Problem Set #8
Sonoma State University
Economics 494- Seminar in Quantitative Marketing II
Dr. Cuellar
The Polynomial Lag Model
Use the polynomial.dta data set to answer the following questions
1.
The Unrestricted Distributed Lag Model.
a. Estimate the OLS relationship between log sales and log advertising using lagged advertising from
zero to nine periods?
b. Use the information criteria (AIC and BIC) to choose the optimal lag length. If there are
conflicting results, choose the longer length.
c. For the model chosen in part (b) show graphically your actual and predicted log sales. Describe.
d. Examine a graph of your residuals. Describe.
e. Examine Durbin’s alternative and the Breusch-Godfery test statistics for indications of serial
correlation. Describe your results.
f. Re-estimate your model using the Prais-Winsten procedure.
g. Show graphically your actual and predicted log sales. Describe.
h. Show graphically the advertising coefficients (weights). Describe.
i. Examine a correlation matrix of your advertising coefficients. Do you see any signs of
multicollinearity?
j. Examine the variance inflation factor (VIF) for your advertising coefficients. Do you see any signs
of multicollinearity?
2.
The Restricted (Polynomial) Lag Model.
a. Estimate a second order (i.e., quadratic) polynomial model using the optimal lag structure from
above. Be sure to use the Prais-Winsten procedure to correct for any serial correlation.
b. Show graphically your actual and predicted log sales. Describe.
c. Show graphically the advertising coefficients from the polynomial lag model compared to those
with your unrestricted lag model. Describe.
d. Suppose instead you estimate a second order polynomial model using a 4-period lag structure.
e. Show graphically the advertising coefficients from the 4-period lag model compared with those
from the model in part a. Describe.
f. What are the marketing implications of the different results in terms of:
i. The length of the positive advertising effect.
ii. The maximum advertising effect.
iii. The period in which advertising reaches its maximum effect.
g. Suppose instead you estimate a second order polynomial model using a 6-period lag structure.
h. Show graphically the advertising coefficients from the 6-period lag model compared with those
from the model in part a. Describe.
i. What are the marketing implications of the different results in terms of:
i. The length of the positive advertising effect.
ii. The maximum advertising effect.
iii. The period in which advertising reaches its maximum effect.
j. Suppose instead you estimate a second order polynomial model using a 12-period lag structure.
k. Show graphically the advertising coefficients from the 12-period lag model compared with those
from the model in part a. Describe.
l. What are the marketing implications of the different results in terms of:
i. The length of the positive advertising effect.
ii. The maximum advertising effect.
iii. The period in which advertising reaches its maximum effect.
3.
Use the monthly.dta data set to answer the following questions.
a. Estimate a second order polynomial model with a six period lag structure (the lag structure
recommended by the information criteria of that problem set).
b. Show graphically the advertising coefficients from the polynomial lag model compared to those
of the unrestricted model of problem set #4. Describe.