What is inverse mills ratio?

The inverse Mills ratio (IMR) is a statistical concept that measures the degree of non-random sample selection bias in probit regression models. It is the ratio of the density function of the standard normal distribution to the cumulative normal distribution. The IMR is used to correct for sample selection bias that occurs when a subset of data is used in a regression analysis.

In probit regression models, the dependent variable is binary (e.g., 0 or 1), and the independent variables are continuous. However, the sample may be selected non-randomly, which can lead to selection bias. The IMR is used to correct for the bias by taking into account the relationship between the dependent and independent variables and the selection mechanism.

The IMR is often used in econometrics and other social sciences to estimate the impact of policy changes. For example, a researcher might use the IMR to estimate the effect of a job training program on employment outcomes. The IMR can be used to adjust the estimates of the treatment effects for the selection bias in the sample.

The IMR is also used in other statistical techniques such as Heckman selection model and Tobit model. These models are used to correct for sample selection bias in regression analysis.