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Dougherty: Introduction to Econometrics 4e Instructors Manual C. Dougherty 2011. All rights reserved. 7 HETEROSCEDASTICITY 7.1 Heteroscedasticity and its implications 7.2 Detection of heteroscedasticity 7.1 The table gives data on government recurrent expenditure, G , investment, I , gross domestic product, Y , and population, P , for 30 countries in 1997 (source: 1999 International Monetary Fund Yearbook ). G , I , and Y are measured in US$ billion and P in million. A researcher investigating whether government expenditure tends to crowd out investment fits the regression (standard errors in parentheses): I = 18.10 1.07 G + 0.36 Y R 2 = 0.99. (7.79) (0.14) (0.02) Country I G Y P Country I G Y P Australia 94.5 75.5 407.9 18.5 Netherlands 73.0 49.9 360.5 15.6 Austria 46.0 39.2 206.0 8.1 New Zealand 12.9 9.9 65.1 3.8 Canada 119.3 125.1 631.2 30.3 Norway 35.3 30.9 153.4 4.4 Czech Republic 16.0 10.5 52.0 10.3 Philippines 20.1 10.7 82.2 78.5 Denmark 34.2 42.9 169.3 5.3 Poland 28.7 23.4 135.6 38.7 Finland 20.2 25.0 121.5 5.1 Portugal 25.6 19.9 102.1 9.8 France 255.9 347.2 1409.2 58.6 Russia 84.7 94.0 436.0 147.1 Germany 422.5 406.7 2102.7 82.1 Singapore 35.6 9.0 95.9 3.7 Greece 24.0 17.7 119.9 10.5 Spain 109.5 86.0 532.0 39.3 Iceland 1.4 1.5 7.5 0.3 Sweden 31.2 58.8 227.8 8.9 Ireland 14.3 10.1 73.2 3.7 Switzerland 50.2 38.7 256.0 7.1 Italy 190.8 189.7 1145.4 57.5 Thailand 48.1 15.0 153.9 60.6 Japan 1105.9 376.3 3901.3 126.1 Turkey 50.2 23.3 189.1 62.5 Korea 154.9 49.3 442.5 46.0 UK 210.1 230.7 1256.0 58.2 Malaysia 41.6 10.8 97.3 21.0 USA 1517.7 1244.1 8110.9 267.9 She sorts the observations by increasing size of Y and runs the regression again for the 11 countries with smallest Y and the 11 countries with largest Y . RSS for these regressions is 321 and 28101, respectively. Perform a GoldfeldQuandt test for heteroscedasticity. Answer: RSS 2 / RSS 1 = 28101/321 = 87.5. The critical value of F (8,8) at the 0.1 percent level is 12.0, so the null hypothesis of homoscedasticity is rejected at that significance level. 7.2 The researcher saves the residuals from the full-sample regression in Exercise 7.1 and regresses their squares on G , Y , their squares, and their product. R 2 is 0.9878. Perform a White test for heteroscedasticity. Answer : In the output below EI2 is the squared residual from the full-sample regression in Exercise 7.1 and the other variables are self-explanatory. The White test statistic is nR 2 = 30*0.9878 = 29.63. Under the null hypothesis of homoscedasticity, this is distributed as a chi- squares statistic with five degrees of freedom. The null hypothesis is rejected at the 0.1 percent level, critical value 20.52. HETEROSCEDASTICITY C. Dougherty 2011. All rights reserved.... View Full Document