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

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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


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)


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!


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


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) = 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)


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


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:


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


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 AnalysisSimple Statistics—Truncated Data


Preliminary AnalysisK-M Estimates—Truncated Data


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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