Financial management indicators to aid decision making (statistics).
A. TESTING OF THE KUMARA SWAMY THEOREM OF INFLATIONARY GAP IN SELECTED COUNTRIES AND TRADE BLOCS
(by Bauer, Faseruk, Glew, Lazaridis, Livanis, Swamy) *
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, viz., inflation. In order to explain the relationship between these variables, Professor M.R Kumara Swarny 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.
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 inflationary gap caused non-economic development factors like maintenance of unproductive enterprises (non-performing assets) and we may add corruption and fraud premiums (1).
This Theorem was successfully tested for the Nigerian economy by Professor Swamy: 1984, Lazaridis and Livanis tested the Theorem outside developing world in Europe during-the ongoing international financial crisis. Inflation has accelerated internationally due to 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 middile 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 favourable results and Swamy tested for the Nigerian economy.
FUNCTIONAL RELATIONSHIP BETWEEN THE KUMARA SWAMY MEASURE OF EXCESS INFLATIONARY GAP AND PRICES: CYPRUS
[FIGURE 1 OMITTED]
Cyprus: We can see that during the period 2004-2007 the excess inflationary gap exceeds consumer prices growth indicating stagflation for cypriot economy.
FUNCTIONAL RELATIONSHIP BETWEEN THE KLMARA SWAMY MEASURE OF EXCESS INFLATIONARY CAP AND PRICES: GREECE
[FIGURE 2 OMITTED]
GREECE : On the other hand, the results for the Greek economy are mixed. As we can see from the above table during the period 2004-2005 the average actual inflationary gap was 8.53 per cent while the average permissible inflationary gap was 2.58 per cent creating an excess inflationary gap (5.95 per cent). For the period 2006-2008 the average actual Inflationary gap was -4.77 per cent while the average permissible inflationary gap was 2.88 per cent. Finally, for the last year (2009) the actual inflationary gap was 10.73 per cent while the permissible Inflationary gap was-1.37 per cent creating an excess inflationary gap (12.10 per cent). According to the above results the excessive money supply growth needed to be checked for the years 2004, 2005 and 2009.
For the Greek economy stagflation is indicated only for 2004-2005. From 2009 the Greek economy seems to be facing again stagflation. Actually, Greece has entered into deep economic recession, reducing productivity, increasing unemployment and continuing inc.rease in prices of most products and services. Tackling stagflation seems difficult as Greece is obliged from International Monetary Fund to take tough economic measures.
MEXICO: INFLATIONARY GAP (PERMISSIBLE AND ACTUAL): EXCESS / INFLATIONARY GAP
[FIGURE 3 OMITTED]
Mexico : The average actual inflationary gap for Mexico over the testing period is 11.99 per cent with the permissible inflationary gap at 5.01 per cent. The excess inflationary gap was negative in only five of the 15 years, which were 2000, 2003, 2004, 2006 and 201 1. The only year in which a negative excess inflationary gap was exhibited for all three countries was in : 2000, which was undoubtedly a result of the meltdown in the exchanges and the economy that resulted from the dot.com bubble bursting. It is again demonstrated that the excess inflationary gaps demonstrate elasticity and can be subject to great swings, such as 24 per cent between 1999 and 2000, 35.7 per cent between 2000 and 2001 and-25.8 per cent between 2002 and 2003.
EXCESS INFLATIONARY GAP UNDER THE KUMARA SWA MY THEOREM OF INFLATIONARY GAP: CANADA
[FIGURE 4 OMITTED]
CANADA : 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 theimplication 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.
U.S.A.: EXCESS/INFLATIONARY GAP
[FIGURE 5 OMITTED]
U.S.A. : In referring to Table for the U.S. economy over the period 1997-2011, the average growth rate of the money supply was 5.04 per cent, while the average rate of real G.N.P. growth was 2.1 per cent. Accordingly, the average annual growth in the money supply is 2.39 times the average annual growth of real G.N.P. While this figure is more than the two times postulated in the theorem, it is closer than the 2.76 figure exhibited by the Canadian economy. Moreover, if the 2011 figures are omitted from the study the results would be more in line with what was postulated in the Theorem. The U.S. money supply grew by 34.6 per cent in 2011 owing to another round of the Federal Reserve's policy of Quantitative Easing. This 34.4 per cent is highly anomalous and is tied to a loose money policy enacted by the Federal Reserve. The actual long-term inflationary gap was 2.93 per cent which is in line with the permissible inflationary gap of 2.1 per cent. The excess inflationary gap for the testing period was a very low 0.85 per cent. However, averages are not the sole measure of the trend. In II of the 14 years in the study, the excess inflationary gap is negative. Positive amounts are exhibited in 2003, 2008, and 2011. From a visual inspection of the data provided in, it is clear that the results can be quite elastic and exhibit great volatility: particularly in the latter part of the series from 2008-201 1. In 2008 the excess inflationary gap had increased by 9.1 per cent from the previous year and then exhibited another 14.2 per cent increase in 2009 (or 23.1 per cent in two years) only to decrease 25.8 per cent in 2010. The largest year-to-year increase at 36.3 per cent was realized in 201 1. Notwithstanding these volatile movements in the data, the highly cogent and well-thought out Kumara Swamy Theorem of Inflationary Gap has proven to be quite robust in testing on the U.S. economy. In comparing the Canadian and U.S., results together, the Theorem is upheld viti respect to the direction but not the magnitude.
G-8/G-20 COUNTRIES : Includes the annual excess inflationary gaps for the G-20 nations calculated as described previously. It is separated into three panels to simplify comparisons between countries. The first panel contains the G-7 countries, which have been holding economic summits since 1976. Russia is included with other developing nations known by the acronym 'BRICS' in the second panel to even out the number of countries in each panel and the corresponding figures that follow. The third panel contains the remaining nations, which form a rather diverse group of countries. This separation is the most convenient and allows more detailed comparisons within the sub-groups.
All G-7 countries exhibit an extreme positive excess inflationary gap resulting from negative GNI growth in 2009, related to the financial crisis in that year. For most of these countries, the rise begins a year earlier providing combined excesses near 30 per cent (15 per cent annually over two years). Japan and France demonstrate the least effect. The more interesting result in this case arises from examining the rest of the 0-20 nations. Brazil, South Africa, Australia, and Indonesia indicate negligible gap in 2009 that suggests some buffering of the crisis effect south of the equator. India and Argentina have increases in the excess inflationary gap to levels comparable to Japan and France, but at their inflation rates these may be considered insignificant increases. These six countries and China sustained positive GNI growth during 2009.
* NAFTA, G-20 & EUROPEAN UNION COMPOSITE COUNTRIES
The recent EU members that have not adopted the Euro follow in succession with average excess inflationary gaps less than 10 per cent but above the average rates of inflation. Finally, the recent EU members that also joined the Eurozone are included alongside the emerging G-20 countries that have suffered through crises. Argentina, Russia, South Korea, and Turkey experienced financial difficulties near the beginning of our time series. The Eurozone countries of Ireland and Cyprus have both suffered from financial crisis that was worsened by the adoption of the Euro. Within the G-20, South Korea and Turkey entered into crisis associated with fixed (pegged) exchange rates and these nations appear low in the table alongside recent EU members that have adopted the Euro as currency. With such economic unrest, agreement with the Kumara Swamy Theorem of Inflationary Gap cannot be expected.
[FIGURE 6 OMITTED]
All countries are ranked using the measure of excess inflationary gap and identified by the major groups and sub-groupings. The NAFTA countries are near the top of the table with results just higher than the Scandinavian countries, relating to small changes in the money supply when compared to economic output, as measured by GNI. The established European Union members fall below the NAFTA countries as expected: per capita resource wealth is higher, public expenditure is lower, and unemployment is lower. The majority of the G-20 countries have higher excess inflationary gaps than the NAFTA members. As might be expected, to the robustness of each country's economy. As with the previous work, negative productive output relating to the global financial crisis resulted in a large excess inflationary gap in 2009 for all countries studied except Bulgaria, Cyprus, and Romania, which had lagged responses to the event. This atypical year forced all averages upwards and suggested that the permissible gap could act as a minimum bound in uncertain economic times. As the countries in this combined dataset were in various stages of crisis and recovery, including austerity, during the sample period, it is difficult to provide a more detailed analysis at this juncture. It suffices to state that the Kumara Swamy Theorem of Inflationary Gap provided an excellent method for cross-country and cross-continent comparison despite the period of relative economic turmoil.
For the U.S.A., Canada and Mexico the Kumara Swamy Theorem of Inflationary Gap has provided notable explanatory power for the relationship between the growth of the money supply and real G.N.P. The growth rate in the actual money supply was on average 5.04 per cent for the U.S.A., 9.02 per cent for Canada, and 16.99 per cent for Mexico. When the rate of real G.N.P. growth is factored in for the three countries at 2.10 per cent, 3.27 per cent and 5.01 per cent the ratio of actual money supply growth to real G.N.P. growth is 2.39 times, 2.76 times and 3.39 times for the U.S.A., Canada and Mexico, respectively. All three of these observations are higher than the two times relationship postulated in the theorem. In some years the relationship is negative while in other years it can be quite extreme such as in 2011 for the U.S.A., wherein a 34.6 times ratio was noted.
TABLE 1 Indicator Year 2004 2005 2006 2009 (A) Excess inflationary Gap (in %) 16.18 3.98 15.68 0.39 (B) How consumer prices have risen (% variation over previous year indicated) 2.30 2.60 2.50 0.30 (C) Variation/Deviation from (%) 13.88 1.38 13.18 0.09 (A-B) Source : Consumer prices growth are from Statistical Service of Cyprus. The base year for the evolution of the annual rates of change of the Overall Consumer Price Index is 2005. TABLE 2 Year Indicator 2004 2005 2007 2009 (A) Excess inflationary Gap (in %) 5.25 6.65 -9.40 12.10 (B) How consumer prices have risen (% variation over previous year indicated) 2.90 3.50 2.90 1.20 (C) Variation/Deviation from (A) (A-B) 2.35 3.15 -12.30 10.90 Source: Consumer prices growth are from Hellenic Statistical Authority. The base year for the evolution of the annual rates of change of the Overall Consumer Price Index is 2005. TABLE 3 Indicator 1997 2000 2003 2006 2009 2011 Actual Inflationaty Gap 24.4 5.0 -0.7 7.0 16.3 5.5 Permissible Inflationary Gap 5.3 9.2 15.5 8.0 -7.2 8.3 Excess Inflationary Gap 19.1 -4.3 -16.2 -1.0 23.5 -2.8 TABLE 4 Indicator 1997 2002 2007 2011 Actual Inflationaty Gap 5.7 4.5 3.4 5.4 Permissible Inflationary Gap 4.4 1.6 3.6 3.8 Excess Inflationary Gap 1.4 2.9 -0.3 1.6 TABLE 5 Indicator 1997 2002 2007 2010 2011 Actual Inflationary Gap -3.8 -0.1 -0.5 -0.4 33.6 Permissible Inflationary Gap 4.3 1.0 0.6 3.2 1.0 Excess Inflationary Gap -8.1 -1.2 -1.1 -3.6 32.7 TABLE 6 EXCESS INFLATIONARY GAP IN GROUP OF TWENTY NATIONS (%) G-7 2000 2001 2002 2003 2004 2005 2006 Canada -2.7 11.9 1.9 0.6 -0.7 -2.2 1.4 France 0.5 2.3 7.9 15.2 1.1 6.7 0.7 Germany 0.7 3.1 13.3 8.5 0.7 11.0 -1.2 Italy 0.3 1.7 5.7 6.2 2.4 6.5 3.0 Japan -0.1 3.4 22.9 18.2 1.8 3.8 -1.5 U.K. 4.5 4.8 -2.2 -0.6 3.4 5.5 6.6 U.S.A. -12.7 -0.5 -1.2 3.4 -1.7 -7.1 -8.8 BRICS Brazil 11.1 6.8 19.8 0.6 3.5 5.8 7.8 Russia 13.8 32.1 18.1 32.9 -4.0 11.1 19.0 India 3.9 0.7 5.6 0.3 0.4 0.4 0.2 China -5.7 -5.8 -7.2 -5.9 -13.3 -14.4 -13.8 South Africa -12.7 -41.8 0.5 6.4 -9.1 5.2 0.3 Others Argentina -11.5 -10.8 102 37.4 1.4 5.0 -14.1 Australia 4.7 9.0 22.4 3.6 -3.0 3.1 2.9 Indonesia -2.6 35.0 10.0 -12.8 0.7 -5.9 7.2 Mexico -4.3 31.4 9.6 -16.2 -8.3 9.5 -1.0 Saudi Arabia -27.5 13.1 6.8 -15.0 -24.8 -47.4 -15.5 South Korea -18.4 356 -4.3 2.8 -7.5 10.1 3.5 Turkey 55.4 84.5 151 14.8 1.0 61.0 -1.0 G-7 2007 2008 2009 2010 2011 2012 Canada 1.1 8.2 23.4 0.7 3.7 -3.5 France -0.2 1.5 11.2 4.6 4.1 2.6 Germany -0.5 9.2 24.1 1.0 2.1 11.5 Italy -0.3 13.7 17.5 -2.0 1.1 7.7 Japan -2.9 6.2 11.9 -2.6 9.6 0.1 U.K. 2.5 15.7 13.8 4.3 1.0 6.5 U.S.A. -1.1 8.0 24.7 -4.2 32.7 4.6 BRICS Brazil 16.1 -19.0 7.6 -8.8 -4.4 11.7 Russia 8.0 -17.1 42.3 12.7 -4.5 -1.8 India -4.1 3.5 10.2 3.4 -5.1 2.6 China -14.6 -14.7 15.1 -6.3 -15.4 -7.2 South Africa 8.7 3.6 -0.7 -0.6 0.6 7.1 Others Argentina 6.7 -28.3 10.4 2.3 -8.5 34.9 Australia 7.5 4.9 -6.9 8.4 -8.2 1.3 Indonesia 3.5 -23.9 -3.8 -4.1 -0.8 4.1 Mexico 3.1 5.6 23.5 3.4 -2.8 5.8 Saudi Arabia 12.2 -17.2 65.0 -11.6 -18.8 -- South Korea -13.6 2.2 16.4 -3.5 0.6 4.1 Turkey 2.2 4.5 35.4 8.6 -7.1 7.6 TABLE 7 COMPARISION OF NAFTA, G-20 AND EUROPEAN UNION COUNTRIES Average Excess Average Range Country Inflationary Inflation Group Sub-Group Gap (%) (%) <0 China -8.39 2.29 G-20 BRICS Saudi Arabia -6.72 2.69 G-20 South Africa -2.50 5.86 G-20 BRICS Norway -2.16 2.05 EU Scandinavia 0-3 Indonesia 0.52 7.64 G-20 India 1.71 6.60 G-20 BRICS Greece 2.29 3.30 EU PIGS Sweden 2.36 1.58 EU Scandinavia Finland 2.59 1.85 EU/Euro Scandinavia U.S.A. 2.79 2.51 G-20/NAFTA G-7 Portugal 2.80 2.59 EU PIGS 3-5 Netherlands 3.17 2.07 EU Established Canada 3.37 2.10 G-20/NAFTA G-7 Belgium 3.54 2.24 EU Established Australia 3.83 3.05 G-20 France 4.49 1.77 G-20/EU G-7 Brazil 4.50 6.61 G-20 BRICS Mexico 4.56 4.91 G-20/NAFTA Austria 4.75 2.08 EU Established Italy 4.88 2.31 G-20/NAFTA G-7 5-7 U.K. 5.07 2.24 G-20/EU G-7 Luxembourg 5.21 2.42 EU Established Japan 5.44 -0.27 G-20 G-7 Germany 6.42 1.62 G-20/EU G-7 7-10 Spain 7.18 2.89 EU PIGS Hungary 7.38 5.84 EU Recent, non-Euro Latvia 7.60 5.15 EU Recent, non-Euro Lithuania 7.67 2.98 EU Recent, non-Euro Poland 8.92 3.54 EU Recent, non-Euro Bulgaria 8.95 6.20 EU Recent, non-Euro Argentina 9.75 8.93 G-20 Slovakia 9.97 4.99 EU Recent, Euro 10-20 Estonia 12.28 4.26 EU Recent, Euro Russia 12.51 12.31 G-20 G-8, BRICS Ireland 14.62 2.77 EU PIGS Iceland 17.86 5.98 EU >20 Slovenia 22.28 4.39 EU Recent, Euro South Korea 26.81 3.10 G-20 Turkey 32.14 20.02 G-20 Cyprus 39.35 2.79 EU Recent, Euro Malta 45.01 2.43 EU Recent,
B. NATURE OF DISTORTIONS CAUSED BY A INFLATION : ANALYSIS OF SELECTED FIRMS IN TURKEY--METHODOLOGICAL ANALYSIS
(Analysis by G. meric & I. Meric *)
As this study has wider applications for examining the functional relationship between the level of investment --related tax shields and the levels of debt-related tax shields at the firm level, the authors have also undertaken an empirical study of 166 firms from 20 four-digit SIC code industries and : Data-for the 1973-75 and 1983-85 time periods--used in the analysis were drawn from the annual COMPUSTAT industrial lapes. Our firm-level tests to test the De Anglelo-Masulis Tax Shield Hypothesis using a methodology that differs from those, yielded two matrices of 60 Spearman rank correlation coefficients between the investment-related and debt-related tax shield measures for the two time periods, of which 90 per cent indicate a positive correlation between the investment-related and debt--related tax shields levels. An analysis utilizing both historical-cost and inflation-adjusted accounting data could show the true differences among the financial characteristics of the industries studied and reveal the nature of distortions caused by inflation. The 1975-77 period, chosen for our study, was characterized by a high level of inflation in the Turkish economy with a rate averaging about 25 per cent per annum.
Twenty-eight financial ratios gathered from the balance sheets and income statements of 81 Turkish private business firms for the years 1975 and 1977 were used in the study. The research sample included 26 firms from the textile industry, 22 firms from the food processing industry, 17 firms from the appliance-manufacturing industry and 16 firms from the chemicals industry. The MANOVA method was used to determine if the firms in the four industries studied had significantly different financial characteristics and, if so, what factors contributed most to differences among them.
The tests were first applied to historical-cost accounting data for the years 1975 and 1977. Since this period was characterized by a high rate of inflation in the Turkish economy, the tests were also repeated with general-price-level-adjusted data for the same sample of firms in order to evaluate the influence of inflation on the findings. Principal component analysis was applied to the 28 financial ratios. Seven principal components with an eigen value greater than one were selected. They may account for about 83 per cent of the variation in the original data matrix. These principal components were named in accordance with the factor loadings of the ratios in each principal component as follows for 1 975 and 1977.
Multivariate Analysis of Variance
MANOVA Applied to Historical Cost: 1975 and 1977 Data
Multivariate variance analysis was applied to the seven principal component values calculated for the firms in the four different industries. The computed multivariate F-ratio was 3.15 (1977) and 3.5 for 1975 which is greater than the critical Fo01 1.88 value. This implies that the financial characteristics of the four industries were significantly different.
The computed univariate F-ratio values of all seven principal components were greater than the critical [F.sub.0.01] = 4.04 value. This indicates the presence of significant differences among the four industries in terms of all seven principal components. The computed univariate F-ratio values (1977) revealed that the most important difference among the four industries Was in terms of profitability ratios. The findings of the MAN OVA application are summarized in Table 1.
Principal Component Analysis: MANOVA Applied to Inflation-Adjusted 1977 Data
It is commonly argued that inflation causes distortions in financial ratio values. The degree of distortion may differ from one industry to another depending on the composition of assets, the method of inventory valuation used and the net monetary asset position. We repeated our tests with general-price-level-adjusted data for the same sample of firms to eliminate the distorting influence of inflation. Therefore we wanted to determine if the differences between the findings for 1975 and 1977 with historical-cost data were in any way affected by the high rate of inflation experienced during this period.
Analysis of Data
Multivariate variance analysis with inflation adjusted data also showed the presence of significant differences among the financial characteristics of firms in the four industries. The computed multivariate F-ratio was 2.98 which is greater than the critical [F.sub.0.01] = 1.88 value. The multivariate F-ratio obtained from inflation adjusted 1977 data was lower than 'the ratio for non-adjusted 1977 data. This shows that inflation caused the financial characteristics of firms in the four industries to appear to be more disparate than they actually were in 1977.
Univariate F-ratio tests applied to the seven principal components obtained from inflation-adjusted 1977 data indicated that only five of the principal components contributed significantly to differences among the four industries and that long-term debt/capitalization and liquidity principal components were statistically insignificant. As with the analysis of 1975 data, univariate F-ratios for inflation-adjusted 1977 data also indicated that the factor contributing most to differences among the four industries was short-term-bank-credit utilization. During inflationary periods, profitability ratios are inflated because of understatement in depreciation and the cost of goods sold. This effect varies from one industry to another depending on the extent of the understatement. Therefore, inflation can be an important factor contributing to the inter-industry differences through profitability ratios.
In Sum :
* Several previous studies have found statistically significant differences among the financial characteristics of firms in different industries. This study, utilizing Turkish industry data and a new methodological approach, found further empirical evidence in support of this conclusion.
* The findings of multivariate variance analysis showed that inflation causes distortions in financial ratio values and makes financial characteristics of firms in different industries appear to be more disparate than they actually are.
* It was also found that inflation changes the significance ranking of factors contributing to differences among the financial characteristics of firms in different industries.
(See Journal of Financial Management and Analysis, January-June 1991)
Om Sai Ram Centre for Financial Management Research
* See Journal of Financial Management and Analysis (1 : 2012, 2 : 2012, 2 : 1993, 1 : 2013)--Bauer, Faseruk, Glew (1 : 2010)--Lazaridis & Livanis (1 : 2009, 2:1988,2:1989, 2 : 1993)--Swamy
TABLE 1 MANOVA APPLICATION TO HISTORICAL COST : 1975 AND 1977 DATA Multivariate F Ratios Principal Among Mean Within Mean F(3, 77) Components Square Square 1975 1977 1975 1977 1975 1977 1. 535.51 1239.59 48.41 127.86 11.06 9.69 2. 3370.42 2479.28 298.66 279.06 11.29 8.88 3. 123.38 843.81 8.41 90.03 14.67 9.37 4. 2731.93 160.93 256.82 28.18 10.64 5.71 5. 324.79 388.36 28.11 52.44 11.55 5.71 6. 2265.38 64.58 197.35 13.64 11.48 4.73 7. 651.38 3048.05 61.84 352.70 10.53 8.64 Wilks' Lanibada(A) 0.4135 0.4469 Multi variate Correlation Ratio (n) 0.7658 0.7437 For equality of centroids, MANOVA (F) (21,204) 350 3.15 TABLE 2 MANOVA APPLICATION TO INFLATION-ADJUSTMENT 1977 DATA Univariate F Ratios Principal Among Mean Within Mean F(3, 75) Components Square Square 1. 1215.67 122.05 9.96 2. 432.61 55.82 7.75 3. 2539.56 274.16 9.26 4. 19.86 6.57 3.02 5. 3.09 5.76 0.54 6. 1228.23 123.25 9.97 7. 698.61 94.36 7.40 Wilks' Lambada (A) 0.4511 Multivariate Correlation Ratio (n) 0.7409 For equality of centroids, MANOVA (F)(21, 195) 2.98
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|Publication:||Journal of Financial Management & Analysis|
|Date:||Jul 1, 2013|
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