*! version 1.0.0 21may2026
help mixi12_trans (Stata)

Title

mixi12_trans -- Kongsted (2005) / Kurita (2011) I(2)-to-I(1)
transformation LR test

Syntax

mixi12_trans , g(matname) [level(#)]

Description

After mixi12_johansen has produced an I(2) decomposition
(, _, _), this command tests the null
sp(tau) = sp(G), where tau = (, _). If the null is
not rejected, the linear combinations represented by the columns of G
constitute a valid transformation that reduces the I(2) data to I(1).

The test statistic is asymptotically chi-squared (Johansen 2006). Typical
choices for G:

- Money multiplier on (m2, mb, p, rd): G = (1, -1, 0, 0)'.

- Long-run price homogeneity on (m, p, y, R): G = (1, -1, 0, 0)'.

- Nominal-to-real on (m, p, y): G = (1, -1, 0)'.

Stored results

Scalars

r(LR) LR statistic

r(df) degrees of freedom

r(p) chi-squared p-value

r(verdict) reject / do not reject sentence

Examples

1. Test the money multiplier on (m2, mb, p, rd)

mixi12_johansen m2 mb p rd, lags(3) rank(1) s1(1)

matrix G = (1 \ -1 \ 0 \ 0)

mixi12_trans, g(G)

Author

Dr Merwan Roudane,
merwanroudane920@gmail.com.

Package

Master: mixi12.
Companions: mixi12_unit, mixi12_haldrup,
mixi12_johansen, mixi12_sw, mixi12_sim,
mixi12_graph, mixi12_cv.