Chapter 14: Econometric Modeling
Definition
Econometrics has been variously defined as "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference" - Samuelson, Koopmans and Stone, 1958 - "and as the art and science of using statistical methods for the measurement of economic relations" - Chow, 1983.
These definitions imply that econometrics and regression analysis, as described above in chapter 13, are closely related, and, indeed, least squares regression is a cornerstone of econometric techniques.
As the definitions above also suggest, however, econometrics is far broader than simply regression, encompassing all methods of statistical inference that can be employed to produce "quantitative economic statements that either explain the behavior of variables we have already seen or forecast (i.e., predict) behavior that we have not yet seen, or both" - Christ (1966). In defining their field, many econometricians would emphasize those techniques - typically extensions or adaptations of regression analysis - created to cope with the special problems that often arise in estimating economic relations. Those that particularly come to mind are techniques to measure and eliminate autocorrelation among residuals and to model lagged relationships among variables in regressions on time series data.
To many practitioners, however, the term "econometrics" when coupled with "modeling" tends to have an even more specialized meaning. It applies especially to the body of techniques utilized to estimate the parameters of economic systems.
An economic system typically consists of many interdependent variables and the relationships among them. In estimating the equations of such systems, econometricians frequently encounter an obstacle known as "the identification problem." The latter is most easily illustrated by reference to the process of determination of price and output in a market. In Figure 14.1 below price and output are shown being simultaneously determined by the intersection of a demand and a supply curve. To model this process the econometrician must develop a quantitative estimate of both the demand and supply functions. Typically the data used to estimate these functions are past observations of price and output determined by the points of intersection between the demand and supply curves. If, in the past, the supply curve has been shifting (due, say, to production cost changes) while the demand curve has
remained fixed, the resultant intersection points trace out the demand function, as shown in Figure 14.2. If the demand curve has shifted (due, say, to income changes) while the supply curve has remained fixed, the intersection points trace out the supply curve (Figure 14.3). The most likely outcome is movement of both curves yielding a pattern of price, quantity intersection points (as shown in Figure 14.4) from which the econometrician will be unable, without further information, to distinguish the demand curve from the supply curve or estimate the parameters of either. This is the identification problem.
Methods of Simultaneous Estimation
In the illustration discussed above price and output are determined by the solution of two simultaneous equations and price and output are said to be jointly determined. This is a very common occurrence in economics. Thus, the statistical methods required to estimate equations for jointly determined economic variables find frequent application. Student projects in which the need to estimate explanatory equations for economic variables arises, - whether for forecasting, policy analysis or impact assessment - will generally require their use.
Several techniques have been developed for the estimation of the structural parameters of an a priori specified system of simultaneous stochastic equations. These include indirect least squares, two stage least squares, instrumental variables, three stage least squares, full information maximum likelihood, limited information maximum likelihood, etc. Of these, only indirect and two stage least squares will be discussed here.
To illustrate the use of these techniques assume that the objective is to develop a model to forecast the annual sales and output of new cars in the United States and that the hypothesized demand function is
A = a + b1P + b2 (#Y) + b3Y +ud
(where A = new car sales
P = new car prices
Y = total personal disposable income and
#Y = change in income per capita)
Suppose further that car prices (P) are believed to depend linearly on auto sales (A) as well as an index of production input costs (C) and production capacity (K). Thus, a simultaneous two way relationship is assumed to exist between A and P. These variables are determined simultaneously by the solution of the demand function given above and the price or supply equation:
P = e + d1C + d2K + d3A + us.
Indirect least squares:
To develop an equation to forecast auto sales the analyst can estimate an equation for the reduced form, which is obtained by substituting the price equation for price in the demand function to get:
A = a +b1 (e + d1C +d2K + d3A) + b2 (#Y) + b3Y
If A is regressed on C, K, #Y, and Y as described above under Multiple Regression (13.3), the result will be an equation with quantitative estimates of the parameters of the reduced form equation for A given above which could be used to forecast future auto sales; moreover, in some cases (though not in the present example) it may be possible to derive estimates of the parameters of the original structural equations from the reduced form coefficients.
Two Stage Least Squares:
An alternative is to employ two stage LS regression by first estimating an equation for P by regressing P on all of the independent variables in the demand function for A, plus one or more other determinants of P, in this case C and K, that do not appear in the demand function. The result is the 1st stage regression equation:
The regression coefficients obtained from this second stage regression are unbiased, consistent estimators of the parameters of the original demand function.
References for Econometrics (14.3)
- Chow, G. C. Econometrics, McGraw-Hill, 1983.
- Christ, C. F. Econometric Models and Methods, John Wiley & Sons Inc., 1966.
- Hirschey, Mark and Pappas, James L. Managerial Economics 7th Ed. , The Dryden Press, 1993, Chapters 6 & 7.
- Lardaro, Leonard Applied Econometrics, Harper Collins, 1993.
- Samuelson, P. A., Koopmans, T. C. and Stone, J. R.N., Report of the evaluative committee for Econometrica, Econometrica 22, 141-6, 1954.
- Theil, Henri Principles of Econometrics, John Wiley & Sons Inc., 1971.
- Wonnacott, Ronald J. and Wonnacott, Thomas H. Econometrics, John Wiley & Sons, Inc. 1970.
Last modified: November 07, 2006 12:46:41