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The Urban Wage Premium: Sorting, agglomeration economies or statistical artifact? The problem of sampling from lognormals

Andres Gomez-Lievano, Vladislav Vysotsky and Jose Lobo

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Abstract: Economic explanations for the urban wage premium (UWP) fall in two categories: sorting of more productive individuals into larger cities, or agglomeration externalities. We present a third hitherto neglected mechanism: a statistical artifact arising from sampling lognormally distributed wages. We show how this artificial UWP emerges, systematically and predictably, when the variance of log-wages is larger than twice the log-size of workers sampled in the smallest city. We present an analytic derivation of this connection between lognormals and increasing returns to scale using extreme value theory. We validate our results analyzing simulated data and real data on more than six million real Colombian wages across more than five hundred municipalities. We find that when taking random samples of $1\%$, or less, of all Colombian workers the estimated real and artificial UWP are both $7\%$, and become statistically indistinguishable, yet both significantly larger than zero. This highlights the importance of working with large samples of workers. We propose a method to tell whether an estimate of UWP is real or an artifact.

New Economics Papers: this item is included in nep-eff, nep-geo and nep-ure
Date: 2018-07, Revised 2018-10
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