## Problem Set

### 1.Consider the following data generatingprocess,  宏观计量经济学代写

yt = β0 + β1xt + βt;

where y and x are variables and the βs are parameters. Moreover, ” is an error term that satisÖes

εt = ρεt-1 + &t2 + η,

where η is i.i.d. (i.e., ‘ is white noise) and & (0; 1) : Clearly, the error term associated with the regression of y on x is not i.i.d.

(a)Regarding the non-i.i.d. issue noted above, is the issue one of serialcorrelation? Please explain.

(b)Regardless of your answer to part (a), is there a version of the transformation strategy that would solve the non-i.i.d. issue? If so, implement it and derive the regression equation that you would operationalize after this If not, pleaseexplain.

### 2.The Stata .dta file called LaborMarketData has four variables: LF (the seasonally adjusted level of the S. labor force);

U (the seasonally adjusted level of U.S. unem- ployment); V (the seasonally adjusted level of U.S. job vacancies); and month (a time variable). Create a Stata .do file called LaborMarketDataCONTROL that does the following:

(a)Clears the memory and loads the data using Stata’s cd and use commands.

(b)Time aggregates the variables LF, U, and V to quarterly  frequency  using the vari-  able q, which you should generate.  Formats  the  variable  q  at  quarterly  frequency and tssets this variable.  宏观计量经济学代写

(c)Generates a variable called Vlag that is equal to the first lag of V and runs a regressionof V on Vlag, checks for first order serial correlation and higher order serial correlation up to a fifth lag, Write down in your Stata code whether there is a problem of serial correlation or not and explain how you can tell.

(d)Fixesany issues of serial correlation found in part (c) using an appropriate strategy (please write directly in your Stata code your reasoning behind every step that you take).

### 3.Thisis a continuation of problem (2). Add code to the same .do file generated for the previous problem that does the following:  宏观计量经济学代写

(a)Generates the variables logV and logU, which are equal to, respectively, the nat- ural logarithm of V and U. Runs a regression of logU on (Comment directly in your Stata code on the regressions R2and whether  or not the slope parameter is in line with intuition.) Checks for first order serial correlation and serial cor- relation up to five lags, inclusive. Is there a problem of serial correlation here? Please explain using commenting in your Stata code.

(b)Fixes any issues of serial correlation found in part (a) using an appropriatestrat- egy (please write directly in your Stata code your reasoning behind every step that you take). If there were issues to fix, try to make sure that they were in- deed fixed and comment on the R2 of your final specification and the impact of contemporaneous vacancies on contemporaneous unemployment as implied by the relevant coe¢cient of your final specification. If there are di§erences relative to the original specification please speculate on why that may be the case.

### 4.This is a continuation of problem (3). Add code to the same .do file generated for the previous problem that does the following:

(a)Generates the variables dlogV and dlogU, which are equal to, respectively, growth rates of V and U. Runs a regression of dlogU on (Comment directly in your Stata code on the regressions R2and whether  or not the slope parameter is in line with intuition.) Checks for first order serial correlation and serial correlation up to five lags, inclusive. Is there a problem of serial correlation here? Please explain using commenting in your Stata code.    宏观计量经济学代写

(b)Fixes any issues of serial correlation found in part (a) using an appropriatestrat- egy (please write directly in your Stata code your reasoning behind every step that you take). If there were issues to fix, try to make sure that they were in- deed fixed and comment on the R2 of your final specification and the impact of contemporaneous vacancies on contemporaneous unemployment as implied by the relevant coe¢cient of your Önal specification. If there are di§erences relative to the original specification please speculate on why that may be the case.