On the heels of a recent post (here) describing a Stata regression command tailored to the unique needs of a dependent variable that takes the form of a ratio/percentage/fraction, comes a recent paper that explores potential problems with finance papers that model ratios. Potentially compounding the problem is that ratios as dependents variables are certainly not uncommon in the finance literature (see, e.g., papers featuring Tobin's Q). In The Ratio Problem, Robert Bartlett (Berkeley) and Frank Partnoy (Berkeley) frame the ratio "problem" in terms of two challenges–omitted variable and measurement error bias–"that arise anytime a researcher uses linear regression to estimate a production function that has a ratio as an output." As the paper notes, "In theory, the [ratio] denominator is not necessarily problematic; in practice, however, there are statistical concerns whenever the output of a production function is a ratio." The paper's abstract follows.
“We use the term ‘ratio problem’ to describe the omitted variable and measurement error bias that can arise when a ratio is the dependent variable in an economic model. First, we show how bias can arise from the omission of two classes of variables based on a ratio’s denominator. As an example, we demonstrate that the widely-cited ‘inverse U’ relationship between managerial ownership and Tobin’s Q is reversed when these variables are included. Second, we show how measurement error in the ratio’s denominator can produce bias. We provide empirical tests and solutions, and urge caution about ratios as dependent variables.”
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