Page 1

The Pakistan Development Review

45 : 2 (Summer 2006) pp. 185–202

Inflation in Pakistan

MOHSIN S. KHAN and AXEL SCHIMMELPFENNIG

This paper examines the factors that explain and help forecast inflation in Pakistan. A simple inflation model is

specified that includes standard monetary variables (money supply, credit to the private sector), an activity variable, the

interest and the exchange rates, as well as the wheat support price as a supply-side factor. The model is estimated for the

period January 1998 to June 2005 on a monthly basis. The results indicate that monetary factors have played a dominant

role in recent inflation, affecting inflation with a lag of about one year. Private sector credit growth and broad money

growth are also good leading indicators of inflation which can be used to forecast future inflation developments.

JEL classification: E31, C22, C32

Keywords: Inflation, Pakistan, Leading Indicators, Forecasting, Monetary Policy

I. INTRODUCTION

After remaining relatively low for quite a long time, the inflation rate accelerated in Pakistan starting

in late 2003. Following the 1998-99 crisis, inflation was reduced to below 5 percent by 2000 and remained

stable through 2003. Tight monetary policy combined with fiscal consolidation appears to have contributed to

this low-inflation environment.1 Figure 1 shows that inflation follows broad money growth and private sector

credit growth closely with a lag of about 12 months. With monetary growth picking up, inflation followed

and increased sharply in late 2003, peaking at 11 percent year-on-year in April 2005. Average annual

inflation stabilised around 8 to 9 percent by September 2005, and has receded somewhat since then.

Controlling inflation is a high priority for policy-makers. High and persistent inflation is a regressive

tax and adversely impacts the poor and economic development. The poor have little options to protect

themselves against inflation. They hold few real assets or equity, and their savings are typically in the form of

cash or low-interest bearing deposits. Thus, this group is most vulnerable to inflation as it erodes its savings.

Moreover, high and volatile inflation has been found to be detrimental to growth [e.g.,

Mohsin Khan <mkhan@imf.org> is Director of the Middle East and Central Asia Department of the International Monetary

Fund. Axel Schimmelpfennig <aschimmelpfennig@imf.org> is an Economist in the International Monetary Fund’s Middle East and

Central Asia Department.

Author’s Note: The views expressed in this paper are those of the authors and do not necessarily represent those of the

International Monetary Fund or its policy. This paper draws on previous work by Khan and Schimmelpfennig, “Inflation in Pakistan:

Money or Wheat?”, published in the State Bank of Pakistan’s Research Bulletin–Papers and Proceedings Vol. 2, No. 1, available at

http://www.sbp.org.pk/research/ bulletin/2006/Inflation_in_Pakistan_Money_or_Wheat.pdf, and in Bokil and Schimmelpfennig “Three

Attempts at Inflation Forecasting,” available as IMF

external/pubs/ft/wp/2005/wp05105.pdf.

1According to the State Bank of Pakistan (SBP) a change in the methodology of deriving the house rent index may also be partly

responsible for the observed slowdown in headline inflation.

Working Paper 05/105 at http://www.imf.org/

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Khan and Schimmelpfennig

186

Sources: National

authorities; and IMF staff calculations.

Khan and Senhadji (2001)] and financial sector development [e.g., Khan, Senhadji, and Smith (2006)]. High

inflation obscures the role of relative price changes and thus inhibits optimal resource allocation.

Understanding the factors that drive inflation is fundamental to designing monetary policy. Certainly in

the long run, inflation is considered to be—as Friedman (1963) stated—always and everywhere a monetary

phenomenon. Workhorse models of inflation typically include monetary variables, such as money growth,

real GDP, the interest rate, and the exchange rate as explanatory variables. Some authors have also pointed to

supply side developments in explaining inflation. This structuralist school of thought holds that supply

constraints that drive up prices of specific goods can have wider repercussions on the overall price level. For

example, in Pakistan, increases in the wheat support price have frequently been blamed for inflation.2

This paper finds that monetary factors are the main drivers of inflation in Pakistan, while other typical

explanatory variables play less of a role. We specify a simple inflation model that includes standard monetary

variables (money supply and credit to the private sector), the interest rate, the exchange rate, an activity variable,

as well as the wheat support price as a supply-side factor. The model is estimated with monthly data for the

period January 1998 to June 2005. The results indicate that monetary factors have played a dominant role in

recent inflation, affecting inflation with a lag of about one year. Monetary factors are also well-suited to forecast

inflation in a leading-indicator type model.

The remainder of the paper is organised as follows. Section II reviews the relevant literature and

introduces a stylised model to structure the analysis. Section III estimates the model and assesses the roles for

explaining inflation played by monetary factors and other variables. Section IV presents a leading indicators

model to forecast inflation, and Section V provides some conclusions.

2The acceleration of inflation in late 2003 coincided with two increases in the wheat support price in September 2003 and in

September 2004, which has re-opened the debate whether the wheat support price was driving inflation in Pakistan [Khan and Qasim

(1996) and Sherani (2005)].

2

Jan-99

4

6

8

10

Jan-00Jan-01

Jan-02

Jan-03

Jan-04Jan-05

0

5

10

15

20

25

30

35

Credit growth (lagged 12 months, right axis)

Broad money growth (lagged 12 months, right axis)

Fig. 1. Pakistan: Inflation and Monetary Growth, 1999:1–2005:6

(Average annual growth in percent)

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Inflation in Pakistan

187

II. BASIC ELEMENTS OF THE MODEL

Several studies highlight the role of monetary factors for inflation in Pakistan.3 For example, Khan and

Qasim (1996) find that overall inflation is only determined by money supply, import prices, and real GDP.

The empirical evidence is inconclusive regarding the role of the exchange rate. Choudhri and Khan (2002) do

not find evidence of exchange rate pass-through in a small VAR analysis, while Hyder and Shah (2004) find

some evidence of exchange rate pass-through using a larger VAR. Some authors have emphasised

structuralist factors in explaining inflation in Pakistan.4 Khan and Qasim (1996) find food inflation to be

driven by money supply, value-added in manufacturing, and the wheat support price.5 Non-food inflation is

determined by money supply, real GDP, import prices, and electricity prices. Sherani (2005), referring to this

work, finds that increases in the wheat support price raise the CPI index (but not necessarily inflation). He

also argues that the high levels of inflation in 2005 largely resulted from a monetary overhang that was built

up by loose monetary conditions.

We start our stylised model from a monetarist perspective. Agents hold money for transaction

purposes, as a store of value, and for speculative purposes. For a constant velocity (ν), inflation ( p & ) results if

money growth (m & ) exceeds real GDP growth ( y & ). The opportunity cost of holding money, that is the interest

rate r, reduces money demand and thus inflation. Moreover, financial deepening and innovations enable

agents to use alternative monetary instruments in lieu of cash. Thus, the velocity of a particular monetary

aggregate, say M2, changes if agents switch from cash or demand deposits to instruments included only in

M3. In an open economy, headline inflation can also be affected by movements of the exchange rate (e).6 We

also allow for the wheat support price (w) as a structuralist factor to drive inflation. The general open-

economy monetary model (incorporating a supply-side variable) is then given by

()

wervymfp

&&&&&&

,,,,,

=

… … … … … … (1)

where lower case letters denote the natural logarithm of a variable and a dot over a variable denotes the first

derivative with respect to time.

For non-stationary time series, Equation (1) only reflects short-run relationships as the variables are in

(log) first differences, and the equation does not include a cointegrating relationship. However, the aspects of

the model that reflect monetarist thinking will tend to be long-run relationships, and the model can be easily

be rewritten in levels and in an error correction representation to differentiate between short-run and long-run

relationships.

3For a comprehensive survey of empirical studies on Pakistan [see Bokil and Schimmelpfennig (2005)].

4Structuralist models of inflation emphasise supply-side factors as determinants of inflation. They emerged in the 1950s as part

of the structuralist theories of development promoted by Prebisch [see Bernanke (2005)]. In these models, inflation is driven by

developments and bottlenecks on the real side of the economy. Food prices, administered prices, wages, and import prices are considered

sources of inflation. Structuralist models assume that such factors have to be accommodated by monetary policy-makers because they are

determined outside the monetary sphere. Monetary developments in themselves are given little importance as independent determinants

of inflation.

5It is hardly surprising that changes in the wheat support price affect the food price index, given that wheat products account for

14 percent of the index. However, this does not automatically imply that headline inflation is affected by changes in the price of one

particular item.

6Import prices could also play a role, in particular if the exchange rate is pegged. Unfortunately, import prices are not available

at a monthly frequency, but since Pakistan had a flexible exchange rate regime during our sample period, import prices should be less

important than in previous years.

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Khan and Schimmelpfennig

188

III. EMPIRICAL RESULTS

We estimate the basic model in growth rates as well as in log levels. Since our sample extends over a

crisis period and subsequent wide ranging economic reforms as well as a growth take-off, it may be difficult

to discern long-run relationships from the data due to structural changes and non-constant parameters.

However, we would still expect short-run relationships to reflect our proposed model structure. Therefore, as

a first step, we estimate Equation (1) to gain an understanding of some basic relationships and short-run

dynamics.7 In the second step, we estimate the model as a vector error correction model (VECM) in log-

levels to investigate whether we can find a cointegrating vector that would provide information about long-

run behaviour.

(a) Data and Sample

Our database covers the period January 1998 to June 2005 on a monthly basis. The choice of sample

reflects a trade-off between having sufficient observations and avoiding structural breaks that would

complicate the empirical analysis. Banking sector reforms were initiated in 1997 and pursued vigorously after

1999, leading to increased intermediation. Financial deepening also occurred as confidence returned in the

aftermath of the 1998-99 crisis and with the new government restoring macroeconomic stability. Taken

together, this implies that the monetary transmission mechanism has evolved and money demand has possibly

shifted over the sample period which may lead to nonconstant parameters, in particular with respect to long-

run parameters.

The definitions of the data utilised are:

• CPI: overall consumer price index—the percentage change of which is also termed “headline

inflation”.

• Monetary variables: Broad money; private sector credit; and the 6-month treasury bill (T-bill) rate

(the SBP’s key policy rate).

• Activity variables: interpolated real and nominal GDP (12-month moving average of the fiscal year

GDP data);8 and the large scale manufacturing index (LSM).

• Exchange rate: nominal effective exchange rate (NEER).

• Wheat support price: guaranteed minimum government purchase price.

The basic correlations between the variables are shown in Table 1.

The log levels of all variables are non-stationary. Most variables are integrated of order one (Table 2).

However, somewhat surprisingly, our interpolated real and nominal GDP series are integrated of order two.

This would suggest that our GDP series cannot be part of a long-run cointegrating relationship with other

variables that are only integrated of order one. Alternatively, the LSM may be a meaningful proxy for the

activity variable.9

Data for Pakistan is subject to overlapping seasonality stemming from Gregorian calendar effects

(including agricultural seasonality) and Islamic calendar effects. Riazuddin and Khan (2005) construct

variables to address Islamic seasonality. For regressions based on growth rates, we control for seasonality by

using 12-month moving averages. In Bokil and Schimmelpfennig (2005), we show that this is sufficient to

take account of both sources of seasonality. The approach has the advantage of requiring no additional

7Note that this model may be mis-specified if we have non-stationary data and there exists a cointegrating vector.

8GDP data is available only at annual frequency.

9The correlation coefficient between the annual LSM index and annual real GDP is 0.97 which suggests that a 12-month moving

average of the LSM index is probably a reasonable proxy for monthly real GDP.

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Inflation in Pakistan

189

regressors. However, for regressions based on log levels, we include monthly dummies and the Islamic

calendar control variables used in Riazuddin and Khan (2005).10

(b) CPI Inflation

We first analyse the impact of changes in the explanatory variables on headline inflation. We estimate

two variants of our stylised model using either broad money or private sector credit to capture the impact of

monetary policy. The models are estimated using the PcGets routine in PcGive which automatically tests

down a general model.11 In our case, we include 12 lags of all variables in the general model. In principle, the

resulting specific model can then include individual lags of the variables from the general model, or exclude

variables altogether.

We focus on summary coefficients that give the direction of influence of a particular regressor after all

dynamics have played out. The estimated specification is an autoregressive distributed lag model (ADL) that

can be written as:

( ) ( )

ttt

uxLBpLA

+=

&&

… … … … … … (2)

where x is the vector of independent variables. A(L) and B(L) are lag polynomials that take the form:

( )

L

∑

=

i

−

−=

12

1

1

itit

p

&

Ap

&

A

and

( )

L

∑

=

j

−

=

12

0

jtjt

x

&

Bx

&

B

.

The ADL can be re-written as:

( )

( )

LA

ttt

x

&

LB

p

&

ε+=

. … … … … … … … (3)

10We thank R. Riazuddin and M. Khan for kindly providing their data to us. In some specifications, the control variables for calendar

effects can be dropped.

11The routine is described and illustrated in Hendry and Krolzig (2004).

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Khan and Schimmelpfennig

190

Table 1

Pakistan: Correlation between Main Variables in Log Levels

(Sample: January 1998 to June 2005)

CPI

1.00

0.98

0.97

0.99

0.96

–0.67

–0.95

0.94

Broad

Money

0.98

1.00

0.97

0.99

0.98

–0.76

–0.91

0.89

Private

Sector

Credit

0.97

0.97

1.00

0.98

0.98

–0.65

–0.91

0.92

Real

GDP

0.99

0.99

0.98

1.00

0.98

–0.73

–0.94

0.93

LSM

Index

0.96

0.98

0.98

0.98

1.00

–0.67

–0.90

0.89

6-month

t-bill

–0.67

–0.76

–0.65

–0.73

–0.67

1.00

0.67

–0.60

NEER

–0.95

–0.91

–0.91

–0.94

–0.90

0.67

1.00

–0.88

Wheat

Support

Price

0.94

0.89

0.92

0.93

0.89

–0.60

–0.88

1.00

CPI

Broad Money

Private Sector Credit

Real GDP

LSM Index

6-month t-bill

NEER

Wheat Support Price

Source: National authorities, IMF staff calculations.

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Inflation in Pakistan

191

Table 2

Pakistan: Test for Non-stationarity of Variables of Log-levels

(Sample: January 1998 to June 2005)

Log

Level Difference

Phillips Perron Test 2/

1.03 –8.00

5.95 –9.21

1.96 –6.26

–1.43 –6.32

5.45 –0.84

4.63 –5.49

–1.57 –7.56

–0.61 –9.59

Augmented Dickey-Fuller Test /2

1.13 –7.98

2.90 –1.84

1.51 –6.25

–1.90 –2.83

1.56 –0.85

2.87 –5.47

–1.53 –7.58

–0.64 –9.59

Source: National authorities, IMF staff calculations.

1/Critical value at the 5 percent level based on MacKinnon (1996).

2/Model includes intercept.

The coefficient β that describes the impact of changes in the independent variables on inflation after all

dynamics have played out is then given by:

( )

( ) 1

A

First Second

Difference

Critical

Value 1/

CPI

Broad Money

Private Sector Credit

6-month t-bill

Real GDP

LSM Index

NEER

Wheat Support Price

CPI

Non-food

Broad Money

Private Sector Credit

6-month t-bill

Real GDP

LSM Index

NEER

Wheat Support Price

–2.89

–2.89

–2.89

–2.89

–2.89

–2.89

–2.89

–2.89

–9.49

–2.89

–2.89

–2.89

–2.89

–2.89

–2.89

–2.89

–2.89

–8.40

–12.12

–9.49

1

B

=β

. … … … … … … … (4)

The empirical results are broadly consistent with our stylised model. Models M1 and M2 in Table 3 are

based on the general specification in Equation (1). In M1, we use broad money, and in M2, we use private

sector credit to measure monetary policy. In both cases, no regressor is completely dropped from the model.

PcGets only eliminates some individual lags. However, in M1, the T-bill rate, and in M2, the NEER, the T-

bill rate, and the wheat support price carry the wrong sign. We therefore drop these regressors (except for the

wheat support price) to arrive at our two preferred specifications M3 and M4. M3 explains CPI inflation as a

function of broad money growth, real GDP growth, NEER appreciation, and the average annual wheat

support price change. M4 explains CPI inflation as a function of private sector credit growth, real GDP

growth, and the average annual wheat support price change. These results illustrate that monetary

factors are

Table 3

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Khan and Schimmelpfennig

192

Pakistan: Inflation Determinants—General-to-specific Modeling1/

(Dependent Variable: Average Annual CPI Inflation in Percent;

Sample January 1998 to June 2005)

M1 M2

3.87

Private Sector Credit 2/

Real GDP 2/ –4.52

NEER 2/ –1.81

6-month t-bill 3/ 0.06

Wheat Support Price 2/ 0.69

Adjusted Rˆ2 0.999

Degree of Freedom 60

Observations 78

Regressors 18

Source: Pakistani authorities and IMF data; own calculations.

1/General-to-specific modeling based on the PcGets algorithm. Columns show the coefficient ß that describes the joint impact of

all lags of the respective regressor: the individual lags are not shown, but are mostly significant at the 5 percent level.

2/ Average annual change in percent.

3/ Absolute change over the last 12 months in basis points.

determinants of inflation, at least in the short run. Likewise, real GDP growth and the wheat support price

matter, and to some extent, there is an impact from NEER appreciation. Monetary growth affects inflation

with a lag of around 12 months.12

(c) A Vector-Error Correction Model

M3

1.46

–2.32

–0.50

0.21

0.999

54

78

24

M4

0.28

–1.67

0.26

0.999

58

78

20

Broad Money 2/

0.65

–1.15

0.54

0.01

–0.17

1.000

35

78

43

Based on the above results, we specify a VECM to identify long-run relationships between our

variables. To limit the size of the VECM, we start with the preferred specifications M3 for a VECM including

broad money and M4 for a VECM including private sector credit. We find that a meaningful cointegrating

relationships exists only in the case of a VECM including private sector credit.

CPI, Private Sector Credit, and Wheat Support Price VECM

The preferred VECM contains the CPI, private sector credit, and the wheat support price. We estimate

the system with monthly dummies and Islamic calendar effect controls used in Riazuddin and Khan (2005).13

Based on the stylised model and the results for the inflation equation above, we initially estimate a system

including the CPI (cpi), private sector credit (credit), real GDP, and the wheat support price (wheat).

However, no meaningful cointegrating relationship is found in this system, and we

12M3 includes a 7 and a 11 month lag of broad money growth. M4 includes a 1, 3, 5, 10, and 12 month lag for private sector

credit growth.

13The lag length is set at 6. Table 4 shows information criteria for different specifications and lag lengths.

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Inflation in Pakistan

193

Table 4

Pakistan: Information Criteria to Determine Optimal Lag Length k of VAR 1/

(Endogenous Variables: CPI, Private Sector Credit, Real GDP, Wheat Support Price all in Log Levels)

k = 2 k = 3 k = 4

(Endogenous variables: CPI, private sector credit, real GDP, wheat support price all in log levels)

Aikaiki Information

Criterion

Schwarz Criterion

–27.655

–27.036

–26.585

–25.903

(Endogenous variables: CPI, private sector credit, wheat support price all in log levels)

Aikaiki Information

Criterion

Schwarz Criterion

–15.681

–15.385

–15.049

–14.617

(Endogenous variables: CPI, broad money, real GDP, NEER, wheat support price all in log levels)

Aikaiki Information

Criterion

Schwarz Criterion

–32.148

–31.251

–30.633

–29.755

Source: National authorities; and IMF staff calculations.

1/VAR includes dummies to control for Islamic and Gregorian calendar effects.

k = 5 k = 6 k = 7 k = 8 k = 9 k = 10 k = 11 k = 12

–30.358

–30.211

–30.238

–30.041

–30.113

–25.483

–30.154

–25.024

–29.995

–24.359

–30.268

–24.119

–30.675

–24.005

–31.198

–24.000

–32.411

–24.676

–17.539

–17.511

–17.446

–17.289

–17.220

–14.268

–17.193

–13.958

–17.036

–13.514

–17.008

–13.195

–16.851

–12.742

–16.783

–12.374

–16.673

–11.960

–35.808

–35.645

–35.770

–35.646

36.210

–29.554

–36.184

–28.752

–36.313

–28.095

–36.489

–27.473

–37.234

–27.408

–39.316

–28.669

–98.016

–86.535

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Khan and Schimmelpfennig

194

estimate a reduced system without real GDP.14 This reduced system has a cointegrating rank of one (Table 5).

The cointegrating vector is given by:

cpi = 1.733 + 0.205 * credit + 0.004 * wheat + 0.002 * trend

(8.472)

(0.120)

(8.871) … (5)

Table 5

Pakistan: Cointegration Test for the CPI, Private Sector Credit,

Wheat Support Price VECM 1/

Trace Test

Statistic

Maximum Eigenvalue

Test

Statistic

Number of Coin-

tegrating Vectors

None

At Most 1

At Most 2

Source: National authorities; and IMF staff calculations.

1/ VECM of lag length 6; include dummies for Islamic and Gregorian calendar effects.

2/ Based on MacKinnon, Haug, Michaelis (1999) at the 5 percent level.

Critical values assume no exogenous series in the VECM.

The t-statistics in parentheses suggest that the wheat support price is not part of the long-run

relationship. We can also drop the seasonal controls, without affecting the white-noise characteristics of the

residuals, which gives us additional degrees of freedom. This yields:

Eigenvalue

0.329

0.109

0.083

Critical

Value 2/

42.915

25.872

12.518

Critical

Value 2/

25.823

19.387

12.518

49.901

16.773

7.179

33.128

9.594

7.179

cpi = 0.994

+ 0.263 * credit

(9.803)

+ 0.001 * trend

(4.887)

… … … (6)

Based on these results, the CPI is affected only by private sector credit in the long-run. The estimated

cointegrating vector describes recent inflation developments well. Starting in early 2003, monetary conditions

were very accommodating, private sector credit growth picked up, and a disequilibrium in the CPI-private

sector credit relationship emerged (Figure 2). As inflation picked up as well, the disequilibrium has been

reduced, but not yet been eliminated through June 2005. The loading coefficient in the equation for the CPI

indicates that 23 percent of a deviation from the long-run relationship is adjusted in the next period.

The CPI increases after shocks in the private sector credit equation. We calculate an impulse response

function based on generalised 1-standard deviation impulses [Pesaran and Shin (1998)]. In response to an

innovation in private sector credit, the CPI initially falls (akin to the price puzzle), but after 4 months steadily

increases (Figure 3).15

14This finding could reflect that real GDP may be integrated of order two while all other variables are integrated of order one.

However, using the LSM instead of real GDP does not alter the result.

15The price puzzle is a fairly common empirical finding where an unexpected tightening of monetary policy initially leads to an

increase rather than a decrease in the price level. This theoretical inconsistency can be addressed by introducing forward-looking

variables [e.g., Brissimiss and Magginas (2004), and Balke and Emery (1994)].

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Inflation in Pakistan

195

-0.05

-0.03

-0.01

0.01

0.03

Jan-98Jan-99 Jan-00Jan-01Jan-02 Jan-03Jan-04 Jan-05

-0.05

-0.03

-0.01

0.01

0.03

Figure 3. Pakistan: The Cointegrating Vector—CPI and Private Sector Credit

Fig. 2. Pakistan: The Cointegrating Vector—CPI and Private Sector Credit

Source: National authorities; and IMF staff calculations.

Source: National authorities; and IMF staff calculations.

-0.002

0

0.002

0.004

0.006

0.008

0.01

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Months After Impulse

Source: National authorities; and Fund staff calculations.

1/ Generalised 1 standard deviation impulse.

-0.002

0

0.002

0.004

0.006

0.008

0.01

Figure 4. Pakistan: Impulse Response Function for CPI Based on the CPI,

Private Sector Credit, Wheat Support Price VECM 1/

Private Sector Credit, Wheat Support Price VECM 1/

Source: National authorities; and Fund staff calculations.

1/ Generalized 1 standard deviation impulse.

CPI, Broad Money, and Wheat Support Price

No meaningful VECM that contains broad money could be identified in the sample. Based on the

stylised model and the findings in the inflation regressions above, we started with a system including the CPI,

broad money, NEER, real GDP, and the wheat support price.16 The system also included controls for

Gregorian and Islamic calendar effects and in some specifications deterministic components. We set the lag

length to 6 to maintain sufficient degrees of freedom; the optimum lag length for this system is 12, but our

sample is not large enough to allow this number of parameters (Table 4). We experimented with different

specifications for the deterministic component, and dropped or retained any of the endogenous variables.

16Alternatively, we used the LSM instead of real GDP, but this did not change the results.

Fig. 3. Pakistan: Impulse Response Function for CPI Based on the CPI,

Months After Impulse

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Khan and Schimmelpfennig

196

Nonetheless, no cointegrating relationship emerged that would be broadly consistent with our model or would

yield sensible impulse response functions.

The failure to find cointegration most likely stems from ongoing changes to fundamental

relationships, in particular money demand, during the sample. As we show in Bokil and

Schimmelpfennig (2005), a money demand equation for Pakistan suffers from nonconstant coefficients

when estimated with either annual or monthly data. For annual data, recursive coefficient estimates

diverge significantly after 1998 from the coefficient estimated in the 1978–2004 sample. With monthly

data, the recursive coefficients fluctuate throughout the 1995–2004 sample, in the case of real GDP even

switching signs. These findings are likely to reflect the impact of the 1998-99 debt crisis on the

Pakistani economy and the reforms that followed. Macroeconomic stabilisation and financial sector

reforms, can be expected to have affected estimated parameters. Moreover, De Grauwe and Polan (2005)

show that standard quantity theory of money relationships are hard to identify in countries with inflation

of less than 10 percent.

IV. FORECASTING INFLATIONARY TRENDS

Inflation forecasts are an important input into monetary policy formation. Given typical time lags,

monetary policy needs to be concerned with future inflation. Current inflation levels, which are themselves

the result of past policies, may provide only insufficient information. Inflation forecasts that link future

inflation to current developments can bridge this gap. Some central banks have even adopted an inflation

forecast target. However, this assumes that inflation forecasts are very reliable. Still, even in situations where

structural relationships are less stable and data quality is evolving, quantitative inflation forecasts can provide

useful information on future developments, though this needs to be combined with additional analysis going

beyond econometric relationships. Leading indicators can be used to generate forecasts, in particular in

situations where time series are short and structural relationships are not stable enough to allow for an

economic model-based inflation forecast.

The leading indicators approach searches for variables that co-move with the variable to be forecasted

without imposing a model structure. Leading indicators do not necessarily need to be causal factors of the

target variable as part of an economic model, though this would presumably strengthen one’s confidence in a

forecasting model [e.g., Marcellino (2004) and Stock and Watson (1989, 1999)]. We again use the general-to-

specific algorithm in PcGets to narrow down the set of possible leading indicators from our full dataset. In

addition, we look at information criteria, root mean square error and similar statistics to optimise the forecast

accuracy and arrive at a final specification. We require indicators to lead inflation by at least 6 months and

allow for leads of up to 12 months.

Private sector credit growth and broad money growth are leading indicators of inflation (Table 6). We

extend the list of possible variables beyond that of our stylised model above to also include variables which

have proven to be good leading indicators in

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197

Table 6

Pakistan: Leading Indicators Model Regression Results

M5 M6 M7 M8

Observations 73 72 72 76

Adjusted R-squared 0.995 0.996 0.996 0.996

F-statistic 2,555.1 881.6 3,560.4 3,412.3

Akaike Information Criterion –1.935 –1.967 –2.136 –1.913

Schwarz Information Criterion –1.716 –1.303 –1.947 –1.729

Root Mean Squared Error 0.397 0.358 0.388 1.409

Mean Absolute Error 0.350 0.280 0.358 1.259

Mean Absolute Percentage Error 5.662 4.300 5.834 18.941

Coefficient

t-statistic Coefficient

t-statistic Coefficient

t-statistic Coefficient

t-statistic

Constant 0.111 2.813 –0.069 –0.585 –0.182 –2.638 0.086 2.082

Inflation

Lagged 1 Month 1.772 14.949 1.680 10.272 1.508 16.025 1.910 37.363

Lagged 2 Months –0.760 –4.629 –0.843 –2.876 –0.651 –8.471 –0.935 –18.128

Lagged 3 Months 0.111 0.346

Lagged 4 Months –0.231 –0.710

Lagged 5 Months –0.194 –1.189 0.126 0.429

Lagged 6 Months 0.144 1.266 0.024 0.182

Private Sector Credit Growth

Lagged 6 Months 0.086 1.623

Lagged 7 Months –0.176 –1.507

Continued—

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Table 6

Table 6—(Continued)

Lagged 8 Months 0.087 0.689

Lagged 9 Months 0.052 0.412

Lagged 10 Months –0.068 –0.532

Lagged 11 Months 0.042 2.711 0.020 0.162

Lagged 12 Months –0.038 –2.444 0.036 0.547 0.041 4.991

Broad Money Growth

Lagged 6 Months –0.157 –2.169 –0.114 –2.270

Lagged 7 Months 0.407 3.164 0.145 3.775 0.210 2.211

Lagged 8 Months –0.262 –1.847 –0.116 –3.392 –0.094 –1.949

Lagged 9 Months 0.028 0.188

Lagged 10 Months 0.074 0.522

Lagged 11 Months –0.072 –0.558

Lagged 12 Months 0.001 0.017

Long-run Coefficient 1/

Private Sector Credit Growth 10.00 3.53 3.47

Broad Money Growth 7.12 4.85 13.99

Source: Pakistani authorities; and own calculations.

1/Calculated as (1- sum of coefficients on inflation) / (sum of coefficients on regressor).

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other countries. The general model, thus, contains the following variables that could be leading indicators for

inflation: wholesale-price index inflation, time-varying intercept, and slope coefficient for the yield curve, the

spread between 12-month and 3-month T-bill rates, large-scale manufacturing index growth, broad money

growth, reserve money growth, private sector credit growth, change in the nominal effective exchange rate,

tax revenue growth, and the 6-month T-bill rate. Of these, only private sector credit growth and lags of

inflation remain in the reduced specification (M5).17 We also show specifications that include broad money

growth as one might expect a relationship between broad money growth and inflation. The best specification

here is M7 which includes lags of broad money growth and private sector credit growth in addition to lags of

inflation. Both specifications are consistent with a monetary transmission mechanism that works through the

credit channel, and also reflect the findings for our stylised model.

The LIMs exhibits a good ex-post forecast quality. Re-estimating the LIMs through May 2004 and

forecasting the remainder of 2004 allows a comparison of the models’ forecast with actual developments

(Figure 4). The ex-post forecast based on M5 (private sector credit growth) seems a bit closer to actual

developments than the ex-post forecast based on M7 (private sector credit growth and broad money growth).

However, the ex-post forecast based on M7 has a lower standard error.

Fig. 4. Pakistan: Leading Indicator Models—Ex-post Forecasts,

Jun.–Dec. 2004 1/

4

6

8

Jun-04Jul-04 Aug-04Sep-04Oct-04Nov-04 Dec-04

4

6

8

Actual

Forecast

2-Sigma Band

(a) Based on M5 (Private Sector Credit Growth)

4

6

8

Jun-04 Jul-04Aug-04 Sep-04 Oct-04 Nov-04 Dec-04

4

6

8

Actual

Forecast

2-Sigma Band

Sources: Pakistani authorities; and own calculations.

1/ Forecast based on model for reduced sample through May 2004.

1/ Forecast based on model for reduced sample through May 2004.

(b) Based on M7 (Broad Money and Private Sector Credit Growth)

Figure 5. Pakistan: Leading Indicator Models—Ex-post Forecasts, Jun.–Dec. 2004 1/

The LIMs yield a fairly accurate forecast, and are consistent with our stylised model. By construction,

the approach picks leading indicators that yield a high forecast accuracy at the current juncture. And, higher

broad money growth and higher private sector credit growth being associated with higher inflation seems

17Detailed results are available from the authors upon request.

Source: Pakistani authorities; and own calculations.