Question 2 Linear Regression (6 Points) Imagine we would like to look at Okun's Law, i.e. the relationship between the c

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Question 2 Linear Regression 6 Points Imagine We Would Like To Look At Okun S Law I E The Relationship Between The C 1 (180.43 KiB) Viewed 22 times

Question 2 Linear Regression (6 Points) Imagine we would like to look at Okun's Law, i.e. the relationship between the change in unemployment and the growth rate of GDP. Let ut denote the unemploy- ment rate in period t and let y, denote GDP in period t. We consider quarterly data starting in Q1 1974 until Q4 2020. We define the annual change in unemployment as audz = Ut – Ut-4 and the annual percentage growth rate of GDP as Yt - Yt-4 Yt-4 aget = 100. Then we estimate the following linear model using ordinary least squares: aud = a + Bagg: +&r. The output of Stata is the following: regress aud agg Source SS df MS Model Residual 234.381846 105.888108 1 234.381846 186 .569290902 Number of obs F(1, 186) Prob > F R-squared Adj R-squared Root MSE 188 411.71 0.0000 0.6888 0.6871 .75451 Total 340.269954 187 1.81962542 aud Coef. Std. Err. t P>It! [95% Conf. Interval] agg cons -.4813667 1.300457 .0237236 .0819186 -20.29 15.87 0.000 0.000 -.5281687 1.138848 -.4345647 1.462066 The top panel provides some measures on the goodness of fit, the bottom panel provides detailed information on the estimated coefficients. The row agg shows the estimated coefficient ß, and some statistics related to it.

Part 2.1 What is the interpretation of our estimate B~ -0.48? Part 2.2 Is ß significantly different from zero? Either justify your answer or explain which extra information you would need. Part 2.3 The last two numbers in the row provide a confidence interval. Students often say that they are 95% confident that the coefficient ß lies between -0.53 and -0.43. What does this mean?