A COMPARATIVE STUDY OF ALTERNATIVE ECONOMETRIC PACKAGES: AN APPLICATION TO ITALIAN DEPOSIT INTEREST RATES

The fixed effect estimator assumes the same numerical value for all three packages. The numerical
differences present in the random effects estimation are due to the different criteria adopted for the variance
component estimation. Maddala and Mount (1973) offer a comprehensive survey on the estimation
methods for the variance component models.

Our analysis focuses on the one-way model in which there is no time-only component in the
disturbance term.

Given the following model y_it = a + Xt β + u_it     i = 1,..., N ; t = 1,..., T_i   where the

^,

disturbance term can be decomposed in the following way: u_t = μ_i + v_it and σ2 = σ^2 + σ_v², and
assuming that the idiosyncratic elements μ_i are random, the estimation of this model consists of the
application of the Ordinary Least Squares technique to the following transformed model:

y_it — θ_i ■ y_i = a ■ (1 — θ_i ) + (X _t — θ_i ■ X_i )■ β + u _it — θ_i ■ u_i

it it i i i ■               X i J      it it i i ■ / ~ it i i ■

where the bar over the variable represents its temporal average. Let us assume the following:

σ_v is the standard deviation of the fixed effects estimation (within the regression);

σ ₁ = 7σ_t²_ot — σ_v² and σtot is the variance of the pooled regression (OLS) achieved with

TSP, if this happens to be negative TSP resorts to the large sample formula given by
σ 1 = ( SSRols — SSRW_ithin) / NOBS where SSR stands for residuals sum of squares and

NOBS is the total number of observations;

σ₁² is the following standard deviation computed with LIMDEP:

b_ols is the pooled OLS coefficient vector;

Nfirm is the number of different groups;

kis the number of explanatory variables;

depending on certain numerical conditions b_ols can be replaced by b_between ;

σ₁ is the following standard deviation computed with STATA;

² / T ) where T is the harmonic mean of the set of T_i.
^,

It is clear that all the numerical differences produced by the random effect estimate are caused by the
difference of the small sample formula for the computation of the between-regression variance. The
parameter θ_i, which discriminates the behaviour of the three packages, is computed in the following ways:

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