A Firm Has Determined That Its Average Level of Sales

Essay

A firm has determined that its average level of sales (S_t) per week in $1,000s during a given year depends on the previous year's level of sales (S_t-1), the previous year's level of advertising (A_t-1) per month in $1,000s, and the current year's rate of annual industry growth (G_t) in percentage terms. The firm has also determined that the level of industry growth in the current period depends on the previous period's rate of industry growth (G_t-1) and on current period sales by the firm. During the current period, the firm's level of sales was $100,000, advertising was $40,000, and the rate of growth in the industry was 4%. The firm estimated the following two-equation econometric model:
S_t = 4 + 0.40 S_t-1 + 0.10 A_t-1 + G_t and G_t = 1 + 0.5 G_t-1 + 0.5 S_t
(i) Formulate a single-equation forecasting equation from this model.
(ii) Forecast the level of sales in the next period.