Taylor rule and the macroeconomic performance in Pakistan.
Malik, Wasim Shahid ; Ahmed, Ather Maqsood
A near-consensus position in modern macroeconomics is that policy
rules have greater advantage over discretion in improving economic
performance. For developing countries in particular, simple instrument
rules appear to be feasible options as pre-requisites since more
sophisticated targeting rules are generally lacking. Using
Pakistan's data, this study has attempted to estimate the Taylor
rule and use it as monetary policy strategy to simulate the economy. Our
results indicate that the State Bank of Pakistan (SBP) has not been
following the Taylor rule. in fact, the actual policy has been an
extreme deviation from it. On the other hand, counterfactual simulation
confirms that macroeconomic performance could have been better in terms
of stability of inflation and output, had the Taylor rule been adopted
as monetary policy strategy. The study also establishes that further
gains are possible if the parameter values of the rule are slightly
modified.
JEL classification: E47, E31, E52
Keywords: Taylor Rule, Macroeconomic Performance, Counterfactual
Simulation
1. INTRODUCTION
A near-consensus position in modern macroeconomics is that policy
rules have greater advantage over discretion in improving economic
performance [Taylor (1993)]. Through seminal papers, Kydland and
Prescott (1977) and Barro and Gordon (1983) have convincingly shown that
discretionary policies are time inconsistent. However, the adverse
outcome can be avoided if private agents pursue a punishment policy of
higher inflationary expectations that may cause loss of reputation of
the monetary authority [Barro and Gordon (1983a)]. Alternatively,
ensuring independence of the Central Bank may also reduce inflationary
bias [Sargent and Wallace (1981), Rogoff (1985), Alesina and Summers
(1993), and Walsh (1995) among others].
Interestingly, despite this overwhelming support initially for
money growth targeting and later for inflation targeting, it was not
clear how a rule could be used in practical policy formulation process
until Taylor (1993) presented a state-contingent interest rate rule that
is both, practicable and simple. (1) It calls for changes in the short
term interest rate (monetary policy instrument) in response to deviation
of output from trend or potential level and that of inflation from the
target with equal weight given to both these objectives in the policy
reaction function. Taylor argues that adoption of the simple rule not
only has the potential of improving macroeconomic performance, it also
avoids the time inconsistency problem. He further maintains that the
rule does not suffer from enforcement problem because of its easy
verifiability by agents outside the central bank. In this context,
commitment to this rule becomes technically feasible.
The purpose of the present study is to revalidate the Taylor rule
by estimating it for Pakistan. It needs to be established whether or not
the State Bank of Pakistan (SBP). the Monetary Authority has been
following such a policy rule for the simple reason that 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 growth varied
between 8.7 percent in 1980 and -0.1 percent in 1997. (2) Besides this
inconsistent macroeconomic performance, Pakistan's economy also
suffered from weak institutional set -up. Not only that the independence
of the central bank was continuously challenged, it also had to
withstand regular fiscal pressures which largely weakened the monetary
policy stance. Furthermore, there was a constant struggle for
maintaining stability of the exchange rate.
Given these weaknesses, one would have argued that adoption of a
simple instrument rule like the Taylor rule might have been a natural
and feasible option. Given this perspective, the second objective of the
study is to assess the macroeconomic performance on the basis of
variability of inflation and output. For this purpose, the economy has
been simulated, with and without Taylor rule, as monetary policy
strategy. Finally, using counterfactual simulations, the study also
investigates whether the parameter values of the Taylor rule (the
weights on output and inflation stabilisation, and the inflation target)
are optimal for Pakistan or some modification is needed to have better
results.
The paper proceeds as follows. In Section 2, the two types of
monetary policy rules, namely the instrument rules and the targeting
rules, are defined and explained. The methodology for estimation,
backcasting, and counterfactual simulation is presented in Section 3. An
exhaustive discussion of empirical findings is the subject matter of
Section 4. The final section summarises the main findings and offers
insights for further research.
2. MONETARY POLICY RULES
A monetary policy rule can be defined as a description--expressed
algebraically, numerically, and/or graphically--of how the instruments
of policy, such as monetary base or the discount rate, change in
response to economic variables [Taylor (1999b)]. Policy rules are
similar to constant growth rate rules for money supply. However, in a
broader sense, feedback rules such as money supply response to changes
in unemployment and/or inflation etc. are preferred policy rules. As
indicated, there is a near-consensus among macroeconomists that policy
rules have greater advantage over discretion in improving economic
performance. This, however, requires that the rule is adopted and
followed for a reasonably long period of time to reap the benefits of
stabilisation and the credibility associated with the rule. The
literature related to rules versus discretion debate distinguishes
between simple instrument rules [proposed by McCallum (1988): Taylor
(1993) and others] and targeting rules due largely to Svensson (1997,
2002, 2003). The choice between the two reduces to such concerns as
simplicity, robustness, reliability, practicability, technical
feasibility, result-orientation and the role of policy-maker's
judgment in decision-making. We begin with a brief review of the two
rules.
Instrument Rules: Instrument rules are state-contingent reaction
functions that link the policy tool with performance indicators of the
economy [Meltzer (1987), McCallum (1988), Taylor (1993), and Henderson
and McKibbin (1993)]. These rules are simple to follow and require
little amount of information. These are robust and technically feasible
in the sense that commitment to rule is easily verifiable. Of different
variants, the one that has attracted most of the attention during 1990s
has been the Taylor (1993) rule. Taylor offered an instrument rule to
conduct monetary policy operations by setting the target for federal
funds rate (operational target) equal to an 'equilibrium' real
funds rate plus the current inflation and adding to it a weighted
average of monetary authority's response to the deviation of
current inflation from the target and percentage deviation of the real
GDP from an estimate of its potential or full-employment level. He
considered it to be an 'optimal' policy as it relates a
plausible instrument to reasonable goal variables and performs
reasonably well in a variety of macroeconomic models. (3) The rule can
be described by the following equation:
[i.sub.t] = [r.sup.*] + [[pi].sub.t] + [[alpha].sub.1][y.sub.t] +
[[alpha].sub.2] ([[pi].sub.t] - [[pi].sup.*]] (1)
where [r.sup.*] is the long-run equilibrium real interest rate,
[[pi].sub.t] is the current inflation rate (Taylor takes this as last
four quarters average inflation including the current quarter),
[[pi].sup.*] is the target inflation rate, and [y.sub.t] is the
deviation of output in period t from its long-run trend. The
restrictions on the coefficients to have macroeconomic stability are:
[[alpha].sub.1] [greater than or equal to] 0 and [[alpha].sub.2 ]
[greater than or equal to] 0. Supposing that the coefficient on
inflation deviation is less than zero, then a rise in inflation would
lead to an interest rate cut, which will induce increased spending. In
turn, this would tend to increase aggregate demand, thereby increasing
the inflation further (an unstable solution). On the other hand, if it
is greater than zero then this instability does not arise, because then
the rule ensures that inflation is equal to its targeted value
[[pi].sup.*] [Taylor (1999a)].
Targeting Rules: Some of the central banks adopted an elaborate
framework to keep inflation on target and output on track during the
1990s. To start with, this framework was not 'tightly'
supported by academic research. However, it recovered from this
deficiency with the evolution of literature on 'inflation
targeting' or 'inflation forecast targeting' [Svensson
(1997)]. The revised framework starts with a rule that allows some
discretion to the central bankers. Hence it was also regarded as
'constrained discretion' by Bernanke and Mishkin (1997) and
targeting rule by Svensson (2002). It proceeds like this. The central
bank announces a numerical inflation target (point target or target
range) and monetary policy has a legislated mandate for achieving this
target with clear instrumental independence. There is a high degree of
monetary policy transparency and accountability of concerned
authorities. The inflation forecast is taken as the intermediate target.
Within targeting rules, a further distinction is made between
'general targeting rule' and 'specific targeting
rule'. While the former specifies an operational loss function,
which the monetary policy is committed to minimise, in the case of the
latter a condition for setting the instrument is specified, e.g.,
marginal rate of transformation and substitution between the target
variables is equalised. It gives an implicit reaction function of the
monetary authority that need not be announced. According to this
framework, central banks collect large amount of data and use a complex
policy formulation to set the path of instrument. (4) The rule has a
good theoretical base as there is no ad hoc representation of reaction
function. Here the condition for instrument path is described by optimal
first order Euler conditions and the central bank behaviour is not
modeled in a mechanical way. There is also a clear role of judgment in
the formulation and implementation of monetary policy [Svensson (2005)].
3. MODEL SPECIFICATION AND METHODOLOGY
Ever since the introduction of the Taylor rule, three issues that
have occupied much space in research are positive analysis of central
banks' strategy to control inflation, robustness of rule to changes
in transmission mechanism and ex-post macroeconomic performance once the
rule is adopted. As indicated, the objective of the present study is not
to identify the policy reaction function of SBP, instead our focus is on
drawing a comparison of actual policy with the one suggested by the
Taylor rule. We are also interested in knowing whether the economic
performance would have improved had the Taylor rule been followed.
Starting with the first objective, the issue can be addressed
either by invoking the standard regression techniques or through a
simple comparison of the actual and the simulated data similar to one
used by Taylor (1993). Regarding the first option, let us re-specify the
Taylor rule as:
[[i.sub.t] - [r.sup.*] + [[pi].sub.t] + [[alpha].sub.1][y.sub.t] +
[[alpha].sup.*.sub.2] ([[pi].sub.t] - [[pi].sup.*]) ... ... ... ... ...
(2)
where
[r.sup.*]--Long run equilibrium real interest rate.
[i.sub.t]--Short interest rate taken as monetary policy instrument.
[[pi].sub.t]--Average inflation over previous four quarters
including the current one.
[y.sub.t]--Output gap calculated as percentage deviation of actual
output from the normal level.
[[pi].sup.*]--Long run inflation target of the central bank.
There are four parameters, [r.sup.*], [[pi].sup.*], [[alpha].sub.1]
and [[alpha].sup.*.sub.2] in expression 2. The values of these
parameters adopted by Taylor were: 2 percent, 2 percent, 0.5 and 0.5,
respectively. Following in Taylor's footsteps, we have also assumed
that the central bank has information on current output and inflation.
The above rule (expression 2) can easily be converted into an
estimable form as
[i.sup.t] [[alpha].sub.0] + [[alpha].sub.1] [y.sub.t] +
[[alpha].sub.2] [[pi].sub.t] ... ... ... ... ... ... (3)
where [[alpha].sub.0] = [r.sup.*] + [[alpha].sub.2] [[pi].sup.*]
and [[alpha].sub.2] = (1 + [[alpha].sup.*.sub.2])
It is contended that if the SBP strictly follows the rule then
parameter values should be [[alpha].sub.0] = 1, [[alpha].sub.1] = 0.5
and [[alpha].sub.2] = 1.5, and if it is not then [[alpha].sub.1] > 0
and [[alpha].sub.2] [greater than or equal to] 1 must hold, otherwise
the system would be unstable. It is relevant to point out that the
second condition is referred to as 'Taylor Principle' in the
literature [Taylor (1999) and Woodford (2001)].
Expression 3 can be estimated by OLS if time-series properties are
satisfied. Otherwise the results are not consistent [Enders (2004)]. (5)
For super consistency of the OLS estimates even in the case of
non-stationary variables, the estimated residuals have to be stationary.
To enforce these constraints, the model parameters in the present study
are estimated after testing the presence or otherwise of unit root in
the estimated residuals of the equation. In the second step, the short
term interest rate is simulated with actual data on output and inflation
assuming the Taylor rule as monetary policy strategy. The conjecture is
that if the central bank has been following the Taylor rule, then both
actual and simulated series should be close to each other showing
similar behaviour and the same basic statistics like mean, range,
standard deviation etc. It may, however, be added that even though
Taylor (1993) has used this approach to evaluate the Fed's policy,
this method is somewhat less sophisticated. It can, nonetheless, perform
well in identifying the behaviour of monetary policy instrument.
To accomplish the second objective of the study, the economy needs
to be simulated with and without the Taylor rule as monetary policy
strategy to assess the macroeconomic performance on the basis of
variability in inflation and output and the loss to society. This
analysis is undertaken for historical as well as stochastic simulation.
In this regard, some issues need further elaboration. The first relates
to macroeconomic model on the basis of which the economy is to be
simulated. The literature highlights three types of transmission
mechanisms emanating from the Lucas-type expectations-augmented Phillips
curve model, Neo-Keynesian model, or the New-Keynesian model [Cukierman
(2002)]. The estimation of the first and the third model not only
requires the assumption of rational expectations, one also needs to have
knowledge of prior values of some of the parameters for model
calibration. Since the rational expectations hypothesis has not yet been
tested in Pakistan, and also no earlier studies are available to provide
prior values of the parameters, the obvious choice for the present study
has been restricted to the use of the Neo-Keynesian type model suggested
by Svensson (1997) and estimated by Rudebusch and Svensson (1999).
According to Svensson (1997) the model although simple, has reasonably
sound theoretical properties and captures the essential features of more
elaborate models which some of the central banks use for policy
analysis. The model is backward looking and assumes price rigidity in
the economy. (6) It can be described by the following two equations
along with the central bank's reaction function given as expression
3,
[y.sub.t] = [[beta].sub.1][y.sub.t-1] + [[beta].sub.2] ([i.sub.t-1]
- [[pi].sub.t-1]) + [u.sub.t] ... .... .... ... ... (4)
[[pi].sub.t] = [[gamma].sub.1][[pi].sub.t-1] +
[[gamma].sub.2][y.sub.t-1] + [[epsilon].sub.t] ... ... ... ... ... ...
(5)
The parameter restrictions are: 0 < [[beta].sub.1] < 1,
[[beta].sub.2] < 0, 0 < [[gamma].sub.1] > 1, and
[[gamma].sub.2] > 0. Since prices are assumed to be rigid, the
central bank can affect aggregate demand through changes in the real
interest rate. Output is affected by one period lagged real interest
rate and its effect on inflation is indirect and takes effect after one
period. This model can be estimated by OLS as long as the variables
under consideration are stationary and there is no cross and
contemporaneous correlation between the residuals of the equations in
the model. If the variables are non-stationary, then this property can
be imposed in the estimation and restricted OLS can be used to estimate
the model [Rudebusch and Svensson (1999)]. Furthermore, if there is
contemporaneous correlation across the equations, then the system needs
to be estimated as a Seemingly Unrelated (SUR) model.
The final objective of the study concerns finding the optimal
parameter values of the rule for Pakistan. This has been done by
back-casting the economy with different combinations of the parameters
in the rule and then comparing the results. The optimal set of
parameters is the one that decreases output and inflation variability
and hence minimises the loss to society. The expression 6 in the
following describes the loss function which is defined over the
variances of output gap and inflation respectively.
L = 1/2 [var ([y.sub.t]) + [alpha] var ([[pi].sub.i])] ... ... ...
... ... ... (6)
where [alpha] is the relative weight assigned by society to
inflation. Finally, stochastic simulation establishes the statistical
significance of the set of parameters.
4. ESTIMATION RESULTS AND DISCUSSION
Regression Approach
To see whether the SBP has been following the Taylor rule, the
model has been estimated for the period 1991-2006 using quarterly data
on call money rate (short interest rate taken as monetary policy
instrument), (7) consumer price index (CPI) as a measure of inflation,
and real output gap. The results clearly indicate that the actual policy
of the SBP does not correspond to the Taylor rule. The coefficient of
output gap has opposite sign while the magnitude of inflation is
different than the one prescribed by Taylor (1993). (8) Since the
residual series from this estimated equation is stationary as null of
the unit root in Augmented Dickey Fuller (ADF) test, it is easily
rejected at the conventional level of significance; therefore, we
conclude that the results are super consistent.
[i.sub.t] = 4.34 - 0.38 [y.sub.t] + 0.51 [[pi].sub.t] ... ... ...
... ... ... (7) (4.28) (-2.28) (4.17)
Adjusted [R.sup.2] = 0.22, DW = 0.89
ADF-stats for residuals = -4.11
There are several points related to these results that need further
discussion. First, the outcome that the SBP has not been following the
Taylor rule should not be taken as a surprise it has never claimed to be
following such a rule. Not only that the policy was ineffective, it was
not pursued independently since prior to the 1990s the SBP was mainly
directed by the government. The monetary authority only got
quasi-independence as a consequence of financial sector reforms
initiated during early 1990s. Since then the job is entrusted to the
SBP, but it is being conducted in a fairly discretionary manner.
The second point relates to the coefficient of output gap.
According to the estimates, the SBP, over the years, has either raised
interest rate or contracted money whenever the economy was in the
recessionary phase; and this policy was relaxed whenever there was
inflationary pressure or the output was above trend or the potential
level. This outcome not only contradicts Taylor (1993), it is difficult
to justify also. One possible explanation could be that, being the
central bank of a developing country, SBP might have resisted leaning
against the wind assuming that the economy is less elastic to domestic
policy changes compared to external shocks. Therefore, whenever the
economy started to blossom due to exogenous factors, the SBP allowed it
to do so to keep the momentum going. While this justification makes
sense only when there is an up-swing, it is less convincing in the
opposite case scenario, especially raising interest rate during a
recession. But to be fair with the monetary authority, one cannot rule
out the possibility of getting such results in an economy where the
central bank's loss function contains monetary policy objectives
other than output and inflation, implying that the reaction function
(expression 7) is mis-specified.
The third issue is concerned with the coefficient of inflation.
According to Taylor Principle, the response of the central bank to
inflation must be at least one-for-one otherwise the system would be
divergent. This is so because the central bank's persistence with
easy money approach when inflation is above target would mean that
prices can potentially move without bounds. We have found the
coefficient of inflation to be substantially less than one. This implies
a pro-cyclical response of monetary policy to the business cycle. (9)
Once again this may have been due to the dominance of shocks to the
economy that were outside the purview of the monetary sector.
Fourth, the [R.sup.2] is only 0.22 indicating that only about
one-fifth of the variation in short interest rate is explained by output
gap and inflation. If so, it is essential to identify factors, other
than output gap and inflation, which play important role in monetary
policy. It is well established that the monetary authority in Pakistan,
like in other developing countries, is also worried about exchange rate
stability, interest rate smoothing, financial sector stability etc.
[Malik (2007)]. Thus an extended specification of the model remains an
alternative option to be considered.
Finally, the value of Durbin-Watson (DW) statistics indicates a
high degree of autocorrelation in the residuals of the estimated
reaction function. One possible implication of this outcome is that the
SBP, instead of pursuing a policy consistent with the Taylor type rule
that might have increased the interest rate volatility, has preferred to
smooth interest rate. (10) Alternatively, it might also be a reflection
of a mis-specified model where important variables have been omitted.
Simulation Approach
Using an alternative methodology, it has been shown that the
rule-induced and the actual short-run interest rate have shown fairly
different behaviour (Figure 1 and Table 1). With the exception of
1997-99 and 2002-04, the latter has lower average level and the
fluctuations are also not as wild as has been the case with the former.
It means that the rule would have favoured a more aggressive response to
output and inflationary fluctuations than the one adopted by the SBP.
This is why the level of variation in the actual interest rate has been
quite low as compared to the rule-induced interest rate.
[FIGURE 1 OMITTED]
Next, following Judd and Rudebusch (1998), the time-series was
divided into three sub-samples consistent with the era of three former
heads of the SBP to see whether or not there was an inclination towards
rule-based policy (expressions 8-10). It is quite revealing to find that
none of the past three Governors of SBP had an appetite for rule-based
policy during 1991-2006. While there was no consideration for output or
inflation during 1991-93, the emphasis changed towards growth during
2000-06, probably due to the fact that inflation was already too low.
The period in the middle had no clear-cut policy objective in fact it
could be placed somewhere in between the two policy regimes.
[i.sub.t=] 17.04 - 0.60 [y.sub.t] - 0.78 [[pi].sub.t] (1991-93
period) ... ... ... (8)
[i.sub.t] = 8.68 - 0.08 [y.sub.t] - 0.19 [[pi].sub.t] (1993-99
period) ... ... ... (9)
[i.sub.t] = 5.77 -0.18 [y.sub.t] - 0.14 [[pi].sub.t] (2000-06
period) ... ... ... (10)
Macroeconomic Performance with Taylor Rule
One of the important considerations in managing the economy is that
there should be consistency of policies irrespective of the nature of
the rule. As indicated, the macroeconomic performance of the economy has
been measured by estimating the society's loss function (11) where
improved macroeconomic performance is defined in terms of less inflation
and less output variability. It is argued that inflation variability is
negatively correlated with growth because it generates uncertainty that
distorts the agents' major economic decisions like saving and
investment [Fischer (1993)].
Given this perspective and to accomplish the second objective of
the paper, the economy has been back-casted for a period ranging between
1992 and 2006 and the results are compared with the original Taylor rule
(using the original parameter values) while the search for the optimal
parameter values in the rule is delayed till the next subsection. (12)
Counter-factual simulations require estimation of the transmission
mechanism (macroeconomic model) of the economy on the basis of which the
previous data can be regenerated with alternative monetary policy
setting. For this purpose, the Neo-Keynesian type model for Pakistan has
been estimated by OLS. The results of estimation are reported as
expressions 11 and 12 (with t-statistics in parenthesis). (13)
[y.sub.t] = 0.53[y.sub.t-1] -0.27 ([bar.i.sub.t-1]] -
[bar.[[pi].sub.t-1]] ... ... ... ... ... (11) (4.68) (-3.96) S.E = 1.60,
DW = 2.08
[[pi].sub.t] = 3.72+0.51[[pi].sub.t-1] + 0.39 [y.sub.t-1] ... ...
... ... ... (12) (3.89) (4.61) (1.88) S.E = 3.42, DW = 2.04
It is evident that the signs of the estimated parameters are
consistent with economic theory and the coefficient values are also in
the acceptable range. Output is affected by its own lagged values and
the average real interest rate over the previous four quarters.
Inflation too has one-period inertia and it is also affected by the
output gap of the previous quarter. These results confirm that, contrary
to popular stance held by the central bank, only about one third of
inflation in Pakistan is explained by monetary factors. Using these
results and invoking the assumption that the Taylor rule has been the
monetary policy strategy, the back-casting exercise of the economy was
undertaken by incorporating in each period the estimated shocks (to
output and inflation) from Equations 11 and 12. The striking outcome of
this exercise has been that the economy would have performed better if
the Taylor rule had been adopted rather than sticking with the
discretionary policy stance (Table 2). Adoption of the Taylor rule would
have decreased the variability in output gap and inflation.
To reconfirm these results further and to avoid over-reliance on
historical simulation (one time estimates), stochastic simulation has
also been carried out. This has been done by bootstrapping the standard
deviation of output and inflation. The average results of 1000 trials
along with the standard errors of estimates, presented in Table 2,
reconfirm the earlier results (reduction in output and inflation
variability) that continue to hold true even when the bootstrapped
measure of variation is used. Similarly the probability (p-value) of
standard deviation of rule based output gap and inflation, being greater
than the one found in the actual data, is quite low. We have found that
in only 20 out of 1000 simulations the standard deviation of simulated
output gap has been greater than or equal to that of the actual data.
For inflation series, it was true for 100 simulations. These results
again prompt us to conclude that the Taylor rule would have performed
significantly better than the actual policy that was pursued by SBP
during 1991-2006. (14)
Finding the Optimal Parameter Values for Pakistan
In an effort to find optimal parameter values (in Taylor rule) for
Pakistan, we start with the optimal inflation target. The anecdotal
evidence suggests that the central banks that have adopted
inflation-targeting as monetary policy strategy announce about 2 percent
inflation target, though with some tolerance range. (15) This is in line
with Taylor (1993) who advocated an inflation target of 2 percent that
was consistent with the 2 percent real economic growth of the USA.
Compared to this, Pakistan being a developing country with a natural
requirement for higher growth rate, cannot opt for a low real growth
(and inflation) target of 2 percent. But to avoid ad hocism, we have
used seven different inflation target options for simulation purpose. To
start this process, the 2 percent target was adopted to simulate the
economy.
Since Pakistan experienced an average rate of about 5 percent real
GDP growth over the period 1980-2006, this rate was selected as another
option. Similarly, following the empirical evidence of Khan and Senhadji
(2001) and Mubarik (2005) five values ranging between 7 percent and 11
percent have also been used.
The long-run equilibrium real interest rate has been calculated for
Pakistan as the difference between the average nominal interest rate and
inflation over the periods, 1973-2006, 1981-2006 and 1991-2006 as shown
in Table 3. (16) Even though the results do not portray a clear pattern,
nevertheless in all the three periods the average real interest rate was
found to be close to zero. As a result, the equilibrium value of zero
real interest rate has been used as benchmark in the counterfactual
simulation.
Finally, the optimal weights for output and inflation in the Taylor
rule for Pakistan have been estimated. Even though Taylor (1993) used
equal weight of 0.5 for both the objectives, i.e., output and inflation,
we have used this scheme as a starting point only. In two subsequent
scenarios, either the entire weight was assigned to output stabilisation
with no regard for inflation deviation or according more importance to
inflation than output deviation. While the former alternative could be
more attractive for the developing countries (at least with asymmetric
response) where output was the primary and inflation the secondary
issue, the latter possibility is obviously more attractive for stable
economies where more emphasis is on inflation control or price
stability. (17)
We have taken these three sets of weights and seven different
targets of inflation (a total of 21 cases) and back-casted the output
gap, inflation, and interest rate using estimated parameters and shocks
in the macroeconomic model comprising equations 11 and 12. From the
results of 21 cases, the best set of parameter values for Pakistan was
selected on the basis of minimised variability in inflation and output
and the minimum values of the loss to society. We have found that
variability in inflation is a decreasing function of the level of
inflation target but the variability of output started increasing above
a certain level of inflation target.
The first best set of parameter values with which the rule has
performed well in reducing the variability of inflation and output is
the case when the central bank assigns equal weights to output and
inflation stabilisation in the reaction function and targets inflation
at 8 percent with zero real interest rate. (18) The rule with this set
of parameter values is given in Equation 13. This roughly indicates the
optimal level of inflation for Pakistan and the results are consistent
with earlier findings of Mubarik (2005) and Khan and Senhadji (2001).
[i.sub.t] = 0 + [[pi].sub.t] + 0.5[y.sub.t] + 0.5 ([[pi].sub.t] -
8) or [i.sub.t] = -4 + 0.5[y.sub.t] + 1.5 [[pi].sub.t] ... ... (13)
The results for the measures of macroeconomic performance by the
rule (both in case of historical as well as stochastic simulation) with
the first best set of parameter values are given in Table 4. The
procedure adopted here for comparison is the same as discussed above for
the actual Taylor rule. It is clear that the variability in output gap
and inflation decreases as we move from discretionary policy towards the
Taylor rule when the first best set of parameter values for Pakistan are
used. However the average values of the variables are somewhat greater.
To confirm these results, and to find the probability of standard
deviation of output and inflation in simulated series being greater than
that in the actual series, we have used stochastic simulation by
re-sampling the estimated shocks. The results indicate that the
variability of both the variables has been lower, even in repeated
simulation and the probability is also quite low. (19)
The second best set of parameter values was found when the central
bank assigned one-hundred percent weight to output stabilisation with no
response to inflation deviation from the target. The implication is that
it does not matter what level of inflation is optimal to target.
Regarding macroeconomic performance by the Taylor rule, the parameter
values given below in Equation 14 were used.
[i.sub.t] = 0 + [[pi].sub.t] + [y.sub.t] + 0 ([[pi].sub.t] -
[[r.sup.*]) or [i.sub.t] = [[pi].sub.t] + [[y.sub.t] ... ... ... ...
(14)
It can be seen from Table 5 that variability in interest rate,
output gap and inflation decreased as one moved away from discretionary
policy towards the proposed Taylor rule for Pakistan. (20,21) The
average values of all the three variables are found to be slightly
greater when the rule is followed. To confirm these results further and
to find out whether or not the probability of standard deviation of
output and inflation in simulated series turns out to be greater than
that in the actual series, stochastic simulation was used to resample
the estimated shocks. The outcome confirmed that the variability
remained lower even in the repeated simulations. It was also found that
the probability of standard deviation of output and inflation being
greater in simulated series than that in the actual data, with the rule
as monetary policy strategy was quite low. (22)
Loss Function and Comparison of Parameter Values
Besides minimising the variability in output and inflation, one can
also calculate and compare loss to society associated with each set of
parameter values as an attractive alternative. The loss function not
only includes both the objectives, it also takes care of the trade off
between them. In this respect it can do a better job of finding out the
optimal parameter values.
For estimating the loss function, expression 6 has been used. In an
effort to ensure comparability, the assumption that society assigns
equal weight to inflation and output has been maintained. Using
expressions 11 and 12, the economy has been back-casted for 21 sets of
parameters discussed above, one at a time and the best set of parameters
was chosen which minimised the loss function.
The results presented in Table 6 show that the loss is minimum when
inflation target is set at 8 percent and equal coefficients of output
and inflation in the reaction function are adopted. The second best set
of parameter values has been found exactly the same as was proposed by
Taylor. The third best option is found when the entire weight is given
to real stabilisation in the reaction function. The results of
stochastic simulation exercise given in Table 6 confirm these findings.
It can be seen that the performance of the rule (with either set of
parameters) is, on average, better than that in case of actual policy.
The results show that there is very low probability (0.02 in all cases)
of loss, associated with the rule, being greater than that with actual
policy setting. Interestingly, Taylor's proposed parameter values
give better results than the second best possibility when historical
simulation is undertaken but the opposite is true in the case of
stochastic simulation.
5. SUMMARY AND CONCLUDING REMARKS
In this study the Taylor rule for Pakistan has been estimated for
the period 1991-2006 and for the sub-samples covering the period of
three former Governors of SBP. One of the important findings of the
study is that monetary policy has been generally conducted through
discretionary measures rather than adopting a rule. This could have been
due to the SBP's concentration on policy objectives other than
inflation and output stabilisation. Through historical and stochastic
simulation, the study has concluded that commitment to the Taylor-type
rule would have significantly improved the macroeconomic performance,
especially in terms of less variability of output and inflation.
Regarding parameter values in the rule, it has been found that targeting
inflation at 8 percent and treating output and inflation equally in the
policy reaction function would have yielded an optimal scenario for the
SBP. (23)
The key messages that emerges from the study are as follows:
First, notwithstanding the fact that the pre-requisites for more
elaborate policy rules are lacking and the institutional capacity is
also quite weak in Pakistan, yet there is ample scope to reap benefits
by committing to simple instrument rules with a clear understanding of
the warning issued by McCallum (2000). It is proposed that adoption of
simple instrument rules may be regarded as a first step for Pakistan and
other developing countries to move from discretionary policy to a more
elaborate inflation targeting framework. Second, although there is a
need for having an elaborate range of targets in the monetary policy
framework (including output and inflation), the study is not putting any
restrictions on these possibilities, i.e., incorporating other
objectives in the simple rules. However, we recommend a humble beginning
as it allows better understanding of ground realities. Third, it is also
advisable to adjust the parameters in the rule (especially the inflation
target) according to the economic conditions prevalent in the economy.
Finally, it may be added that currently this is a passionately
pursued area of research in macroeconomics. Thus, there is ample scope
for further research. To start with, the inconclusiveness of literature
on the Taylor rule, especially the coefficients of variables other than
output and inflation in the policy reaction function, can provide
further insights for developing countries, including Pakistan. There is
also a possibility for exploring ways and means for adopting a more
elaborate inflation targeting framework. In this regard the research can
focus on the pre-requisites such as central bank independence, and
transparency and accountability of its actions. These three notions
might be the outcome of elaborate policy rules and not just the
pre-requisites for it. Research in this area would be quite beneficial
for developing countries where institutions are not yet strong and the
focus on issues like monetary policy transparency and accountability is
generally quite weak.
APPENDIX--A
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
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Authors' Note: The authors are thankful to the participants of
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of Pakistan for useful comments and suggestions.
(1) As instrument rules are simple, robust, easily verifiable and
strict and there is fundamentally no role of policy-maker's
judgment in time to time decisions, commitment to these rules is a good
and feasible monetary policy strategy for developing countries. Compared
to this, targeting rules (attributed to Svensson) are even though
optimal and flexible, but not simple.
(2) It may be recalled that a country cannot graduate from
low-income to middle-income status unless it registers a long period of
high and sustained growth where the stability of prices is also ensured
[Fischer (1993)].
(3) This indicates the robustness of the rule.
(4) Examples of such policy formulation are the Reserve Bank of New
Zealand and the Bank of England.
(5) Other techniques like Two Stage Least Squares (TSLS),
Generalised 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.
(6) In the case of Pakistan, inertia in output and inflation is
consistent with VAR study by Malik (2006).
(7) This is the only interest rate data on which are available for
the sample period. Call money rate indicates liquidity conditions in the
money market and is not directly an indicator of monetary policy stance.
(8) t-statistics in parentheses.
(9) SBP, being central bank of a developing country, does not
always play a reactionary role. If the economy is in boom it may let it
go. While in other times it is proactive in stimulating the economy.
(10) While alternative variants of the Taylor rule are proposed in
the literature to deal with interest rate smoothing, the weight on this
objective is not yet agreed upon.
(11) It is assumed that the society puts equal weight to inflation
and output stability.
(12) The entire process has followed the following course of
action. The three-equation model includes demand and supply equations
and a money reaction function. Here the Taylor rule generates the value
of real interest rate, which when used in the demand function allows us
to determine the value of output y. When substituted in the supply
function, it generates value of [pi]. The rule based values of y and
[pi] are then compared with actual values. An outcome is preferred where
variations in these variables are low.
(13) Results by SUR model and by FIML have been found almost the
same as there is insignificant contemporaneous correlation between the
residuals of the two equations in the model.
(11) It is assumed that the society puts equal weight to inflation
and output stability.
(12) The entire process has followed the following course of
action. The three-equation model includes demand and supply equations
and a money reaction function. Here the Taylor rule generates the value
of real interest rate, which when used in the demand function allows us
to determine the value of output y. When substituted in the supply
function, it generates value of [pi]. The rule based values of y and
[pi] are then compared with actual values. An outcome is preferred where
variations in these variables are low.
(13) Results by SUR model and by FIML have been found almost the
same as there is insignificant contemporaneous correlation between the
residuals of the two equations in the model.
(14) The comparison of actual and backcasted data on inflation,
output-gap and interest rate using Taylor rule is given in Appendix A,
Figure 2.
(15) None of the central banks, with any monetary policy strategy,
target zero-inflation as central banks are not inflation nutters in King
(1997a) terminology.
(16) Judd and Rudebusch (1998) used this methodology for the U.S.
data.
(17) It should be noted however that none of the central banks,
even the inflation targeting ones, practically do this, as inflation
targeting is flexible in the sense that central banks put some weight on
output stabilisation too, [Svensson (1997) and Ball (1999)].
(18) The coefficient values are same as proposed by Taylor but
inflation target is different.
(19) Comparison of actual and simulated data on inflation, output
gap and interest rate using this proposed rule is given in Appendix A,
Figure 3.
(20) By the proposed Taylor rule we mean the rule with parameter
values found optimal for Pakistan.
(21) Detailed comparison of actual and simulated data on inflation,
output gap and interest rate with this proposed rule is given in
Appendix A, Figure 4.
(22) However this probability is higher in case of inflation.
(23) These results are based on the assumption of zero real
interest rate.
Wasim Shahid Malik (wmaliki11@yahoo.com) is Assistant Professor of
Economics at Quaid-i-Azam University, Islamabad. Ather Maqsood Ahmed
(dr.athar@nbs.cdu.pk) is Professor of Economics at NUST Business School,
Rawalpindi.
Table 1
Actual and Taylor Ride-induced Short Interest Rate
Actual Rule-induced
Mean 8.24 10.42
Maximum 15.42 20.3
Minimum 1.05 0.51
Range 14.37 19.79
Variance 11.8 32.96
St. Deviation 3.44 5.74
Table 2
Simulation with the Tavlor Rule and the Estimated Model
Rule Based
Actual Historical Stochastic *
Interest Rate Average 8.28 9.24
St Deviation 3.53 3.18
Output Gap Average -0.24 -0.83
St Deviation 2.47 1.72 1.80 (0.21)
(0.21)
Inflation Average 7.36 7.00
St Deviation 4.31 3.50 4.04 (0.47)
(0.47)
Rule Based
p-value **
Interest Rate Average
St Deviation
Output Gap Average
St Deviation 0.002
Inflation Average
St Deviation 0.10
* Average of 1000 values of standard deviations in bootstrap
simulation. Standard errors in parenthesis.
** Probability of standard deviation of a variable with rule
being greater than that of actual data.
Table 3
Estimation of Long-run Real Interest Rate
1973-2006 1981-2006 1991-2006
Average Interest 8.34 8.01 8.24
Rate
Average CPI 9.16 7.52 7.89
Inflation
Average GDPD 8.92 8.02 8.92
Inflation
Equilibrium Real -0.82 0.49 0.35
Interest Rate *
Equilibrium Real -0.58 0.00 -0.68
Interest Rate **
* When inflation is calculated as percentage growth in CPI.
** When inflation is calculated as percentage growth in GDP
Deflator.
Table 4
Simulation with the First Best Set of Parameter Values
First Best Set
Actual Historical
Interest Rate Average 8.28 8.08
St Deviation 3.53 3.11
Output Gap Average -0.24 0.3
St Deviation 2.47 1.67
Inflation Average 7.36 7.88
St Deviation 4.31 3.49
First Best Set
Stochastic * p-value **
Interest Rate Average
St Deviation
Output Gap Average
St Deviation 1.72 (0.24) 0.05
Inflation Average
St Deviation 3.91 (0.47) 0.2
* Average of 1000 values of standard deviations in bootstrap
simulation.
** Probability of standard deviation of a variable with rule being
greater than that of actual data.
Table 5
Simulation with the Second Best Set of Parameter Values
Second Best Set
Actual Historical Stochastic *
Interest Rate Average 8.28 8.17
St Deviation 3.53 2.58
Output Gap Average -0.24 0.25
St Deviation 2.47 1.55 1.70 (0.20)
Inflation Average 7.36 7.84
St Deviation 4_31 3.62 4.18 (0.48)
Second
Best Set
p-value **
Interest Rate Average
St Deviation
Output Gap Average
St Deviation 0.03
Inflation Average
St Deviation 0.2
* Average of 1000 values of standard deviations in bootstrap
simulation.
** Probability of standard deviation with rule being greater
than that of actual data.
Table 6
Loss Associated with Different Parameter Values for the Rule
Variance Loss to Society
Output Inflation Historical Stochastic * p-value **
Actual Data 6.10 18.54 12.32
First Best 2.80 12.15 7.48 7.82 0.02
(1.92)
Second Best 2.40 13.11 7.76 8.10 0.02
(1.78)
Taylor Rule 2.94 12.25 7.60 8.26 0.02
(1.72)
* Standard error in parenthesis.
** Probability of loss associated with rule being greater than that of
actual data.
