ps_10_sol - Department of Economics Columbia University...

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Department of Economics W3412 Columbia University Spring 2010 SOLUTIONS TO Problem Set 10 Introduction to Econometrics Prof. Marcelo J. Moreira and Seyhan E Arkonac, PhD for all sections Spring 2010 Suggested Solutions are in 10 point Arial Question I: To determine whether there is a tradeoff, on average, between unemployment and inflation, we can test H 0 : β 1 = 0 against H 1 : β 1 < 0 in the following equation. If the classical linear model assumption holds we can use the usual OLS t statistic. Inf t = β 0 + β 1 unem t + u t 1. Estimate the above equation using phillips.dta and report the results in the usual form. Do the results suggest a tradeoff between unemployment and inflation? Inf t = 1.05 + 0.502 unem t t stat is 1.89, if anything there is a positive relationship between unemployment and inflation not a tradeoff 2. Now run the regression using only the years 1997 through 2003. How do your estimates differ? Can you draw any firm conclusion? Explain. Inf t = 4.16 - 0.378 unem t t stat is -1.13. There is a tradeoff between unemployment and inflation but it is not significant, besides with only 7 observations this result cannot be reliable. 3. Now consider an alternative form of the expectation Augmented Phillips curve that allows the natural rate of unemployment to depend on past levels of unemployment. In the simplest case, the natural rate of unemployment at time t equals unem t -1 . If we assume adaptive expectations, we obtain a Phillips curve where inflation and unemployment are in first differences: Δ Inf t = β 0 + β 1 Δ unem t + u t Estimate this model report the results in the usual form, and discuss the sign and statistical significance of beta hat one. Δ Inf t = - 0.072 - 0.832 Δ unem t and the t stat is -2.87 which gives a p value of 0.006 which is significant, this form of the Phillips curve presents a tradeoff between the change in inflation and the change in unemployment. 4. Which model fits the data better, model in part 1 or in part 3? Explain. The model in 3 fits better because adjusted R square, F test and t test gives better results and the result in part 4 is what the theory suggests also.
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Question II: Milton Friedman’s 1957 theory of consumption – the Permanent Income Hypothesis (PIH) – posited that people base their consumption not only on what they earn today, but also on their past and expected future earnings. Under this theory, consumers compute their “permanent income,” then consume a fraction of that permanent income. In this problem set you will explore some implications of the permanent income hypothesis for the time series properties of consumption, specifically, the implication (first derived by Robert Hall in 1978) that the PIH, plus “rational expectations,” implies that consumption will follow a random walk. Testing this implication provides a test of a particular mathematical formulation of the PIH.
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This note was uploaded on 02/05/2012 for the course ECON W3412 taught by Professor Seyhanarkonac during the Fall '11 term at Columbia College.

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ps_10_sol - Department of Economics Columbia University...

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