Question

A firm has determined that its average level of sales (St) per week in thousands of dollars during a given year depends on the previous year's level of sales (St–1), the previous year's level of advertising (At–1) per month in thousands of dollars, and the previous year's rate of annual industry growth (Gt-1) in percentage terms. In the previous period, the firm's average level of sales was $35 thousand, advertising was $5 thousand, and the rate of growth in the industry was 2 percent. The firm estimated the following econometric model:

St = 10 + 0.75St–1 + 0.55At–1 +2.00Gt–1

i. Forecast the level of sales in the current period.

ii. Calculate and interpret the firm’s sales elasticity with respect to the previous year’s level of rate of growth in the industry (Gt-1).

iii. Assume Moving Average method was also used to forecast sales for the current year. If the Moving Average method has a RMSE of 2.5 while the Econometric Model above has a RMSE of 2.0, which method is more accurate, and why?

Answer 1

St = 10 + 0.75St–1 + 0.55At–1 +2.00Gt–1

i)

We have St-1=$35 (thousands)

At-1=$5 (thousands)

Gt-1=2

St=10+0.75*35+0.55*5+2*2=43

Forecast sale in current period is $43 thousand.

II)

Differentiate St with respect to Gt-1, we get

dSt/d(Gt-1)=2.0

Sale elasticity with respect to previous year growth level=[dSt/d(Gt-1)]*[(Gt-1)/St]=2*2/43=0.093

Absolute value of sale elasticity is 0.093. It is less than 1, we can say it inelastic in this range.

It means that sale in current period will increase by 0.093 percent for every 1% rise in growth level in previous level.

c)

Lower RSME means that predicted values are closer to the observed values. It means that Econometric model gives the close predictions in this case.