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This paper models how to use widely available data on wages and housing costs to infer land rents, local productivity, and the total value of local amenities in the presence of federal taxes and locally produced nontraded goods. I apply the model to U.S. metropolitan areas with the aid of visually intuitive graphs. The results improve measures of productivity and feature large differences in land rents. Wage and housing cost differences across metropolitan areas are accounted for more by productivity than quality-of-life differences. Regressions using individual amenities reveal that the most productive and valuable cities are typically coastal, sunny, mild, educated, and large.
David Albouy (2016) studied this question.