The common trends representation

Measuring common driving trends

From Chapter 2:

With long-run price homogeneity:

Illustrations

Just-identification of alpha orthogonal

The transformation matrix:

1980 1990 2000

-0.1

0.0

0.1Cumulated residuals from money equation

1980 1990 2000

-0.05

0.00

0.05

0.10Cumulated residuals from income equation

1980 1990 2000

0.00

0.05Cumulated residuals from inflation rate equation

1980 1990 2000

0.000

0.005

Cumulated residuals from the short rate equation

1980 1990 2000

0.000

0.005

0.010 Cumulated residuals from the bond rate equation

1975 1980 1985 1990 1995 2000

-0.01

0.00

0.01

0.02

Common trend 1

1975 1980 1985 1990 1995 2000

-0.01

0.00

0.01

Common trend 2

Is a weakly exogenous variable a common stochastic trend?

The MA representation under the weak exogeneity restriction

Assessing the economic scenario

Where does the nonstationarity of the hypothetical relations come from?

The income – inflation relationship:

The nonstationarity of real interest rates:

Imposing exclusion restrictions on commontrends

If nominal money stock and price levels contain just one I(2) trend, thenInflation should only be affected by one stochastic trend. This can be achieved by a linear transformation.

Example 1:

Example 2:

Example 3: