New Keynesian macroeconomic model and monetary policy in Pakistan.
Nawaz, Shahzada M. Naeem ; Ahmed, Ather Maqsood
The New Keynesian (NK) models have advantage over the Real Business
Cycle (RBC) models as they allow rigidities in the structure of the
model, hence provide built-in mechanism to incorporate the structural
shocks. The estimation of the NK model for Pakistan's economy
remains a relatively unexplored area. This study attempts to estimate a
closed economy version of the NK model using robust econometric
technique. On the empirical side macroeconomic dynamics have been
investigated in response to unanticipated monetary shock. The reaction
of the monetary authority (the State Bank of Pakistan) in response to
structural shocks has been assessed by exploring the role of forward
looking expectations. The SVAR model has been employed to estimate the
structural parameters. The response of macroeconomic aggregates to
structural shocks has also been simulated along with discussing the
forecast error variance decomposition. The role of forward looking
expectations is found to play prominent role in the prevailing market
structure of the country. The State Bank of Pakistan (SBP) has been
found to respond to shocks after a lag of one or more periods indicating
time inconsistency problem which is due to discretionary monetary policy
stance being adopted by the monetary authority. The distorted beliefs of
economic agents about the stance of monetary policy have pointed towards
weak effectiveness of the monetary policy. The results suggest that the
SBP would have to adopt an independent and transparent monetary policy
by following some sort of Taylor-type rule.
JEL Classification: C32, C51, E52, E58
Keywords: New Keynesian Models, Real Business Cycle Models, Forward
Looking Expectations, SVAR Model, Price Puzzle
1. INTRODUCTION
The macroeconomic models of the 1970s were heavily criticised due
to lack of theoretical foundations. (1) The New Keynesian (NK) models of
today have vastly improved the earlier versions as they include the role
of expectations of economic agents and require policy makers to
incorporate the role of expectations to attain macroeconomic stability.
These models have the advantage over the Real Business Cycle (RBC)
models as they allow rigidities in the structure of the model, hence
provide built-in mechanism to incorporate the structural shocks. The
theoretical model developed in the present study resembles to most of
the closed economy Dynamic Stochastic General Equilibrium (DSGE) models
that emphasise the importance of inter-temporal optimisation behaviour
of economic agents, the role of forward looking expectations and nominal
price rigidities. The four main objectives of the study are as follows.
First is to investigate the macroeconomic dynamics in response to
unanticipated monetary shock in the presence of rigidities in the goods
and labour markets; second, to assess the reaction of monetary authority
(the State Bank of Pakistan) to structural shocks; third to highlight
the importance of forward looking expectations of economic agents in
policy-making; and finally the identification of sources of variations
in the macroeconomic aggregates.
This paper takes the lead over others as the rational expectations
NK model has been estimated through maximum likelihood estimation
procedure--a pioneering attempt in Pakistan. The identification scheme
applied is unique in the sense that it has not been adopted earlier for
modeling the Pakistan's economy. We have also attempted to
implement the expectations type Taylor rule which provides an insight to
the policy makers to target inflation and output gap in order to
stabilise the economy. The estimation proceeds in two steps, following
Keating (1990) who categorised this approach as the SVAR model. The
impulse response analysis has been conducted which provides a valuable
insight into the significance of structural shocks to the macroeconomic
dynamics of the economy. Forecast error variance decomposition has also
been computed which has the advantage to identify the sources of
variation in the macroeconomic aggregates.
The results seem to confirm that the SBP has been pursuing
discretionary policy rather than adopting any rule. This has been
observed by examining the structural parameter estimates of the interest
rate rule and the response of interest rate to the structural shocks.
These findings highlight the role of expectations and the need for
incorporating the direct and indirect impacts of factors which affect
the macroeconomic dynamics. It, therefore, provides an insight to the
policy-makers to achieve the short term and medium term targeted levels
of inflation and economic growth in a more effective manner.
The paper is arranged as follows. Section 2 presents the closed
economy model under rational expectations. Section 3 derives the
identifying restrictions based on the structural macroeconomic model
along with discussing the methodology. Section 4 presents and discusses
the estimated results. Finally, Section 5 concludes the discussion,
derives policy implications, and also suggests the scope for future
research in the area of macroeconomic modeling for Pakistan. 2
2. FRAMEWORK OF FORWARD LOOKING MACROECONOMIC MODEL
One important aspect missing in the non-DSGE macroeconomic models
is the lack of microeconomic foundations and nominal rigidities. In
essence, the requirement is to develop a structural model which is free
from such criticism and could be useful for policy analysis. Before we
start discussing the model it is important to acknowledge the work of
Haider and Khan (2008) and Ahmed, et al. (2012) that have worked on the
structure of DSGE model. Both these studies have, however,
'managed' the unavailability of microeconomic parametric
values by relying on 'borrowed' values from the countries
other than Pakistan.
We start with the final equations of the closed economy version of
the model presented by Clarida, et al. (1999) which consists of three
main economic agents. First, the households who generate demand for
goods and services hence provide aggregate demand equation (forward
looking IS equation). Second, the profit maximising firms who provide
forward looking Phillips curve equation (aggregate supply equation) and
the third is the central bank that follows the Taylor type interest rate
rule. We discuss these three components briefly.
2.1. Aggregate Demand Equation
Expectations type aggregate demand equation derived through the
optimum behaviour of the household can be expressed as
[x.sub.t] = - [phi][[i.sub.t] - [E.sub.t][[pi].sub.t+1] - [rho]] +
[E.sub.t][x.sub.t+i] + [[epsilon].sup.f.sub.t] ... ... ... ... (2.1)
The equation is obtained through log-linearising the Euler equation
of consumption after imposing condition that consumption expenditure
equals output minus government purchases. Since [[epsilon].sup.f.sub.t]
depends on expected changes in government purchases relative to expected
changes in potential output, hence it shifts the IS curve. Therefore it
is named as demand or fiscal shock. (2) The parameter [phi] represents
inter-temporal elasticity of substitution and [rho] is the time discount
factor.
This forward looking IS equation shows that domestic output gap
depends inversely on the real interest rate [[i.sub.t] -
[E.sub.t][[pi].sub.t+1] - [rho]], that is, it reveals that with the rise
in real interest rate consumers will save more which, in turn, will
result in reduction in aggregate spending. The central bank can
influence the consumption pattern of households through changes in the
nominal interest rate, which results in changes in the real interest
rate due to sluggish changes in the prices. The domestic output gap is
directly determined by the future output gap expected in the current
period([E.sub.t][x.sub.t+1]). [[epsilon].sup.f.sub.t] is the disturbance
term which obeys: [[epsilon].sup.f.sub.t] = [mu]
[[epsilon].sup.f.sub.t-1] + [[??].sub.t] ; 0 [less than or equal to]
[mu] [less than or equal to] 1 and [[??].sub.t] is i.i.d. random
variable with zero expected value and constant variance.
2.2. Aggregate Supply Equation
The nature of inflation dynamics, which is the most distinctive
feature of the new Keynesian paradigm, is captured by the New Keynesian
Phillips Curve which is based on
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
[y.sub.t] - [[??].sub.t] + [g.sub.t] as investment is suppressed.
Thus [y.sub.t] - [g.sub.t] = [[??].sub.t] and [[??].sub.t+1] =
[y.sub.t+1] - [g.sub.t+1]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Using [x.sub.t] = [y.sub.t] - [y.sup.p.sub.t], where [x.sub.t] is
output gap, [y.sub.t] is the actual output and [y.sup.p.sub.t] is the
potential level of output. The above equation can be written as
[y.sub.t] - [y.sup.p.sub.t] = [E.sub.t]([y.sub.t+1] -
[y.sup.p.sub.t+1]) - (1/[delta]) ([[??].sub.t] - [E.sub.t][[pi].sub.t+1]
- [rho]) + [E.sub.t]([y.sup.p.sub.t+1] - [DELTA][g.sub.t+1])
[x.sub.t] = [phi][[i.sub.t] - [E.sub.t][[pi].sub.t+1] - [rho]] +
[E.sub.t][x.sub.t+1] + [[epsilon].sup.f.sub.t]
Calvo's (1983) model. According to this model inflation is
determined by expected future inflation and firm's real marginal
costs. The literature on the New Keynesian Phillips Curve is focused on
two main issues: First, what measures can be appropriate in order to
account for real activity. Second, expectations are a crucial element
that can affect the results. The relation of inflation, evolved from the
Calvo model, is of the following form [[pi].sub.t] = [lambda][??] +
[beta][E.sub.t][[pi].sub.t+1]. Following Clarida, et al. (2001), cost
push shock can be added with the marginal cost which represents the
imperfections in the labour market. Thus, [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] linearising and solving gives us the following
relationship [[??].sub.t] = [[lambda].sub.0][x.sub.t] +
[[epsilon].sup.c.sub.t] where [[lambda].sub.0] represents output
elasticity of real marginal cost. The aggregate supply equation, derived
from the optimising behaviour of firms can be transformed as under:
[[pi].sub.t] = [beta][E.sub.t]{[[pi].sub.t+1]] +
[[lambda].sub.0][x.sub.t] + [[epsilon].sup.c.sub.t] ... ... ... ... ...
(2.2)
This equation shows that inflation ([pi]) depends on inflation
expectations and domestic output gap ([x.sub.t]) and
[[epsilon].sup.c.sub.t] is the cost-push shock, which can be described
by [[epsilon].sup.c.sub.t] = [mu][[epsilon].sup.c.sub.t-1] +
[[??].sub.t] Inflation expectations play a central role in the Phillips
curve models. For long time horizons, inflation expectations may be a
sign of a monetary authority's credibility to fulfil the commitment
to price stability.
2.3. Forward Looking Monetary Policy Rule
Central banks target inflation and output gap to stabilise the
economy by adjusting the interest rate which results in changes in real
interest rate due to price rigidity. The interest rate reaction function
is derived by inserting the reduced form of output gap in the aggregate
demand equation and solving it for the nominal interest rate.
[i.sub.t] = [[gamma].sub.3] + [[gamma].sub.1]
([E.sub.t][[pi].sub.t+1]) + [[gamma].sub.2][x.sub.t] +
[[epsilon].sup.i.sub.t] ... ... ... ... ... (2-3)
There is now a general acceptance for policy rule instead of
discretionary policy to improve the economic performance. In this
regard, the seminal paper by Barro and Gordon (1983) is a classic
example where the time inconsistency associated with discretion rather
than rule has been highlighted. Among others, Walsh (1995) has also
argued for an independent central bank for reducing the inflationary
bias. To circumvent this bias, Taylor (1993) formulated a very simple
and practicable rule necessitating changes in short term policy rate in
response to changes in inflation and output gap. It requires that the
parameters of inflation and output gap should be positive. However,
Taylor (1999) suggested more than one-to-one adjustment in policy rate
due to changes in inflation and the parameter for output gap should not
fluctuate significantly from 0.5 which otherwise indicates instability
of the system. On the other hand if parameter values are negative then
it simply shows that the central bank is not following the Taylor Rule
and instead there is a satiation for discretionary monetary policy.
There is evidence to prove that lack of transparency in policy
deteriorates macroeconomic performance rather than improving it.
3. METHODOLOGY AND IDENTIFICATION OF RESTRICTIONS
Both DSGE and SVAR models have emerged after the failure of large
scale models in the 1970s. Whereas the DSGE models have been developed
on the basis of strong assumptions about the functional forms,
exogeneity, market structure and dynamic structure of the constraints,
the SVAR models were initially proposed with minimal restrictions on the
dynamics of the endogenous variables. However, they impose cross
equation restrictions so that models are robust enough to capture the
true structure of the economy in comparison with the alternative ad hoc
models. Gali (1999) viewed the SVAR models as informative as the DSGE
models.
The fundamental departure from traditional to micro-based models
started when Lucas (1976) presented his famous critique. In a
drastically changed paradigm, today the emphasis is on micro-foundations
in a forward looking environment. The models now rely on utility and
profit functions of economic agents who formulate and reformulate their
expectations as and when there are changes in the policy by government
or the central bank. These changes in the expectations result in poor
guides for the policy makers to evaluate the new regime thus there is
need to estimate the deep structural parameters which have the feature
of being invariant to policy changes. Such models with rational
expectations, derived through optimisation by the agents, have the
ability to identify the rational expectations restrictions. As indicated
in the introduction, Keating (1990) has proposed a two steps procedure
for estimating the structural model having forward looking components
and named it as SVAR model. The procedure, prescribed by Keating (1990),
facilitates the researchers to make the SVAR and DSGE models compatible.
Impulse response functions and variance decomposition can also be
generated using the restrictions and the model is named as structural
VAR model. Following the procedure to identify the restrictions, the
structural model is converted into a representation comprising the
structural shocks and the residuals of unrestricted VAR model along with
structural parameters. Forward looking expectations are formulated
through innovations of the dynamic economic structure.
3.1.. Identification of Restrictions
The complete DSGE model conforming to the NK framework for a closed
economic environment, discussed in the previous section, is reproduced
below.
[x.sub.t] = -[pi][[i.sub.t] - [E.sub.t][[pi].sub.t+1] - [rho]] +
[E.sub.t][x.sub.t+1] + [[epsilon].sup.f.sub.t] ... ... ... ... (3.1)
[[pi].sub.t] = [beta][E.sub.t]{[[pi].sub.t+1]) +
[[lambda].sub.0][x.sub.t] + [[epsilon].sup.c.sub.t] ... ... ... ... ...
(3.2)
[i.sub.t] = [[gamma].sub.3] + [[gamma].sub.1]
([E.sub.t][[pi].sub.t+1]) + [[gamma].sub.2][x.sub.t] +
[[epsilon].sup.i.sub.t] ... ... ... ... ... (3-3)
Subtracting all variables in the above equations from their
expected values at time t-1 yield the following set of equations
[x.sub.t] - [E.sub.t-1][x.sub.t] = -[phi]([i.sub.t] -
[E.sub.t-1][i.sub.t]) + [phi]([E.sub.t-1][[pi].sub.t+1] -
[E.sub.t-1][[pi].sub.t+1]) + ([E.sub.t][x.sub.t+1] -
[E.sub.t][x.sub.t+1]) + [[epsilon].sup.f.sub.t] (3.4)
[[pi].sub.t] - [E.sub.t-1][[pi].sub.t] =
[beta]([E.sub.t][[pi].sub.t+1] - [E.sub.t-1][[pi].sub.t+1]) +
[[lambda].sub.0]([x.sub.t] - [E.sub.t-1][x.sub.t]) +
[[epsilon].sup.c.sub.t] ... ... (3.5)
[i.sub.t] - [E.sub.t-1][[pi].sub.t] = [[gamma].sub.1]
([E.sub.t][[pi].sub.t+1] - [E.sub.t-1][[pi].sub.t+1]) +
[[gamma].sub.2]([x.sub.t] - [E.sub.t-1] [x.sub.t]) +
[[epsilon].sup.c.sub.t] ... ... (3.6)
In the above equations, [y.sub.t] - [E.sub.t-1][y.sub.t] for all
the variables represent the respective reduced form residuals. However,
([E.sub.t][[pi].sub.t+1] - [E.sub.t-1][[pi].sub.t+1]) and
([E.sub.t][x.sub.t+1] - [E.sub.t-1][x.sub.t+1]) are the forward looking
components in the model and need to be estimated on the basis of
contemporaneous observations of the variables. The procedure to
calculate these forward looking components is elaborated as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3.7)
[Y.sub.t] = A[Y.sub.t-1] + Q[e.sub.t] ... ... ... ... ... ... (3.8)
One step conditional expectation of Equation (3.8) can be written
as follows.
[E.sub.t][Y.sub.t+1] = A[Y.sub.t] ... ... ... ... ... ... (3.9)
It may be considered that the expected value of residuals is equal
to zero, i.e. [E.sub.t]([e.sub.t]) = 0.
As Y vector consists of all the endogenous variables, therefore to
locate the variables of interest, i.e., output gap and inflation, there
is a need to introduce vectors of length nq where n denotes the number
of endogenous variables and q denotes their lag order.
[r.sub.x] = (1,0,0, ..., 0) for the output gap
[r.sub.[pi]] = (0,1,0, ..., 0) for inflation
Pre-multiplying Equation (3.9) with the above vectors results in
the following expected values of forward looking output gap and
inflation.
[E.sub.t][x.sub.t+1] = [r.sub.x]A[Y.sub.t]
[E.sub.t][[pi].sub.t+1] = [r.sub.[pi]]A[Y.sub.t] ... ... ... ...
... ... ... (3.10)
[E.sub.t][x.sub.sub.t+1] = [a.sup.x.sub.11][x.sub.t] +
[a.sup.x.sub.12][[pi].sub.t] + [a.sup.x.sub.13][i.sub.t] ... ... ... ...
... (3.11)
[E.sub.t][[pi].sub.t+1] = [a.sup.[pi].sub.11][x.sub.t] +
[a.sup.[pi].sub.12][[pi].sub.t] + [a.sup.[pi].sub.13] [i.sub.t] ... ...
... ... ... (3.12)
It helps us to calculate the expectations revision process for
output gap ([E.sub.t][x.sub.t+1] - [E.sub.t-1][x.sub.t+1]) and inflation
([E.sub.t][[pi].sub.t+1] - [E.sub.t-1][[pi].sub.t+1])
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3-13)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3-14)
Putting values of ([E.sub.t][x.sub.t+1] - [E.sub.t-1][x.sub.t+1])
and ([E.sub.t][[pi].sub.t+1] - [E.sub.t-1][[pi].sub.t+1]) in Equations
(3.4)-(3.6) results in the following set of equations
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3.15)
[[pi].sub.t] - [E.sub.t-1][[pi].sub.t] =
[beta]([[??].sub.pi]A([Y.sub.t] - [E.sub.t-1][Y.sub.t])) +
[[lambda].sub.0]([x.sub.t] - [E.sub.t-1][x.sub.t] +
[[epsilon].sup.i.sub.t] ... ... (3.16)
[i.sub.t] - [E.sub.t-1][i.sub.t] = [[gamma].sub.1]
([[??].sub.[pi]]A([Y.sub.t] - [E.sub.t-1][Y.sub.t])) + [[gamma].sub.2]
([x.sub.t] - [E.sub.t-1][x.sub.t]) + [[epsilon].sup.i.sub.t]... ...
(3.17)
Now the next step is to replace the values of ([E.sub.t][x.sub.t+1]
- [E.sub.t-1][x.sub.t+1]) and ([E.sub.t][[pi].sub.t+1] - [E.sub.t-1]
[[pi].sub.t+1]) from Equations (3.13) and (3.14) in Equations
(3.15)-(3.17) which yield the required rational expectation
restrictions. The structural model based on economic theory corresponds
to structural representation of structural shocks and reduced form
innovations with reduced form and structural parameters. Therefore,
explicit representation of restrictions on the structural parameters is
not required as the derived rational expectations restrictions are
entirely based on dynamic structural representation of the economy which
is in line with Keating (1990). These restrictions are being used to
estimate the dynamic closed economy structural VAR model through maximum
likelihood procedure in the next section.
4. ESTIMATION AND ANALYSIS
The model is estimated by using quarterly data for the period
starting from first quarter of 1993 to fourth quarter of 2013. The
output gap is calculated by adopting its basic definition, i.e., the
differential between log of actual real GDP and potential GDP. There are
various methods to get potential GDP, e.g. it can be measured by
regressing the log of real GDP on its trend or by the HP filter.
Following Malik (2007), we have used the former approach. Data for
quarterly GDP is based on estimates provided by Arby (2008) and Hanif,
et al. (2013). The data for annual GDP (at constant US$ with base year
2005-06) is taken from WDI (2014) and the Economic Survey of Pakistan.
CPI inflation is calculated using log of CPI adjusted for quarterly
chain base method. The call money rate (i) is used as a measure for
interest rate. Data for CPI and call money rate are taken from IFS
(2014) wherein few observations for the year 2013 are picked from
official website of the IMF.
To employ maximum likelihood estimation procedure through
structural VAR model, we need to incorporate the estimated values of
reduced form parameters and residuals' series for the restrictions
identified on the basis of structural model, as derived in the previous
section. According to Canova (2007), VAR model is appropriate to employ
even if the variables are non-stationary. Consistent parameter estimates
are obtained even if unit roots are present in the variables [Sims,
Stock, and Watson (1990)]. Following Sims, et al. (1990) and Sims
(1992), the cointegration test is applied here to investigate the long
run relationship between variables for which unit root test for all
variables is a pre-requisite.
The primary condition for employing unrestricted VAR model is to
ensure the stationarity of all the variables at first difference
(variables need to be 1(1)). Considering the fact that we are using
quarterly data, the Augmented Dickey Fuller test (ADF test) has low
power to capture the potential seasonal unit roots and non-linearity in
the data series, therefore, HEGY test, proposed by Hylleberg, Engle,
Granger and Yoo (1990) is used to check the unit roots. This test has
the advantage to pretest data before seasonal adjustment or to use data
without seasonal adjustment [Charemza and Deadman (1997)]. Since
seasonal adjustment can result in loosing information about peak and
trough in the data series, therefore it is not advisable in models which
are based on economic theory. The results are presented in Table 1.
The results indicate that we cannot reject the presence of unit
root at zero frequency in all variables. However for seasonal
frequencies, there is no evidence of unit roots. Thus we can safely
conclude that the variables are 1(1). The residuals for all the
auxiliary regressions were found to be white noise.
Based on the results produced by AIC, FPE, LM, lag length is set to
be 5. Although SC and HQ support lag length of 4 but it is ignored due
to the presence of autocorrelation in the residuals of reduced form VAR
model.
To empirically analyse the long run relationship between the
macroeconomic aggregates (the output gap, inflation and interest rate),
we have used the Johansen and Juselius's (1990, 1992, 1994) system
cointegration test. It has the advantage of utilising all available
information in the data set, thereby increasing reliability of the
estimates. Gonzalo (1992) has shown that the Johansen's maximum
likelihood techniques perform better in finite samples than the
univariate methods. It also does not rely on arbitrary normalisation
Engle and Granger's (1987) method. Test results, presented below
show that all the variables are cointegrated which means that a long run
relationship exists among all the variables.
Once the reduced form VAR model is estimated, the residuals need to
be statistically adequate. For the purpose, diagnostic tests are
required to test the hypothesis of no autocorrelation, no
heteroskedasticity, and normality. The results show that there is no
evidence of serial correlation and heteroskedasticity even at 99 percent
level of significance. (3)
4.1. Maximum Likelihood Structural Parameter Estimates
Conventionally, VAR studies along with studies based on DSGE
framework focus on the mutual relationships of the endogenous variables
(impulse response functions) rather than estimating structural
parameters. (4) The structural parameter estimates are discussed here to
show the dimension and magnitude of the impact of different independent
variables on the dependent endogenous variable (in the specific
macroeconomic relationship) in simultaneous equations system. These
estimates also help to understand the macroeconomic dynamics in response
to different structural shocks.
The transformation of endogenous variables and identifying
restrictions are largely different from the previous studies that have
used macroeconomic data for Pakistan. The reason could be that none of
these studies have estimated the NK macroeconomic model through maximum
likelihood estimation method. In this perspective, the estimated
parameters are not comparable with any of the previous studies of
Pakistan. Nonetheless, the results are consistent with the literature.
The structural parameters estimated through maximum likelihood
estimation are presented in Table 3.
All the parameters are significantly different from zero which
reflects the significant impact of the variables on the corresponding
dependent variables. In the aggregate demand equation, (p (the
elasticity of inter-temporal substitution in consumption by the
households) is significant even at 99 percent significance level which
shows that reduction in real interest rate [[i.sub.t] -
[E.sub.t][[pi].sub.t+1]] increases the aggregate demand. The finding is
in consonance with the theory expounded by Gali and Gertler (2007) along
with others.
The parameter of forward looking inflation (P) in the Phillips
curve equation has a value of 0.7362 which indicates that agents place
larger weight to future expected inflation than inflation of past
periods. This outcome is in line with the findings of Cho and Moreno
(2002) and Gali and Gertler (1999). Finally, [[lambda].sub.0] indicates
the effect of output gap on the inflation dynamics of the country.
While majority of the literature for developed countries [including
that of Gali and Gertler (2007)] confirm positive impact of output gap
on inflation in the short run. The output gap may, however, have a
negative impact on inflation for the developing countries like Pakistan
where Central Banks deal with the dual mandate of not only controlling
inflation but also achieving high economic growth in the country Akbari
(2005). The negative impact of output gap on inflation, as is obtained
in our estimated model, shows that economic growth is inflation
reducing. It is not surprising to see the negative sign for the
estimated parameter of inflation and positive sign of output gap (with
more than one-to-one adjustment) in the interest rate rule because SBP
has never claimed to follow the Taylor rule. The negative impact of
inflationary expectations on the interest rate shows that the policy was
both ineffective and not independent. The positive impact of output gap
on interest rate, with more than one-to-one adjustment, indicates that
SBP has mainly targeted high economic growth in the country during the
period of estimation. One possibility could be that the economy enjoyed
a relatively better growth during this period due to external factors
and the authorities in the SBP allowed this momentum to continue. This
is also evident from the work of Malik and Ahmed (2010). They have found
that the SBP has not followed a rule based policy in the past and the
preference has always been for discretionary policy, which at times was
accommodating in nature, notwithstanding the inflationary pressure.
4.2. Impulse Response Functions
From policy perspective it is important to know the impact of
various macroeconomic shocks on key macro aggregates. The literature
reveals that monetary policy affects the economy with lag(s) and also
generates variability and uncertainty about target achievement. It
forces the monetary authority to be forward looking to take necessary
steps to stabilise the economy. The study focuses on two sets of Impulse
responses--the response of macroeconomic variables to a monetary policy
shocks and the response of interest rate (call money rate) to
macroeconomic variables. We have also analysed the impact of fiscal
shock and aggregate supply shock to complete the discussion. One
standard deviation shock is applied and 95 percent confidence bands of
the standard errors are projected using the analytical framework.
4.2.1. Contractionary Monetary Policy Shock
An unanticipated contractionary monetary policy shock in the shape
of an increase in call money rate has been examined. It has been found
that the unanticipated innovation in the call money rate by the SBP
results in an immediate, but slight increase in the output gap in the
same quarter which gets lower than the potential level up to fourth
quarter. However, a large reduction in the output gap occurs in the
fifth quarter and it continuously remains below the stability path up
until the tenth quarter. Since the SBP, like other Central Banks of
developing economies, pursue the objectives of growth and price
stability in the short run, the theory suggests that with an increase in
interest rate there is a decrease in consumption and investment
spending. This should lead to a decrease in aggregate demand. Whereas
the impulse response apparently shows fluctuations in the first four
quarters, one observes that the output gap remains below the long run
stability path or the steady state from fifth quarter onwards. This
indicates the success of SBP in controlling aggregate demand through
contractionary monetary policy action. It may be added that besides
private expenditure, an important component of aggregate demand is
government spending, especially for economies like Pakistan where fiscal
dominance prevails [Choudri and Malik (2012)]. In such a scenario,
growth and inflation targets are mostly set by the Government and the
role of the SBP reduces to follow this 'dependent policy
scenario'.
Panel (b) of Figure 1 confirms that the SBP is successful in
lowering inflation in the country with a monetary policy tightening. The
results are consistent with the idea of 6-18 months lag in achieving
reduction in the demand pressures. Inflation touches the long run
stability path after twenty five quarters. Thus, the identification
scheme generates no price puzzle. The monetary easing in the subsequent
periods has resulted in expansionary effects. The results further
indicate that the monetary shock has immediately transmitted positive
signals to interest rate which dies out to zero in the seventh quarter.
[FIGURE 1 OMITTED]
4.2.2. Assessing Reaction Function
The focus on the dynamic response of interest rate to fiscal and
aggregate supply shocks is expected to allow us to see whether or not
the policy reaction function is specified correctly or whether or not
the SBP has ever adopted the policy reaction function during the period
of investigation. The responses can be traced in Figure 2 below. The
results show that in response to a fiscal shock, interest rate increases
and takes twenty quarters to get back to its long run path which is
facilitated by the expansionary policy in the subsequent periods. In
response to positive cost push shock in the country, interest rates
started increasing and remained on the higher side up to twenty five
quarters.
[FIGURE 2 OMITTED]
4.2.3. Impact of Fiscal and Aggregate Supply Shocks on
Macroeconomic Dynamics
In response to positive fiscal shock, both output gap and inflation
started rising. However, whereas the output gap increases immediately
after the fiscal shock hits the economy, the inflation rate started to
rise after four quarters.
[FIGURE 3 OMITTED]
The cost push shock originates from labour market imperfections.
Inflation started rising soon after the cost push shock hits the economy
but the output gap decreases during the first few quarters but it
largely remains close to the long run stability path. This outcome
indicates that the cost push shock does not have any significant impact
on aggregate demand in the country.
[FIGURE 4 OMITTED]
4.3. Variance Decomposition
The relative importance of each structural shock can be examined by
studying the variance of forecast error which is decomposed for each
structural shock separately.
The top panel of Table 4 depicts the variance of forecast error in
the output gap for each structural shock separately for long time
horizon. It is evident that the fiscal shock is the major contributor to
variations in the output gap which is around 83.6 percent for up to 40
quarters. The monetary policy shock, on the other hand, is the second
contributor which remained around 12.84 percent of the forecast error
variance. This confirms the significance of fiscal shock in influencing
the output gap. The results are in line with the impulse response which
shows that even though the SBP is successful in managing the demand
pressures, the economy mainly remains demand driven.
The second panel of Table 4 displays the relative importance of the
structural shocks in explaining inflation in the country. The results
show that supply shock is the main contributor in explaining inflation.
From the remaining two shocks, monetary shock has high power to explain
variations in inflation which contribute up to 32.72 percent to
variations. Thus the role of the SBP is vital in managing inflation in
the country.
Finally, the monetary shock plays the most prominent role in
explaining variations in interest rate. The fiscal shock turns out to be
the second important determinant of variations in interest rate.
5. CONCLUDING OBSERVATIONS
In a path breaking article Lucas (1976) highlighted the inability
of macroeconomic models to forecast the consequences of unannounced
policy changes. The NK macroeconomic models of recent years possess
sundry features, the most consequential being the forward looking
expectations modeling approach. The model presented in the present study
has been adopted taking into account the NK perspective that
incorporates the role of expectations and rigidities.
Rather than relying on 'borrowed' values of parameters,
the maximum likelihood estimation procedure through structural VAR model
has been used to estimate these values. The parameter estimates
confirmed that an increase in real interest rate results in subsequent
decrease in output gap which is supported by the theory. The results
also demonstrated that forward looking expectations played important
role in determining inflation. Output gap helped to lower the inflation
rate. The structural parameter estimate of expected inflation rate has
shown a negative impact on interest rate. The output gap has an
explosive positive impact on interest rate. These results have allowed
us to conclude that despite adopting a discretionary stance, the
monetary policy has been ineffective, partly because the SBP did not
enjoy 'real' autonomy. Since discretionary policy stance
generally lacks transparency, it may be useful for the SBP to stick to
some sort of rule as has been suggested earlier by Malik and Ahmed
(2010). Furthermore, as expectations play prominent role in the
prevailing market structure in the country, it is important for the SBP
to show commitment towards controlling inflation along with the need for
stabilising the demand pressures.
Investigation of the macroeconomic dynamics in response to
unanticipated monetary shock has always been an area of interest for the
economists that have normally been investigated by analysing impulse
response functions. The results have shown that in response to monetary
tightening by the authority, aggregate demand displayed a trend
consistent with the idea of 6-8 months lag in achieving reduction in the
output to its long run stability point. There is no evidence of price
puzzle. On the other hand, in response to positive fiscal shock, the
monetary authorities raised interest rate to counter the negative
effects of fiscal shock to the economy. The results exposed the
importance of expectations of economic agents in determining
macroeconomic dynamics of the economy which are found to be forward
looking. Finally, variance decomposition has emphasised the relevance of
fiscal, monetary and cost push shocks as major sources of variation in
forecast errors of output gap, inflation and interest rate.
Before closing the discussion, it may be useful to add that there
are various methods to estimate DSGE models other than the SVAR model.
These alternatives, however, require microeconomic survey based values
of parameters which are seldom available. Hence, there has been a
'natural' limitation to rely only on SVAR model. Accordingly,
future research in the area of modeling would require that microeconomic
surveys are conducted to generate the values of microeconomic
parameters. These surveys will also allow the possibility of inclusion
of informal sectors of the economy in the modeling approach to have a
holistic view of the economy.
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(1) See the extensive work of 1970s of such luminaries as Lucas,
Barro, Sargant, and Wallace.
(3) The results of reduced form VAR model and Diagnostic tests can
be shared, if required.
(4) According to Joiner (2002), this is due to the underlying
feature of the impulse responses to reflect the dynamic response of
macroeconomic variables and that structural parameters do not reflect
the dynamics.
Shahzada M. Naeem Nawaz <shahzadal45@gmail.com> is PhD
Scholar (Economics) at the International Institute of Islamic Economics,
International Islamic University, Islamabad and this research paper is
based on his Dissertation submitted for the partial requirement of PhD
degree. Ather Maqsood Ahmed <ather.ahmed@s3h.nust.edu.pk> is
Professor of Economics at School of Social Sciences and Humanities,
National University of Sciences and Technology, Islamabad.
Table 1
The HEGY Test Results
t-test for Ho: t-test for Hi:
[[pi].sub.1] = 0 [pi]2 = 0
Auxiliary (Non-seasonal/ (Biannual
Variable Regression Zero Frequency) Unit Root)
Output With Intercept and
Gap Seasonal Dummies -1.69 -2.64 **
With Intercept, Time
Trend and Seasonal
Dummies -1.68 -2.64 **
Interest With Intercept and
Rate Seasonal Dummies -1.84 -4.18 ***
With Intercept, Time
Trend and Seasonal
Dummies -1.83 -4.14 ***
Inflation With Intercept and
Seasonal Dummies -1.75 -3.56 **
With Intercept, Time
Trend and Seasonal
Dummies -1.98 -3.56 **
F-test for
H: [[pi].sub.3] =
Auxiliary [[pi].sub.4] = 0
Variable Regression (Annual Unit Root)
Output With Intercept and
Gap Seasonal Dummies 9.79 ***
With Intercept, Time
Trend and Seasonal
Dummies 9.64 ***
Interest With Intercept and
Rate Seasonal Dummies 36.42 ***
With Intercept, Time
Trend and Seasonal
Dummies 35.01 ***
Inflation With Intercept and
Seasonal Dummies 20.67 ***
With Intercept, Time
Trend and Seasonal
Dummies 20.17 ***
Table 2
The Cointegration Test Outcome
Unrestricted Cointegration Rank Test (Trace)
Hypothesised Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob. **
None * 0.278671 41.05337 29.79707 0.0017
At most 1 0.141998 15.24723 15.49471 0.0545
At most 2 0.039070 3.148429 3.841466 0.0760
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesised Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob. **
None * 0.278671 25.80615 21.13162 0.0102
At most 1 0.141998 12.09880 14.26460 0.1070
At most 2 0.039070 3.148429 3.841466 0.0760
Table 3
The Maximum Likelihood Structural Parameter Estimates
Coefficient Std. Error z-Statistic Prob.
[phi] 0.178022 0.002399 74.21324 0.0000
[beta] 0.736175 0.000416 1770.512 0.0000
[[lambda].sub.0] -0.002851 0.000663 -4.303656 0.0000
[[gamma].sub.1] -4.828962 0.014359 -336.2983 0.0000
[[gamma].sub.2] 1.440747 0.019326 74.55026 0.0000
[x.sub.t] = -[phi]([i.sub.t] - [E.sub.t][[pi].sub.t+1] - [rho]] +
[E.sub.t][x.sub.t+1] + [[epsilon].sup.f.sub.t]
[[pi].sub.t] = [beta][E.sub.t]{[[pi].sub.t+1]) +
[[lambda].sub.0][x.sub.t] + [[epsilon].sup.c.sub.t]
[i.sub.t] = [[gamma].sub.3] + [[gamma].sub.1]
([E.sub.t][[pi].sub.t+1]) + [[gamma].sub.2][x.sub.t] +
[[epsilon].sup.i.sub.t]
Table 4
Forecast Error Variance Decomposition
Period S.E. Fiscal Supply Monetary
Shock Shock Shock
Output Gap 1 0.01358 100 0 0
2 0.01361 99.67213 0.077648 0.250222
3 0.01462 95.10921 0.810396 4.080392
4 0.01471 94.70157 0.969436 4.328993
5 0.01673 95.30892 0.771204 3.919878
9 0.01778 92.42992 0.819893 6.750182
13 0.01851 88.63415 1.328436 10.03741
17 0.01897 87.94153 1.8474 10.21107
21 0.01944 87.03123 2.850895 10.11788
25 0.01983 85.54143 3.375936 11.08263
29 0.02006 84.27488 3.551183 12.17393
33 0.02017 83.65552 3.547379 12.7971
37 0.02022 83.59664 3.536292 12.86707
40 0.02025 83.60757 3.549026 12.8434
Inflation 1 0.00541 0.014161 99.98584 0
2 0.00933 0.020945 98.87868 1.100378
3 0.012 0.161422 97.76989 2.068685
4 0.0141 0.154935 94.98598 4.859086
5 0.01529 0.241972 88.09243 11.6656
9 0.01758 5.984871 69.96725 24.04788
13 0.01955 5.277532 69.05278 25.66969
17 0.02055 4.887102 63.54804 31.56486
21 0.02092 5.222687 62.47403 32.30329
25 0.0211 5.752717 61.51857 32.72871
29 0.02116 6.25228 61.18585 32.56187
33 0.02119 6.460753 61.03369 32.50555
37 0.02121 6.4608 60.97638 32.56282
40 0.02121 6.469064 60.96894 32.562
Interest Rate 1 0.10628 0.713581 0.500079 98.78634
2 0.12042 3.020116 3.208405 93.77148
3 0.13247 2.982892 4.90387 92.11324
4 0.1371 3.405951 8.020343 88.57371
5 0.14605 8.479319 11.06629 80.45439
9 0.17634 27.09277 16.94016 55.96707
13 0.20522 32.50431 20.0214 47.4743
17 0.22588 30.14057 19.71455 50.14487
21 0.23589 27.81507 18.77032 53.41461
25 0.24047 27.93342 18.10356 53.96301
29 0.24334 29.28425 17.82769 52.88807
33 0.2457 30.072 17.67618 52.25182
37 0.2472 30.02404 17.54731 52.42865
40 0.24779 29.89015 17.46739 52.64246
