Problem Set #5-Key Sonoma State University Dr. Cuellar Economics 318- Managerial Economics Use the data set for gross domestic product (gdp.xls) to answer the following questions. (1) Show graphically nominal gdp for the years provided. Be sure to correctly label your axes. GDP (Billions of Dollars) 12000 10000 8000 6000 4000 2000 Nominal and Real U.S. GDP 1960-2001 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 Year (2) Based on the data, calculate the average annual dollar growth of nominal gdp. Nominal Simple Linear Multiple R 0.965225 R 0.931659 Adjusted R 0.92995 Standard Error 789.4347 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -1288.68 248.0414-5.19544 6.34E-06-1789.99-787.375 X Variable 1 234.6787 10.04977 23.35165 6.4E-25 214.3674 254.99 Based on the simple linear regression, nominal GDP grew approximately 234.68 billion dollars per year from 1960-2001.
(3) Based on your data, calculate the average annual growth rate of gdp, assume annual The growth formula assuming annual compounding is, Y t = Y 0 (1 + g) t To find g, the average annual growth rate assuming annual compounding take the log of GDP and regress against time. LogY t = LogY 0 + Log(1 + g)t, where Y 0 is GDP at time zero and g is the average annual growth rate. Nominal Growth Rate Compounded Annually Multiple R 0.994717 R 0.989462 Adjusted R 0.989198 Standard Error 0.043069 Standard t Stat P-value Lower 95% Upper 95% Coefficients Error Intercept 2.684734 0.013532 198.3931 1.7E-61 2.657384 2.712083 X Variable 1 0.033601 0.000548 61.28393 3.6E-41 0.032493 0.034709 Based on the summary output, LogY t = Log(2.684734) + Log(0.033601)t Taking the anti-log gives Y t = 483.8754(1.080441) t The average annual growth rate of nominal GDP is 8% per year assuming annual
(4) Based on your data, calculate the average annual growth rate of gdp, assume continuous The growth formula assuming continuous compounding is, Y t = (Y 0 )e gt Which can be linearized by taking the natural logarithm of both sides to get, LnY t = LnY 0 + gt Nominal Growth Rate Continuous Compounding Multiple R 0.994717 R 0.989462 Adjusted R 0.989198 Standard Error 0.09917 Standard Lower Upper 95% Coefficients Error t Stat P-value 95% Intercept 6.181827 0.031159 198.3931 1.7E-61 6.118852 6.244803 X Variable 1 0.077369 0.001262 61.28393 3.6E-41 0.074818 0.079921 LnY t = Ln(6.181827) +.077369t The average annual growth is 7.8%per year assuming continuous Exponentiating both sides Y t = 483.8754(1.080441) t (5) Based on your answer from (4), estimate gdp for the year 2005. The prediction 2005 is period 2005-1959 = 46 Y t = 483.8754e.077369*46 = $16,997.41 Note that if no rounding is done, base 10 log and natural log methods result in the same answer, Y t = 483.8754(1.080441) 46 = $16,997.41 (6) Construct a 95% prediction interval for your estimate in (4). $16,997.41 ± t df,α/2 SE 1% 1 n % (x p & x)2 j (x i & x)2 $16,997.41 ± 2.02(.09917) 1% 1 42 % (46&21.5)2 (42&1)150.5 2
$16,997.41 ±.212 Nominal GDP in 2005 is expected to be between $16,997.618 and $16,997.194 (7) Calculate real gdp for the years provided. (8) Graph real and nominal gdp together for the years provided. Be sure to correctly label your axes. (9) Based on the data, calculate the average annual dollar growth of real gdp. Nominal Simple Linear Multiple R 0.987857 R 0.975861 Adjusted R 0.975258 Standard312.3749 Error Standard t Stat P-value Lower 95% Upper 95% Coefficients Error Intercept 1839.213 98.14859 18.73907 2.06E-21 1640.847 2037.579 X Variable 1 159.9117 3.976638 40.21278 5.72E-34 151.8746 167.9487 Based on the simple linear regression, nominal GDP grew on average approximately 159.9117 billion dollars per year from 1960-2001.
(10) Based on the data, calculate the average annual growth rate of real gdp, assume annual Real Growth Rate Compounded Annually Multiple R 0.996052 R 0.99212 Adjusted R 0.991923 Standard0.015192 Error Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3.396159 0.004773 711.4782 1.13E-83 3.386511 3.405806 X Variable 1 0.013725 0.000193 70.96707 1.07E-43 0.013334 0.014116 Based on the summary output, LogY t = Log(3.396159) + Log(0.013725)t Taking the anti-log gives Y t = 2489.766(1.032108) t The average annual growth rate of nominal GDP is 3.2% per year assuming annual (11) Based on the data, calculate the average annual growth rate of real gdp, assume continuous Real Growth Rate Continuous Compounding Multiple R 0.996052 R 0.99212 Adjusted R 0.991923 Standard0.034981 Error Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 7.819944 0.010991 711.4782 1.13E-83 7.79773 7.842158 X Variable 1 0.031603 0.000445 70.96707 1.07E-43 0.030703 0.032503 LnY t = Ln(7.819944) + 0.031603 t The average annual growth is 3.1% per year assuming continuous
(12) Based on the answer from (11), estimate real gdp for the year 2005. Y t = 2489.766e.031603*46 = $10,654 (13) Construct a 95% prediction interval for your estimate in (12). $10,654 ± t df,α/2 SE 1% 1 n % (x p & x)2 j (x i & x)2 $10,654 ± 2.02(0.034981) 1% 1 42 % (46&21.5)2 (42&1)150.5 2 $16,997.41 ±.075 Real GDP in 2005 is expected to be between $10,653.924 and $10,654.074