Growth and Technological Leadership in US Industries: A Spatial Econometric Analysis at the State Level, 1963-1997

or Maximum Likelihood (ML) depending on the appropriate spatial process indicated by the
LM tests of the OLS version of the model (Anselin and Rey 1991, Anselin and Florax 1995).
Coefficients and variances are allowed to vary across groups and the Chow-Wald test is used
to test the stability of coefficients across groups. The GM-HET is used to estimate the
spatial error model while the ML-HET is used to estimate the spatial lag model.⁴ Following
Anselin and Rey (1991) we decided on the appropriate spatial process based on the LM test
with the highest value.

Results presented in Table 5 indicate that the coefficient of initial GDP per worker is
negative for both high and low GDP clubs in all sectors. The rate of convergence is typically
higher for the low as compared to the high GDP club. This is consistent with the prediction
from the neoclassical theory which stipulates that poor economies grow faster than richer
ones. The Chow-Wald test of equality of coefficients across regimes is only significant for

⁴ With two regimes, the spatial error model reads as:

where ε ~(0,(I - λW)^-1 Ω(I - λW)). X₁ and X ₂ are matrices of observations on the explanatory
variables for each spatial regime, and Ω is the variance covariance matrix given by:

^{σ 1}1   ⁰

_0          σ 2212 J^,

where σ₁² and σ₂² are the variances corresponding to each regime.

The spatial lag model with regimes is given as follows:

Where ρ is a coefficient indicating the spatial correlation between the productivity level of a given state and
its neighbors.

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