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Posted on Aug 01, 2024

1 ON- 3.0 7 4.8 B D E Tax revenue Average number of Average number of (million Ghanian Tax revenue 3-point shots in the 3-point

1 ON- 3.0 7 4.8 B D E Tax revenue Average number of Average number of (million Ghanian Tax revenue 3-point shots in the 3-point shots in the NBA Year cedis) (in log-level) NBA (in log-level) 1990 16.453 2.801 2.3 0.833 1991 25.701 3.247 2.5 0.916 1992 23.973 3.177 1.099 1993 39.885 3.686 3.3 1.194 1994 67.063 4.206 5.5 1.705 1995 86.351 4.458 5.9 1.775 1996 127.731 4.850 6.0 1.792 1997 146.356 4.986 4.4 1.482 1998 196.778 5.282 4.5 1.504 1999 213.783 5.365 1.569 2000 441.466 6.090 4.8 1.569 2001 655.652 6.486 1.649 2002 854.224 6.750 5.1 1.629 2003 1,317.846 7.184 5.2 1.649 2004 1,779.984 7.484 5.6 1.723 2005 2,122.698 7.660 5.7 1.740 2006 2.464.612 7.810 6.1 1.808 2007 2.997.420 8.006 6.6 1.887 2008 3,762.243 8.233 6.6 1.887 2009 4,395.896 8.388 6.4 1.856 2010 6,000.123 8.700 6.5 1.872 2011 9,052.363 9.111 6.4 2012 1.856 11,574.599 9.357 7.2 2013 13,284.043 1.974 9.494 7.7 2014 2.041 17,855.417 9.790 7.8 2015 2.054 21,455.181 9.974 8.5 2016 25,929.478 2.140 10.163 9.7 2.272 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 5.2 colo D F G K L M N O D CHINE PU 100 1000 1001 09 9 10 11 92 13 Average number of 3 point shots per Tax wenuse team in the han NDA Yew 1900 28 1991 32 2 1000 37 1.10 49 1.105 1903 45 17 1900 4.8 1.700 100 140 33 1504 1190 54 1509 2000 0.1 1600 2001 65 1.640 2002 1620 2000 72 7040 2004 7.5 1723 2005 1.740 TB 100 2007 BO 1897 2000 0.2 3 1 2010 8.7 18 2011 0.1 180 2012 94 1974 2013 95 2011 2014 98 2054 2015 100 2.140 2010 102 2.272 15 10 17 2000 10 20 25 22 23 36 2000 2007 TH 2004 2 30 2 3000 - hand 27 min 20 c D 1 M N 0 P . 8 YOUTPUT 0879 0773 a 764 1.11 AR Stardardo CO MON MS RE 0000 11 PM 3117 1.24 25 20 Sundado 2 -3201 Lower -000 -4201 D SOM 010 2020 TESTERISER HELAL DUTIRUT PREY tinai 14 101 0907 1992 3245 VO 2009 7011707 0 1 2 ) - 2321 2017 . 2 20 25 2 -0.00 - 10 4 0004 IU 11 BRO w PLOD WHO To -19 OS TECH 09 72670 003 TOP 5142 TIN 100004 2000 2001 2000 2002 700 ca 30 3000 7000026 2000 2007 me TS 2000 2010 2011 700 2012 MM DAT De 0.00 046715 G4513 DO DOTTA 2010 MI WHO CESTO ICO w BE De S736 12 B17540 5+ HDOT HECHOD 102 20 2014 1 BA DDT 1024 COS 2011 2011 01 d WED 2005 200 000 9.00 LLO DE COCO TO DE WOO FOTO wo COCWORD FOTO CO 2008 1201 2007 0.114 Anden w DODO CO GOOD SOHO WID STO SE ACIDO CRIS WOO ZOO 30 27 . 27 2 S2 2004 02345 2009 OTTO 0002005001 0 000 2000 190 0 0.25 100 0 0.0 10 COLLO CEO RE GEO ce WORLD NOCH GE TO COOL HIRO GO COLO woro A IND GE SOUL OUTPUT We eo TE LEO SER 000 PF 2009 2013 win 4100 ER EL VALHO WHO 0100 CIDO AR R MOR SUMMARY OUT US 0 It stands to reason that, from an economic perspective, the number of three-point shots made by NBA basketball players and Ghanaian tax receipts are unlikely to be correlated. That is, three-point shots in the NBA are unlikely to be a useful predictor of Ghanaian tax revenue. Nevertheless, let us conduct an experiment. Let us estimate an OLS linear regression with Ghanaian tax revenue, T, as the dependent variable, and the average number of three-point shots, NBA,, as the independent variable, as shown in the following equation: Interpret the results. Select all that apply beta_1 approximates the elasticity of Ghanaian tax revenue with respect to the number of three-point shots. The estimated betaj is high and statistically significant, suggesting that Ghanaian tax revenue and the number of three-point shots are strongly correlated. The results from this regression confirm that Ghanaian tax revenue and the number of three-point shots are not correlated. Assuming our estimates are reliable, when the number of three-point shots increases by 1 percent, tax revenue in Ghana increases, on average, by 5.8 percent. Naturally, the results from the previous question would draw suspicion from an experienced tax analyst. To assess the results' validity, let us plot the residuals over time. Do you detect any potential issues? Interpret the results. Select all that apply. Long periods of increasing values of the residuals are followed by long periods of decreasing values, suggesting the presence of serial correlation. The residuals are well behaved with no sign of autocorrelation. The residuals do not rapidly revert to the zero mean. The residuals appear to be randomly distributed. Now run the regression in first differences: Aln(T) = Yo + Y1.Aln(NBA) + Et Interpret the results. Select all that apply. Y approximates the elasticity of Ghanaian tax revenue with respect to the number of three-point shots. The estimated y, is high and statistically significant, suggesting that Ghanaian tax revenue and the number of three-point shots are strongly correlated. The estimated y, is not statistically significant, suggesting that the growth rate of Ghanaian tax revenue and that of the number of three-point shots are not correlated. The regression in levels appears to be spurious. As a final check, let us plot the residuals from the regression in first difference over time. What does a careful examination of this chart reveal? Interpret the results. Select all that apply. Long periods of increasing values of the residuals are followed by long periods of decreasing values, suggesting strong autocorrelation of the residuals. The residuals are reasonably well behaved with no sign of autocorrelation. The residuals rapidly revert to the zero mean. The residuals may be stationary. When estimating tax elasticity using a linear regression, which of the statement(s) hold(s) true? Select all that apply. A forecaster should always estimate an equation with tax revenue and tax base in levels. An equation estimated in log levels may give reliable results if neither the tax revenue nor tax base displays a steady upward trend over time. One may account for policy shocks using dummy variables. Estimates should be very carefully interpreted, with a clear assessment of all the pitfalls. 1 ON- 3.0 7 4.8 B D E Tax revenue Average number of Average number of (million Ghanian Tax revenue 3-point shots in the 3-point shots in the NBA Year cedis) (in log-level) NBA (in log-level) 1990 16.453 2.801 2.3 0.833 1991 25.701 3.247 2.5 0.916 1992 23.973 3.177 1.099 1993 39.885 3.686 3.3 1.194 1994 67.063 4.206 5.5 1.705 1995 86.351 4.458 5.9 1.775 1996 127.731 4.850 6.0 1.792 1997 146.356 4.986 4.4 1.482 1998 196.778 5.282 4.5 1.504 1999 213.783 5.365 1.569 2000 441.466 6.090 4.8 1.569 2001 655.652 6.486 1.649 2002 854.224 6.750 5.1 1.629 2003 1,317.846 7.184 5.2 1.649 2004 1,779.984 7.484 5.6 1.723 2005 2,122.698 7.660 5.7 1.740 2006 2.464.612 7.810 6.1 1.808 2007 2.997.420 8.006 6.6 1.887 2008 3,762.243 8.233 6.6 1.887 2009 4,395.896 8.388 6.4 1.856 2010 6,000.123 8.700 6.5 1.872 2011 9,052.363 9.111 6.4 2012 1.856 11,574.599 9.357 7.2 2013 13,284.043 1.974 9.494 7.7 2014 2.041 17,855.417 9.790 7.8 2015 2.054 21,455.181 9.974 8.5 2016 25,929.478 2.140 10.163 9.7 2.272 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 5.2 colo D F G K L M N O D CHINE PU 100 1000 1001 09 9 10 11 92 13 Average number of 3 point shots per Tax wenuse team in the han NDA Yew 1900 28 1991 32 2 1000 37 1.10 49 1.105 1903 45 17 1900 4.8 1.700 100 140 33 1504 1190 54 1509 2000 0.1 1600 2001 65 1.640 2002 1620 2000 72 7040 2004 7.5 1723 2005 1.740 TB 100 2007 BO 1897 2000 0.2 3 1 2010 8.7 18 2011 0.1 180 2012 94 1974 2013 95 2011 2014 98 2054 2015 100 2.140 2010 102 2.272 15 10 17 2000 10 20 25 22 23 36 2000 2007 TH 2004 2 30 2 3000 - hand 27 min 20 c D 1 M N 0 P . 8 YOUTPUT 0879 0773 a 764 1.11 AR Stardardo CO MON MS RE 0000 11 PM 3117 1.24 25 20 Sundado 2 -3201 Lower -000 -4201 D SOM 010 2020 TESTERISER HELAL DUTIRUT PREY tinai 14 101 0907 1992 3245 VO 2009 7011707 0 1 2 ) - 2321 2017 . 2 20 25 2 -0.00 - 10 4 0004 IU 11 BRO w PLOD WHO To -19 OS TECH 09 72670 003 TOP 5142 TIN 100004 2000 2001 2000 2002 700 ca 30 3000 7000026 2000 2007 me TS 2000 2010 2011 700 2012 MM DAT De 0.00 046715 G4513 DO DOTTA 2010 MI WHO CESTO ICO w BE De S736 12 B17540 5+ HDOT HECHOD 102 20 2014 1 BA DDT 1024 COS 2011 2011 01 d WED 2005 200 000 9.00 LLO DE COCO TO DE WOO FOTO wo COCWORD FOTO CO 2008 1201 2007 0.114 Anden w DODO CO GOOD SOHO WID STO SE ACIDO CRIS WOO ZOO 30 27 . 27 2 S2 2004 02345 2009 OTTO 0002005001 0 000 2000 190 0 0.25 100 0 0.0 10 COLLO CEO RE GEO ce WORLD NOCH GE TO COOL HIRO GO COLO woro A IND GE SOUL OUTPUT We eo TE LEO SER 000 PF 2009 2013 win 4100 ER EL VALHO WHO 0100 CIDO AR R MOR SUMMARY OUT US 0 It stands to reason that, from an economic perspective, the number of three-point shots made by NBA basketball players and Ghanaian tax receipts are unlikely to be correlated. That is, three-point shots in the NBA are unlikely to be a useful predictor of Ghanaian tax revenue. Nevertheless, let us conduct an experiment. Let us estimate an OLS linear regression with Ghanaian tax revenue, T, as the dependent variable, and the average number of three-point shots, NBA,, as the independent variable, as shown in the following equation: Interpret the results. Select all that apply beta_1 approximates the elasticity of Ghanaian tax revenue with respect to the number of three-point shots. The estimated betaj is high and statistically significant, suggesting that Ghanaian tax revenue and the number of three-point shots are strongly correlated. The results from this regression confirm that Ghanaian tax revenue and the number of three-point shots are not correlated. Assuming our estimates are reliable, when the number of three-point shots increases by 1 percent, tax revenue in Ghana increases, on average, by 5.8 percent. Naturally, the results from the previous question would draw suspicion from an experienced tax analyst. To assess the results' validity, let us plot the residuals over time. Do you detect any potential issues? Interpret the results. Select all that apply. Long periods of increasing values of the residuals are followed by long periods of decreasing values, suggesting the presence of serial correlation. The residuals are well behaved with no sign of autocorrelation. The residuals do not rapidly revert to the zero mean. The residuals appear to be randomly distributed. Now run the regression in first differences: Aln(T) = Yo + Y1.Aln(NBA) + Et Interpret the results. Select all that apply. Y approximates the elasticity of Ghanaian tax revenue with respect to the number of three-point shots. The estimated y, is high and statistically significant, suggesting that Ghanaian tax revenue and the number of three-point shots are strongly correlated. The estimated y, is not statistically significant, suggesting that the growth rate of Ghanaian tax revenue and that of the number of three-point shots are not correlated. The regression in levels appears to be spurious. As a final check, let us plot the residuals from the regression in first difference over time. What does a careful examination of this chart reveal? Interpret the results. Select all that apply. Long periods of increasing values of the residuals are followed by long periods of decreasing values, suggesting strong autocorrelation of the residuals. The residuals are reasonably well behaved with no sign of autocorrelation. The residuals rapidly revert to the zero mean. The residuals may be stationary. When estimating tax elasticity using a linear regression, which of the statement(s) hold(s) true? Select all that apply. A forecaster should always estimate an equation with tax revenue and tax base in levels. An equation estimated in log levels may give reliable results if neither the tax revenue nor tax base displays a steady upward trend over time. One may account for policy shocks using dummy variables. Estimates should be very carefully interpreted, with a clear assessment of all the pitfalls