The study examines the effect of inflation, investment, life expectancy and literacy rate on per capita GDP across 20 countries using ordinary least squares regression. Initially, the regression results show inflation, investment and literacy rate have a negative effect, while life expectancy has a positive effect on per capita GDP. Sri Lanka, USA and Japan are identified as potential outliers based on their high residuals. Running the regression after removing these outliers improves the model fit and explanatory power of the variables. Diagnostic tests find no evidence of misspecification or heteroskedasticity, validating the OLS estimates.

1. STUDYING THE EFFECT OF INFLATION, INVESTMENT, LIFE EXPECTANCY AND LITERACY RATE ON PER CAPITA GDP GUIDE: PROF. SAMARJIT DAS REPORT BY: UDAY THARAR MSQE 1 ST YEAR QE0703 INDIAN STATISTICAL INSTITUTE

2. DATA Country GDP PC ($) Inflation (%) Investment ratio (%) Life Expectancy (years) Literacy Rates (%) (PCI) (I) (INV) (LE) (LIT) India 1348 9.8 25 61.3 51.2 China 2604 9.3 40 68.9 80.9 Sri Lanka 3277 11.8 25 72.2 90.1 USA 26397 3.2 16 76.2 99 UK 18620 5.1 16 76.7 99 Russia 4828 148.9 25 65.7 98.7 Pakistan 2154 9.2 19 62.3 37.1 Bangladesh 1331 6.4 17 56.4 37.3 Australia 19285 3.7 23 78.1 99 Canada 21459 2.9 19 79 99 France 20510 2.8 18 78.7 99 Germany 19675 3 21 76.3 99 Japan 21581 1.4 29 79.8 99 Kenya 1404 13 19 53.6 77 Argentina 8937 255.6 18 72.4 96 Zimbabwe 2196 20.9 22 49 84.7 Indonesia 3740 8.8 38 63.5 83.2 Korea 10656 6.7 37 71.5 97.9 Norway 21346 3 23 77.5 99 Thailand 7104 5 43 69.5 93.5

3. PLOT OF DATA

4. THE METHOD USED IS OLS WITH PER CAPITA GDP AS THE EXPLAINED VARIABLE AND INFLATION, INVESTMENT RATIO, LIFE EXPECTANCY AND LITERACY RATE AS EXPLANATORY VARIABLES. We now provide a brief explanation of the explanatory variables-- ANALYSIS

7. REGRESSION RESULTS Dependent Variable: PCI Method: Least Squares Sample: 1 20 Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob. I -38.4496 13.3138 -2.888 0.0113 INV -392.582 98.1917 -3.9981 0.0012 LE 571.6545 119.109 4.7994 0.0002 LIT 156.2885 54.5576 2.8647 0.0118 C -31508 6827.77 -4.6147 0.0003 R-squared 0.883177 Mean dependent var 10923 Adjusted R-squared 0.852024 S.D. dependent var 8981.6 S.E. of regression 3455.021 Akaike info criterion 19.345 Sum squared resid 1.79E+08 Schwarz criterion 19.594 Log likelihood -188.454 F-statistic 28.35 Durbin-Watson stat 2.4797 Prob(F-statistic) 0.000001

9. RESIDUALS Obs. No. Actual Fitted Residual 1 1348 1345 2.99884 2 2604 4461.83 -1857.83 3 3277 13578.8 -10301.8 4 26397 21120.2 5276.75 5 18620 21333 -2713.02 6 4828 5935.65 -1107.65 7 2154 2091.55 62.4482 8 1331 -357.129 1688.13 9 19285 19439.1 -154.092 10 21459 21554.7 -95.6699 11 20510 21779.6 -1269.6 12 19675 19222.2 452.807 13 21581 18143.8 3437.15 14 1404 3207.96 -1803.96 15 8937 7989.27 947.734 16 2196 300.271 1895.73 17 3740 2538.75 1201.25 18 10656 9882.75 773.245 19 21346 19123 2222.99 20 7104 5761.65 1342.35

10. RESIDUAL ANALYSIS THE RESIDUAL TABLE AND GRAPH INDICATE THE PRESENCE OF SOME OUTLIERS.THE OBSERVATIONS 3, 4 & 13 HAVE HIGHER RESIDUALS THAN THE OTHERS. THESE COUNTRIES ARE SRI LANKA, USA AND JAPAN RESPECTIVELY. THOUGH ANALYSING THE RESIDUALS IS NOT A VERY GOOD INDICATOR OF OUTLIERS BUT BY LOOKING AT THE INDIVIDUAL OBSERVATIONS ONE CAN GET THE INTUITION THAT THESE COULD BE OUTLIERS SINCE SRI LANKA HAS HIGH LITERACY AND LIFE EXPECTANCY RATES INSPITE OF BEING A LOW PER CAPITA INCOME COUNTRY AND THE REMAINING 2 HAVE A HIGH PER CAPITA INCOME AS COMPARED TO THE OTHER COUNTRIES. THESE DIFFERENCES COULD BE DUE TO DIFFERENT NATIONAL POLICIES THAT THEIR GOVERNMENTS FOLLOW. WE WILL RUN ANOTHER REGRESSION AFTER DELETING THESE.

11. REGRESSION RESULTS AFTER DELETING THE OUTLIERS Dependent Variable: PCI Method: Least Squares Sample: 1 17 Included observations: 17 Variable Coefficient Std. Error t-Statistic Prob. I -36.57134 6.271489 -5.831365 0.0001 INV -360.7367 47.65338 -7.570013 0.0000 LE 553.5307 56.83341 9.739529 0.0000 LIT 149.2246 25.52452 5.846322 0.0001 C -30431.88 3279.835 -9.278479 0.0000 R-squared 0.972098 Mean dependent var 9835.118 Adjusted R-squared 0.962798 S.D. dependent var 8295.732 S.E. of regression 1600.071 Akaike info criterion 17.83341 Sum squared resid 30722718 Schwarz criterion 18.07847 Log likelihood -146.584 F-statistic 104.5204 Durbin-Watson stat 1.23126 Prob(F-statistic) 0.00000

12. COMPARISON BETWEEN THE TWO EQUATIONS Variable Coefficient Std. Error Prob. of t- statistic NEW OLD NEW OLD NEW OLD C -30431.88 -31508.03 3279.84 6827.771 0.0000 0.0003 I -36.57134 -38.44955 6.27149 13.31378 0.0001 0.0113 INV -360.7367 -392.5823 47.6534 98.19166 0.0000 0.0012 LE 553.5307 571.6545 56.8334 119.1089 0.0000 0.0002 LIT 149.2246 156.2885 25.5245 54.55759 0.0001 0.0118 OLD R-squared = 0.883177 NEW R-squared = 0.97208

14. WE WILL NOW CHECK IF OUR OLS ESTIMATES ARE VALID OR NOT BY CHECKING IF SOME OF THE STANDARD CLRM ASSUMPTIONS ARE VIOLATED. FOR THIS WE CARRY OUT A FEW TESTING EXERCISES. Estimated Equation: PCI = - 30431.88104 - 36.57134273*I - 360.736706*INV + 553.5306553*LE + 149.2245611*LIT Thus while Inflation and Investment are inversely related with PCI, Life Expectancy and Literacy Rate influence it positively.

15. JARQUE-BERA NORMALITY TEST ON THE RESIDUALS The test is to check for normality of the disturbance terms. The null hypothesis of the test is that the error terms or the residuals are N(0, σ ²). This test actually tests for the joint null hypothesis that the skewness E( ) is zero and the kurtosis E( ) is equal to 3 , which holds if the s are N(0, σ ²) distributed. Under the null hypothesis the test statistic involved (for large n) has a χ 2 distribution.

16. The Null Hypothesis cannot be rejected both at 5% & 1% level of significance. So we conclude that the residuals are indeed normally distributed. However, the Jarque-Bera test is an asymptotic test. Our sample size is only 17 so the validity of the test is under suspect.

17. THE RAMSEY RESET TEST The Ramsey Reset Test is a test for Functional Specification. It checks for any functional mis-specification. As suggested by Ramsey, the Null Hypothesis of a zero u vector is based on an augmented regression on the powers of the estimated or predicted values of the dependent variable namely y ² , y ³ , …. and testing whether the coefficients are significant or not. This test has been done by taking the no. of fitted items as 1.

18. RESULTS We can see that the coefficients of higher powers are indeed zero as suggested by the Probability value. Thus we can assert that our Regression has a Linear Specification . F-statistic 0.213322 Probability 0.653176 Log likelihood ratio 0.326523 Probability 0.567714 Dependent Variable: PCI Method: Least Squares Sample: 1 17 Included observations: 17 Variable Coefficient Std. Error t-Statistic Prob. I -25.19922 25.46244 -0.989662 0.3436 INV -252.5063 239.4612 -1.054477 0.3143 LE 436.2553 260.6334 1.673827 0.1223 LIT 117.1873 74.22027 1.578913 0.1427 C -24374.78 13546.16 -1.799387 0.0994 FITTED^2 1.01E-05 2.18E-05 0.461868 0.6532 R-squared 0.972629 Mean dependent var 9835.118 Adjusted R-squared 0.960188 S.D. dependent var 8295.732 S.E. of regression 1655.246 Akaike info criterion 17.93185 Sum squared resid 30138250 Schwarz criterion 18.22593 Log likelihood -146.4207 F-statistic 78.17742 Durbin-Watson stat 1.147307 Prob(F-statistic) 0.00000

19. WHITE HETEROSKEDASTICITY TEST Heteroskedasticity refers to the situation in which the variance of the error term in the regression equation is not constant but varies with the independent variable. In the presence of Heteroskedasticity, the Ordinary Least Square estimates, although still unbiased are no longer efficient. We refer to the WHITE HETEROSKEDASTICITY TEST for the detection of Heteroskedasticity, wherein one simply computes an auxiliary regression of the squared OLS residuals on a constant and all nonredundant variables in the set consisting of the regressors, their squares and their cross products.

20. F-statistic 0.227803 Probability 0.96688 Obs*R-squared 10.44798 Probability 0.728753 Dependent Variable: RESID^2 Method: Least Squares Sample: 1 17 Included observations: 17 Variable Coefficient Std. Error t-Statistic Prob. C -75374067 3.54E+08 -0.213016 0.8511 I -10081278 11074801 -0.91029 0.4588 I^2 -2498.45 9178.294 -0.272213 0.811 I*INV -63434.68 162973.3 -0.389234 0.7346 I*LE 20712.75 82431.95 0.251271 0.8251 I*LIT 107716.9 144434.2 0.745785 0.5335 INV -575564.1 4728705 -0.121717 0.9143 INV^2 -7644.143 39704.83 -0.192524 0.8651 INV*LE 66620.99 66914.45 0.995614 0.4243 INV*LIT -39814.76 46810.45 -0.850553 0.4846 LE 280836.1 8263663 0.033984 0.976 LE^2 23553.41 63113.34 0.373192 0.7448 LE*LIT -60564.7 75744.67 -0.79959 0.5078 LIT 3163495 4311567 0.733723 0.5395 LIT^2 5397.202 18044.68 0.299102 0.7931

22. SORTED DATA Country GDP PC Inflation Investment ratio Life Expectancy Literacy Rates (PCI) (I) (INV) (LE) (LIT) Zimbabwe 2196.0 20.9 22.0 49.0 84.7 Kenya 1404.0 13.0 19.0 53.6 77.0 Bangladesh 1331.0 6.4 17.0 56.4 37.3 India 1348.0 9.8 25.0 61.3 51.2 Pakistan 2154.0 9.2 19.0 62.3 37.1 Indonesia 3740.0 8.8 38.0 63.5 83.2 Russia 4828.0 148.9 25.0 65.7 98.7 China 2604.0 9.3 40.0 68.9 80.9 Thailand 7104.0 5.0 43.0 69.5 93.5 Korea 10656.0 6.7 37.0 71.5 97.9 Argentina 8937.0 255.6 18.0 72.4 96.0 Germany 19675.0 3.0 21.0 76.3 99.0 UK 18620.0 5.1 16.0 76.7 99.0 Norway 21346.0 3.0 23.0 77.5 99.0 Australia 19285.0 3.7 23.0 78.1 99.0 France 20510.0 2.8 18.0 78.7 99.0 Canada 21459.0 2.9 19.0 79.0 99.0

24. PARAMETER STABILITY TESTS THE CUSUM TEST SINCE THE CUMULATIVE SUM IS INSIDE THE AREA BETWEEN,THE TWO CRITICAL LINES,WE CAN SAY THAT THE PARAMETERS ARE CONSTANT IN TERMS OF INTERCEPT. THE CUSUMSQ TEST HERE WE CAN SAY THAT THE PARAMETERS ARE CONSTANT IN TERMS OF VARIANCE.

25. THE RECURSIVE RESIDUALS TEST THE RESIDUALS ARE INSIDE THE STANDARD ERROR BANDS. IT SUGGESTS THAT THE PARAMETERS ARE STABLE.

27. Chow Forecast Test: Forecast from 15 to 17 F-statistic 1.476388 Probability 0.285454 Log likelihood ratio 6.80347 Probability 0.078433 Dependent Variable: PCI Method: Least Squares Sample: 1 14 Included observations: 14 Variable Coefficient Std. Error t-Statistic Prob. I -34.69875 6.000098 -5.783031 0.0003 INV -394.0349 58.12046 -6.779625 0.0001 LE 534.8819 54.46534 9.820593 0.0000 LIT 144.0358 24.30871 5.925275 0.0002 C -28332.41 3331.343 -8.504801 0.0000 R-squared 0.978415 Mean dependent var 9149.357 Adjusted R-squared 0.968821 S.D. dependent var 8565.987 S.E. of regression 1512.535 Akaike info criterion 17.75341 Sum squared resid 20589850 Schwarz criterion 17.98165 Log likelihood -119.2739 F-statistic 101.9883 Durbin-Watson stat 1.396911 Prob(F-statistic) 0.0000

28. From the statistical table under F distribution, we see that: F 3,9,0.05 = 3.86 F 3,9,0.01 = 6.99 From the table the Chow F-statistic obtained is F(3,9) = 1.476388 Thus the value of the F-statistic obtained is less than the tabular value at both 5% and 1% level of significance. We therefore accept the Null Hypothesis of parameter constancy at both 5% and 1% level of significance.

30. We have obtained the following results: From the results obtained above we see that in our model the VIF of all the estimated coefficients are close to 1. Thus we conclude that the model is free from multicollinearity or in other words, the explanatory variables are uncorrelated. Regressors VIF I 1.123 INV 1.105 LEX 1.781 LIT 1.911

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