Limited Dependent Variable Models - Econometrics - Lecture Notes, Study notes of Econometrics and Mathematical Economics

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Limited Dependent Variable Models The Problem Limited Dependent Variable Models are models in which the dependent variable takes only a limited range of values. Examples are (i) where the dependent variable is a discrete outcome, such as a “yes or no” decision, or (ii) where the dependent variable takes on only non-negative values and equals zero for a fraction of the observations, such as expenditures on durables. If we have to explain these types of variables a linear regression model is generally Typically these models are |. estimated using either Non-Linear Least Squares (NLLS, GMM), or MLE. We will be inappropriate, our models are intrinsically non-linear mode Be making distributional assumptions and need to realise that our parameter estimates will be sensitive to the choices we make, Our models will be of the form Ye = E(yalas) +28 = g (#48) + es where g(-) is a known non-linear function. NLLS is an estimator of / that solves arg S Yue — 9( 248) Binary Choice Models In the setting where y,; takes only takes two values (say zero and one), in that case g(i3) = Efyeas) = Pr(y; = 12). Suppose we would use a linear regression model to explain yz ye = B+ es it should lie between zero and one. This is Since {should be interpreted as a probabil only possible if the x; values are bounded and if certain restrictions on / are satisfied. In