Financial Econometrics Lecture Notes 4 University of Piraeus Antypas Antonios

Binary Models Suitable when yj is a dichotomous dependent variable Remember that yj is observable 2

Binary Models Plot of a dichotomous variable 1 3

Binary Models LS Regression is not the optimal method for estimating a model with a dichotomous dependent variable Non-normal errors ( Efficiency Loss ) Non constant error variance ( Heteroskedasticity) Nonsensical Predictions: The linear model can create predicted values that are not bounded by zero and one 4

Binary Models Latent Variable Approach There exists an unobservable continuous variable which measures the underlying propensity of the occurrence of an event of interest A. r The problem is that we can not either observe or measure Instead we observe a dichotomous indicator corresponding to 5

Binary Models Q: What is our underlying model? Desirable but infeasible scenario: Model the propensity of event A using information available now. where Xj is a set of potential determinants of the propensity of the occurrence of A. 6

Binary Models Therefore, we can write: Turning the infeasible to feasible… We only observe the following realizations of Therefore, we can write: 7

Binary Models Therefore This final result suggests that once we have defined and estimated a model that measures the propensity of event A, we can calculate the probability of the occurrence of the event A. Probability of occurrence of A’ will then be: 8

Binary Models Choose Probability Density Function for random errors uj,t Standard Logistic Distribution (LOGIT Model) Standard Normal Distribution (PROBIT Model) LOGIT models are preferable in Finance because they have fatter tails. 9

Binary Models How to estimate a Binary Model using gretl

Binary Models How to estimate a Binary Model using gretl