Keynes hypothesized that the consumption function of income is C_t = beta_0 + be

Question

Keynes hypothesized that the consumption function of income is C_t = beta_0 + beta_1 Y_t + u_t..... (1) Where C_t is consumption, Y_t is income and u_t is the error term But suppose the true model is C_t = beta_0 + beta_1 Y_t + beta_2 R_t + mu_t, ..... (2) and R_t is interest rates. a. Show how we can use the Ramsey Reset test to investigate whether there is misspecification b. What would it mean for any of the equations if the error term is omitted? c. Describe and apply the F-test to equation (2) above.

Explanation / Answer

a.

Endogenous variable: If x variable is correlated with the error term it is called endogenous variable.

When a relevant variable is omitted from the model, the OLS estimators are biased and inconsistent. In the special case that the omitted variable is a function of an explanatory variable in the model, the model suffers from functional form misspecification. Or in other words, functional form misspecification means multiple regression models do not properly account for the relationship between dependent and observed explanatory variables.

Ramsay's RESET test is designed to detect if there are any neglected nonlinearities in the model.

Detection of misspecification using Ramsey RESET test:

Given regression model (consumption function of income) is,

Ct=0+1Yt+ut

If the assumption of exogenous x (that is x is not endogenous variable ) is satisfied then this implies that no nonlinear function of an independent variable (such as squares and cubes of x' s should be significant when added in the model.)

RESET Test:

The auxiliary regression model for RESET test can b written as follows:

Ct=0+1Yt+1Y2+ 2Y3+ut

The null hypothesis of RESET test says that the model is correctly specified.

H0 : 1 = 0, 2= 0

In large sample and under Gauss Markov assumptions the usual F restrictions test follows the F(2, n k 3) distribution. If the F statistic is greater than the critical value at a given significance level then we reject the null hypothesis of correct specification. This indicates that there is a functional form misspecification.

b.Error term in regression equation represents the effect of the variables that were omitted from the equation.In other words, error term represents the effect on Yi of omitted variables.

In the case for any of the regression equation if the error term is omitted, then that effect of explanatory variables which are omitted from a model is not considered. And OLS estimators obtained from that regression equation are not correct (that is they are biased and inconsistent.)

c.

Follow the procedure described in (a).

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