Then the income will be regressed on non- consumption expenditure as shown below: In the Indirect Least Squares method, the consumption expenditure will be regressed on non-consumption expenditure as shown below: Thus in two stage least squares method the assumption of zero co-variance between X e and U will to some extent be satisfied to reduce an upward bias in MPC.Įstimation of an MPC by Indirect Least Squares Method: The co-variance between X e and U will be close to zero. The trend values of X will be estimated with the help of the values of b 0 and b 1 estimated by OLS method.Īt the second stage, the trend values of income will be considered as the independent variable to regress Y 1 on X e as follows: In order to reduce the bias in mpc, both two-stage least squares method and indirect least squares method would be used in the empirical studies.Įstimation of an MPC by Two-Stage Least Squares Method:Īt the first stage the income will be regressed on non- consumption expenditure as shown below: Therefore, the numerical value of mpc will be biased. Thus, there will be two- way causation between X and Y 1. Thus, the covariance between X and error term will not be zero, i.e., X is dependent variable on random variable i.e., consumption expenditure depends on income and income depends on consumption expenditure. In the above equation if Y 1 = b 0 + b 1X + U is substituted, then we get the following: The probable value of the elasticity of aggregate consumption expenditure with respect to disposable income can be inferred on the basis of the sign of the intercept of the simple linear consumption function. The proportionate change in consumption expenditure will be equal to the proportionate change in disposable income and The growth rate in consumption expenditure will be equal to the growth rate in disposable income. If it is unity, then an MPC will be equal to APC The proportion of consumption expenditure in disposable income will be constant with an increase in disposable income. The proportionate change in consumption expenditure will be lower than the proportionate change in disposable income and The growth rate in consumption expenditure will be lower than the growth rate in disposable income. If it is less than unity, then MPC will be lower than APC The proportion of consumption expenditure in disposable income declines with an increase in disposable income. If the numerical value of elasticity of consumption expenditure with respect to disposable income is more than unity, then MPC will be higher than APC The proportion of consumption expenditure in disposable income increases with an increase in disposable income The proportionate change in consumption expenditure will be higher than the proportionate change in disposable income and The growth rate in consumption expenditure will be higher than the growth rate in disposable income. In the empirical studies the value of elasticity would be evaluated at the mean value of Y 1 and X. An increase in X inflates the value of elasticity of consumption expenditure with respect to disposable income and a decline in X deflates the value of elasticity of consumption expenditure with respect to disposable income, all else equal. The value of elasticity of consumption expenditure, if estimated at different values of Y 1 and X, varies from point to point change in X and Y 1. X/Y 1 = b 1 X / Y 1 which can be b 1* X i/Y 1 i or b 1 * mean value of X/mean value of Y 1 or b 1 * ∑ X/∑Y 1. In the linear regression model, the numerical value of the elasticity will be estimated as follows: dY 1/dX. The responsiveness of consumption expenditure to the changes in disposable income (elasticity of y 1 with respect to X or ratio of marginal propensity to consume to Average propensity to consume ) will be estimated as follows: The derivative of Y 1 with respect to X, dY 1/dX, b 1, is an mpc whose value will be less than unity as the increase in the consumption expenditure will be smaller than the increase in disposable income leaving some margin for savings. If such relationship exists then the consumption expenditure will always be influenced by the disposable income, all else equal, evincing the fact that disposable income will be exogenous. The numerical values of b 0 and b 1 in the equation will be estimated by OLS method under the main assumption that there is one-way causation between income and consumption expenditure, i.e., If Y depends on X or X influences Y, then X will be an exogenous variable. If the relationship between Consumption expenditure and disposable income is linear, then the specification will be as follows: