ECOM30001 Lecture Notes - Lecture 15: Probit, Probit Model, Latent Variable
27 Jul 2018
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In a random sample from a population, yi is a random variable: (cid:1877)(cid:3036)={(cid:883) (cid:1872)h (cid:1868)(cid:1867)(cid:1854)(cid:1853)(cid:1854)(cid:1864)(cid:1872)(cid:1877) (cid:1868)(cid:3036) (cid:882) (cid:1872)h (cid:1868)(cid:1867)(cid:1854)(cid:1853)(cid:1854)(cid:1864)(cid:1872)(cid:1877) (cid:4666)(cid:883) (cid:1868)(cid:3036)(cid:4667) Binary choice models: marginal effects for continuous variables in lpm are constant, don"t vary with the level of x variables, source of predicted probabilities outside interval [0, 1] The probability density function for a random variable with this structure is a bernoulli distribution: The random errors are bernoulli distributed assumption of normally distributed errors is not appropriate: (cid:1831)[(cid:1877)(cid:3036)|(cid:1850)(cid:3036)]=(cid:1868)(cid:3036)=(cid:2869)+(cid:2870)(cid:1850)(cid:2870)(cid:3036)+ +(cid:1850)(cid:3036) (cid:1877)(cid:3036)=(cid:2869)+(cid:2870)(cid:1850)(cid:2870)(cid:3036)+ (cid:1850)(cid:3036)+(cid:3036) Is heteroskedastic with a variance that varies in a quadratic manner with the explanatory variables. Since the variance function depends on unknown s (heteroskedastic) we use fgls: estimate (cid:1877)(cid:3036, confidence intervals and hypothesis tests based on these errors may be misleading. If we ignore this heteroskedasticity the standard errors usually computed for ols estimators are incorrect. R a n d o m e r r o r: obtain the estimators for b"s and calculate:
