Question

2. (a) Distinguish between autocorrelation and heteroscedasticity and explain their implications for the OLS estimators.

(b) Briefly discuss the alternative tests, at least two in case, employed to detect the problems of autocorrelation and heteroscedasticity in the estimated regression model.

(c) Using the data on consumer prices, broad money (M2) and Treasury bill rate, as given in question (1), test the quantity theory of money (QTM) as represented by:

pt=β0+β1mt+β1yt+ut such that β0>;β1>0;β2<0;β1=1;β2=-1

1. Show the estimated regression model, together with all necessary statistics such as the estimated values of the standard errors of the parameters, their t ratios, residual sum of squares, R², adjusted R², F test and Durbin Watson test for serial correlation and variance co-variance matrix of the parameters. 10
2. By apply the diagnostic tests, such as Jarque-Bera test for normality, Breusch-Godfrey LM test for serial correlation, Breusch-Pagan-Godfrey test for heteroscedasticity and Ramsey Reset test for model specification, report their estimated values. 8
3. Based a priori economic expectations (restriction imposed on the model), statistical tests (t and F) and goodness of fit, explain whether the estimated results are consistent with the QTM. 12

Based on the estimated value of the diagnostic tests, describe whether the model suffers from any problems such non-normality, autocorrelation, heteroscedasticity and model mis-specification.

Answer 1

Explanatory variable is manipulated by the researcher for the given experimental study. Here, the researcher imposes conditions on the variable and the results are observed. Hence, it is clear that result of the manipulated variable is noted and the manipulated variable is known as explanatory variable. Also, there may be more than one explanatory variable for the given study.

For example consider the variables number of hours spent in studying and the test scores of the students. Here, the number of hours spent influences the test score obtained by the student. Hence, the variable number of hours spent is known as explanatory variable.

Also, there is one major difference between an independent variable and explanatory variable. The independent variable remains unaffected by other independent variables whereas for the explanatory variables, the variables are not independent.

For example, consider the two explanatory variables in an experiment are fast food and soda. Many fast food restaurants encourage having soda after intake of food. Hence, the two variables involved in the study are not independent to each other. Moreover, both the variable influences the weight gain of the subject. Hence, it can be concluded that these two variables are explanatory variables.