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Testing the Kumara Swamy Theorem of Inflationary Gap: empirical evidence from Canada.


This paper empirically tests the Kumara Swamy Theorem of Inflationary Gap for Canada over the period 1997-2011 and compares the results with Lazaridis and Livanis (2010) for the Greek and Cypriot economies. While this paper finds favorable results in the direction of the hypothesis, it demonstrates weak support for the postulated magnitude but concedes that there were confounding factors over the testing period. The paper concludes with suggestions for further extensive research to test the Theorem further.

Keywords: Inflationary Gap; Canada; Confounding factors

JEL Classification : C82, E31, E52, E58


Financial economists have long postulated about the relationship between various economic variables, such as the level of economic activity (often as evidenced by growth in GNP), growth of the money supply and, of course, the most persistent problem that has plagued many economies since the 1960s, inflation. In order to explain the relationship between these variables, Professor M.R Kumara Swamy proposed the unique and well-researched Kumara Swamy Theorem of Inflationary Gap in his convocation lecture on Inflation and Economic Development of Nigeria delivered at the Institute of Management and Technology, Enugu, Nigeria on March 3, 1978. This Theorem states (2).

The growth of the money supply in a country must be twice the growth of real output to maintain price stability. Thus the difference between money supply and real output is the actual inflationary gap, while the permissible inflationary gap is the difference between real output and double (permissible) money supply. The excess of the actual gap over the permissible gap is referred to as the excess inflationary gap caused by non-economic development factors like maintenance of unproductive enterprises (non-performing assets) and we may add corruption and fraud premiums (Swamy (1,2)).

This Theorem was successfully tested for the Nigerian economy by Professor Swamy : 1984 (1), 2009 (2). Lazaridis and Livanis tested the Theorem (3) outside the developing world in Europe during the ongoing international financial crisis. The Euro zone economies are expected to grow at significantly lower rates over the foreseeable future, given the non-resolution of significant economic events that are expected to persist beyond 2012. Inflation has accelerated internationally due to the persistence of high oil prices and increases in food prices fueled by these high oil prices and shortages of several foodstuffs for a variety of reasons, notably growth in population, increased consumption by emerging middle classes in China and India, and drought conditions in Africa and North America during 2012. Lazaridis and Livanis investigated the Kumara Swamy Theorem of Inflationary Gap for the Cypriot and Greek economies over the period 2004-2009 and found favorable results (3).

While the Cypriot and Greek economies are strongly interrelated and both are members of the European Union, only Greece is a member of the 34 countries within the Organization for Economic Cooperation and Development (OECD). Neither country is a G 8 member. Accordingly, the favorable results that have been obtained for the Kumara Swamy Theorem of Inflationary Gap in Nigeria, Cyprus and Greece may not be reflected in more developed and larger economies, such as Canada which is both an OECD and G 8 nation.


Though many financial economists have produced various explanations for the often sharp increase in prices and mounting budgetary deficits, their efforts have not fully captured all the effects within either cost push or demand pull regimes of inflation. Often policy makers in developed western economies tend to be centered in either political capitals, such as Washington, D.C. in the U.S.A. or in financial capitals, such as New York or Chicago. These policy makers will quickly categorize developing countries as inflationary owing to changes in both core and non-core inflation, but without reference to the source and conditions of the inflation, thereby providing limited use in explaining the actual capital market conditions of countries experiencing various types of inflation. Politicians and sociologists designate these countries as experiencing stagflation (simultaneously observing both high and persistent levels of inflation and unemployment that are significantly in excess of natural unemployment and not explained by either structural or frictional unemployment). Swamy demonstrates that financial managers designate those countries as 'sorry-no-money' economies.

Previous research has focused on explaining the effects of inflation (such as expected, uncertain, actual, and unexpected) on security prices, rates of return and the level of economic activity. Faseruk, Roubi and Barth (4) along with Swamy (5) have contended that chronic high levels of inflation began to haunt markets in the late 1960s persisting through most of the 1970s with its effects still being felt today. In many instances the persistence of inflation is exacerbated by policy makers that enact policies designed to control core inflation without adequate knowledge of the permissible inflationary gap and the excess inflationary gap, demonstrated in the Kumara Swamy Theorem of Inflationary Gap (Swamy (6&7)).

Consequently, it is important to have a model that both explains the nature of the inflation in terms of the permissible inflationary gap and excess inflationary gap, as well as outlining the need to have the growth in the money supply outpace the growth of real GNP to maintain price stability and measure the rational size of the inflationary gap as determined by establishing a synchronized correlation between the growth of real GNP and the money supply. All these antecedent conditions were cogently articulated into a concise testable model referred to as the Kumara Swamy Theorem of Inflationary Gap which succinctly states (Swamy (1&2)).
   The growth of money supply of a country must be twice
   the growth of real GNP to maintain price stability, and the
   rational size of inflationary gap is determined by
   establishing a synchronized correlation between the growth
   of real GNP and money supply.

Testing of Kumara Swamy Theorem for the Canadian Economy

The purpose of this study is to test the Kumara Swamy Theorem of Inflationary Gap in the Canadian economy over the period January 1, 1997 to December 31, 2011.

* Data Collection and Methodology Used

The data used in this study comprise annual figures for the Canadian Money Supply, Gross National Product, and Consumer Price Index spanning the 15-year period January 1, 1997 through December 31, 2011. The data were obtained from Statistics Canada's CANSIM database. Statistics Canada was formed as the Dominion Bureau of Statistics in 1918 and assumed its current name in 1971. Both The Economist and Public Policy Forum have consistently commented on the high quality of the data collected by Statistics Canada and have on occasion ranked these data as the best in the world. The particular data used in this study are as follows:

* Actual Money Supply

CANSIM Table 176-0020, column M1+ (gross): Currency outside banks plus personal and non-personal chequable deposits held at chartered banks plus all chequable deposits at trust and mortgage loan companies, credit unions/caisses populaires (excluding deposits of these institutions) plus continuity adjustments. A caisse populaire is simply the name used for a credit union in the French-speaking areas of Canada. These organizations are owned by their members in order to provide affordable banking services and loans to their members. The majority of the money supply in Canada is, however, in the form of cash or chequable deposits in the largely oligopolistic chartered banking system which discharges the monetary policy as articulated by the Bank of Canada, Canada's central bank. Chequable deposits in Canada are largely non-interest bearing.

* Gross National Product

CANSIM Table 380-0030, column Gross National Product (GNP) at market prices. The nominal values were converted to their real equivalent using the prevailing Consumer Price Index.

* Consumer Price Index

CANSIM Table 326-0020, column Core Consumer Price Index (CPI) (Bank of Canada definition): The Bank of Canada's core index excludes eight of the Consumer Price Index's most volatile components (fruit, fruit preparations and nuts; vegetables and vegetable preparations; mortgage interest cost; natural gas; fuel oil and other fuels; gasoline; inter-city transportation; and tobacco products and smokers' supplies), as well as the effects of changes in indirect taxes on the remaining components.

Research Findings

In referring to the Table for the Canadian economy over the period 1997-2011, the average growth of the money supply was 9.02 per cent, while the average growth rate of real GNP was 3.27 per cent. Accordingly, the average annual growth in the money supply is 2.76 times the average annual growth of real GNP, which is more than the two times postulated in the Theorem. It should also be noted that the money supply did not contract over the period under observation. Only in 2009 did the Canadian economy exhibit negative economic growth at -6.3 per cent. This year reflects the meltdown, which occurred in North American markets following the collapse of the sub-prime mortgage market. It is also interesting to note that Canada did not experience a recession owing to the meltdown surrounding the bursting of the high tech ( bubble in 2000 although economic growth slowed to 1.0 per cent and 1.6 per cent in 2001 and 2002, respectively, before returning to the more normal economic expansion of 3.2 per cent nearly matching the long-run average of 3.27 per cent.

It is essential to realize that the policy objective of the Bank of Canada is to have moderate but consistent economic growth approximating 3.0 per cent per annum while maintaining inflation within a band of 1-3 per cent, most preferably at the midpoint of the band. Given these guidelines for the Canadian economy and the various macroeconomic indicators outlined previously, it is not surprising that the average actual inflationary gap over the period 1997 to 2011 stood at 5.75 per cent, while the permissible inflationary gap was 3.27 per cent resulting in an excess inflationary gap of 2.47 per cent.

For the Cypriot economy, Lazaridis and Livanis found that the average actual inflationary gap was 15.74 per cent, while the average permissible inflationary gap was 4.62 per cent resulting in an excess inflationary gap of 11.13 per cent. From the seminal work of Swamy on the Nigerian economy, his cogent caveat is that "excessive money supply growth should be checked." Given the data for Canada and Cyprus, it would appear that Canada's levels are well within the established Bank of Canada policies whereas Cyprus should be checked, particularly since, following the time period of 2004-2007 used in the study of Lazaridis and Livanis (3), Cyprus was preparing for entry into the Euro zone on January 1, 2008. Following the admission to the Euro zone in 2008-2009, the average actual inflationary gap was 3.39 per cent, while the average permissible inflationary gap was 3.15 per cent and so the excess inflationary gap was negligible at 0.24 per cent The Canadian data exhibited greater variability in the excess inflationary gap with a range of 30.6 per cent from a low of -4.9 per cent in 2000 to a high of 25.7 per cent in 2009.

A visual of the movements in the excess inflationary gap is portrayed in the Figure. Adjacent year swings can be quite pronounced, as evidenced by steep increases in 2000-2001 (-4.9 per cent to 10.2 per cent) and in 2008-2009 (8.1 per cent to 25.7 per cent). Subsequently, the data can also show steep declines in 2001-2002 from 10.2 per cent to 2.9 per cent and in 2009-2010 from 25.7 per cent to 0.1 per cent. While the excess inflationary data can be negative, as it was in Canada for seven years [1998, 1999, 2000, 2003, 2004, 2005 and 2007], only in three years [1999, 2000 and 2005] of the 15 years in the dataset was it less than -1.0.

These observations are in contrast to the Greek experience reported over 2004-2009 in Lazaridis and Livanis (3), when the Greek economy demonstrated negative excess inflationary gaps in three of the six years under review. Significant negative observations were witnessed during 2006, 2007 and 2008 at -6.59 per cent, -9.40 per cent and -6.98 per cent, respectively. The authors demonstrate that these significantly negative inflationary gaps had disappeared by 2009 with a return to stagflation in the Greek economy as the inflationary gap had again become positive and was trending upward. Given the unfolding debt crisis and intervention by outside agencies including the International Monetary Fund, there is the potential for the Greek economy to enter into a prolonged economic recession. Stagflation as an explanatory part of the Kumara Swamy Theorem of Inflationary Gap was demonstrated by Swamy (3).

The Canadian data demonstrated elasticity in upward movements of the excess inflationary gap but was not as elastic in downward movements. From the Figure, it can be seen that the positive observations of the excess inflationary gap dominates the negative observations in only two years, 2001 (non-recessionary) and 2009 (a recession that quickly disappeared). Therefore, stagflation over this time period was not a concern for the Canadian economy. Although negative observations occurred in seven of the 15 years, only in three of these are they more significant than -1 per cent. An interesting observation is that there are two runs of three years when a monotonically decreasing function is observed, between 1998-2000 and 2003-2005. Canada only experienced one year of negative economic growth which was outside these two runs. This contraction in the Canadian economy occurred in 2009 and while the excess inflationary gap was high at 25.7 per cent, it quickly reverted to 0.1 per cent in the following year. Hence, stagflation is not tenable as an explanatory argument for the Canadian economy. Moreover, the value of the Canadian dollar and the economy are tied to other market forces, primarily movements in the U.S. dollar and the price of oil as Canada is the largest supplier of oil to the U.S.A. with the implication that the Canadian economy, its growth rate and inflation are tied to the U.S. economy and the price of oil. They are not tied as much to the value of the Euro and the requirements of the International Monetary Fund as are Greece and Cyprus.

Conclusions and Prospects for Future Research

For Canada, the Kumara Swamy Theorem of Inflationary Gap has provided limited explanatory power for the relationship between the growth of the money supply and real GNP. The growth rate in the actual money supply was on average 9.02 per cent, with the real GNP growing at an average annual rate of 3.27 per cent, meaning that the relationship was on average 2.76 times. This observation is higher than the two times relationship postulated in the Theorem. In some years it was almost exactly double, such as 1998 and 2010, but the intervention of central bank authorities and government policy makers over this 15-year sample period may be confounding the testing of the Kumara Swamy Theorem of the Inflationary Gap. Additional research is clearly needed.



One of the most extreme observations from the Table is in 2001 when the actual money supply increased by 12.2 per cent and the real GNP by 1.0 per cent but that time frame may not be representative of the markets, as Alan Greenspan, then Chair of the Federal Reserve of the U.S.A., cut interest rates 11 times to attempt to hold off a recession by excessive use of monetary policy. This trend of lower interest rates is also currently being undertaken by current Chairman of the U.S. Federal Reserve Board Bernanke in the quantitative easing policies of the U.S. Federal Reserve. Swamy criticized Fama (8) for a monetarist bias which can also be witnessed in the policies of the U.S. Federal Reserve. In order to correct for the bias, the Kumara Swamy Theorem of Inflationary Gap on Canada needs to be retested with American data used alongside Canadian data. Moreover, as these economies are now integrated to a large extent with Mexico, the appropriate test for the model should include these three countries of the North American Free Trade Association (NAFTA).

This subsequent study will be fruitful additional research for two important reasons: first, it will allow enhanced data to provide a more accurate testing of the Kumara Swamy Theorem of Inflationary Gap; and, second it will use more than one country in a trading block in order to facilitate additional insights and comparisons with Lazaridis and Livanis (3).

The authors own full responsibility for the contents of the paper.


(1.) Swamy, M.R.K., A Financial Management Analysis of the Nigerian Economic Situation, Nigerian Journal of Financial Management (December 1982)

(2.) Swamy, M.R.K., Empirical Testing of the Kumara Swamy Theorem on Inflationary Gap: Nigerian Economy in Perspective, Journal of Financial Management and Analysis (1: 2009)

(3.) Lazaridis, I.T. and Livanis, E.S., Testing the Kumara Theorem of Inflationary Gap in the Cypriot and Greek Economies-Research Findings, Journal of Financial Management and Analysis (1: 2010)

(4.) Faseruk, A., RRoubi, R. and Barth, R., Does Inflation Influence Equity Risk Premiums? A Methodological Analysis, Journal of Financial Management and Analysis (2: 1993)

(5.) Swamy, M.R.K., A Financial Analysis of Prudent Management of Investment Cycle and Inflationary Gap: Empirical Evidence, Journal of Financial Management and Analysis (2: 1993)

(6.) Swamy, M.R.K., Focus on Functional Relationship Between Technology Gap and Poverty Gap: Financial Management Considerations for Developing Countries, Journal of Financial Management and Analysis (2: 1988)

(7.) Swamy, M.R.K., Financial Management Analysis of Inflationary Gap and Agricultural Loan Administration: Empirical Evidence from a Developing Country, Journal of Financial Management and Analysis (2: 1989)

(8.) Fama, E., Stock Returns, Real Activity, Inflation and Money, American Economic Review (5: 1981)


Associate Dean


Professor ALEX FASERUK, Ph.D.

Professor (Finance)


Faculty of Business Administration

Memorial University

St. John's, NL, CANADA A1B 3X5

                                1997   1998   1999   2000   2001   2002

Actual Money Supply             10.1   4.0    7.8    12.4   12.2   6.1
Real GNP                        4.4    2.1    5.8    8.6    1.0    1.6
Actual Inflationary Gap         5.7    1.9    2.0    3.7    11.2   4.5

Permissible Money Supply        8.8    4.3    11.7   17.3   2.0    3.2
Real GNP                        4.4    2.1    5.8    8.6    1.0    1.6
Permissible Inflationary Gap    4.4    2.1    5.8    8.6    1.0    1.6

Excess Inflationary Gap         1.4    -0.3   -3.8   -4.9   10.2   2.9

                                2003   2004   2005   2006   2007   2008

Actual Money Supply             5.7    9.0    6.4    10.2   7.0    13.0
Real GNP                        3.2    4.9    5.0    4.4    3.6    2.4
Actual Inflationary Gap         2.5    4.0    1.4    5.9    3.4    10.6

Permissible Money Supply        6.5    9.8    10.0   8.7    7.2    4.8
Real GNP                        3.2    4.9    5.0    4.4    3.6    2.4
Permissible Inflationary Gap    3.2    4.9    5.0    4.4    3.6    2.4

Excess Inflationary Gap         -0.7   -0.9   -3.6   1.5    -0.3   8.1

                                2009    2010   2011

Actual Money Supply             13.0    9.1    9.3
Real GNP                        -6.3    4.5    3.8
Actual Inflationary Gap         19.4    4.6    5.4

Permissible Money Supply        -12.7   9.0    7.6
Real GNP                        -0.3    4.5    3.8
Permissible Inflationary Gap    -6.3    4.5    3.8

Excess Inflationary Gap         25.7    0.1    1.6

Note: The first panel of the Table shows the actual inflationary gap,
defined as the difference between the actual money supply (Ml) and
real GNP. The second panel of the Table shows the permissible
inflationary gap under the 'Kumara Swamy Theorem of Inflationary Gap:
The Growth of Money Supply in a Country Must be Twice the Growth of
Real Output to Maintain Price Stability'. Hence, by construction, the
permissible money supply is twice the real GNP. The third panel of
the Table shows the excess inflationary gap, which is the difference
between the actual inflationary gap and the permissible inflationary
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Author:Bauer, Lawrence; Faseruk, Alex
Publication:Journal of Financial Management & Analysis
Article Type:Report
Date:Jan 1, 2012
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