Describe the relationship between sales and advertising

Question

Question 1:

Consider the following distributed lag model relating the percentage growth in private ins estment (INVGINTH) to the federal funds rate of interest (FFRATE).

INVGINTH = 4 - 0.4FFRATE_T, - 0.8 FFRATE_t-1 - 0.6FFRATE_t-2 - 0,2FFRATE_t-3

(a)  Suppose FFRATE = 1% fort = I. 2 3. 4. Use the above equation to forecast. INVGINTH for t = 4,

(b) Suppose FFRATE is raised to 1.5% in period t = 5 and then returned to its original level of 1 % fort = 6, 7, 8. 9. Use the equation to forecast INVGINTH for periods t = 5, 6. 7, 8, 9. Relate the changes in your forecasts to the values of the coefficients. What are the delay multipliers?

(c)  Suppose FFRATE is raised try 1.5% for periods r = 5, 6, 7, 8, 9. Use the equation to forecast INVGWTH for periods t = 5, 6. 7. 8, 9. Relate the changes in your forecasts to the values of the coefficients, What are the interim multipliers? What is the total multiplier?

Question 2:

The file ex9_2401 contains 105 weekly observations on sales revenue (SALES) and advertising expendituretADV) in millions of dollars for a large midwest department store in 2008 and 2009. The following relationship was estimated:

.SALES = 25.34 1.842 ADV, + 3.802 ADV., i + 2.265 ADV,

(a) Describe the relationship between sales and advertising expenditure. Include an explanation of the lagged relationship. When does advertising have its greatest impact? What is the total effect of a sustained $1 million increase in advertising expenditure?

a) The estimated covariance matrix of the coefficients is

		ADV	AM',-,	At)V 2
C	25598	-0.7099	t 317	-0,7661
ADV	-0-7099	1.3946	-1_0406	0.0984
ADVt t	-0.1317	-1_0406	2_1606	-1.0367
ADVet.:	-0.7661	0.0984	-1.0367	1.4214

using a two-tail test and a 5% significance level, which lag coefficients are significantly different lion zero? Do your conclusions change if you use a onetail test.? Do they change if you use a 10% significance level?

(c) Find 95 % confidence intervals for the impact multiplier, the ,one-period interim multiplier, and the total multiplier.

Attachment:- Data file.rar