Presentación

This chapter presented the basic techniques of estimating demand functions and forecasting future sales and prices. Estimation of demand functions is most often accomplished using the technique of regression analysis. Two specifications for demand, linear and log-linear, are presented in this chapter. When demand is specified to be linear in form, the coefficients on each of the explanatory variables measure the rate of change in quantity demanded as that explanatory variable changes, holding all other explanatory variables constant. In linear form, the empirical demand specification is

Q = a + bP + cM + dPR

where Q is the quantity demanded, P is the price of the good or service, M is consumer income, and PR is the price of some related good R. The estimated demand elasticities are computed as

As in any regression analysis, the statistical significance of the parameter estimates can be assessed by performing t-tests or examining p-values.

When demand is specified as log-linear, the demand function is written as

Q = aPbMcPdR

In order to estimate the log-linear demand function, it is converted to natural logarithms:

ln Q = ln a + b ln P + c ln M + d ln PR

In log-linear form, the elasticities of demand are constant, and the estimated elasticities are

To choose between these two specifications of demand, a researcher should consider whether the sample data to be used for estimating demand are best represented by a demand function with varying elasticities (linear demand) or by one with constant elasticity (log-linear demand). When price and quantity observations are spread over a wide range of values, elasticities are likely to vary, and a linear specification with its varying elasticities is usually a more appropriate specification of demand. Alternatively, if the sample data are clustered over a narrow price (and quantity) range, a constant-elasticity specification of demand, such as a log-linear model, may be a better choice than a linear model.

The method of estimating the parameters of an empirical demand function depends on whether the price of the product is market-determined or manager-determined. Managers of price-taking firms do not set the price of the product they sell; rather, prices are endogenous or "market- determined" by the intersection of demand and supply. Managers of price-setting firms set the price of the product they sell by producing the quantity associated with the chosen price on the downward-sloping demand curve facing the firm. Since price is manager-determined rather than market-determined, price is exogenous for price-setting firms.

D.R. Universidad Virtual del Tecnológico de Monterrey,2010

When estimating industry demand for price-taking firms, complications arise because of the problem of simultaneity. The simultaneity problem refers to the fact that the observed variation in equilibrium output and price is the result of changes in the determinants of both demand and supply. Because output and price are determined jointly by the forces of supply and demand, two econometric problems arise when a researcher tries to estimate the coefficients of industry demand: the identification problem and the simultaneous equations bias problem.

The identification problem involves determining whether it is possible to trace out the true demand curve from the sample data. Industry demand is identified when supply includes at least one exogenous variable that is not also in the demand equation. The problem of simultaneous equations bias arises when price is an endogenous variable, as it is when price is market- determined for price-taking firms. In order for the standard or ordinary least-squares (OLS) regression procedure to yield unbiased parameter estimates, all explanatory variables must be uncorrelated with the random error term in the demand equation. An endogenous variable is always correlated with the error term in both the demand and supply equations. (This can be verified by examining the reduced form equation for Q, which shows how Q is related to

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