Econometric methods of analysis and forecasting of financial markets Lecture 6. Models of restricted dependent variables.

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Presentation transcript:

Econometric methods of analysis and forecasting of financial markets Lecture 6. Models of restricted dependent variables

This lecture helps to understand: Different types of restricted dependent variables Censored and truncated dependent variables Appropriate model choice Probit and logit estimations Heckman 2-step procedure Tobit model Probit model in estimation of default probability

Contents Binary dependent variable Linear probability model Limited dependent variables Logit and Probit Some examples 2-step Heckman procedure Censored and truncated dependent variables Tobit Probit model in estimation of default probability

Binary dependent variable

Linear probability model

Limited dependent variables General case of binary dependent variable is limited dependent variable, when its range of values is somehow restricted: only positive (negative) values Count variables

Some examples some stocks pay dividends and others do not which factors affect whether countries default on their sovereign debt some firms are engaged in stock splits and others do not

Logit and Probit

The Logit model

The Probit model

Logit and Probit estimation

Probit or logit?

Heckman 2-step procedure Multinomial linear dependent variables: more alternatives for dependent variable (for example, investor choice between different mutual funds or credit ratings). In case of credit ratings, dependent variable is ordered. First case: multinomial logit/probit, second case: ordered logit/probit. In case when firms would have received lower credit ratings (because of weak financials) they elect not to solicit a rating => sample selection bias => inconsistent coefficients => 2-step Heckman procedure

Heckman 2-step procedure

Censored and Truncated Variables the range of dependent variables values is limited for some reason (not necessary dummies) Example: charitable donations by individuals When many values of dependent variable are zero, OLS gives biased and inconsistent estimates => use maximum likelihood method Censored: dependent variable is censored so that values above or below this point are not observable. Truncated: observations are missing when dependent variable is above or below some point.

Tobit model

Probit model in estimation of default probability Default modelling helps to identify factors that affect the ability of firms to pay back borrowed money. This ability is called the financial health of the firm. The model:  Find out firm determinants of financial health. Take into account ratios of the firm: profitability ratios, liquidity ratios, leverage ratios...  Identify the weights given to these factors to construct a single measure of financial health of the firm.  This single measure of financial health is then turned into a probability of default.

Conclusions We’ve covered different types of restricted dependent variables, censored and truncated dependent variables We’ve learned how to make appropriate model choice How to perform probit and logit estimations What is Heckman 2-step procedure what is Tobit model How to use probit model in estimation of default probability

References Brooks C. Introductory Econometrics for Finance. Cambridge University Press Cuthbertson K., Nitzsche D. Quantitative Financial Economics. Wiley Tsay R.S. Analysis of Financial Time Series, Wiley, Y. Ait-Sahalia, L. P. Hansen. Handbook of Financial Econometrics: Tools and Techniques. Vol. 1, 1st Edition Alexander C. Market Models: A Guide to Financial Data Analysis. Wiley Cameron A. and Trivedi P.. Microeconometrics. Methods and Applications Lai T. L., Xing H. Statistical Models and Methods for Financial Markets. Springer Poon S-H. A practical guide for forecasting financial market volatility. Wiley, Rachev S.T. et al. Financial Econometrics: From Basics to Advanced Modeling Techniques, Wiley, 2007.