A researcher is interested in estimating a demand function for gas

A researcher is interested in estimating a demand function for gas

SECTION A

ANSWER BOTH QUESTIONS 1 AND 2

  1. A researcher is interested in estimating a demand function for gas. Monthly data on the quantity of gas consumed (after converting hundreds of cubic feet of gas into kilowatt hours) and the price of gas (in dollars) are available spanning 250 months.
  1. What are the conditions under which the natural logarithm of gas consumption (Ln(gc)) and the natural logarithm of the price of gas (Ln(gp)) series are stationary? How would you test whether both series contain a unit root? What are the null and the alternative hypotheses?

A researcher is interested in estimating a demand function for gas

b) The researcher performs an ADF test with one lag and a deterministic trend for each series (Ln(gc) and Ln(gp)) and for their first differences (D.Ln(gc) and D.Ln(gp)) and obtains the following test values:

Variables testsADF t-stat
Ln(gc)-1.03
Ln(gp)-1.70
D.Ln(gc)-8.21
D.Ln(gp)-11.50

Given a 5% critical value of -3.427 for the ADF test for both cases, which of the series (Ln(gc), Ln(gp), D.Ln(gc), D.Ln(gp)) are stationary? Determine the appropriate order of integration of Ln(gc) , Ln(gp), D.Ln(gc) and D.Ln(gp).

c)  The following relationship between the log of gas consumption and the log of the price of gas is then estimated (with OLS and standard errors reported in parentheses) and reported by the researcher:

                                      Ln(gc)t = 1.225 –   0.551 Ln(gp)t + ût    

                                                                            (1.077)    (0.122)

Interpret these estimates. Are the standard errors valid in this case? Explain your answers.                                   (                                                                 

d) Explain what an econometrician means when they say: ”Ln(gc) and Ln(gp) are cointegrated.” Explain in your own words how an econometrician would test whether Ln(gc) and Ln(gp) are cointegrated.                                                                           

  •  A researcher estimates the relationship between the natural log of per capita beer consumption (Ln(bc)) and the natural log of consumers’ expenditure (Ln(c)) between 1965-2015 using yearly observations.
  1. The researcher runs the following regression: (standard errors in parentheses)

                             (0.075)    (0.212)               (0.210)                  (0.102) 

What type of an econometric model is this?                              

  • Interpret the estimated coefficients corresponding to ∆Ln(c)t and Ln(bc)t-1 in the above regression model.                                                           
  • An F-test has been used to test the coefficients of the Error Correction Model.  The value of the test F was higher than the critical upper value (Fu) of the relevant non-standard F-distribution (Pesaran-Singh-Smith). Compute and interpret the long run solution for the model estimated in (a). What is the advantage of this specification compared to a long run relationship estimated by a simple OLS regression?