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Stata Technical Bulletin

zero if the parameters are stable, in which case the test statistics will be small. If the parameters are not stable, the cumulative
first-order conditions for the subsamples will wander away from zero, in which case the statistics will be large. Note that the
Hansen statistics are based on full-sample estimates only, in contrast to the CUSUM and CUSUM of squares tests which require
calculation of the recursive (rolling, one-step-ahead) residuals.

The Hansen statistics follow a nonstandard distribution. However this distribution depends only on the number of parameters
being tested. Hansen’s Table 1 (1992) presents asymptotic critical values for the test statistics. The 5 and 10 percent critical
values for tests of individual parameters (tests with one degree of freedom) are 0.470 and 0.353, respectively.

Example

We use hansen to test the stability of the parameters in an error correction model for bank loans. The data and the example
are taken from Becketti and Morris (1993).

An important question in monetary economics is whether nonbank sources of short-term business finance have become
better substitutes for bank commercial and industrial (C&I) loans. In the traditional view, demand for C&I loans is relatively
inelastic. As a consequence, the central bank can exert a powerful influence over economic activity by adjusting the quantity of
bank reserves and thereby adjusting the supply of C&I loans. The increasing globalization of financial markets in recent years
along with the growth both of finance company business lending and of the commercial paper market have raised questions
about the continued relevance of the traditional view. If businesses have come to regard nonbank sources of short-term finance
as good substitutes for C&I loans, the central bank’s ability to influence economic activity through the quantity of bank reserves
may be diminished.

An increase in the substitutability between bank and nonbank loans would be observed as an increase in the own-price-
elasticity of demand for C&I loans. It is difficult to estimate this elasticity directly because it is difficult to estimate the structural
equation for bank loan demand. However, a change in any of the structural parameters of a model will, in general, change all
of the parameters of the reduced form model (the transformation of the structural form that eliminates endogenous variables as
regressors). In other words, the reduced form equation for C&I loans should exhibit parameter instability if bank and nonbank
loans have become better substitutes over time.

Becketti and Morris derive the direction in which some of the reduced form parameters should move if the own-price-
elasticity demand of bank loans has increased. They apply a variety of tests for parameter instability to this reduced form
equation—including the Chow, Quandt, CUSUM, and CUSUM of squares tests—and find little evidence that bank and nonbank
loans have become better substitutes.

The following are the data used by Becketti and Morris:

. use bankloan, clear

(1955:Q2-1992:Q3)

. describe

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