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A Brief Overview of Really Current Research on Dividends

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### A Brief Overview of Really Current Research on Dividends

Gretchen A. Fix

Department of Statistics

Rice University

6 November 2003

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

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

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

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

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

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

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

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)

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!

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

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

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

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

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

Functions of Interest in Survival Analysis

- Hazard function, λ(t)
- λ(t) = limt0 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)

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

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.

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)

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

Cox PH Regression Model

- The proportional hazards assumption
- Ratio of the hazards is constant over time

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)}

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

Incorporation

Listing

Dividend

85-95 group

Incorporation

Listing

Dividend

Preliminary AnalysisData- We think the average observation from each period looks something like this:

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

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.

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.

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

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

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)

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

Preliminary AnalysisCox Regression—First Model Try

- Model with ROA, INV, GRPIND
- Model with ROA, INV, GRPIND, AGEATLIST

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

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

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

Preliminary AnalysisCox Regression—Truncated Data

- Model with ROA, INV, GRPIND
- Model with ROA, INV, GRPIND, AGEATLIST

Preliminary AnalysisCox Regression—Interacted Model

- Model with ROA1, ROA2, INV1, INV2, GRPIND
- Model with ROA1 -- GRPIND, AGEATLIST

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