Question 3: (35 marks) In this question you must estimate a time series model for value added tax (VAT) collections, for South Africa. You are provided with the following data: Variable names and description: VAT : Value added tax revenue, nominal (R millions) HCE Final consumption expenditure by households, nominal (R millions) HYD Disposable income of households, nominal (R millions) M3 Money supply, nominal (R millions) LAB Nominal labor costs in the non-agricultural sectors (Index, 2010 = 100) INF : Inflation (percentage, quarter on previous quarter at annual rate) CPI Consumer price index (Index, 2015 = 100) (2) 3.1 Provide a description of the data (type, interval, etc.) 3.2 Calculate and provide a graph of the real value added tax for the period 1990 to 2018. Discuss the trends you observe in VAT collection, before and after 2008. (3) (6) 3.3 Test the real value added tax and inflation variables for stationarity. Provide your results in the table below (please add rows where necessary): 'L'indicates the logarithmic function 'R' indicates that real values are used. Variable Model Lags ADF test statistic TTT LRVAT and Trend Intercept Intercept None Trend Intercept Intercept None INF and Statistically significant at the: 10% level (*), 5% level (**), 1% level (***) You can assume that all other variables are non-stationary, integrated of order 1(1). 3.4 Test for possible cointegration between variables: (i) Estimate the following long run cointegration equation. Copy and paste your EViews results window in your answer sheet. (2) LRVAT, = a + BLRHCET + TLRM3t + res (ii) Evaluate the potential long-run equation. Do the estimated coefficients correspond to your a priori expectations in terms of sign? Explain. (2) (ii) Generate the residual series for your long run equation. (Name your residual series as follows: res underscore the first three letters of your name, e.g. res_fan) Demonstrate, how you can use the residual series to test if cointegration exists between the variables in the long run model. (3) 3.5 Construct a short run (Error Correction) component for your model (i) Estimate the following short run cointegration equation. Copy and paste your EViews results window in your answer sheet. (2) D(LRVAT): = a + BD(LRHCE) + WD(LRHYD)+ +D(LAB)-2 + INFt-2 + pres_###_1 (ii) Evaluate the ECM statistically. Also, comment on the number of lags included, and whether this makes sense in terms of your a priori expectations. (4) (i) Perform diagnostic checks on the ECM. Test only for the potential problems as indicated below. In each instance, provide the name and a brief description of the test you perform. Also, clearly indicate how you draw your conclusions based on the results. (6) A. Normality B. Serial correlation C. Heteroscedasticity 3.6 Complete the model Create a model statement in EViews to combine your long-run and ECM. Provide your model statement (3 marks), and a copy of the graph depicting the actual and modelled values (2 marks), in the space provided. (5) [Total = 60 marks] INF M3 1 VAT 2 1990/01 3 1990/02 4 1990/03 5 1990/04 6 1991/01 7 1991/02 8 1991/03 9 1991/04 10 1992/01 11 1992/02 12 1992/03 13 1992/04 14 1993/01 15 1993/02 16 1993/03 17 1993/04 18 1994/01 19 1994/02 20 1994/03 21 1994/04 22 1995/01 23 1995/02 24 1995/03 25 1995/04 26 1996/01 27 1996/02 28 1996/03 29 1996/04 30 1997/01 HCE HYD LAB 4354 41214 40565 4307 44545 47981 4608 46549 46352 4268 51102 54700 5108 48924 49720 4628 51714 57844 4528 52868 50880 4745 58202 60196 4912 55488 60446 3666 58769 66324 4440 60502 62280 4862 65523 66926 4548 61290 66504 5409 65955 74744 6736 67715 69569 6561 74914 72183 6759 70528 71002 6568 74472 81465 7153 77635 78643 7800 86135 87860 7751 81921 81613 7533 86714 92175 8039 88409 92298 8384 96614 96706 8811 90969 91743 8156 96311 102283 9109 99485 104265 8551 110261 107540 10087 104079 109324 16,6 17,6 18,2 18,9 19,5 20,4 21,5 22,6 24,1 25,3 26,2 27 27,1 27,4 28,4 29,6 29,5 31 32,1 32,7 33 33,5 34,5 35,4 35,9 36,4 37,6 38,8 39 CPI 15,2 18,58251 13,1 19,16513 13,4 19,77841 16,8 20,56035 14,4 21,26562 15,9 22,06289 15,3 22,86016 18,9 23,87208 13,5 24,63869 12,5 25,37463 11,9 26,09524 5,5 26,44788 8 26,95383 17,2 28,07308 6,5 28,54837 7,4 28,94701 7,8 29,56029 7 30,08158 14,6 31,15483 9,8 31,78345 8,5 32,50406 9,9 33,28599 2,9 33,56197 5 33,86861 8,4 34,61989 8,3 35,30983 9 36,12243 10,8 36,9657 10,3 37,94695 149684 153060 154147 161339 170651 177155 178752 180876 185371 189145 195195 196763 196127 195403 203829 211358 221253 225172 232320 243771 247207 265106 269968 280377 296070 314513 320967 328037 347150 31 1997/02 32 1997/03 33 1997/04 34 1998/01 35 1998/02 36 1998/03 37 1998/04 38 1999/01 39 1999/02 40 1999/03 41 1999/04 42 2000/01 43 2000/02 44 2000/03 45 2000/04 46 2001/01 47 2001/02 48 2001/03 49 2001/04 50 2002/01 51 2002/02 52 2002/03 53 2002/04 54 2003/01 55 2003/02 56 2003/03 57 2003/04 58 2004/01 59 2004/02 60 2004/03 8537 10415 10423 10721 10060 10593 11283 11741 9446 13290 12777 12863 11821 13818 13554 15261 12791 14857 15615 17794 16283 17334 17096 19437 17184 18910 21093 23494 21384 22986 109145 111126 120921 113496 118796 121823 130036 123446 129483 133249 143092 138683 146954 150992 160597 154147 161692 165333 176721 171162 180799 186076 201806 189191 197391 201320 214894 213030 224910 228246 115748 117248 119511 119098 124808 124207 129238 128837 135196 140523 136795 144088 151358 157995 155651 159666 166491 172035 169167 182722 182916 196194 189821 197261 193518 216550 204027 224020 232700 229462 39,3 40,5 41,3 43,3 44,5 45,3 47,3 47 47,7 48,4 48 49,4 49,7 49,4 49,5 50,4 51,6 52,2 53,3 53,9 56,5 58,4 58 57,9 58,5 59,2 59,3 61,3 62,7 62,9 7,5 38,62156 5,9 39,23485 4 39,51083 4,7 40,03212 5,8 40,59941 16,9 42,2706 9,5 43,09854 2,2 43,42051 1,1 43,5585 0,7 43,68116 4,2 43,9418 5,3 44,63175 9,4 45,70499 7,5 46,56359 6,2 47,02356 6,7 47,94348 5 48,63343 1,2 48,78675 4,6 49,04739 12,3 50,70916 13,1 52,4425 11,8 54,01534 13,7 55,70281 5,1 56,49153 1,1 56,78729 -1,4 56,38377 -1,6 55,29699 3,9 55,49647 2,1 55,81057 0,8 55,88624 357055 379288 383858 400072 415135 426722 439464 437710 448514 464401 485768 480461 483668 499609 515750 543610 554866 573950 594077 649060 664968 682704 701634 730859 771290 785588 800031 834779 854675 903615 61 2004/04 62 2005/01 63 2005/02 64 2005/03 65 2005/04 66 2006/01 67 2006/02 68 2006/03 69 2006/04 70 2007/01 71 2007/02 72 2007/03 73 2007/04 74 2008/01 75 2008/02 76 2008/03 77 2008/04 78 2009/01 79 2009/02 80 2009/03 81 2009/04 82 2010/01 83 2010/02 84 2010/03 85 2010/04 86 2011/01 87 2011/02 88 2011/03 89 2011/04 90 2012/01 25255 28534 23457 27472 29810 33613 28347 33522 33971 38624 32371 35260 39756 43057 34170 37523 37154 45495 23579 36419 43215 44730 37965 43379 44480 57748 37737 43811 55000 54473 247350 236485 248776 255425 275190 260228 274613 286609 316267 296948 315456 326155 358437 324964 346902 360549 389380 353020 365600 371630 402019 381652 396041 406521 437621 419777 437552 448675 495087 466265 235837 240371 252832 259309 268417 254144 285176 281100 297808 286264 323982 324214 333779 309151 352231 359288 385982 319064 376975 383774 404623 358165 401021 429566 419672 384521 443104 463936 486887 422791 64,9 65,2 66,7 67,7 68,6 69,8 69,7 70,6 72,5 71,5 73,4 74,3 75,9 79,5 81,4 83,8 85,5 88,3 89 91,4 95,1 97,3 99,2 99,9 103,7 103,1 104,7 108,2 109,6 111,1 5,9 56,20952 910382 2,7 56,56948 938754 3,5 56,8492 998508 3,4 57,22521 1062468 5 57,36736 1103406 3,2 57,72733 1202128 4,6 58,29364 1237184 8 59,37812 1283600 6,4 60,00863 1350994 4,8 60,69417 1443477 8,8 61,79929 1523351 7,7 63,10846 1603241 12,6 64,34885 1681099 15,2 66,12771 1745309 9 67,94441 1831050 12,1 70,19711 1869995 6 70,81479 1915400 6,1 71,97747 1932543 6,9 73,46716 1945799 6,5 74,66618 1943527 4,9 74,95685 1944458 4,2 75,82887 1966170 2,4 76,55555 1999453 2,7 77,17322 2040120 4,4 77,50023 2073926 5,5 78,66291 2097839 6,1 80,11627 2123027 5,7 81,35162 2173574 6,9 82,33264 2244819 5,6 83,53166 2235746 91 2012/02 92 2012/03 93 2012/04 94 2013/01 95 2013/02 96 2013/03 97 2013/04 98 2014/01 99 2014/02 100 2014/03 101 2014/04 102 2015/01 103 2015/02 104 2015/03 105 2015/04 106 2016/01 107 2016/02 108 2016/03 109 2016/04 110 2017/01 111 2017/02 112 2017/03 113 2017/04 114 2018/01 115 2018/02 116 2018/03 117 2018/04 43082 53112 56804 62025 47111 60756 61638 68163 51857 65420 71025 72993 57214 67565 72315 84018 57194 72958 80514 78501 63223 73078 79063 82635 75634 86187 80246 483178 493717 540445 508945 524757 534301 576182 542677 557256 568390 613714 570526 591136 603859 654618 608104 630506 644903 700860 647624 671841 687648 749427 692864 711055 726409 790666 492990 502047 527081 446327 538839 541025 569683 475742 577732 582787 600223 526891 620730 618724 633865 545723 662859 656575 696002 607324 697523 717474 739813 648511 735978 758646 774822 112 115,7 116 118,1 120 120,6 120,6 124,7 124,8 126,7 127,8 128,9 132,1 133,9 136,3 138,6 138,9 140,7 142,2 145,6 146,9 147,4 149,1 151,4 152,4 155,2 156,8 4,3 84,80334 2268502 3,8 85,56635 2331166 9 87,01971 2370890 5,9 88,4004 2414312 3,9 89,56308 2468950 6,2 90,94377 2491667 5,8 91,70679 2520289 7,7 93,59615 2598672 6,3 95,48551 2642758 5,2 96,72086 2686734 3,7 96,93887 2700163 1,4 97,52021 2782235 7,8 99,77291 2874512 6,2 101,1173 2913488 4,1 101,5896 2975755 8 103,915 3020881 6,8 106,2767 3040952 5,4 107,5847 3076204 6,1 108,6021 3146951 6,8 110,6368 3187198 3,2 111,7994 3231085 3,3 112,5261 3295139 5,4 113,5071 3343869 4,5 114,9968 3391748 4,7 116,6318 3420479 5,5 118,0489 3525428 4,9 118,9936 3526865 ECS4863 2022 Assignment 01 Question 3: (35 marks) In this question you must estimate a time series model for value added tax (VAT) collections, for South Africa. You are provided with the following data: Variable names and description: VAT : Value added tax revenue, nominal (R millions) HCE Final consumption expenditure by households, nominal (R millions) HYD Disposable income of households, nominal (R millions) M3 Money supply, nominal (R millions) LAB Nominal labor costs in the non-agricultural sectors (Index, 2010 = 100) INF : Inflation (percentage, quarter on previous quarter at annual rate) CPI Consumer price index (Index, 2015 = 100) (2) 3.1 Provide a description of the data (type, interval, etc.) 3.2 Calculate and provide a graph of the real value added tax for the period 1990 to 2018. Discuss the trends you observe in VAT collection, before and after 2008. (3) (6) 3.3 Test the real value added tax and inflation variables for stationarity. Provide your results in the table below (please add rows where necessary): 'L'indicates the logarithmic function 'R' indicates that real values are used. Variable Model Lags ADF test statistic TTT LRVAT and Trend Intercept Intercept None Trend Intercept Intercept None INF and Statistically significant at the: 10% level (*), 5% level (**), 1% level (***) You can assume that all other variables are non-stationary, integrated of order 1(1). 3.4 Test for possible cointegration between variables: (i) Estimate the following long run cointegration equation. Copy and paste your EViews results window in your answer sheet. (2) LRVAT, = a + BLRHCET + TLRM3t + res (ii) Evaluate the potential long-run equation. Do the estimated coefficients correspond to your a priori expectations in terms of sign? Explain. (2) (ii) Generate the residual series for your long run equation. (Name your residual series as follows: res underscore the first three letters of your name, e.g. res_fan) Demonstrate, how you can use the residual series to test if cointegration exists between the variables in the long run model. (3) 3.5 Construct a short run (Error Correction) component for your model (i) Estimate the following short run cointegration equation. Copy and paste your EViews results window in your answer sheet. (2) D(LRVAT): = a + BD(LRHCE) + WD(LRHYD)+ +D(LAB)-2 + INFt-2 + pres_###_1 (ii) Evaluate the ECM statistically. Also, comment on the number of lags included, and whether this makes sense in terms of your a priori expectations. (4) (i) Perform diagnostic checks on the ECM. Test only for the potential problems as indicated below. In each instance, provide the name and a brief description of the test you perform. Also, clearly indicate how you draw your conclusions based on the results. (6) A. Normality B. Serial correlation C. Heteroscedasticity 3.6 Complete the model Create a model statement in EViews to combine your long-run and ECM. Provide your model statement (3 marks), and a copy of the graph depicting the actual and modelled values (2 marks), in the space provided. (5) [Total = 60 marks] INF M3 1 VAT 2 1990/01 3 1990/02 4 1990/03 5 1990/04 6 1991/01 7 1991/02 8 1991/03 9 1991/04 10 1992/01 11 1992/02 12 1992/03 13 1992/04 14 1993/01 15 1993/02 16 1993/03 17 1993/04 18 1994/01 19 1994/02 20 1994/03 21 1994/04 22 1995/01 23 1995/02 24 1995/03 25 1995/04 26 1996/01 27 1996/02 28 1996/03 29 1996/04 30 1997/01 HCE HYD LAB 4354 41214 40565 4307 44545 47981 4608 46549 46352 4268 51102 54700 5108 48924 49720 4628 51714 57844 4528 52868 50880 4745 58202 60196 4912 55488 60446 3666 58769 66324 4440 60502 62280 4862 65523 66926 4548 61290 66504 5409 65955 74744 6736 67715 69569 6561 74914 72183 6759 70528 71002 6568 74472 81465 7153 77635 78643 7800 86135 87860 7751 81921 81613 7533 86714 92175 8039 88409 92298 8384 96614 96706 8811 90969 91743 8156 96311 102283 9109 99485 104265 8551 110261 107540 10087 104079 109324 16,6 17,6 18,2 18,9 19,5 20,4 21,5 22,6 24,1 25,3 26,2 27 27,1 27,4 28,4 29,6 29,5 31 32,1 32,7 33 33,5 34,5 35,4 35,9 36,4 37,6 38,8 39 CPI 15,2 18,58251 13,1 19,16513 13,4 19,77841 16,8 20,56035 14,4 21,26562 15,9 22,06289 15,3 22,86016 18,9 23,87208 13,5 24,63869 12,5 25,37463 11,9 26,09524 5,5 26,44788 8 26,95383 17,2 28,07308 6,5 28,54837 7,4 28,94701 7,8 29,56029 7 30,08158 14,6 31,15483 9,8 31,78345 8,5 32,50406 9,9 33,28599 2,9 33,56197 5 33,86861 8,4 34,61989 8,3 35,30983 9 36,12243 10,8 36,9657 10,3 37,94695 149684 153060 154147 161339 170651 177155 178752 180876 185371 189145 195195 196763 196127 195403 203829 211358 221253 225172 232320 243771 247207 265106 269968 280377 296070 314513 320967 328037 347150 31 1997/02 32 1997/03 33 1997/04 34 1998/01 35 1998/02 36 1998/03 37 1998/04 38 1999/01 39 1999/02 40 1999/03 41 1999/04 42 2000/01 43 2000/02 44 2000/03 45 2000/04 46 2001/01 47 2001/02 48 2001/03 49 2001/04 50 2002/01 51 2002/02 52 2002/03 53 2002/04 54 2003/01 55 2003/02 56 2003/03 57 2003/04 58 2004/01 59 2004/02 60 2004/03 8537 10415 10423 10721 10060 10593 11283 11741 9446 13290 12777 12863 11821 13818 13554 15261 12791 14857 15615 17794 16283 17334 17096 19437 17184 18910 21093 23494 21384 22986 109145 111126 120921 113496 118796 121823 130036 123446 129483 133249 143092 138683 146954 150992 160597 154147 161692 165333 176721 171162 180799 186076 201806 189191 197391 201320 214894 213030 224910 228246 115748 117248 119511 119098 124808 124207 129238 128837 135196 140523 136795 144088 151358 157995 155651 159666 166491 172035 169167 182722 182916 196194 189821 197261 193518 216550 204027 224020 232700 229462 39,3 40,5 41,3 43,3 44,5 45,3 47,3 47 47,7 48,4 48 49,4 49,7 49,4 49,5 50,4 51,6 52,2 53,3 53,9 56,5 58,4 58 57,9 58,5 59,2 59,3 61,3 62,7 62,9 7,5 38,62156 5,9 39,23485 4 39,51083 4,7 40,03212 5,8 40,59941 16,9 42,2706 9,5 43,09854 2,2 43,42051 1,1 43,5585 0,7 43,68116 4,2 43,9418 5,3 44,63175 9,4 45,70499 7,5 46,56359 6,2 47,02356 6,7 47,94348 5 48,63343 1,2 48,78675 4,6 49,04739 12,3 50,70916 13,1 52,4425 11,8 54,01534 13,7 55,70281 5,1 56,49153 1,1 56,78729 -1,4 56,38377 -1,6 55,29699 3,9 55,49647 2,1 55,81057 0,8 55,88624 357055 379288 383858 400072 415135 426722 439464 437710 448514 464401 485768 480461 483668 499609 515750 543610 554866 573950 594077 649060 664968 682704 701634 730859 771290 785588 800031 834779 854675 903615 61 2004/04 62 2005/01 63 2005/02 64 2005/03 65 2005/04 66 2006/01 67 2006/02 68 2006/03 69 2006/04 70 2007/01 71 2007/02 72 2007/03 73 2007/04 74 2008/01 75 2008/02 76 2008/03 77 2008/04 78 2009/01 79 2009/02 80 2009/03 81 2009/04 82 2010/01 83 2010/02 84 2010/03 85 2010/04 86 2011/01 87 2011/02 88 2011/03 89 2011/04 90 2012/01 25255 28534 23457 27472 29810 33613 28347 33522 33971 38624 32371 35260 39756 43057 34170 37523 37154 45495 23579 36419 43215 44730 37965 43379 44480 57748 37737 43811 55000 54473 247350 236485 248776 255425 275190 260228 274613 286609 316267 296948 315456 326155 358437 324964 346902 360549 389380 353020 365600 371630 402019 381652 396041 406521 437621 419777 437552 448675 495087 466265 235837 240371 252832 259309 268417 254144 285176 281100 297808 286264 323982 324214 333779 309151 352231 359288 385982 319064 376975 383774 404623 358165 401021 429566 419672 384521 443104 463936 486887 422791 64,9 65,2 66,7 67,7 68,6 69,8 69,7 70,6 72,5 71,5 73,4 74,3 75,9 79,5 81,4 83,8 85,5 88,3 89 91,4 95,1 97,3 99,2 99,9 103,7 103,1 104,7 108,2 109,6 111,1 5,9 56,20952 910382 2,7 56,56948 938754 3,5 56,8492 998508 3,4 57,22521 1062468 5 57,36736 1103406 3,2 57,72733 1202128 4,6 58,29364 1237184 8 59,37812 1283600 6,4 60,00863 1350994 4,8 60,69417 1443477 8,8 61,79929 1523351 7,7 63,10846 1603241 12,6 64,34885 1681099 15,2 66,12771 1745309 9 67,94441 1831050 12,1 70,19711 1869995 6 70,81479 1915400 6,1 71,97747 1932543 6,9 73,46716 1945799 6,5 74,66618 1943527 4,9 74,95685 1944458 4,2 75,82887 1966170 2,4 76,55555 1999453 2,7 77,17322 2040120 4,4 77,50023 2073926 5,5 78,66291 2097839 6,1 80,11627 2123027 5,7 81,35162 2173574 6,9 82,33264 2244819 5,6 83,53166 2235746 91 2012/02 92 2012/03 93 2012/04 94 2013/01 95 2013/02 96 2013/03 97 2013/04 98 2014/01 99 2014/02 100 2014/03 101 2014/04 102 2015/01 103 2015/02 104 2015/03 105 2015/04 106 2016/01 107 2016/02 108 2016/03 109 2016/04 110 2017/01 111 2017/02 112 2017/03 113 2017/04 114 2018/01 115 2018/02 116 2018/03 117 2018/04 43082 53112 56804 62025 47111 60756 61638 68163 51857 65420 71025 72993 57214 67565 72315 84018 57194 72958 80514 78501 63223 73078 79063 82635 75634 86187 80246 483178 493717 540445 508945 524757 534301 576182 542677 557256 568390 613714 570526 591136 603859 654618 608104 630506 644903 700860 647624 671841 687648 749427 692864 711055 726409 790666 492990 502047 527081 446327 538839 541025 569683 475742 577732 582787 600223 526891 620730 618724 633865 545723 662859 656575 696002 607324 697523 717474 739813 648511 735978 758646 774822 112 115,7 116 118,1 120 120,6 120,6 124,7 124,8 126,7 127,8 128,9 132,1 133,9 136,3 138,6 138,9 140,7 142,2 145,6 146,9 147,4 149,1 151,4 152,4 155,2 156,8 4,3 84,80334 2268502 3,8 85,56635 2331166 9 87,01971 2370890 5,9 88,4004 2414312 3,9 89,56308 2468950 6,2 90,94377 2491667 5,8 91,70679 2520289 7,7 93,59615 2598672 6,3 95,48551 2642758 5,2 96,72086 2686734 3,7 96,93887 2700163 1,4 97,52021 2782235 7,8 99,77291 2874512 6,2 101,1173 2913488 4,1 101,5896 2975755 8 103,915 3020881 6,8 106,2767 3040952 5,4 107,5847 3076204 6,1 108,6021 3146951 6,8 110,6368 3187198 3,2 111,7994 3231085 3,3 112,5261 3295139 5,4 113,5071 3343869 4,5 114,9968 3391748 4,7 116,6318 3420479 5,5 118,0489 3525428 4,9 118,9936 3526865 ECS4863 2022 Assignment 01