Nominal and Real U.S. GDP

Transcription

1 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) Nominal and Real U.S. GDP Year (2) Based on the data, calculate the average annual dollar growth of nominal gdp. Nominal Simple Linear Multiple R R Adjusted R Standard Error Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept E X Variable E Based on the simple linear regression, nominal GDP grew approximately billion dollars per year from

2 (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 R Adjusted R Standard Error Standard t Stat P-value Lower 95% Upper 95% Coefficients Error Intercept E X Variable E Based on the summary output, LogY t = Log( ) + Log( )t Taking the anti-log gives Y t = ( ) t The average annual growth rate of nominal GDP is 8% per year assuming annual

3 (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 R Adjusted R Standard Error Standard Lower Upper 95% Coefficients Error t Stat P-value 95% Intercept E X Variable E LnY t = Ln( ) t The average annual growth is 7.8%per year assuming continuous Exponentiating both sides Y t = ( ) t (5) Based on your answer from (4), estimate gdp for the year The prediction 2005 is period = 46 Y t = e *46 = $16, Note that if no rounding is done, base 10 log and natural log methods result in the same answer, Y t = ( ) 46 = $16, (6) Construct a 95% prediction interval for your estimate in (4). $16, ± t df,α/2 SE 1% 1 n % (x p & x)2 j (x i & x)2 $16, ± 2.02(.09917) 1% 1 42 % (46&21.5)2 (42&1)

4 $16, ±.212 Nominal GDP in 2005 is expected to be between $16, and $16, (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 R Adjusted R Standard Error Standard t Stat P-value Lower 95% Upper 95% Coefficients Error Intercept E X Variable E Based on the simple linear regression, nominal GDP grew on average approximately billion dollars per year from

5 (10) Based on the data, calculate the average annual growth rate of real gdp, assume annual Real Growth Rate Compounded Annually Multiple R R Adjusted R Standard Error Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept E X Variable E Based on the summary output, LogY t = Log( ) + Log( )t Taking the anti-log gives Y t = ( ) 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 R Adjusted R Standard Error Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept E X Variable E LnY t = Ln( ) t The average annual growth is 3.1% per year assuming continuous

6 (12) Based on the answer from (11), estimate real gdp for the year Y t = e *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( ) 1% 1 42 % (46&21.5)2 (42&1) $16, ±.075 Real GDP in 2005 is expected to be between $10, and $10,