RATIO Instruction

RATIO( options ) start end

#< supp. card > list of first set of series

#< supp. card > list of second set of series

RATIO computes a likelihood ratio statistic based upon the log determinants of two sets of series of residuals. Although you can use it in other situations, the primary purpose of RATIO is testing hypotheses in vector autoregressions: either block exogeneity restrictions or lag length restrictions.

Parameters

start, end

Range over which the covariance matrices are computed. If you have not set a SMPL, this defaults to the maximum common range of all the series in the two sets.

Supplementary Cards

On the two supplementary cards, list the two sets of series to use in the test. RATIO will compare the covariance matrices of these two sets of series. Both sets should have the same number of series. You don’t need to worry about which of the two is from restricted estimates and which is from the unrestricted as RATIO takes the absolute value of the computed statistic.

Options

DEGREES=degrees of freedom for test [no default] (required)

This is the degrees of freedom for the chi-squared statistic, that is, the number of restrictions. You must use this option.

MCORR=correction for multiplier [0]

The multiplier correction is the c in the formula below. Sims (1980, p.17) suggests a correction equal to the number of variables in each unrestricted equation in a vector autoregression. The use of the proper correction improves the small sample properties of the test.

SMPL=Standard SMPL option [unused]

SPREAD=residual variances series [unused]

WEIGHT=series of weights for the data points[unused]

The residuals which are generated by the regression commands are “unweighted.” So, if you used a SPREAD or WEIGHT option to compute residuals, you should use the same option on RATIO.

[PRINT]/NOPRINT

TITLE="title for output" [none]

Use NOPRINT to suppress the printing of the test results. If you are showing the output, you can use the TITLE option to provide your own title for the output.

Description

RATIO takes two lists of residual series, computes the two covariance matrices (\({\Sigma _1}\) and \({\Sigma _2}\)) and generates the chi-squared statisic:

\(\left( {T - c} \right){\kern 1pt} {\kern 1pt} {\kern 1pt} \left| {{\kern 1pt} \log \left| {{\Sigma _1}} \right| - \log \left| {{\Sigma _2}} \right|{\kern 1pt} {\kern 1pt} } \right|\)

where T is the number of observations and c is given by the MCORR option. Note that RATIO does not compute centered covariance matrices, that is, it does not subtract means from the input series.

The null hypothesis is that the two log determinants are equal. Small test statistics and significance levels close to 1.0 suggest the hypothesis can be accepted. Larger statistics and significance levels close to 0.0 suggest the hypothesis is rejected.

Variables Defined

%CDSTAT	the computed test statistic (REAL)
%SIGNIF	the marginal significance level (REAL).
%NOBS	the number of observations(INTEGER)
%NVAR	the number of variables (INTEGER)

Example

ratio(degrees=27,mcorr=10)

# ures1 ures2 ures3

# rres1 rres2 rres3

tests the difference between the covariance matrix of series ures1, ures2 and ures3 and that of series rres1, rres2 and rres3. The test statistic is compared with a \({\chi ^2}\) distribution with 27 degrees of freedom. Output such as:

Log Determinants are -46.441108 -44.054300

Chi-Squared(100)= 90.698721 with Significance Level 0.73622035

would suggest that the null hypothesis can be accepted.