
Research Article


Are the Effects of Monetary Policy Asymmetric in India? Evidence from a Nonlinear Vector Autoregression Approach 

Goodness C. Aye
and
Rangan Gupta



ABSTRACT

Even though there exist quite a number of studies analysing the impact of monetary policy in India, none of these papers looks into the whether monetary policy has an asymmetric impact on the output and price level. In light of this, this paper uses Indian quarterly data for the period of 1960:Q22011:Q2 to test for nonlinearity in a standard monetary vector autoregression (VAR) model comprising of output, price and money, using an estimation strategy that is consistent with wide range of structural models. We find that positive and negative monetary policy shocks have an immediate shortlived and a delayed persistent asymmetric effect on output and price, respectively. In addition, we show that compared to a linear VAR, the nonlinear VAR has a bigger impact of a monetary policy shock on output and price. In general, we conclude that there are clear gains from modelling monetary policy using a nonlinear VAR framework.





Received: January 13, 2012;
Accepted: March 31, 2012;
Published: May 25, 2012


INTRODUCTION
The monetary policy framework in India has undergone series of transformations
since the beginning of the planning period in 1951 (Mishra
and Mishra, 2010). Therefore, understanding the response of goal variables
(output and prices) to exogenous monetary policy shocks is essential for sustained
economic growth in India. Determining whether monetary shocks have asymmetric
effect is a key concern in macroeconomics (Weise, 1999).
This is because a number of economic theories imply that monetary policy may
have asymmetric effects based on the socalled “Keynesian” and “Classical”
regions of the aggregate supply curve, the liquidity trap theory, credit constraint
models and menu cost models, as observed by Morgan (1993),
asymmetric wage indexation and price adjustment (Kandil,
1995) and asymmetric real rigidities in the form of irreversibility of investment
(Abel and Eberly, 1994)^{1}.
Purely from a policy perspective, it is important to investigate if the monetary
authority needs to change the money supply asymmetrically to contract and expand
the economy.
Vector autoregressive (VAR) approach is one of the most commonly used methods
of analysing the effects of monetary shocks. Barring a few^{2},
most studies generally use a linear VAR. These studies ignore the possibility
of nonlinearities between the time series of economic variables which may arise
due to structural breaks or regime changes. The main difference between the
standard linear VAR and the nonlinear VAR is that the latter allows some coefficients
to be statedependant.
In this study, we estimate the asymmetric effects of monetary policy shocks
in India using a logistic smooth transition vector autoregression (LSTVAR) as
detailed in Weise (1999). Although, there are a number
of studies on monetary policy impacts in India that used the VAR approach (Goyal
and Pujari, 2005; Srimany and Samanta, 1998; Chowdhury,
2008; Ghosh, 2009; Kubo, 2009;
Mallick and Sousa, 2009; Inoue, 2010;
Mishra and Mishra, 2010; Patnaik,
2010). Although, none of these studies consider asymmetric effects or nonlinearities.
Given this, the objective of this study is to analyze whether nonlinearities
exist among the dynamic relationship between key macroeconomic variables and
also, if monetary policy shocks tend to have an asymmetric effect on the output
and price level of the Indian economy. Thus we contribute to monetary policy
literature for India by considering asymmetry in a nonlinear VAR framework^{3}.
ECONOMETRIC METHODOLOGY AND THE DATA
An unrestricted reducedform, nonlinear vector autoregression following a smooth
transition autoregressive form is used. The nonlinearity is based on the fact
that the dynamic behaviour of time series depends on states or regimes of the
variables. Terasvirta and Anderson (1992) used such
a nonlinear model in a single equation framework, but here the LSTVAR is estimated
in a multiequation setting following Weise (1999)^{4}.
By ignoring moving average terms, our empirical LSTVAR model is given as:
where, X_{t} = (y_{t}, p_{t}, m_{t})’ is the vector of endogenous variables with y_{t} being the growth rate of industrial production index, p_{t} is consumer production index inflation and m_{t} is growth rate of money supply which in turn is measured by M1. A(L) and θ(L) are pthorder polynomials in the lag operator. θ_{t} is interpreted as a technology shock with E(θ_{t}) = 0. u_{t} is the residual. z_{t} is a "switching variable" that represents the state of the economy. F(z_{t}) is a function which lies between zero and one with the two extremes values corresponding to two regimes. We assume that F(z_{t}) is a logistic function expressed by: The parameter c in Eq. 2 represents the threshold around which the dynamics of the model change. In the limit as z_{t}c approaches minus infinity (plus infinity), F(z_{t}) approaches zero (one). The parameter γ is the "smoothness" parameter. As γ approaches zero, F(z_{t}) converges to a constant, the nonlinear terms become redundant and the model becomes linear. As γ approaches infinity the model becomes a threshold autoregression model. The model’s dynamics change abruptly depending on whether z_{t} is greater than or less than the threshold value.
Note that, although, M2 or an interest rate variable is more commonly used
as a standin for the monetary policy variable, M1 is found to have more desirable
properties in the context of a threevariable monetary VAR, since it tends to
avoid the socalled price puzzle, whereby prices tend to fall following a monetary
expansion (Sims, 1992). The puzzle is usually resolved
by including more variables such as the commodity price index, however, this
tends to be impractical in our case, since the number of coefficients to be
estimated in the LSTVAR model rises in proportion to the number of coefficients
in the standard linear model. Hence, there is a virtue to working with a three
variable VAR. The fact that we do not see the price puzzle, as will be seen
below, using a VAR based on M1, suggests that monetary shocks are more successfully
identified in a ypm ordered model.
There is a possibility, that one could reject linearity for this VAR because
of timedependent structural breaks. If nonlinearity is solely due to structural
breaks, the problem can be handled by including appropriate dummy variables,
with deeper notions like asymmetric nominal rigidity can be ignored. For this
reason each series, is filtered by regressing it on a constant, seasonal dummy
variables, intercept dummies for the post 1991 (financial liberalization) and
post 2007 (the “Great Recession”) periods, a time trend and the time
trend interacted with seasonal dummies. The order of differencing, the lag length,
stability and cointegration in the VAR model are based on conventional tests.^{5}
Each of the filtered data series is stationary based on standard unit root tests,
with loglevels of the industrial production, CPI and M1 containing unit roots.
Since, it is wellknown that the velocity of M1 is nonstationary and theory
suggests no other cointegrating vector, the series are assumed not to be cointegratedan
assumption vindicated by the trace test proposed by Johansen
(1991). The Schwarz information criterion suggested four lags. Given this,
the benchmark model was estimated as a fourthorder VAR using the difference
in the log of industrial production, the CPI and M1. Note that all data are
obtained from the International Financial Statistics (IFS) database maintained
by the International Monetary Fund (IMF) and covers the period of 1960:Q12011:Q1.
Since, we use growth rates of the variables, our effective sample begins in
1960:Q2.
RESULTS AND DISCUSSION
We start off with a test of linearity performed on the baseline VAR. We test
the null hypothesis H_{0}: γ = 0 against the alternative H_{1}:
γ>0. As in Weise (1999), the tests of linearity
employed here are based on a loglikelihood test of the null hypothesis. Based
on the loglikelihood of the restricted and unrestricted models, we then obtain
a LikelihoodRatio (LR) test statistic. Based on the LR statistics for each
equation and the entire system and the corresponding pvalues, the switching
variable for this study is found to be the third lag of the change in the rate
of inflation, i.e., Δp_{t3}. Note that we looked at the growth
rate of industrial production, the rate of inflation, the change in the rate
of inflation and the growth rate of M1, lagged one, two, three or four periods,
as possible switching variables. All these variables are plausible candidates
as suggested by theories on the asymmetric impact of monetary policy (Weise,
1999). In general, we found strong evidence against linearity in this standard
VAR and in favour of the LSTVAR model.^{6} However,
whether this nonlinearity yields in economically meaningful asymmetry in the
effects of monetary policy shocks must be determined by examining the dynamic
effects of these shocks in the LSTVAR model. Thus, next we discuss a bit on
the estimation strategy of the LSTVAR model.
The LSTVAR could be estimated using FullInformation Maximum Likelihood (FIML)
techniques by imposing coefficient restrictions that set certain elements of
A(L) and θ(L) equal to each other as in Terasvirta
and Anderson (1992). However, imposing arbitrary coefficient restrictions
is problematic because the results may be sensitive to which restrictions are
imposed and the choice of restrictions cannot be guided by economic theory.
In this study, the model is estimated using a twostage procedure following
Weise (1999). In the first stage, the threshold parameter,
c is fixed at zero. In the second stage, the model is then estimated by OLS
equationbyequation using the value for c, allowing the smoothness parameter,
γ to vary. The value of γ that minimizes the log of the determinant
of the variancecovariance matrix of residuals from these regressions is used
in the final regressions which in our case happens to be 3.51.
Once we have estimated the LSTVAR model, we are now ready to explore the asymmetric
effects, if any, of a positive and negative monetary policy shock on the growth
rate and inflation of the Indian economy. We use the impulse response functions
for answering this question.^{7} Monetary shocks are
identified using the Cholesky decomposition, whereby the money equation is ordered
last to ensure that money growth has no contemporaneous effect on inflation
and output growth.^{8} The same ordering is retained
for the benchmark linear VAR model as well. The impulse response functions obtained
from the LSTVAR model and the linear VAR model for a onetime (one standard
deviation shock) to the growth rate of money supply, using the differences in
log industrial production, consumer price index and M1, filtered for trends
and structural breaks, are presented in Fig. 1. For the sake
of comparability, we plot the responses of output growth and inflation to the
negative shock by reversing the sign. The impulse response functions track the
responses of the output growth and inflation from the linear and nonlinear VARs
for over twenty quarters following the monetary policy shock.
The impulse responses, in general, do not tend to provide much evidence of
asymmetry for the effects of positive and negative monetary policy shocks especially
for the output growth, since, barring the initial two quarters where the positive
shock has a bigger impact on the output growth relative to the negative shock,
the responses lie virtually on top of one another. For the inflation, the negative
shock has bigger effect compared to the positive shock post quarter four. Further,
the effect on the inflation is quite persistent. Though, the effect starts to
die off after the 10th quarter, it does not revert back to its initial level
within twenty quarters as with the output growth. The linear model predicts
weaker effects relative to the LSTVAR model for both output and inflation, though
the effect on the inflation continues to be quite persistent as in the nonlinear
case. So in general, there seems to be more evidence of asymmetry for a positive
and negative monetary shock for Indian inflation than on output growth, where
the asymmetry is only restricted to the first few quarters.

Fig. 1(ab): 
Impact of a one standard deviation money supply growth rate
shock (m) on output growth (y) and inflation (p) in linear and nonlinear
VARs. POS (NEG) indicates the impulse responses for a positive (negative)
money supply growth rate shock in the LSTVAR model; SYM indicates the impulse
response from the linear VAR model for a money supply growth rate shock 
Unlike Weise (1999), who found no asymmetric effect
of monetary policy for the US economy, our study does indicate that asymmetry
is an important component of monetary decisions in India, especially with regards
to the inflation rate. So, we indicate that the conclusions from the previous
studies (Goyal and Pujari, 2005; Srimany
and Samanta, 1998; Chowdhury, 2008; Ghosh,
2009; Kubo, 2009; Mallick and
Sousa, 2009; Inoue, 2010; Mishra
and Mishra, 2010; Patnaik, 2010) on monetary policy
conducted for India might be inaccurate in their conclusions, since they fail
to account for nonlinearity.
CONCLUSION
The objective of this paper was to analyze if positive and negative monetary
policy shocks affect the output growth and inflation asymmetrically for India.
For this purpose, we estimated a three variable monetary VAR model comprising
of output growth, CPI inflation and the growth rate of M1 using quarterly data
covering the period of 1960:Q2 till 2011:Q2. The monetary policy shock was identified
using the standard Cholesky decomposition. We found that, the evidence of asymmetric
effect for the output growth is only limited to the first few quarters, where
the positive monetary shock tend to have a bigger effect than the negative shock.
For inflation, though, the differences in the effects of the positive and negative
monetary policy shocks are much more visible, with the latter variety of shocks
having a bigger impact after a year or so. Compared to the linear model, the
nonlinear model is found to produce stronger effects. Clearly then, there are
gains from modelling monetary policy in a nonlinear set up for India, since
money shocks have asymmetric effect on both growth and inflation, though slightly
limited for the former. In addition, our results also highlight the fact, that
if nonlinearities are not taken into account, we are likely to underestimate
the effect of monetary policy on growth and inflation.
^{1}Refer to Weise (1999)
for further details.
^{2}Terasvirta and Anderson (1992),
Garcia and Schaller (2002), Weise
(1999), Karame and Olmedo (2002), Holmes
and Wang (2000) and Rahman and Serletis (2010)
^{3}For a recent set of studies dealing with monetary
policy, see also, Javed and Sahinoz (2005), Ozturk
(2006), Agbeja (2007), Saibu
and Oladeji (2007), Berument et al. (2009),
Ahortor and Olopoenia (2010), Mukherjee
et al. (2011), Krishnapillai and Thompson (2012)
and Simwaka et al. (2012)
^{4}Weise (1999) for a detailed
specifications and description of the methodology.
^{5}The details of these results are available upon
request from the authors
^{6}The evidence against linearity when the growth
rate of M1 is used as the switching variable was found to be very weak. What
was most striking was the fact that linearity was never rejected in the output
equation when the growth rate of M1 was the switching variable. This, however,
does not imply that shocks to money supply have symmetric effects. Positive
and negative monetary policy shocks could have asymmetric effects due to the
dynamic interactions of the model that uses other switching variables. By contrast,
linearity was rejected in a number of specifications when output growth, inflation
or the change in the rate of inflation acted as the switch variable, especially
in the money equation. This result suggested that the monetary policy reaction
function is asymmetric. There is hardly any evidence of nonlinearity in the
output equation though. Details of the Langrange Multiplier Tests for Linearity
is available upon request from the authors.
^{7}The technical details involved in obtaining the
impulse response functions can be found in Weise (1999).
^{8}Note that, in addition to this being the conventional
ordering, this also allows us to avoid the problem that the contemporaneous
relationships are state dependent under the assumption of heteroskedasticity,
and hence, the Cholesky decomposition cannot be used. Thus, we do not identify
output and inflation shocks

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