Question

State the general relationship between consumption Y and disposable income X in ( a ) exact linear form and ( b ) stochastic form. ( c ) Why would you expect most observed values of Y not to fall exactly on a straight line?

Answer 1

1. The purely mathematical model for consumption is of limited interest to the econometrician, for it assumes that there is an exact relationship between consumption and income. But relationship between economic variables is generally inexact. Thus if we were to obtain data on consumption expenditure and disposable income and graph these data on graph paper with consumption expenditure on the vertical axis and disposable income on the horizontal axis, we would not expect all 500 observations to lie exactly on straight line because in addition to income, other variables affect consumption expenditure. For example, size of family, age of members in the family, family religion etc are likely to exert some influence on consumption.

The Econometric Model can be expressed as;

Y = β₁ + β₂ X + μ

Where Y = Consumption expenditure, X = Income, where β₁ and β₂ known as parameters of the Model, are respectively the intercept and slope coefficients. The variable appearing on the left side of equality sign is called the independent variable and the variable(s) on the right side are called independent or explanatory variables(s).

Where μ known as disturbance, or error term is a random variable that has well defined probabilistic properties. The disturbance μ may well represent all those factors that affect consumption but are not taken into account explicitly.

Equation is an example of an econometric model. More technically it is an example of a linear regression model. The Econometric consumption Function hypotheses that the dependent variable Y (consumption) is linearly related to the explanatory variable X (income) but the relationship between the two is not exact; it is subject to individual variation. The Econometric model of the consumption function can be depicted as shown in Figure

C. Because Regression line y = a +bx is generated using "Least Square Method" in which Sum of square of error of all datapoints is minimized

from data there can be lot of line which gives approximate linear relationship of income and consumption but only the line which gives Least square error , that is selected