. This may distort the propercomparison of the outcome from two periods. In order to find out a resolution
for this problem, the newly introduced econometric technique, identified Markov
Switching Vector Autoregression, is employed in this paper. With this method,
the model is computed without any prior knowledge about break point, since
the structural break is expressed as Markovian regime shift which is determinedby estimation. Further, as the estimation is conducted for the whole period,
there is no distortions from the difference in degrees of freedom. As long as theregimes derived by Markov switching estimation are long-lived and distinct, it
is appropriate to compare the impulse responses between different regimes as
the analysis on the structural break.
The paper consists as the following. Section one reviews the prior researchconcerning the interest mentioned above. First part is about the developments
in Markov switching regressions, and the latter is on the research with VAR on
monetary policy transmission mechanism. In section two, the VAR model formonetary policy analysis with explicit interest rate channel is constructed. It
will also explain how to estimate the Markov switching model, how to derive
the impulse response and how to draw the confidence interval by bootstrapping
method. Further, results are also summarised. In response to the consequences
attained in the previous section, the VAR model with implicit interest ratechannel is built in section three so that the analysis with the current policy
1 Hayashi and Prescott (2002) uses this word and seeks for the cause of the lost decade.
Researchers become paying more attention to Japan’s unusual experiences after the bubble
economy, as found in Bayoumi and Collyns (2000) and Ramaswamy and Rendu (2000).

2

scheme employed by the bank of Japan, namely ”Quantitative Easing” policy,
could be possible. Section four is to conclude.

2

Prior Research

In this section, prior research on Markov switching model is reviewed, then the
VAR on the monetary policy transmission mechanism.

2.1

Markov Switching Model

Hamilton (1989) is the first research to introduce Markov switching model intime series econometrics. Based on the stylised fact of nonlinearity in economic
time series, especially asymmetric business cycle established by Neftci (1984)
and others, which find that US business cycle is characterised by the combinationof long but gradual expansion and short but sudden recession, Hamilton (1989)
presents an alternative method for dating the expansion and recession to theconventional NBER method by recognising the periodic shift from a positive
growth rate to a negative growth rate as a recurrent feature of US businesscycle.
Since this seminal research, Markov switching model has been widely applied
to analyse various economic phenomena such as the Phillips curve with regime
shift and the comovement of the European business cycle since the introductionof EMI system etc. The various application of this Markov switching model andhow to estimate these models in detail are shown in Krolzig (1996) and Kim
and Nelson (1999).
Krolzig (1998) develops MSVAR with user friendly application which runson the Ox.2 It enables many researcher to be very accessible to the Markov
switching model, the programme for which is normally very complicated. The
econometric analysis below uses MSVAR.
Krolzig and Toro (1999) first recongnises the existence of impulse response
function in Markov switching vector autoregression model. It tries to derive
the impulse response functions which can account for the endogenous regime
shift. However, since my research interest lies in the comparison of the impulse responses between different regimes, regime dependent impulse responses,
namely impulse response function in each period, need to be computed. Recently, Ehrmann, Ellison and Valla (2003) shows how to derive regime dependent
impulse response functions.3 The analysis below follows their methodology.

2.2

Analysis on Monetary Policy with VAR

The researches on monetary policy transmission mechanism using VAR is quite
vast. Indeed, the seminal paper on identified VAR of Sims (1980), which is well
2 You can download the MSVAR for Ox at www.econ.ox.ac.uk/people/members/krolzighm.htm.

3 Minor extension which enables the analysis on the five variables system is made by theauthor.

3

known for the ”Sims critique” on traditional large macromodels for their implausible identifications, is also about monetary transmission. Since then, quitea large number of researches with various identification schemes have been published. Among them, it is popular to identify the system for contemporaneous
relationships between macroeconomic variables. In this context, some such as
Christiano, Eichenbaum and Evans (1999) use Choleski decomposition, which isreferred to as the recursive framework, and the other such as Leeper, Sims andZha (1996) employ non-recursive framework4 for identifying monetary policy
shocks.
As it is strongly craved for to obtain the robust results which will not change
significantly with the different estimated period so that the results obtained inthis paper could be used as the reference to check the validity of theory based
macromodel which is sometimes called as dynamic stochastic general equilibrium (DSGE) model as indeed suggested by Christiano, Eichenbaum and Evans(1999),5 several estimations are conducted with different starting date. For
this purpose, the simple identification framework which is thought to be robust
throughout the time is better to be implemented. Therefore, the model considered in this paper is based on the simple recursive framework for identification.6
As for the research on Japanese monetary policy, Teruyama (2001) well summarises the developments in this field with very good introduction for how to
identify as well. Concerning the possibility of structural change in the monetarytransmission mechanism, Miyao (2000) estimates three variables (industrial production, call rate and monetary base) and four variables (plus nominal exchangerate) VAR where all the non-financial variables are expressed as log difference
value. Miyao (2000) concludes that according to testing procedure suggested by
Christiano (1986) and Cecchetti and Karras (1994), the effect of monetary policy
has significantly weakened during 1990s. Further, on the impulse responses tomonetary expansion under the zero nominal interest rate, Kimura, Kobayashi,
Muranaga and Ugai (2002) estimates time-varying VAR and concludes that the
response of the inflation rate to the monetary base expansion becomes weaker
now than before.
Although the aim is similar to that of Miyao (2000), what is new in thispaper is first that the model is estimated with levels. Sims (1980) and otherrelated research recommend against differencing even if the variables are notstationary.7 As the main purpose of the study using VAR is not to determine
the parameter estimates but to know the inter-relationship among the variables,
differencing should not be employed because it throws away important informa4 Identification in the non-recursive framework is established by Bernanke (1986) and Sims
(1986).
5 Teruyama (2001) claims that this suggestion by CEE is implicitly assuming the righteousness of indentification structure, which is not neccesarily always right.
6 I am not saying that the simple structure is more robust, rather that the comparison
becomes very difficult if identifications are different in each estimated periods. Hence, thesimple recursive structure is employed in this paper.
7 Non-stationarity in data has no problem in estimation since the residuals behave quite
reasonably. Further, Sims, Stock and Watson (1990) claims that even if the system includes
non-staionary variables, the estimator pocesses consistency in level estimation.

4

tion concerning the comovements in the data.8 Therefore, the impulse response
obtained in this research may be rich in information. Further, as stated above,by including the Markovian regime shifts, the model is not estimated separately
for each regimes. Hence, impulse responses for each regime can be directlycomparable without any distortion from the differences in degrees of freedom.

3

Model with Explicit Interest Rate Channel

In this section, two models are estimated. One is the four variables VAR consisted of output, price level, call rate and money supply. The other is fivevariables VAR. It consists of the above four plus whole price index (WPI), theleading indicator for the price level. All are monthly data9 . This is a quite standard form of analysing monetary policy as described in Christiano, Eichenbaumand Evans (1999) and Teruyama (2001).
Perhaps, the latter may be more common as it has been recognised to escapethe ”price puzzle.” Price puzzle is a phenomenon that the price level tends toincrease right after the tightening of monetary policy, rise in the nominal interest
rate, in impulse response analysis.10 As described in Walsh (1998), ”the mostcommonly accepted explanation for the price puzzle is that it reflects the factthat the variables included in the VAR do not span the information available to
the FED in setting the funds rate.” Since Sims (1992) finds that the inclusionof commodity price, which are supposed to be sensitive to changing forecastsof future inflation and therefore serves as an additional information for themonetary policy decision making, tends to mitigate this problem as this is due
8 Doan (1996), which is the user’s manual for RATS, one of the most commonly usedsoftware for time series analysis, claims that ”Should I difference? Our advice is no, in general.
In Box-Jenkins modeling, appropriate differencing is important for several reasons: i) It is
impossible to identify the stationary structure of the process using the smaple autocorrelationsof an integrated series; ii) Most algorithms used for fitting ARIMA models will fail whenconfronted with integrated data. Neither of these applies to VAR’s. In fact, the result inFuller (1976, Theorem 8.5.1) shows that differencing produces no gain in asymptotic efficiency
in an autoregression, even if it is appropriate. In VAR, differencing throws infomatin away(for instance, a simple VAR on differences cannot capture a co-integrating relationship), while
it produces almost no gain.” Further, it recommends not to use a deterministic trend term as
the most economic time series are best represented as a random walk with trend.
9 The details for the data employed here are as follows; output: Seasonally adjusted Industrial production (Ministry of Economy, Trade and Industry), price level: Seasonally adjusted
Consumer Price Index at 2000 price (Ministry of Public Management, Home Affairs, Posts
and Telecomunications) , Call rate: with collateral bases before 1995 and without collateralbases after 1995 (Bank of Japan), money supply: seasonally adjusted M2+CD, however disconnection due to the different difinition is solved by using quartely growth rate (Bank ofJapan), and WPI: at 1995 price (Bank of Japan).
10 Another famous puzzle concerning identified VAR is ”liquidity puzzle”. Liquidity puzzle
is a symptom that the increase in interest rate occurs after the increase in monetary aggregates. Bernanke and Mihov (1998) conjectures that the misspecification for the choice of thevariables of the monetary instruments. However, their approach is based on non-recursive
assumption unless Strongin (1995) identification is employed. Further, the number of thevariables included tends to be large in those specification and this brings considerable decrease in the degrees of freedon in Markov switching estimation. Hence, in this analysis, noprescription is made to tackle this puzzle.

5

to the misspecification of central bank’s information set, five variables VAR has
been a standard approach.11 As for the analysis on monetary policy in Japan,
WPI is often used to fulfil this role as a proxy variable.
Two estimated periods with different starting dates are chosen, from January 1980 and January 1985. The ending date is always set at August 2002.
The choice of the estimated period may have a significant effect on the resultsin Markov switching estimation as regimes are estimated automatically within
the estimated period12 and therefore different estimated periods may suggest
different composition of regimes. Hence, in order to keep the robustness of theresults, estimated periods with quite different starting date as above are chosen
to estimate.
Number of lags are chosen as the majority of the suggested optimal lengthof lags according to the three information criteria: Akaike information criteria(AIC), Hannan Quinn criteria (HQ) and Schwarz Bayesian information criteria(SBIC).13
Since this is the regime switching model, the number of regimes needs to be
fixed beforehand. It is true that the likelihood ratio test which is embedded in
MSVAR may be used for the decision of the optimal number of regimes. However, Krolzig (1997) claims that due to the existence of nuisance parameters,
the likelihood ratio test against the null hypothesis of linearity or more numberof regimes has no asymptotic standard distribution.14 Furthermore, it is desirable for each regime to last a while as opposed to frequently changing so thatthe existence of structural breaks could be monitored.15 Therefore, the model
should be kept as parsimonious as possible. Considering these information into
account, the number of regimes are fixed at two.
11 However, recently, several new research can be found against this common view. Hanson (2000) deals with the price puzzle seriously and concludes that the inclusion of leading
indicator to price level does not necessarily resolve the puzzle. Further, Barth and Ramey(2001) states that if thinking about cost channel of monetary policy, the price puzzle does
not have to be a puzzle any more. It concludes that the tightening of monetary policy may
increase the cost of the firm and therefore it is quite possible to have the increase in pricelevel immediately after the increase in nominal interest rate.
12 Precisely, regime probabilities and transition probabilities are directly estimated.
13 As more parameters such as the transition matrix need to be estimated in Markov switching model, the optimal number of lags tends to be smaller than in the case of linear model.
14 One of the regularity condition for the likelihood ratio test to have an asymptotic Chi
square distribution is that the information matrix is non-singular. However, this condition
fails to hold if an m state model is to be fitted when the true process has m-1 state because
the parameters which describe mth state are unidentified under the null hypothesis.
15 Indeed, Ehrmann, Ellison and Valla (2001) claims ”Regime-dependent impulse response
functions are conditional on a given regime prevailing at the time of the disturbance andthroughout the duration of the response. The validity of regime conditioning depends on thetime horizon of the impulse response and the expected duration of the regime. As long as
the time horizon is not excessive and the transition matrix predicts regimes which are highly
persistent then the conditioning is valid and regime-dependent impulse response function area useful analytical tool. For a longer time horizon or frequently switching regimes, it would
be more attractive to condition on the expected path of the regime throughout the response.”

6

3.1

Identified Markov Switching Vector Autoregression
Model

In this analysis, all the parameters including intercept, coefficients and variancecovariance matrices for the reduced-form VAR are assumed to switch according
to the hidden Markov chain.16 Denoting the number of regimes and of lags by
m and p respectively, the equation to be estimated is expressed as follows.
Yt = v (st ) + B1 (st ) Yt−1 + · · · + Bp (st ) Yt−p + A (st ) Ut

(1)

st = 1, · · ·, mUt ˜N (0, IK )K is the dimension of the coefficient matrix Bp , namely the number ofendogenous variables. Ut , the vector of fundamental disturbances, is assumed
to be uncorrelated at all leads and lags. In case when the number of regimes mis two17 , equation (1) is reduced to
Yt = {

v1 + B11 Yt−1 + · · · + Bp1 Yt−p + A1 Ut , if st = 1.
v2 + B12 Yt−1 + · · · + Bp2 Yt−1 + A2 Ut , if st = 2(2)

st is assumed to follow the discrete time and discrete state hidden stochastic
process of Markov chain. The probability in regime i next period conditionalon that current regime is j 18 is fixed. This stochastic process is defined bytransition matrix P as follows.

p11 p12(3)P =p21 p22
pi,j = Pr (st+1 = j | st = i) ,2
X

pij = 1 ∀i, j ∈ (1, 2)

(4)

j=1

3.1.1

Estimation

The estimation of the Markov switching model is conducted by applying EM(Expectation-Maximisation) algorithm.19 As mentioned in Ehrmann, Ellison
and Valla (2003), ”since the Markov chain is hidden, the likelihood function has arecursive nature: optimal inference in the current period depends on the optimal
inference made in the previous period. Under such conditions the likelihood
cannot be maximised using standard techniques.” Under the procedure of EM
16 According to the terminology by Krolzig (1997), this specification is called as MSIAH(m)VAR(p).
17 Superscripts denote the regime.
18 i may equal to j.i and j are either 1 or 2 in this case.
19 For the details on the estimation, see Hamilton (1994) and Krolzig (1997).

7

algorithm, first, the hidden Markov chain is inferred in the expectation step fora given set of parameters, then the parameters for the hidden Markov chain
is re-estimated in the maximisation step. These two steps are continued untilconvergence.
This procedure estimates coefficient matrix, variance-covariance matrix foreach regime, transition matrix, and the optimal inference for the regimes throughi
out the sample period, which is called regime probabilities b
ξ t , where T denotes
the ending period for estimation.
ibξ t = Pr (st = i) for i = 1, 2 and t = 1, · · ·T

There exist three types of regime probabilities depending on the differencesin the information. The following analysis uses smoothed probabilities which
are defined as below.
ibξ t|τ , t < τ ≤ T

3.1.2

Identification

Matrix Ai is computed from the regime dependent variance covariance matrix
from reduced form VAR Σi .

Σi = E Ai Ut Ut0 Ai0 = Ai IAi0 = Ai Ai0(5)elements.
Matrix Ai has K 2 elements, on the other hand Σi has only K(K+1)
2
missing
restricIn order that Ai is defined from equation (5), there exist K(K−1)
2
tions. Sims (1980) introduces additional restriction based on recursive structureso that Ai is just identified from equation (5). If Ai is restricted to be a lower
triangular matrix, Ai is easily recovered by applying Choleski decomposition toequation (5).
When using the Choleski decomposition, the order of the variables in VAR
may have significant effect on the shape of impulse response function since, forexample, disturbance to the second variables has no contemporaneous effect on
the first variables. In the analysis below, I choose the very conventional order ofthe variables according to such researches as Christiano, Eichenbaum and Evans(1999) and Teruyama (2001). For the four variables VAR, the order is output,
price level, call rate and money supply. For the five variables VAR, the orderis output, price level, leading indicator to the price level, call rate and money
supply.
3.1.3

Impulse Response

Regime-dependent impulse response functions depict the relationship between
endogenous variables and fundamental disturbances within a regime. As isstandard approach for impulse responses, they draw expected changes in theendogenous variables after a one standard deviation shock to one of the fundamental disturbances. However, regime-dependent impulse response functions
8

are conditional on regime prevailing at the time of the disturbance and throughout the duration of the responses. Therefore, as mentioned earlier, this concept
is valid only when each regime is persistent.
Mathematically, this regime-dependent impulse response function at time
t+h for the case of the one standard error shock to kth fundamental disturbances
at time t when the prevailing regime is i is expressed as follows.
∂Et Yt+h|st =····=st+h =i = θik,h , for h ≥ 0∂Uk,tA series of K dimensional response vectors θ ik,1 ,..., θ ik,h show the response of
the endogenous variables to the shock to kth fundamental disturbances. Here,the duration for the impulse response is set at 48 months as this is reasonable
length of time span judged from the expected duration of each regime estimatedbelow.
These response vectors are computed by combining the unrestricted parameter estimates of reduced-form Markov switching vector autoregression model B
and identified matrix A. The first response vector is easily computed since this isa case where a one standard shock is added to the kth fundamental disturbances
which is shown as the initial disturbance vector U0 =(0, · · ·, 1, · · ·, 0), namely avector of zeros apart from the kth element which is one. Using equation (2),this is shown asibbi U0 .
θk,0 = A(6)

The remaining response vectors are also easily calculated by solving forward
for the endogenous variables in equation (2).
ibθ k,h =min(h,p) 

X

bji
B

h−j−1bi U0 , for h > 0
A

(7)

j=1

3.1.4

Confidence Interval

Bootstrapping is now widely used to gauge the precision of the impulse response
function.20 However, the bootstrapping in Markov switching model is complicated due to the existence of hidden Markov chain determining the regimes.
Therefore, it needs to first compute artificial history for the regimes. I follow
the procedure advocated by Ehrmann, Ellison and Valla (2003) as below.
1) Create a history for the hidden regimes stThis can be done recursively using the definition of a Markov process inequation (3) and (4), and replacing the transition matrix with its estimated
20 It is widely recognised that bootstrapping method may be inconsistent for autoregressivemodels with unit roots. However, that for non-stationary VAR is not very clear. Although
Choi (2002) reports that bootstrapping may be inconsistent for non-stationary bivariate ARprocess, I will not consider this point as nothing has been still very clear for VAR with morethan two variables.

9

value Pb . At each time t we draw a random number from a uniform [0, 1] distribution and compare it with the conditional transition probabilities to determine
whether there is a switch in regime.
2) Create a history for the endogenous variables
Again, this is done recursively, on the basis of equation (2). All parameters
are replaced by their estimated values and new fundamental residuals are drawn
from the normal distribution Ut ˜N (0, IK ). Equation (2) can then be appliedrecursively using the artificial regime history created in step one.
3) Estimate a Markov switching vector autoregression
Using the data from the artificial history created in step two, a Markov
switching vector autoregression
gives bootstrappedon is re-estimated. Estimatione i , · · ·, B
ei , Σ
e i for i = 1, 2, the transition
estimates of the parameters vei , B1pimatrix Pe , and the smoothed probabilities b
ξ t for i = 1, 2 and t = 1, ..., T .

4) Impose identifying restrictions
Applying the same restrictions as the data, recursive structure in this case,e2 .
e1 and, A
provides bootstrapped estimates of the matrices A
5) Calculate the bootstrapped estimates of the response vectors
e i and A
ei into equation (6) and (7)e i , ···, B
Substituting the new parameters B
1pgives bootstrapped estimates of the response vectors θik,1 ,..., θik,h for k = 1, .., K
and i = 1, 2.
Applying the above five steps for a sufficiently large number of histories gives
a numerical approximation to the distribution of the original estimates of regime
vectors. In this analysis, bootstrapping is conducted 100 times. The distribution
obtained from 100 times bootstrapping forms the basis for the adding confidence
interval bands to the impulse response functions.

3.2

Results

First, we will see the impulse responses from the linear VAR model as a reference for further analysis. Then, the results from identified Markov switching
vectorautoregression models are shown.
3.2.1

Linear model

The linear VAR as below is estimated for the periods of January 1980 to August
2002 and January 1985 to August 2002. As four and five variable VAR are
estimated respectively, in total, four VAR models are estimated.
Yt = v1 + B1 Yt−1 + AUt

10

Lag length is chosen as one except for the VAR of the four variables system
for the periods of January 1980 to August 2002, in which the number of lags
are two. Although in linear case information criteria employed here, namely
AIC, HQ and SBIC, usually suggest that the optimal lag length is longer than
the non-linear case,21 the lag length are set to be the same as the ones for the
non-linear case so that the direct comparison of impulse responses is possible
without any distortion from the difference in the models.
Table 1 shows the estimated parameters22 for all four VAR models. It may
be possible to show the matrix A, and reproduce monetary reaction function.
However, Rudebusch (1998) claims that it is suspicious to consider the monetary
reaction function derived from VAR model as the true one since the relationshipbetween the parameters obtained from VAR and deep structural parameter inthe true monetary reaction function is unclear.23 Therefore, it will not be shown.
A shock to nominal interest rate Chart 1 draws the impulse responses
from the four variable system to the positive shock on call rate. Almost similar
results are obtained in both models with different starting date. Positive shock
to call rate will lower the output level and money supply. However, as contrary
to the theory, monetary tightening here is bringing higher price level initially.
This is indeed the price puzzle mentioned earlier.
Chart 2 shows the impulse responses to the same shock from the five variable
VAR which include the leading indicator for the future inflation in order to avoid
price puzzle. As indeed suggested by prior researches, the degree of price puzzle
is significantly mitigated compared to the four variables case as above. Other
responses seem to be reasonable except for the persistent increase in money
supply in the case of the estimated period from 1985.24
Although very rough, in both charts the effect of monetary policy seems
to be weaker in the estimated periods from 1985. This may already suggest
the declining trend in the effectiveness of monetary policy through interest ratechannel.
A shock to money supply Chart 3 depicts the impulse responses to theshock on the money supply in the four variables VAR. A shock to money supply
21 However, the results are almost same with reasonable lag length.

22 Sims (1980) points out that ”Because estimated AR coefficients are highly correlated,
standard errors on the individual coefficients provide little of the sort of insight into the shapeof likelihood we ordinarily glean from starndard errors of regression coefficients.” Therefore,
here just information about parameters are introduced.
23 In its title and abstract, Rudebusch (1998) claims that ”Do measures of monetary policy
in a VAR make sence? No. In many vector autoregressions (VARs), monetary policy shocks
are identified with the least squares residuals from a regression on the federal funds rate on
an assortment of variables. Such regressions appear to be structurally fragile and are at odds
with other evidence on the nature of the U.S. federal Reserve’s reaction function; furthermore,
the residuals from these regressions show little correlation across various VARs or with funds
rate shocks that are derived from forward-looking financial markets.”
24 This may be due to the fact that the relationshp between the money supply and othermacroeconomic variables becomes very unclear in 1990s.

11increases the output and price level and at the same time is supposed to lower
the interest rate according to the conventional LM theory.25 However interest
rate is initially increasing after the expansion of money supply. This is indeed
the liquidity puzzle. From the reason mentioned earlier, no measure is taken
against liquidity puzzle in this analysis.
As for chart 4 which shows the same impulse responses in five variables
system, all the results are similar and reasonable except that liquidity puzzle isoccurring.
Contrary to the conjecture above, no significant chronological tendency inthe effect of monetary policy has been found in the case with the transmission
mechanism through money supply.
3.2.2

Identified Markov switching model

To check the stability of the monetary policy effect and the conclusion advocated by Miyao (2000) and Kimura, Kobayashi, Muranaga and Ugai (2002).
As in the case of linear VAR models, four identified Markov switching vector
autoregression models are estimated. Results from all four models are shown
below.
Estimated period: 1980-2000
Case with four endogenous variables Estimated parameters including
coefficient, the transition matrix, the variance-covariance matrix for the unrestricted VAR and information criterion as well as the results from linearity tests
are shown in Table 2.
The linearity test suggest that the model is non-linear and parameters switch
significantly between regimes. Furthermore, each regime is very persistent according to transition matrix. Therefore, in this case regime dependent impulse
responses will be a quite useful analytical tool.
Although not shown here, diagnostic tests in all cases mentioned later confirm that errors are considered to be normally independently distributed.26
Hence, even if some of the endogenous variables are not stationary, this does
not impose problems with the estimations.
Chart 5 shows smoothed regime probabilities, which suggest that the economy is in regime one throughout 1980s and regime two after 1995. The period
between 1990 and 1995 can be considered as transition period.
Impulse responses to nominal interest rate shock are shown in Chart 6. Dotted lines are confidence interval for one standard error from bootstrapping. In
25 Although conventional, recently McCallum and Nelson (1999) derives the LM curve, ormoney demand function equivalently, in an optimised framework.
26 Results from all the other three models below show that the each regime is distinct andpersistent, and further diagnostic tests support that they are all congruent. Hence, nothing
will be mentioned for the usefulness of regime-dependent impulse responses and diagnostic
tests hereafter.

12

regime one, impulse responses as expected27 are obtained with slight price puzzle. However in regime two, the positive shock to nominal interest rate increases
output and money supply.28 This impulse responses are hardly understood by
the standard macroeconomic theory.
As for the impulse responses to money supply shock in chart 7, theoretically consistent impulse response function is obtained without liquidity puzzle
in regime one, but in regime two, a shock to money supply brings lower level ofprice levels.29
Case with five endogenous variables Table 3 summarises the estimatedresults.
Chart 8 shows smoothed regime probabilities which suggest that the economy is in regime one almost during 1980s and regime two in 1990s and after.
The impulse responses to nominal interest rate shock in chart 9 show thatin regime one, theory consistent impulse responses are obtained without pricepuzzle. However in regime two, the positive shock to nominal interest rate raises
the output and the leading indicator for the future inflation. Further it just has
a slight restraining effect on the price level.
As for the impulse responses to money supply shock in chart 10, impulse
responses as expected are obtained in both regimes with some odd responses of
WPI which tend to decrease after monetary expansion shock. However, comparing the magnitude of the responses, while there is no significant differencein price level reaction between the two regimes, the response of output is muchstronger in regime one than in regime two.
Estimated period: 1985-2002
Case with four endogenous variables Table 4 summarises the estimated results.
Smoothed regime probabilities in chart 11 show that the economy is in regime
one throughout the 1980s and in regime two after 1995. Period between themcan be considered as the transition period.
The impulse responses to nominal interest rate shock in chart 12 show that
results as expected are obtained in both regimes with price puzzle solved inregime two. However, the increase in call rate raises the money supply in thiscase.3027 ”Impulse responses as expected” means the impulse responses with common features suchas price puzzle or iquidity puzzle obtained in many prior researches.
28 Notice that one root of the companion matrix is very slightly larger that unity in regime
two, which is 1.0228.
29 Kimura, Kobayashi, Muranaga and Ugai (2002) also states on the shape of recent impulse
responses that ”we seem to be witnessing something very unusual in the relationship between
money and the economy.
30 It should be noted that two roots from the companion matrix is slightly larger thanunity(1.0081 and 1.0041) in regime two.

13

As for the impulse responses to money supply shock in chart 13, almost
theoretically consistent impulse responses are obtained in regime one. However,in regime two, responses of all the endogenous variables are deviating to thewrong direction.
Case with five endogenous variables Table 5 summarises the estimatedresults.
Smoothed regime probabilities in chart 14 show that the economy is in regime
one throughout the 1980s and in regime two after 1995. Period between themcan be considered as the transition period.
The impulse responses to nominal interest rate shock in chart 15 showsthat impulse responses as expected are obtained in regime one with slightly odd
responses of money supply. Looking into the responses of price related variables,
responses of CPI and WPI decrease in regime one, but they are increasing in
regime two.
As for the impulse responses to money supply shock in chart 16, impulse
responses as expected are obtained in regime one with liquidity puzzle. However,in regime two, responses of output and WPI are moving in the opposite direction
to the prediction.

4

Model with Implicit Interest Rate Channel

The findings in the previous section suggest that 1) the interest rate channel
since the introduction of de-facto zero nominal interest rate is collapsed as is
expected, 2) the effect of monetary expansion may be smaller now than before.
As for the second point, indeed, proper comparison of the effect of monetary
expansion between in regime one and two is unfeasible since the interest ratechannel is not functioning after 1996 but it is included in the whole sample.31
Although VAR coefficients on call rate as a explanatory variable should not besignificantly different from zero in statistical sense as it has been almost zero
without any significant fluctuation since then, the parameters are not remarkably smaller in regime two than in regime one.
Reflecting these caveats, I here construct three variables VAR which consistsof price level, output level and money supply, namely VAR with implicit interest
rate channel. By doing this, we can learn about the consequences of nonnegativity constraint of nominal interest rate on the effect of monetary expansion
without any possible distortion on estimation from almost fixed interest ratesince 1996 so that we could confirm the latter finding mentioned above.
That the analysis on the monetary transmission mechanism without explicit
interest rate channel is useless is possible criticism. However, some prior researches suggest alternative channels where the money could have impact on
31 Further, the monetary policy rule employed by the Bank of Japan must be quite different
between before 1996 and after 1996 as the room for the further lowering the nominal interest
rate is very limited.

14

other macroeconomic variables such as price level and output, even if the traditional interest rate channel, which is defined as LM curve, is not functioning due
to the zero nominal interest rate bound. Koenig (1990) reports that empiricallyreal money growth enters positively and significantly in consumption equation.
Recently, the portfolio re-balancing effect,32 supported by such researches as
Meltzer (1995) McCallum (2000), and Orphanides and Wieland (2000), has become popular as one of the measure to combat deflation under zero nominalinterest rate. According to this theory, as long as the money is not the perfect
substitute for all other asset, monetary expansion affects nominal demand boththrough wealth and substitution effects on real assets, and through adjustments
in a wide range of financial yields relevant to expenditure decisions. Further,
Ireland (2001) constructs a model where the utility obtained from consumption
and money holdings are non-separable so that the money could have a direct
effect on consumption decision, although the effect through this channel turns
out to be minuscule.
Although I here do not specify any candidate of transmission channel aroundmonetary expansion as above but consider that such transmission mechanism
is implicitly included, how the transmission channel of monetary expansion onother macroeconomic variables changed due to the introduction of zero nominalinterest rate will be monitored in this three variables VAR estimated here.

4.1

Results

The estimated period for this three variables VAR is January 1985 to August
2002.33 Again, the number of lags are chosen as the majority of the suggested
optimal length of lags according to the three information criteria: AIC, HQ and
SBIC and the number of regimes is fixed at two.
Table 6 shows the estimated results. Information Criteria suggests thatthe model should be estimated with two lags. That the parameters are quite
different between regime one and two as well as each regime is quite longlived suggest usefulness of the impulse response analysis with identified Markov
Switching model.
Chart 17 shows smoothed regime probabilities, which seem to suggest thatthe economy is in regime one throughout 1980s and regime two after 1995 although there exists some short-lived switching. The period between 1990 and1995 can be considered as transition period.
Impulse responses to nominal interest rate shock are shown in Chart 18.
In both regimes, monetary expansion results in higher price level and output.
However this positive effect is smaller and less long-lived in regime two than inregime one. This result indicates that the effect of monetary expansion becomes
32 Kimura, Kobayashi, Muranaga and Ugai (2002) shows three candidates for the channels
through which this effect is working: a relative asset-supply effect, a reduction of transaction
cost by providing amply money, and the expectation effect.
33 If we estimate the model from January 1980, the regime switches around 1990. As the aimof this section is to understand the effect of zero nominal interest rate bound on the monetarytransmission mechanism, the analysis with the estimated period starting at 1980 is excluded.

15

significantly smaller when the nominal interest rate is almost zero.34

5

Conclusion

Several intriguing results are obtained from five identified Markov Switching
Vector Autoregression models I have estimated. These are summarised as follows;
1) There seems to be at least one break point of macroeconomic dynamics,
which depict the transmission mechanisms of monetary policy, during 1990s.
Candidates for this break point are sometime around 1990 and around 1995
with more possibility.
2) Monetary policy’s impact on macroeconomy, whether it be through nominal interest rate or money supply, becomes weaker than before or is not fulfilling
the role as expected in the regime which is prevailing now. Its effects on output
or price level tend to be smaller now. Furthermore, impulse responses whichcannot be understood from standard macroeconomic theory has been found in
the currently prevailing regimes when the break point is just the time when the
Bank of Japan resumed the de-facto zero nominal interest rate policy in 1996.
3) The price puzzle and the liquidity puzzle, which usually happen when one
estimates the impulse response functions of VAR and indeed are found in thelinear VAR models estimated in this paper, are not observed in some impulse
responses for regime one, namely before 1990s.
1) and 2) support the conclusions in Miyao (2000) and Kimura, Kobayashi,
Muranaga and Ugai (2002). Although recent research by Boivin and Giannoni (2003) states that ”Recent studies using vector autoregressions (VAR) findthat the impact of monetary policy ”shocks” - defined as unexpected exogenouschanges in the Federal funds rate - have had a much smaller impact on output
and inflation since the beginning of the 1980’s. .... An alternative interpretation
could thus be that monetary policy itself has come to systematically respond
more decisively to economic conditions, thereby moderating the real effects ofdemand fluctuations. In this case, the change in the responses to monetaryshocks would reflect an improvement in the effectiveness of monetary policy”,
observing that the possible break point is around 1995 when the de-facto zeronominal interest rate policy has started, it is not feasible to assume that thesmaller responses to monetary shocks are due to the improvement in the effectiveness of monetary policy in Japan. Hence, it could be concluded that theeffects of monetary policy have become weaker during 1990s.
Furthermore, 2) suggests that the Japanese economy may now be in the state
where the conventional monetary transmission mechanism is not fully functioning and this seems to be due to the introduction of de-facto zero nominal interest
34 Fujiwara (2003) confirms that the same results are obtained if the order of the variables
are changed.

16

rate policy since 1996.35 For example, if we look carefully at the impulse responses of all three models including explicit interest rate channel which further
suggest that break point is around 1995, the impulse responses after the shockto the money supply is hard to be interpreted. Even if we interpret this finding
as the failure of the proper estimation due to the almost fixed interest rate since
1996, the results from three variable VAR reports that the effect of monetary
expansion is significantly smaller. These suggest that the current problem the
Bank of Japan is facing, deflation under the almost zero nominal interest rate, isvery tricky. If the Bank of Japan could control the money supply by quantitativeeasing, its role on other macroeconomic variables would be extremely limited.
The monetary expansion without the transmission mechanism through nominalinterest rate channel seems to have just inadequate impact on macroeconomic
variables.
The existence of the break in the macroeconomic dynamics has some very
important implication for the dynamic macro modelling, either in the form
of VAR or DSGE. Needless to mention VAR, the analysis on macroeconomic
dynamics without considering the possible structural break may lead to the
misjudgment of the current state and wrongful monetary policy.36 Even forthe dynamic stochastic general equilibrium model either in the form of strong
or weak econometric interpretation in the terminology of Geweke (1999),37 themodel with parameters which is set based on the whole sample, may have wrong
explanation of the current state of economy. Tendency of the DSGE becoming
more data-oriented, namely more in the strong econometric interpretation, as in
Ireland (1999) and Smets and Wouters (2002) should be preferable as it makes
DSGE more realistic and useful for the policy analysis. However, caution always
needs to be paid to use the model for the analysis on the current economic stateas there may have been some structural break and the economic dynamics might
be quite different at the moment.
Probably, more intriguing finding is 3). This by-product hints another explanation for the famous puzzles in VAR models: price puzzle and liquidity
puzzle. Concerning the former, as mentioned earlier, the conventional explanation is the incorrect specification of central bank’s information set when deciding
monetary policy as in Sims (1992). The recently established one is the effectthrough the cost channel of monetary policy in Barth and Ramey (2001). For
the latter, as mentioned in Bernanke and Mihov (1998), the misspecification in
35 Ueda (2003) further points out that the asset price deflation causes the ”financial accelerator” to work by reducing the collateral value, and this results in the weaker monetary policy
effects.
36 Indeed, Kimura, Kobayashi, Muranaga and Ugai (2002) criticises Baig (2002) which argues
that Japan’s data support the existence of the monetary base channel even at zero interest
based on the results obtained from time invariant VAR for the whole sample.
37 The weak econometric interpretation is such that the parameters of DSGE model are
calibrated in such a way that selected theoretical moments given by the model match as
closely as possible those observed in the data, which is first adovocated by Kydland andPrescott (1982). On the other hand, the stong econometric interpretation attempts to provide
a full characterisation of the observed data series. Details on the these two interpretations arefound in Geweke (1999) or Smets and Wouters (2002).

17

the way of monetary policy conducted by central bank is the most persuasive
clarification so far. However, the result in this paper proposes an integrated
explanation to these two puzzles, each with quite different explanations so far.
Results seem to suggest that the cause of these puzzles is the coexistence ofequilibrium dynamics and disequilibrium dynamics in economic time series. Aslong as the usual economic time series contain the disequilibrium dynamics dueto the bounded rationality of the economic agents to some extent, the derivationof impulse responses according macroeconomic theory tends to be impaired, although I admit that further research will be needed in order to establish thishypothesis more persuasive for the explanation of conventional puzzles.38
38 One possible caveat on this point is that we may need to employ different identification
when comparing the impulse responses between regimes.

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22

Table 1
Coefficients of the linear VAR models

VAR(4): 1980C
Y(-1)
Y(-2)
P(-1)
P(-2)
I(-1)
I(-2)
M(-1)
M(-2)

Y
0.06950.55520.42180.6280-0.6768-0.0033
0.00251.0428-1.0261P
0.0440-0.00520.01080.91270.06500.0012-0.0010-0.00220.0043I
7.70551.9159-1.0152
12.5696-15.5834
1.2688-0.3156-0.5851
0.7152M
0.16740.0168-0.0041-0.1358
0.09130.0000-0.0005
1.2497-0.2510Y-0.3882
0.9447-0.1715
0.1082-0.00110.0602

P
0.09170.00520.9845-0.0109
0.00040.0003W
0.52580.0118-0.00100.91180.0007-0.0111I
5.8745
1.1876-5.0760
0.85450.94570.5190

VAR(5): 1980C
Y(-1)
P(-1)
W(-1)
I(-1)
M(-1)

VAR(4): 1985Y
P
C
0.1768Y(-1)
0.9228P(-1)-0.0951I(-1)
0.0006M(-1)
0.0395I

M
0.12010.0148-0.08190.0224-0.00091.0057M

0.00200.01000.98730.00020.00074.98060.9908-3.1573
0.97060.31900.26670.0056-0.0746-0.0005
1.0034P-0.14190.00830.96780.0306-0.0001
0.0072W
0.02540.0172-0.0375
0.9962-0.0001
0.0054I-22.9849
0.6704-6.9472
5.95290.9077
1.5792

VAR(5): 1985C
Y(-1)
P(-1)
W(-1)
I(-1)
M(-1)

Y
-0.3003
0.9174-0.1597
0.1015-0.0005
0.0610

Y: Output
P: Price level
I: Call rate
M: Money supply
W: Leading indicator to priceM
0.40780.0072-0.0555-0.0300-0.0002
0.9971

Table 2
Estimated results of MSVAR(4): 1980(1) Coefficients
Regime 1
C
Y(-1)
Y(-2)
P(-1)
P(-2)
I(-1)
I(-2)
M(-1)
M(-2)

Y
-0.04080.51730.42620.4994-0.5563-0.00250.00181.2238-1.1875P-0.0140-0.0138
0.00370.77640.19550.0016-0.0009
0.1311-0.1190I
17.1720
4.2774-1.101622.7290-25.81301.2305-0.3213-19.1590
18.0260

M
0.26920.02470.0041-0.1035
0.0514-0.0009-0.0002
1.0535-0.0638

C
Y(-1)
Y(-2)
P(-1)
P(-2)
I(-1)
I(-2)
M(-1)
M(-2)

Y
0.58660.53070.39920.7208-0.7495
0.0033-0.0038
0.6142-0.6227P
0.18860.00240.0086
0.93820.0276-0.00480.00460.0359-0.0411I
1.4221
0.19810.1291-2.1532
1.0634
1.1232-0.1150
0.4330-0.2999M
0.1084-0.00160.0001-0.0979
0.08150.0093-0.0089
1.0575-0.0591

Regime 2(2) Transition Matrix

Regime 1
Regime 2

Regime 1 Regime 2
0.95581 0.049179
0.044190.95082

Note that p[i][j]=Pr{s(t)=i|s(t-1)=j}(3) Variance-covariance Matrix
Regime 1
Y
PIM
Y
0.000175 -0.000002 -0.000102 0.000002
P-0.000002 0.000007 0.000025 0.000000
I-0.000102 0.000025 0.112750 -0.000054
M
0.000002 0.000000 -0.000054 0.000005
Regime 2
Y
P
I
M

Y
P
I
M
0.000294 0.000003 0.000039 -0.000009
0.000003 0.000006 -0.000014 0.000000
0.000039 -0.000014 0.002149 0.000024-0.000009 0.000000 0.000024 0.000006(4) Information criteria

lag1
lag2
lag3

AIC
HQ
SBIC
non-linear
linearnon-linear
linearnon-linear
linear
-23.8536 -22.6638 -23.5227 -22.5037 -23.0295-22.265-24.0997 -23.0714 -23.5966 -22.8252 -22.8469 -22.4583-24.0603 -23.2027 -23.3841-22.87 -22.3766 -22.3742(5) Linearity test
LR linearity test: 373.6461

C hi(46) =[0.0000] ** C hi(48)=[0.0000] ** DAVIES=[0.0000] **Table 3
Estimated results of MSVAR(5): 1980(1) Coefficients
Regime 1
C
Y(-1)
P(-1)
W(-1)
I(-1)
M(-1)

Y
P
W
-0.42758 0.025046
0.592120.71169 -0.005415 0.0096192-0.50390.88947 -0.19915
0.082544 0.026607
0.98768-0.001135 8.50E-05 -0.000901
0.23848 0.024525 0.020797

IM
48.92 0.36341
0.88083 0.010007-16.854 0.007324
1.0253 -0.040242
0.78122 -0.000758
1.223 0.98384

C
Y(-1)
P(-1)
W(-1)
I(-1)
M(-1)

Y
P
W
-0.085371 -0.19993
0.40332
0.90721 0.007268 0.012851-0.053213
0.95789 -0.006545
0.031685 0.045773
0.936670.000746 -0.000322 0.0004142
0.039241 0.009667 -0.009187

I
M
48.85
0.85771.1025 0.014648-1.7365 -0.035911-6.5443 -0.10673
1.0166 0.000395-1.0257 0.98276

Regime 2(2) Transition Matrix
Regime 1 Regime 2
Regime 1
0.97737 0.0055999
Regime 2 0.022627
0.9944Note that p[i][j]=Pr{s(t)=i|s(t-1)=j}(3) Variance-covariance Matrix
Regime 1
Y
P
W
I
M
Y
0.000169 -0.000003 0.000001 -0.000243 0.000001
P-0.000003 0.000007 0.000004 -0.000133 -0.000001
W
0.000001 0.000004 0.000018 0.000562 -0.000001
I-0.000243 -0.000133 0.000562 0.120500 -0.000148
M
0.000001 -0.000001 -0.000001 -0.000148 0.000005
Regime 2
Y
P
W
I
M

Y
0.000343
0.000007
0.000004-0.000160-0.000004

P
W
I
M
0.000007 0.000004 -0.000160 -0.000004
0.000007 0.000002 0.000000 0.000000
0.000002 0.000005 -0.000029 0.000000
0.000000 -0.000029 0.031529 0.000091
0.000000 0.000000 0.000091 0.000007(4) Information criteria

lag1
lag2
lag3

AIC
non-linear
linearHQ
non-linear
linear

-32.2633-32.5127-32.5713-31.7723-31.7527-31.5409(5) Linearity test
LR linearity test: 312.3684-31.4575-31.9967-32.1453

SBIC
non-linear linear-31.2174 -31.0405-31.6221 -30.6202-31.6355 -30.0055-30.859-31.064-30.876

Chi(45) =[0.0000] ** Chi(47)=[0.0000] ** DAVIES=[0.0000] **Table 4
Estimated results of MSVAR(4): 1985(1) Coefficients
Regime 1
C
Y(-1)
P(-1)
I(-1)
M(-1)

Y
P
0.10191 0.0074147
0.65916 -0.004709-0.50289
0.95779
0.00397 0.000467
0.2428 0.013343

IM
10.2480.30894
3.6687 -0.003888-1.1131 -0.091206
0.94399 -0.000368-1.42611.0083

C
Y(-1)
P(-1)
I(-1)
M(-1)

Y
P
1.392 0.095382
0.89566 0.0067904-0.10815
0.98814-0.001428 1.91E-05-0.02649 -0.004619

IM
5.09820.38206
0.35374 0.0032747-1.7922 -0.074224
1.0012 -0.000224
0.097018
0.99661

Regime 2(2) Transition Matrix
Regime 1 Regime 2
Regime 10.95776 0.028534
Regime 2 0.042243
0.97147
Note that p[i][j]=Pr{s(t)=i|s(t-1)=j}(3) Variance-covariance Matrix
Regime 1YPY
0.000231 -0.000001
P-0.000001 0.000006
I
0.000024 0.000009
M-0.000003 0.000000

I
M
0.000024 -0.000003
0.000009 0.000000
0.092869 0.000052
0.000052 0.000005

Regime 2
Y
P
I
M

Y
P
I
M
0.000358 0.000006 0.000037 -0.000009
0.000006 0.000006 -0.000009 0.000000
0.000037 -0.000009 0.002172 0.000022-0.000009 0.000000 0.000022 0.000006(4) Information criteria

lag1
lag2
lag3

AIC
HQ
SBIC
non-linear
linearnon-linear
linearnon-linear linear-33.9739 -32.4835 -33.3832 -32.1945 -32.5124 -31.7686-32.089 -32.2605 -30.7407 -31.5958-33.004 -32.7115-33.0054 -32.6285-31.764 -32.0142 -29.9349 -31.1092(5) Linearity test
LR linearity test: 322.3788

Chi(30) =[0.0000] ** Chi(32)=[0.0000] ** DAVIES=[0.0000] **Table 5
Estimated results of MSVAR(5): 1985(1) Coefficients
Regime 1
C
Y(-1)
P(-1)
W(-1)
I(-1)
M(-1)

Y
P
W
-2.7892 -0.066981
0.22659
0.51862 0.011168 0.060786-1.0538
0.96667 0.029457
0.60876 0.015462
0.95454-0.000919 -7.67E-05 -0.000489
0.45381 0.0063243 -0.027806

IM-37.171
0.42291.0719 0.007709-11.243 -0.059449
10.283 -0.025031
0.87223 -0.000313
2.35170.99558

C
Y(-1)
P(-1)
W(-1)
I(-1)
M(-1)

Y
P
W
1.9582-0.46163
0.53232
0.89788 0.0004474 0.0076759-0.099399
0.96633 0.014411-0.078493 0.081715
0.90963-0.001232 -0.000348 0.0008973-0.043014 0.015418 -0.014204

IM
11.5280.885410.40811 0.006486-1.5283 -0.047127-0.99393 -0.082133
1.00660.00033-0.11756
0.97948

Regime 2(2) Transition Matrix

Regime 1
Regime 2

Regime 1 Regime 2
0.9428 0.040416
0.057202
0.95958

Note that p[i][j]=Pr{s(t)=i|s(t-1)=j}(3) Variance-covariance Matrix
Regime 1YPY
0.000215 0.000004
P
0.000004 0.000009
W
0.000005 0.000005
I-0.000361 -0.000013
M-0.000001 0.000001

WI
M
0.000005 -0.000361 -0.000001
0.000005 -0.000013 0.000001
0.000011 0.000097 0.000000
0.000097 0.085933 0.000071
0.000000 0.000071 0.000005

Regime 2
Y
P
W
I
M

Y
P
0.000355 0.000004
0.000004 0.000004
0.000004 0.000000
0.000056 -0.000002-0.000009 -0.000001

WI
M
0.000004 0.000056 -0.000009
0.000000 -0.000002 -0.000001
0.000002 0.000000 0.000000
0.000000 0.002252 0.000025
0.000000 0.000025 0.000007(4) Information criteria

lag1
lag2
lag3

AIC
HQ
SBIC
non-linear
linearnon-linear
linearnon-linear
linear
-23.8536-22.6638 -23.5227 -22.5037 -23.0295 -22.265-24.0997-23.0714 -23.5966 -22.8252 -22.8469 -22.4583-24.0603-23.2027-23.3841-22.87 -22.3766 -22.3742(5) Linearity test
LR linearity test: 408.4790

Chi(45) =[0.0000] ** Chi(47)=[0.0000] ** DAVIES=[0.0000] **Table 6
Estimated results of MSVAR(4): 1980(1) Coefficients
Regime 1
C
Y(-1)
Y(-2)
P(-1)
P(-2)
M(-1)
M(-2)

Y
-0.033628
0.89938
0.10595
0.017729
0.0042932
0.096839-0.10273

P
0.23674-0.42752
0.20346
0.496190.454310.74418-0.67874

M
0.22428-0.24083
0.13481-0.031192
0.011571
1.1243-0.10143

C
Y(-1)
Y(-2)
P(-1)
P(-2)
M(-1)
M(-2)

Y
0.19879
0.99354-0.037222-0.0086305
0.016762
0.11904-0.12134P-0.54708
2.5931-2.24680.45081
0.3936
0.62139-0.64253

M-0.24824
0.0038021
0.066448
0.0067696-0.015023
1.0813-0.083541

Regime 2(2) Transition Matrix

Regime 1
Regime 2

Regime 1
Regime 20.93898
0.065057
0.061018
0.93494

Note that p[i][j]=Pr{s(t)=i|s(t-1)=j}(3) Variance-covariance Matrix
Regime 1
YPM
Y
0.0000090 0.0000021 0.0000002
P
0.0000021 0.0001497 -0.0000058
M
0.0000002 -0.0000058 0.0000085
Regime 2
Y
P
M

Y
P
M
0.0000021 0.0000027 -0.0000004
0.0000027 0.0003369 -0.0000102-0.0000004 -0.0000102 0.0000027(4) Information criteria

lag1
lag2
lag3

AIC
non-linear-23.4159-23.6227-23.4204(5) Linearity test
LR linearity test: 107.4325

HQ
linearnon-linear-23.1718-23.1424-23.2618-23.3873-23.3837-22.9419

SBIC
linearnon-linear
linear
-23.0269 -22.8122 -22.8565-23.2133 -22.7301 -22.9569-23.1509-22.237 -22.8079

Chi(27) =[0.0000] ** Chi(29)=[0.0000] ** DAVIES=[0.0000] **Chart 1
Impulse responses to nominal interest rate shocks: Linear VAR(4) models

OutputPrice level

0.001

0.00080.000600.0004-0.0010.0002-0.0020-0.003-0.0002-0.0004-0.004-0.0006

80-0.005-0.000885-0.006-0.001
0

5

10

15

20

25

30

35

40

45

Call rate

0

5

10

15

20

25

30

35

40

45

10

15

20

25

30

35

40

45

Money Supply

0.4

0.001

0

0.3

-0.001
0.2-0.0020.1-0.0030-0.004-0.1-0.005
0

5

10

15

20

25

30

35

40

45

0

5

Chart 2
Impulse responses to nominal interest rate shocks: Linear VAR(5) models

OutputPrice level

0.001

0.00080.000600.0004-0.0010.00020-0.002-0.0002-0.003-0.0004-0.004-0.0006
0

5

10

15

20

25

30

35

40

0

45

Leading indicator to price

5

10

15

20

25

30

35

40

45

30

35

40

45

Call rate
0.3

0.002

0.2
0.001

0.1

0
0

-0.001

-0.1
0

5

10

15

20

25

30

35

40

45

10

15

20

25

30

35

40

45

Money Supply
0.001

0

-0.001-0.002-0.003-0.004-0.005
0

5

0

5

10

15

20

25

Chart 3
Impulse responses to monetary shocks: Linear VAR(4) models

OutputPrice level

0.003

0.00080.00070.00250.00060.002

0.00050.00040.00150.00030.001

0.00020.00010.000500-0.0001
0

5

10

15

20

25

30

35

40

45

Call rate

0

5

10

15

20

25

30

35

40

45

10

15

20

25

30

35

40

45

Money supply

0.045

0.004

0.04
0.035
0.003
0.03
0.025
0.02

0.002

0.015
0.01
0.001
0.005
0
-0.005

0
0

5

10

15

20

25

30

35

40

45

0

5

Chart 4
Impulse responses to monetary shocks: Linear VAR(5) models

OutputPrice level
0.00070.00180.00160.00060.00140.00050.00120.001

0.00040.00080.00030.00060.00020.00040.00010.0002
0

0
0

5

10

15

20

25

30

35

40

0

45

Leading indicator to price

5

10

15

20

25

30

35

40

45

30

35

40

45

Call rate

0.001

0.1

0

-0.001

0
0

5

10

15

20

25

30

35

40

45

10

15

20

25

30

35

40

45

Money supply
0.003

0.002

0.001

0
0

5

0

5

10

15

20

25

Chart 5
Regime probabilities
VAR(4): 19801

Probabilities of Regime 1

.75
.5
.25

1980
1985
Probabilities of Regime 2
1

1990

1995

2000

1990

1995

2000

.75
.5
.25

1980

1985

Chart 6
Impulse Responses to the nominal interest rate shock
VAR(4): 1980Regime 1yRegime2

0

.02

-.01

0

-.02

-.02
0

10

20

30

40

50

.005

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0
-.01

0

p

-.02
0

10

20

30

40

50
3

1

2

i

0

1
0

10

20

30

40

50
.005

0

m

.0025

-.0025

0

-.005
0

10

20

30

40

50

Chart 7
Impulse Responses to the monetary shock
VAR(4): 1980Regime 1

Regime2
1.5
1
.5
0

1.5

y

1
.5
0

p

10

20

30

40

50

.4

.2

.2

0

0

10

20

30

40

50

25

20

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

-25
0

10

20

30

40

50
1.5

1.5

m

10

-.2

0

i

0

1.25
1

1
0

10

20

30

40

50

Chart 8
Regime probabilities
VAR(5): 1980Probabilities of Regime 1
1
.75
.5
.25

1980
1985
Probabilities of Regime 2
1

1990

1995

2000

1990

1995

2000

.75
.5
.25

1980

1985

Chart 9
Impulse Responses to the nominal interest rate shock
VAR(5): 1980Regime 1

Regime2
.02

.01

y

.01

0

0
0

p

10

20

30

40

10

20

30

40

50

0
0

10

20

30

40

50

1

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

1
.5
0

.5
0
0

m

10

.0075
.005
.0025

.005

i

0

.0025
0
-.0025

.002
0
-.002
0

w

50

10

20

30

40

50

0

10

20

30

40

50

40

.001
0
-.001
-.002
50
0

10

20

30

40

50

.001
0
-.001
0

10

20

30

Chart 10
Impulse Responses to the monetary shock
VAR(5): 1980Regime 1yRegime2

.75
.5
.25
0

.4
.2
0
0

10

20

30

40

50

.2

p

10

20

30

40

50

.1
0
-.1

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

-.1
10

20

30

40

50

10
0
-10

0
-10
0

10

20

30

40

50

1

m

20

0

0

i

10

.1

.1
0

w

0
.2

1
.8
.6

.75
.5
0

10

20

30

40

50

Chart 11
Regime probabilities
VAR(4): 19851

Probabilities of Regime 1

.75
.5
.25

1

1985
1990
Probabilities of Regime 2

1995

2000

1985

1995

2000

.75
.5
.25

1990

Chart 12
Impulse Responses to the nominal interest rate shock
VAR(4): 1985Regime 1

Regime2

.01
0
0

y

-.01
-.01
-.02
0

10

20

30

40

.005

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

.0025

.0025

p

50

0

0

-.0025-.0025
0

10

20

30

40

50

1
1

i

.5
.75
0
.5
0

10

20

30

40

.0005

0

m

50

0

-.0025

-5e-4

-.005
0

10

20

30

40

50

Chart 13
Impulse Responses to the monetary shock
VAR(4): 1985Regime 1

Regime2

.75
.2

.5

y

.25

0

0

-.2
0

10

20

30

40

50

.3

p

.1
0

10

20

30

40

50

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

10
5
0
-5

10
0
-10
0

10

20

30

40

50
1.25

1

m

10

.1
0
-.1
-.2

.2

20

i

0

1

.75

.75

.5

.5
0

10

20

30

40

50

Chart 14
Regime probabilities
VAR(5): 1985Probabilities of Regime 1
1
.75
.5
.25

1

1985
1990
Probabilities of Regime 2

1995

2000

1985

1995

2000

.75
.5
.25

1990

Chart 15
Impulse Responses to the nominal interest rate shock
VAR(5): 1985Regime 1yRegime2
.01
0
-.01
-.02

.005
0
-.005
0

10

20

30

40

50
0
.0075
.005
.0025
0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

.002

p

w

0

.01

.0025
0
-.0025

.005
0
0

i

20

30

40

50
1
.5

0

m

10

1
.5
0
10

20

30

40

50
.001
.0005
0
-5e-4

.001
0
-.001
0

10

20

30

40

50

Chart 16
Impulse Responses to the monetary shock
VAR(5): 1985Regime 1

Regime2
.25
0
-.25

1

y

.5
0
0

p

40

50

10

20

30

40

50

.2
.1
0
-.1

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

-.1
10

20

30

40

50

20
10
0
-10

0
-5
-10
0

m

30

0

0

i

20

.15
.1
.05
0
0

w

10

.3
.2
.1
0

10

20

30

40

50
1
.75
.5

1
.75
.5
.25
0

10

20

30

40

50

Chart 17
Regime probabilities
VAR(3): 1985Probabilities of Regime 1
1
.75
.5
.25

1

1985
1990
Probabilities of Regime 2

1995

2000

1985

1995

2000

.75
.5
.25

1990

Chart 18
Impulse Responses to the monetary shock
VAR(3): 1985Regime 1

Regime2

1

y

1

.5
0

0
-.5
0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

.4
.2

p

.1

.2

0
0

-.1
0

10

20

30

40

50

1.5
1.5

m

1

1.25

.5

1
0

10

20

30

40

50