Demand Estimation and Measurement
An accurate estimate of the demand or the response of demand to change in price or other explanatory variables is very difficult. Further, the cost of statistical analysis required for this purpose may exceed the benefits, particularly, when uncertainty is great or when the volume of work involved is too small to provide a reasonable return on the research expenditure.
That is why business firms have to rely on subjective estimates of experienced managers for an effective analysis of a wide range of business problems, relating to pricing and marketing. Such empirical estimates and their interpretations are useful for control and management of external factors. For this purpose, surveys and statistical techniques can be used.
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Consumers buy some minimum quantities of various commodities, irrespective of prices. These are minimum requirements to keep the consumers alive. The supernumerary income (income left after the minimum quantities are covered) is allocated among the different commodities on the basis of prices. Consumer surveys deal with the intentions of the consumers.
They help in demand estimation. However, the likely demand revealed by these surveys may not coincide with the actual demand. Alternatively, experimental surveys or controlled experiments can be used to estimate the effect of demand determinants under management control. But, care should be taken to reduce the influence of unimportant variables to a minimum.
Statistical techniques combined with the controlled experiments provide reliable estimate of the demand function. Since, trend analysis variable postulating time series of a single independent variable generally ignores the important determinants of demand such as prices, more sophisticated techniques are used.
That is why economists normally use regression techniques to isolate and measure the fluctuations in demand occurring in response to main demand determinants like price and disposable income. This technique involves four steps.
Identification of Casual Variables
Casual variables should be chosen with utmost care for estimating the demand function. Non-inclusion of important variables (determinants) as well as inclusion of irrelevant variables jeopardises the accuracy of estimates. Further, the units of measurements for different variables have to be carefully specified.
Collection of Historical Data
Data is the raw material for estimation. If the data on relevant variables is inaccurate, estimated function will be unreliable. The estimation could be based on either time series or cross-section date or both, depending upon the date availability and problem in hand.
While the former refers to observations on a variable of a given population over time, the latter pertains to observations on a variable at a point of time across different populations. Another important thing is the sample size of the data.
The greater the sample size, the more reliable are the estimates. The size f the sample should be greater than the numbers of demand determinants to use the regression method of estimation. If the data on an important variable is not available, proxy or dummy variables could be used. Researchers often use time variable as a proxy for consumers’ tastes and preferences.
Choice of an Appropriate Functional Form
This stage relates to choice of an appropriate form of the function. The functional form could be linear, quadratic, cubic, double log, semi-log or reciprocal, on the basis of experiment with theoretically plausible forms. The form actually chosen by the researcher should be ideal on both theoretical and empirical grounds.
For this, the researcher will have to estimate the function in a few alternative forms. Thereafter, with the aid of some statistical tests and a prior knowledge of some of the signs and magnitudes of the coefficients, the most appropriate form can be chosen. The linear and double-log forms are some of the most popular functional forms.
Estimation of Function
The last step is economic estimation of the function. The most popular method available for this purpose is the least-squares method of estimation, which is based on unconstrained optimisation technique.
In this method, estimates of parameters are obtained in such a manner that the sum of the squares of the errors between the actual values of the dependent variable and its estimated value is minimised with respect to each of the parameters under estimation.
This method can also be used for estimating equations with more than one cause variable, called as multiple regression equation.
Analysis of Estimated Demand Functions
Estimated demand function has an edge over the theoretical demand function. It not only explains the factors influencing the market as well as the direction of their effects (like the theoretical demand function) but also the magnitudes of such effects. Thus, managers and decision makers prefer the estimated demand function to its theoretical counterpart.
Statistically estimated empirical demand functions give us information on elasticity. Such information is very useful for corporate planning and business policy decisions. The specific values of elasticity can be used to analyse the effect (magnitude as well as direction) of market forces on demand, as explained in this chapter under ‘Demand Forecasting’.
Further, the estimated demand function can be used to derive the equations of the demand and Engel Curves for given values of other variables, by substituting the values of all variables other than the own price or income (as the case may be) in the estimated demand function.
This can then be used to derive equation for Average Revenue (AR), Total Revenue (TR) and Marginal Revenue (MR) curves. Furthermore, the estimated demand function can be used to provide policy guidelines. Finally, the estimateddemand function can be used for forecasting demand by setting the values of casual (independent) variables in the forecast period.