Scale effects found!

Abstract

A key feature of early endogenous growth models is their prediction of scale effects – the larger the economy, as measured by population, the number of firms or employment, the faster the economy should grow. However, empirical work has failed to support the existence of scale effects. As a result, much human capital has been expended in order to ‘fix’ this problem by eliminating scale effects in endogenous growth models. We contend that econometric techniques used in the empirical search for scale effects are inconsistent with growth theory. Using data from US states and an econometric technique that better matches growth theory by allowing each economy to have its own steady state, we provide empirical support for the existence of scale effects. Results call into question the need to reformulate the first models of endogenous growth.

Notes

¹ Similar models are developed in Kortum (1997) and Segerstrom (1998).

² Jones (1995) eliminates the scale effect in terms of population levels by assuming diminishing returns in knowledge creation such that Equation 2 is written as where . In the steady state, this allows Equation 3 to be rewritten in terms of the growth rate of population (n) as . Thus, the scale metric of the economy is transformed from population level to the growth rate of population.

³ Intuitively, adding variables to the right-hand side of Equation 6 ‘pulls out’ the heterogeneity in the intercept term. If all the heterogeneity is accounted for, each economy, in essence, will have the same steady state and thus B should be negative and significant.

⁴ See Barro and Sala-i-Martin (1999, pp. 41–6) for a formal theoretical model which is consistent with this view.

⁵ Though it is commonly assumed that the US states are homogeneous in terms of the other variables that determine the steady-state (the savings rate (s), rate of depreciation (δ) and population growth rate (n)), Sedgley and Elmslie (2000) argue that this method of controlling for differing steady-state values, as opposed to the proxy method mentioned earlier, is more accurate because current proxy variables may or may not have any relation to their long-run counterparts. In support, the authors cite the work of Ramsey (1928) in which the Solow model is extended to include consumer optimization. It can be shown that, depending upon the parameters of the model, the savings rate can either rise, fall or remain constant as the economy approaches the steady-state.

⁶ Data for total employment and GSP comes from the Bureau of Economic Analysis. GSP is in chained 1996 dollars (1996 = 100).

⁷ GSP assigns product to the state in which it is produced, whereas personal income is attributed to the state in which the owner of the input resides. Barro and Sala-i-Martin (1999) show that, empirically, results are similar.

⁸ Islam (1995) uses an IV estimator based on Chamberlain (1982). Minimum distance estimation, as it is called, does not address the potential for small-sample-bias.

⁹ Where N = 48 states and T = 5 time periods.

¹⁰ After rejecting the null of no autocorrelation using the Wooldridge (2002) panel data test, Newey–West SEs, which correct for autocorrelation and heteroscedasticity, are reported for regressions (1) and (4). We failed to reject the null using the same test for the shorter time period. As a result, only robust SEs are reported for regressions (2) and (3).

¹¹ Tests for intercept equality were rejected for all specifications.