1. A Brief Overview of Really Current Research on Dividends Gretchen A. Fix Department of Statistics Rice University 6 November 2003

2. Outline Restatement of problem Fama and French hypothesis Our hypothesis Introduction to survival analysis and tools to be used Kaplan-Meier estimator Cox regression Preliminary results

3. Restatement of Problem Dividends are important—they are the primary determinant of equity value Papers in the finance literature discuss the changing prevalence of dividends Proportion of dividend paying (industrial) firms has decreased over the past 25 years Real and nominal dividends paid out by industrial firms have increased over this period

4. Fama and French Hypothesis Proportion of public firms paying dividends 66.5 % in 1978 20.8 % in 1998 Relevant characteristics of dividend payers Profitability Investment opportunities Size

5. Fama and French Hypothesis Attribute the decline to Changing characteristics of the population of firms in the market Decreased propensity to pay Make note of the “surge” of new lists that began in 1979 Contributed to changing characteristics

6. Our Hypothesis A firm can do two things with its earnings: Pay them out to equity holders Reinvest in positive NPV projects As a firm matures, growth opportunities will become limited and it will run out of projects and resort to dividends

7. Our Hypothesis This adds another characteristic to Fama and French’s list Profitability Investment opportunities Size Maturity Time origin for maturity INCORPORATION By default, age seems to be measured by listing

8. Our Hypothesis We compare the dividend initiation behavior of new lists from two time periods Group 1: New lists in 1965-1975 Group 2: New lists in 1985-1995 We model our lifecycle hypothesis using the Cox regression framework Model the hazard of initiating dividends Find that accounting for age in terms of incorporation has significant effects on the model output

9. Data Structure IncorporationListing Dividend/ Censoring  Three time points of interest: incorporation, listing, dividend/censoring  Status of firm is coded as a “1” if endpoint is dividend initiation and “0” if it is a censoring  Censorings are the result of losing a firm (due to merger or bankruptcy) or failure to initiate dividends over the life of the study (12/31/2002)

10. Data Structure IncorporationListing Dividend/ Censoring  From incorporation to listing, the firm is technically not at risk of becoming a dividend payer; we only care about dividends paid after a firm lists  This looks like delayed entry into the risk set or left-truncation—but it is not!

11. Data Structure—Left Truncation ExposureRecruitment Death  Left-truncation is a result of study design  For example, subjects are exposed to a toxin; at some time after exposure, they are recruited into a study focusing on mortality resulting from toxin exposure; any subject who died from toxin exposure prior to recruitment would not be eligible to participate in the study  Subjects are not at risk of an observable death during the interval between exposure and recruitment into the study

12. Data Structure—Challenges We have identified the interval from incorporation to dividend/censoring as the relevant period to study; however Firms are not technically at risk between incorporation and listing It will be difficult to build models using this interval, since there is no comprehensive database for balance sheet information until after firms list

13. What is Survival Analysis? “a collection of statistical procedures for data analysis for which the outcome variable of interest is time until an event occurs” Kleinbaum, p. 4 Typical applications Biostatistics—study treatment effects in clinical trials Industrial—study failure behavior of a machine

14. Typical Characteristic of Survival Analysis Data—Censoring Exact survival time of a subject is unknown Usually occurs at the right side of the follow-up period; but can have left or interval censoring Typical reasons for right censoring: 1. Subject does not experience the event before the study ends 2. Subject is lost to follow up during the study 3. Subject withdraws from the study

15. Functions of Interest in Survival Analysis Survival/survivor function, S(t) Gives probability that a subject survives longer than specified time t S(t) = P(T > t) = 1 – P(T  t) = 1 – F(t) Properties Non increasing S(0) = 1; at the start of the study, all observations are alive S(  ) = 0; if the study time were increased without limit, eventually there would be no observations left alive

16. Functions of Interest in Survival Analysis Hazard function, λ(t) λ(t) = lim  t  0 P(t  T < t +  t | T  t) /  t “Instantaneous potential per unit time for the event to occur, given that the individual has survived up to time t” Conditional failure RATE (probability per unit time)

17. Kaplan-Meier Estimator Method for estimating survival curves; aka The Product Limit Estimator In theory, the survival function is a smooth curve; in practice, it is estimated by a right-continuous step function It can be shown that the K-M estimator is the NPMLE of the survival function when one has censored data

18. Kaplan-Meier Estimator Let t 1, t 2, … t n be the ordered failure times of the sample D i = number of subjects who fail at time t i N i = number of subjects at risk of failure at t i ; these are the subjects that are alive and under observation just prior to t i.

19. Cox PH Regression Model λ(t,X) = λ o (t)exp{ß 1 X 1 + ß 2 X 2 +...+ ß k X k } Hazard at time t is product of two factors λ o (t), the baseline hazard function (does not depend on X) Exponentiated linear sum of the X i (does not depend on t)

20. Cox PH Regression Model Popularity of the model Form of the baseline hazard left unspecified—gives robustness Exponentiation ensures that fitted model will always give non-negative estimates of the hazard Although the form of the baseline hazard unspecified, after model fitting, it can be recovered and corresponding survival curves for individual observations can be estimated

21. Cox PH Regression Model The proportional hazards assumption Ratio of the hazards is constant over time

22. Extended Cox Regression Model Allows time-varying covariates Previously, covariates were not allowed to depend on time (ensured proportionality of hazards) λ(t,X(t)) = λ o (t)exp{ß 1 X 1 (t) + …+ ß k X k (t)}

23. Preliminary Analysis Data Dataset consists of approximately 2750 firms that listed in 1965-75 or 1985-95 For each firm we have Years of incorporation, listing, dividend/censoring Covariate data (roa, investment, repurchase activity) for each year post listing Dataset was stratified by exchange (NYSE/AMEX or NASDAQ) and market value (above yearly exchange median or below during year of last contact) All analysis presented here was done on the large- NYSE/AMEX stratum

24. Preliminary Analysis Data We think the average observation from each period looks something like this: Incorporation Listing Dividend 65-75 group IncorporationListing Dividend 85-95 group

25. Preliminary Analysis Data The length of the interval from incorporation to listing was much longer for the early group firm Equivalently, the early group firm had a greater age at list than the late group firm Market conditions of the 80s and 90s allowed firms to go public relatively early in their lifecycles

26. Preliminary Analysis Simple Statistics The median age of a firm at dividend initiation (or censoring) is 1 year measured from listing. However, the median age at listing is 22.5 years. The median age of a firm at dividend initiation (or censoring) is 3.5 years measured from listing. However, the median age at listing is 5 years.

27. Preliminary Analysis Simple Statistics Looking only at the uncensored observations: The median age of a firm at dividend initiation is 1 year measured from listing and 33 years measured from incorporation. The median age of a firm at dividend initiation is 1 year measured from listing and 9 years measured from incorporation.

28. Preliminary Analysis Kaplan-Meier Estimates

29. Curves generated using listing as time origin show lower propensity to pay for 85-95 group Curves generated using incorporation as time origin show higher propensity to pay for 85-95 group

30. Preliminary Analysis Kaplan-Meier Estimates Limitation of K-M: non-parametric method; cannot take into account any of the covariates which we think affect dividend initiation Attempt to implement our lifecycle model using the Cox regression framework Model the hazard of initiating dividends

31. Preliminary Analysis Cox Regression—First Model Try λ(t,X(t)) = λ o (t)exp{ß ROA X ROA (t) + ß INV X INV (t) + [ ß AGE X AGE AT LIST ]+ ß GRP X GRP } X ROA (t)(time varying) return on equity value X INV (t)(time varying) investment value X AGE AT LIST age of firm at listing X GRP group indicator (0 if in 65-75 group, 1 if in 85-95 group)

32. Preliminary Analysis Cox Regression Our hypothesis suggests the following output of the model Positive, significant coefficient for ROA Negative, significant coefficient for INV Negative, significant coefficient for GRPIND when AGEATLIST omitted from model Positive, significant coefficient for AGEATLIST; less negative and/or insignificant coefficient for GRPIND when AGEATLIST included in model

33. Model with ROA, INV, GRPIND Model with ROA, INV, GRPIND, AGEATLIST Preliminary Analysis Cox Regression—First Model Try

34. Preliminary Analysis Cox Regression Further tweaks to be made DATA: Truncating the data so that we only try to model dividend initiation up to 25 years post incorporation; (accepting that some firms do not conform to our lifecycle hypothesis) MODEL: Consider industry effects (stratify by SIC code) MODEL: Allow the coefficients for ROA and INV to vary for the two time periods Under this model, are we able to pick up the propensity to pay effect? MODEL: Instead of including AGEATLIST, stratify

35. Preliminary Analysis Truncated Data Truncating the data at 25 years will have the effect of eliminating firms that did not list within 25 years of incorporation from the model Group 1 originally 170 firms, now 88 firms Group 2 originally 186 firms, now 150 firms

36. Preliminary Analysis Simple Statistics—Truncated Data

37. Preliminary Analysis K-M Estimates—Truncated Data

38. Preliminary Analysis Kaplan-Meier Estimates Curves generated using listing as time origin show lower propensity to pay for 85-95 group; however, this lower propensity is not as strong as before Previous curves showed an increased propensity to pay from incorporation for the 85-95 group, these curves show little difference between the groups

39. Preliminary Analysis Cox Regression—Truncated Data Model with ROA, INV, GRPIND Model with ROA, INV, GRPIND, AGEATLIST

40. Preliminary Analysis Cox Regression—Interacted Model Model with ROA1, ROA2, INV1, INV2, GRPIND Model with ROA1 -- GRPIND, AGEATLIST