Monetary Policy Reaction Function in Pakistan
Wasim Shahid Malik
Pakistan Institute of Development Economics, Islamabad
Ather Maqsood Ahmed
National University of Science and Technology. Islamabad
Abstract
During the last three decades the view has emerged that monetary policy can achieve only
limited number of objectives and in an economy with rational economic agents, policy can
achieve its objectives only by committing to consistent policy. Using Pakistani data, this study
attempts to estimate Taylor-type reaction function and its slight modified version defined over
inflation and real GDP growth. Our results indicate pro-cyclical response of SBP to economic
fluctuations. Furthermore, instead of focusing on price stability along with output stabilization,
economic growth has been given priority. The study also establishes that policy remained
inconsistent as parameters in the reaction function show significant variation in recursive
estimation.
1
I. Introduction
During the last three decades the view has emerged that monetary policy can achieve
only limited number of objectives and in an economy where economic agents form expectations
rationally, policy can achieve its objectives only by committing to a rule. As monetary policy has
persistent effects only on limited number of variables, it cannot be assigned goals that are beyond
its control, (Friedman 1968; Svensson 2002). To achieve these goals, commitment to rule is the
only option as discretionary policies become time inconsistent, (Kydland and Prescott 1977;
Barro and Gordon 1983a; Taylor 1993)1.
For most of the central banks in the world, price stability has become the prime objective
of monetary policy along with a concern to real stabilization in the short run. Thus summarizing
monetary policy objectives by a loss function defined over deviations of inflation from target and
that of output from potential level has become a norm in the literature on monetary economics.
But monetary policy can stabilize real economic activity only in the short run. Assigning
monetary policy the objective of long run growth requires setting operational target in such a
way that real interest rate is always below neutral interest rate2.
Policy rules have greater advantage over discretionary policy in achieving monetary
policy objectives. This however requires that the rule has to be in place for a reasonably long
period of time to gain advantages of stabilization and the credibility associated with the rule. In
simple words monetary policy rule is nothing more than consistent policy with rational
objectives. Hence to establish credibility and thus achieving goals of monetary policy,
consistency in the state contingent reaction for reasonably long period of time is unavoidable.
1
While Barro and Gordon (1983) highlights the optimality of the rule, Taylor (1993) also focuses on feasibility of
the rule.
2
Neutral real interest rate is the real interest rate consistent with zero output gap.
2
The purpose of present study is to estimate Taylor-type reaction function to establish
whether or not the focus of SBP has remained on two objectives: price stability along with real
stabilization. Historically Pakistan has experienced cycles in inflation and real economic activity.
Inflation reached its peak of 23 percent in 1974, and touched the lowest level of 2.4 percent in
2002. Similarly, the real output gap varied between -7 percent in 2002 and 6.5 percent in 2008.
Historically, there has been more focus of SBP on growth objective instead of focusing on
inflation and output gap, which, most of the time, resulted in pro-cyclical response of SBP.
Besides, there has been more variation, over time, in setting objectives of monetary policy and in
degree of leaning against the wind, (Malik and Ahmed 2007). Hence the second objective of the
paper is to investigate, whether or not the policy has remained consistent over time.
The paper proceeds as follows. In Section 2, data and methodology for estimation are
explained. Discussion of empirical findings is the subject matter of Section 3. Finally section 4
concludes the paper.
II. Data and Methodology
We start with the following monetary policy reaction function given by Taylor (1993).
it = r* + πt + α1yt + α*2 (πt – π*)
…
…
…
…
(2)
where
r* – Long run equilibrium real interest rate
it – Short interest rate taken as monetary policy instrument
πt – Previous four quarters (including the current one) average inflation
yt – Output gap calculated as percentage deviation of actual output from the normal level.
π* – Long run inflation target of the central bank
3
There are four parameters, r*, π*, α1 and α*2 in expression 2. The values of these parameters
adopted by Taylor were: 2%, 2%, 0.5 and 0.5, respectively.
The above rule (expression 2) can easily be converted into an estimable form as
it = α 0 + α1 yt + α 2 πt …
…
…
…
… (3)
where α 0 = r * +α 2 π * and α 2 = (1 + α*2 )
with the following parameter restrictions:
α0 = 1, α1 = 0.5 and α2 = 1.5,
However the minimum requirement for counter-cyclical response of monetary authority is that
α1 > 0 and α 2 ≥ 1 must hold; otherwise the system would be unstable3.
Expression 3 can be estimated by OLS if time-series properties are satisfied. Otherwise
the results are not consistent [Enders (2004)].4 Now regarding first objective of the study, we
estimate expression 3 by OLS5 and investigate the statistical significance of parameters. If output
gap is found to be insignificant determinant of policy instrument, we will try to investigate the
SBP’s focus on growth. It is expected that growth in real GDP more significantly explains
3
The second condition that the response of interest rate to changes in inflation must be atleast one-for-one is
referred to as ‘Taylor Principle’ in the literature [Taylor (1999); and Woodford (2001)].
4
Other techniques like Two Stage Least Squares (TSLS), Generalized Method of Moments (GMM), and
Vector Autoregression (VAR) etc may improve estimation efficiency, but it would be at the cost of loss of rule’s
theory, as the rule specifies interest rate as a linear function of output gap and inflation.
5
If the residuals from estimated regression are stationary then all the three variables are cointegrated as pointed out
by Engle – Granger (1987).
4
variation in the monetary policy instrument. For the second objective we apply Dummy Variable
Test and Recursive Parameter Estimation Method.
III. Empirical Findings
Annual data on call money rate (short term interest rate), inflation and real GDP gap are
used for the period 1973 to 20086. Inflation is calculated as annual percentage growth in GDP
deflator. Output gap is estimated as percentage deviation of real GDP from its quadratic trend. It
should be noted that SBP was not independent in setting monetary policy instrument before the
financial sector reforms of early 1990s. But we have taken data from 1973 to investigate longer
period. However, we have used dummy variable to distinguish between two time periods, that is,
before and after reforms.
To see whether or not SBP has been targeting inflation and output gap, Taylor-type
reaction function in expression 3 has been estimated for the period 1973 – 2008 using annual
data on call money rate (taken as monetary policy instrument), inflation and real output gap. The
results clearly indicate that the actual policy of SBP does not correspond to the Taylor rule7. The
results (presented below in Table 1) indicate that the coefficient of output gap is statistically zero
and that of inflation is too small compared to what is prescribed by Taylor (1993)8.
6
All the data are taken from International Financial Statistics (IFS)
Here we have discussed only some of the points regarding estimation results of Taylor rule. For more detailed
discussion for Taylor rule for Pakistan, see Malik and Ahmed (2007)
8
The OLS estimates are super consistent as the residual series from this estimated equation is stationary.
7
5
Table 1: Regression Results for Reaction Function with Output Gap
Indep Variables
Intercept
Output gap
Inflation
Regression 1
6.44
(7.90)
0.005
(0.05)
0.21
(2.66)
Dummy
Regression 2
6.32
(6.42)
0.003
(0.03)
0.21
(2.61)
0.17
(0.23)
Regression 3
6.13
(7.01)
-0.02
(-0.23)
0.20
(2.62)
Dummy*Output gap
Regression 5
6.71
(8.05)
-0.41
(-2.32)
0.14
(1.80)
0.57
(2.64)
0.56
(2.60)
0.07
(1.00)
0.27
0.77
0.27
0.83
0.08
(1.00)
Dummy*Inflation
Adj R-square
DW statistics
Regression 4
7.01
(9.00)
-0.39
(-2.21)
0.14
(1.82)
0.14
0.69
0.11
0.69
0.14
0.75
t-stats in parentheses
Some results in Table 1 need further discussion. First, monetary authority, while setting
monetary policy instrument, has not been focusing on output gap. One potential reason for
ignoring real stabilization could be overwhelming effort by monetary authority to curb inflation
even in the short run. But this argument looses its worth when we see the coefficient of inflation
in the reaction function, which is significantly less than one. These two findings suggests
including economic growth in the reaction function as one possible reason for these findings
could be that there has been continuous focus of SBP on economic growth instead of output
stabilization. We have estimated this modified version of Taylor rule but we will discuss its
result at length.
Second, on average, there is no change in setting monetary policy instrument after
financial sector reforms. We defined a dummy variable that has value 1 for period 1989 to 2008
and zero otherwise. Then expression 3 has been estimated including this dummy variable to see
the effect of financial sector reforms on setting monetary policy instrument. Results in third
column of Table 1 show that there is, on average, no change in policy making, as coefficient of
dummy variable is not statistically different from zero. To estimate whether or not there was a
6
shift in response of monetary authority to changes in output gap and inflation after 1990, we
estimated expression 3 with slope dummy and results are given in the last three columns of table
1. It has been found that there was a significant shift in response of SBP to output gap
fluctuations. Before financial sector reforms there was pro-cyclical response to output gap but
after that the coefficient of output gap in the reaction function has become effectively zero.
Interestingly there was no change in policy response to inflation.
Next, to test whether or not monetary policy in Pakistan has been pursuing growth
objective, we estimated Taylor-type reaction function given in expression 3 with a slight
modification. Instead of including output gap, we use annual growth rate of real GDP as
indicator for real activity. Results in column 2 of Table 2 show that monetary authority has been
continuously focusing on the growth objective. Coefficient of inflation is significantly less than 1
and that of output growth is negative; both indicate pro-cyclical response of monetary policy9.
While setting monetary policy, SBP has been giving priority to growth objective over inflation10.
As Malik and Ahmed (2007) mentioned, being the central bank of a developing country, SBP
might have resisted counter-cyclical response for economic growth ignoring the objective of price
stability. Therefore, whenever the economy started gaining momentum SBP allowed it to do so to
achieve higher economic growth rate. While this justification seems appropriate for the periods when
there is up-swing in the economy but it is difficult to justify it in economic down turns.
To differentiate between boom and recession we have defined another dummy variable that
has value 1 for boom periods and 0 for recessionary phase and estimated interest rate reaction
function in expression 3 using this dummy variable to test whether or not there is any break in the
9
Low values of coefficient on inflation indicate pro-cyclical response only in case of demand pull inflation. If
inflation is a result of shocks occurring on supply side, loose monetary stance is countercyclical.
10
According to SBP Act 1956 SBP has dual objectives of inflation control and output growth without clear
prioritization.
7
coefficients of output growth and inflation. Interestingly, results in the last column of Table 2 show
that there is no change in the monetary authority’s response to growth and inflation no matter
economy recovers from recession or moves into recession.
Table 2: Regression Results for Reaction Function with Output Growth
Indep Variables
Intercept
Output Growth
Inflation
Regression 1
8.71
(7.51)
-0.41
(-2.53)
0.20
(2.84)
Dummy*Output
growth
Regression 2
9.15
(7.66)
-0.40
(-2.45)
0.18
(2.58)
-0.16
(-1.31)
Regression 3
8.67
(6.42)
-0.41
(-2.25)
0.20
(2.79)
0.004
(0.06)
Dummy*Inflation
Regression 4
7.81
(6.08)
-0.10
(-0.49)
0.12
(1.72)
-0.52
(-2.58)
0.26
(2.18)
0.05
(0.20)
0.006
(0.04)
SD*Output growth
SD*Inflation
Adj R-square
DW statistics
•
•
Regression 5
8.65
(7.19)
-0.44
(-2.29)
0.21
(2.58)
0.28
0.77
0.36
0.85
0.32
0.77
0.45
1.29
0.33
0.76
t-stats in parentheses
SD stands for state dummy, which has value 1 for boom
To estimate whether or not there was a shift in response of monetary authority to changes
in output growth and inflation after financial sector reforms, we estimated expression 3 with
slope dummy. Interestingly coefficient of inflation, though still below 1, increased somewhat but
that of output growth increased with negative sign. The astonishing aspect of result is that
response of monetary authority to output growth is zero before 1990 and is negative and
significantly different from zero after that. It is important to note that if pro-cyclical response
after 1990 has been due to monetary policy objectives other than inflation then it is in contrast to
what was envisaged before financial sector reforms.
8
In Pakistan annual targets for inflation and real GDP growth are announced each year and
then monetary and fiscal policies are set accordingly. We have estimated monetary policy
reaction function (expression 3) using target values of real output growth and inflation, instead of
their actual values11. Results in first column of Table 3 show that interest rate responds one-forone to inflation targets of the year and by 50 percent to output growth targets. Theoretically, for
pro-cyclical response, monetary authority should cut interest rate if there is positive change
either in growth target or inflation target. Surprisingly, interest rate has been found to be
positively responding to increase in both targets.
Table 3: Regression Results for Expression 3
Indep Variables
Intercept
Output Growth Target
Inflation Target
Regression 1
Regression 2
Regression 3
-2.00
(-0.67)
0.53
(0.88)
1.02
(3.08)
6.81
(11.13)
7.40
(8.83)
-0.06
(-4.36)
0.005
(0.48)
Output Deviation*
Inflation Deviation*
-0.10
(-0.30)
0.49
(1.70)
Output Deviation**
Inflation Deviation**
Adj R-square
DW statistics
0.58
1.89
0.56
1.30
0.08
1.15
* Deviation of actual values from the targets for the same year
** Deviation of actual values for the last year from the targets of current year
When reaction function is estimated with deviations of output growth and inflation from
their respective targets, there has been found pro-cyclical response if growth rate deviates from
11
These results are based on data for the period 1990 – 2008 due to unavailability of data for the remaining years.
9
the target for the year but inflation deviations from the target seem to be ignored12. The final
result is more interesting and contradicts all other results. The coefficient of deviation of
previous period’s inflation from the current inflation target is found to be about 0.5, which is
exactly equal to what has been prescribed by Taylor (1993). But we have found insignificant
response to deviation of output growth of previous period from the current target.
Policy Consistency
As explained above, long term goals of monetary policy can be achieved only by
committing to consistent policy. Inconsistent policies create uncertainty and it becomes difficult
for private agents to forecast inflation properly. In this case private agents punish policy maker
by expecting inflation other than what is announced, thus increasing inflation volatility, (Barro
and Gordon 1983 b).
To test policy consistency we have found recursive estimates for the coefficients of
output gap and inflation in the reaction function. For this purpose we have started estimating
expression 3 for the period 1973 – 1983. Results in figure 1 show that there is significant
variation in both coefficients over the sample period. Coefficient of output gap touched the
lowest value of -0.42 and reaches maximum of zero. There is increasing trend in this coefficient
after financial sector reforms and policy does not remain pro-cyclical, though not anti-cyclical
too. Similarly there has been increase in policy consistency after 2002 as coefficient of output
gap reaches zero and remains there after that period. Coefficient of inflation also moves between
0.05 and 0.2 and again the coefficient shows increasing trend.
12
The response to output deviation from the target, though statistically significant, is found close to zero in
magnitude.
10
Figure 1: Recursive Estimates for the Coefficients of Output gap and Inflation
C o e f f ic ie n t o f O u t p u t G a p
0 .1 0
0 .0 0
- 0 .1 0
- 0 .2 0
- 0 .3 0
- 0 .4 0
2000
2002
2004
2006
2000
2002
2004
2006
1998
1996
1994
1992
1990
1988
1986
1984
- 0 .5 0
C o e f f ic ie n t o f In f la t io n
0 .2 5
0 .2 0
0 .1 5
0 .1 0
0 .0 5
1998
1996
1994
1992
1990
1988
1986
1984
0 .0 0
The coefficient of inflation showed same trend when we estimated reaction function with
real GDP growth rate rather than output gap but that of output growth has shown reverse of what
is found for the case of output gap [Figure 2]. It has shown a continuous decline from -0.1 to -0.4
after 1990. Interestingly we have found different pictures when different indicators for the real
activity are used. In nutshell we can conclude that policy consistency in Pakistan has increased
from the beginning of this decade.
11
Figure 2: Recursive Estimates for the Coefficients of Output Growth and Inflation
C o e f f ic ie n t o f O u t p u t G r o w t h
0 .0 0
- 0 .1 0
- 0 .2 0
- 0 .3 0
- 0 .4 0
2000
2002
2004
2006
2000
2002
2004
2006
1998
1996
1994
1992
1990
1988
1986
1984
- 0 .5 0
C o e f f ic ie n t o f In f la t io n
0 .2 5
0 .2 0
0 .1 5
0 .1 0
0 .0 5
1998
1996
1994
1992
1990
1988
1986
1984
0 .0 0
12
IV. Summary and Concluding Remarks
In this study the interest rate reaction function for Pakistan has been estimated for the
period 1973-2008 and for the sub-samples covering the period before and after financial sector
reforms. One of the important findings of the study is that SBP has been conducting pro-cyclical
policy, though the degree of pro-cyclicality decreased significantly after financial sector reforms.
This could have been due to SBP concentration on policy objectives other than inflation and
output stabilization. One of such objectives has been found to be economic growth. Surprisingly,
the degree of pro-cyclicality towards economic growth has increased after 1989. Interestingly,
monetary authority’s response matches the one prescribed by Taylor if we estimate reaction
function with deviation of previous period’s inflation from the current target. Finally, the study
establishes inconsistent response of SBP to inflation and output deviations from their respective
targets, though policy consistency has improved since the beginning of this decade.
State Bank of Pakistan has gained autonomy in setting policy instrument as a result of
financial sector reforms. The reason why SBP’s response has not become counter-cyclical could
be the focus of policy on objectives other than price stability in the long run and real stabilization
in the short run. Besides, SBP also has to withstand regular fiscal pressures which largely
weaken the monetary policy stance and there is a constant struggle for maintaining stability of
exchange rate. For achieving price stability, there must be legislation to reduce fiscal pressure
and SBP has to pay due attention to this objective; otherwise inflationary expectations could not
be controlled.
13
References
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Rate Model. Journal of Political Economy 91, 589–610.
Barro, Robert J., and David B. Gordon (1983b) Rules, Discretion and Reputation in A Model Of
Monetary Policy. Journal of Monetary Economics 12:1, 101–121.
Enders, Walter (2004) Applied Econometric Time Series. John Wiley & Sons, Inc.
Kydland, Finn, and Edward Prescott (1977) Rules Rather Than Discretion: The Inconsistency of
Optimal Plans. Journal of Political Economy 85, 473–490.
Malik, W. Shahid (2007) Monetary Policy Objectives in Pakistan: An Empirical Investigation.
Essay in PhD Dissertation, PIDE.
Malik, W. Shahid and Ather Maqsood Ahmed. (2007), Taylor Rule and the Macroeconomic
Performance in Pakistan, PIDE working paper no 34.
Svensson, Lars E. O. (2002), Monetar Policy and Real Stabilization, Rethinking Stabilization
Policy,A Symposium The Federal Reserve Bank of Kansas City
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Conference Series on Public Policy 39, 195–214.
14