Key - Problem Set 3 2011

# Key - Problem Set 3 2011 - Key - Problem Set 3 (8)...

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Key - Problem Set 3 Econometrics I Resource Economics 702 (8) 1. The data set money. xlsx on the course website contains time series data for the following variables: M2 = seasonally adjusted M2 monetary aggregate measured in billions of dollars; GDP = seasonally adjusted annual real GDP measured in billions of chained 1996 dollars; interest = discount rate (%). a. What signs do you expect for the parameters of the model: For this demand function, we should expect that the “price of money,” the interest rate, will have a negative effect on the demand for money ( β 2 < 0) and that the income effect will be positive ( β 1 > 0). b. Estimate the model and interpret the estimates. My SAS printout: 01 2 2 tt t t m gdp interest u   The REG Procedure Model: MODEL1 Dependent Variable: M2 M2 Number of Observations Read 43 Number of Observations Used 43 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 93330127 46665063 1100.29 <.0001 Error 40 1696464 42412 Corrected Total 42 95026591 Root MSE 205.94075 R-Square 0.9821 Dependent Mean 2018.30698 Adj R-Sq 0.9813 Coeff Var 10.20364 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > |t| Intercept Intercept 1 -1644.79939 113.17908 -14.53 <.0001 GDP GDP 1 0.73897 0.01575 46.91 <.0001 interest interest 1 -32.34785 13.06426 -2.48 0.0176

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The estimated effect of a \$1 billion increase in GDP on money demand is an increase in money demand (M2) by \$0.74 billion, holding interest rates constant. This is our expected sign. (Remember, we interpret these estimated coefficients as partial effects – any other variables in the model are “held constant.”) A 1% increase in the rate of interest, causes money demand to decrease by \$32.35 billion, holding GDP constant. This is the expected sign. c. Are the estimated effects of GDP and interest rates statistically significant? Explain clearly your conclusions. In both cases, we conduct one-tail tests. For the effect of GDP: Ho: β 1 0; Ha: β 1 > 0. Now, compare the calculated t-value (in this case 49.91) to the critical t-value or note that the p-value for the estimated effect of GDP is virtually zero – the probability is virtually zero that we would get a t-value this large purely by chance. The estimated effect is statistically greater than zero. For the effect of interest: Ho: β 2 0; Ha: β 2 < 0. Again, compare the calculated t-value (in this case -2.48) to the critical t-value or note that the p-value for the estimated effect of GDP is 0.0088 – the probability is very small, that we would get a t-value this small or smaller
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## This note was uploaded on 12/08/2011 for the course ECON 702 taught by Professor Staff during the Spring '08 term at UMass (Amherst).

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Key - Problem Set 3 2011 - Key - Problem Set 3 (8)...

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