Another key estimation procedure for regression models is the maximum likelihood approach that requires the probability distribution of the variable is known.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

ADVANCED ECONOMETRICS

Question One

Below is data on money supply, exchange rates, and inflation. As an economist, you are tasked to analyse the impact of money supply.

Money Supply	Inflation	Exchange rates
30	10	5.6
32.5	9.5	4.8
28.7	11.2	5.9
29.2	7.6	5.5
33.7	8.8	4.9
28.9	6.4	5.8
27.6	5.5	6.2
26.9	5.7	6.5
26.6	4.5	6.8
27.0	4.9	7.3

 

              i.        Express the above data in Matrix form.                                             [3 Marks]

            ii.        Using Matrix Algebra, derive the OLS estimator of the ’s.                  [6 Marks]

           iii.        Using Matrix Algebra, derive the variance of                                     [6 Marks]

           iv.        Compute the matrix                                                                            [10 Marks]

            v.        Compute the variance covariance of the residuals                             [5 Marks]

           vi.        Compute the variance covariance matrix of                                       [4 Marks]

          vii.        Compute and interpret the R²                                                            [6 Marks]

        viii.        Compute the F statistic                                                                         [5 Marks]

                                                                                                                        [TOTAL: 45 MARKS]

 

Question Two

Another key estimation procedure for regression models is the maximum likelihood approach that requires the probability distribution of the variable is known.

Consider the probability distribution below;

a)    Derive the MLE of .                                                                                [12 Marks]

b)    Given that t =  show that the MLE of t is asymptotically unbiased.      [5 Marks]

c)    If the variance of   is t, show that t is asymptotically efficient.             [3 Marks]

                                                                                                            [TOTAL: 20 MARKS]

 Question Three

The Output below shows the relationship between Profits and company expenditures.

 

Cross-sectional regression           Number of obs = 37

Root MSE           =            2.6e+10                                                                      

F (  1,    35)           =             10.81

Prob  > F              =             0.0023                  

R-squared           =             0.2360

Adj R-squared        =             0.2142       

  Profits*               Coef.                    Std. Err.      z              P>|z|                        [95% Conf. Interval]

 

Advertising*       -.00042           .0000835     5.03         0.000                    .0002564    .0005835

C_service             -.0017295      .0009139    -1.89         0.058                    -.0035207    .0000618

Investment*         -.0597211     .0190178    3.14          0.002                   .0224469    .0969953

* Indicates variables in log form 

a)    Provide interpretations for the coefficients of advertising and customer service.                                                                                                [4 Marks]                     

b)    Using any approach, test if advertising has a positive significant impact on profits at 5% level of significance.                                                 [6 Marks]

c)    Carry out a test of overall significance of the model above at 1% level of significance.                                                                                        [6 Marks]

d)    Assuming the Durbin Watson statistic is 3.41, carry out a test of autocorrelation.  Use 5% level of significance.                                                 [7 Marks]

e)    Generalised least squares is one of the approaches used to correct autocorrelation or heteroscedasticity. Show how this can be used to correct for heteroscedasticity and the assumption made.                  [6 Marks]         

[TOTAL: 35 MARKS]

Attachments:

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