On the effectiveness of the weighted least squares technique for urban scaling: Empirical evidence on the relationship between labor productivity and city size in the u.s., europe, and latin america

The cities are the places where scale economies are created. Therefore economics of agglomeration is important to understand different aspects of urbanization. The principles of agglomeration economies can be quantified by scaling analysis. The standard statistical method for scaling analysis is simple linear regression (ordinary least squares). However, the special characteristics of city data such as non-normal ity and non-constant variance (heteroskedasticity) complicate the statistical estima tion and make it necessary to use special estimation techniques. In this paper, to overcome these problems, the standard approach of utilizing the classical weighted least square technique is suggested. The novelty of the paper is the derivation of a specific weighting rule starting from a lognormal model of the individual-level metric. We applied the ordinary least squares (OLS) and the weighted least squares (WLS) technique for the investigation and comparison of the scaling behaviors of labor productivities in the cities of three different regions (Latin America, Europe, and the USA). It is revealed that while in the US and Europe OLS and WLS yield similar results, the OLS is incapable of detecting the scaling behavior in Latin America. The WLS is capable of identifying the “increasing return to scale” rela tionship between city size and labor productivity.