ED 085 551

DOCUMENT RESUME

95 CE 000 731

AUTHOR Post, Arnold R.TITLE Enrollment Forecasting Procedures. A Vocational

Education Planning System for Local School Districts.Volume V.

INSTITUTION Government Studies & Systems, Philadelphia, Pa.SPONS AGENCY New Jersey State Dept. of Education, Trenton. Div. of

Vocational Education.PUB DATE Jun 73NOTE 83p.; For related documents, see CE 000 732-5 and CE

00.0 785-8

EDRS PRICE MF-$0.65 HC-$3.29..DESCRIPTORS *Administrator Guides; Community Surveys; *Computer

Oriented Programs; Educational Planning; EnrollmentInfluences; *Enrollment Projections; *SecondarySchools; *Vocational Schools

IDENTIFIERS COMENR; VOCEDENR

ABSTRACTThe document, one in a series to assist in planning

procedures for local and State vocational agencies, describes twocomputer programs, COMENR and VOCEDENR, to be used in secondaryenrollment forecasts. The steps in the procedure are; 1) gather dataon past public enrollment, new housing trends, census data, andcurrent vocational enrollments and feed them into the computer; 2)the computer yields estimates of public school secondary andvocational enrollment by grade and year; 3) the output is evalutedand an estimate of intersystem transfers and institutional enrollmentis added; 4) the new data is fed into the computer; and 5) thecomputer reforecasts and projects enrollment five years into thefuture. The manual covers the administrative procedures forcollecting and processing the data. The program COMENR is forcommunity enrollment forecasting. The program VOCEDENR is forvocational education enrollment forecasting. (AG)

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FILMED FROM BEST AVAILABLE COPY

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NEW JERSEY STATE DEPARTMENT OF EDUCATIONDIVISION OF VOCATIONAL EDUCATION

225 WEST STATE STREETTRENTON, N.J. 08625

with the assistance ofGOVERNMENT STUDIES & SYSTEMS, INC.

3401 MARKET STREETPHILA., PA. 19104

FORE _STINGEMME.Mila

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I

A VOCATIONAL EDUCATION PLANNING SYSTEM

FOR1-4

Lf"N LOCAL SCHOOL DISTRICTS

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urN

Volume V: Enrollment Forecasting Procedures

Produced For

Edison Township

Linden

Lower Camden County RegionalHigp School District

Middlesex County Vocational Schools

Somerset County Vocational Schooland Technical Institute

and

The State Department of EducationDivision of Vocational Education

With the Assistance of

Government Studies and Systems, Inc.

The project presented herein was performedpursuant to a grant from the New Jersey StateDepartment of Education, Division of VocationalEducation under Public Law 90-576, Part C,Section 131, (b).

July 1970 June 1973

Acknowledgments

The Division of Vocational Education of the New Jersey

State Department of Education has long recognized the need

to introduce more science into the art of educational plan-

ning. This publication is an outgrowth of its efforts to

devise more systematic, objective, and precise bases for

program. decisions. The Division has determined, moreover,

that the key to the success of its system is to insure that

the Local Education Agency has an advanced planning capability.

Grateful acknowledgment is given to Dr. Robert M.

Worthington, former Assistant Commissioner of Education (DVE),

for initiating this study and to Mr. Stephen Poliacik,

Assistant Commissioner of Education (DVE), for his guidance

and support in continuing the study when problems seemed

insurmountable. Also, to Former Commissioner of Education,

Dr. Carl L. Marburger, and Acting Commissioner of Education,

Dr. Edward W. Kilpatrick for their support and patience.

Appreciation is further expressed to the Superintendents

of the five LEAs: Mr. Charles A. Boyle, Edison; Mr. Americo R.

Taranto, Linden; Mr. Joseph R. Wilson, Somerset; Mr. Leonard A.

Westman; Lower Camden County Regional High School; and

Dr. J. Henry Zanzalari, Middlesex County Vocational Schools

and Technical Institute for their coope4ation and under-

standing.

Finally, Lo the staff of the Division of Vocational

Education, and particularly Dr. Morton Marqules, Associate

Director, State Division of Vocational Education (Ancillary

Services); Mr. Harold R. Seltzer, Director, Bureau of

Occupational Research and Development; and Mr. Alvin Weitz,

Director of Program Development for their invaluable assist-

ance and insights. To Government Studies & Systems, Inc.,

Mr. Charles P. Cella, Director; Mr. Roger L. Sisson, Associate

Director; Mr. Joseph H. Bosworth, Program Director; and

Mr. Nelson G. Freed, Project Manager for their knowledge

and technical capability so necessary in developing and

testing this planning system.

The principal author of Volume V is:

Arnold R. Post

II

Series Preface

Planning is a universal concept based on the propo-

sition that if you think a bit about what you intend to

do, you are likely to do whatever it is better than if

you don't think about it.. This process of thinking ahead

generally involves gathering information, analyzing the

information and then formulating one or more courses of

action to follow. The planning system presented here

embodies these elements in operational procedures for

planning for school districts.

The Vocational Education Planning System for Local

School Districts draws heavily upon a growing body of

experience in educational planning which has been gene-

rated by Government Studies & Systems (GSS). The intro-

duction describes these concepts. Out of this experience

has evolved a set of planning techniques, particularly

suited by design and through actual use, to enable effec-

tive planning. The bases for and uses of indicators,

planning factors, forecasts, models and others of these

techniques are clearly laid out in this manual as they

appear in the normal course of the planning cycle.

This manual is one of several resulting from a project

to design planning procedures for local and state vocational

education agencies. This manual describes the overall

planning process for LEAs. It is to be used in conjunction

with the following manuals:

iii

Volume I: Local Education Agency Users' Manual

Volume II:

Volume III:

Volume IV:

Volume V:

Volume VI:

Volume VII:

Volume VIII:

Volume IX:

Local Education Agency Users' DataCollection Manual

Local Education Agency PlanningAnalyst's Procedures

State Application Funding Procedures

Enrollment Forecasting Procedures

Procedures for Estimating Adult andPost-Secondary Potential Enrollment.

Job Demand Forecasting Program

Training Materials

Guide to Project Manuals

The most important in(jredients in effective planning,

however, are the people who do the planning. The planning

team itself should include, at the very least, those who

are going to be directly responsible for the execution of

the plan, once developed, and those who are otherwise

directly affected by the plan. People who participate in

the planning process, who see their input take shape in a

plan, tend to be better advocates and implementors of that

plan.

iv

TABLE OF CONTENTS

Page

Acknowledgments

Series Preface iii

Glossary 1

Section I 5

Section II

Section III 17

Section IV 27

Section V 33

Section VI 37

Section VII 41

APPENDIX A

Research Mobility Analysis

List of Figures & Charts

Page

Figure 1 9

Figure 2 12

Figure IV-1 28

Figure IV-2 29

Chart IV-3 27

Chart IV-4 31

Chart V-1 34

Chart V-2 35

Chart VII-1 41

Chart VII-2 53

Chart VII-3 57

Chart VII-4 63

Chart VII-5 63

vi

GLOSSARY

The Glossary which follows is provided so that readers will

know meanings of special terms used in this report. Some terms

will be familiar, but some are statistical terms not common to

anyone except statisticians. We have tried to keep technical

language to a minimum, although in some sections it was necessary

to use a certain amount of statistical terminology.

Age Distribution - the number of people in each age group

among the total population.

Base Case - expectation of what will happen in the future if

the present school programs and staffing policy remain in effect.

COMENR - community enrollment forecaster computer program

which yields prospective public secondary school enrollment by

grade and year for a district.

Community Development - new housing.

Community Enrollment students enrolled in all types of

schools --public, private, parochial--within a particular school

district.

-1-

Entry Status - the year at which students are expected to

enter the school district for which a forecast is being prepared.

EPS - (educational planning system) an analysis process (in

part computerized) yielding among other things the base case

analysis.

Grade Retention Ratio - same as "succession rate."

Input - information entered into computer.

Output - information from computer.

Override - new or judgmental data put into conipiter after

initial run to adjust the final enrollment forecast (override

data is usually supplied by LEA staff).

Persistence Rate - the number of people in housPhold units

in year n+1 who were in those units in year n.

Printout - printed data from computer.

Run - computer processing and printout of data.

/

Sending District - the school district transferring students

into school district for which a forecast is being prepared.

-2-

Service Time Distribution number of years, on the average,

a student remains within a given school or district service area.

Standard Deviation a technical term, in general use among

statisticians, meaning a measure of the spread of the data about

the average, (technically the square root of the variance).

Student Intentions File - information from students on their

next and future year's plans in regard to program selection.

Succession Rate also called retention ratio or survival

ratio, meaning if there are s students in a grade this year and n

is the number of those students who are in the next higher grade

(in the same school) next year then n/s is the succession rate.

Example

year 70-71 71-72

grade 9 10

students 100 90 then succession

rate = 0.9

(from same school)

The Model - the enrollment forecasting plan, in whole or in

part, depending on context (used rather loosely).

Tolerable Forecast Error - the level of error within which

it is possible to forecast realistically, and beyond which

accurate forecasting could not be done.

-3-

Transfer Rate -the number of students transferring from a

sending school to the school district being projected.

Type of Student or Student Type - a breakdown of students

into categories: handicapped, disadvantaged, gifted, regular.

VOCEDENR - a computer program which will yield a first

estimate of prospective public school vocational-education

enrollment by school grade, year, voc-ed program, area and type

of student.

Weighted, weighting - making some information have more

significance than other in the model, for example, more recent

information is viten heavier weight in the analysis than older

information.

-4--

SECTION I

INTRODUCTION

&a,

Introduction

Enrollment forecasting, the art of predicting the number of

students who will attend a given school in a given year, is

familiar to every school administrator. It is a most necessary

ingredient in all planning for educational facilities. Clearly

the objective is to come up with a figure as close as possible to

actual enrollment so that advance planning will be knowledgeable

and realistic. The method of enrollment forecasting described

here will enable administrators to reach this objective more

accurately than in the past, and, further, will enable them to

plan realistically five years in advance.

Secondary Enrollment Forecasting is only one part, although

an important one, of the New Jersey Vocational Education Planning

System Project, which has been prepared by Government Studies &

Systems, Inc. The overall project includes design,

implementation, production of user manuals, training materials,

forecasters, for use by both state and local vocational education

agencies.

While this report is directed specifically towards secondary

enrollment forecasts for the New Jersey Vocational Education

Planning System Project, the forecasting method obviously has

general application for forecasting overall enrollment, or for

any particular enrollment needed.

To use this enrollment forecaster for the first time

requires an initial information-gathering effort by school

administrators and staff. The administrators will be adding their

judgments on the data. Gathering the data and coming up with an

estimate of enrollment and the judgments will go like this: 1)

-5-

past public enrollment, new-housing trends, census data, and

current vocational enrollments will be fed into the computer; 2)

the computer will yield estimates of public school secondary and

vocational enrollment by grade and year; 3) the LEA staff will

evaluate this output and add its estimate of intersystem

transfers and non-household (institutional) enrollment; 4) LEA

,f.eturns the corrected and judgmental data to the computer; 5) the

computer reforecasts using the new data and comes up with a

closer enrollment for five years into the future.

After the initial information-gathering is completed, the

job will then be to feed the computer updated information. The

computer will then, taking into account past and future

projections and new situations, turn out predictions, thereby

freeing admininstrators from this task and enabling planning

officials to get a better overall picture of educational needs.

This manual covers the administrative procedures for

collecting and processing of data. Most LEA's have procedures

already established for similar purposes. The procedures

introduced here are to be interpreted as suggestions for

modifying or augmenting the existing procedures.

The General Forecasting Scheme

One of the most important factors in five-year enrollment

forecasting is new housing planned for the area being forecast.

New housing directly effects population figures. Therefore the

number of new units to be built must be known as accurately as

possible in order to predict enrollment.

-6-

SECTION II

OVERVIEW OF PROGRAMS

Since the distribution of enrollment by grade correlates

closely with the distribution by population by age, it is

possible to develop enrollment estimates by grade on the basis of

expected new housing in the school district.

Public school enrollment constitutes only a part, although

the largest part, of most district's school enrollment. Private

and parochial school enrollments, and student transfers to or

from public or private or parochial schools must be taken into

account. Much of the uncertainty involved in estimating future

public school enrollment results from the variability of such

transfers.

This enrollment forecaster prepares estimates of recent

intersystem transfers primarily on the assumption that both

public and non-public enrollments will grow or decline at equal

rates subject to the pattern of new housing. This assumption is

reasonable in districts where new housing is potentially of major

importance. Its usefulness in areas where this is not true has

not been explored.

-7-

Description of Computer Programs

The flow chart on the next page, Figure 1, shows how the

secondary level enrollment forecaster operates. The community

enrollment forecaster (mom) requires three groups of

information each year for its initial run: 1) how many new

housing units were authorized by municipal officials the previous

year, 2) how many net resident births occurred within the LEA's

jurisdiction, 3) active enrollment by grade K-12 and post-

graduate as of March 31. Active enrollment here means LEA area

resident, non-tuition, non-institution students attending public

schools which feed the LEA schools.

COMENR first generates an estimate of annual housing

increases, using historical data from the previous year's output.

This estimate is then combined with the most recent community

age distribution estimate in order to estimate increases or

decreases in school age population (5-19 years old). From this

estimate a'forecast of enrollment by grade which is consistent

with the housing trend is derived.

The next step COMENR takes is to assume that, in the absence

of intersystem student transfers, enrollment in both public and

non-public school systems would change in proportion to changes

in the community's age distribution, induced by changes in the

housing supply. Any past divergence of actual public school

enrollment from this assumption (including divergences due to

statistical bias) is attributed to intersystem student transfers.

EstiMates of intersystem transfers are then printed out by grade

and year. COMENR calculates a weighted average estimate of

Forecasting ActivitiesSchematic Summary

Past publicenrollment history

LEA policy groupevaluation of pro-spective development,intersystem transfers,and non-householdenrollment: enteradjustments

Fast and prospectivetrends in census,housing and birth data

Forecast enrollmentusing COMENR: yieldsprospective publicsecondary enrollmentby grade and year

Run VODEDENR toyield prospectivepublic enrollmentby school, grade,year, voc-ed pro-gram

Obtain currentenrollment invoc-ed by graderby program, byschool

II Planning system:Base case analysis

Figure 1

-9-

transfers, with weighting arranged to make past year data four

times as significant as four-year-old data.

The standard deviation of transfers by grade is calculated

about the weighted averages; and a tolerable forecast error is

calculated as plus or minus twice these standard deviations. In

the data explored so far, this range of error is adequate to

include all the variations observed. The tolerable forecast

error has been approximately 2 percent of public school

enrollment at the secondary level (grades '7-12, in the

aggregate). The public school percentage of total community

enrollment is also printed out by grade and year.

Outputs are discussed in detail in the next section of this

document.

(The final printed output is a set of index numbers by which

the actual September enrollments, when known, can be extended to

yield estimated grade 9-12 enrollment for the next five years.)

This enrollment estimate is subject to LEA satisfaction that

the COMENR assumptions on housing growth, intersystem transfers,

and tuition and institutional enrollments are realistic. Staff

can provide override information on these items, and COMENR can

be run until all appropriate assumptions are incorporated. (When

final September 30 enrollment figures are entered, the program

will extend them according to the given set of index numbers to

yield a final estimate of fall enrollment by grade and year for

the entire district.)

The next program, VOCEDENR, produces estimates of enrollment

by grade, year, voc-ed program in vocational courses. This is

done for each school and summed for the LEA district as a whole.

Figure 2 is a more detailed flow of the process.

Particularizing the General Scheme

The model deals with five age groups: births, 0-4, 5-9, 10-

14, and 14-19. An assumption is made that population changes due

to changes in the number of households are evenly distributed

within five-year age groups. Thus, if one hundred students aged

10-14 years old are expected to arrive in the community as a

result of new housing, it is assumed that twenty of them will be

10 years old, twenty will be 11 years old and so on. Another

assumption made is that various statewide statistical averages

apply to each district.

The enrollment estimate is based on reported housing and

birth information for the previous year, estimates of new housing

for current and future years, and an average allowance for

intersystem student transfers.

The enrollment forecaster is first run in August. This run

estimates enrollment for April of the coming year and for five

future years. April is chosen since (a) it allows easier

coordination with census data (the census is taken in April), (b)

it represents a good average level between September and June.

(Enrollment tends to decline over the year.) When actual

September enrollment figures for the current year are available,

they are compared to the August run (April forecast), the LEA

reviews the run and the actual enrollment figures and other

actual data, and then stipulates changes, if necessary.

To assure the relevance of the forecast, the LEA should:

Policy

Make adjust

-I-

ments

Make

Overall Flow

Attendance Analysts

Collect and update housing

and population information

Have data keypunched

Run COMENR

Edit printout

s Enter adjustments

adjustments

(if any) (no further adjustments)

Issue overall enrollment forecast

Have keypunched

I

Run VOCEDNER-o,

Edit printout

s- Enter adjustments

Guidance

Collect current

voc-ed program

enrollment data.

Issue Voc Ed enrollment forecast

(to planning process)

Figure 2

-Compare the housing trend in the forecast with reports of

actual building activity since the beginning of the year and

with ascertained plans of major builders in the district.

-Measure the number of estimated intersystem transfers

against non-public school crowding, expansion plans,

expected tuition changes, etc.

-Check the number of tuition students from other districts or

students from institutions predicted to transfer into the

district against actual trends and against a sending agency

or district's estimate of how many they expect to transfer.

To assist in these judgments, the computer prints out the bases

on which the estimate is reached.

In this model, the estimates of prospective housing growth

are designed to be somewhat generous without being unrealistic.

The forecasting goal, here, is to be most accurate among those

who tend to overestimate.

The model is designed to operate for clusters of

municipalities. It is suitable for areas where clusters of

municipalities closely approximate school district boundaries,

provided that the boundaries have not changed for six years and

no changes are expected within the five-year forecast period. If

boundaries are changed, two separate compute- runs must be made.

The reason for using the "cluster of municipalities" boundaries

instead of school district boundaries is that the State census

information used in the forecasts is obtained by censusing

municipalities and not school districts. However, we know of no

case in New Jersey where school district boundaries split a

municipality, so that the "clusters of municipalities" method

-13-

should be applicable to all school districts, with possibly a

rare exception.

Theoretical Background

The factors affecting public school enrollment are complex.

This is why enrollment estimates based on grade retention ratios,

the traditional estimating device, are not accurate except in the

short run. Such estimates, using only internal data, are highly

conditioned by past experience, and fail to take into account

important factors in the outside world. The alternative employed

here is to relate enrollment forecasts to specific geographic

area and its changing conditions.

The demographic model has been named "mobility analysis', and

departs from the traditional natural increase, net-migration

models in several important respects. In the traditional

approach, one assumes that the most recently censused population

stays put. Then one calculates what this population would number

after a few years if certain birth and death rates prevailed.

Final adjustments to account for net migration are then made by

using past biases to project into the future. This method does

not allow for the variations in fertility of migrating population

nor does it provide for migration increases.*

The model employed here initially assumes no new housing in

the community, and subsequently adjusts its forecasts to reflect

reported or expected changes in the housing supply. This initial

assumption allows for both the fertility of migrated population

and the tendency of existing population to spread out over wider

areas as time goes by. Adjustment for housing supply changes is

*See Appendix A-14--

not difficult, particularly since housing development statistics

are generally well reported and available in New Jersey.

References

The rationale for this approach is discussed in Appendix D

of Handbook of Statistical Procedures for Projections of Public

School Enrollment, available through Superintendent of Documents,

Government Printing Office, Washington D.C. 20402, as document

HE5. 224: 24027.

Further discussion is avzilable in the Journal of the

American Institute of Planners, November 1969, and the 1969

Proceedings of the American Statistical Association, Social

Statistics Section, p.216f.

Since these documents were written, the model employed has

been further refined to accommodate housing supply growth in

terms of both apartments and single family developments and to

incorporate information on births. Without these refinements,

accuracy of estimate over the short-run of one to three years

with regard to total population has been at the 5 percent level

or better in 2/3 of the cases.

-15-

SECTION III

DETAILS OF PROGRAMS

COMENR - Description of Output - Refer to example printout at endof the Manual (Section VI)

The critical output appears on page four of the example

printout. For an eleven year span, from five years before the

current year to five years after, the following are printed:

A. Annual Housing Gain (number of new housing units):

There are two options for producing these figures. One4

is for the user to do their own forecasting by

inputting the figures for all eleven years; this was

done in the example case and will be explained in the

description of the "override" feature on page two of

the printout. The second option is to input the

figures for earlier years and let the program do the

forecasting. For details on the method of calculation,

see the comments in the section of the program listing

entitled "Calculate Housing Growth."

B. Community Total Enrollments by Grade:

The first four years of school enrollments for the

total community are printed out as they were input by

the user, for kindergarten through post-graduate

(thirteenth grade). Then follows a printout of the

community enrollment by grade-group (e.g., 7-8) for

those years, calculated by summing the appropriate

enrollment figures. The seven future years'

enrollments are projected by the program, taking into

account the population expected and other factors. For

-17-

details on the calculations, see the section of the

programs labelled "Project Community Enrollment from

POP and ENROPR Arrays."

C. Public Enrollmentz, by Grade:

As with the community enrollments, the information for

the first four years, for kindergarten through post-

graduate, is provided by the user and input to the

program and the grade-groups are calculated by summing

enrollments for appropriate grades. The future years

are projected by taking into account the percent of the

community enrolled in public schools, "transfer rates"

and "succession rates" (see glossary).

The calculations can be found in the section of the

program beginning °Calculate Percent Public, Succession

Rates and Transfers". The calculations for the

kindergarten are done differently than for the other

grades. This is because the basic figures are

calculated on a diagonal, going down grades and across

years, which would leave the kindergarten row

undefined. Therefore, the year to year change in

enrollment for the kindergarten is calculated on the

basis of the year-to-year change in the total community

enrollment for kindergarten, taking into account the

average transfer rates.

-18-

The programs begins by printing out the data which the user

has provided as input.

Page one of the ex'ample printout shows:

A. Persistence Rates by Age Grp:

The age groups referred to are as follows: 1) birth 2)

zero-four 3) five-nine 4) ten-fourteen 5) fifteen-

nineteen 6) total. The term "persistence rates" refers

to the proportion of people in an age group that will

still be in residence next year.

B. People Per Added-Household y Age Group:

These figures are also given by the age groups

described above. The "Technical Details" section

explains how the user is to arrive at these figures.

C. Enrollment Operators by Age-Group_Index (1-3):

Enrollment operators is a matrix relating grade

enrollment to age group population. Here, figures for

three age groups 1) five -nine 2)ten-fourteen 3) fifteen-

nineteen are printed out for each grade from

kindergarten to post-graduate. Again, the calculations

can be found in the "Technical Details" section.

D. CY-2 Population by Age Group:

These are population figures for the year CY-2 (two

years before the current year), for each of the six age

groups mentioned previously.

-19-

E. Community Enrollment by Grade-Index:

These figures are for the first four years of the

eleven year span discussed previously. They represent

the total number of students enrolled in all the

schools of the community, by grade, for each of the

years. They are calculated by adding the public school

enrollments (obtained from the school business office)

to the private school enrollments (usually obtained

from the private school agency offices or the State

Department of Education).

F. Public Enrollments by. Grade Index:

As stated above, these figures, for the first four

years, can be obtained from the school business office.

G. New Housing Figures by Year:

These figures are provided by the user for a five year

period from seven years before the current year. They

are divided, as can be seen in the example printout,

into single-family and multi-family housing units.

Multi-family refers to apartments, dwellings containing

five or more units. Single family refers to all non-

apartment housing units or all dwellings with three

bedrooms or more. This information can be obtained

from the Office of Business Economics of the New Jersey

Department of Labor E Industry.

Page Two of the example printout is a continuation of the user

provided data.

Housing Supply CY-2: This is the total number of housing

units in the community, divided into single-family and multi-

family, for the year CY-2.

Housing Protection Rule: For the same year, according to

whether the actual number of new housing units is greater or

smaller than the expected number, one of two rules for projecting

future numbers of housing units is selected. For details on the

different methods of calculation, see the section of the program

beginning "Determine New Housing Growth." The next two items

printed on page two are Expected New Single Family musing for

CY-2 mentioned above and the Actual New Single Family Multi -

Family Housing for CY-2. For that same year, the Births for CY-2

are input and printed out on page two. The birth data is

obtained from the N.J. Department of Health; birth figures are

adjusted to show place of residence rather than place of birth.

Net infant death figures are also obtained so that these births

will not be taken into account in the future estimates. Both the

housing and birth data are reported by county and municipality,

so that it is necessary for the LEA to sum up the information for

all municipalities in its territory for input to COMENR.

Public Enrollment y Grade-Index for CY-1: As with the

previously mentioned four years' public school enrollments, this

information, which is for one year before the current year, can

be obtained from the schools.

-21-

Override Input for New- Housing Figures by Year: This

feature is optional. If the user wishes to forecast the number

of new housing units for future years, rather than letting the

program do it, the word "OVRRIDE--" is punched on a card just

following the data card with the public school enrollment for CY-

1. This indicates to the computer that the next two cards to

follow will contain user supplied estimates of new housing units

for the seven year period from the year before the current year

(CY-1) to five years after (CY+5), one card for single-family and

one card for multi-family units.

For details on the automatic methods of housing projection

calculation used in the program, see the section of the program

listing beginning "Determine New Housing Growth Rule". The last

item on page two of the example printout, also only printed if

the override option is used, is a reprint of the new housing

data, from seven years before the current year to five years

after. This completes the printing of the user input data.

All input data is punched on cards, according to the format

specifications in the section of this report entitled

"Preparation of Data Inputs", and submitted with the program

cards to enable the computer to produce the rest of the output.

The actual order and setup of the cards for the whole forecasting

system will be discussed in "Operation Instructions ".

Page Three of the example printout has a table of population

figures by age group for one year before the current year to five

years after, projected by the program. The calculations take

into account persistence rates and effects of new housing. The

-22-

next line of print on page three represents the effective birth-

rate for the same seven year period, based on the total

population for the year, by applying the effective birth-rate of

the previous year. The section of the program in which these

calculations are made begins "Prrject Population (all age groups)

and Births". The last item on page three is the projected

housing supply (total number of housing units) divided into

single-family and multi-family units, for that same seven year

span. The total housing supply is calculated by adding the

projected new housing for the year in question to the total

housing for the previous year (total housing for CY-2 was input

by the user, as you may recall).

Page four of the example printout has already been discussed.

Page Five has a table by grade across the same eleven year span

as shown on page four containing 1) the percent of the total

community school enrollments which refer to non-tuition public

school, 2) the succession rates (see glossary), 3) the transfer

rates (see glossary) and the mean and standard deviation of the

transfer rates for each grade.

Page ais, the last page of the example printout, has another

table of the succession rates by grade, showing the year to year

change on a diagonal.

-23-

VOCEDENR - Description of Output

The main output of COMENR is a table of enrollments (both

for the whole community and for the public schools alone), by

grade and by grade group. VOCEDENR provides for tables of just

vocational education enrollment figures, also by grade and grade

group, separated out by program of study. If the user has

available current program enrollments separated into the

different schools in the district, this program will produce

tables by school, as in the example printout. VOCEDENR takes as

input the total public school enrollments by grade from COMENR,

from the current year to five years beyond. If the user prefers

to supply "override" enrollment information instead of that

forecasted by COMENR, this can be done, as will be explained in

the "Operations Instructions". The formula used for calculation

of the vocational education enrollments is as follows:

Forecasted Enrollment for a Particular Year, Grade and Program =

Current Enrollment Total Public School Enrollment forfor that Grade 6 Program X the Year of Forecast 6 that Grade

The Current Total Public SchoolEnrollment for that Grade

The output, as can be seen in the example printout, simply

gives for each school and then for the whole district ("Total for

all Schools") a table for each grade, by program of study, of the

vocational education enrollments, across the six years just

mentioned, current year to five years beyond. If the user has

not prcvided current vocational education data for a particular

grade (either because there are no vocational courses given in

that grade, or because the information was not available), or for

-24-

a particular program within a grade, there will be no table

printed (or line of print within the table) for that item. The

last table in the output is a total for all schools in the

district and all grades in the schools.

-25--

SECTION IV

DETAILS OF PROGRAMS

Input Preparation

Preparation of Data Inputs A-COMENR

This section deals with the data cards containing the user-

supplied information which is printed out on pages one and two of

the example printout. Exhibit VI-1 is a printout of the data

cards used in the example case, exactly as they are punched. The

chart which follows shows what each of the cards contains and in

which columns the information should be punched. Numbers should

be right - justified within the columns allotted to them. This

means, for example, if you have the number 123 and it is to be

punched in columns 11-20, the card should look like this:

1121315 14 1 %4 1? 18 v5 to

Preparation of Data.Inputs B- VOCEDENR

If the total public school enrollment figures are taken from

COMENR, as was done in the example case, then the first set of

data to be provided by the user is the list of program

identification numbers and names of the vocational programs of

study in the school district. The number of cards is equivalent

to the number of programs, and the cards are punched as follows:

COLUMNS

Chart IV-3

CONTENTS FORTRAN FORMAT

1-5 Any 5 digit and/or letter iden-tification code for program

(A5)

9-24 Program Name (2AB)

-27-

Figure IV-1

Col

.C

ol.

Col

.C

ol.

111

2725

23

CARDTYPE

1

2

3

4

5

6

8

9

Page 1 of 2 pagesFigure IV-2

PREPARATION OF DATA INPUTS - A-COMENR

NO.CARDS CONTENTS COLUMNS

2 GRADE HEADINGS 10 col/grade

These cards can remain as inExhibit VII-5. There shouldbe no need to change them.

1 RUN HEADING 1-80

Any title which the userwishes will appear at thetop of every page of out-put.

1 CURRENT FISCAL YEAR 2-5

1 PERSISTENCE RATES 8 col/agegrp. includ-

Punch all 6 age groups ing decimalacross one card. point

2 PEOPLE-PER-ADDED-HOUSEHOLD 5 col/agegrp. includ-

Punch all 6 age groups ing decimalacross each card; one cardfor single-family, one cardfor multi-family.

point

14 ENROLLMENT OPERATORS 8 col/agegrp. includ-

Punch the three age groups ing decimalacross each card, one cardper grade.

point

1 POPULATION 6 col/agegrp.

For year CY-2; punch the 6age groups across one card.

4 COMMUNITY ENROLLMENTS 5 col/grade

Punch all 14 grades acrosseach card - one card peryear.

4 PUBLIC ENROLLMENTS 5 col/grade

Punch all 14 grades acrosseach card - one card peryear.

-29-

FORTRANFORMAT

(10A8)

(10A8)

(6F8.4)

(6F5.3)

(3F8.4)

(616)

(1415)

(1415)

CARDTYPE

NO.CARDS

Figure IV-2 (cont'd)

PREPARATION OF DATA INPUTS A-COMENR(continued)

CONTENTS

Page 2 of 2 pages

COLUMNSFORTRANFORMAT

10

11

12

13

14

15

16

17

2

1

1

1

1

1

1

(optional)

2

(optional)

NEW HOUSING

Punch all five years acrosseach card - one card peryear.

HOUSING' SUPPLY CY-2

Punch 2 types of housingunits across one card.

HOUSING RULE AND EXPECTEDNEW HOUSING FOR CY-2(SINGLE-FAMILY)

ACTUAL NEW HOUSING CY-2

Punch 2 types of housingunits across one card.

BIRTHS CY-2

PUBLIC ENROLLMENT CY-1

Punch all 14 grades acrossone card.

OVERRIDE

OVERRIDE INPUT FOR NEWHOUSING FIGURES CY-1-CY-5

Punch all 7 years acrosseach card-one card/housingtype.

5 col/year

6 cols/hsg.type

5 cols/each

5 cols/hsg.type

1-5

5 cols/grade

1-8

5 cols/year

(515)

(216)

(215)

(215)

The next set of cards consists of the current enrollments in

vocational educational programs, (by school),* by program by

grade. The number of cards is optional. The program will

process as much or as little information as it is given. One

card represents (a single school), a single program and a single

grade within that program. The grades are represented by their

number values, except for elementary which is denoted 'E ', and

Post Secondary which is denoted 'PS'. Seventh, eighth and ninth

grades are punched with a zero before the number, as illustrated

in the chart below:

Chart IV -4

COLUMNS CONTENTS FORTRAN FORMAT

1-2 Current Fiscal Year (last twodigits)

(12)

4-9 District (or School) Code - 6digit number

(16)

11-34 District and/or school name (6A4,A1)

37-38 Grade (1,_..07,08...PS) (A2)

40-44 Program Code (5 numbers and/orletters)

(A5)

46-49 Enrollment (4 digit number) (14)

*school categorization is optional5

Current year, district/school code, program code and

enrollment must be "right- justified" (as explained earlier).

-31-

If VOCEDENR is to be run separately, with "override" total

public school enrollment data provided by the user, the following

8 cards must precede the program list: one card per grade (first

grade through sixth are summed to give a card for "elementary"),

in order by grade, from elementary to post graduate, with total

public school enrollments for six years, from current year to

five years after-years going across the card.

Each card should thus have six numbers punched across, each

number being given five columns, right-justified within those

five columns. See the data printout section labelled "override

total public enrollment figures."

-32-

SECTION V

OPERATION INSTRUCTIONS

The following charts represent card deck setups for running

,,,,.e0MENR and VOCEDENR from source decks on an IBM 360 or 370

computer. If another machine is to be used job contr4)1 language

cards must be changed accordingly.

-33-

JCL to mark endof computer run

VOCED enrollmentdata

Chart V -1

RUN INSTRUCTIONS: CCMENR VOCEDENR FROM SOURCE DECKS

JCL to say morecard data follows

JCL to mark endof program list

Data: Hit ofprogramsof study

JCL to say carddata follows

JCL to receiveenrollmentsfrom COMENR

Program

Fortran JCLfor next program

- -

JCL to pASSenrollmentfigures toVOCEDENR(need thesecards evenif runningCOMENR alone)

Program

FortranJCL for

first -I`

program

//

CURRENT VOCED ENROLLMENT FIGURES IN ORDER BYSCHOOL (IF THERE IS TO BE A DISTINCTION BY SCHOOL)

//FT05F002 DD *

//SYSIN DD *

PROGRAM CODES AND NAMES

//FT01F001 DD DSN=MLENRPAS,UNIT=SYSDA,DISP=(OLD,DELETE)

//SOURCE DD *

VOCEDENR PROGRAM SOURCE DECK

// EXEC FORTGCG

//SPACE=(TRK,(1,1)),DCB:(RECFM=FB,LRECL=30,BLKSIZE=240)

//FTO1F001 DD DSN:&&ENRPAS,UNIT=SYSDA,DISP=(,PASS),

//SOURCE DD *

/ EXEC FORTGCG

CCMENR PROGRAM SOURCE DECK

JOB CARD

If running tt-

two programs,separately,these cardswill runCCMENR; seenext pagefor runningVOCEDENRseparately

Chatt V-2

RUN INSTRUCTIONS: VOCEDENR WITH OVERRIDE INFO PROVIDED BY USERFOR TOTAL PUBLIC SCHOOL ENROLLMENT

JCL to mark endof computer

VOCED enrollmentdata

JCL to say morecard data follows

_

JCL to mark endof program list

Dati; prOiramlist

JCL to say carddata follows

Total enrollmentdata

JCL to say totalpublic schoolenrollment datato follow

Program

1

FortranJCL

9

CURRENT VOCED ENROLLMENT FIGURES

PROGRAM CODES AND NAMES

"OVERRIDE" TOTAL PUBLIC SCHOOL ENROLLMENT DATA

VOCEDENR SOURCE DECK

JOB CARD

SECTION VI

TECHNICAL DETAILS 5 PREPARATION OF PARAMETERS

Procedures fox Estimating Persistence and People-Per-New Housing

Unit Factors

The persistence factore are deduced from data from the past

two census (ten years apart) using linear regression.

(Users are assumed to have access to the necessary statistical

competence.)

Let P2a

= population in age group a in the second of two census

Let Pla

= population in age group a in the earlier of two

census

The age groups of interest are:

1: 0-4,

2: 5-9,

3: 10-14,

4: 15-19,

5: Total population,

6: 0-4 in relation to total population

A sample of about 20 counties with characteristics similar

to the county in which the district exists (and including that

county, if one wishes) should be-chosen. From the census data

for these counties, determine Pa10,

-37-

ca by, regression:

peaa -a10 V

la

for a=6 use

+ haH + ca for a = 1-5

p26

_p610 P25 + h6H + c

6

Here H is the number of new housing units built between the.

census years (including the former); data which is available from

the census.

Assuming that the standard errors are low, the regression

coefficient reasonably high, and the constant terms ca are

negligible, the relationships are a good fit. We can use them to

extrapolate into the future.

The Pa (the 10th rooth of Pal° ) are the persistence

factors. The ha are the people in the corresponding age group

per housing unit. The ha can be used as input to the

enrollment forecaster (unless better estimates for future values

are available from some other source).

P6is called the "generation" rate.

Enrollment-Operations

The census data provides directly the data for translating

population by age group to enrollment by grade group. (The

latest census should be used.) The data by age group will not

add up to 1.0 since not all children are in school (grades 1-12)

especially age groups 5-9 and 14-19.

-38-

The inverse of this matrix will provide data for translating

enrollment by grade to population by age group.

-39-

SECTION VII

PROGRAM LISTINGS

EXAMPLE OUTPUTS

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PAGE 0007

A%0 SMALLEST VALUES

C'i2P

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12't':3 cP3.oc-cLusrER).----

c-c

, _miry- 7.--riargno----Py-murry

rAFT-3-t-.77mr-CL

Li 5

1 E

q I-

--curcFissioN .!.TE RY GRAM,

r-

--7ANSFE,S

FlY

GDADE

._.

i0

cP;ps,- 1%cp.:::

1--

----

';) F

ri -

--1

i750--111' 7E (WTI T-1.1M;i")G-TV. TM MI PC

i '.i

0'

0171

IP6=IPGri

0172

-'

4PITi'-(6,21) IKY.PIyE4PtXr.YFAPPX=6.161

I

.7;

....

C

i

"C C -PRINT NFt.. i-OUSING 3Y HOUSING-TYPE

11-,-

0i A il

A -.1

001-75

C-0 1S40

..Yzr):=6,16

0173

',-;RITF(6.1E20I((NEKH5GIYF4REXFSGTYP), YEARF)'(.6,16), HSGTYP=1,2)

J174

- 1920 FOPMAT

HOUSING 'GAIN,/

".'SING.Fitm.,10X,11170 .,.m0LT.P490.10X,1117)

r 17-1ztrt. 71-70-TC37.-FTITTr'Y-771R r7t-L-

YG

Pr-7G-t-LITTTP.

0176

IC 1:P.10

GPMYEX,-.751;13

S 'O

t

F-U:"tN_IM_G_LEVEL_ 20______. _

__

PAIN . ___ _ _

DATE__2_7222.3____ __ ___23118/_48

_0177

L.COmENR(YEAREK,GRADEX)

0173

IF (GRADEX.CE.

8 .AND. GRAOFX-A.F.

R)

1CU.1NRLyEnFX1151=GOMENPIYEAZFX.15)+L

0174

IF (GPA0EX.G8. 10 .AND. GRADEX.LE. 13)

Cc:1RirreREx,16)=ComFNR(YFARX,1614_

0180

IF (GPAOEX.GE.

8 AND. GRADEX.LE. 13)

_____

1CGMENRIYEAREX117)=COMENRIYEAREX)171+L

. _

0181

IF (GRADEX.GE.

8 .ANG. GRAOFX.LE. 10)

1CEMENPIYAREX,191=COMEN/CYF4RFX,18).1_

0132

IF (GPAOEX.GE. 11 .AND. GRADFX.LE. 13)

_1

GCMENRIYEAREX,191.COMENR(YEA1EX,14)4.1.

_J183

i330 CONTINUE

01B4

1340 CONTINAIG

,-

C C.

01:3

3117

CPRINT COM?UNITY ENROLLMENT BY GRADE AND GR40E-CLUSTER

C

dRITrt6,13501

1350 FTJmAT

TOTAL ENR711.01FNTS BY GRADE')

1i 1860

GPA0EX=1,19

5163

IF IGRNDFX.E0.15

ORAGEX.80.191

PRINT 2

wR711(6.20)

CA-51-176-TPAnEx),(CnriFOTWAREX,GRADEX),YEAREI=6,1b)

u189

0190

1860 CONTINUE

C!

0.4tGw_ArF PFPG:NT-P0H1_IC, cUCCFSSION 2ATFS, AND TRANsFERS

C-Mr) ',FIC41755-50ETOIr4SFEW5--END 1R&VTEWS*T4-2)

41

C

FoR YFAPS

CY-

T6

UGH CY-1.

r.LN

7 flo

Ar.

=-I

N2E

xT

ro,.-

.qc,

1414

FOR

PEDCENT-RusitC

5AG

1-

vr:.cs

ry-4 T;-i-W,uCH CY-1

Lri

-1

;.,.:, 61.f.,-!prin

YT4'ffuGH 14

roR 7-4E OTHERS

C)

i0 t

i-.,/

g..

C..

_0101

.G.11381 YFAREX=6.10

0192

TPNP8E1YEAPFX+1.11=DN9ENIYEAPEX+1.11-1(C3MENR(YEAREX+1:1)

1 1AL

law

.

1/CC!,,,%7,(YEAREX.1))*PuBENR)YeAPEX,1))

01 13

1411 Ci1NT!NoE

j40

_...

'0116

+31.74

0195

!

771 1Ra2

7TV7k7,1-b-

.T5(1)=TS(1)+7RN=nSIYEII;4sFIc,HT

dEIGHT=YF,REX-6

.

i,

7

10197

rlz.;II").T15111+7ANERE.AyB4REx,112awErGHT

' a

0143

1:19,i ri"iriv.1,=

.

31'4'7

0 I,.0

YE:AI-x=6.10

'

/',..-------7.1--.

.---

---;

:: 1.

170

rAS-rs.. 5x =1 , 14

1 a

02-J1

D.-_.c.i7-.!E'!=cY:::.1rX,GEX)

:

1,

0202

IF (O.GT.G.1

-PCTPUP,CY,-.J'EX.GRLD8X)=P1)8FNqIYEAPIX,GRADE4)*100./0

41"

.:2J4

'

CC-NotYiArEY-1,GkA0EX-11

!-

30203

IF CYFAGrx.F0.6 .nr,s.

G8All!FX.E0.1)

GO T3 1870

4A,

__ ..

. __________

----

--5.

73-z

---

nr,L

p5ha

tyl-

-,17

1,A

nra-

lw:0

1.--

7ucT

iN,p

1k-F

T:r

.,;(r

g.!;

(r.x.7.3.)

5!/C%R'rtYEL/rX,7,PAPFX1=61Mi:NRIYAPEX,GPAF)(14.100./11

*

.i

C'235

..

61

.PuRCNIPticaFFx-1,oiftox-1)_

__.

....

6;:-/=Rc(yrx=8X,G4ADE-X1,-T

:40

3,:,4

1-'.(6,-.Y.)- TS(G.PAG,FX)* Tft',,,FT.GHT

it,

J3,10

Tc7.(rPaGEX)=-cSIGQ10EXI+T4J,4WEIGHT

1;.;.;11

1070

i0212

le;.0 cr-,.-.7!).oF

!-.

C

i0

1

i; i!

0

....

,,,ve

C16

4140

...s.

r...1

.,...v

..14.

***4

014M

*044

44i,d

~Zed

akei

libili

atid

ii010

006I

iided

lifir

ser.

ft

0

flAT

= 72223_

2,3118/48

PA.GF 0011_

CwEICHTFc AVOAC,E AND STiNDADD nFv!,rioN

CF.

TcNFps

(IN YEARS

CY-4 TH0CINCH CY-) 1

0.:13

GPADEX=1,14

0214

Av = T5(D0APFX)/10.

3215

vto.

=(TSSii:PADEX1- AV*TS(GRADFX11/9.0

(VAP.L?.0.)

VAR=O.

0217

TS((,:t0FX) =AV

021,

7S5(rFACFX)=SORT(VAP)

0210

1300 CL:NTINUt

C_

.

c

C%LCULATE SUCCESSION RATES, PUBLIC ENROLLMENT, AND PEPCENT PUBLIC

riPYI-A;7 5

CY TH/CUr,H CYr5

7.'1;

17PAi":,-INDEX

7 THuU 13

-

1.1.'..0

1P

1)G'

Y,,AGIX=11,16

.40 ' '1

?u:Ar:,;L 00.:,:a!,

, 1 I= (CT:mENR (YEAR EX, 11/COMN3( YEAR EX-1,1))

'71,E'

1

"-

2..2

l',..) C'NI,1'

'Jr

0:n

r,r'.0,.-.X.2,13

,I7.

51:-

Yr-L2.FXI.,1

....

.

.

J.!..:3

314D

..2.:',

0=cc!,r:;:(yw-:JEX-1,:',;A0cX-1)

IF

(^..;".(%)

cuct.4T(yEAREx,C0A1Ex)=fil.F.4(YkARFX,GPAOEXI*100./0

AA EX ,r.-1-1D-tiyi

i1

.pu,Etiv(rE.4-1,-.:,AnEx-1)

TS(C,PADEX)+.5

0=cr,!.,%:(,(FAIIF.<0-4.AuEx)

Ul

1.

02:10

I',

In.GT.0.)

PCTP.ra(yEAPEx,CnADEi).aUFEvt(YFAQFX,CRADEX)100./0

I'-'

1'

(,2.30

---

:J"'-W

IA

C CN:i..,E:, co:ADE-INDEX

:4

1

pc7p;IFOEF.%0EX,141= PCTPLM110,14)

OZ.i

PUlENPIYEA2EX,141=0.018PCTPuB(YEAPFX,1410C0'E1R(YEAREX,14) +0.5

.

I

02.3

"1910 CONTINUE

1.

C CCAICw ATE

ft,i_TC cNucUmENT rlY CE-C1UTE

nO 103c

YE,10.1.x.b.16

40

0(

1..,20 C.PPIDFX=:2,13

-

L=PuBr%cOr-Ar.F(,r.pADEX)

:------:T57-

rrIG?LnFY.17:7:7.N.Er."-T.71,c-Fa,ITF,x)Frriqu'rElirocifi.

iOK

4vo

32.13

IF (GPAPFx.GE.

B .AND. GRADEX.LE.

91

.

1PLISCN;(YEAREX,15)=MIPENP(YFAREX,151+1.-

IF

(GRADEX.CF. 10 .AND. GDADEX.LE. 11)

1e li

gar

DUilENQ(YEAREX,161=PUPEN0IYEAPEX,16).1.---

.

IF IGI:nEX.(,E.

a -IND. Gqan;x.Lc. 13)

i1

--PU1N7TYCA,77.VX-,-171=P1513,N),(fE

,if)"

3241

1 ;

IF (GP11E.X.OE.

8 .AND. 'GRA0FX.LE.

101

1PUSENP(YEAREX,1R)=PUBENP(YEAREX,18)+17

3242

IF IGFAnEx.6F. 11 .4N1. GRAVFX.LE. 13)

_

PIMENRIYFAREX,1,1)=DURENBIYEARCX,1114L-------

C243

1,120 CONTIWF

1 q5, T rrri

rt

C

01IPLIC Ft:PCLL.ENT BY GRAD

AND CPADE-3LUSTEP

1 -,

::

.

i i I,

41

[

S to

'. .

40

1 I

4f0

1 I

0I

47.,

0245

0746

iivEL

A3 tio /At__

..2

C

WR1

(6TF,1940)

1940 EORMAT

(/1 1,1PU3LIC ENROLLMENTS RY GRADE')

C247

DO 1950

GRACEX=1,19

.

0248

JF (cP4nLx.B,15 011. GRADEX.E0.191

wRITEI6,21

wRITE(6.20)

GROHDG(GRA0EXIOPUBENRCYEAREX,GR4DEXI.YEAREX.6.161

0249

0250

1950 CONTINUE

0251

wpiTF/1,1111)1ELENR(YEAREX),YEAREX=6.111

0252

1111 =oRmAT(05/

02.11

00 1951 GRADEX=3,14

0254

dRITF(1.,1111)1PuRFNRIYEAREX,GRADEXI.,YEAREX*11,16)

1951 CONTINUE

,

C

0255

I41

C rPP/NT

BERrEN7 pumLiC, SUrCESSTON RATE, AND TRANSFERS

1C

W:CLuDING WEIGHTED AVG. AND S.D. OF TRANSFERS

'

1C

OVER YEARS

CY-4 THROUGH CY-1)

___

C.

ALL BY GRADE

C

025:3

PO%('0G,KYQ(Il),IDG

025i

ARI7E(6,7fTOCAREXITTM,FX=6.161

)25

413.(TF(6.1n60)

J260

1960 Fop:, A*

.('.' ,Q'X.'AVE

S.D.

AA

0261

0202

;Ol"Fl6i1q70)

--1976Eor,WA7

(/1

PuBCIr

OLC-Art DE CommbiaiyqciCii.

L4-

1SuCCEES1r4

LND ToaNSFrPS...$)

Ct

IPP0

ClADFX=1,14

,--

.44117(6,2?)

!:40W,C,(1,1ADEXY.OFT0111 (yEA.EFX, GP ADE11, YEAPEX=6.161

13266

w-ItTE16,27)

G--,.Ow;c/c,:Anrx).t:C'IErtyF.%4Ex,GRADEx1,YEA4Fx=6,161

LEI

,(6,2:1

0Hoc,/ c..?AnCX1. -=7.=P S I YE:-4:7X,GR ADEX 1 ,YEA4E X=6.16I,

1T Sl GRADE x1

TS

ci C

.P.1

0=X

IA i

.j.')

Cr"( T-r-.ur---

II. C

i.

'P, I

N"

C;(

CC

ES

SIO

N-:

TE

.TABLE

Dv CoADF

.01T

F(6

.11

ow.r

wcY

R(1

1) ,1

0C02/0

IPG=1PG+1

00!!1

v1217E16,1,190)

1910 5-GkM4T

(/' .,,SUCC,ESSION P.:TES W GqADF (READ nIAGUVALLY)./

1,wr.-.7.0m1)

1W

) 20

)0r.;::(''', =1,13

1 A

0.2/ )

AS TY4..C77.161

L/STYR.16

"DC /0.7:3

.YPAPFX=6,LASTyR

427f

MIF

F.(YrAPFX)=1.F13

[F (YEtPqX.F0.11)

XwCPK cyrAp=x)-100.0

C0.79

IF

(Yrt.PrX.LF.11) O TO 2000

rnP(11;C9e1EA-YEAPFX+11)

1..;:"32

/YEAR EXTETOJR-ENTrnrr- A R-EX7C,;, ADEX)41.007,77D

?OW

) C

tNrr

lIF

17E

(4.

22)

- C

RO

HD

C(G

P405

X)

,Ner

gicK

CY

7A1F

X)

YEAPE X=6 ,LA STYR1-

2010 CCNTIMJE

)'A=1.-7(6,1) AUNVOG,KYR(I1),IPG

0236

STO

P02,;/

7MTI

0

iV 6..C./ L

77%/0:TY,P::7 r-r,(7,:r7r:/: RkFri:rsENROLLmFNtS FY SCHOOL BY cQUE OR

IC'A6E Cc:CUP rfiR EACH PROGRAM gnP CURRENT YEAlICYY TO CURRENT YEAR

.1.5

C(YS) USTIC

!PUT FRCm CCMFNR FnR TOTAL ENR.711_44ENTS

C ,rF(erAR0-.RA1r.) TorAL ENROLLAENTS_FRCM COMENR

PRNYIPPO6RAM,4) &PRAY OF pRoG04m NAmcs;

COATA ON couRFNT

EN

RO

LLM

EN

TS

:_

.

ICY CUPPFNT YEAR

RSCHL FCHlrL 10 F00 SCHOOL BEING' READ IN

C.

CC;ArF

IN THE FO;M E

READ IN AL0Ht

PR:SIRAM(A-N) READ IN ALPHA

CCoPRENT ENROLLMENT FOR THAT yFAR,SCHOOL. G* 10E AN0 ',Pm:0AM

1f

FOR INPUT

0.1°

115:

112,1X,16,1X,6A4M1,1k,A2,1%,11,1X,14)

Alk

3C

04,-111

ID IS STOt1") IN cOirnL, RaFv1OUS scilonL.NAAE IN SPvNAm

cTESTING ARRAYS:

4 17y(P)

rliTs IS uSED TO DErF0mINE prolnER SUBSCRIPT FOR ALPHA GRAOF.

C.PPY(151 THIS IS USED

OETFRMINF PRQPFR SUBSCRIPT FOR ALPHA PROGRIM In

FLAilS(13) loGICALvI ELEMFNTS ARE SET TO .TPUE. IF CqRRESPONOIN7.

GRADE

GzADF

ICTS Fn' PARTICULAR SCHOOL BEING P,OCEcSFD: THIS IS

7:1

r.v%Trl

TAH_gs RFINO PRINTED PUT

TFEJ

FP

4ENO OF OA-A- POINT OUT LAST TABLr AMP rALcuLATF

TOT/IS

:-.-tyFtc,G7nE,PRuGPAv.) ENROLLmENT FORCASTED.F1P

AR.wricuLAR 5r.iinOL BY

;;PP06./AM r(1° CY TO Ys; ALGOPITH4 R10 CALCULAfinN.:

Fo7RE,NT

nY /ATIO Or TJ'AL EN'ArLLMc%T Pm. Y112 IN

F:.Lzi..LL4ENT F-OP CY

'17rrrec.,,,.:z.,1.-)c,n)O.:-.1 TOTAL CF FF FOR AIL SCHOOLS

'

TGpFrlyr:%:,pc:,) TOTAL Cr TO'F" FOR ALL GIADFS

-

T(.:7P(Y7.141 TOTAL C.Vt7R

ALL nRry.RAms OF EACH yFt.R, FOR

A PA,TIrIn AP

:CF'L

CP1. LIv

cRnip

1,71-GtAc4 TrIA,.1I,FF(6,13,301/2340.0/,T)TFFI6,13.301/2340,0/,

7-.,,,Fc-10,7'Cl/IROAO/fTCTPR(6)/6,-0/,CY.GR,Y7,PR,T.CmnOL.PS:HL

7) ,FVPCL .SAVNAM.17)

_

LIT

L7t-AC!Li-1 FLTeX/13//1.1 .-141-37%/,ENT/Ji:VALSF./

4)

F=0

;F:,1

FRP° CCMENR

))''

In !=I.3

;41

)11.1

i',AC(1.1)(7*F1YR.I1.Y0=1,61

.))11

1 Fi0mAT(1615)

3)12

CJN-Psu-7..-1.1 TO N. AND t,AMFS

Co C 15 C=1,30

PFAO(5,151,END.1661(Pv.NY1I.J1,J=1,31

151 Fr=.ATIA5,1x,?!i9)

15.cinT!NUF

'

17,6-TOPROC=T-1

CREA!). AN INPUT CA0n

21 v7AfM5,2,Mr=2002).CY.RSCHL.SCHNAM,GRADE,P4AC,ENPCL.

e)1)

2 FC'imAT112,1N,16,1X.644.41.1X,A2,1X;A5,1X,141

40

.1

41

cIE rIPST

THPflUGH. STORE SCHOOL

AN

DSC-4001 t!AME IN vAcIABLEs FOR

CP,ET/101/5-SCW.111-TKM=

3321

IFIA.EC.11 Or T') 202

CIF hFt. sCHCGL, C9 TO OUTPUT SECTION "FOR- 'PREVIOUS' SCHOOL--

IF(*SCHL.NF.SCH)OL1 CO TO 1000

WA

IN.

_72271_

71/20/1-4

PAGE 0001

0

!0

1

Chart VII-2

Program Listing - VOCEDENR

0 9I

0 0

...

'4 1

0032

41 FLAGS( q).. TRUE.

:t0A70113027TraoF.---

1:

IIP

G335

43

:LLAAGG::111:):::::

0334

.

-- -

3)33

_ _

_ _

.

!V G_LityL

20

.

mAIN

72223

cm_f

uLA

TF

s.u

Rsr

o10T. F35 Gv.A0E; _5FT (*,OPPES1,341-1ING

AG

C123

24 PO 25 1=10

jc(GRA0r.FO.GDY( 1)1 GO TO 30

L:J25

'

25 CONTINHF

-

332c.

GcA

l-c-r

0027

F-L

&G

S(G

PA

nE)=

.TP

0E.

C.)

26r (Gz AOF.F0.2.11R.GPADE.E0.3)

GO

TO

41

0029

F(GP3OF.F0.4)

GO

TO

43

0330

,'

IF(G

rk.,.

0F.G

F.5

.AN

D.G

RA

CE

.LE

.7)

GO

TO

44

0031

Go

-ro

3?

21/20/14

PAGE 0002

.0.):-.7

FL 4GS111 I ---Tzt.;9.

I4,.

la

0":38

FL AGS 121.. TPUE.

o.13

-.)

Gn 'To 32

-

0340

,44 Ti .1C5c(11).-.TQiiP.

FL AGS11.21,- .TPOS.

.

C)42

,.:L.AGc(13 )=.Tp.Hr..

:.

-- ____

-- S

OF

7S. c

-frt

-pT

-r(la

-n-c

cn4-

-4

AM

:).f. 3

1, or 3;

1.....-1,NoPqnG

_-

IF( Pc AG. FC. PoNY ( 1,1) )GO T040

qi.

1)45

334b

0144

35 CON:1kt.*

.

.:1-, ITN 3,1771 PqA0'

1Mk

:4

U047

177 ..,--na m..k7 (1 1 ppnr,p i4 1.::Jmpr,t

., A9.. NOT IN L 1ST Fos THIS 0151'111:T.

s K IP

rraP 0 Arti

L-4-!Y---ki-F-x-r--

.

1 0

.

.

034A

6:149

G^ TP 21

4c)

P-'!.-.G -.1

I,.;

3sTo[v,FT,:z1T

T., cF Ctn., '-'PENT YFII,..'

Ln .1

gs ..70))J

GAz:.

!!.

.,J0:1

1:f'

f ! 0

1;1:

F ,P

w'':

,1,7

IT C'..

,r;''

t;-T

,Pri

c,)+

FN20

1-I

---- .77

-----.--"- f: .; t ,-

::

-, T

: -,-

,,--f

-

10

CJ52 . -

---

' '. 74

I ,-2,r..

0053

-rt 1 ,:.!:.,!.:',.7,Plii701=EN4C1*(7FI 1 ,GRA1F1/ ITFI 1,GRADF1.1. )1

-

.154

75 70TFPII ,GcAOF,P406)=TOTEF I T

, GRAPE ,PRoG1f EcI 1 'CPA fl=. ',ROG/

-0

CGL. PACK AND

r..' FAD NEXT INPUT CM r1

r.

0)55

^.

Tfl

70

'

n 2-

.,CAM{

..r.)

,..7-

-t4

41)

0.".57

3" 20:5

15t:=1. 7

=L P

co-;

,C.

-: 24

- -

- "-C - .-IIITPUT

7!1N: ;10ST fp:AC.113,TE

FV

IOLL

AD

ITS

FO

R--

Gq4

GE

- G

RO

UP

S

'II--

---.

----

0-3-

1-1-

----

00o3

100n Pr.'

1010 P= 1.NOPV_IC

-17) -a-y.

30

00.,2

00 1010

03o3

1 ;:0 X.rr I Yo,GP .PR1

_

1J304

IF( cl.GE.2.ANo.r,R.L F.3) 'GO TO 1011

3 0

-036

5-

--101:1- 'IF IGR.GE.4-.NO:GP .LE .71- GO TO 1012

10112

11- 1::,: .1F .2.ANO.r,4.1.-7.71'

Go

TO 2013

1----'--: .-,7r------- -171I3-1T1-0,,z-7:7.7.V":;;--.TE-741-1;1717-113r4

.ii 0

JO6S

10114 IF I 0P .Gr.5.ANo.GR .LE.7) GO

TO

1015

G0 TO 1010

.

r_

1

"

00,J9-

--

:-

-

1J11 iFI VP ,9,P:.1=Fr CYP,1014- Nox

1.41 v,

3071

- -

- -

TriT

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-- ---

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GO TO 10113

1014 f.P(Y° t 10 .PP I=FF( YR.10,r; )1INOX

72223

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.PAGE

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1 ! ,.0

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1010 CONTIAUr

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0.-1

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0..)

i',1r

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1,34

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4

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2114

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2t7

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3.00

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A

3.0

2.17

000.

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7x1?

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1100

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4414

10

CY

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1-6

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107

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1

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475

474

671

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626

554

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432

434

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CUPFENTYEAR= A972

PAGE

4

-1

41

1967

1969

1969

___1

970

1971

1572

1973

1.97

419

75.1

976

1977

_A

nt.:U

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560

600

610

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600

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600

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340

516

351

680

780

780

780

800

800

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593

910

939

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1068

1139

1207

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169

879

898

931

990.

1060

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12.60

1320

2843

863

892

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939

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1068

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1270

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1197

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101.31 100.00 100.00 100.00

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1973

1974

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19 72 (CURRENT FISCAL YEAR)

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(PERSISTENCE RATES)

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3.50) - (PEOPLE - PER -ADDED - HOUSEHOLD)

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(HOUSING SUPPLY CY-2)

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516

(ACTUAL NEW HOUSING CY-2)

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750

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600

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(OVERREDE INPUT FOR NEW HOUSING FIGURES

Chart VII -5

Data Printout-COMENR

Current

PKINTooT:

Sch:c1

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ri ccala r

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Vor School Name.

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Data Printout-VOCEDENR

APPENDIX A

Edited by Robert E. Coughlin

Research ReportMOBILITY ANALYSIS

Arnold R. Post

Mobility analysis is described as a technique more usefulin small area demography than traditional methodswhich rely on conc.:pts of natural increase and netmigration. The proposed model relates to observationsthat in the absence of new housing- construction, localpopulations are likely to decrease. The advantages oftraditional analysis in dealing with development of agedistributions are preserved.

Population analysis often seeks to estimatethe impact of major components of population growthfor a given place. These components are usually con-sidered: natural increase, resulting from births anddeaths of people; and net migration, resulting fromtheir comings and goings. Traditional cohort-survivalmethods of analysis treat these components as thoughthey were independently generated in time (naturalincrease) and space (net migration). In areas as smallas or smaller than a metropolitan area, this treatmentmay be quite deceptive.

Traditional analysis defines primary clusters of peo-ple by geographic unit. An alternate approach, "mobil-ity analysis," considers the household to the primarypopulation cluster. Geographic analysis, however, maybe done in terms of households so that, for a givenarea, mobility analysis offers a method of simultaneouslyworking conditional demographic solutions in time andspace.

The first part of this paper identifies' elementary flawsin the logic of cohort-survival analysis and points up aseldom noted difference in naturalization proceduresthat makes a simple joining of census returns and vitalstatistics invalid for small areas. The second part ofthis paper describes the nature of mobility analysis.Thirdly, a conjectural analysis is developed as a basis

Arr..04 R. Post has been on the staff of the Government StudiesCenter at Fels Institute, lJniversity of Pennaylvania, for thepast aineteen years and during Much of that time has beenresponsible for demographic analyses and estimates fornumerous municipalities.

RESEARCH 11SPORT: POST

for judging the reasonableness of statistics that havebeen derived. The fourth part outlines the major stagesin calculation and presents some statistical findings.

Categories and Shortcomings of Traditional AnalysisMeyer Zitter and Henry S. Shryock ' performed yeomanservice when they applied the U.S. Census Bureau'sf.tamponent Method 11 to arrive at their estimate ofthe known 1960 populations of forty-six large metro-politan areas on the basis of 1950 census returns andlater data on vital statistics and school enrollments.Their fi..iings revealed a marked downward bias inthe estimates and some rather large individual errorsrelatUig in particular to the population under ten-years-old. Although the authors took a dim view of theirfindings, they did not question the basic concepts em-ployed. These findings, I think, do relate to conceptualshortcomings.

Component methods imply two categories of people:natural resident and migrant. Regarding the compo-nents of growth they generate, a standard text '2 puts itthis way: -Migration is not considered in the calcula-tion of natural increase. In 1960, the United Stateshad a natural increase (which excludes migration) of2,545,000 because . . ." births exceeded deaths by thisamount.

Actually, of course, the same types of vital eventshappen to people of both dasses. The treatment ofmigrants as sterile and immortal constitutes one ele-mentary flaw in the logic of cohort-survival methods.The second \basic flaw, which is apparent at the smallarea level, is failure to allow for attrition among naturalresidents as they enter the migrant category.

Now, if people become migrants by moving about,it is clear that there must be some procedure by whichmigrants become natural residents again. Otherwise,we would have run out of natural residents long ago.Migrants \ are naturalized when determination is madeof their proper place of residence. There are two pro-cedures for migrant naturalization: (1) census takersnaturalize the population, all at once, every ten years;and (2) vital statisticians naturalize persons individ-ually and immediately on the report of a vital event.Since migrants, too, bear children, the honest demogra-pher has difficulty in applying the concept of naturalincrease to anticipate the census \taker when the vitalstatistician 4.applies the data.

Exception is taken here to the standard definitionquoted above. The generally recognized problem fordemographe'fs in estimating net migration is actuallypart of an equally difficult problem in estimatingnatural increase. It would foster greater accuracy toredefine natural increase, taking migration into con-sideration. The information system required to makethe definition operational, however, would have to behighly complex.

Alternatively, it may be more reasonable to apply adifferent rationale, particularly since, at the local level,

417

net migration is constrained by land use patterns.which are not sufficiently. reflected in traditional anal-ysis. Housing unit methods of estimate are sensiti%eto these «instraints, but they du not yield age distribu-tions.

The Nature of Mobility AnalysisMobility analysis is, by and large, a synthesis of com-ponent and housing unit methods of estimate. Thetechnique is based on the insights of Robert M. Reams,supervisor of many special municipal censuses con-ducted by the U. S. Census Bureau in 1957 and 1958.

Reams had taken part in the New York City censusof 1957, which revealed a completely unexpected lossof population since 1950, especially in Manhattan.Careful investigation showed that many of the samefamilies were still living in Manhattan but their chil-dren had moved to the suburbs. From this, Reamssurmised that current population should be estimatedby making some routine discount on the last knowncensus return with an adjustment to be added to reflectchanges in housint, supply. Within his experience alongmost of the eastern seaboard, he found that 1958 specialcensus returns were equal to about 90 percent of the1950 population plus about 3.75 times housing supplychange.

His insights have not gained currency, I suppose,because of their ad hoc nature and because they seemsomewhat contrary to established notions. In estimatingnatural increase, it is assumed, to begin with, that thelast censused population stays pub Since rates of naturalincrease are generally positive, there is a predispositionto expect positive growth trends if other things areequal. Reams' formula, on the other hand, would indi-cate that where the housing supply is quietly stable,a substantial decline of population is underway. Thereis actually a positive implication in the formula; but itis one that undermines the appropriateness of rnalysisby natural increase and migration. The positivfJ impli-cation is that a population over the course of timeshould be expected to spread out over a wider areawithin or beyond a municipal boundary. This disper-sion happens because of an increase in housing needcaused by family formation; and this "natural increasein housing need" will contribute to outmigration ifnot locally satisfied.

Ream's formula is also in conflict with standard pro-cedure for applying housing unit methods of estimatewhere the researcher' establishes a trend for populationper household, then estimates the number of householdsto arrive at an estimate of population. If Ream?formula is correct, the absence of a household gainimplies a drop of about 10 percent in average popula-tion per household in the course of a decade. Othercharges in population per dwelling would be specifi-cally associated with particular changes in the numberof households. The formula has the advantage ofmaking allowance for the transfer of population from

418

an original to an expanded housing supply. It is thisw:iich ,:rites space and time in the analyos.

Sp /c,: Probably the main difficulty with the;011;crfs ot natural increase and migration is that th, ydo out laiivide a standard pattern of /oia/ populatio;ibehavior. The tuncepts are person-specmc and coin.triunity -1,ctific, retpectii ay. What seem to he lice& Iare rniRcpts that arc «imniunity-specific al well :nperson ,specific.

A persoii ;s related to a community by his resideni c;and pia; es of residence offered by a community are

ommunity-specific. So long as almost all thepopulation lives in households and so long as thevast majority of households occupy durable and im-mobile quarters, it is reasonable to define the numberof households as a characteristic common both t' thepopulation and to the community.

Let a community be defined as declining, stable, orgrowing if the net change in number of householdsis negative, zero, or positive. Population changes instable communities would then represent the degreeto which population tends tp persist in a given numberof households. Further population changes associatedwith community instability would then be in termsadditional population per additional household, whichis marginal change. Population growth would consist.;4 two components: persisttr..e. and marginal change.

Conjectural AnalysisNet Parameters Janet Abu-Lughod and MaryMix Foley' estimate on the basis of surveys made dur-ing the 1940's and 1950's that about 1 percent of thepopulation in 1954-55 engaged in household forma-tion. Presumably then, over the decade, stable comma,-nities would be left with .991° or about 89 percent oftheir initial hOusehold population. This figure shouldbe a!,proximately equal to a ten year persistence rate.

It is somewhat more difficult to draw a bead onaverage size of marginal household. Abu-Lughod andFoley indicate that change in family size is one of themost significant factors associated with household gen-eration and taking new quarters. Positive changes areclearly the more pressing, and these come about mostlythrough marriage and birth.

Ned Shilling observes that the ratio of householdheads in a cohort rises as the cohort ages and that fora given age-group the ratio over time is stable.' Hisresearch covers the period 1880 to 1950 and wouldappear to have been confirmed to a high degree in thecensus returns of 1960, at least those which I have in-spected. The number of household heads generated bya cohort reaches a maximum by middle age sincesubsequent increases in headship ratio are more thanoffset by increases in the death rate. Eventually, ofcourse, household heads vanish with extinction of thecohort. Since young children and their parents areassociated with household increase, it is reasonable toexpect average size of marginal household, that is;

AIP JOURNAL NOVEMBER 1969

TABLE 1

1960Age. group

Age - Specific Coe jficteritt of Margtnal Change, if the data are of h:gh quality. School enrollment,,1950-60 (PerJorz Per h.zdtehold) themselves, may ,-nnstitute the best information on

local population trends. Using the enrollment data andWest Regression census cross-tabulations of school children by age andapproximation values

Deptford

_C1 4_

.681, .6655-9 56 I, .560

10-1415-19

-36 .307.307

20-24 .12 .35925-29 .44 .37630-34 .60 .35-3

35-39 .40 .34040-44 .2845-49 16

.254

.17350-54 .12 .14155-59 .12 .09460-64 .04 .04765-on .00 .12J

Total 4.00 4.146

From analysis of a random sample of 20 Pennsylvania Col,nties.b Migrants under 10 years of age were estimated in proportion to

migrant adults of child - bearing age, the proportions lx-in ''-w:en forthe Township's total 1960 age distribution.

coefficient of marginal change, to !lave a value higherthan average population per In 1967, averagefamily size in the United States was 3.70, up slightlyfrom 1960's average of 3.67. We can expect thecoefficient of marginal change to have a value at leastthis high.

Since household generation is most closely associatedwith young adults, vo! should expect this coefficient tohave a value less than the average for all families ator approaching maturity. in the source referred to, theCensus Bureau reports an average of 4.38 personshusband-wife families with the husband under 45.We can therefore expect the coefficient of marginalchange to lie in a range between 3.7 and 4.4; and theprinciple of insufficient reason bids us take a roundnumber in the middle, leading to a conjectural estAateof 4 persons per marginal household.

Thus, we have fashioned a rule thumb that cor-responds well with Reams' formula for estimatingpopulations of small areas. If P(t) refers to populationat time of most recent census; P(t-10) to populationat time of previous census; and dH, to change in num-ber of households at the interim, we have )\

P(t) =.89 P(t-to) +4 dH. (1)This rule of thumb is not significantly different fromfindings by multiple linear regression utilizing datafrom census tracts in the Philadelphia Standard Metro-politan Statistical Area. See relation (2) helow.Practical Considerations If the rela;.on holds ina general way, it does much to simplify analysis oflocal population trends since the increase :A householdsrepresents the only unknown to be defined. Buildingpermit and school census information may be pertinent,

RESEARCH RiseORT: POST

grade, a relationship between enrollment trends andnet change in households can be found.

A distinct practical advantage offered by this methodof analysis is that lay people find change in housingsupply a familiar and pertinent variable and :an relateit to contexts of building activity and land useconstraints.\Age-Specific Parameters To return to more gen-eral matters, since headship ratios are age-specific andstable and since the processes of household generationare also age-related, it is not unreasonable to expectpersistence rates and marginal changes to be age-specific.

)We should expect low persistence rates among teen-imagers (about to set up housekeeping for themselves)

and higher persistence rates among children and youngadults. The highest persistence rates may well beamong the middle-aged, whose household heads 're-main nearly constant for ten to fifteen years, or so.

In small communities experiencing rapid populationgrowth, one might expect the relative age distributionsof marginal changes and net migratory increments toapproximate each other. If so, then application of thepercentage age distribution of the net-migratory incre-ments to a IL ,se of 4.0 (0--e conjecturally estimatedaverage population per marghaal household) shouldyield an approximation of age-specific coefficients ofmarginal change.

The net-migratory age distribution for West Dept-ford Township, Glou-ester County, New Jersey, is

typical of the suburban townships in the developmentfringe of the Philadelphia area. The Township in-creased in population from 5,446 to 11,152 between1950 and 1960. Table 1 offers a comparison betweeninformation derived from the Township's data and find-ings from regressions on a sample of is Qnty randomlyselected counties in Pennsylvania, most of them ruraland several of them losers of population. The chief dif-ferences are among teenagers and young adults, groupsthat are presumaE, subject to particularly low persist-ence rates, and among the elderly. The latter may relateto a lack of apartment development in the Townshipduring the 1950's.

Persistence rates were simultaneously derived fromthe regressions on the random sample of twenty coun-ties. Then are compared with national survival ratesin Table 2. Application of persistence rates shoulddefine a residual population in a stable commuaity. Itis reasonable to assume that the processes of dying andmovement to new quarters are independent within aparticular age group, that is, if a person is ten-years-old,his prospects of survival are not apt to be greatlyaltered by the family's taking new quarters. Thus, anage-specific persistence rate can be taken as the productof the appropriate survival rate and a "net remaining"

419

TABLE 2 Age-Specific Per Capita Rates, 1959 -60

Agegroup

. Net NetSurvival Peristence remain Death depart-

rate a rate b mg rate rate ing rate

(a) (b) (e=_-b/.4) (I-a) (1-

0-4 1.I.:20 .818 802 -.020 .1985-9 .988 .751 .76i .012 .239

10-14 .96? .575 .598 .038 .41J2.1

15-19 .)91 .635 .641 .000 .359

20-24 1.014 .739 .708 -.014 .29225-29 .996 .754 .757 .001 .24330-34 .989 .798 .807 .011 .19335-39 .950 .829 .873 .050 .127

40-44 .929 .803 .864 .071 .13645-49 .927 .807 .S75 .0'.; .125

50-54 .859 .782 .910 .141 .09055 -'9 .871 .756 .868 .1:9 .132

60-64 .790 .666 .843 _10 .15765-on .464 .408 .880 .530 .120

Source: U.S., Bureau o; the Cel,,,ts, Current Population Report, P.-23,No. 15, March 12, 1965.

b From analysis of 20 Pennsylvania Counties.See note a.

TABLE 3 Tentative Estimating Equations for Poin 20 PennsylvaL a Counties, 1950-1961'

fation by Age Group

Persons byage group

1960

, Persistence ratetimes

1950 cohort

Population perhousehold timeshousehold incre-ment, 1950-60,

(dH)

Xi (0-4) =: 7 .665Xs (5-9) 8 .1- .560Xs (10 -24) .818 Y, (0-4) + .356Xs (15-19) .751 Y. (5-9) .307X. (20-24) .575 Y, s 10 -14) .359Xs (25-29) .635 Yt (15-19) .376X7 (30-34) .739 Y, ( ) .354X. (35-39) .754 Ye, (25-29) 340X. (40.-44) .798 Y, ( 3034 ) .254,Xi. (45-49) .829 Y, ;1;5-39) ,173

(50-54) .803 Ys (40 -.44) .141Xu (55-59) .807 Yss (45-49) .094Xu (60-64) .782 Yu (50-54) .047X14 (6549) .756 Y (55-59) .041Xis (70-74) .666 YI3 (60-64) .035Xis (75-on) .408 Y,. (65-on) .044

Note: fs(Ys) is the product of the ila cohort's persistence rate,an age-specific birth rate, and the number of persons inhe 1950cohort. "Z" indates that these products are to be added togetherfoe the six indicated i-values. In the regression analysis, X, and X,were taken as functions of Y4, (i = 2, . , 14) and ZY4,(1= 3 , , . , 14), respectively, in combination with dH, yield.ing generation rates of .091 and .0§6, for the first two 1960 cohorts.The determination of proper age-specific birth rates involves averagir-g over both time and age and has not, been attempted in thisresearch to date.

rate, with the complements of these rates being thedeath rate and a "nrt departing" rate. The applicationof net departing rates, then, should yield an agedistlibution of population generating what has beenreferred to as a "natural increase in housing need."

As tan be seen in Table 2, persistence rates are muchlower than survival rates. The negative death rates arean anomaly and relate to age groups where errors ofunderenumeration in the 1950 census were more sig-nificant than th.: actual death rate. The net departingrate is clearly of greater significance than the deathrate for all age groups under forty-five. These tworates approximate each other for ages forty-five to sixty;and the death rate is more significant for the populationover

If a community is losing households, then, it willgenerate an out-migratory stream, wh'cli would havetwo components: those in "natural need" of shelterand those whose needs are more nearly preferential.In a community gaining households, some of those innatural need (on net) would not enter the migratorystream. If enough households were added, none of thefootloose population would be obliged to leave; andthe net departing rate could then be termed a mobilityrate. Such terminology would seem appropriate at thenational level. "Mobility analysis" therefore suggestsitself as a good name for procedures relying on theseconcepts of persistence and marginal change.

Statistical Findings and Estimating ProcedureTable 3 lists a first attempt at establishing age-specificparameters for mobiiity analysis. Each line of the tablerepresents an estimating equation for the age grouplisted in the first column. Calculations proceed in fivesteps:

1. The age groups in the initial population aremultiplied by, the appropriate persistence rates to yieldestimates of surviving population ten or more years oldremaining in the initial number of households.

2. Age-specific birth rates modified to apply topopulations of both sexes are arttlied to the residualpopulation to estimate persistent population under ten.

3. An estimate is developed independently ofthe comminity's ten-year gain in households.

4. The coefficients of marginal change are eachmultiplied by the ten-year gain in households to providean age distribution of population in the added house-holds. (In view of the established change in birthrates since 1960, it may be desirable- to modify theestimate of marginal population under ten-years-old.)

5. The two components are added together.

Data from the 427 census tracts outside the city ofPhiladelphia, but within the Philadelphia StandardMettopolitan Statistical Area (PSMSA) as of 1950,were also analyzed with respect to aggregate (non-age-specific) population and housing changes. Theestimating equation for aggregate household populationin occupied dwellings is only slightly different from the

420 AIP JOURNAL NOVEMBER 1969

TABLE :'apulation,. 1966 Jusar.1!)

PSA1SA eft:mate.

Burl r.

RepOiledP( 1960

1,0.1

Estimatedp( 6)o)

.116

100

Percentageerror of

dli estimate

- 1.3(hewer, 198 f, 195.2 I.-11cLu are, Pd. 5 +1.6 5;3.7 -- 1.5

Monigomrry. 199.h 511.8 3uPhd.idelpha. Pa. 1,946 5 1.894.8 _2.7

195 2 19 Li 0.4

Camden, N.J. 385.9 ;82.8 -0.8Gloucester. N.J. I 3 1;0.5 - 2.4

Total of countyestimates

1,20(.2 -1.1

Philadelphia Standard Metropolitan Statistnal AreaInclusion of the constant trim by adding 28 persons pet census tract would

lessen the negative bias by about 23,000 persons. 'Hie constant term, howeNer, isnot statistically significant.

rule of thumb base' on conjectural analysis {Relation(1)}; it is

P(1) - -.89 P(t -10)+4.1 dH. (2)

An estimator was also derived with respect to changein total housing sup,* (ITH), which includes vacantunits; it is

P(t)=.89 P(t-10)+3.92,./TH. (3)

Another analysis was made distinguishing betweenmajor components of the total housing supply. WithdApt referring to increments in apartment units (thosein structures with five or- more units) and dSF refer-ring to increments in sinz,le family units (actually, allothers), we have

PM= .90 P(I-10) +3.94 d.SF +2.68 (4)

Standard errors for these relations are less than 400persons, or 7.5 percent of 5.300. the tract average inhousehold population as of 1960. Constant terms weresmall. Relation 2 was the most precisely defined, hav-ing a standard error of about 350 persons with 95percent of the errors of estimate less than a standarderne i'.

The impression one gains from "-his type of analysis,as currently applied to Philadelphia, is that the city'spopulation is now between 1.85 and 1.95 million, some5 percent down from 1960's population of 2.002 mil-lion. School enrollment data indicate a gain of about20,000 households (by 1970) whereas about 50,000would be necessary to stabilize the population total.Other estimates of current population that I am familiarwith indicate small gains for the city since 1960. Thespecial census of Manhattan in 1957 proved that alarge city can lose tens of thousands of peOple a yearwithout anyone being very much aware of the changeon a day-to-day basis. I suspect the same sort of thing

RESEARCH REPORT: POST

has happened in Philadelphia since 1960.One finJ table may be of particular interest to statis-

tical geographers. Relation 2 was applied to data forcounties in the Philadelphia SMSA with the resultslisted in Table 4.. The results are reasonably accurateeven for Philadelphia, whose census tracts were ex-cluded from the regression analysis which establishedRelation 2. The item of interest is that the tine-grainedanalysis seems pertinent to coarse-grained data, a con-dition not necessarily expected. It is common forstatistical findings to depend critically on the physicalextent of the areal units sampled.'

SuggestionsPerhaps all that can be sa:d at this time is that thestatistical analysl> inspired by Reams' observations seemsto have been justified and that the conjectural analysishas not been disproved.

Without going into an extended discussion of statis-tical findings, it can be noted that the results have beenderived by multiple linear regression analysis and thatall the coefficients listed are of very high statisticalsignificance. In addition, constant terms are small, asare standard errors; residuals are well distributedaccording to normal expectations.

The data have been drawn from slums, rural hinter-land,and all types of areas inbetween, and include thelarge cities of Camden, New Jersey, and Chester,Pennsylvania. The population in the set of census tractstotaled well over two million.

It is suggested that if estimates of current populationare far out of line with application of these formulae,it may be desirable to consider- the results only asindicative of a range of uncertainty. Unfortunately,there can be no guarantee that Pennsylvania's experi-ence during the 1950's is appropriate to conditions inthe 1960's. An important development of the 1960'shas been the heightening of social tensions in manycentral cities. If such tensions have increased themobility of mature families, persistence rates may wellhave been lowered in some areas with a concomitantrise in the size of marginal families in other areas.

Author's Note: Acad,mic rights reserecd by :Lb. author.

NOTES

1 Meyer Litter and Henry S. Shryock. 'Accuracy of Methodsof PrCparing Postcensal Population Estimates for States and LocalAreas," Demography. I. No. 1 (1964), 237 and Table 8.

11 Warren S. Thompson and David T. Lewis. ob-lem.f (Fifth Ed., New York: McGraw-Hill. 1965), p. 10.

a Janet libu-Lughod and Mary Mix Foley. "Consumer Suite-gies." Part 11 of Nelson Foote, et .:!.. i1 o, my Chai.es andHoming Cauitraints (New York: PACirau-Hill. 1960), Table19, p. 99 and p. 100 (footnote).

1 Ned Shilling, "Net Household Formation-A DemographicAnalysis" (unpublished Master's essay, Columbia University. 1055),cited by I ti.ns Winnick, American Housing dud Itr Us, (NewYork: Wiley and Sons. 1957). p. 81.

5 U.S.. Bureau of tile Census. Corrent Population Report, P-21).No. 173 ( June 25, 1968), Tables 1 and 5,

6 See. Duncan, Cuszort, and Duncan. Statistical Geo,grai:q.Problem.;, in Analyziug Areal Data (Glen, tie, Illinois: Free Pres:,1961),

421