2.4 Endogenous explanatory variables  (Page 8/10)

In this exercise we address this issue by using data used originally by Richard Schmalensee (1972) in his Ph.D. dissertation. You will use these data to estimate a simple two-equation model of the cigarette advertising industry.

We use annual data for the period 1955 to 1967 to estimate the impact of cigarette advertising on aggregate demand for cigarettes and the impact of cigarette consumption on cigarette advertising. We begin with a model of the demand for cigarettes. We assume that the demand for cigarettes is given by:

where

q _t = cigarettes consumed per person over age 15,

pc _t = retail price of cigarettes,

y _t = real disposable personal income per capita (1958 dollars),

A _t = real advertising expenditures per individual over age 15 (1960 dollars), and

D64 = a dummy variable equal to 1 for the years 1964 through 1967 and zero otherwise.

We include the dummy variable for years after 1964 to pick up the negative impact on cigarette sales of the 1964 report of the US Surgeon General’s Advisory Committee (1964) announcing that the government believed that there was enough evidence available to conclude that cigarette smoking causes cancer. We expect the signs of the parameters with the price of cigarettes and the dummy variable to be negative. We expect that the sign of the parameters with income and advertising to be positive.

Next we turn to a model of the supply of advertising. We assume:

where:

pa _t = advertising price index, and

m _t = gross profits as a percentage of gross sales.

The last variable needs a bit of explaining. The amount of advertising in the industry should be a function of degree of competition in the industry. If the market were perfectly competitive, there would be no reason for any firm to advertise. If the firm were a monopoly, there also would be no reason to advertise. However, if the market is an oligopoly, then a firm would advertise in an effort to gain market share by differentiating its product from the product of its competitors.

The traditional measure of the degree of monopoly power that a firm has is the ratio of its marginal profits to its marginal cost:

where p is output price, mc is marginal cost, and m is the measure of monopoly power. Since we cannot observe the firms’ marginal costs, we approximate m by the ratio of gross profits to gross sales. We expect the impact of the degree of monopoly to have a non-linear impact on advertising expenditures.

The data used to estimate our two equations are listed in Table 5 and are available in the MS Excel file Cigarette sales and advertising data.xls . These data are with the exception of disposable personal income from Schmalensee (1972: 273-290). The disposable personal income data are from the Department of Commerce (1975: Table F26, page 225).

Specification of the Model. Equations (18) and (19) are, as written, very general and need further specification before they can be estimated. We will assume that the two equations take a log-log form. In particular, we assume that we want to estimate: