A Brief Overview of Really Current Research on Dividends

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

Data Structure

Incorporation Listing 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)

Data Structure

Incorporation Listing 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!

Data Structure—Left Truncation

Exposure Recruitment 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

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:1. Subject does not experience the event before the study

ends2. Subject is lost to follow up during the study3. 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.

tti i

iiKM

iN

DNtS

:

)(ˆ

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)


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


The proportional hazards assumption

Ratio of the hazards is constant over time

)(...)( exp),(

),(111 jkikkji

j

i xxxxXt

Xt

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


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

Incorporation Listing Dividend

65-75 group

Incorporation Listing Dividend

85-95 group


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

Variable N 25th Pctl 50th Pctl 75th Pctl 90th Pctlfrominc 170 14 33.5 51 69fromlst 170 1 1 5 15ageatlist 170 8 22.5 49 67.5

Group 1 (1965-1975 Lists)

Variable N 25th Pctl 50th Pctl 75th Pctl 90th Pctlfrominc 186 6 13 23 63fromlst 186 1 3.5 9 12ageatlist 186 1 5 16 58

Group 2 (1985-1995 Lists)

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 StatisticsLooking only at the uncensored observations:

Variable N 25th Pctl 50th Pctl 75th Pctl 90th Pctlfrominc 153 13 33 52 69fromlst 153 1 1 2 7ageatlist 153 8 29 51 67

Group 1 (1965-1975 Lists) Payers

Variable N 25th Pctl 50th Pctl 75th Pctl 90th Pctlfrominc 111 2 9 25 64fromlst 111 1 1 2 6ageatlist 111 1 6 24 63

Group 2 (1985-1995 Lists) Payers

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


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

XGRP group 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

Parameter Standard HazardVariable Estimate Error Pr > Chisq Ratio

roa 3.13076 0.8624 0.0003 22.891inv -0.07379 0.14561 0.6123 0.929ageatlist 0.01474 0.00251 <.0001 1.015grpind -0.54248 0.13194 <.0001 0.581


roa 2.67705 0.84939 0.0016 14.542inv -0.16897 0.12733 0.1845 0.845grpind -0.64399 0.12944 <.0001 0.525

Model with ROA, INV, GRPIND

Model with ROA, INV, GRPIND, AGEATLIST

Preliminary AnalysisCox Regression—First Model Try

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 2 originally 186 firms, now 150 firms

Variable N 25th Pctl 50th Pctl 75th Pctl 90th Pctlfrominc 88 7 15 21.5 34fromlst 88 1 3 9.5 30ageatlist 88 2 8 14 19

Group 1 (1965-1975 Lists) Truncated at 25 Years

Preliminary AnalysisSimple Statistics—Truncated Data

Variable N 25th Pctl 50th Pctl 75th Pctl 90th Pctlfrominc 150 4 10 15 20fromlst 150 1 5.5 9 12ageatlist 150 1 3 7 14

Group 2 (1985-1995 Lists) Truncated at 25 Years

Preliminary AnalysisK-M Estimates—Truncated Data


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


roa 3.13423 0.93954 0.0009 22.971inv -1.33461 0.41558 0.0013 0.263grpind -0.4282 0.16512 0.0095 0.652


roa 3.0767 0.9503 0.0012 21.687inv -0.07379 0.41662 0.0015 0.267ageatlist 0.01063 0.0143 0.4575 1.011grpind -0.38796 0.17401 0.0258 0.678


roa1 1.94416 2.10849 0.3565 6.988roa2 3.17688 1.06641 0.0029 23.972inv1 -0.45388 0.89311 0.6113 0.635inv2 -1.55589 0.48417 0.0013 0.211ageatlist 0.01144 0.0143 0.4238 1.012grpind -0.26443 0.26391 0.3164 0.768

Preliminary AnalysisCox Regression—Interacted Model

Model with ROA1, ROA2, INV1, INV2, GRPIND

Model with ROA1 -- GRPIND, AGEATLIST


roa1 2.10035 2.09385 0.3158 8.169roa2 3.21627 1.05313 0.0023 24.935inv1 -0.50506 0.88715 0.5691 0.603inv2 -1.56366 0.48257 0.0012 0.209grpind -0.30776 0.25732 0.2317 0.735

Documents

A Brief Overview of Really Current Research on Dividends