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Paul A. Johnson Economics 210 Second Applied Project Your completed projects are due at my office no later than 5 PM on Monday, May 17, 2010. Your...

paul johnson econometrics applied project 2
© Paul A. Johnson Economics 210 Second Applied Project Your completed projects are due at my office no later than 5 PM on Monday, May 17, 2010. Your responses should include answers to each of the questions below as well as a type-written log file (in a fixed pitch font such as ) showing all of the (or other statistical courier new package approved by me) commands and the resultant supporting your answers. You may output consult any written source you choose regarding the project but you may communicate only with me about this project prior to turning in your answers. Unauthorized communication with any 1 person about this project shall result in the awarding of a failing grade. While some of the tasks that you need to perform (e.g. testing for heteroskedasticity) are available as "canned" procedures in , use of such procedures will earn no credit. Each of the 15 parts below is worth a maximum of 5 points except for parts (a), (e) and (i) which are each worth a maximum of 10 points. There are a further 10 points for presentation. Late work will be penalized at a rate of 10 points for each 24 period or part thereof that the work is late. As I hope you remember from your studies of macroeconomics, Okun's Law is a relationship between the unemployment rate and real GDP, , that is sometimes written as ] > ?# ) ? % ?œ  C >> > (1) where and are parameters to be estimated, is the first-difference operator #) ? ( ), is the unemployment rate at time , is 100 times the log of real GDP, , ? BœBB ? >C ] >>> " > > > and is an error term. The data set " .dta", available on , % > appliedproject2dataspring10 contains data on , , and some other variables over the period 1950:Q1 to 2009:Q4 using ?] >> obvious mnemonics. 2 (a) What, if any, sign to you expect to have? Will OLS likely yield consistent estimators of the ) parameters and ? If yes, prove so being careful to state and justify your assumptions. If no, #) determine the size and sign of the inconsistency of the OLS estimator of . ) (b) Provide a time-series graph showing and against time. ?? ?C >> (c) Provide a scatter plot of against . ?? ?C >> 1 Of course, any external sources consulted must be cited. 2 The first few commands in your do file, after that opening your log file, should be clear use appliedproject2dataspring10 g t=_n-41 format t %tq tsset t
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(d) Using OLS, estimate the parameters of equation (1). Report your results in the usual way. Does your estimate of have the expected sign? State and interpret the of the regression. Test ) V # the hypothesis that . ) œ! (e) The variables are, respectively, real government spending (i.e. purchases of goods gs pop >> and and services) and an indicator variable that is one if the sitting President was a Democrat and zero otherwise. Explain why might be suitable gsgro 100 gs gs pop >> > " > [ (log log )] and œ‚ instruments for . ? C > (f) Explain why for might also be suitable instruments for . ?? C3   " C >3 > (g) Estimate the “first-stage” regression of on and Comment on ?? ? CC C >> > gsgro , pop , >> 12 the results. (h) Perform a Hausman-Wu test for the endogeneity of in the model in part (d) using the ? C > instruments and . gsgro , pop , >> ?? CC > > 12 (i) Using 2SLS, with and as instruments, estimate the parameters of gsgro , pop , >> ?? CC > > 12 equation (1). Report your results in the usual way. Compare them to the results in part (d). Does your estimate of have the expected sign? Test the hypothesis that . )) œ! (j) Is there any evidence of heteroskedasticity in the error term in the model estimated in part (i)? (k) Test for the presence of up to fourth-order serial correlation of the error term in the model estimated in part (i). Do this in two ways, one that assumes a homoskedastic error term and another that is robust to violations of that assumption. (l) Perform a test of the hypothesis that is robust to violations of both the assumption of ) œ! homoskedasticity and that of no autocorrelation of the error term in the model estimated in part (i). (m) Perform a Sargan test of instrument validity for the model estimated in part (i). (n) There have been claims that the response of to changes in the growth rate of GDP ? ? > real (i.e. ) is asymmetric with rising more quickly in recessions than it falls in expansions. Test ? C >> ? this hypothesis by examining or not the response of to is larger (in absolute whether ?? ? >> C value) when is negative that when is positive. HINT: An indicator variable might help. ?? CC >> (o) After thoroughly checking the veracity of the assumptions required to make the test that you used in part (n) statistically meaningful, comment on the veracity of the claim that the response of ?? ? >> to changes is asymmetric. C
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