## Example 201

To study the interrelationships among advertising, concentration (as measured by the concentration ratio), and price-cost margins, Allyn D. Strickland and Lenord W. Weiss formulated the following three-equation model.18

Ad/S = a0 + a1M + a2(CD/S) + a3C + a4C2 + a5Gr + a6Dur (20.6.1)

Concentration function:

Price-cost margin function:

M = c0 + c1(K/S) + c2Gr + c3C + c4GD + c5(Ad/S) + c6(MES/S) (20.6.3)

where Ad = advertising expense S = value of shipments C = four-firm concentration ratio CD = consumer demand MES = minimum efficient scale M = price/cost margin

Gr = annual rate of growth of industrial production Dur = dummy variable for durable goods industry

K = capital stock GD = measure of geographic dispersion of output

By the order conditions for identifiability, Eq. (20.6.2) is overidentified, whereas (20.6.1) and (20.6.3) are exactly identified.

The data for the analysis came largely from the 1963 Census of Manufacturers and covered 408 of the 417 four-digit manufacturing industries. The three equations were first estimated by OLS, yielding the results shown in Table 20.3. To correct for the simultaneous-equation bias, the authors reestimated the model using 2SLS. The ensuing results are given in Table 20.4. We leave it to the reader to compare the two results.

(Continued )

18See their "Advertising, Concentration, and Price-Cost Margins," Journal of Political Economy, vol. 84, no. 5, 1976, pp. 1109-1121.

IV. Simultaneous-Equation Models

20. Simultaneous-Equation Methods

CHAPTER TWENTY: SIMULTANEOUS-EQUATION METHODS 779

EXAMPLE 20.1 (Continued)

TABLE 20.3 OLS ESTIMATES OF THREE EQUATIONS (t Ratios in Parentheses)

Dependent variable