Binary response model with latent variable

In statistics, the binary response model with latent variable is constructed as:

$y=1[y^{*}>0]$

where $y^{*}=x\beta +\varepsilon$ and $\varepsilon \mid x\sim G$ This model can be applied in many economic contexts. For instance, $y$ is the decision of a manager whether invest to a program, $y^{*}$ is the expected net discounted cash flow and $x$ is a vector of variables which can affect the cash flow of this program. Then the manager will invest only when she expects the net discounted cash flow is positive.

Usually, the error term $\varepsilon$ is assumed to have a homogeneous normal distribution conditional on the exogenous explanatory variables $x$ and namely $G$ is the standard normal distribution. It is called the standard probit model under this assumption.

See also

• Binary regression
• Latent variable model
• Discrete choice#Binary choice

Bibliography

• Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass, pp 479.