The ultimate determinants of central bank independence

[y’, x’]’ is

Assuming that the latent explanatory variables (ξ) equal the observed (x), thus ξ = x, then
Θ_δ = 0 and Λ_x = I, and equation (4.7) simplifies to¹⁴⁾

The parameters occuring in Σ (Λ_y, B, Φ, Ψ, Θ_γ) are estimated on the basis of the matrix S
of second sample moments of x and y. In order to identify all parameters, additional
restrictions on the parameters have to be imposed. Given these restrictions and the
structure that equation (4.8) imposes on the data, LISREL computes FIML estimates of the
parameters when [y’, x’] is normally distributed, i.e. when the following criterion is
minimized

ln I ∑ + tr [SΣ^-1]                                                                              (4.9)

To be able to identify all parameters of the model, we have made the following two
additional restrictions:

(i)  λ_y3 = 1, which implies that the latent optimal degree of central bank independence

(η) has the same unit of measurement as the observed legal index of Eijffinger
and Schaling (ES_M);¹⁵⁾ and

¹⁴⁾ So, we make only a distinction between the latent optimal degree of central bank independence (η) and
the observed actual degree (y) measured by the legal indices of central bank independence. Thus, the
optimal degree of central bank independence is derived from the covariances of the four legal indices.

¹⁵⁾ It is, however, also possible to choose as the unit of measurement for the latent optimal degree one of the
other observed legal indices (λ_y1 =1,λ_y2 =1orλ_y4 = 1). In principal, this choice will not make a
difference regarding the identification of the parameters.

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