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Methodology of Econometrics

     Econometric research, in general, involves the following three stages:

Stage 1. Specification of the model or maintained hypotheses in explicit stochastic equation form, together with the/a priory theoretical expectations about the sign and the size of the parameters of the function.

Stage 2. Collection of data on the variables of the model and the estimation of the coefficients of the functions with the appropriate econometric techniques.

Stage 3. Evaluation of the estimated coefficients of the function on the basis of the economic, statistical and econometric criteria.

 The first stage in econometric research in consumption theory is to state the theory in explicit stochastic equation form as in Eq. (1.1), with the expectation that b₀ > 0 (i.e. at Y_d = 0, C > 0 as people dissave and/or borrow) and 0 < b₁ < 1 the second stage involves the collection of data on consumption expenditure and disposable income and estimation of Eq.(1.1). The third stage in econometric research involves 1) checking to see if the estimated value of b₀ > 0 and if 0 < b₁ < 1; 2) determining if a "satisfactory" proportion of the variation in c is "explained" by changes in Y_d and if b₀ and b₁ are "statistically significant at acceptable levels" and 3) testing to see if the assumptions of the basic regression model are satisfied or if not, how to correct for violations. If the estimated relationship does not pass these tests, the hypothesised relationships must be modified and reestimated until a satisfactory estimated consumption relationship is achieved.

Consumption theory tells us that, in general, people increase their consumption expenditure C as their disposable (after-tax) income Yd increases, but not by as much as the increase in their disposable income. This can be stated in explicit linear equation form as

                                     C = b₀ + b₁Y_d                                   (1.1)

where b₀ and b₁ are unknown constants called parameters. The parameter b₁ is the slope coefficient representing the marginal propensity to consume, MPC. Since even people with identical disposable income are likely to have somewhat different consumption expenditures, the theoretically exact and deterministic relationship represented by Eq.(1.1 must be modified to include a random disturbance or error term, u, making it stochastic:

                                     C = b₀ + b₁Y_d + u                             (1.2)  

Example: In Demand Theory

There is another example that we can take into account and its based on the demand theory.

Consumer demand theory states that the quantity demanded of a commodity, D_x, is a function of or depends on its price, P_x, consumers' income and the price of other (related) commodities, say, commodity Z ( that is P_z). Assuming that consumers' tastes remain constant during the period of analysis, we can state the preceding theory in a specific or explicit linear form or equation and in a stochastic form.

   D_x = b₀ + b₁P_x + b₂Y + b₃P_z              Explicit linear form         (1.3)

   D_x = b₀ + b₁P_x + b₂Y + b₃P_z + u        Stochastic form              (1.4)

The coefficients to be estimated are b₀, b₁, b₂ and b₃ and they are called parameters.

With reference to the consumer demand theory the first step in econometrics analysis is to express the theory of consumer demand in stochastic equation form, as in Eq.(1.4), and indicate the/a priory theoretical expectations about the sign and possibly the size of the parameters of the function.

Consumer demand theory postulates that in Eq.(1.4), b₁<0 (indicating that price and quantity are inversely related), b₂>0 if the commodity is a normal good (indicating that consumers purchase more of the commodity at higher incomes), b₃>0 if X and Z are substitutes and b₃<0 if X and Z are complements. The second stage in econometric research, involves the collection of data on the dependent variable and on each of the independent or explanatory variables of the model and utilizing these data for the empirical estimation of the parameters of the model. This is usually done with multiple regression analysis.

The third stage in econometric research involves the evaluation of the estimated model on the bases of the/a priory economic criteria, statistical and econometric criteria and the forecasting ability of the model.

The priory economic criteria refer to the sign and the size of the parameters of the model postulated by economic theory. If the estimated coefficients do not conform to those postulated, the model must be revised or rejected.

The economic criteria referred to tests that the assumptions of the basic regression model and particularly those about the disturbance or error term, are satisfied.

The forecasting ability of the model refers to the ability of the model to accurately predict future values of the dependent variable based on known or expected or future value(s) of the independent or explanatory variable(s).  

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Evgenia Vogiatzi                                                                    <<Previous  Next>>