John Montgomery

Econ 401/Dr. Townsend
December 7, 2009

       Appendix 14.1 is a highly aggregated model of real gross d...
Case set four calls for us to create a simplified structural model of the U.S.

economy. The model uses the Fair method, w...
The first equation examined is the equation for tax. It is a very simple equation, and is

the calculation of total busine...
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S.E. of regression          18.49246    Sum squared resid            44456.23
           F-statistic                 60252...
Above is the graph for the historical simulation of consumption, and as our r-

squared value indicates we have a strong f...
As you can see there is actually a very close fitting ex-post forecast provided, and

the MAPE of .01%.


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Inverted AR Roots                .98



        Moving forward we next look at the equation for nonresidential investment,...
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Sample: 1960Q1 1993Q4
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The historic simulation shows an actual set of values that oscillates regularly between

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Method: Least Squares
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Inverted AR Roots                           .97




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The annual rate of growth in wages will be a positive function of overall price inflation, a

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Housing Starts Forecast

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Housing Starts Forecast

  1. 1. John Montgomery Econ 401/Dr. Townsend December 7, 2009 Appendix 14.1 is a highly aggregated model of real gross domestic product and its major components. The Model contains 11 behavioral equations and two identities. One of these identities is for real disposable income, and the other is the accounting identity for real GDP. Each equation within the model is estimated using two stage least squares. There are 12 endogenous variables: personal consumption expenditures, GDP, rate of growth of CPI, nonresidential fixed investment, change in business inventories, residential fixed investement, imports of goods and services, average yield on AAA corporate bonds, interest rate on 3-month treasury bills, personal and indirect business tax payments, civilian unemployment rate, wage inflation, and disposable personal income. In addition to these endogenous variables, there are 9 exogenous variables: government purchases of goods and services, potential GDP, money stock, household net worth, rate of growth of oil prices, corporate profits, rate of growth of labor productivity, transfer payments to persons, and exports of goods and services. The instruments used for the individual behavioral equations differ compared to what we will be using for our model. Furthermore this model uses two-stage least squares for each of the equations, and we use ordinary least squares for the recursive equations. Comparatively the model provides a good forecast, and the flow chart is a good representation of the equation visually.
  2. 2. Case set four calls for us to create a simplified structural model of the U.S. economy. The model uses the Fair method, which uses two stage least squares, and includes the lagged dependent and independent variables as instruments. These lagged variables are included as such in order to obtain consistent parameter estimates when autocorrelated disturbances create a problem. The model contains 11 behavioral equations, and two identities. The majority of the equations are estimated using two stage least squares, although there are three recursive equations which are estimated using the ordinary least squares method. Using quarterly data from 1960-1993 I have created a historical simulation which I will explain here. Dependent Variable: TAX Method: Two-Stage Least Squares Date: 12/07/09 Time: 20:36 Sample: 1960Q1 1993Q4 Included observations: 136 Convergence achieved after 7 iterations Instrument list: C GDPPOT INFL INR INV IR M M2 RL RS X YPD GDP(-1) TAX(-1) Lagged dependent variable & regressors added to instrument list Variable Coefficient Std. Error t-Statistic Prob. C -3.967408 22.99851 -0.172507 0.8633 GDP 0.186861 0.005053 36.98054 0.0000 AR(1) 0.781575 0.054284 14.39795 0.0000 R-squared 0.995351 Mean dependent var 790.8930 Adjusted R-squared 0.995281 S.D. dependent var 235.3508 S.E. of regression 16.16703 Sum squared resid 34762.61 F-statistic 14231.47 Durbin-Watson stat 2.331248 Prob(F-statistic) 0.000000 Inverted AR Roots .78
  3. 3. The first equation examined is the equation for tax. It is a very simple equation, and is the calculation of total business and personal taxes. Its instruments are potential gdp, inflation, nonresidential fixed investment, change in business inventories, residential fixed investment, imports of goods and services, the money stock, average yield on AAA corporate bonds, interest rates on three-month treasury bills, exports, disposable personal income, gross domestic product lagged by one quarter, and finally itself lagged by one quarter. The high r-squared number indicates that we should have a very good fitting line, and we also see a Durbin-Watson statistic within the acceptable range. I have used the auto-regressive model to help correct for any serial correlation, so that explains why we have such a good D-W stat. 1400 1200 1000 800 600 400 200 1960 1965 1970 1975 1980 1985 1990 TAX TAX (Baseline) Above is the historical simulation of taxes, and as our r-squared value had indicated we have a decently nice fitting line. The MAPE for the historical simulation is .05%.
  4. 4. 1320 1300 1280 1260 1240 1220 1200 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 TAX TAX (Scenario 1) Above is the ex-post ante forecast for the tax equation. We have been able to generate a fairly strong forecast which has a MAPE of .019. Dependent Variable: CONS Method: Two-Stage Least Squares Date: 12/07/09 Time: 20:38 Sample: 1960Q1 1993Q4 Included observations: 136 Convergence achieved after 44 iterations Instrument list: C G GDPPOT INFL INR INV IR M M2 RL WINF X CONS CONS(-2) NETWRTH(-1) YPD(-1) Lagged dependent variable & regressors added to instrument list Variable Coefficient Std. Error t-Statistic Prob. C -146.5984 35.31959 -4.150627 0.0001 YPD 0.192170 0.039694 4.841345 0.0000 NETWRTH 0.040520 0.009706 4.174715 0.0001 RS -5.241978 1.330045 -3.941204 0.0001 CONS(-1) 0.586638 0.085641 6.849938 0.0000 AR(1) 0.406659 0.116241 3.498412 0.0006 R-squared 0.999569 Mean dependent var 2834.458 Adjusted R-squared 0.999552 S.D. dependent var 873.7046
  5. 5. S.E. of regression 18.49246 Sum squared resid 44456.23 F-statistic 60252.24 Durbin-Watson stat 2.165461 Prob(F-statistic) 0.000000 Inverted AR Roots .41 The above table is the results of the two stage least squares regression for the consumption equation. Personal consumption represents two-thirds of GDP and is one of the most important behavioral equations within the entire model. Because of the presence of the lagged dependent variable in the equation, and in accordance with Fair’s method, I have included the consumption variable lagged twice upon itself in the instruments. In addition to this I have included a lagged variable of both net worth and personal disposable income because they are also endogenous variables. Again, we notice a high r-squared value, indicating a good-fitting line. Also, the Durbin-Watson statistic is within its accepted values, which has happened again because of the addition of the autoregressive model. The negative coefficient present for the variable representing the three-month treasury bill interest rates makes sense as one can assume that as consumption increases, the interest on these would in turn decrease. The positive coefficients for both net worth and disposable personal income also makes sense as it is only logical to assume that consumption would increase as these two variables do as well. 4500 4000 3500 3000 2500 2000 1500 1000 1960 1965 1970 1975 1980 1985 1990 CONS CONS (Baseline)
  6. 6. Above is the graph for the historical simulation of consumption, and as our r- squared value indicates we have a strong fit; the MAPE for the historical simulation of consumption is .017%. 4640 4600 4560 4520 4480 4440 4400 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 CONS CONS (Scenario 1) Above is a graphical representation of the ex-post ante forecast for the consumption equation. Although it looks like it is dipping far below the actual line, it really isn’t, as can be seen in a graphical representation including the historical simulation. 4800 4400 4000 3600 3200 2800 2400 2000 1600 1200 1965 1970 1975 1980 1985 1990 1995 CONS (Scenario 1) CONS CONS (Baseline)
  7. 7. As you can see there is actually a very close fitting ex-post forecast provided, and the MAPE of .01%. Dependent Variable: M Method: Two-Stage Least Squares Date: 12/07/09 Time: 21:14 Sample: 1960Q1 1993Q4 Included observations: 136 Convergence achieved after 5 iterations Instrument list: C CONS G GDP GDPPOT INFL INR INV M2 RL RS X YPD(-1) Lagged dependent variable & regressors added to instrument list Variable Coefficient Std. Error t-Statistic Prob. M(-1) 0.997952 0.019728 50.58575 0.0000 C -5.780378 8.064005 -0.716812 0.4748 YPD 0.002797 0.003503 0.798507 0.4260 AR(1) 0.120054 0.089127 1.347008 0.1803 R-squared 0.996581 Mean dependent var 345.2206 Adjusted R-squared 0.996503 S.D. dependent var 182.2808 S.E. of regression 10.77870 Sum squared resid 15335.81 F-statistic 12825.49 Durbin-Watson stat 1.984664 Prob(F-statistic) 0.000000 Inverted AR Roots .12 The next equation is for imports of goods and services. The r-squared value is strong, and the Durbin-Watson statistic is again within the acceptable region. The positive coefficient of personal disposable income makes sense in the fact that the more money people have, the more they will spend, and the more goods and services we will import.
  8. 8. 800 700 600 500 400 300 200 100 1960 1965 1970 1975 1980 1985 1990 M M (Baseline) The historical simulation shows a decent fitting line, and the simulation has become a strong trend. The MAPE for the import equation is .092%. 920 900 880 860 840 820 800 780 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 M (Scenario 1) M
  9. 9. 1000 900 800 700 600 500 400 300 200 100 1965 1970 1975 1980 1985 1990 1995 M (Scenario 1) M M (Baseline) The first graph above shows the ex-post forecast, and the graph directly below shows the ex-post forecast included with the actual numbers, and the historical simulation. The MAPE for the ex-post forecast is .06%, and it continues along the trend that the historical simulation begins. Dependent Variable: INR Method: Two-Stage Least Squares Date: 12/07/09 Time: 20:42 Sample (adjusted): 1960Q2 1993Q4 Included observations: 135 after adjustments Convergence achieved after 26 iterations Instrument list: C CONS G GDPPOT INFL INV IR M M2 X YPD GDP( -1) INR(-1) RL(-5) Lagged dependent variable & regressors added to instrument list Variable Coefficient Std. Error t-Statistic Prob. C 21.67766 108.1270 0.200483 0.8414 GDP 0.107208 0.015837 6.769528 0.0000 RL(-4) -6.854006 3.604487 -1.901520 0.0594 AR(1) 0.977314 0.021144 46.22132 0.0000 R-squared 0.995463 Mean dependent var 425.6459 Adjusted R-squared 0.995359 S.D. dependent var 126.2919 S.E. of regression 8.603287 Sum squared resid 9696.167 F-statistic 9578.989 Durbin-Watson stat 1.365430 Prob(F-statistic) 0.000000
  10. 10. Inverted AR Roots .98 Moving forward we next look at the equation for nonresidential investment, and immediately we notice that it has a positive effect on aggregate economic activity. However, it has a negative effect on the opportunity cost of investment. Again, we see a high r-squared value, which translates to a good fitting line. 800 700 600 500 400 300 200 100 1960 1965 1970 1975 1980 1985 1990 INR INR (Baseline) The historical simulation shows a line that doesn’t fit quite as well as many of the previous equations historical simulations have, and we see a MAPE of .144%.
  11. 11. 740 720 700 680 660 640 620 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 INR (Scenario 1) INR 800 700 600 500 400 300 200 100 1960 1965 1970 1975 1980 1985 1990 INR (Scenario 1) INR INR (Baseline) As we look at the above graphs we also see a larger separation between the actual numbers, and the ex-post forecast. The MAPE for nonresidential investment is .058%. Dependent Variable: IR Method: Least Squares Date: 12/07/09 Time: 20:43
  12. 12. Sample: 1960Q1 1993Q4 Included observations: 136 Convergence achieved after 33 iterations Variable Coefficient Std. Error t-Statistic Prob. C 12.99230 60.40403 0.215090 0.8300 YPD(-1) 0.048791 0.013085 3.728651 0.0003 RS(-1) -3.810494 0.941601 -4.046825 0.0001 AR(1) 0.949368 0.029951 31.69789 0.0000 R-squared 0.961015 Mean dependent var 190.7934 Adjusted R-squared 0.960129 S.D. dependent var 43.58628 S.E. of regression 8.703175 Akaike info criterion 7.194223 Sum squared resid 9998.374 Schwarz criterion 7.279890 Log likelihood -485.2072 F-statistic 1084.643 Durbin-Watson stat 1.109263 Prob(F-statistic) 0.000000 Inverted AR Roots .95 Residential investment is a variable that reflects household demand for new homes. It is estimated as a function of real disposable income and the cost of borrowing. We are using the interest rates for three-month treasury bills as a proxy for mortgage rates. 280 240 200 160 120 80 1960 1965 1970 1975 1980 1985 1990 IR IR (Baseline)
  13. 13. The historic simulation shows an actual set of values that oscillates regularly between peaks and troughs, but the simulation almost begins to show a trend. The MAPE for the historical simulation is .13%. 272 268 264 260 256 252 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 IR IR (Scenario 1) The ex-post forecast shows a forecast that falls below the values of the actual numbers. The MAPE is .032%. Dependent Variable: INV Method: Two-Stage Least Squares Date: 12/07/09 Time: 21:23 Sample: 1960Q1 1993Q4 Included observations: 136 Convergence achieved after 10 iterations Instrument list: C CONS G GDPPOT INFL INR IR M M2 RL RS X INV( -2) (GDP-CONS-GDP(1)+CONS(-1)) Lagged dependent variable & regressors added to instrument list Variable Coefficient Std. Error t-Statistic Prob. C 2.837186 1.626528 1.744321 0.0834 D(GDP-CONS) 0.360108 0.058365 6.169931 0.0000 INV(-1) 0.709656 0.054278 13.07454 0.0000 AR(1) -0.182547 0.106412 -1.715472 0.0886 R-squared 0.675370 Mean dependent var 21.58603
  14. 14. Adjusted R-squared 0.667992 S.D. dependent var 22.24099 S.E. of regression 12.81529 Sum squared resid 21678.58 F-statistic 50.06773 Durbin-Watson stat 2.073371 Prob(F-statistic) 0.000000 Inverted AR Roots -.18 The next equation is for the change in business inventories. Reasearch has shown that much of the variation in real output growth over the course of a business cycle can be attributed to variations in the rate of inventory accumulation. This equation is estimated as a function of the change in the difference between total output and consumption. 200 160 120 80 40 0 -40 -80 1960 1965 1970 1975 1980 1985 1990 INV INV (Baseline) The historic simulation of business inventories is represented graphically above. Immediately one’s eyes would be drawn to the beginning of the cycle in which there is an impossibly large peak in the simulation. This peak could be controlled through the use of a dummy variable, but doesn’t affect the simulation greatly. The MAPE of the historical simulation is the largest of all the equations at 2..77%. However, it is important to note that this number is still below the 5% threshold that is generally considered in good form for a forecast.
  15. 15. 80 70 60 50 40 30 20 10 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 INV (Scenario 1) INV 200 160 120 80 40 0 -40 -80 1960 1965 1970 1975 1980 1985 1990 1995 INV (Scenario 1) INV INV (Baseline) The above graphs show the ex-post forecast for the equation regarding business inventories. The MAPE improves from the historical simulation to .449%. Dependent Variable: RS Method: Two-Stage Least Squares Date: 12/07/09 Time: 20:52
  16. 16. Sample: 1960Q1 1993Q4 Included observations: 136 Convergence achieved after 8 iterations Instrument list: C CONS G INR INV IR M RL X INFL(-1) RS(-1) M2(-1) YPD(-1) Lagged dependent variable & regressors added to instrument list Variable Coefficient Std. Error t-Statistic Prob. C -44.76644 12.53438 -3.571492 0.0005 YPD 0.014637 0.003054 4.792746 0.0000 M2 -0.021874 0.005354 -4.085905 0.0001 INFL 0.303852 0.129569 2.345099 0.0205 AR(1) 0.956617 0.022165 43.15966 0.0000 R-squared 0.906337 Mean dependent var 6.210196 Adjusted R-squared 0.903477 S.D. dependent var 2.809331 S.E. of regression 0.872807 Sum squared resid 99.79487 F-statistic 325.5120 Durbin-Watson stat 1.981729 Prob(F-statistic) 0.000000 Inverted AR Roots .96 Short-term interest rates (rates on three-month treasury bills) are modeled as a normalization of a traditional money demand equation. When personal disposable income increasing demand for money increases, but decreases when real short-term interest rates rise as the opportunity cost of holding money increases. The r-squared values for this equation are lower than other equations, and that makes sense. Interest rates are more volatile than any of the other variables, and therefore much more difficult to predict.
  17. 17. 20 16 12 8 4 0 -4 1960 1965 1970 1975 1980 1985 1990 RS RS (Baseline) As you can see the historical simulation isn’t quite as fitted as many of the other simulations that I have introduced today. The spike in the 80’s is consistent with Paul Volker increasing the interest rates to battle inflation. The MAPE for this historical simulation is .59%. 6.4 6.0 5.6 5.2 4.8 4.4 4.0 3.6 3.2 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 RS RS (Scenario 1) The MAPE for the ex-post forecast is .179%. Dependent Variable: RL
  18. 18. Method: Least Squares Date: 12/07/09 Time: 20:53 Sample: 1960Q1 1993Q4 Included observations: 136 Convergence achieved after 9 iterations Variable Coefficient Std. Error t-Statistic Prob. C 0.301862 0.110459 2.732789 0.0071 RS 0.188788 0.020330 9.286057 0.0000 RL(-1) 0.822268 0.021359 38.49828 0.0000 AR(1) 0.213139 0.088868 2.398388 0.0179 R-squared 0.987126 Mean dependent var 8.211863 Adjusted R-squared 0.986833 S.D. dependent var 2.743314 S.E. of regression 0.314787 Akaike info criterion 0.555132 Sum squared resid 13.08002 Schwarz criterion 0.640798 Log likelihood -33.74896 F-statistic 3373.660 Durbin-Watson stat 2.028879 Prob(F-statistic) 0.000000 Inverted AR Roots .21 This is the regression for average yield on AAA bonds. It is a member of the recursive block, so it was run using only ordinary least squares. 20 16 12 8 4 0 1960 1965 1970 1975 1980 1985 1990 RL RL (Baseline) The MAPE for the historic simulation is .38%.
  19. 19. 8.8 8.4 8.0 7.6 7.2 6.8 6.4 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 RL (Scenario 1) RL The MAPE for the ex-post fore cast is .08%. Dependent Variable: UR Method: Least Squares Date: 12/07/09 Time: 22:46 Sample (adjusted): 1960Q3 1993Q4 Included observations: 134 after adjustments Convergence achieved after 8 iterations Variable Coefficient Std. Error t-Statistic Prob. C 6.582626 1.181766 5.570160 0.0000 (D(LOG(GDP)))-(D(LOG(GDPPOT))) -3.592488 2.730454 -1.315711 0.1906 AR(1) 0.973305 0.019730 49.33012 0.0000 R-squared 0.949410 Mean dependent var 6.178109 Adjusted R-squared 0.948637 S.D. dependent var 1.554937 S.E. of regression 0.352400 Akaike info criterion 0.774035 Sum squared resid 16.26835 Schwarz criterion 0.838912 Log likelihood -48.86033 F-statistic 1229.218 Durbin-Watson stat 0.650476 Prob(F-statistic) 0.000000
  20. 20. Inverted AR Roots .97 The unemployment rate is estimated according to a tradition Okun’s law equation relating change in the unemployment rate to the change in GDP. It makes sense that there is a negative effect of the unemployment rate on GDP. This equation is also in the recursive block, and therefore is estimated using ordinary least squares. 11 10 9 8 7 6 5 4 3 1960 1965 1970 1975 1980 1985 1990 UR UR (Baseline) The MAPE for the historical simulation is .19%.
  21. 21. 6.8 6.6 6.4 6.2 6.0 5.8 5.6 5.4 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 UR (Scenario 1) UR The MAPE for the ex-post forecast is .13%. Dependent Variable: WINF Method: Two-Stage Least Squares Date: 12/07/09 Time: 20:55 Sample: 1960Q1 1993Q4 Included observations: 136 Convergence achieved after 8 iterations Instrument list: C CONS G GDP GDPPOT INFL(-1) INR INV IR M NETWRTH PRFT RL RS TR UR WINF(-1) X Lagged dependent variable & regressors added to instrument list Variable Coefficient Std. Error t-Statistic Prob. C -14.26324 3.091834 -4.613198 0.0000 INFL 0.691501 0.014116 48.98761 0.0000 UR(-2) 0.032879 0.096548 0.340545 0.7340 PROD 0.152321 0.046329 3.287830 0.0013 AR(1) 0.934047 0.033211 28.12424 0.0000 R-squared 0.999885 Mean dependent var 47.85147 Adjusted R-squared 0.999882 S.D. dependent var 28.87696 S.E. of regression 0.314002 Sum squared resid 12.91624 F-statistic 285411.2 Durbin-Watson stat 1.438084 Prob(F-statistic) 0.000000 Inverted AR Roots .93
  22. 22. The annual rate of growth in wages will be a positive function of overall price inflation, a negative function of the unemployment rate, and a positive function of productivity growth. We have a very strong r-squared value, indicating a good fiiting line. 120 100 80 60 40 20 0 1960 1965 1970 1975 1980 1985 1990 WINF WINF (Baseline) The MAPE for the Historic simulation is .11% 110 109 108 107 106 105 104 103 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 WINF WINF (Scenario 1) The MAPE for the ex-post forecast is .01%
  23. 23. Dependent Variable: INFL Method: Two-Stage Least Squares Date: 12/07/09 Time: 20:57 Sample (adjusted): 1960Q2 1993Q4 Included observations: 135 after adjustments Convergence achieved after 19 iterations Instrument list: C CONS CONS(-2) G GDP(-1) GDPPOT INV IR M NETWRTH PRFT RL RS TR WINF(-1) X YPD Lagged dependent variable & regressors added to instrument list Variable Coefficient Std. Error t-Statistic Prob. C 2.645615 2.952583 0.896034 0.3719 WINF 0.676700 0.140916 4.802149 0.0000 CONS(-1) 0.000505 0.001582 0.318843 0.7504 POIL 0.092758 0.022974 4.037453 0.0001 INFL(-1) 0.479845 0.090355 5.310660 0.0000 AR(1) 0.926117 0.041998 22.05126 0.0000 R-squared 0.999943 Mean dependent var 72.17086 Adjusted R-squared 0.999941 S.D. dependent var 38.74432 S.E. of regression 0.296935 Sum squared resid 11.37400 F-statistic 456242.9 Durbin-Watson stat 2.116613 Prob(F-statistic) 0.000000 Inverted AR Roots .93 The annual rate of growth in the consumer price index is estimated to be a function of wage inflation, consumer demand, and oil prices. We have a high r-squared value, and the Durbin-Watson statistic falls within the accepted values.
  24. 24. 160 140 120 100 80 60 40 20 1960 1965 1970 1975 1980 1985 1990 INFL INFL (Baseline) The MAPE for the historic simulation is .10%. 154 153 152 151 150 149 148 147 146 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 INFL INFL (Scenario 1) The MAPE for the ex-post forecast is .006%.
  25. 25. 7000 6000 5000 4000 3000 2000 1960 1965 1970 1975 1980 1985 1990 GDP GDP (Baseline) After completing estimations of all the equations we can simulate the model as a complete system. The above simulation is the historical look at GDP. It is a good fitting line, and we are ultimately given a MAPE of .05% 7000 6000 5000 4000 3000 2000 1960 1965 1970 1975 1980 1985 1990 1995 GDP (Scenario 1) GDP GDP (Baseline) Above is a graph of the historic simulation, actual numbers, and ex-post forecast combined into one. From this view we see that the ex-post forecast looks pretty good. Below is a closer look at the ex-post forecast.
  26. 26. 6900 6800 6700 6600 6500 6400 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 GDP GDP (Scenario 1) The MAPE based on this simulation is .008%. This is a strong forecast for the gross domestic product. 6000 5000 4000 3000 2000 1000 0 1960 1965 1970 1975 1980 1985 1990 YPD YDP_0 Looking at the results for the disposable personal income equation confirm our findings for gross domestic product. The steady growth of personal disposable income is consistent with the growth of gross domestic product. The MAPE of the historical simulation for personal disposable income is .06%.
  27. 27. 6000 5000 4000 3000 2000 1000 0 1960 1965 1970 1975 1980 1985 1990 1995 YDP_1 YPD YDP_0 5900 5850 5800 5750 5700 5650 5600 94Q1 94Q2 94Q3 94Q4 95Q1 95Q2 95Q3 95Q4 YPD YDP_1 The MAPE for the ex-post forecast of personal disposable income is .01%.

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