SMODIFY Instruction

SMODIFY( options ) equations VCVmatrix

# oldequation newequation column(one for each equation)

SMODIFY is rarely used, and thus is no longer documented in the Reference Manual. It reparameterizes a system of equations so that covariance matrix has either a diagonal or block diagonal form.

Parameters

equations	number of equations
VCVmatrix	SYMMETRIC covariance matrix of residuals

Supplementary Cards

Supply one supplementary card for each equation in the system.

oldequation	The original equation.
newequation	The equation to take its place. newequation must be different from oldequation.
column	The column (row) of VCVmatrix that corresponds to this equation. By default, column is the supplementary card position.

Options

BLOCK=size of first block, 0=diagonal matrix [0]

The size of the unmodified first block. The default of 0 requests a diagonal covariance structure for the residuals.

CVOUT=SYMMETRIC matrix for new covariance matrix [unused]

This saves the covariance matrix of the residuals in the modified system. Its columns correspond to the new equations in the supplementary card order.

PRINT/[NOPRINT]

Use PRINT if you want RATS to print the modified equations.

Description

SMODIFY takes the standard vector autoregression and changes the normalization so the \(\Sigma\) matrix has a particular structure. The two structures allowed are:

1.Block diagonal, with the BLOCK option. The system is multiplied by a block lower triangular matrix. The first block of equations do not change; the second block changes to include the current y’s from the first block.

2.Diagonal, with the default BLOCK value of 0. The system is multiplied by a lower triangular matrix. The first equation does not change; all subsequent equations will include current y’s from all the earlier equations.

If the system is an OLS vector autoregression (no prior), SMODIFY produces equations identical to the ones that would result from a direct estimation of the equations with the new form.

Example

system 1 2 3 4

variables cpr m1 ppi ip

specify .5

lags 1 2 3 4 6 9 12

det constant

end(system)

estimate

smodify(block=2,cvout=vblock) 4 %sigma

# 1 5

# 2 6

# 3 7

# 4 8

Equations 5 through 8 are now an equivalent system, but equations 7 and 8 include current CPR and M1 and the residuals in those equations are uncorrelated with the residuals from 5 and 6 (which will be the same as 1 and 2).