Economic & static Project.
Annki lee
finalRyan.docx
Relationship of Poverty Rate to Income Inequality
Dr. Terry Olson
December 19, 2009
1
Final Draft
I. Introduction
The traditional goals of economics are short run price level stability and long run output growth. For centuries, these goals were sufficient to occupy the minds of economists and accurately reflect the political goals of the period. However, following the industrial revolution, the earnings from long run economic output growth began to be increasingly concentrated in the hands of a few select entrepreneurs. As this stratification of output continued, its appearance became completely apparent to observers by the mid-twentieth century. That same period brought with it an increased value placed in the equality of citizens of democratic nations. These two things coupled together have led to a reconsideration of the goals of economics by some economists. These economists desired to find a way to measure how the long run output growth had been divided rather than just the level of that growth. The desired measurement was a measurement of income inequality. The measure that eventually won out was the Gini coefficient, or the similar Gini index. The Gini coefficient finally allowed a useful study of income inequality. That study became the subfield of economics focusing on the relationship of income to income inequality. This paper will review the literature on that topic before expounding on the theory connecting poverty rate and income inequality and then testing those theories empirically.
II. Literature Review
The literature in the subfield of economics focusing on the relationship of income inequality and income begins with Simon Kuznets’ (1955) groundbreaking article “Economic Growth and Income Inequality”. Since this article is the foundational article on this topic and provides the basic model all of the other papers build upon, an understanding of the other literature requires an understanding of Kuznets’ article. Kuznets begins his article by lamenting the lack of high quality data on the subject on economic inequality when he wrote. Despite the lack of reliable data on a broad spectrum of countries Kuznets does go on and draws a conclusion about the data. He concludes that there is an inverse-U shaped relationship between inequality in a country and that country’s income. The inverse U-shape means that as a country’s income grows at first income inequality grows, levels out, and then finally decreases in the final stages of growth. Kuznets goes on to point out the reasons that inequality should go up with growth, and uses those reasons to support the first half of the inverse-U shape. He then goes on to demonstrate the reasons explaining the second half of the curve’s shape. These reasons were dormant during the early stages of growth, but they become dominant during the later stages of growth. Kuznets demonstrates his idea with an extended example based on two sectors that are modeled after the rural and urban workforces at the time. The example allows Kuznets to show a case roughly modeled after the industrialization of the Western nations in which economic growth causes inequality to rise and then decline. Kuznets concludes with a discussion on the difference of growth in developed versus underdeveloped nations.
Despite a few objections, such as those from Deininger and Squire (1996) and Anand and Kanbur (1985), the relationship Kuznets uncovered has withstood the test of time. Numerous authors including but in no way limited to Nielsen(1994), Dovring(1991), Ram(1997), and Jha(1996), have concluded that the inverse U-shape holds in general. The basic formula used by authors following Kutnetz in order to empirically test his model consisted of terms for an intercept, the natural logarithm of a country’s income, and the natural logarithm of a country’s income squared. The coefficients in these equations have repeatedly been found to be statistically significant. In addition to supporting Kuznets with empirical evidence, authors have reinforced and expanded on Kuznets theoretical model. Almost twenty years later, Chenery et al. (1968) lay out more clearly the conceptual reasons why there should be no trade off between growth and inequality. Besides attempts to empirically prove or disprove Kuznets’ hypothesis, the recent research on income and inequality focuses on the impact of the economic growth rate rather than the level of economic development to further explain the cross-country rates of inequality. Ahluwalia(1976) and Fields(1980) added additive growth terms to the equation in attempts to see if there was a relationship between the growth rate and income inequality, but they each found that relationship to be statistically insignificant. However, Winegarden(1979) and Ram(1997) found a theoretical basis for the economic growth rate to affect the level of income inequality and found the additive growth term to be statistically significant. Although, the growth term helped explain discrepancies in the model, there was still no literature helping to explain why the high income countries had developed when they did while the low income countries had failed to develop. Chang and Ram(2000) offered a study on the differences between the two groups in their paper “Level of Development, Rate of Economic Growth, and Income Inequality”.
Chang and Ram also offer a concise summarization of the theoretical reasons for the Kuznets hypothesis. These reasons leave two major parts of the relationship between growth and income inequality unexplored. The first such area, which Chang and Ram touch on but do not go into, is the different effects of income inequality within a large portion of the population beneath the poverty line and income inequality with only a negligible portion of the population below the poverty line. Since Chang and Ram wrote in 2000, the passage of time and the economic changes that have happened since give the perspective to see the other area they have missed. That area is the effect that the recent and ongoing technological revolution will have on a model based on the idea of the industrial revolution. An attempt to fill in the first of these holes constitutes the basis for this paper.
III. Theory
Simon Kuznets and subsequent authors clearly laid out the relationship of income and income inequality. The reasons they espoused to explain the negative relationship between income and income inequality at high levels of income are political interference, demographics, the emergence of new industries, and work incentives. Political interference is the tendency of countries with higher levels of income to become democracies, and those democracies tend to force equality on the populace through progressive taxes and the like. The idea behind demographics is the tendency of wealthier citizens to reproduce less often that leads to the descendents of the top five percent of population being less than the top five percent of the population, which offsets the effect of cumulative savings in income inequality. The emergence of new industries is the tendency for new explosive industries to benefit their founders far more than they benefit others, and those founders tend to not already be in the top percentage of wealth holders. Work incentives are the tendency of richer individuals to work less strenuously because there are less possible advancement benefits. However, they neglected to distinguish between poverty levels and levels of income inequality. Three out of the four reasons for decreasing income inequality with higher levels of income only apply with full magnitude when income inequality and the level of poverty are correlated. When the poverty level drops while income increases, it offsets the effects of political interference, demographics, and work incentives on income inequality. Democracies’ tendency to redistribute wealth is decreased when poverty rates are low as they will be at very high levels of income because the political will to redistribute income begins to fail as the tragedies of poverty become rarer. Thus, the political interference reason loses force at low levels of poverty, and so it ceases its reduction of income inequality. Also at low levels of poverty, the birthrate of the entire population decreases to match the lowered birthrate of the wealthy. This decrease reduces the offsetting of cumulative savings by demographics, which keeps demographics from decreasing income inequality. Lastly, low levels of poverty also reduce the work incentives of the entire population to some extent. Even if work incentives are not completely offset, their effect on reducing income inequality is reduced. Thus, low levels of poverty should be associated with higher levels of income inequality.
IV. Data & Variables
In order to study the effect of the poverty rate on income inequality, it is necessary to have the correct variables and the data to accompany them. Obviously, variables are needed for income inequality and poverty rate, labeled INEQ and POVR, respectively. In addition, in accordance with the Kuznets hypothesis, variables are needed for the logarithm of income, labeled LRY, and the logarithm of income, quantity squared, labeled LRYSQ. Lastly, a variable for the overall development is added to account for the standard of living that has a similar effect as poverty rate, but cannot be measured in the poverty rate, labeled HDI.
INEQ is the rate of inequality measured by the Gini coefficient. The Gini coefficient is the area of between the 45 degree line of complete income equality and the Lorenz curve. The Lorenz curve is the increasing function that plots the percentage of income against the percentage of population who earn that percent of the income. This variable measures the income inequality in a nation. This data was collected from the 2003 edition of World Development Indicators.
LRY is the logarithm of the Gross Domestic Product of a country. The logarithm adjusts for the vast difference between the outputs of different nations. The adjustment allows for a linear relationship to be derived. This variable measures part of the effect of a country’s income on income inequality. This data was based on the GDP data collected from the 2003 edition of World Development Indicators.
LRYSQ is the logarithm of the Gross Domestic Product of a country, quantity squared. Again, the logarithm adjusts for the vast difference between the outputs of different nations, but this adjustment allows for a quadratic relationship to be derived. This variable measures the rest of the effect of a country’s income on income inequality in that it checks for the inverse U-shape of the relationship between income and income inequality. This data was based on the GDP data collected from the 2003 edition of World Development Indicators.
HDI is the ranking of a country on the United Nations’ Human Development Index. This index is a measurement of a country’s overall development. In this study, development is taken as a proxy for poverty rate due to a lack of reliable available numbers comparing poverty between nations. A higher level of development, which means a lower HDI ranking, is associated with lower levels of poverty so the sign of this variable will be the same as the expected sign of poverty rate. Thus, this variable measures the effect of a nation’s poverty on income inequality. The data for HDI was collected from the United Nations’ Human Development Index.
V. Model & Results
The model used is based upon the model used throughout the literature on income and income inequality. That model is
INEQ = α + β0*LRY + β1*LRYSQ + ε
where INEQ, LRY, and LRYSQ are the same as explained in the data section. The constant term is α, and ε is the error term. The term needed for this study can be added into this equation. When, they are added the equation becomes
INEQ = α + β0*LRY + β1*LRYSQ + β2*HDI + ε.
The results in Table 1, Table 2, and Table 3 in the rest of the section are from two separate regressions. Regression 1 is the regression using all 119 available data points from the above sources, and Regression 2 is the regression using the largest 25 economies by income level. In these regressions, INEQ is the dependent variable with all other variables being independent.
Table 1[footnoteRef:1],[footnoteRef:2] [1: The standard errors in the first set of parentheses for each term is the standard errors using the standard ordinary least squares method, and the standard errors in the second set of parentheses for each term is the standard errors using the heteroskedasticity-consistent covariance method] [2: * Significant at the 15% level, **Significant at the 5% level, and ***Significant at the 1% level]
|
|
Regression 1 |
Regression 2 |
|
Coefficient on LRY |
-0.13139 (0.1588) (0.1245) |
1.5423 (1.148) (0.9596)* |
|
Coefficient on LRYSQ |
0.0067255 (0.007451) (0.005637) |
-0.061512 (0.04807) (0.04007)* |
|
Coefficient on HDI |
0.00099077 (0.0002271)*** (0.0002016)*** |
0.0012448 (0.0003837)*** (0.0004678)*** |
|
Constant |
0.94956 (0.8482) (0.6885) |
-9.3026 (6.844) (5.735)* |
|
R2 |
0.2247 |
0.4422 |
|
R2-Adjusted |
0.2045 |
0.3625 |
|
Durbin-Watson |
2.0493 |
2.4477 |
|
F-value from ANOVA table-From Mean |
11.110 |
5.549 |
|
χ2 Test Statistic |
3.173 |
4.853 |
|
# of Runs |
62 |
12 |
|
# of Positive Errors |
52 |
9 |
|
# of Negative Errors |
67 |
16 |
|
Normal Statistic |
0.4576 |
-0.2314 |
Based on regression 1, the model equation could be written as
INEQ = 0.94956 - 0.13139*LRY + 0.0067255*LRYSQ + 0.00099077*HDI,
but based on regression 2 the equation could be written as
INEQ = -9.3026 + 1.5423*LRY - 0.061512*LRYSQ + 0.0012448*HDI
The interpretations of the coefficients are as follows for regression 1. The Gini coefficient of a country is expected to fall by 0.13139 for every 1 percent increase in the income of that country, all else constant. The Gini coefficient of a country is expected to rise by 0.0067255 for every 1 percent increase in income, quantity squared of that country, all else constant. The Gini coefficient of a country is expected to fall by 0.13139 for every 1 spot increase in the Human Development Index Ranking of that country, all else constant.
The interpretations of the coefficients are as follows for regression 2. The Gini coefficient of a country is expected to rise by 0. 1.5423 for every 1 percent increase in the income of that country, all else constant. The Gini coefficient of a country is expected to fall by 0.061512 for every 1 percent increase in the income, quantity squared for that country, all else constant. The Gini coefficient of a country is expected to fall by 0.0012448 for every 1 spot increase in the Human Development Index Ranking of that country, all else constant.
Individually testing each coefficient for significance led to the results listed in Table 1. As a summary of those results for regression 1 using the standard OLS method, the values of the coefficient of LRY, the coefficient of LRYSQ, and the constant were found to be insignificant at all reasonable levels while the coefficient of HDI is significant at the 1% level. As a summary of those results for regression 1 using the heteroskedasticity-consistent covariance method, the values of the coefficient of LRY, the coefficient of LRYSQ, and the constant were found to be insignificant at all reasonable levels while the coefficient of HDI is significant at the 1% level. As a summary of those results for regression 2 using the standard OLS method, the values of the coefficient of LRY, the coefficient of LRYSQ, and the constant were found to be insignificant at all reasonable levels while the coefficient of HDI is significant at the 1% level. As a summary of those results for regression 2 using the heteroskedasticity-consistent covariance method, the values of the coefficient of LRY, the coefficient of LRYSQ, and the constant were found to be significant at the 15% level while the coefficient of HDI is significant at the 1% level.
From the R2 values, 22.47% of the sample variability in the Gini coefficient is explained by regression model 1 and 44.22% of the sample variability in the Gini coefficient is explained by regression model 2. From the adjusted R2 values, 20.45% of the sample variability in the Gini coefficient is explained by regression model 1 controlling for the number of degrees of freedom and 36.25% of the sample variability in the Gini coefficient is explained by regression model 2 controlling for the degrees of freedom.
A goodness of fit test was performed. The test used the F-values from ANOVA table- from mean listed in Table 1. For regression 1, it can be concluded that the model does have significant explanatory power at the 2% level. For regression 2, it can be concluded that the model has significant explanatory power at all reasonable levels of significance.
The rule of thumb test for simple multicollinearity requires Tables 2 and 3 below.
Table 2: The Correlation Matrix of Variables for Regression 1
|
Variable |
INEQ |
LRY |
LRYSQ |
HDI |
|
INEQ |
1.0000 |
N/A |
N/A |
N/A |
|
LRY |
-0.28855 |
1.0000 |
N/A |
N/A |
|
LRYSQ |
-0.28176 |
0.99847 |
1.0000 |
N/A |
|
HDI |
0.46235 |
-0.73264 |
-0.72734 |
1.0000 |
Table 3: The Correlation Matrix of Variables for Regression 2
|
Variable |
INEQ |
LRY |
LRYSQ |
HDI |
|
INEQ |
1.0000 |
N/A |
N/A |
N/A |
|
LRY |
0.31334 |
1.0000 |
N/A |
N/A |
|
LRYSQ |
0.30743 |
0.99974 |
1.0000 |
N/A |
|
HDI |
0.45043 |
-0.25446 |
-0.25626 |
1.0000 |
Using that test reveals only the expected multicollinearities. The only multicollinearity between independent variables in regression 1 is between LRY and LRYSQ, which are obviously related because the second is the square of the first. In regression 2, the only multicollinearity between independent variables is again between LRY and LRYSQ, which are obviously related.
Since only the expected simple multicollinearity was found using the rule of thumb, the use of Klein’s rule of thumb is needed to test for higher-order multicollinearity. The highest R2 for any independent variable regressed against the other independent variable is 0.9970 for regression 1 and 0.9995 for regression 2. Those numbers are far higher the R2 values from their respective regressions. So in both regressions there is an indication of severe multicollinearity.
In order to test for first-order autocorrelation, the runs test is used. In regression 1, the number of positive error terms is 52 and the number of negative error terms is 67. Since 52>20 and 67>20, the small sample test cannot be used. Then using the normal statistic, it is found that there is no problem with first-order autocorrelation at any reasonable level of significance. In regression 2, the number of positive error terms is 9 and the number of negative error terms is 16. Since 9<20 and 16<20, for regression 2, the small sample test can be used. Since the number of runs is 12, which is greater than the critical value 7 and less than the critical value of 18, we can conclude that we have no problem with first-order autocorrelation.
As another check for first-order autocorrelation, we can use the Durbin-Watson test. For regression 1, the Durbin-Watson test concludes at both the 0.10 and 0.02 levels that there is no first-order autocorrelation. For regression 2, the test concludes that there is no first-order autocorrelation at the 0.10 level but is inconclusive at the 0.02 level.
The last statistical measure that was checked was heteroskedasticity. This was checked using the χ2 test statistic. Using that statistic, both regressions were evaluated. Both regressions were found to have severe heteroskedasticity. As a result, the heteroskedasticity-consistent covariance method was used to correct the standard errors, which made each coefficient more significant.
VI. Conclusion
Looking at both regressions, regression 2 has far better results than regression 1. Regression 2 confirms the Kuznets hypothesis. However, both regressions refute my hypothesis that higher HDI rankings should mean less inequality. The problem could come from one of two sources. Either the problem is in my theory or in my data. I believe that my theory is well reasoned and that leads to the conclusion that there is a problem with the data. Most likely, the Human Development Index fails to be sufficient proxy for level of poverty in a nation. Given the likely data errors, I do believe that further research in this area could lead to statistically significant results confirming my hypothesis.
VII. Bibliography
Ahluwalia, Montek S. "Income Distribution and Development: Some Stylized Facts,” The American Economic Review 66, 2 (1976): 128-135. http://www.jstor.org/stable/1817209 (accessed October 27, 2009).
Anand, Sudhir and S.M.R. Kanbur. "Poverty Under the Kuznets Process,” The Economic Journal 95 (1985): 42-50. http://www.jstor.org/stable/2232868 (accessed October 27, 2009).
Chang, Jih Y. and Rati Ram. "Level of Development, Rate of Economic Growth, and Income Inequality,” Economic Development and Cultural Change 48, 4 (2000): 787-799. http://www.jstor.org/stable/1155035 (accessed October 27, 2009).
Chenery, Hollis B. and Lance Taylor. "Level Development Patterns: Among Countries and Over Time,” The Review of Economics and Statistics 50, 4 (1968): 391-416. http://www.jstor.org/stable/1926806 (accessed October 27, 2009).
Deininger, Klaus and Lyn Squire. "A New Data Set Measuring Income Inequality,” The World Bank Economic Review 10, 3 (1996): 565-591. http://www.jstor.org/stable/3990058 (accessed October 27, 2009).
Dovring,Folke. Inequality: The Political Economy of Distribution. New York: Praeger, 1991.
Fields,Gary S. Poverty, Inequality, and Development. New York: Cambridge University Press, 1980.
Jha, Sailesh K. "The Kuznets curve: A reassessment,” World Development 24 (1996): 773-780.
Kuznets, Simon, and "Economic Growth and Income Inequality," The American Economic Review 45, 1 (1955): 1-28. http://www.jstor.org/stable/1811581 (accessed October 27, 2009).
Nielsen, Francois. "Income Inequality and Industrial Dvelopment: Dualism Revisited,” American Sociological Review 59, 5 (1994): 654-677. http://www.jstor.org/stable/2096442 (accessed October 27, 2009).
Ram, Rati. "Level of Economic Development and Income Inequality: Evidence from the Postwar Developed World,” Southern Economic Journal 64, 2 (1997): 576-583. http://www.jstor.org/stable/1060869 (accessed October 27, 2009).
Winegarden, C.R. "Schooling and Income Distribution: Evidence from International Data,” Economica 46, 181 (1979): 83-87. http://www.jstor.org/stable/2553099 (accessed October 27, 2009).
VIII. SHAZAM Output
Regression 1
Welcome to SHAZAM - Version 10.0 - JUL 2004 SYSTEM=WIN-XP PAR= 4000
CURRENT WORKING DIRECTORY IS: C:\PROGRA~1\SHAZAM
|_Sample 1 119
|_Read (Y:\classes\mydata.sha) INEQ LRY LRYSQ HDI/ List Skiplines = 1
UNIT 88 IS NOW ASSIGNED TO: Y:\classes\mydata.sha
4 VARIABLES AND 119 OBSERVATIONS STARTING AT OBS 1
INEQ LRY LRYSQ HDI
0.4080000 13.00283 169.0735 12.00000
0.3490000 12.61715 159.1925 8.000000
0.3520000 12.56664 157.9205 3.000000
0.3820000 12.26625 150.4608 22.00000
0.3600000 12.15354 147.7085 16.00000
0.3270000 12.11721 146.8267 10.00000
0.4030000 12.06410 145.5424 81.00000
0.3600000 12.03693 144.8877 20.00000
0.3150000 11.84166 140.2248 4.000000
0.5190000 11.79086 139.0244 52.00000
0.3250000 11.76479 138.4103 13.00000
0.5910000 11.70114 136.9168 70.00000
0.3780000 11.67883 136.3951 128.0000
0.3160000 11.62548 135.1519 26.00000
0.3260000 11.57994 134.0950 9.000000
0.4560000 11.49129 132.0498 67.00000
0.3310000 11.39286 129.7972 7.000000
0.2500000 11.36099 129.0721 17.00000
0.2500000 11.32183 128.1839 6.000000
0.3050000 11.27542 127.1350 15.00000
0.3160000 11.24614 126.4758 37.00000
0.2580000 11.22049 125.8993 2.000000
0.2470000 11.20829 125.6257 14.00000
0.4000000 11.16933 124.7539 84.00000
0.3030000 11.16228 124.5966 107.0000
0.4910000 11.09673 123.1374 74.00000
0.2560000 11.08226 122.8166 11.00000
0.3540000 11.06881 122.5186 24.00000
0.4320000 11.05949 122.3124 78.00000
0.4300000 11.05710 122.2595 94.00000
0.5930000 11.05413 122.1938 121.0000
0.3850000 11.04061 121.8952 29.00000
0.3550000 11.03473 121.7652 23.00000
0.3590000 11.01409 121.3102 5.000000
0.3440000 10.99333 120.8533 112.0000
0.4920000 10.94468 119.7861 63.00000
0.4250000 10.93272 119.5243 25.00000
0.5710000 10.91599 119.1587 75.00000
0.4610000 10.85393 117.8078 90.00000
0.5750000 10.82249 117.1264 40.00000
0.3300000 10.76840 115.9585 136.0000
0.2540000 10.75423 115.6534 32.00000
0.3530000 10.73783 115.3010 104.0000
0.4620000 10.73277 115.1924 87.00000
0.2440000 10.71538 114.8195 36.00000
0.3620000 10.70265 114.5466 19.00000
0.3180000 10.66937 113.8355 140.0000
0.5060000 10.61672 112.7147 158.0000
0.3030000 10.58791 112.1039 60.00000
0.2900000 10.57505 111.8317 76.00000
0.3950000 10.53427 110.9708 126.0000
0.3610000 10.51485 110.5621 105.0000
0.3120000 10.35003 107.1232 73.00000
0.4740000 10.32656 106.6379 79.00000
0.5990000 10.31167 106.3305 118.0000
0.2580000 10.31088 106.3143 42.00000
0.2900000 10.30664 106.2268 47.00000
0.4170000 10.30081 106.1067 91.00000
0.2840000 10.27439 105.5631 27.00000
0.4480000 10.27105 105.4945 46.00000
0.4370000 10.25484 105.1617 89.00000
0.4590000 10.20704 104.1837 48.00000
0.3440000 10.20170 104.0746 99.00000
0.5080000 10.13796 102.7781 103.0000
0.3190000 10.13204 102.6581 53.00000
0.3040000 10.08704 101.7483 64.00000
0.3630000 10.07889 101.5841 43.00000
0.4450000 10.05675 101.1383 148.0000
0.2680000 10.05192 101.0412 113.0000
0.3670000 10.01749 100.3502 166.0000
0.4850000 10.00736 100.1473 62.00000
0.3820000 9.970393 99.40874 159.0000
0.3340000 9.967361 99.34828 153.0000
0.5680000 9.956984 99.14154 151.0000
0.4030000 9.946551 98.93387 59.00000
0.3640000 9.945912 98.92116 86.00000
0.4770000 9.929470 98.59437 144.0000
0.4470000 9.901404 98.03780 117.0000
0.3790000 9.891203 97.83589 101.0000
0.3240000 9.877889 97.57270 45.00000
0.5770000 9.857694 97.17414 95.00000
0.5900000 9.805229 96.14251 115.0000
0.4860000 9.794697 95.93609 169.0000
0.4080000 9.775392 95.55829 109.0000
0.3740000 9.753966 95.13985 154.0000
0.3650000 9.747023 95.00446 98.00000
0.3670000 9.745231 94.96953 142.0000
0.3760000 9.742332 94.91304 44.00000
0.3960000 9.724358 94.56313 135.0000
0.6300000 9.715669 94.39423 124.0000
0.4130000 9.666986 93.45061 156.0000
0.4600000 9.663135 93.37618 143.0000
0.5260000 9.560982 91.41238 165.0000
0.3960000 9.557146 91.33904 172.0000
0.2820000 9.534787 90.91217 69.00000
0.4040000 9.531990 90.85882 131.0000
0.3890000 9.496653 90.18642 96.00000
0.7070000 9.491362 90.08595 125.0000
0.4030000 9.475526 89.78559 160.0000
0.5090000 9.471145 89.70259 145.0000
0.5050000 9.422754 88.78829 173.0000
0.4820000 9.395501 88.27544 176.0000
0.3790000 9.325926 86.97289 83.00000
0.5050000 9.290925 86.32128 174.0000
0.3700000 9.245759 85.48407 130.0000
0.5030000 9.242790 85.42916 164.0000
0.2890000 9.231215 85.21532 161.0000
0.2900000 9.183270 84.33245 116.0000
0.3620000 9.169968 84.08832 111.0000
0.6090000 9.098644 82.78532 141.0000
0.3470000 9.023664 81.42651 122.0000
0.4400000 9.020775 81.37439 114.0000
0.3730000 9.003029 81.05454 137.0000
0.6130000 8.985426 80.73789 171.0000
0.5600000 8.901458 79.23596 138.0000
0.6290000 8.874482 78.75643 177.0000
0.3330000 8.838219 78.11412 167.0000
0.4780000 8.591065 73.80639 155.0000
0.4700000 8.298853 68.87096 175.0000
|_STAT INEQ LRY LRYSQ HDI/PCOR
NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM
INEQ 119 0.40489 0.10077 0.10155E-01 0.24400 0.70700
LRY 119 10.377 0.95497 0.91197 8.2989 13.003
LRYSQ 119 108.59 20.178 407.16 68.871 169.07
HDI 119 89.336 53.866 2901.6 2.0000 177.00
CORRELATION MATRIX OF VARIABLES - 119 OBSERVATIONS
INEQ 1.0000
LRY -0.28855 1.0000
LRYSQ -0.28176 0.99847 1.0000
HDI 0.46235 -0.73264 -0.72734 1.0000
INEQ LRY LRYSQ HDI
|_OLS INEQ LRY LRYSQ HDI/ ANOVA AUXRSQ LIST
REQUIRED MEMORY IS PAR= 10 CURRENT PAR= 4000
OLS ESTIMATION
119 OBSERVATIONS DEPENDENT VARIABLE= INEQ
...NOTE..SAMPLE RANGE SET TO: 1, 119
R-SQUARE OF LRY ON OTHER INDEPENDENT VARIABLES = 0.9970
R-SQUARE OF LRYSQ ON OTHER INDEPENDENT VARIABLES = 0.9970
R-SQUARE OF HDI ON OTHER INDEPENDENT VARIABLES = 0.5425
R-SQUARE OF CONSTANT ON OTHER INDEPENDENT VARIABLES = 0.0000
R-SQUARE = 0.2247 R-SQUARE ADJUSTED = 0.2045
VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.80789E-02
STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.89883E-01
SUM OF SQUARED ERRORS-SSE= 0.92908
MEAN OF DEPENDENT VARIABLE = 0.40489
LOG OF THE LIKELIHOOD FUNCTION = 119.881
MODEL SELECTION TESTS - SEE JUDGE ET AL. (1985,P.242)
AKAIKE (1969) FINAL PREDICTION ERROR - FPE = 0.83505E-02
(FPE IS ALSO KNOWN AS AMEMIYA PREDICTION CRITERION - PC)
AKAIKE (1973) INFORMATION CRITERION - LOG AIC = -4.7855
SCHWARZ (1978) CRITERION - LOG SC = -4.6920
MODEL SELECTION TESTS - SEE RAMANATHAN (1998,P.165)
CRAVEN-WAHBA (1979)
GENERALIZED CROSS VALIDATION - GCV = 0.83599E-02
HANNAN AND QUINN (1979) CRITERION = 0.86731E-02
RICE (1984) CRITERION = 0.83701E-02
SHIBATA (1981) CRITERION = 0.83322E-02
SCHWARZ (1978) CRITERION - SC = 0.91679E-02
AKAIKE (1974) INFORMATION CRITERION - AIC = 0.83503E-02
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.26927 3. 0.89756E-01 11.110
ERROR 0.92908 115. 0.80789E-02 P-VALUE
TOTAL 1.1983 118. 0.10155E-01 0.000
ANALYSIS OF VARIANCE - FROM ZERO
SS DF MS F
REGRESSION 19.778 4. 4.9444 612.016
ERROR 0.92908 115. 0.80789E-02 P-VALUE
TOTAL 20.707 119. 0.17401 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 115 DF P-VALUE CORR. COEFFICIENT AT MEANS
LRY -0.13139 0.1588 -0.8277 0.410-0.077 -1.2451 -3.3675
LRYSQ 0.67255E-02 0.7451E-02 0.9026 0.369 0.084 1.3466 1.8037
HDI 0.99077E-03 0.2271E-03 4.363 0.000 0.377 0.5296 0.2186
CONSTANT 0.94956 0.8482 1.120 0.265 0.104 0.0000 2.3452
OBS. OBSERVED PREDICTED CALCULATED
NO. VALUE VALUE RESIDUAL
1 0.40800 0.39005 0.17945E-01 I*
2 0.34900 0.37031 -0.21313E-01 *I
3 0.35200 0.36344 -0.11441E-01 *I
4 0.38200 0.37157 0.10434E-01 I*
5 0.36000 0.36192 -0.19196E-02 *
6 0.32700 0.35482 -0.27818E-01 * I
7 0.40300 0.42350 -0.20504E-01 *I
8 0.36000 0.36223 -0.22330E-02 *
9 0.31500 0.34068 -0.25679E-01 *I
10 0.51900 0.38684 0.13216 I *
11 0.32500 0.34749 -0.22492E-01 *I
12 0.59100 0.40228 0.18872 I *
13 0.37800 0.45917 -0.81172E-01 * I
14 0.31600 0.35676 -0.40761E-01 * I
15 0.32600 0.33879 -0.12794E-01 *I
16 0.45600 0.39415 0.61848E-01 I *
17 0.33100 0.33249 -0.14895E-02 *
18 0.25000 0.34171 -0.91708E-01 * I
19 0.25000 0.32998 -0.79981E-01 * I
20 0.30500 0.33794 -0.32942E-01 * I
21 0.31600 0.35915 -0.43152E-01 * I
22 0.25800 0.32397 -0.65969E-01 * I
23 0.24700 0.33562 -0.88621E-01 * I
24 0.40000 0.40423 -0.42306E-02 *
25 0.30300 0.42689 -0.12389 * I
26 0.49100 0.39299 0.98010E-01 I *
27 0.25600 0.33031 -0.74315E-01 * I
28 0.35400 0.34296 0.11042E-01 I*
29 0.43200 0.39630 0.35703E-01 I *
30 0.43000 0.41211 0.17892E-01 I*
31 0.59300 0.43881 0.15419 I *
32 0.38500 0.34742 0.37576E-01 I *
33 0.35500 0.34138 0.13621E-01 I*
34 0.35900 0.32320 0.35804E-01 I *
35 0.34400 0.42886 -0.84864E-01 * I
36 0.49200 0.37953 0.11247 I *
37 0.42500 0.34169 0.83307E-01 I *
38 0.57100 0.39097 0.18003 I *
39 0.46100 0.40490 0.56099E-01 I *
40 0.57500 0.35491 0.22009 I *
41 0.33000 0.44928 -0.11928 * I
42 0.25400 0.34605 -0.92047E-01 * I
43 0.35300 0.41717 -0.64167E-01 * I
44 0.46200 0.40026 0.61742E-01 I *
45 0.24400 0.34951 -0.10551 * I
46 0.36200 0.33250 0.29499E-01 I *
47 0.31800 0.45197 -0.13397 * I
48 0.50600 0.46919 0.36812E-01 I *
49 0.30300 0.37177 -0.68769E-01 * I
50 0.29000 0.38748 -0.97481E-01 * I
51 0.39500 0.43659 -0.41588E-01 * I
52 0.36100 0.41558 -0.54584E-01 * I
53 0.31200 0.38241 -0.70408E-01 * I
54 0.47400 0.38817 0.85828E-01 I *
55 0.59900 0.42670 0.17230 I *
56 0.25800 0.35140 -0.93398E-01 * I
57 0.29000 0.35632 -0.66321E-01 * I
58 0.41700 0.39987 0.17127E-01 I*
59 0.28400 0.33628 -0.52279E-01 * I
60 0.44800 0.35508 0.92919E-01 I *
61 0.43700 0.39758 0.39424E-01 I *
62 0.45900 0.35666 0.10234 I *
63 0.34400 0.40716 -0.63155E-01 * I
64 0.50800 0.41077 0.97226E-01 I *
65 0.31900 0.36121 -0.42206E-01 * I
66 0.30400 0.37190 -0.67898E-01 * I
67 0.36300 0.35106 0.11942E-01 I*
68 0.44500 0.45500 -0.99993E-02 *I
69 0.26800 0.42030 -0.15230 * I
70 0.36700 0.47269 -0.10569 * I
71 0.48500 0.36962 0.11538 I *
72 0.38200 0.46561 -0.83613E-01 * I
73 0.33400 0.45966 -0.12566 * I
74 0.56800 0.45765 0.11035 I *
75 0.40300 0.36647 0.36525E-01 I *
76 0.36400 0.39322 -0.29224E-01 * I
77 0.47700 0.45065 0.26349E-01 I*
78 0.44700 0.42385 0.23155E-01 I*
79 0.37900 0.40798 -0.28975E-01 * I
80 0.32400 0.35247 -0.28471E-01 * I
81 0.57700 0.40198 0.17502 I *
82 0.59000 0.42175 0.16825 I *
83 0.48600 0.47525 0.10749E-01 I*
84 0.40800 0.41580 -0.78002E-02 *
85 0.37400 0.46039 -0.86386E-01 * I
86 0.36500 0.40490 -0.39904E-01 * I
87 0.36700 0.44850 -0.81499E-01 * I
88 0.37600 0.35140 0.24596E-01 I*
89 0.39600 0.44157 -0.45573E-01 * I
90 0.63000 0.43068 0.19932 I *
91 0.41300 0.46244 -0.49435E-01 * I
92 0.46000 0.44956 0.10439E-01 I*
93 0.52600 0.47157 0.54428E-01 I *
94 0.39600 0.47852 -0.82518E-01 * I
95 0.28200 0.37654 -0.94536E-01 * I
96 0.40400 0.43797 -0.33973E-01 * I
97 0.38900 0.40342 -0.14416E-01 *I
98 0.70700 0.43217 0.27483 I X
99 0.40300 0.46691 -0.63906E-01 * I
100 0.50900 0.45206 0.56938E-01 I *
101 0.50500 0.48001 0.24987E-01 I*
102 0.48200 0.48312 -0.11166E-02 *
103 0.37900 0.39136 -0.12356E-01 *I
104 0.50500 0.48173 0.23267E-01 I*
105 0.37000 0.43844 -0.68443E-01 * I
106 0.50300 0.47215 0.30850E-01 I *
107 0.28900 0.46926 -0.18026 * I
108 0.29000 0.42504 -0.13504 * I
109 0.36200 0.42019 -0.58190E-01 * I
110 0.60900 0.45052 0.15848 I *
111 0.34700 0.43241 -0.85410E-01 * I
112 0.44000 0.42451 0.15487E-01 I*
113 0.37300 0.44748 -0.74481E-01 * I
114 0.61300 0.48135 0.13165 I *
115 0.56000 0.44959 0.11041 I *
116 0.62900 0.48855 0.14045 I *
117 0.33300 0.47908 -0.14608 * I
118 0.47800 0.47070 0.73029E-02 *
119 0.47000 0.49571 -0.25714E-01 *I
DURBIN-WATSON = 2.0493 VON NEUMANN RATIO = 2.0667 RHO = -0.02520
RESIDUAL SUM = -0.66582E-13 RESIDUAL VARIANCE = 0.80789E-02
SUM OF ABSOLUTE ERRORS= 8.2866
R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.2247
RUNS TEST: 62 RUNS, 52 POS, 0 ZERO, 67 NEG NORMAL STATISTIC = 0.4576
COEFFICIENT OF SKEWNESS = 0.6739 WITH STANDARD DEVIATION OF 0.2218
COEFFICIENT OF EXCESS KURTOSIS = 0.1887 WITH STANDARD DEVIATION OF 0.4401
JARQUE-BERA NORMALITY TEST- CHI-SQUARE(2 DF)= 8.8666 P-VALUE= 0.012
GOODNESS OF FIT TEST FOR NORMALITY OF RESIDUALS - 10 GROUPS
OBSERVED 0.0 1.0 7.0 29.0 30.0 24.0 11.0 9.0 6.0 2.0
EXPECTED 1.0 3.3 9.4 18.9 26.9 26.9 18.9 9.4 3.3 1.0
CHI-SQUARE = 15.8515 WITH 4 DEGREES OF FREEDOM, P-VALUE= 0.003
|_DIAGNOS / HET
REQUIRED MEMORY IS PAR= 26 CURRENT PAR= 4000
DEPENDENT VARIABLE = INEQ 119 OBSERVATIONS
REGRESSION COEFFICIENTS
-0.131393476530 0.672545686654E-02 0.990770599959E-03 0.949555814016
HETEROSKEDASTICITY TESTS
CHI-SQUARE D.F. P-VALUE
TEST STATISTIC
E**2 ON YHAT: 3.173 1 0.07488
E**2 ON YHAT**2: 2.876 1 0.08992
E**2 ON LOG(YHAT**2): 3.455 1 0.06307
E**2 ON LAG(E**2) ARCH TEST: 0.001 1 0.97680
LOG(E**2) ON X (HARVEY) TEST: 12.322 3 0.00636
ABS(E) ON X (GLEJSER) TEST: 9.561 3 0.02270
E**2 ON X TEST:
KOENKER(R2): 5.002 3 0.17167
B-P-G (SSR) : 5.329 3 0.14922
...MATRIX INVERSION FAILED IN ROW 5
...RESULTS MAY BE UNRELIABLE
E**2 ON X X**2 (WHITE) TEST:
KOENKER(R2): ********** 6 *********
B-P-G (SSR) : ********** 6 *********
...MATRIX INVERSION FAILED IN ROW 5
...RESULTS MAY BE UNRELIABLE
E**2 ON X X**2 XX (WHITE) TEST:
KOENKER(R2): ********** 9 *********
B-P-G (SSR) : ********** 9 *********
|_OLS INEQ LRY LRYSQ HDI/ HETCOV
REQUIRED MEMORY IS PAR= 10 CURRENT PAR= 4000
OLS ESTIMATION
119 OBSERVATIONS DEPENDENT VARIABLE= INEQ
...NOTE..SAMPLE RANGE SET TO: 1, 119
USING HETEROSKEDASTICITY-CONSISTENT COVARIANCE MATRIX
R-SQUARE = 0.2247 R-SQUARE ADJUSTED = 0.2045
VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.80789E-02
STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.89883E-01
SUM OF SQUARED ERRORS-SSE= 0.92908
MEAN OF DEPENDENT VARIABLE = 0.40489
LOG OF THE LIKELIHOOD FUNCTION = 119.881
MODEL SELECTION TESTS - SEE JUDGE ET AL. (1985,P.242)
AKAIKE (1969) FINAL PREDICTION ERROR - FPE = 0.83505E-02
(FPE IS ALSO KNOWN AS AMEMIYA PREDICTION CRITERION - PC)
AKAIKE (1973) INFORMATION CRITERION - LOG AIC = -4.7855
SCHWARZ (1978) CRITERION - LOG SC = -4.6920
MODEL SELECTION TESTS - SEE RAMANATHAN (1998,P.165)
CRAVEN-WAHBA (1979)
GENERALIZED CROSS VALIDATION - GCV = 0.83599E-02
HANNAN AND QUINN (1979) CRITERION = 0.86731E-02
RICE (1984) CRITERION = 0.83701E-02
SHIBATA (1981) CRITERION = 0.83322E-02
SCHWARZ (1978) CRITERION - SC = 0.91679E-02
AKAIKE (1974) INFORMATION CRITERION - AIC = 0.83503E-02
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.26927 3. 0.89756E-01 11.110
ERROR 0.92908 115. 0.80789E-02 P-VALUE
TOTAL 1.1983 118. 0.10155E-01 0.000
ANALYSIS OF VARIANCE - FROM ZERO
SS DF MS F
REGRESSION 19.778 4. 4.9444 612.016
ERROR 0.92908 115. 0.80789E-02 P-VALUE
TOTAL 20.707 119. 0.17401 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 115 DF P-VALUE CORR. COEFFICIENT AT MEANS
LRY -0.13139 0.1245 -1.055 0.294-0.098 -1.2451 -3.3675
LRYSQ 0.67255E-02 0.5637E-02 1.193 0.235 0.111 1.3466 1.8037
HDI 0.99077E-03 0.2016E-03 4.916 0.000 0.417 0.5296 0.2186
CONSTANT 0.94956 0.6885 1.379 0.171 0.128 0.0000 2.3452
DURBIN-WATSON = 2.0493 VON NEUMANN RATIO = 2.0667 RHO = -0.02520
RESIDUAL SUM = -0.68612E-13 RESIDUAL VARIANCE = 0.80789E-02
SUM OF ABSOLUTE ERRORS= 8.2866
R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.2247
RUNS TEST: 62 RUNS, 52 POS, 0 ZERO, 67 NEG NORMAL STATISTIC = 0.4576
COEFFICIENT OF SKEWNESS = 0.6739 WITH STANDARD DEVIATION OF 0.2218
COEFFICIENT OF EXCESS KURTOSIS = 0.1887 WITH STANDARD DEVIATION OF 0.4401
JARQUE-BERA NORMALITY TEST- CHI-SQUARE(2 DF)= 8.8666 P-VALUE= 0.012
GOODNESS OF FIT TEST FOR NORMALITY OF RESIDUALS - 10 GROUPS
OBSERVED 0.0 1.0 7.0 29.0 30.0 24.0 11.0 9.0 6.0 2.0
EXPECTED 1.0 3.3 9.4 18.9 26.9 26.9 18.9 9.4 3.3 1.0
CHI-SQUARE = 15.8515 WITH 4 DEGREES OF FREEDOM, P-VALUE= 0.003
|_Stop
Regression 2
Welcome to SHAZAM - Version 10.0 - JUL 2004 SYSTEM=WIN-XP PAR= 4000
CURRENT WORKING DIRECTORY IS: C:\PROGRA~1\SHAZAM
|_Sample 1 25
|_Read (Y:\classes\mydata.sha) INEQ LRY LRYSQ HDI/ List Skiplines = 1
UNIT 88 IS NOW ASSIGNED TO: Y:\classes\mydata.sha
4 VARIABLES AND 25 OBSERVATIONS STARTING AT OBS 1
INEQ LRY LRYSQ HDI
0.4080000 13.00283 169.0735 12.00000
0.3490000 12.61715 159.1925 8.000000
0.3520000 12.56664 157.9205 3.000000
0.3820000 12.26625 150.4608 22.00000
0.3600000 12.15354 147.7085 16.00000
0.3270000 12.11721 146.8267 10.00000
0.4030000 12.06410 145.5424 81.00000
0.3600000 12.03693 144.8877 20.00000
0.3150000 11.84166 140.2248 4.000000
0.5190000 11.79086 139.0244 52.00000
0.3250000 11.76479 138.4103 13.00000
0.5910000 11.70114 136.9168 70.00000
0.3780000 11.67883 136.3951 128.0000
0.3160000 11.62548 135.1519 26.00000
0.3260000 11.57994 134.0950 9.000000
0.4560000 11.49129 132.0498 67.00000
0.3310000 11.39286 129.7972 7.000000
0.2500000 11.36099 129.0721 17.00000
0.2500000 11.32183 128.1839 6.000000
0.3050000 11.27542 127.1350 15.00000
0.3160000 11.24614 126.4758 37.00000
0.2580000 11.22049 125.8993 2.000000
0.2470000 11.20829 125.6257 14.00000
0.4000000 11.16933 124.7539 84.00000
0.3030000 11.16228 124.5966 107.0000
|_STAT INEQ LRY LRYSQ HDI/PCOR
NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM
INEQ 25 0.35308 0.80948E-01 0.65526E-02 0.24700 0.59100
LRY 25 11.746 0.50250 0.25250 11.162 13.003
LRYSQ 25 138.22 12.006 144.15 124.60 169.07
HDI 25 33.200 35.680 1273.1 2.0000 128.00
CORRELATION MATRIX OF VARIABLES - 25 OBSERVATIONS
INEQ 1.0000
LRY 0.31334 1.0000
LRYSQ 0.30743 0.99974 1.0000
HDI 0.45043 -0.25446 -0.25626 1.0000
INEQ LRY LRYSQ HDI
|_OLS INEQ LRY LRYSQ HDI/ ANOVA AUXRSQ LIST
REQUIRED MEMORY IS PAR= 3 CURRENT PAR= 4000
OLS ESTIMATION
25 OBSERVATIONS DEPENDENT VARIABLE= INEQ
...NOTE..SAMPLE RANGE SET TO: 1, 25
R-SQUARE OF LRY ON OTHER INDEPENDENT VARIABLES = 0.9995
R-SQUARE OF LRYSQ ON OTHER INDEPENDENT VARIABLES = 0.9995
R-SQUARE OF HDI ON OTHER INDEPENDENT VARIABLES = 0.0713
R-SQUARE OF CONSTANT ON OTHER INDEPENDENT VARIABLES = 0.0000
R-SQUARE = 0.4422 R-SQUARE ADJUSTED = 0.3625
VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.41772E-02
STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.64631E-01
SUM OF SQUARED ERRORS-SSE= 0.87721E-01
MEAN OF DEPENDENT VARIABLE = 0.35308
LOG OF THE LIKELIHOOD FUNCTION = 35.1825
MODEL SELECTION TESTS - SEE JUDGE ET AL. (1985,P.242)
AKAIKE (1969) FINAL PREDICTION ERROR - FPE = 0.48455E-02
(FPE IS ALSO KNOWN AS AMEMIYA PREDICTION CRITERION - PC)
AKAIKE (1973) INFORMATION CRITERION - LOG AIC = -5.3325
SCHWARZ (1978) CRITERION - LOG SC = -5.1375
MODEL SELECTION TESTS - SEE RAMANATHAN (1998,P.165)
CRAVEN-WAHBA (1979)
GENERALIZED CROSS VALIDATION - GCV = 0.49728E-02
HANNAN AND QUINN (1979) CRITERION = 0.51007E-02
RICE (1984) CRITERION = 0.51600E-02
SHIBATA (1981) CRITERION = 0.46317E-02
SCHWARZ (1978) CRITERION - SC = 0.58726E-02
AKAIKE (1974) INFORMATION CRITERION - AIC = 0.48321E-02
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.69541E-01 3. 0.23180E-01 5.549
ERROR 0.87721E-01 21. 0.41772E-02 P-VALUE
TOTAL 0.15726 24. 0.65526E-02 0.006
ANALYSIS OF VARIANCE - FROM ZERO
SS DF MS F
REGRESSION 3.1862 4. 0.79654 190.690
ERROR 0.87721E-01 21. 0.41772E-02 P-VALUE
TOTAL 3.2739 25. 0.13096 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 21 DF P-VALUE CORR. COEFFICIENT AT MEANS
LRY 1.5423 1.148 1.343 0.193 0.281 9.5742 51.3098
LRYSQ -0.61512E-01 0.4807E-01 -1.280 0.215-0.269 -9.1236 -24.0797
HDI 0.12448E-02 0.3837E-03 3.244 0.004 0.578 0.5487 0.1171
CONSTANT -9.3026 6.844 -1.359 0.188-0.284 0.0000 -26.3471
OBS. OBSERVED PREDICTED CALCULATED
NO. VALUE VALUE RESIDUAL
1 0.40800 0.36666 0.41341E-01 I *
2 0.34900 0.37465 -0.25650E-01 * I
3 0.35200 0.36877 -0.16769E-01 *I
4 0.38200 0.38798 -0.59789E-02 *
5 0.36000 0.37598 -0.15979E-01 *I
6 0.32700 0.36672 -0.39717E-01 * I
7 0.40300 0.45219 -0.49186E-01 * I
8 0.36000 0.37463 -0.14626E-01 *I
9 0.31500 0.34036 -0.25359E-01 * I
10 0.51900 0.39561 0.12339 I *
11 0.32500 0.34463 -0.19627E-01 * I
12 0.59100 0.40929 0.18171 I *
13 0.37800 0.47917 -0.10117 * I
14 0.31600 0.34639 -0.30388E-01 * I
15 0.32600 0.31999 0.60071E-02 *
16 0.45600 0.38128 0.74724E-01 I *
17 0.33100 0.29333 0.37669E-01 I *
18 0.25000 0.30123 -0.51233E-01 * I
19 0.25000 0.28178 -0.31782E-01 * I
20 0.30500 0.28592 0.19084E-01 I*
21 0.31600 0.30871 0.72924E-02 I*
22 0.25800 0.26102 -0.30247E-02 *
23 0.24700 0.27398 -0.26978E-01 * I
24 0.40000 0.35466 0.45343E-01 I *
25 0.30300 0.38210 -0.79099E-01 * I
DURBIN-WATSON = 2.4477 VON NEUMANN RATIO = 2.5497 RHO = -0.28994
RESIDUAL SUM = 0.15545E-12 RESIDUAL VARIANCE = 0.41772E-02
SUM OF ABSOLUTE ERRORS= 1.0731
R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.4422
RUNS TEST: 12 RUNS, 9 POS, 0 ZERO, 16 NEG NORMAL STATISTIC = -0.2314
COEFFICIENT OF SKEWNESS = 1.3407 WITH STANDARD DEVIATION OF 0.4637
COEFFICIENT OF EXCESS KURTOSIS = 2.6959 WITH STANDARD DEVIATION OF 0.9017
JARQUE-BERA NORMALITY TEST- CHI-SQUARE(2 DF)= 10.5862 P-VALUE= 0.005
GOODNESS OF FIT TEST FOR NORMALITY OF RESIDUALS - 10 GROUPS
OBSERVED 0.0 0.0 2.0 3.0 11.0 4.0 3.0 0.0 1.0 1.0
EXPECTED 0.2 0.7 2.0 4.0 5.6 5.6 4.0 2.0 0.7 0.2
CHI-SQUARE = 12.1449 WITH 4 DEGREES OF FREEDOM, P-VALUE= 0.016
|_DIAGNOS / HET
REQUIRED MEMORY IS PAR= 9 CURRENT PAR= 4000
DEPENDENT VARIABLE = INEQ 25 OBSERVATIONS
REGRESSION COEFFICIENTS
1.54231745843 -0.615124099293E-01 0.124483191568E-02 -9.30264694552
HETEROSKEDASTICITY TESTS
CHI-SQUARE D.F. P-VALUE
TEST STATISTIC
E**2 ON YHAT: 4.853 1 0.02760
E**2 ON YHAT**2: 4.988 1 0.02553
E**2 ON LOG(YHAT**2): 4.590 1 0.03216
E**2 ON LAG(E**2) ARCH TEST: 0.233 1 0.62962
LOG(E**2) ON X (HARVEY) TEST: 7.387 3 0.06053
ABS(E) ON X (GLEJSER) TEST: 14.274 3 0.00255
E**2 ON X TEST:
KOENKER(R2): 7.299 3 0.06296
B-P-G (SSR) : 14.435 3 0.00237
...MATRIX ERROR...MAGNITUDE BELOW MACHINE PRECISION IN ROW -5.
THIS IS USUALLY CAUSED BY SINGULAR MATRIX.
...RESULTS MAY BE UNRELIABLE
E**2 ON X X**2 (WHITE) TEST:
KOENKER(R2): ********** 6 *********
B-P-G (SSR) : ********** 6 *********
...MATRIX ERROR...MAGNITUDE BELOW MACHINE PRECISION IN ROW -5.
THIS IS USUALLY CAUSED BY SINGULAR MATRIX.
...RESULTS MAY BE UNRELIABLE
E**2 ON X X**2 XX (WHITE) TEST:
KOENKER(R2): ********** 9 *********
B-P-G (SSR) : ********** 9 *********
|_OLS INEQ LRY LRYSQ HDI/ HETCOV
REQUIRED MEMORY IS PAR= 3 CURRENT PAR= 4000
OLS ESTIMATION
25 OBSERVATIONS DEPENDENT VARIABLE= INEQ
...NOTE..SAMPLE RANGE SET TO: 1, 25
USING HETEROSKEDASTICITY-CONSISTENT COVARIANCE MATRIX
R-SQUARE = 0.4422 R-SQUARE ADJUSTED = 0.3625
VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.41772E-02
STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.64631E-01
SUM OF SQUARED ERRORS-SSE= 0.87721E-01
MEAN OF DEPENDENT VARIABLE = 0.35308
LOG OF THE LIKELIHOOD FUNCTION = 35.1825
MODEL SELECTION TESTS - SEE JUDGE ET AL. (1985,P.242)
AKAIKE (1969) FINAL PREDICTION ERROR - FPE = 0.48455E-02
(FPE IS ALSO KNOWN AS AMEMIYA PREDICTION CRITERION - PC)
AKAIKE (1973) INFORMATION CRITERION - LOG AIC = -5.3325
SCHWARZ (1978) CRITERION - LOG SC = -5.1375
MODEL SELECTION TESTS - SEE RAMANATHAN (1998,P.165)
CRAVEN-WAHBA (1979)
GENERALIZED CROSS VALIDATION - GCV = 0.49728E-02
HANNAN AND QUINN (1979) CRITERION = 0.51007E-02
RICE (1984) CRITERION = 0.51600E-02
SHIBATA (1981) CRITERION = 0.46317E-02
SCHWARZ (1978) CRITERION - SC = 0.58726E-02
AKAIKE (1974) INFORMATION CRITERION - AIC = 0.48321E-02
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.69541E-01 3. 0.23180E-01 5.549
ERROR 0.87721E-01 21. 0.41772E-02 P-VALUE
TOTAL 0.15726 24. 0.65526E-02 0.006
ANALYSIS OF VARIANCE - FROM ZERO
SS DF MS F
REGRESSION 3.1862 4. 0.79654 190.690
ERROR 0.87721E-01 21. 0.41772E-02 P-VALUE
TOTAL 3.2739 25. 0.13096 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 21 DF P-VALUE CORR. COEFFICIENT AT MEANS
LRY 1.5423 0.9596 1.607 0.123 0.331 9.5742 51.3098
LRYSQ -0.61512E-01 0.4007E-01 -1.535 0.140-0.318 -9.1236 -24.0797
HDI 0.12448E-02 0.4678E-03 2.661 0.015 0.502 0.5487 0.1171
CONSTANT -9.3026 5.735 -1.622 0.120-0.334 0.0000 -26.3471
DURBIN-WATSON = 2.4477 VON NEUMANN RATIO = 2.5497 RHO = -0.28994
RESIDUAL SUM = 0.16875E-12 RESIDUAL VARIANCE = 0.41772E-02
SUM OF ABSOLUTE ERRORS= 1.0731
R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.4422
RUNS TEST: 12 RUNS, 9 POS, 0 ZERO, 16 NEG NORMAL STATISTIC = -0.2314
COEFFICIENT OF SKEWNESS = 1.3407 WITH STANDARD DEVIATION OF 0.4637
COEFFICIENT OF EXCESS KURTOSIS = 2.6959 WITH STANDARD DEVIATION OF 0.9017
JARQUE-BERA NORMALITY TEST- CHI-SQUARE(2 DF)= 10.5862 P-VALUE= 0.005
GOODNESS OF FIT TEST FOR NORMALITY OF RESIDUALS - 10 GROUPS
OBSERVED 0.0 0.0 2.0 3.0 11.0 4.0 3.0 0.0 1.0 1.0
EXPECTED 0.2 0.7 2.0 4.0 5.6 5.6 4.0 2.0 0.7 0.2
CHI-SQUARE = 12.1449 WITH 4 DEGREES OF FREEDOM, P-VALUE= 0.016
|_Stop
