1. Department of Statistics
University of Karachi
Statistical Analysis of the Factors
Affecting Inflation in Pakistan
Prepared by:
Hassan Moin
Muhammad Zaid Uddin
Muhammad Jawwad
Nafees A. Siddique
Course incharge: Researchcoordinator:
Prof. Dr. AfrozeUddin Sir TayyabRaza

2. ii
Statistical Analysis of the Factors Affecting Inflation in Pakistan
Hassan Moin, Muhammad Zaid Uddin, Muhammad Jawwad
and Nafees A. Siddique
Abstract
The main theme of the study was to design such a model that could be used to
estimate inflation rate of Pakistan using only two factors, namely; exchange rate and
population of Pakistan. And also to show relation between inflation rate with these two
factors. In this research, it was meant to show that these two factors affects inflation rate
up to certain extent and can be used in a model for estimation. Normal log-linear model
was used with inflation rate as dependent variable and independent variables were
exchange rate and population of Pakistan. The range of data was from 1975 to 2011 that
includes 37 observations. The correlation matrix was also used, which shows that there is
negative correlation among inflation and exchange rate of Pakistan and positive relation
with population. The estimated model also give significant evidence that there is negative
relation between inflation and exchange rate and positive relation with population. The
model obtained was found significant enough to be used for estimation. This decision
was made on the basis of p-value and other criteria. The simplicity and selection of
variables of this model makes it unique for estimation.

3. iii
LIST OF TABLES
Table 1(a) Log-linear Model (type I).........................................................................16
Table 1(b) Log-linear Model (type II) .......................................................................16
Table 1(c) Log-linear Model (type III) ......................................................................17
Table 1(d) Log-linear Model (type IV)......................................................................17
Table 2 Descriptive Statistics of Residuals ..........................................................18
Table 3 Heteroscedasticity Test: ARCH ..............................................................18
Table 4 Correlogram Plot .....................................................................................19

4. iv
TABLE OF CONTENTS
Title Page ............................................................................................................... I
Abstract .................................................................................................................. II
List of tables........................................................................................................... III
Table of Contents................................................................................................... IV
CHAPTER I............................................................................................................... 1
INTRODUCTION
1.1Background of the study .......................................................................................................................1
1.2 Objective of the study.........................................................................................................................1
1.3 Rationale of the study............................................................................................................................1
1.4 Organization of the study......................................................................................................................2
CHAPTER II..............................................................................................................3
LITERATURE REVIEW
2.1 Fischer study .........................................................................................................................................3
2.2 Sarel study .............................................................................................................................................4
2.3 Ghosh and Phillips study.....................................................................................................................4
2.4 Khan and Senhadji study....................................................................................................................6
CHAPTER III ............................................................................................................7
DATA & METHODOLOGY
3.1 Data ........................................................................................................................................................7
3.2 Inflation .................................................................................................................................................7
3.3 Exchange rate ......................................................................................................................................7

5. v
3.4 Population ............................................................................................................................................7
3.5 Model ....................................................................................................................................................8
3.6 Assumption ...........................................................................................................................................8
CHAPTER IV...........................................................................................................10
DATA ANALYSIS & RESULTS
4.1 Regression model.................................................................................................................................11
4.2 Validation of assumption .................................................................................................................11
4.2.1 Assumption 1(Residuals with zero mean) ...................................................................................12
4.2.2 Assumption 2 (homoscedascity) ...................................................................................................12
4.2.3 Assumption 3(No correlation among residuals) .........................................................................12
4.2.4 Assumption 4(Residuals follow normal distribution) ...............................................................12
4.3 Results ...................................................................................................................................................13
CHAPTER 5.............................................................................................................14
CONCLUSION & RECOMMENDATION
5.1 Conclusion ................................................................................................................14
5.2 Recommendation .......................................................................................................14
REFERENCES.........................................................................................................15
APPENDIX...............................................................................................................16

6. 1
CHAPTER I
INTRODUCTION
CPI stands for consumer price index which basically measures changes in the price
level of the market basket of consumer and services purchased by households. So, in
other words, it can be said that CPI refers to inflation. The CPI is a statistical estimate
constructed using the prices of a sample of representative items whose prices are
collected periodically and then its change is determined from a particular year, and this
year is known as the base year. The annual percentage change in a CPI is used as a
measure of inflation. Hence the basic purpose of CPI is to estimate the inflation in an
economy. The other commonly known method used to calculate inflation is GDP
deflator. It will not be discussed as in this research, CPI method has been used. Inflation
is a general increase in prices and fall in the purchasing value of money. Hence, inflation
plays an important role in understanding economic growth.
Forecasting and modeling of inflation is very important in determining the condition of
the economy. Many factors are involved in increasing or decreasing the inflation rate,
such as; Gold price, oil price, exchange rate, imports/exports, foreign investment, pattern
of growth of population etc. Hence, the main concerns of this study are the population
and exchange rate factors that will be used in order to predict inflation and estimate a
suitable model for the inflation in Pakistan. Exchange rate is basically the price or value
of a nation’s currency in terms of another currency.
Different approaches are used to determine inflation. As inflation is time dependent, so,
mostly time series models are used. Time series models like autoregressive (AR) models,
moving average (MA) models, autoregressive moving average (ARMA) models,
autoregressive integrated moving average (ARIMA) models, autoregressive conditionally
heteroscedastic (ARCH) models and generalize autoregressive conditionally
heteroscedastic (GARCH) models. However, econometrics models are occasionally used
based on theories of econometrics, which define how inflation will respond to specific
variables, like the variables discussed above.

7. 2
As inflation rate forecasting is very important, there are number on institutions in
Pakistan that calculate and estimate inflation rate, such as, State Bank of Pakistan (SBP),
commercial banks, financial institutions and investment management firms.
1.1 BACKGROUND:
Inflation is used as an indicator of an economy. Over the past few year inflation in
Pakistan has shown dramatically an increasing and decreasing trend, where it attain a
high value up to 17.24 percent in 1975 and16.87 percent in 2008, and a low value of 2.14
percent in 2003. This increase and decrease is due to economical, political, social and
ethical factors. Like in the era of 70’s, the East Pakistan was separated from West
Pakistan which created a great impact on the economy and increases the inflation to high
extents. Therefore, forecasting inflation and identifying its pattern is very helpful in terms
of examining economic growth of country like Pakistan.
1.2 OBJECTIVES OF THE STUDY:
The main objective of the study is to design a model for estimating inflation rate, using
only the exchange rate and population of Pakistan based on past37 years of data from
1975 to 2011.
1.3 RATIONALE OF STUDY:
Most of the countries in the world use inflation as a benchmark for making future plans
and policies. Thereby, knowing the expected value of inflation, a country can decide
which policy will be the best for the development of a country. And as a developing
country of the world, estimation of inflation is very important in Pakistan too. In fact,
State Bank of Pakistan (SBP) calculates the expected inflation and based on the results
obtained, different policies are made. Therefore, prediction of inflation plays an
important role in determining the policies in Pakistan.

8. 3
1.4 ORGANIZATION OF STUDY:
The first thing is the introduction followed by literature review in which past study
related to inflation forecasting and estimating will be discussed. Then comes
methodology and formulae, which are being used. After that analysis and proofs for the
results. And finally conclusion, which will highlight the final results obtained through
this study.

9. 4
CHAPTER II
LITERATURE REVIEW
The creative work by Fischer (1993) was one of the first approaches to examine the
occurrence of nonlinearities in the relationship between economic development and
inflation mainly in the long run. Using cross-sectional and time-series cross-sectional
data(panel data) for a sample that includes developing and developed countries, Fischer's
parameter estimates indicate a negative/declining relationship between inflation and
economic development. Afterwards, many experimental studies on inflation threshold
used a large panel data of different countries. Sarel (1996) used annual data from 1970
to1990 for 87 countries and concluded that the threshold is at 8 percent below which the
effect of inflation on economic development is almost negligible but beyond 8 there is
a substantial, and very powerful negative effect on economic development. Similarly,
Ghosh and Phillips (1998) used a large set of panel data, in which they covered IMF
member countries over a period from 1960 to 1996. Their results proposed a negative
relationship between inflation and development which is statistically and economically
substantial. The relationship is nonlinear in two cases: firstly, at low inflation rates, the
relationship is positive; secondly, at other inflation rates, the plain marginal effect of
inflation on development becomes less important as only the high inflation rates are taken
into consideration.
Khan and Senhadji (2001) used a dataset of 140 countries (consists of both developed and
developing countries) from 1960 to 1998. They concluded that the threshold inflation
level above which it substantially slows development is estimated at 1 to 3 percent for
developed countries and 11 to 12 percent for developing countries. Drukker,
Hernandezand Gomis(2005) supported the existence of a threshold using a panel dataset
of 138 countries, but they figured its higher level, at around 19 percent. This threshold
level, higher than the usual estimate, was supported by Pollin and Zhu (2006) who also

10. 5
split up the sample by decades and proposed that threshold would be approx. 15-18 per
cent. A much smaller value of threshold was obtained by Burdekin et al. (2004), who
worked on a panel data of 72 countries and, allowing for multiple thresholds, concluded
that for developing countries, inflation turns out to be costly when it is more than 3
percent. A second break was also found at 50 percent, above which marginal growth
costs goes down substantially. Espinoza et al. (2010) used a panel dataset of 165
countries from 1960–2007. They figured a threshold of around 10 percent for all country
groups (except for highly-developed countries) above which inflation quickly becomes
destructive to development. However, for the highly-developed economies, threshold was
much lower.
If we talk about our neighbor country, India, different contexts provide different
perspectives on inflation threshold. Chakarvarty Committee (1985) mentioned it as the
satisfactory rise in prices at 4 percent. This, according to the Committee, reflects changes
in relative prices required to attract resources to development sectors. “As development is
not constant in different sectors, keeping absolute price stability, which means zero rate
of increase in prices, is not possible and nor is it suitable.” Rangarajan (1998), who
initiated the idea of threshold inflation, brought central bank emphasis on inflation rate at
6–7 percent known as “satisfactory level”. His concept of threshold was: at what inflation
level do adverse effects set in? The study by Vasudevan et al. (1998) and, Kannan and
Joshi (1998) figured the threshold level to be around 6 percent. Conclusions of
Samantaraya and Prasad (2001) are also on the same line as they estimated the threshold
level to be around 6.5 percent. In comparison, Singh and Kalirajan (2003) using annual
data from 1971–1998 provided statement against any threshold level for India. A more
recent study by Singh (2010) which used both, yearly and quarterly data, estimated
threshold inflation level for India at 6 percent but failed to support the same in
Sarel(1996) sense.
After thoroughly studying different research papers, the final conclusion is that; the role
of monetary factors is very important in calculating the inflation in Pakistan. For
example, Khan and Qasim (1996) found out that the total inflation is determined by real

11. 6
GDP, money supply, and import prices. While the role of the exchange rate in calculating
the inflation was still ambiguous. Choudhri and Khan (2002) did not find any evidence of
exchange rate pass-through in a small VAR analysis, while Hyder and Shah (2004)
concluded that there is some evidence regarding the role of exchange rate pass-through
using a larger VAR. Some authors have underlined structural factors in explaining the
inflation of Pakistan. Khan and Qasim (1996) found food inflation to be motivated by
money supply, value-addition in preparation, and the wheat support price. Whereas the
non-food inflation is influenced by money supply, real GDP, import/exports prices,
electricity and gas prices. Sherani (2005), concerning to his work, found that the increase
in the wheat support price also increases the CPI index (but not particularly inflation). He
also stated that the immense level of inflation in 2005 mostly resulted from a monetary
overhang that was come up by poor monetary policies.
By reviewing different research papers, it was found that no one used exchange rate and
population to estimate inflation rate in Pakistan. Therefore, in this research, we try to
focus the importance of exchange rate along with population for estimate the inflation
rate in Pakistan.

12. 7
CHAPTER III
DATA AND METHODOLOGY
The study uses multiple regression model (log-linear model) with two independent
variables that are population of Pakistan (in millions) and exchange rate. Only two
regressors is going to be used for examining their effect on inflation and determining
their effectiveness for the estimation of inflation in Pakistan. For this, past 37 years of
yearly based data is used starting from 1975 to 2011.Throughout the study, software
package e-views version 6 is used.
3.1 Data: The type of data used in this research report is entirely secondary data that is
obtained from International Monetary Fund (IMF), International Financial Statistics and
World Bank national accounts data.
3.2 Inflation: A general increase in prices and fall in the purchasing value of money is
defined as inflation. Two common methods for calculating inflation are Consumer Price
Index (CPI) and GDP deflator. First method, which is CPI method, is applied in this
study for the calculation of inflation. Inflation with respect to CPI is calculated as:
Inflation = (
Current CPI−Previous CPI
Previous CPI
) X 100
3.3 Exchange rate: The price of a nation’s currency in terms of another currency is
exchange rate. In this study, exchange rate used is in US dollars (USD). Its formula in
terms of Pakistani rupees PKR to USD is given as:
Exchange rate =
PKR
USD
3.4 Population: Population of a country plays an important role in the development of its
economy. In most of the country, it is calculated over a fixed period of time. The

13. 8
procedure of collecting the information about the population by the government if called
censes.
3.5 Model: In this study, log-linear model is used where inflation rate is taken as
dependent variable and the independent variables are exchange rate and population.
Mathematically, it can be expressed as:
log(Y) = α + β1 X1 + β2 X2 + β3 X1X2
Where,
Y = Inflation rate (inf)
α = Intercept of Y
X1 = Exchange rate (ext)
X2 = Population (pop)
and, βi’s = Slope of the regressors
In other form, this model may be written as:
log(inf) = α + β1ext + β2pop + β3ext*pop
And exponential of the above model will provide the forecasts for inflation rate.
3.6 Assumptions: For the model to be applicable, there are some assumptions that must
be satisfied. The assumptions for multiple regression are:
i – Mean value of errors/residuals must be zero.
ii – Variance of errors/residuals must be constant σ.
iii – There should be no correlation among errors/residuals.
iv – Errors/residuals must follow normal distribution N(0,σ).
There are multiple tests for validating these assumptions. For first assumption to hold, a
simple t-test is used with the null hypothesis of mean zero. Variance will be constant if

14. 9
the ARCH test for heteroscedasticity with null hypothesis of constant variance is
accepted. Now, for the third assumption, a correlogram plot will be constructed to
observe whether there is correlation among residuals or not. And for the last one, if the
Jarque-Bera value is less than chi-squared with 2 degrees of freedom, i.e. approx. 6, than
it can be said that residuals follows normal distribution with mean zero and constant
variance.

15. 10
CHAPTER IV
DATA ANALYSIS AND RESULTS
The first step of all analysis starts with the plotting of the dependent variable and then
obtaining its descriptive statistics. Below is the simple plot of inflation rate along with its
descriptive statistics:
From the graph, a visible up and down pattern can be observed. These ups and downs are
from different factors as explained before in the previous chapter. Mean inflation rate is
8.01% with standard deviation of ±3.449%. Also the correlation between inflation rate
and exchange rate was found to be negative and correlation between inflation rate and
population was positive.

16. 11
For estimating a model for inflation, several different combinations of exchange rate and
population variable were used of which the best model was chosen on the bases of
different statistics such as, Akaike info criterion (AIC), Schwarz criterion (SC) and root
mean square errors (RMSE).
4.1 REGRESSION MODEL:
The model having the least value of the statistics discussed recently was found to be:
log (inf) = 1.0787 –0.094*ext+ 0.019*pop +0.0003*(ext*pop)
S.E.: (0.7545) (0.0253) (0.0091) (0.0001)
Where, inf = Inflation rate (in percentage)
ext = Exchange rate (in percentage)
pop = Population (in millions)
and, ext*pop = Combined effect of population and exchange rate.
Hence, the estimation of inflation rate will be made from this regression model as all the
coefficients have p-value less than 0.05, which is a good sign that the model has
significant coefficients. The complete output of the estimated equation can be seen in
tables 1(a) through 1(d).
4.2 VALIDATION OF ASSUMPTIONS:
There are some assumptions which were discussed in the previous chapter, that have to
be satisfied in order to use the model.
To satisfy all the four assumptions of MLR as proposed in the previous chapter,
following tests are performed to satisfy each and every assumption.

17. 12
4.2.1 Assumption 1 (Residuals with zero mean):
From the descriptive statistics of residuals, the mean of residuals was found to be
approximately zero with standard deviation of 0.3572. Output can be seen in table 2.
A simple t-test was applied for the confirmation of this value with the null hypothesis that
the mean of residual is zero against the alternative hypothesis that it is not equal to zero.
At 95% of level of significance, it was verified through the t-test that the mean of
residuals is zero. P-value was found to be approximately 1, which gives strong evidence
that the mean of residual is zero.
4.2.2 Assumption 2 (Homoscedasticity):
To verify homoscedasticity, that is, constant variance of residuals, most commonly used
ARCH (1) test was used. In this test, the null hypothesis is homoscedasticity of variance
against the alternative hypothesis heteroscedasticity of variance.
This test gives significant evidence that the residuals have constant variance. In table 3,
p-value was found to be 0.6547 which proves that the residuals have constant variance.
4.2.3 Assumption 3 (No correlation among residuals):
By plotting the correlogram, it can easily be observed that there is no correlation amongst
residuals. As shown in table 4, there is no correlation between residuals so this
assumption is also not violated.
4.2.4 Assumption 4 (Residuals follows Normal distribution):
This is one of the most important assumptions if a prediction is going to be made. If this
assumption doesn’t holds than there will be biasness in the predicted values. Again going
to the table 2, it can be seen that the Jarque-Bera statistics is less than 6, which is a good

18. 13
sign showing that the residuals is following normal distribution with mean zero and a
constant variance.
As all the assumptions are satisfied, the regression model can now be used for predicting
the expected value of inflation rate.
4.3 RESULT:
Finally, all this statistics tells that there is a significant impact of exchange rate and
population on inflation rate of Pakistan. This result was observed from 1975 to 2011, and
it was found that the p-value was less than 98% of level of significance for the estimated
model. This shows that the model estimated was adequate enough to accept that there is a
significant relation between inflation rate and exchange rate along with population.
Hence, it is reasonable enough to estimate inflation rate on the basis of exchange rate and
population.

19. 14
CHAPTER V
CONCLUSION AND RECOMMENDATION
5.1 CONCLUSION:
From the results and tests applied, it can be concluded that the model for estimating
inflation in Pakistan on the basis of exchange rate and population was significant, when
the data was from 1975 to 2011. The p-value was approx. 0.005 for the model against
98% of level of significance. This suggests that the model was valid; however, this does
not mean that the model is best for estimating inflation in Pakistan. The impact of
exchange rate on inflation rate is negative but the effect of population was positive. Also,
the combined effect of exchange rate and population was also found to be positive.
5.2 RECOMMENDATION:
Many factors are responsible for affecting inflation and out of those many factors only
two were included in the model for the sake of simplicity and to highlight their
importance. This has its own drawbacks as well as advantages. It is recommended that
including more variable will increase the estimating precision of the inflation such as
monetary value, interest rates etc.; however, this will require tedious work and a lot of
study before estimating such a model.

20. 15
REFERENCES
Muhammad S. Akmal (2007). Stock returns and inflation: an ARDL econometric
investigation utilizing Pakistani data. Pakistan Economic and Social Review Vol
45(1), pp. 89-105 (2007).
Cogley, T. and Sargent, T.J. (2001), “Evolving Post World War II U.S. Inflation
Dynamics”, NBER Macroeconomics Annual, 16, 331-373.
Sims, C.A. (2001), “Comment on Sargent and Cogley’s ‘Evolving Post World War U.S.
Inflation Dynamics’ ”, NBER Macroeconomics Annual, 16, 373-379.
Stock, J. H. and Watson, M.W. (1999a) “Forecasting Inflation”, Journal of Monetary
Economics, 44, 293-335.
Stock, J. H. and M. W. Watson (2003), “Forecasting output and inflation: the role of asset
prices”, Journal of Economic Literature 41(3), 788-829.
Aurangzeb, and A.U. Haq, (2012), “Determinants of Inflation in Pakistan”, Universal
Journal of Management and Social Sciences, 2(4): 89-96.
Aamir, et al., (2011) “Inflation in Pakistan: Antecedents and Consequences”, European
Journal of Social Sciences, 25(3): 77-86.
Imran, et al., (2011) “Foreign Exchange Reserves and Inflation in Pakistan: Evidence
from ARDL Modelling Approach”, International Journal of Economics and
Finance, 3(1): 69-76

21. 16
APPENDIX

22. 17
These estimation outputs were discussed in the starting of chapter 4.

23. 18
The above output was for used in proving the assumption 2 of MLR.

24. 19
The above output was the proof of assumption 3 of MLR.