This paper looks at potential implications emerging from including shares as a control variable in fixed effect estimations. By shares I refer to the ratio of a sum of units over another, such as the share of immigrants in a city or school. As will be shown in this paper, a logarithmic transformation of shares has some methodological merits as compared to the use of shares defined as mere ratios. In certain empirical settings the use of the latter might result in coefficient estimates that, spuriously, are statistically significant more often than they should.
consistency Törnqvist index symmetry spurious significance