A Brief Overview of Really Current Research on Dividends

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. Incorporation Listing Dividend/ Censoring Data Structure • 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. Incorporation Listing Dividend/ Censoring Data Structure • 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. Exposure Recruitment Death Data Structure—Left Truncation • 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: • Subject does not experience the event before the study ends • Subject is lost to follow up during the study • 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 t1, t2, … tn be the ordered failure times of the sample • Di = number of subjects who fail at time ti • Ni = number of subjects at risk of failure at ti; these are the subjects that are alive and under observation just prior to ti.

19. Cox PH Regression Model • λ(t,X) = λo(t)exp{ß1 X1 + ß2 X2 + . . .+ ßk Xk} • Hazard at time t is product of two factors • λo(t), the baseline hazard function (does not depend on X) • Exponentiated linear sum of the Xi (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)) = λo(t)exp{ß1 X1(t) + …+ ßk Xk (t)}

23. Preliminary AnalysisData • 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. 65-75 group Incorporation Listing Dividend 85-95 group Incorporation Listing Dividend Preliminary AnalysisData • We think the average observation from each period looks something like this:

25. Preliminary AnalysisData • 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 AnalysisSimple 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 AnalysisSimple 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 AnalysisKaplan-Meier Estimates

29. Preliminary AnalysisKaplan-Meier Estimates • 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 AnalysisKaplan-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 AnalysisCox Regression—First Model Try • λ(t,X(t)) = λo(t)exp{ßROA XROA(t) + ßINV XINV(t) + [ ßAGE XAGE AT LIST ]+ ßGRP XGRP } • XROA(t) (time varying) return on equity value • XINV(t) (time varying) investment value • XAGE AT LIST age of firm at listing • XGRPgroup indicator (0 if in 65-75 group, 1 if in 85-95 group)

32. Preliminary AnalysisCox 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. Preliminary AnalysisCox Regression—First Model Try • Model with ROA, INV, GRPIND • Model with ROA, INV, GRPIND, AGEATLIST

34. Preliminary AnalysisCox 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 AnalysisTruncated 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 2originally 186 firms, now 150 firms

36. Preliminary AnalysisSimple Statistics—Truncated Data

37. Preliminary AnalysisK-M Estimates—Truncated Data

38. Preliminary AnalysisKaplan-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 AnalysisCox Regression—Truncated Data • Model with ROA, INV, GRPIND • Model with ROA, INV, GRPIND, AGEATLIST

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