17
"That interest in such models had to be restimulated at all may seem surprising", in the
opinion of Aigner et al., "since there can be no doubt that economic quantities frequently
are measured with error and, moreover, that many applications depend on the use of
observable proxies for otherwise unobservable conceptual variables" (p. 1323).
Estimation of a simultaneous equations model with latent variables can be done by means
of a computer program for the analysis of covariance structures, such a LISREL (Linear
Structural Relations). The idea behind LISREL is to compare a sample covariance matrix
with the parametric structure imposed on it by the hypothesized model. Under normality,
LISREL delivers Full Information Maximum Likelihood (FIML) estimates of the model
parameters. Because of its general availability, LISREL is the most important tool for
handling latent variables.
The specification of the latent variables model to be analyzed by LISREL is as fol-
lows.13) Let η be the latent dependent variable, i.e. the latent optimal degree of central
bank independence, and ξ be the latent explanatory variables, in our case the four ultimate
determinants of central bank independence, satisfying a system of linear structural
relations
η =B ∙ ξ + ζ, (4.2)
with B being the coefficient matrix and ζ the disturbances. It is assumed that η, ξ and ζ
have zero expectations, and that ξ and ζ are uncorrelated. Instead of the latent vectors η
and ξ, the vectors y and x are observed, such that
y = Λy ∙ η + γ (4.3)
and
x = Λχ ∙ ξ + δ, (4.4)
with Λy and Λx the coefficient matrices, and γ and δ the vectors of measurement errors,
uncorrelated with η, ξ, ζ and each other, but possibly correlated among themselves. The
observed vectors y and x are measured as deviations form their means, thus, having zero
expectations and a covariance equal to E[x y]. This implies, of course, that γ and δ have
13) In order to avoid overlapping symbols between sections II and III (theoretical model) and section IV
(latent variables model), our notation differs from that of the LISREL manual. Having one latent
dependent variable, we use B and γ, respectively, instead of the symbols Γ and ɛ for the LISREL
manual. Compare also Aigner et al. (1984, pp. 1370-1371) in this respect.