Revista Empresarial Inter Metro / Inter Metro Business Journal

Fall 2016 / Vol. 12 No. 2 / p. 1

EXAMINING THE LONG-RUN RELATIONSHIP BETWEEN MONEY

OUTPUT, INFLATION, AND EXCHANGE RATES: INTERNATIONAL

EVIDENCE OF THE QTM AND PPP IN EMERGING MARKET

ECONOMIES

by

Giovanni M. Pérez-Juanaso

Adjunct Professor

Escuela Politécnica del Litoral, ESPOL

Guayaquil, Ecuador

Miguel Ruíz-Martínez

Assistant Professor

Escuela Politécnica del Litoral, ESPOL

Guayaquil, Ecuador

Antonio Fernós-Sagebién.

Assistant Professor

School of Economics

Metropolitan Campus

Inter-American University of Puerto Rico

San Juan, Puerto Rico

Abstract

The Quantity theory of Money (QTM) and the Purchasing Power Parity theory (PPP) have been

long tested in the literature. This paper aims to contribute by analyzing QTM and PPP main

propositions regarding the long-run relation of money, prices, output, and exchange rates from a

combined framework. The empirical analysis is performed over a dataset of 22 countries

considered to be emerging market economies by the IMF. The implications of this paper are of

importance for these types of countries because as open-economies, careful attention should be

paid to the relation among the variables in this study. Results support the propositions of QTM

when tested individually, but the same is not true for PPP. Evidence supports the idea of some

studies that PPP does not hold in the long-run. In the combined framework, mixed results are

found.

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Introduction

A central implication of the Quantity Theory of Money (QTM) tells as that in the long-run

a given change in the rate of growth of the quantity of money (M) induces an equal change in the

rate of growth of price inflation (Lucas 1980)1. Another very important implication of QTM is

that there is not long-run correlation between either money growth or inflation and the growth rate

of output.2The latter is not as robust as the former; McCandless and Weber (1995) found a positive

correlation between real growth and money growth, but not inflation. Kormend and Meguire

(1984) and Geweke (1986) argued that the data reveal no long-run effect of money growth on real

output. Barro (1995) reported a negative correlation between inflation and growth in a cross-

country sample. On the other hand, the Purchasing Power Parity (PPP) tells us that the difference

in the growth rate of prices in two different economies, namely the difference in the inflation rates,

is equal to the percentage depreciation or appreciation of the exchange rate. Moreover, according

to PPP exchange rates move in the same proportion to prices in the long-run. Recent work on PPP

among high-income countries has found evidence in favor of the hypothesis that real exchange

rates converge to their PPP level in the long run. Other studies using long data series find evidence

in favor of long-run PPP (by rejecting either the null hypothesis of unit roots in real exchange rates

or the null of no cointegration between nominal exchange rates and relative prices (Engel 2000)3.

Ng and Perron (2002) support Engle’s idea that in the long-run PPP does not hold. Implication of

the above two theories have been tested extensively using different data sets, different time

1 Berentsen, Menzio, and Wright (2008) replicated Lucas’s paper using data from 1955 to 2005 and found similar

results.

2 McCandless and Weber (1995) provide a summary of long-run monetary relationships examining data covering 30

years from 110 countries using different definitions of money.

3 T Frankel (1986), Edison (1987)) reached the conclusion that real exchange rates do not have unit root.

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periods, and different empirical approaches. But there are few studies that have analyzed for PPP

and QTM propositions jointly. This paper tries to do exactly that under the idea that combining

QTM and PPP into one theory, one can derive the proposition that money, exchange rates, and

prices should all move proportionally in the long run (De Grauwe and Grimaldi 2001)4. In this

paper, I want to test the propositions presented above by QTM and PPP; following De Grauwe and

Grimaldi 2001 paper. In their paper, De Grauwe and Grimaldi tested the validity of these

propositions in the long run using a cross-section of approximately 100 countries over a thirty-

year period. They found the PPP and QTM propositions to hold quite well for the sample as whole.

However, when distinguishing between high and low inflation countries the results were different.

In low inflation countries an increase in the growth rate of money stock does not have a long run

proportional effect on inflation. All this contrasts with the results of the high inflation countries

where the proportionality propositions hold very tightly both in the context of the QTM and of

PPP. Although the present paper follows De Grauwe and Grimaldi 2001 ideas closely, it differs

from the latter in some important aspects: (a) this paper uses data from 22 countries considered

Emerging Market Economies (EME); (b) this paper does not make a distinction between high and

low inflation countries, but the distinction is made on the basis of the monetary policy tool used

by the countries in the sample, namely Inflation Targeting (IT) or other (non-Inflation targeting);

(c) I used panel data regressions instead of cross-section; and (d) the estimation time-period is

from 1971 to 2010 (40 years). I think the following analysis is especially important, from an

emerging market country perspective, given that as open-economies countries, exchange rate

4 De Grauwe and Grimaldi 2001 presented their paper On April 19 – 20, 2001 the Oesterreichische National bank

sponsored a Workshop organized by Richard Clarida (Columbia University), Helmut Frisch (TU Wien) and Eduard

Hochreiter (OeNB) on „Exchange Rate and Monetary Policy Issues”.

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movements play an important role in the transmission process that links monetary disturbances to

output and inflation movements (Walsh 2006, 3rd Edition). Moreover, it is important because

having a better understanding of the long-run relationship among economic variables is crucial to

implement effective policies that can contribute to further economic stability and growth. The rest

of the paper is organized as follows. In section 2 a simple model that is introduced to combine the

QTM and PPP in the same context. In Section 3 the empirical analysis is presented along with the

data information and variables description. Section 4 presents the testing of the long-run

convergence of exchange rates towards its PPP values. Section 5 tests the long-run neutrality of

money. Section 6 concludes.

A simple theory

The Quantity Theory of Money and the Purchasing Power Parity Theory provoked an

extensive number of studies that tries to explain the long-run behavior of the growth rates of money

(m), output(y), inflation (p), and the rate of depreciation of the currency. The QTM can be

represented by the following equation:

𝑝 = 𝑚 + 𝑣 – 𝑦 (1)

where p is the percent change in the domestic price level (inflation), m is the percent change in

money supply, v is the percent change in velocity, y is the growth rate of output. In the case of a

foreign country, we have the following:

𝑝 ∗ = 𝑚 ∗ + 𝑣 ∗ − 𝑦 ∗ (2)

where the variables with * relate to the foreign country. The QTM formulates two important

propositions: (a) in the long-run money (m) is neutral; this means that changes in money do not

affect output changes when a sufficiently long period of time is allowed for; and (b) in the long-

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run changes in money and prices are proportional, this means that an percentage increase in the

money stock leads to an equal percentage change in the price level. In the other hand, PPP can be

represented with the following equation:

𝑒 = 𝑝 – 𝑝 ∗ + 𝑘 (3)

where e is the nominal rate of depreciation of the domestic currency relative to the foreign

currency, k is the real rate of depreciation of the domestic currency. The PPP theory implies that

there is proportionality between the rate of depreciation of the domestic currency and the rate of

change in domestic prices. After substituting (1) and (2) into (3), the new equation allows us to

combine QTM and PPP, and is defined as:

𝑒 = (𝑚 – 𝑚 ∗) + (𝑣 – 𝑣 ∗) – (𝑦 – 𝑦 ∗) + 𝑘 (4)

Equation (4) implies that there is a proportional relation between the changes in money, the

exchange rate and the price level. The validity of (4) and its propositions are the main focus of this

paper. By further analyzing (1), (2), and (4), we can test additional propositions of the QTM and

PPP theory concerning the long run effect of the output changes. It follows that (a) a higher rate

of domestic output growth (for a given foreign growth rate) leads to lower inflation, given the

money growth; and (b) a higher rate of domestic output growth (for a given foreign growth rate)

leads to an appreciation of the domestic currency, given the money growth. An important issue

regarding this theory is that the propositions mentioned above are assumed to hold for all countries

irrespective of the institutional differences between them. This issue will be taken into

consideration by analyzing the individual country random effects in the empirical section below.

At this point is worth mention, that there may be many sources of institutional differences between

countries; one important one is the difference between monetary policy regimes that countries

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adopt (issue analyze in this paper). Some countries use Inflation Targeting (IT), others use a type

of interest rates, and others use exchange rates. These differences affect institutions within each

country, and are worthy to analyze if they affect the validity of the QTM and PPP in the long-run.

Empirical Analysis

In order to provide a different approach to De Grauwe and Grimaldi 2001 this paper uses

panel data analysis. De Grauwe and Grimaldi 2001 use information for 20 years from 100 countries

in their estimations. They calculate yearly averages over the period 1970-99 (therefore the data

refer to averages of almost 30 years). The authors assume that such a period can be considered as

representing the long run. Under their approach, each variable has roughly 100 observations. If

one wants to focus on EME, the number of countries will be significantly reduced given the

availability of data. In my dataset information for 22 countries is included; therefore following De

Grauwe and Grimaldi 2001 yearly average approach means that each variable will only have 22

observations. After performing the analysis with only 22 observations per variable, results (which

are not provided in this paper) were not very significant and provide so many mixed conclusions.

Therefore, I opted to perform a panel data analysis that will make use of around 880 observations

per variable. Another important reason for use panel data is that the analysis allows you to control

for variables you cannot observe or measure like cultural factors or difference in monetary policy

regimes across countries; or variables that change over time but not across entities (i.e. national

policies, federal regulations, international agreements, etc.). On the latter, for example, open

economies face the possibility of economic disturbances that originate in other countries, and this

raises questions of monetary policy design that are absent in a closed-economy environment5. The

5 Walsh, Carl. “Monetary Theory and Policy”, Chapter 9, 3rd Edition, MIT Press 2010

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monetary regimes adopted by each country in the sample can affect the propositions of the model.

In particular, countries that adopt IT to other type of monetary instrument may experience different

transmission processes of money to prices and to exchange rates. In order to account for these

cross-country differences, the regression analysis in this paper will make use of the Random

Effects (RE) tools. I chose to account for random effects in my regression analysis because it will

allow to correct for unique, time constant attributes of each country that are the results of random

variation and do not correlate with the regressors. This model is adequate, as we want to draw

inferences about the whole population, not only the examined sample. Also after running the

Hausman test6, the results verified that in this dataset random effects are the preferred method over

fixed effects.

Data and variables creation

The empirical analysis is performed over a data set personally created that includes information

on Gross Domestic Product (GDP); Consumer Price Index (CPI); monetary aggregates (M1, M2,

and M3); and exchange rates (XR). The data was collected using different sources. One point

worth mention here is the difficulty of working with EME countries data-wise. EME data sets do

not have long series; in contrast to countries like the U.S. or the U.K where one can find

information for hundred of years, in EME one can optimistically find data for the last 30 or 40

years. Data sources included the International Financial Statistic (IFS) from the International

Monetary Fund (IMF), the World Economic Outlook (WEO) from the World Bank (WB), the

Federal Reserve Economic Data (FRED) from the Federal Reserve Bank of St. Louis, the

ERS/USDA dataset from the U.S. Department of Agriculture, and many of the included countries

6 See Hausman (1978)

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central banks or statistics offices. The dataset encompasses 22 EME countries. In this paper a

country is classified as EME if is consider either an emerging market economy or a developing

economy by the IMF. Then using the WB upper-middle income classification the 22 countries

where chosen. The time period of the variables differed from one country to another; then in order

to create the panel dataset, the start date of 1971 was selected (given that most of the 22 countries

have complete information from this date). So the time period for the analysis is from January

1971 to December 2010. The dataset includes information of GDP, CPI, M1, M2, M3, and XR.

The velocity variable was calculated using the available information on nominal GDP and

monetary aggregates. Yearly growth rates of each variable across countries were calculated; this

new variables are the ones used in the calculations7. The list of the 22 countries used in this paper

is provided in the Appendix section.

Testing the proportionality of the variables

In order to test both the proportionality between money growth and inflation and between money

growth and exchange rate, the following relations need to be specified:

𝑝 𝑖 = 𝑎 1 + 𝑎 2𝑚 𝑖 + 𝑎 3𝑦 𝑖 + 𝑎 4𝑣 𝑖 + 𝜇 𝑖 (5)

𝑒 𝑖 = 𝑏 1 + 𝑏 2𝑚 𝑖 + 𝑏 3𝑦 𝑖 + 𝑏 4𝑣 𝑖 + 𝜔 𝑖 (6)

where 𝑒 𝑖 is the rate of depreciation of currency i against the US dollar; 𝑝 𝑖 , 𝑚 𝑖 , 𝑦 𝑖 , and 𝑣 𝑖 are the

rates of growth of prices (CPI), money, output (GDP) and velocity. As mention above, all the

variables include cross-section information refer to almost 40 years (the period 1971-10). I

calculated the velocity for M1 and M2. A test of proportionality consists in checking whether the

estimated coefficients of money (𝑎 2 and 𝑏 2) are equal to one. An econometric issue that arises

7 When interpreting the regressions coefficient values, one needs to be careful in order to provide an accurate

interpretation.

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with the specification (5) and (6) is the potential for collinearity between the regressors (De

Grauwe and Grimaldi 2001). Table 1 shows the correlation matrix of the regressors M2, GDP, and

V. In contrast to De Grauwe and Garibaldi’s paper, the correlation coefficients in this data set are

high; especially, between M2 and its velocity. When M1 and its velocity are used, the correlation

coefficient decrease but is still above 0.5, as we can see in table 2 below.

Table 1. Correlation Matrix

M2

GDP

V

M2

1

-0.47398048

-0.70095324

GDP

-0.47398048

1

-0.013469

V

-0.70095324

-0.013469

1

Table 2. Correlation Matrix

M1

GDP

V

M1

1

-0.35541301

-0.50445011

GDP

-0.35541301

1

-0.01973743

V

-0.50445011

-0.01973743

1

In order to reduce to some extent the collinearity problem, I will use M1 and its velocity in the

subsequent calculations. Table 3 presents the regression results of estimating (5). The explanatory

power of the variables is high considering panel data, but lower than previous studies. Almost

86% of cross-country difference in inflation is explained by the macroeconomic money growth,

output growth, and velocity growth. The coefficient for M1,𝑎 2, is very significant and very close

to one8. This supports the QTM proposition of a proportional relation between exchange rate

changes and money growth. The coefficient of GDP, 𝑎 3, is significantly different from zero and

8 For the coefficient value of 0.9759. See Table 5 for t-statistic of the null that the coefficients are equal to one

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by the negative sign we can see how a higher output growth leads to a lower inflation, for any

given level of (m). By the magnitude of 𝑎 3, we can infer that a 1 percent change in output growth

will result in a 4.3 percent decrease of inflation. Similarly, the coefficient of velocity is significant

and has the expected positive sign; which means that an increase in velocity leads to an increase

in inflation. On the other hand, the proportionality proposition between money growth and

exchange rate is not supported. These results are presented in table 4. In contrast to De Grauwe

and Grimaldi (2001), the explanatory power of the variables is much lower at around 7.3%

compared to their 98.5%. But the most dramatic difference is that one of the M1, 𝑏 2, coefficient.

Table 3. Panel EGLS (Cross-section random effects)

Dependent Variable: GCPI

Sample: 1971 2010

Periods included: 40

Cross-sections included: 22

Total panel (unbalanced) observations: 797

Swamy and Arora estimator of component variances

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

17.20283

7.339647

2.343823

0.0193

GM1

0.975948

0.014898

65.50725

0.0000

GGDP

-4.288590

1.046115

-4.099541

0.0000

GV2

1.736726

0.233020

7.453120

0.0000

Effects Specification

S.D.

Rho

Cross-section random

13.54491

0.0102

Idiosyncratic random

133.1615

0.9898

Weighted Statistics

R-squared

0.852130 Mean dependent var

51.33182

Adjusted R-squared

0.851570 S.D. dependent var

345.8011

S.E. of regression

133.2275 Sum squared resid

14075406

F-statistic

1523.271 Durbin-Watson stat

1.909963

Prob(F-statistic)

0.000000

Unweighted Statistics

R-squared

0.854098 Mean dependent var

60.57034

Sum squared resid

14177116 Durbin-Watson stat

1.896261

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Even though 𝑏 2 is statistically different than zero, we can see that the magnitude of 0.005056 is

far from the expected value of one9. This means that in the long-run money growth has little effect

on the depreciation of the currency. By its small value, I can assume that in the long run money is

very close to be neutral with respect to exchange rate growth rates. Table 4 results also differ from

De Grauwe and Grimaldi (2001) in the sense that the coefficient of the growth rate of GDP, 𝑏 3, is

significant. The negative sign goes along with the expected assumptions of the model that a higher

output growth leads to an appreciation of the currency, for any given level of money growth. The

effect that a change in output growth has over the currency appreciation is less than its effect on

inflation, as can be observed by the magnitude of 𝑏 3. The coefficient for the velocity is not

significant and has a negative sign; which means that an increase in velocity leads to depreciation

in the currency.

Table 4. Panel EGLS (Cross-section random effects)

Dependent Variable: GXR

Sample: 1971 2010

Periods included: 40

Cross-sections included: 22

Total panel (unbalanced) observations: 797

Swamy and Arora estimator of component variances

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

8.550707

1.665368

5.134426

0.0000

GM1

0.004706

0.002509

1.875702

0.0611

GGDP

-1.317803

0.179978

-7.322033

0.0000

GV2

-0.013764

0.038775

-0.354978

0.7227

Effects Specification

S.D.

Rho

Cross-section random

5.685107

0.0621

Idiosyncratic random

22.08857

0.9379

9 See Table 5 for t-statistic of the null that the coefficients are equal to one

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Weighted Statistics

R-squared

0.073204 Mean dependent var

1.617328

Adjusted R-squared

0.069698 S.D. dependent var

22.98924

S.E. of regression

22.16770 Sum squared resid

389685.7

F-statistic

20.87877 Durbin-Watson stat

1.659694

Prob(F-statistic)

0.000000

Unweighted Statistics

R-squared

0.063581 Mean dependent var

2.902323

Sum squared resid

414695.6 Durbin-Watson stat

1.559599

Table 5 present the t-statistic for the null hypothesis that 𝑎 2 and 𝑏 2 are equal to one.

Table 5. T-statistic for the null that M1

coefficients are equal to one (t alpha= 2.33 at 1% level)

Eq. 5

-1.718

Eq. 6

-392.63

As we can see in (5) we can not reject the null that the coefficient of the money growth is

statistically equal to one; while in (6) there is a strong rejection of the null that the coefficient of

M1 is equal to one. Until this point, results support that the QTM and the PPP theory seem to hold

very well for the inflation in the panel data setup of 22 countries over 40 years of data (1971-

2010); while the contrary is true for the exchange rate. In the appendix section, the tables A1 and

A2 show the results for regressions of (5) and (6) using M2 and its velocity respectively. In table

A1, we can see similar results when using M2 instead of M1 as the monetary aggregate. Table A2

results are similar to table 4, but with an even more dramatic contradiction of De Grauwe and

Grimaldi (2001) conclusions on the long-run relation between the exchange rate and money

growth.

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Testing the quantitative importance of the variables

Next I proceed to analyze the quantitative importance of the different regressors in explaining

cross-country differences in inflation over the time period. First, by omitting velocity from the

regression analysis, I want to find the effect of this action on the regression results. Table 6 shows

that the exclusion of velocity from the model has no perceptible effects on the explanatory power

of the equation. The 𝑅 2𝑠 are practically unaffected, in both cases, changing only by decimal points.

The coefficients of money and output continue to be significant and change slightly. It is important

to mention that 𝑎 2 and 𝑏 2 are still very close to one. I also note that the results of estimating the

equations with M2 leads to very similar results; with the difference that in (6) the coefficient is not

longer significant (results not shown).

Table 6. Panel EGLS (Cross-section random effects)

Panel A: Dependent Variable: GCPI

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

21.12122

7.294656

2.895417

0.000390

GM1

0.974729

0.015366

63.44587

0.000000

GGDP

-4.738813

1.072720

-4.426907

0.000000

R-squared

0.842482

Panel B: Dependent Variable: GXR

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

8.497624

1.7047518

4.983606

0.000000

GM1

0.004751

0.002532

1.893657

0.058600

GGDP

-1.313005

0.179659

-7.307673

0.000000

R-squared

0.072887

Now, if the output growth is omitted from the equation, one can evaluate the additional explanatory

power of output in explaining inflation and exchange rates differentials across-countries. Table 7

shows the results of the estimations when output growth is omitted. Results suggest that in the long

run, inflation changes are dominated by money growth (84% of the long-run variation of inflation

is explained by money growth). This is supported by the fact that the 𝑅 2 varies slightly when

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output growth is omitted. On the other hand, as expected from previous estimations above, the

long-run variation of the exchange rates is not affected by money growth.

Table 7. Panel EGLS (Cross-section random effects)

Panel A: Dependent Variable: GCPI

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

GM1

-0.145165

5.463192

-0.026571

0.978800

0.986208

0.015313

64.40385

0.000000

R-squared

0.838842

Panel B: Dependent Variable: GXR

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

2.675458

1.486258

1.800130

0.072200

GM1

0.007612

0.002558

2.975376

0.003000

R-squared

0.010949

Panel C: Dependent Variable: GXR

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

8.878451

1.662695

5.339796

0.000000

GGDP

-1.348816

0.177459

-7.600735

0.000000

R-squared

0.067145

The explanatory power of the model is highly reduced (from 7.2% to 1%) when output growth is

omitted. Moreover, in panel C of table 7, one can see that the long-run variation of the exchange

rates is somewhat explained by output growth (around 7%). From table 7, one can also conclude

that, even when, output growth has a statistically significant effect on inflation, it is not

quantitatively important in explaining cross-country differences in inflation changes. The contrary

is true for the effects of output growth on exchange rate changes in the long-run (it is quantitatively

and statistically significant).

4. Testing the long-run convergence of exchange rates towards its PPP values

In this section I turn the focus towards directly estimating PPP (notice that in previous sections

PPP has been estimated indirectly). Then one can specify the following equation:

𝑒 𝑖 = 𝑐 1 + 𝑐 2𝑝 𝑖 + 𝑧 1 (7)

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Where 𝑝 𝑖 represents the yearly inflation rate of country i during the sample period, and 𝑧 1 is the

error term. It is assume that exchange rate changes and inflation are endogenous variables. Then,

a simultaneity problem arises in estimating (7). Following De Grauwe and Grimaldi (2001) to

correct for this issue, I used the two stages least squares (2SLS) method to estimate (7). Money

growth will be used as the instrumental variable for inflation. Since the exchange rate changes and

the inflation rates are endogenous variables, equation (7) is affected by simultaneity. Therefore we

used a 2SLS procedure and we used the money growth as instrument for inflation10. The results

are presented in the Table 8. Here it is worth mention that when using 2SLS 𝑅 2 lacks its

conventional interpretation11. As a matter of fact, the 𝑅 2obtained in the regression is very small

and negative (actual value not shown).

Table 8. Panel Two-Stage EGLS (Cross-section random effects)

Dependent Variable: GXR

Sample: 1971 2010

Periods included: 40

Cross-sections included: 22

Total panel (unbalanced) observations: 798

Swamy and Arora estimator of component variances

Instrument specification: C GM1

Constant added to instrument list

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

2.657222

1.471078

1.806309

0.0712

GCPI

0.007716

0.002642

2.920146

0.0036

Effects Specification

S.D.

Rho

Cross-section random

5.615210

0.0553

Idiosyncratic random

23.20545

0.9447

10 See Wooldridge (2002), Econometric Analysis of Cross Section and Panel Data for further explanations on 2SLS

and instrumental variables.

11 See Pesaran and Smith (1994) and Pesaran (1999) and Taylor for further details.

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The results of Table 8 are in line with the results in table 4 and panel B in tables 6 and 7. There is

not proportional relation between inflation and exchange rate changes. The coefficient on inflation

is significant but very small (the t-statistic, not presented, reject the null of equality to one). This

implies that in the long run, PPP does not hold; and therefore the links between exchange rate

changes and inflation rates are weak. Moreover, one can say that inflation is close to be neutral in

the long-run. These results are in line with Engel (2000) that argues that the in the long PPP does

not hold after all. On the other hand, these results contrast with previous time series studies on PPP

that found that exchange rates converge to their PPP value over long periods of time (see Cheung

and Lai 2000, Frankel 1981, Kim 1990). Table A3 in the appendix section shows OLS regression

analysis of PPP instead of 2SLS. The results are very much similar to those in table 8, only that

using OLS the coefficient of inflation is very small and negative; contradicting much more PPP

predictions.

Testing the long-run neutrality of Money

As mentioned above, there has been a lot studies testing for one of the main propositions of the

QTM, the long-run neutrality of to money. In this section, I want to analyze this proposition from

a panel data of EME perspective12. To test this proposition, the following equation is estimated:

𝑦 𝑖 = 𝑐 1 + 𝑐 2𝑚 𝑖 + 𝜀 𝑖 (8)

12 See Duck (1993), Nwafor et al. (2007), Wanaset (2009), Mishra et al. (2010), and Ahmed et al. (2011) for

international evidence of the QTM and evidence of specific countries.

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Fall 2016 / Vol. 12 No. 2 / p. 17

and,

𝑣 𝑖 = 𝑑 1 + 𝑑 2𝑚 𝑖 + 𝜗 𝑖 (9)

where 𝑦 𝑖 is the yearly output growth of country i, 𝑣 𝑖 is the yearly growth in velocity,

𝑚 𝑖 represents the yearly money growth and 𝜀 𝑖 and 𝜗 𝑖 are the error terms. Table 9 shows the results

of estimating equations (8) and (9) with OLS.

Table 9. Panel EGLS (Cross-section random effects)

Panel A: Dependent Variable: GGDP

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

4.396378

0.410072

10.72099

0.000000

GM1

-0.002168

0.000484

-4.478137

0.000000

R-squared

0.024552

Panel B: Dependent Variable: GV2

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

1.237093

0.737531

1.677344

0.093900

GM1

-1.94E-05

0.002234

-0.008673

0.993100

R-squared

0.000000

These results support the proposition that the growth of money has no long-run effect on the output

growth or velocity growth; in other words money is neutral. As we can see in table 9, money

growth has very little explanatory power on explaining variation on either output growth or

velocity growth (𝑅 2in panel A and B are very low). The coefficient of money growth, in panel A

although significant, is very close to zero. In panel B the coefficient of money growth in not only

close to zero but insignificant as well. From these results, one can conclude that money is very

close to be neutral in the long-run. In line with the findings of De Grauwe and Grimaldi (2001),

the coefficients in the money growth are negatives. This indicates that an increase in inflation leads

to a decline in output growth. These results go in line with Barros (1995) findings that show that

a negative correlation exists only when high inflation countries are added to the sample.

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Fall 2016 / Vol. 12 No. 2 / p. 18

Conclusions

Following De Grauwe and Grimaldi (2001), this paper intended to analyze the different

propositions of the Quantity Theory of Money and the Purchasing Power Parity theory. This was

done by combining both theories into one theoretical framework. Using a panel data set that

includes 22 EME for a period of 40 years between 1971 and 2010, different regression approaches

were performed. Controlling for cross-countries differences in monetary regimes using random

effects panel data estimations, this paper found evidence to support the long-run proportional

relation between money growth and inflation. The explanatory power of the long run variation of

inflation is mainly explained by the growth rate. Moreover, the growth rate and the growth of

velocity, although, significant have little quantitative effects in the long-run variation of inflation.

On the other hand, no evidence of a proportional relation between money growth and exchange

rates were found. The money growth does not explain any of the long-run variation of changes in

exchange rates, and has not significant effect on this. Output growth somewhat explain some of

this variation. There is not proportional relation between inflation and exchange rate changes. The

PPP theory did not hold in the long run; and there is no evidence that the links between exchange

rate changes and inflation rates are strong. Moreover, one can say that inflation is close to be

neutral in the long-run. When testing for the long-run neutrality of money, strong evidence

supporting this proposition was found. Coefficients of the money growth variable were very close

to zero, providing evidence that in the long-run money is close to be neutral. However, the

coefficients had negative signs; which indicate that in the long-run an increase in inflation leads to

a decline in output growth. All the conclusions in this are somehow supported by previous

literature. Future studies can look for further analyze the institutional cross-country differences.

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Fall 2016 / Vol. 12 No. 2 / p. 19

For example, the regressions can be re-estimated with sub-samples of the data; including in each

subsample countries with common monetary policy regimes. Another idea for future research

would be to test for the long-run relation between money, inflation, output and exchange rates

from a VAR approach.

References

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Fall 2016 / Vol. 12 No. 2 / p. 21

Appendices

A1. Dependent Variable: GCPI

Panel Least Squares

Sample: 1971 2010

Periods included: 40

Cross-sections included: 22

Total panel (unbalanced) observations: 798

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

23.64767

6.964119

3.395644

0.0007

GM2

0.979306

0.016031

61.08768

0.0000

GGDP

-4.686652

1.118792

-4.189028

0.0000

GV

5.517926

0.274479

20.10328

0.0000

Effects Specification

Cross-section fixed (dummy variables)

R-squared

0.857858 Mean dependent var

60.52371

Adjusted R-squared

0.853445 S.D. dependent var

349.1707

S.E. of regression

133.6714 Akaike info criterion

12.65947

Sum squared resid

13811991 Schwarz criterion

12.80616

Log likelihood

-5026.130 Hannan-Quinn criter.

12.71583

F-statistic

194.3844 Durbin-Watson stat

1.710130

Prob(F-statistic)

0.000000

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A2. Dependent Variable: GXR

Panel EGLS (Cross-section random effects)

Date: 01/08/12 Time: 21:26

Sample: 1971 2010

Periods included: 40

Cross-sections included: 22

Total panel (unbalanced) observations: 798

Swamy and Arora estimator of component variances

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

9.041025

1.716649

5.266669

0.0000

GM2

-0.000239

0.002625

-0.091165

0.9274

GGDP

-1.370188

0.180563

-7.588437

0.0000

GV

-0.002747

0.045358

-0.060567

0.9517

Effects Specification

S.D.

Rho

Cross-section random

6.002111

0.0684

Idiosyncratic random

22.14580

0.9316

Weighted Statistics

R-squared

0.068759 Mean dependent var

1.549246

Adjusted R-squared

0.065240 S.D. dependent var

22.96213

S.E. of regression

22.19458 Sum squared resid

391123.8

F-statistic

19.54182 Durbin-Watson stat

1.708030

Prob(F-statistic)

0.000000

Unweighted Statistics

R-squared

0.060324 Mean dependent var

2.879279

Sum squared resid

416455.4 Durbin-Watson stat

1.604136

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Panel EGLS (Cross-section random effects)

Dependent Variable: GXR

Sample: 1971 2010

Periods included: 40

Cross-sections included: 22

Total panel (unbalanced) observations: 800

Swamy and Arora estimator of component variances

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

3.231885

1.469442

2.199396

0.0281

GCPI

-0.002333

0.002387

-0.977177

0.3288

Effects Specification

S.D.

Rho

Cross-section random

5.648717

0.0572

Idiosyncratic random

22.93624

0.9428

Weighted Statistics

R-squared

0.001190 Mean dependent var

1.629247

Adjusted R-squared

-0.000061 S.D. dependent var

22.98865

S.E. of regression

22.98318 Sum squared resid

421524.7

F-statistic

0.950979 Durbin-Watson stat

1.683011

Prob(F-statistic)

0.329766

Unweighted Statistics

R-squared

0.001542 Mean dependent var

2.837609

Sum squared resid

443211.3 Durbin-Watson stat

1.600660