Abstract
We address how independent variables of inherently different sizes across units, e.g., small vs. large industries, in panel regression is an advantage interpretively. Analyzing a Norwegian industry panel, we find that wage inequality is a function of industry size, particularly size increase, in an absolute number of firms. A possible reason is that specialized skilled employees negotiate higher wages when there are many legal entities. The findings can also imply that wage inequality is more sensitive to random change, particularly an increase, in large rather than small industries. We conclude that particularly large industries are positive carriers of wage inequality and discuss potential underlying causal mechanisms such as monopolistic competition.
Highlights
Let us assume that we do panel regressions where the independent variables are of inherently different sizes across units
Assuming that we in panel regression find that wage inequality is a function of industry size in an absolute number of firms, how can we interpret this result? The most intuitive and obvious interpretation, in our opinion, is that industry size affects wage inequality, but can we learn more from the data? Yes, we argue, and the reason, as we have asserted above, is that industries are of inherently different sizes across units
An industry of 10,000 firms at the outset that increases its size by one percent will impact the dependent variable roughly 100 times more in magnitude than a small industry of only 100 firms that increases its size by one percent. (As noted, empirically, we study industry size both in the number of employees and firms, but in the following illustration, we only refer to industry size in the number of firms.) According to our above argument, a marginal change in industry size from one year to another, by one percent, can partly be explained as a random process most marked for large industries in absolute terms
Summary
Let us assume that we do panel regressions where the independent variables are of inherently different sizes across units (for a general introduction to panel regression, see, e.g., Cameron and Trivedi 2010; Wooldridge 2010, 2019). (As noted, empirically, we study industry size both in the number of employees and firms, but in the following illustration, we only refer to industry size in the number of firms.) According to our above argument, a marginal change in industry size from one year to another, by one percent, can partly be explained as a random process most marked for large industries in absolute terms Due to this randomness, the larger the industry size is at the outset, the more impact it will have on the dependent variable. Returning to the illustration of two industries of 10,000 and 100 firms at the outset, assuming some distributed random variation in the size from one year to another, the large industry’s average impact on the dependent variable is roughly 100 times stronger than of the small industry. In the panel regression, we suggest the inclusion of both measures, (1) and (2), as independent variables
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