# The Relationship Between Inflation And Money Economics Essay

## Introduction

"Workmen are given their pay twice a day now--in the morning and in the afternoon, with a recess of a half-hour each time so that they can rush out and buy things--for if they waited a few hours the value of their money would drop so far that their children would not get half enough food to feel satisfied."

## (Erich Maria Remarque, The Three Comrades)

This paper attempts to establish the relationship between inflation, money in the economy and economic activity in Pakistan for a period from 1970 to 2004. Inflation is defined as a persistent rise in general price level over time in an economy and is a very basic phenomenon that affects all in an economy. It signals to the producer about the prevailing demand for his product in the market and in effect generates economic activity. Creeping prices thus ensure a circle of economic activity over time and contribute to the overall growth of an economy.

Different school of thoughts in economics has given different views on primary sources of inflation. Monetarists claim that monetary expansion is the sole contributor to inflation while Keynesian school highlights demand to be the major primary source of inflation [1] .

Inflation from demand occurs with an expanding economy when demand growth results in expanding output coupled with rising prices. Persistency of this process over time constitutes real output growth and inflation on a macroeconomic level.

On the contrary, Friedman’s Quantity Theory of Money (QTM) gives a different measure of inflation. Milton Friedman, the pioneer of monetarists’ school of thought, claims;

“Inflation is always and everywhere a monetary phenomenon”.

The QTM states that for every set of economic conditions increase in the money supply translates directly into an increase in the prices.

M = P (1)

(2)

So from equation 1 and 2, for every particular level for the output there is a consistent level of Money Supply that balances out generating a constant set of general price level. This is to say that since prices of all goods and services in an economy are defined (or denominated) in terms money, when the supply of money for a particular level of output in an economy doubles; ceteris paribus there exists double the amount of money for the same number of goods and services and so their prices double.

Pakistan is developing country marked by recurrent and huge fiscal deficits. The most frequent and readily available source of funding for these deficits is by printing money. This can serve as an evidence for money supply growth beyond real output growth. Khan and Qasim (1996) conclude that inflation in Pakistan has shown trends of direct linking with money supply in the long run while Khan and Schimmelpfennig (2006) found the same and that for different time frames real output growth has shown inverse trends with inflation signifying factors other than real output growth as responsible for inflation in Pakistan.

Considering the money in the economy and the economic activity as seen in the quantity theory of money, so the objective of this paper is the find this primary source of inflation in Pakistan by constructing some theoretical and statistical foundation that are discussed in coming chapters.

## Literature Review

Historically, there has been much effort performed to investigate inflation phenomenon. However first scientific approach was by classic economists – Adam Smith and David Hume who proposed two hypothesis to interpret inflation: quality theory of inflation for production and a quantity theory of inflation for money. Most of modern view of inflation gets its origins from Keynesian perspective obvious from Keynes's dominated (1919) quote –

"Lenin is said to have declared that the best way to destroy the Capitalist System was to debauch the currency. By a continuing process of inflation, government can confiscate, secretly and unobserved, an important part of the wealth of their citizens."

One of those outstanding attempts was long-run causality analysis between money supply and prices investigating inflation restrained UK & US economies by Friedman and Schwartz (1982) for the span of more than hundred years showing simple example of correlation between money supply and price level. Authors failed to prove their claims because they could not show statistical evidence and it showed there was a need for enhanced model. Crowder (1998) showed both statistical and substantive evidence regarding strong cointegration between monetary base growth and inflation while considering US economy under post-war – 1998 period with state-of-the –art time series technique and he also justified that in short run both are effected by real income innovations considerably.

(Grauwe and Polan, 2005) used a sample of around 160 countries over the last 30 years and checked for the quantity theory relationship between money and inflation and they deduced that, an increase in price level in comparison with trading companions can cause unfavorable imbalances in international transactions which is summarized in balance of payments and reduces social welfare by reducing real value of currency. They concluded that, there is proportionate link between money growth and inflation in long run. But they qualm Friedman’s emphasized pronouncement – “inflation is always and everywhere a monetary phenomenon” for countries which have experienced low inflation like European Monetary Union member states whereas it might not be true for ones having high inflation.

Inflation is subject matter to debate over in Pakistan. Corresponding studies done on inflation in country show different perspective for explaining inflation. Nasim (1995) and Hossain (1990) indicate variations in real money balances as main element of explaining current inflation rate in Pakistan. Khan and Qasim (1996) & Chaudhary and Ahmad (1995) underline that deficit bias created as a result of fiscal deficits financed through massive borrowings from banks result in monetary expansion. Thus, budget deficit keeping on for a considerable period of time by increasing monetary supply, will lead to inflationary bias in the long run. Advancement in availability of goods and services can improve situation by increasing supply of them so that deriving the price level down. Conversely, Khan & Gill (2010) oppose to this proposition that in the long run inflation is not affected by budget deficit. Studying 1970-2007 time span authors made rebellious conclusion that increase in M2 money aggregate does affect none of measures of inflation such as CPI, WPI, SPI and GDP deflator in the long run. This revolutionary assumption states that money base growth does not does not change the path of inflation measured by traditional measures to us in Pakistan.

Khan and Schimmelpfennig (2006) investigated comparative significance of monetary and supply side circumstances and concluded that in long run excess money supply and growing private sector credits held main responsibility for inflation, whereas on the other hand, calling attention to other aspects – instutional problems stimulating inflation. Furthermore they developed the idea that high and stubborn inflationary trends should be regarded as harmful to economic growth. They also noticed that State Bank of Pakistan (SBP) can run its own self-regulating monetary policy to attain favourable macroeconomic stability. In their opinion Pakistan can achieve economic growth by retaining the stable price level in medium and long run periods. Kemal (2006) supports the conception that Quantity theory of money holds in the long run and is monetary phonomenon. Money supply growth does not affect inflation promptly in the short run. Nonetheless the most imperative conclusion comes that if any of these variables is shocked, equilibrium will not be established for a long period. Conversely, in the short run the relationship between inflation and money base is not constant. Agha et al. (2005) at the same time as learning monetary transmission mechanism in Pakistan, revealed that inflation and GDP substantially react and do not converge to balance for a long period due to shocks in one of monetary policy instruments.

Malik (2006) approves the fact that monetary dynamics are main contributing factors to inflation in Pakistan. His conclusion comes in the following form: it takes six months for monetary policy transmission onto inflation and a year to take the highest value. He also states that monetary authorities does not learn anything from earlier experience of high inflation.

While considering 1960–2005 period Qayyum (2006) revealed long run one to one relationship between money supply increase and inflationary rise. His findings support the monetarist point of view of inflation that it is monetary phenomenon in Pakistan. He encouraged the same argument with Malik (2006) that central monetary authority (State Bank of Pakistan) when deciding on money supply growth gives more significance to growth rate of real GDP. It might affect real income in short run, but produces inflation. Paper also represents some statistically insignificant correlation between money growth and real GDP growth.

After studying above mentioned papers, which have presented many contradictory assumptions about understanding inflation in Pakistan. As this mechanism is the most investigated one, so the objective of this paper is to make empirical research on QTM for checking the relationship between real GDP, money supply and inflation whether or not it holds for case of Pakistan. This paper will examine the stated theory and then make some policy recommendation for SBP.

## Theoretical Model

In this section, paper will first set up the basic model that shows the relationship between money and inflation. To provide enough intuition, the paper will employ famous Quantity Theory of Money (QTM). Although there are different extensions of monetary models that incorporate QTM (see Walsh) the main dynamics of the all models are the same. For our purposes, it is important to see the dynamics of the model as well. The specification of QTM is as follows:

MsV=PY (3)

Where

Ms: Money Supply

V: Velocity of money

P: Prices

Y: Aggregate Output

Since the natures of these variables are discrete, so this paper will use stochastic discrete-time version of Cagan’s model and later this paper will expand it. In this set up, demand for real money balances (M/P) depends on expected future prices i.e., expected inflation. The log-linearized version of Cagan model is

mdt-pt=-σE{pt-pt-1∣Ωt} (4)

Where m= ln(M), p= ln(P) and σ: semi-elasticity of real money demand with respect to expected inflation

This fundamental equation of Cagan model is a simplified version of classical LM curve however, since the Cagan model is developed to explore hyperinflations the effect of output and interest rate are ignored in (4). Rather than solving this extended model, this paper will solve the basic Cagan model with perfect foresight and discuss the implications of the model. For detailed discussion of extended Cagan model can be found Sargent (1987), Obstfeld and Rogoff (1996).

In the equilibrium mdt = mst = mt which is based on the assumption that money supply is exogenous. Under perfect foresight assumption and with equilibrium condition, (4) turns out to be:

mt-pt=-σ(pt-pt-1) (5)

By rearranging (5) we have,

pt=(1/(1+ σ))mt+ (σ/(1+ σ))pt-1 (6)

By forward iteration of (6) we can eliminate pt+1, pt+2 and so on, we obtain

pt=ms+ pt+T (7)

The second term on the right hand side converges to zero in the limit. The reason that model claims the log price level grows smaller than (σ/ (1+ σ)). This assumption is not only a mathematical simplification but also consistent with the reality. That is, violation of this assumption leads to ever-increasing price levels since in that case logarithm of price level (pt) must grow equal or higher than (σ/ (1+ σ)) which in turn implies higher growth rate for price level. Thus, imposing this restriction to (7), we have

pt=ms (8)

This equation (8) provides the key intuition behind the model. Observe that the infinite summation on money supply is simply one, but the weights geometrically decline. Thus today’s price level depends not only today’s money supply but also future money supply although the contribution declines as time passes. Hence this result in equation (8) suggests that the coefficient on ms is positive one.

Although Cagan model gives the relationship between money supply and inflation rate in a compact form, but if more general environment of inflation is considered rather than hyperinflation case, so that the effect of prices cannot sweep away the effects of the other components. Thus, following from equation (3) we have,

(9)

So for estimation purposes, this model (combining with Cagan’s own regression equation) implies

β0 mt + β1πet+β2yt = εt. (10)

Here in equation (10), εt denotes a equilibrium path [2] , and in equilibrium mdt=mst= mt as in the Cagan model, and πet denotes expectation about the inflation. Observe that -σ and β0 [3] , has the same interpretation. Although equation (4) seems as a linear relationship and OLS is a trivial candidate for the estimation procedure, the problem is expected inflation is unobservable. One possible and trivial solution of this problem can be assigning some expectation formation process like adaptive expectation for the inflation (see Sargent and Wallace (1977) for details). This extended model which enriched by the rational expectation motives can be estimated by using non-linear techniques. However, in this paper our aim is to estimate or identify long-run and short-run dynamics of the relationship behind the QTM. So the main econometric model which is employed in this paper will be the system of error correction models by looking at the long and short run impacts of these variables on each of these variables one by one..

## Data:

## Table no. 1 Consumer Price Index

Duration

Average

Consistency Coefficient

CPI

Inflation

1972Q1-81Q4

12.03

12.3

18.80

1982Q1-91Q4

26.012

7.8

89.06

1992Q1-01Q4

61.88

9.7

68.63

2001Q1-10Q2

114.03

8.4

78.61

Data Source: IFS 2010 and FBSInflation:

Inflation [4] being the main focus is change in the general price level that is discussed previously; it is being estimated from the calculation of percentage change in the Consumer price Index [5] . This quarterly time series data comprises of years from 1971Q3 to 2003Q2 and taken from the International Financial Statistics 2010. Figure 1 show the historical pattern of the inflation in Pakistan where it represented peaks in the 1970’s due to of political turmoil and division of the country in two parts and in the late 2000’s where there was shortage of food [6] . Table 1 represents the average level of general prices and inflation in the stated decades which are also depicted by the normalized composition of natural logged CPI, where magnitude represents the consistency in the variable around the mean hence lowest value in the 1972Q1 to 1981Q4 period is also justified in the high inflation.

Figure 1 – source IFS 2010

Money Supply:

## Table. 2 M2 (Million Rupees)

Duration

Average

Consistency Coefficient

1962Q1-71Q4

9850.08

0.0012

1972Q1-81Q4

37880.26

0.00018

1982Q1-91Q4

159928.89

0.00003

1992Q1-01Q4

581401.93

0.000013

Data Source: IFS 2010According to the Quantity theory of money, the inflation is proportional to the amount of money that is available in the economy so broader the money used more finer the results can be expected but of the case of Pakistan being a developing country, so there is no official documentation of broader definition of money than M2. Thus M2 is used as an indicator of quantity of money in the economy. This quarterly time series data comprises of years from 1971Q3 to 2003Q2 and taken from the International Financial Statistics 2004. Looking at the table 2 [7] money supply does not seem to be consistent around its mean hence representing that money shocks were frequently used to stabilize or boost the economy. The average money supply increased 1534% from the 1972Q1-81Q4 to 1992Q1-01Q4 in the table hence it seems to be the contender to explain the rise in the CPI in this era which is 514%. Figure 2 also represent a rapid increase in money supply from the 1990’s decade.

Figure 2 – IFS 2010

Real GDP:

Real GDP used as the indicator of the economic activity in the economy which is according to the quantity theory of money have negative proportionality with inflation. As there is no formal institution that collects the real GDP data in quarterly form, for this purpose data is taken from the work done by Kemal and Arby (2004). Considering the fact that there is not officially collected data and this paper is using quarterised data as a proxy the Real GDP. The span of quarterly time series data is constrained by this transformed data that is from 1971Q3 to 2003Q2. In the table 3 and figure 3 the real GDP seem to be unstable as the values of consistency coefficient are small and the quarterised Real GDP graph cycling trend upward. Hence due to this transformed data there are limitations in the expected results that they might represent non-expected equilibrium pattern because the increase in the depth of the data came at the cost of cycles in the data.

## Table 3 Real GDP (Million Rupees)

Duration

Average

Consistency Coefficient

1972Q1-81Q4

23022.59

0.00109

1982Q1-91Q4

44288.66

0.00074

1992Q1-01Q4

71459.72

0.00092

Data Source: Kemal & Arby (2004)

Figure 3 – Source Kemal & Arby (2004)

Relationship between Indicator

## Table 4 Correlations

M2

Real GDP

CPI

0.911

0.9829

Self calculated data source IFSIn this section, the paper is intended to investigate the possible links between the historical trend of Real GDP, Inflation and M2 of Pakistan so that it can create a foundation for the flow of causality in long run. From figure 4 it can be seen that in the first five years there are common periods of high deviations in inflation and Money supply growth and after 1980, money supply growth and the inflation are relatively stable as compared to rest of the time period. In figure 5 real GDP growth and inflation shared common periods of high deviations till 1980 indicating the oil shocks as suspects. Table 4 represents the other dimension of the association between CPI, Real GDP and M2. It tells that the overall deviations of CPI around its mean are 91% similar to deviations in M2 and 98% similar to Real GDP around their mean on average. From table 5 in the appendix the test represents that the series are not skewed but they are different from normal kurtosis of 3 and this can be reasoned from the fact that the series contains some extreme values and looking at the figure 4 and 5 it can be concluded that they all have extreme values at similar time periods. So if the growth rates are incorporated in the model, then it is expected to increase the explaining power, hence replication of the reality will seem more realistic. This preliminary analysis provides a platform for the further more extensive analysis to try to reap out a feasible image that resembles the real life relationship between these variables. Following chapter will focus on the route map for the quantification of the proposed Quantity Theory of Money, it will also describes major econometric issues in the way of the objective of this paper and provide its solutions and alternatives.

## Econometric Issues with the Model

Now proceeding with this paper, the quantification of the Quantity theory of money using the indicators that are discussed in the previous chapter and assuming the linearized [8] data generating process for inflation [9] is given by

Pt = α + βYt + γMt + Ɛt ------------- (11)

Where dependent variable is P = Ln(CPI) and independent variable is Y = Ln(Real GDP), M = Ln(M2) and Ɛt is the unused and inestimable variables.

This quantification using Ordinary Least Squares method can be done if the result generated residuals that are totally white noise (i.e. Ɛt ~ iid (0, δ2)), which is one of the most important assumptions otherwise the relationship is considered to be spurious [10] . Work done by (Granger & Newbold, 1974) & (Yule, 1926) states that any pair uncorrelated I(1) [11] series tend to represent some correlation due to of their common stochastic trends. Considering the fact that most of the economic series exhibits some persistence in them such that its new realization is somewhat determined by past experiences. Hence it is expected that the used indicators to be non-stationary. [12]

So if in equation (11), Pt = f (Pt-1), Yt = f (Yt-1) and Mt = f (Mt-1) then their linear combination will generate residual series that is Ɛt = f (Ɛt-1) such that the series is not independent now because prediction of relationship in every time is now dependent on the past time period. So the suspected spurious relationship will only be meaningful if their residuals are stationary I(0), which is also called co-integrating relationship. In this case we can explain the change in the growth of CPI via growth in Real GDP, Money and the co-integrating vector. In this way the regression can be made independent, valid and meaningful. It takes following form:

A(L) ΔP = α + B(L)ΔY + C(L)ΔM – λ(Pt-1 + βYt-1 + γMt-1) + Ɛt ----(12)

Where in equation (12), λ is the coefficient that determines how the deviation from this linear equilibrium washes away in the changes in the short run (growth rates). This mechanism is called 1-step Error Correction Model. The advantage here is that now the effect of equilibrium on Inflation (ΔP) can be directly observed.

But this mechanism is putting restriction [13] that the equilibrium is affecting only dependent variable, where as in reality equilibrium should affect all series in the equilibrium. This way of constructing three ECM’s simultaneously is called Vector Error Correction Model (VECM). The mathematical specification is as follows:

ΔXt = a + b(L)ΔXt-i + Π Xt-1 + Ɛt , i = 1 . . n [14] ------(13)

Here , , , , , and

This valid Vector Error Correction Model is transformed [15] through a Vector Auto Regressive (VAR) Structure which has following specifications:

Xt = a + b(L)Xt-i + Ɛt --------(14)

Here , , , , and

Now following are the steps to quantify the valid long run estimation of the quantity theory of money.

## Presenting Evidence:

Checking Stationarity:

To proceed with the presentation of the evidence, the first thing that needs to be done is to see whether the series are stationary or not, since if the series are non-stationary then ordinary least squares cannot be used. Following are some ways through which nature of the series can be tested.

Analyzing the time trend

Suppose the for a certain series

Xt = α + βt + Ɛt----- (15)

If β parameter is significant then it means that the E (ΔXt) = β ≠ 0 [16] , hence it is not stationary.

## Analyzing the trend

Table no [17]

Series

Intercept

P value

Time parameter

P value

6

Ln(CPI)

1.94

0.00

0.021

0.00

7

Ln(Real GDP)

9.74

0.00

0.014

0.00

8

Ln(M2)

9.69

0.00

0.034

0.00

Results generated for equation (15)

These results shows that the parameter of time for each of the series (Ln(CPI), Ln(Y) and Ln(M2)) is significantly representing the mean of these series to be the function of time, hence there is a hint of trend stationarity in the series. These results are by no means final as they are expected to be biased due to excluded variable bias.

Auto and Partial correlation function

Let a series

---- (16)

Here each is partial autocorrelation and is auto correlation coefficient. Every preceding value of the partial and autocorrelation function represents how persistent the series is when comparing the particular time period with the current time. Hence the stationary series must have smaller values or values that are getting diminished quickly and should have insignificant Q-statistic.

For the case of Ln (CPI), the table 9 represents that the values of the Autocorrelation function are significant and they are not diminishing quickly. Hence this is also an indicator of non stationary series. For the case of Ln (Real GDP) the table 10, the Autocorrelation function is showing the slow decay hence this series is non-stationary. For the case of Ln (M2) the table 11, similar to the previous case the persistent autocorrelations are the reasons for the non-stationary nature of M2.

Hence this test identifies the stationary or non-stationary series by examining the persistence in the series but it cannot tell about the nature of the non-stationarity.

Unit Root Test

Suppose the data

Xt = α0 + α1Xt-1 +α2t + Ɛt ------ (17) [18]

Johnston, J., & Dinardo, J. (2007) provided explanation for this estimation as if α2 = 1 then its conditional mean and variance will not exist. Here the series will be differenced stationary if α1= 1 and α2 = 0 and trend stationary if α1 = 0 and α2 ≠ 0 [19] .Hence Wald test is applied to test the α1 = 1 having following hypothesis.

H0; α1 = 1 (series is non-stationary, I(1)) H1; α1 ≤ 1 (series is stationary, I(0))

## Unit root test results

Table

Series

Intercept

Lag parameter

Time parameter

Wald

B-Godfrey

1st order

2nd order

3rd order

4th order

12

Ln(CPI)

0.099

(0.00)

0.965 (0.00)

0.0005 (0.13)

3.83 (0.052)

10.8 (0.00)

12.6 (0.00)

17.5 (0.00)

28.7 (0.00)

13

Ln(Real GDP)

8.388 (0.00)

0.139 (0.11)

0.0119 (0.00)

96.21 (0.00)

10.7 (0.00)

33.5 (0.00)

33.5 (0.00)

86.0 (0.00)

14

Ln(M2)

1.65 (0.00)

0.841 (0.00)

0.005 (0.00)

11.02 (0.00)

25.6 (0.00)

25.8 (0.00)

36.0 (0.00)

63.7 (0.00)

Results are generated for equation 17. P values are in parentheses

This table representing the set of results of unit root rest. The Wald test on unit root for CPI accepts the presence of unit root at 5% level so the series is differenced stationary only because of insignificant time trend. Unit Root test represent that the Real GDP is not difference stationary (significant Wald test) so significant trend parameter suggests the series is trend stationary. Similar the case with M2 does not have a unit root and it has a significant trend but all of these tests cannot be considered to be final argument for the series due to the presence of significant auto-correlating residuals (B-Godfrey Test).

Dickey Fuller test / Augmented Dickey Fuller test:

(Dickey & Fuller, 1979) used modification to the unit root test so that it will be more dynamic and useful.

ΔXt = α + βXt-1 + λt+ Ɛt ------- (18) [20]

Where β = (α1 – 1) in eq. (17)

There is a problem that ΔXt = f(ΔXt-i) , which can make Ɛt = f(Ɛt-i) where i = 1, 2, ….,n [21]

ΔXt = α + βXt-1 + λt +ΣΩiΔXt-1-i + Ɛt ----- (19)

Ho; β = 0 (non-stationary series I(1) and α1=1) H1; β ≠ 0 (stationary series, I(0) and α1≠ 1)

## Augmented Dickey Fuller Test

Table

Series

Intercept

Lag level parameter

Time parameter

No of dynamics

Wald

B-Godfrey

1st order

2nd order

3rd order

4th order

15

Δln(CPI)

0.16 (0.00)

-0.078 (0.00)

0.001 (0.00)

4

19.54 (0.00)

0.33 (0.566)

1.95 (0.376)

2.84 (0.416)

2.87 (0.582)

16

Δln(Real GDP)

0.60 (0.38)

-0.053 (0.44)

0.0004 (0.656)

4

0.58 (0.44)

1.38 (0.238)

1.70 (0.427)

2.11 (0.548)

5.57 (0.233)

17

Δln(M2)

0.81 (0.02)

-0.081 (0.03)

0.002 (0.038)

4

4.56 (0.034

0.13 (0.71)

0.79 (0.671)

7.81 (0.050)

10.34 (0.035)

Results generated for equation 19. P values in parentheses

A valid Augmented Dickey Fuller (ADF) test and Wald test for CPI suggests that the series does not have a unit root. But significant parameter of trend suggest that the series is trending in its mean, so it is considered as I(1).

Analyzing the ADF test for the Real GDP, the insignificant lag level parameter and the Wald test suggests that there is a unit root in series so it is Differenced stationary hence it is also I(1).

The ADF test and Wald test for M2 series rejected the presence of the unit root but justifies significant trending mean. So the series is trend stationary i.e. I(1).

As none of the test has majority of significant autocorrelation in the several orders of residuals so these tests are considered to be valid.

Hence it has been confirmed that the series are non-stationary so simple Ordinary Least Squares cannot be done on this series and the alternative way to estimate the long run causality is by using Error Correction Mechanism (ECM).

Estimation of ECM:

So in order to estimate long run when the series are I(1), Error correction model is used.

## 1 step Error Correction Model

Table

Series

Intercept

Short run effects

EC

Long Run Effects

Wald

B-Godfrey

Δln(M2)

Δln(RGDP)

## M2t-1

## RGDPt-1

First four orders

18

Δln(CPI)

0.285 (0.21)

-0.37 (0.474)

0.056 (0.290)

-0.091 (0.00)

## -0.93 (0.00)

## 1.07 (0.016)

10.43 (0.00)

2.95 (0.08), 5.95 (0.051), 7.48 (0.058), 7.53 (0.11)

Calculation for equation 12, p values in parentheses

First thing to notice in this valid ECM is that the signs of the coefficients in the error correction term of RGDP and M2 are opposite to what was expected and this might be due the fact that in this equilibrium there are three variables and CPI (Inflation) only is not the factor that is being determined by the deviations from this equilibrium. Hence model must be expanded to see how all the variables are being affected by this disequilibrium. So in making a system, first step is to construct an Unrestricted Vector Autoregressive Model (UVAR).

Estimation of UVAR:

The main objective of this system is to determine how many lags for each of the series is required to make a valid VAR system following equation (14). Hence by using a selection order criterion (table 20), it can be seen that Likelihood Ratio (LR) test suggests 8 lags whereas Log Likelihood and AIC suggest 6 lags and all other suggest 5 lags. So this paper will start from the largest suggested lags and go down until it finds a valid [22] VAR structure. Table 19 shows the estimated VAR structure with order 6.

Transformation to VEC

This VAR structure can be transformed into a vector error correction model that is considered as a system of ECM, showing the flow of the disequilibrium and the response of all the series to it. So before making the VEC structure, the “Π” in equation 3 needed to be specified, where each row in it represents the co-integrating vector that effects the relevant dependent series. So the number of statistically different [23] rows represents the number of equilibriums that can be formed. The number of different rows can be checked by maximum Eigen Value or trace test.

So the rank test at 6 lag length in table 20 represent that there is one co-integrating vector that is statistically different so the VEC will be formed considering rank equal to 1.

Estimation of VECM

Following is the vector error correction model with order 8

## Vector Error Correction

Series

Short run parameter

ECt-1

Long run parameters

Δln(CPIt-1)

Δln(RGDPt-1)

Δln(M2t-1)

RGDPt-1

M2t-1

Δln(CPIt)

0.213 (0.017)

0.074 (0.079)

-0.042 (0.418)

-0.08 (0.00)

1.47 (0.00)

-1.13 (0.00)

Δln(RGDPt)

0.221 (0.010)

-0.882 (0.00)

-0.232 (0.052)

-0.09 (0.01)

Δln(M2t)

-0.284 (0.112)

-0.048 (0.570)

-0.263 (0.011)

-0.009 (0.76)

Calculation of equation 13, p values in parentheses, table 21

## Validity test for VECM

ADF test for Residual

ADF test for Equilibrium

Lag level parameter

Time parameter

Lags

B-Godfrey

Lag level parameter

Time parameter

Lags

B-Godfrey

-0.65 (0.00)

0.00002 (0.52)

4

All orders insignificant

-0.381 (0.00)

0.0003 (0.08)

7

All lags insignificant

P values in parentheses, table 21 & 22

First table represent that there is long run equilibrium between Money supply, Real GDP and CPI. Here 1 percentage point increase in the Real GDP will reduce the CPI by 1.47 percentage point in long run and 1 percentage point increase in the money supply will increase CPI by 1.13 percentage point in long run. The values of these parameters are near to one which is similar to the expected from equation 2 and 8. As a whole 1 percentage point deviation from this equilibrium will decrease Inflation by 0.08 percentage point and Real GDP growth by 0.09 percentage point in short run on average keeping other factors remain constant (insignificant for the case of Money Supply growth). So for the case of inflation, it means, it takes around 13 time periods to recover to the original position if there is shock creating disequilibrium which is approximately 3 years [24] .

After using a valid specification of the ADF test to determine the nature of the residuals and equilibrium generated by the VECM represent that both of there are stationary (i.e. I(0)). Hence Quantity Theory of Money justified as CPI is confirmed to be determined by Real GDP and Money Supply for the case of Pakistan during the period of 1971Q3 to 2003Q2.

Impulse responses

Following impulse responses are generated from the VAR structure which are representing the direction and intensity of the motion of the variable due to the shock given by the other independent variable, hence figure 6 represent that impulse of RGDP and M2 are being responded by CPI though decreasing and increasing respectively, and these figures are representing per time period effect. So for the case of RGDP the effect is almost insignificant and for the M2 the effect becomes significant after around about 5 time periods, hence it is also representing the fact that money effects the inflation in the economy in the long run.

## Figure 6 – orthogonal effect of RGDP and M2 (impulses) on CPI (response)

Figure 7 is the cumulative effect in response to the RGDP and M2. Here CPI is representing significant cumulative decrease and increase in response to RGDP and M2 respectively.

They also depict the effect in same direction as the last figure 6, and there both complement the expected direction of effect generated form Quantity theory of Money and the results from the Vector Error Correction Model.

Figure 7 – cumulative effect of RGDP and M2 (impulses) on CPI (response)

## Conclusion:

Beginning with the question that can quantity theory of money explain the inflation pattern in Pakistan, a firm proof is found using VECM and Impulse Response Functions that money in the economy and the economic activity are playing their role positively and negatively respectively in explaining the persistent rising consumer price level (Inflation). The results represented that the equilibrium takes time to recover from any shock this can be expected from the fact that full role of the money and the financial markets are not represented by the use of the M2 definition for the money in the economy.

This long lag effect of money on the inflation also predicted by Kemal (2006) and Malik (2006) suggests that policy makers must forecast the rising inflation before time so that it can give ample time for the tight monetary policy to kick in.

Results represented that the real GDP is more elastic than money to effect the inflation, so it hints that demand side (fiscal) polices are suitable in maintaining a suitable inflation rate in the economy.

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## Figure 5 – test for the skew-ness and kurtosisAppendix I

## Estimation Tables [25]

Table 6 – testing existence of trend in ln(CPI)

Table7 - testing existence of trend in ln(Real GDP)

Table 8 - testing existence of trend in ln(M2)

Table 9 – Auto and Partial Correlation Function of ln(CPI)

Table 10 – Auto and Partial Correlation Function in ln(Real GDP)

Table 11 – Auto and Partial Correlation Function of Ln(M2)

Table 12 – unit root test for ln(CPI)

Table 13 – Unit Root Test for ln(Real GDP)

Table 44 – Unit Root test for ln(M2)

Table 15 – Augmented Dickey Fuller test for CPI

Table 15 a - testing the unity of the root for CPI

Table 16 – Augmented Dickey Fuller test for Real GDP

Table 16 a – testing the unity of the root of Real GDP

Table 17 – Augmented Dickey fuller test for M2

Table 17 a - testing the unit of the root of M2

Table 18 – 1 Step Error Correction Model

Table 19 a – test for validity and restrictions on co-integration and long run relationship

Table 20 – determine appropriate lag length using Selection Order Criterions.

Table 21 – UVAR structure order (6)

Table 22 – Rank test for the Π matrix

Table 23 – VECM result with hidden Dynamics

Table 24 – checking for the stationarity of the residuals

Table 25 – checking the stationarity of the co-integrating vector

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