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

(logYt^s-logY0^s)=(logAt^s-logA0^s)+α(logKt^s-logK0^s)+β(logL^st-logL^s0)
+ (logε_t^s - logε₀^s),

where Y_t^s is GDP per worker, K _t^s physical capital, L_t^s labor, A_t^s the level of technology, ε_t^s
an error term, and s represents the sectors.

Concisely, the Benhabib and Spiegel (1994) version of the model assumes that the
level of technology can be explained by the level of human capital “domestically” and a
catch-up term that depends on the distance to the technology leader in terms of GDP per
capita, and the level of human capital that is available to adopt the ideas and technologies
originating from the technology leader. In formal terms the level of technology is expressed
as:

where i (= 1, 2, ..., n) indexes states, H refers to human capital available in the state, and
Y_max refers to the state GDP per worker for the technology leader (i.e., the state with the
highest productivity).⁷ In a sense, Equation (3) can be seen as an a-spatial endogenous
growth model which, after rearranging, reads as:

⁷ For each sector, the state with the highest productivity level in the year 1997 is considered as technology
leader. The top five most productive states in 1997 are presented in Table 4.

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