Correlation and Simple Linear Regression

Assignment Task

A model of the logarithms of income (y), consumption (c), and savings (s) is estimated with OLS as Yt

Yt = 0.3+0.65ct +0.4st +ût (0.1) (0.15) (0.2)

Aut = −0.85ût-1 +0.45 ût-1 – 0.25 ût-2 (0.22) (0.25)

Using 100 observations. We know that all variables are I(1). The residuals of the above regression are saved and used in the following regression:

Where standard errors of the estimated coefficients are reported in (·).

(a) Is there any evidence of cointegration between consumption, income, and savings at the 5% significance level?

Using 205 observations we estimate (using OLS) the VAR(2) system

Yt = B10 B11Yt-1 +ẞ12t-1 + a11yt-2 +α12t-2 +U1t

xt = B20+ B21Yt-1 + ẞ22xt-1 + A21Yt-2+ a22xt-2 + Ult

and we get the residual sum of squares (RSS) for equation (1) to be RSS1= 550 and for equation (2) to be RSS2 = 600: Using information from the following estimated equations

(a) Test at the 5% level the null hypothesis that x is Granger Causing yt.

(b) Test at the 5% level the null hypothesis that yt is Granger Causing xt.

(c) Test at the 5% level the null hypothesis that the 2nd lags of the variables in the system are insignificant for the determination of yt.

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