ED 199 457

. AUTHORTITLE

DOCUMENT RESUME

CE 028 222

Bassi, Laurie J.Estimating the Effect of Training Programs withNonrandom Selection. Final Report., July-November1980.

SPONS AGENCY Office of the Assistant Secretary for poii y,Evaluation and Research (DOW, Washington, D.C.Nov 80DOI-B-9-m-0-106(430p.

PUB DATECONTRACTNOTE

-__EBBS PRICE MF01/PCO2 Plus Postage.DESCRIPTORS Adults; *Employment Programs; *Evaluaton riteri

,,viluation Needs; Federal Programs; *Job Training;Participant Characteristics; *Program Effectiveness;Program, Evaluation; Research Methodology; *ResearchProblems: *Selection

IDENTIFIERS Comprehensive Employment and Training Act; *NonrandomSelection

ABSTRACTA study was conducted to develop a theoretical

framework for unbiased estimation of the dynamic net impact of--Comprehensive Employment ,and Training Act (CETA) programs on

participants* eatni4gs. (The possibility, of selectivity bias Arisesfrom the non-random nature of participation in the program. That is,if participation is a function of unobservable variables such asability or motivation, and these variables arealso determinants ofearnings, it will be impoSSible to distinguish the effects of theunobservables from the effects of the program without controlling forAle selection process.) In the study, selectivity biases werecontrolled for through the use of an error components model.. Themodel relieson the longitudinal nature of tide data to eliminate theeffects of the unobservables by differencing them away. Theestimation techniques developed allow or participation to be anon-random function of individual, unobServed.variables that are bothfiAed and changing over time, and temporary fluctuation in earnings

--Tritifto- the program. This framework represents an advance in .thestate of the art in impact estimation for employment and trainingprograms,. since it places fewer restrictions On the natureand typeof comparison group necessary for unbiased estimation and, thereby,contributes to solving a problem- that has long plagued evaluations ofempl.cyment and training programs. (Author/KC)

************* *** ** *** **** *** **** *Reproductions supplied by EDRS are the best that can be made

from the original document.********* ***********************************

u-NESTIMATING THE EFFECT OF TRAINING

PROGRAMS WITH NONRANDOM SELECTION

by

Laurie J. Bassi*

November, 1980

This report was prepared for the Office of the AssistantSecretary for Policy, Evaluation and Research, U.S. Depart-ment- of Labor, undercontract/purchase order No. 9-9-M-0-1064.Since oentradtors conducting research and development projectsunder Government sponsorship are encouraged to express theirown judgement freely, this report-does not necessarily repre-sent the official opinion or policy of the Department of Labor.The contractor is solely responsible for,the contents of thisreport.

*The author wishes to acknowledge helpful discussions withGary Chamberlain and Phil Moss. Particular thanks, go toOrley Ashenfelter.

U S DEPARTMENT OF HEALTH.EDUCATION A WELFARENATIONAL INSTITUTE OF

EDUCATION

THIS DOCUMENT HAS BEEN REPRO-DuCEO EXACTLY AS RECEIVED FROMTHE PERSON OR ORGANIZATION ORIGIN.ATING IT POINTS OF VIEW OR OPINIONSSTATED DO NOT NECESSARILY RERRE-

= SENT OFFICIAL NATIONAL INSTITUTE OFEDUCATION POSITION DR POLICY

50277-

REPORT WOOPAGE

4 end Subtitle

ENTATION REPORT

ASPER/PURSO 1064/2

Estimating the Effect of Training Prog aNonrandom Selection

7. Author

Pe rf orming ;anirat on Name and Address

Laurie J. BassiBox 17--Graduate CollegePrinceton, New Jersey 08544

nig Organize _n Name and Address

U.S. Department of Labor ASPER200 Constitution Avenue, N.W.Washington, D.C. 20210

Supplementary No

Recipient's A ccession

with5 Report irate

t-QI_Le_iriber 1980

Performing Orgenliation Rept= No.

10. Project/Task Unit No.

Contract(C) or Grant(G) No

(c) _8-9-M-0-1064

(G)

13. Type of Report & Period Covered

Final7/80 to 11/80

14.

5. A¢tract (IAmt: 200 words)

The purpose of this study was .to develop consistent econometricestimators for measuring the net impact of employment and! trainingprograms on participants' post-training'-earnings. The estimatorsderived here will provide unbiased measures of net impact when par-ticipation in the program is a non-random function of individual,unobservables variables. These unobserved Niariables may be: fixed,changing over time, or purely transitory. The most generalizedversion of the estimation technique allows for participation to besimultaneously determined by all three types of unobservables.

Analysis 8. Descriptors

EcOnometrics, Economic mod

Identifiers /Open -Ended Terms

Selectivity Bias

-c' COSATI i eld /Group 5CA,..ellahility Statement

-,-

1.3. Security Ulla (This RePorli 21. No. Of PagesRelease unlimited. Available from National Tech°UNCLAESIrT7nical Information Service, Spr lagtiold, Va. m. Security Class

22161 UNCLASSIFone on Revers

cation, Evaluation, cal models

Sae ANS

22. Price

OPTIONAL FORM 272WOrinerh(NTIS

4-77)

TABLE OF CONTENTS

Page

Executive Bummay

introduction1

Methods for Consistent Estimation 2

An Earnings Function with Heterogeneityand Time Effects

Data and Estimation Agenda15

Appendix A17

Appendix B19

21References

EXECUTIVE SUMIRY

The purpose of this study is to develop a theoretical frame-

work for unbiased estimation of the dynamic net impact of CETA

on participants' earnings. The framework is developed for

empirical application to the Continuous Longitudinal Manpower

Survey (CLMS).

This paper presents a method of estimating CETA's effect,

free of selectivity bias. The possibility of selectivity bias

arises due to the non-random nature of participation in the pro-gram. That is, if participation is a function of unobservablevariables (such as ability or motivation), and these'va-iables

are also determinants of earnings, it will,be impossible to

distinguish the effects of the unobservables L_om the effects of

the program without controlling for the selection process.

In this paper, selectivity biases are controlled for through

the use of an error cot Tonent- model. The model relies on the

longitudinal nature of the data to eliminate the effects of the

unobse- ables by differencing them away. The estimation techniques

developed here allow for participation to be a non-random functionof: individual unobserved variables that are both-fixed-and

changing over thee, and temporary fluctuations in'earnings priorto the program.

This framework represents an advancement in the, stathe. state of

the art in impact estimation for employment and training programs.

Further, is fewer restrictions on the nature and type of

comparison group necessary for unbiased estimation and, thereby,

contributes to solving a problem that has long plagued evallia-

tions of employment and training programs.

ii

INTRODUCTION

Federally funded employment and training programs have

become a permanent and major feature of labor market policy in

the United States. Most of these programs are now funded through

the Comprehensive Employment and Training Act of 1973 (CETA).

By fiscal year 1979 CETA funding had reached 4 billion.

Despite the magnitude of employment and training programs,

little is known about their effect on participants after leaving

the program. Our inability to isolate program impacts is a

result of the massive amount of data that are necessary. With-

oYlt specifically controlling for: time, social factors, demo-

c-raphic variables, the economic ate, and unobservable factors

sociated with each individual - it,is impossible 'to olate the

independent effect of the program.

Recent availability of,the Continuous Longitudinal Manpower

Survey will eliminate many of these insurmountable data problems

of the past. a-nese date; contain a representative sample of CETA

participants, well as comparison groups which have been drawn

from the Current Population Survey. The availability of the

comparison groups will permit an isolation of the effect of the

program on participants' earnings, independent from the effects

of time and the state Of the,economy. The longitudinal nature

of the d tzl enable ar. examination of the dynamic impact of the

program. perhaps most importantly, the longitudinal data also

provide us with a much better opportunity to control for individi-

al, unobservable characteristics than would be available from

pur ly cross - sectional data

The plan of the paper is as follows. Section II describes

technicues to control for selectivity bias. Section III develops

consistent estimators for the net impact of employment and train-

ing programs on participants earnings, allowing for the poosi-

bilitv that participation in the program is correlated with indi-

vidual, unobservable characteristics that are both fixed and

changing over time. These estimators are then generalized to

allow for participation to be a function of transitory earnings

fluctuations prior to participation. Section IV describes the

data that will be used, and outlines the estimation agenda.

II. METHODS FOR CONSISTENT ESTIMATION

_ncreased awa,=en-. --s among economists as to t_ pervasive-

ness o_ nonrandom selection has spawned a rapidly growing/

literature attempting to deal with the econometric problems that

it introduces. If the selection process is a function of un-

observed variables that are correlated with the dependent

regressors, ordinary least squares will ield in onH.stent

para ete_ 4 Lima us. The literature, t6 date, has developed two

strategies for breaking the correlation between the error term

(the unobservables) and the independent regressors.

The first approach (developed by Heckman and Maddala a

Lee) attempts to timate the value of the unobserved (latent)

variables by first predicting the outcome of the select n process

using probit analysis. By assuming that the error terms are

2 -

nor ally distributed, the expected value of the latent variahles

can be calculated by taking the inverse of the Mill's Ratio of the

predicted value of the participation variable. By including this

estimated value in the earnings equation, the cmtitk__d variables

problem is eliminated. The resultant ordinary lea _ squares

estimates are condistent.

This approach has a great deal of appeal sin, adjust-

ment for so _ctivity, bias is based on a model of the economic

to enter a program. Unfortunately, in the pr h

being studied here, there is a second seection process in addi-

'tion to self-selection. This sel,_tion is based on program'

administrato decisions about who will be permitted to parti-

cipate in the program from the pool of eligible applicants. Since

this decision is likely to be a function of many non-economic

considerations which are unknown t, rin analyst, it is impossible

to estimate the probit without introducing additional latent

dude inconsistent estimates.

Given this problem it seems likely that an error components

model, the second method of controlling for selectivity bias,

is the appropriate technique. These models generally specify

the latent variable as including both a permanent component

which is associated with an individual, as Well as a transi-

tory component which is common across indi iduals. For the pur-

pose of net impact estimation, the existence of a transitory'

component makes it necessary to have.data on both Participants

and nonparticipants. Otherwise it is impossible to isolate the

independent effects of the program from that of the transitoryerror component.

If the permanent component of the error (the latent ria-

ble) is constant over time, then first differencing of the c_ta.,

will eliminate any correlation between the remaining error and

the independent regressors. If, h. wever, the latent variable

changes over time, then simple first differencing will not be

sufficient to eliminate the correlation. The next section

develops a model which allows for latent variables which are

both fixed and changing ,over time, as well as transitory unob-

served components. Consistent estimates are derived, allowir

for the possibility that both ypes of unobserved components are

correlated with the independent regressors.

III. AN EARNINGS FUNCTION WITH CHANGING

HETEROGENEITY AND TIME EFFECTS

A unique characteristic of longi.tudi-.al data tha

enables us o control for individualunobserved.characteristics

(heterogeneity) to an extent that is not possible using purely

cross-sectiona.L data A frequently used specification of ea n-

determination is

(1) Yit = OiXi 13 Zit

(

4- E.

wh re Yit is the earnings of the inn individual in time t, Xi

is a vector of background variables for the thindividual that

remains fixedover time, and Zit iF a vector of variables that

changes over time. The error term consists of the components;

which is unique t the individual and fi%ed over tine, Et1

which is comm_n across all individuals at time t, and which

is specific to individual at time t.

In recent work, Asbenfelter has used this model to estimate

the impact of employment and training programs on participants'

earnings. He assumed that Zit included a participation dummy

variable and a cubic in age, and that sit was a random error term

with zero expectation. Using longitudinal data on a sample of

1954 MDTA participants, as well as a comparison group drawn from

the CPS, Ashenfelter was able to estimate

(2) Yit -1y. (E

s ) 2(zit

wh- e, s was the base (pre- program) year and t represents a series

of post-program years.

Any selectivity bias present in equation (1) due to correla-

tion between the fwd unobservables, Ei, and the independent\

regressors, zip, i as beer eliminated from equation by first

differencing. participation in the program is a function

of unobservables that are constant over time (such as innate

ability), equation (2) will yield unbiased net impact estimates.

If, however, participation the program a,funet f indi-

vidual, unobservable variables that are not fixe ver time, the

sit term, equation (2) will produce biased estimates since t

assumption that E(eit-Z1 , ), 9 o is violated.

An example of anetuch a variable might be local labor market

conditions. Since employment and training programs .ire generally

funded at higher levels in areas experiencing unusually high

levels of structural or cyclical unemployment, rartici =tien is

likely to be a functivn of local labor market conditions. Since

these conditions re r t fixed over tithe, any selectivity bias

created by them will not be eliminated_by_equation (2) .

It is possible to generalize the specification of the earn-

ings function in equation (1) to allow for correlation between

latent variables that are not fixed over time (changing hetero-

geneity) and program participation. By assuming that these

variable change over time at a constant rate 0 a generalized

version of equation (1) is rewritten below.

3) Y'k 131-:i 82Zik ask

(4) Eik PEik-1 uik

and (5) k Qek Qnk

the

where Qek is a random (transitory) error for program participants

and Qnk is a random error term for non-participants. The sum of

these two terms, uik is a random error term with zero expectation

and no serial correlation haA been written in this way to

all for the possibility that participation is a function of

transitory fluctuations in earnings, prior to the procram. This

would captUre the possibility that cyclically unemployed corkers,are more likely to participate in the program. The Q term could

also incorporate the effect of "creaming" 'If program administra-

tors "cream" from the pool of eligible applicantS, then

E(Qek) E(Qnk).

E,Nek_ E(Qnk)

where t is the period of participation. This would mean that

6

while-the participants met the eligibility requirements for the

program, their eligibility was only temporary because of an unlucky1

year prior to program participation. By-allowing for the possi-

bility that E(Qk) + 0 prior to the program, any correl-4ion be-,

tween uk_i and Zk can be removed. As we will see below, this is

critical if p +.0.

for the sake of expositional Simplicity we will begin by

assuming that E(Qk) F 0, forall t. Towards the end of this o-

tion,.,this assumption will be relaxed. The availability of an2

"appropriate" comparie6n group is assumed. Also it will beassur ed throughout that he 01, 62, and p are constant overtime,

although these parameters may vary between the participants and3

non - participants.

Using this assumption, equation (3) is rewritten below in

first differences fora.(6) Yit s Yit_ ct-1) 4. 6 (tit z. -1) +

(sit eit-1)

TheseTequirements generally restrict participation in theprogram to,individuals whohaVeexperienced a spell .ofunemployment, have very low earnings, or are welfare reCi-pients.

2 -.Techniques for choosing an "appropriate" comparison groupsare described in the- next section.

3 The model is written here using theHassumption that theparameter values are constant aoross.the two groups.. ThiSassumption can be easily relaxed. It is also possible togeneralize the- model to allow-for a higherdrdir autoregress-ivescheme, although no such:generalization will be reportedin 'this paper. It is not poasible,--hoWeVer,:tp relax theassumption that p is constant and simultaneouslY:-maintainidentification of 07ogram,impaote.

she- program on .participants' earnings in period :t4

is captured in :--,J6L9p that the fixed heterogeneity (ci) has

been eliminated by differencing. If, however, the heterogeneity

changes over time, then imple\differencing will not completely

eliminate the possibility of selectivity bias. Any remaining

inconsist ncy can be eliminated by using-equation (4) to rewrite

the error term in equation. (6).

(7)

Lit = t-1 Eit-

cit t-1/- PC(Yit-1

- ui .- --1

131x-2zit-1 ei )

it-2-01Xi-82Zit-2-ci-c -2)]

it-uit71)

-1 = P

P(Yit-1

it-i-zit

It is not possible to use (7) as the basis for con intent estima-

.tion of p since criers negative correlation of p between: the

error term and. P (sY This problem cannot be eliminated-it-1 Yit-2)*5

by diffrencing. o "er two periods. -To-see this consider equation

(8) .

(8) _P t-3-c

P(Yit-1-Yit-

-1t-1-Zit-3(uit- uit °2)

)

4'-:Note that if _ :2\ct_l -- 0, no coMparison group would be neoess-, ary since the intercept would.. then measure the program's impact.In a dynamic economy, however, this condition is unlikely tohold.

.

Thankeare,due,to Gary Chamberlain for pointing out a mistakeIn tiiii section of an earlier draft of the paper.

From eqUations 3 and ( we have

(9) Yit-1 02zit-1 et-1 2eit -'3 Ouit-2

uit-i

By 'substituting equation (9) into 8) we ould be left with a

negative correlation of p2 between the error term and p(Yit_i-

Yit-3)- Higher order differencing would reduce the magnitude

of the bias that is created by this 'correlation, but it would

never be eliminated.

The only way to consistently estimate p is by using an

instrument, Yit_i, for Yit=1 in equation '(7). By substituting

equ_tion (7) into (6) we are then left with

(10) Y Yit-1 = Ect-ct-1 O(-t-l-Et-2)7

82(zit-zit-1 t-2)]

Now suppose that t is the period of program articipation,

and the program results in a shift in earnings of.Ot during

that time. Equation (9) can be rewritten ai

(11),Yt

Some not

Yt-1 °O a2*at* 13t P P

(Ut ut-1)

-1- 2)

ional simplification has been introduced here which

will be maintained throughput. The 1, subsCripf has been dropped.

0o indicates a combination of transitory error components, 132*

represents a non-linear combination of 82'and p, and Zt*'repre-,/

sents differencing of the Zt-vector, where Zt n 'longer contains

the participation variable P is a dummy variable measuring pro-

gram particiation, and 8t is an unbiased estimate of the programs'

of fact in year t. Program impacts in period t11-1 are calculated

below in a similar manner.

12) Yt+1 Yt t+1 +1pat)P t a Yt-1

In order to consistently estimate the cumulative impact of the

-t1 i.program, it is necessary to first estimate p from equation,

/

.(11). Then multiplying equation (11) by p and adding it to (12),

leaves

(13) Yt+1 a (l+p)Yt-pY s p2(Yt_l-Yt =2 ) = o +1

t=1-1P (ut+1-(1-p ),Ut

It is possible to continue to solve for the cumulative program.'

impacts in later years in a similar manner. However, the left

hand side -of the equation becomes extremely Complicated. A

more straight .forward method is -to. solve for the impacts

re'cursiVely,using the estimated values in period (t+j) and

(t+itl)_to solve' for the impact in period- (t+j+2).. Both solution

Methods are consistent. The cumulative impact in any period can

b calculated by the use of 'equation (14).

(14)Yt .4:n Yt411-1 0+0 *Z*ti-n tin-

P

P(Yt+n-1 n-2 ± t+n-2)

(u uti-n =n:1)

Once p. has been estimated from equation (11), and 13t+11,1 and/

,t.+1.1_2 have been solved for, it would then be possible to' e tiniate

13t-En by re-

(15) Y

'ting equation .(14) as

n Yt4-11-1 °(Yt+n-1-

Po+ 2Vt n

10

+--1.- Y-t-1-11-2

-ct-1-11-?t:n-1)

n-2-

The- unique feature of this technique is that it provides us

with a fr ework for consistent estimation of the dynamic impact

of the program on participants' earnings under a very broad range

of non-random selection processes. Equation (15) is sufficiently

general to allow for participation to be correlated with latent

variables that are both fixed and changing over time. Previous

estimates have allowed for either fixed heterogeneity or changing6

heterogeneity, but not both simultaneously.

As was mentioned earlier, it is also important to consider

the possibility that participation in the program may be correlated

with the pr program transitory error component, t-l* For

instance, if program administrators .'creamed" from the pool

eligible applicants, then E(ut-1)<0 for Participants This

would create correlation between utl and participation in the

-program. Since 9t_1 is an element of the error component in the

net impact estimation equations developed here [see equation

(13)1, thiS will create an additional sou ce-oi inconsiitency

unless specifically controlled for. Once it is recognized that the Q

variable has the same' role in the pre-prograM years as the P

Variable does in the post- program years, it follows, that'equa-

tions (13) and (15) are sufficiently general for consistent net

6 Ashenfelter's eetimates, of equation (2) have eliminated,anybias frot-non-random selection due to fixed latent variables.He also estimated equation (1) where Zit included lagged valuesof Y. This method is sufficient to eliminate any bias createdfrOm non- random, selection due to changing latent variables Itwill not, however', eliminate fixed effects bias.

impact estimatiOn in the case. when Qt_k 4 O. For instance,

we knew the value of Qt-k, we could estimate the net impact of8

the program in period t from equation ,(16). below.

(16) Yt - Yt i +0(Qt-1 -2).

atP (ut-ut-1)

As in the case :If net.impact esti 7n, Where it was necessa

to first estimate 8t before estimatim rit we must first

estimate\Q,1, In to 1-p. able to do this, however, it is\ -

necessary

side- th fz:

not constraz

(17)

assume Qt- =(2) for j 2. To see thisi c n-

7re-programearaings equation w ereQt -j

be zero.

Without as-

estimate c =1.

with

-(18t-2.-.

t-2)

4-(ut_1-ut_2)

is not possible to

im Lsing this assumption, we are left'

*z*t-i-EP(Yt- 4.(Qt-l+ut- t-2)

The reEidual from equation (18) giyes us an estimate of Qt_,

since W,-t-1 t-3) =O. By, including Qt_i In the., net impact=

estimation equation, any bias that results -from the program

7 It is assumed that p created a shift in theearning's functionof participants after the prograM. The .Q variable assumes thesame role prior to the program.8 -.This Simply rewrites. equation (15).

- 12 -

on the basis of the pre-progra_ transitory error component

has been eliminated. The:most general version of equation (15)9

is given below.

(19 Yt-j-1-2-Yt+j+1T(Yt+'

130132*Vttj+3+Rti-j+2+

where Rz = Z > t

= tR = -1

Rz = 0 <t -1

yt+j) +(Rt+j +lIlt 3)

t+.j+2-ut-Fj+1

Estimation of equation (19) will provide consistent eSti-

es under very general conditions. Its validity, ver,%is

dependent upon the follOwing key assumptions: (1) p is con- Nscant over the entire time span being considered, (2) theearn

ins equations to be estimated are the same for the comparison

group as for the participants except for the P and Q,terms,

t-r for j?2, and (4') both P and Q enter the earnings equa-/tidns linearly. The validity of the first three assumptions

easily-tested. It is possible to relax assumption .(4) by doing/separate net impact estimation, for the differentAge/race/sex

groups.

9 Unlike it is 'necessary to estimate Q.for non-participantsas welA:as participants. However, a- eparate value of Q isestimated for each group.

10- The analysis could be done separately y whatever variablesin X or Y seem likely to interact with P or Q in the, earningsequations.

Perhaps the most serious drawback of this,approach is that

it is not appropriate for very young participants of employment

and training programs. 3ince very few of the youngest partici-

pants would have any earnings for the three years prior'to pro-

gram participation, it is impossible to estimate p for this

group. This is especially unfortunate since employment and

t.7air .g programs generally have a large number of young parti-

cipants. Nevertheless, a thorough examination of this problem

iS beyond the scope of the current analysis. The empirical

,dnalySis will be done only for participants who were at. least

twenty -three -years of age upon entering the program.

It seems, likely, however, that, the advantagesof this

approach more than outweigh its shortcomings.. It provides a frame-

work for consistent estination o'f the dynamic impact of employment

and training programs on participants' earnings. The modelfi

fi

allows for unobserved variables which are both fixed (such

ability), and changing overtime (such as health or local labor

market conditions). These unobservables, as well as the transi-

tory error, component, may be correlated with parti

program. Finally, the model, is consistent ith a

.'specification of the earnings. function. It is con

cipation in the

vary general

scent with

a model in which: ,(1) aagged values of earnings, affect current'

earTings (above and beyond the eXtent to which they represent

fixed effects) or (2) disturbances in earnings are correlated11

over

IV. DATA AND ESTIMATIONESTIMATION.AGENDA

The Continuous Longitudinal Manpower Survey (CLIMB) public

use tapes will be used forthe estimation suggested by Section

III. The CLMS represents a iajJor data development effort of the

Department of Labor for evaluation of CETA funded employment and

training programs. For a representative sample of 6,700 indivi-

duals that participated i It.he program during'1975 and 13,300

who participated during fiscal year 1976, the file contains: a four

year record of labor forbe experience beginning one year prior

to CETA enrollment, basic demographic characteristics, a his-

tory of Public benefits received by the individual and/or the

individual's familyi family-related variables, and reported

annual. social security earnings for 1951-1977- For purposes0f comparison, the March CPS (the 'annual demographic:file) laas

been included with reported 'annual social security ea hings and

counts of quarters worked appended.

11 In general, if is riot pos ible to empirically.,distinguishbetween these two models. See. Appendik'A for a discussionof the necessary conditions for identification.

Data collection and preparation have been:carried out by

the Bureau of Census. Westat, Inc. has been responsible for data

.management, preliminary analysis, and development of comparison

groups for the CETA participantS from the CPS. The comparison

groups have been generated by "matching" CETA participants with

their CPS counterparts on a variety of socio-demographic and

past earnings variables, using different prioritieS in the

matching process. These procedures has been used to generate

six (6) comp,rison groups for the 1975 participants and three (3)

comparison groups for the 1976 participants.

The results derived in Section III suggest a framework for

the empirical work. It-is first necessary to estimate p fo each

of several years before and after the participation year. Next, the

data should be pooled in order to estimate the aggregate value o12

This should be done separaEely -for the participants, the

comparison group, and the two combined. Chow tests should be

performed within each group, and across the two groups in order

to determine:, (1) appropriateneSs of pooling p, and (2) the13

appropriateness of the comparison group. : At this point it -ill /

possible to re-estimate the preprogram earnings equatioils ih

Order to,estimate Qt..j. By including a dummy variable for parti

cipatiCn in the pre - program equations; we will be-able to.deter/

mine if for d2. This entire process will be done with

each comparson group in' order to determine which comes closest' to

matching the participants.

12 - See-Appendix B for a consistent estimator of an,agg .gate f)13 Note that it is not necessary that $2 and p are the same across,,the two groups. The Chow tests can be done-by constrainingonly; the o.terr to be the same for the participants and,nonrparticipants-.

- 16

APPENDIX A

Identification of Alternative bdels

For the purposes of this Appendix, we will be using the1

allowing specification of earnings deteination

(1)

(2)

52Yt-2 + Et

PlEt-1 P26t-2 ut

where ut is a random Variable with an expected value of zero.

We will consider the following cases:

52 7 PI =

51 52 P2

P2 0

P1 = P2

51 52 = 0

0

0

First. differencing of equation (1) for cases .11 4Ves the

following equations:

(Al) Yt =1 Yt-1) U- t-1

(Ely Y- Yt_i -1 Yt-1) ut Ut-1

(Cl) Y Yt_l (01*P1) ( ta1-Yt-2 alPi(Yt -Yt-3 )+u

- The X and Z vectors used in the text have been excluded. for thesake of expositional simplicity. In generali. adding them to-equation (1) does not affect any of the results.

2Equations (A1) and B1) are not empir cally stin uishable

If we are unable to reject the null hypothesis that Sipl = 0,

it, would then be necessary to generalize the model in the text

to allow for a second order autoregressive error structure. This

follows since it is impossible to distinguish (D), a second order

autoregressive structure from (C) or (E). To see this, equation

(1) is written below in first differences form for (D) and (E).

(D1) Yt s Yt-1 ''01(Yt-1

(El) Yt Yt-1 = Pl(Yt-1

Yt-2) 02 (Yt-2-Yt3) Ut-Ut_l

Yt-2) ± P2(Yt-2-Yt-3) Ut-Ut_l

So if we are able to accept the null hypothesis that p1 is

zero in equatior (Cl)', then we can conclude that either: (1) the

specification of the earnings function should include a lagged

value of the dependent variable, the disturbances in the

earnings function follow a first order autoregressive scheme.

If we reject the null hypOthesis, then we can conclude that

either: (a) the previous two alternatives are simultaneously

true, or (b) the specification of ,.the earnings function should

include two lagged values of the dependent variable, or (3) the

diSturbances in the earnings function follow a second order

autoregressive scheme, All of these alternatives are

with heterogeneity that changes over time.

These findings can be generalized t

,specifications_of_eguatiOns-(1)- and--(2)

Consistent=

handle more complicated

If Z changes over time in a non-trend like fashion, it maybe possible to identify (A)` from (B) through Z. In general,the observable changus in/Z. (such as age or experience) willnot be sufficient to enable us to distinguish between (A)and (B).

1

APPENDIX B

Consistent Estimation of Aggregate p1

Continuing to use the notation developed in the text.

(1) Ytm--6X-1-(32Zt+Rt-I-c

Rewriting (1) by first differencing gives

(2) Yt-Yt--1'(1 -J1+0t711-Pt-21.1- .(14-iD)Rt_

0 E (1+p)Zt_i p2t_21 P(Yt 1-1rt_2

ut ut-1

Introducing some notional simplification

(3) Yt9Yt71. = 13t +'- t 132Zt P(Yt°1where 6t is an intercept term common to the compariSbn:groupand

the participants, and Rt is a shift in the intercept term for ,parti

dipants. .Roth of these terms are unique to period t. This suggests

that if a pooled version \of (3) were to be estimated, it- would -be

necessary to allow for a separate intercept term for each year, as

well as for each of the two groups The nature of the error struc-

ture in equation makes it ;mpossible to obtain consistent esti-

mates of an aggregate)) by limp _y pooling (3) over time. To. see

this, consider equations (4)-(1)belOW Here.the specific

years that We are concerned ith'have been used in the.snbecri-

ing

(4) Y777 76 677+_77 z*77+p(y96-y7677 76

(5)Y76-Y75 = -76 76 2Z*76+P(Y75-Y74 u76 -u75

(6) Y75-Y74 675 +u75 -u74

R751-62Z 754.0(y74-y73)

(7) Y74-Y73 = 74 R744-2"74+P (Y7 Y72 ) +u74-u73

.- 19 -

Note that possible to pool any two consecutive equa-

tion since this would create negative correlation between the

.error term and p (Y -Yn 1 )_ In fact, no linear combination of-,- .

equations (4)-(7) can completely eliminate this negative correla-

tion. It is, therefo necessary to estimate equations (4)-(7)

as a system of equ , imposing constraints across the aquas

tions to obtain aggregate estimates of p and 62. Ordinary

leditquares estimates will be-consistent but inefficient.

Zeller Seemingly Unrelated-Regression techniques will produce

efficient as well as consistent estimates.

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