DISTURBANCE TERM
As noted in Section 2.4, the disturbance term ui is a surrogate for all those variable that are omitted from the model but that collectively affect Y. The obvious question is: Why not introduce these variables into the model explicitly? Stated otherwise, why not develop a multiple regression model whit as many variables as possible? The reason are many.
1. Vagueness of theory : The theory, if any, determining the behavior of Y may be, and often is, incomplete. We might know for certain that weekly income X influence weekly consumption expenditure Y, but we might be ignorant or unsure about the other variables affecting Y. Therefore, ui may be used as asubstitute for all the excluded or omitted variables from the model.
2. Unavailability of data: Even if we know what some of the excluded variables are and therefore consider a multiple regression rather than a simple regression, we may not have quantitative information about these variables. It is a common experiences in empirical analysis that the data we would ideally like to have often are not available. For Example, in principle we could introduce family wealth as an explanatory variable in addition to the income variable to explain family consumption expenditure. But unfortunately, information on family wealth generally is not available. therefore, we may be forced to omit the wealth variable from our model despite its great theoretical relevance in explaining consumption expenditure.
3. Core variables versus peripheral variables: Assume in our consumption income example that besides income X1, the number of children per family X2, sex X3, religion X4, education X5, and geographical region X6, also affect consumption expenditure. But it is quite possible that the joint influence of all or some of these variables may be so small and best non systematic or random that as a practical matter and for cost considerations it does not pay to introduce them into the model explicitly. One hopes that their combined effect can be treated as a random variable ui .10
4. Intrinsic randomness in human behavior: Even if we succeed in introducing all the relevant variables in to the model, there is bound to be some "intrinsic" randomness in individual Y's that cannot be explained no matter how hard we try. The disturbances, the u's may very well reflect this intrinsic randomness.
5. Poor proxy variables: Although the classical regression model ( to be developed in Chapter.3 ) assumes that the variables Y and X are measured accurately, in practice the data may be plagued by errors of measurement. Consider, for example Milton Friedman's well-known theory of the consumption function.11
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10.A further difficulty is that variables such as sex, education , and religion are difficult to quantify.
11Milton Friedman, A Theory of the Consumption Function, Princeton University Press, Princeton, N.J., 1957
12"That descriptions be kept as simple as possible until proved inadequate"The World of mathematics, vol.2,J.R. Newman ( ed.), Simon & Schuster, New York, 1956,p.1247,or"Entities should no be multiplied beyond necessity,"Donald F. Morrison, Applied linear Statistical Method, Prentice Hall, Englewood Cliffs,N.J.,1983, p.58.
2. Unavailability of data: Even if we know what some of the excluded variables are and therefore consider a multiple regression rather than a simple regression, we may not have quantitative information about these variables. It is a common experiences in empirical analysis that the data we would ideally like to have often are not available. For Example, in principle we could introduce family wealth as an explanatory variable in addition to the income variable to explain family consumption expenditure. But unfortunately, information on family wealth generally is not available. therefore, we may be forced to omit the wealth variable from our model despite its great theoretical relevance in explaining consumption expenditure.
3. Core variables versus peripheral variables: Assume in our consumption income example that besides income X1, the number of children per family X2, sex X3, religion X4, education X5, and geographical region X6, also affect consumption expenditure. But it is quite possible that the joint influence of all or some of these variables may be so small and best non systematic or random that as a practical matter and for cost considerations it does not pay to introduce them into the model explicitly. One hopes that their combined effect can be treated as a random variable ui .10
4. Intrinsic randomness in human behavior: Even if we succeed in introducing all the relevant variables in to the model, there is bound to be some "intrinsic" randomness in individual Y's that cannot be explained no matter how hard we try. The disturbances, the u's may very well reflect this intrinsic randomness.
5. Poor proxy variables: Although the classical regression model ( to be developed in Chapter.3 ) assumes that the variables Y and X are measured accurately, in practice the data may be plagued by errors of measurement. Consider, for example Milton Friedman's well-known theory of the consumption function.11
10.A further difficulty is that variables such as sex, education , and religion are difficult to quantify.
11Milton Friedman, A Theory of the Consumption Function, Princeton University Press, Princeton, N.J., 1957
12"That descriptions be kept as simple as possible until proved inadequate"The World of mathematics, vol.2,J.R. Newman ( ed.), Simon & Schuster, New York, 1956,p.1247,or"Entities should no be multiplied beyond necessity,"Donald F. Morrison, Applied linear Statistical Method, Prentice Hall, Englewood Cliffs,N.J.,1983, p.58.
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