Demographic Methods

8/7/2019 Demographic Methods

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Demographicmethods

Temple University AmblerCommunity and Regional Planning

CRP 410 Planning Methods

Professor Kurt Paulsen

November, 2005



Demography

• The scientific study of human populations,primarily with respect to their size, structure anddevelopment

• For planners, we would want to include: location



Demography and planning

• 53 P.S. § 10301.2

– “In preparing the comprehensive plan, the planningagency shall make careful…analyses of housing,

demographic, and economic characteristics andtrends.”



In re Petition of Dolington Land Group and Toll Brothersfrom the Decision of the ZHB of Upper Makefield Twp.,

839 A.2d 1021(Pa.2003)

• “The periodic analytic process employed…is, inour view, an entirely appropriate method for amunicipality or multimunicipal jointure to meet itsobligation to provide for the proportion of regionalneed for higher density, multi-family housingfairly ascribed to it. Implemented conscientiouslyand in good faith, this method will ensure thatland is available for development of anappropriate variety of housing types on a

continuous basis.”



Demography

• To demographers, you only do a few interestingthings in your life (undergo a “demographicevent”– Be born

– Give birth– Move

– (Attract a migrant)

– Die

• The rest is details, I guess…



Demography

• This gives rise to the 3 major components of demographic analysis:– Fertility

– Mortality

– Migration



Demography

• Each of these components can be modeled ascomplexly or simply as needed.– Simple e.g.: Calculate “crude” rates

– Complex: disaggregated regression model of migration

decisions by age, race, sex, education, and economicstructure

– Complex: simulation models







Demography - components

• What influences fertility?– Age

– Education

– Economic status

– Rates and timing of marriage/cohabitation– Religion

– …and many others




• What influences mortality?– Age

– Gender

– Income/Socio-economic status

– Genetics– Behavior

– Access to health care…..

– ….and of course many more




• What influences migration/immigration?– Age

– Economic structure/opportunities

– Public policies

– Quality of life, cost of living– Climate

– ….and many more of course!




• You probably noticed that age plays a significant role inall three components. Demography frequently employslife-cylcle/temporal models. People’s probability of givingbirth, dying, migrating, etc. exhibit clear age effects.

• An important way demographers model “age” is to groupall those with a similar age into a “cohort.”



Demography

• Three basic types of demographic analysis usedby planners– Descriptive – tools, data, and methods to describe the

population of an area

– Trends analysis – look at how demographic data haschanged over time

– Projections – estimates of future population andpopulation structure



Descriptive Demography

• You can access/acquire demographic data for aplace from a number of sources:– PASDC

• http://pasdc.hbg.psu.edu

– Census• http://www.census.gov

– Health Data:• Pennsylvania: Bureau of Health Statistics and Research

• http://www.dsf.health.state.pa.us/health/CWP/view.asp?A=175&

• National Vital Statistics System:http://www.cdc.gov/nchs/nvss.htm

http://pasdc.hbg.psu.edu/

http://www.census.gov/

http://www.dsf.health.state.pa.us/health/CWP/view.asp?A=175&QUESTION_ID=228721

http://www.dsf.health.state.pa.us/health/CWP/view.asp?A=175&QUESTION_ID=228721

http://www.census.gov/

http://pasdc.hbg.psu.edu/



Descriptive Demography

• After acquiring data for a place, you can calculateall of the descriptive statistics we learned earlierin the course, and use the statistics to tell a storyabout a place



Descriptive demography

• Demographic-specific methods– Age-Sex pyramids

– Dependency ratio = children + seniors divided by totalworking age population

• Or: non-working population divided by working population• Some researchers specify under 15 + over 65 as

“dependent”



Age-sex pyramids

• Age-sex pyramids are graphic representations of the age and sex distribution of a population. Theshow the percentage of a population for each sexby age category/cohort. Typically they present

data in 5 year bins, although this is dependent onyour data.



Bin data – a note

• A lot of demographic data we have is notindividual data, but rather counts of the numberof people who fall into a certain category.– Travel time (25 to 29 minutes)

– Age (birth to 4, 5 to 9 …)

• Some of our descriptive statistics have biaseswhen used on bin data



Bin data – descriptive statistics

• Consider calculating the mean travel time for anarea based on knowing the number of people whofall into each category of time intervals. How dowe do it?

• To perform calculations, we have to makeassumptions about the distribution of data withinthe bin.

Consider this travel time bin: 339 people in Richland Twp



Consider this travel time bin: 339 people in Richland Twp,Bucks Co., travel between 25 and 29 minutes to work

25 2927

339 people?

OR?



OR?

25 292726 28

67.8 people



Bin data

• How do our two options differ in contributionsto overall average and standard deviationcalculations?

• Recall the formula for an average:

n

x x x x

xn

...321+++

=

−

Option 1 = 339*27 =9153

Option 2 = 67.8*25+67.8*26+…67.8*29= 9153



Bin data

• So, in this example, these two options areequivalent in their effects on the overall mean….

• But what about the standard deviation?

• Ok, but what if, instead the real data looked likethis:

Non symmetric distribution within a bin



25 292725 292725.8 28.1

300 people

39 people

Non-symmetric distribution within a bin

25.8*300+28.1*39=8835.9



Bin data

• What are we left with? We have to makeassumptions about the distribution of data withinbins, but we have no a priori way to determiningwhich is “best”, and with the understanding that

our output is dependent on our assumptions.



Bin data strategy

• State your assumptions clearly• Easiest solution is to assume all members of the

bin share the mid-point value.

• If exact results are important enough, calculate at

least 3 ways and present all 3 results (sensitivityanalysis)

• You could chose all lower values and then allupper values for upper and lower “bounds”

• Don’t believe standard deviation calculationsfrom bin data!



Back to age-sex pyramids

• Age-sex pyramids provide a visual representationof population structure. Consider the followingthree national level pyramids from the U.S.,Bangladesh and Germany.









Age-Sex Pyramids

• You can also produce pyramids for populationforecasts, to show the underlying demographicstructure.







Constructing an Age-Sex Pyramid

• See Excel Spread Sheet…Population Example.xlson class server

• Step 1. Download age-sex data from the CensusBureau website or other data server.

(factfinder.census.gov)– Find variable P12 (Census 2000): Sex by age (total

population)

– If you wanted to, you could find sex by age for differentracial/ethnic groups



Age-Sex Pyramids

• Step 2. Unzip downloaded data, and transposedata into columns.

• Step 3. Clean data such that it is 5-year age binswith consistent labels.

•Step 4. Multiply Males by –1 (so on left side of pyramid)

• Paste in format appropriate to Chart Wizard

• Make stacked Bar Chart. (second option on barchart chart wizard)



Special Excel Trick

• Reformat Axis to eliminate negative numbers.Double click on bottom axis, chose “number” tab,chose custom, in box type:

0;0

Click Ok.



Population Example

• Calculate Male/Female ratio, overall and for eachage category. Graph this to show general trends.

• Calculate overall dependency ratio. (For example= 0.532) This means there are 53 dependents for

every working-aged person.

MALE/FEMALE RATIO BY AGE LOWER MACUNGIE



MALE/FEMALE RATIO BY AGE, LOWER MACUNGIE

TOWNSHIP, LEHIGH COUNTY PA, 2000

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 to 4 5 to 9 10 to

14

15 to

19

20 to

24

25 to

29

30 to

34

35 to

39

40 to

44

45 to

49

50 to

54

55 to

59

60 to

64

65 to

69

70 to

74

75 to

79

80 to

84

85

plus

Age Cateogy

M a l e / F e m

a l e R a t i

MALE/FEMALE RATIO UNITED STATES 2000 CENSUS



MALE/FEMALE RATIO, UNITED STATES, 2000 CENSUS

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 t o

4

5 t o

9

1 0 t o

1 4

1 5 t o

1 7

1 8 t o

1 9

2 0 y e a

r s

2 1 y e a

r s

2 2 t o

2 4

2 5 t o

2 9

3 0 t o

3 4

3 5 t o

3 9

4 0 t o

4 4

4 5 t o

4 9

5 0 t o

5 4

5 5 t o

5 9

6 0 t o

6 1

6 2 t o

6 4

6 5 t o

6 6

6 7 t o

6 9

7 0 t o

7 4

7 5 t o

7 9

8 0 t o

8 4

8 5 a n d

o v e

r

h d l i



Demography – trend analysis

• Often, an analysis and visual presentations of thedemographic trends in a community can tell astory and highlight significant planning issues.

• Recommended:

– Tufte, The Visual Display of Quantitative Information– The Planner’s Use of Information

T d i i l i



Trends – quantitative analysis

• One of the more common simple quantitativeanalyses of past trends is to calculate “rates of change” (works not just in demography)

• Rate formula:

t

t 1t

X

X X r

−=

+

C l l ti R t



Calculating Rates

• The population of a census tract in MontgomeryCounty grew from:– 1990 population: 2371

– 2000 population: 3353

4142.0

2371

23713353=

−=r

We read this as saying the population growth ratefrom 1990 to 2000 was 41.42 percent

G th t l



Growth rates example

• If the growth rate from 1990 to 2000 was 41.42percent, what was the average annual growthrate?

• If you said 41.42 / 10 = 4.142 percent per year,that would be….WRONG – but a common mistake

• Why? COMPOUNDING!!!

R t f th ( d d li )



Rates of growth (and decline)

• UGH!! Well, we might as well learn them now,they’ll come in handy later in Cost BenefitAnalysis

• Open Word Document: “Growth Rates andDecline Rates.doc”

S1

t V This is the



So….

• So what is the average annual growth rate of population for this Montgomery Census Tract?

10

−

= n

V

V g

03526.01

2371

3353 101

=−

= g

formula

We read this as a 3.526 percent average annual growth rate.

Growth rates



Growth rates

• Calculated growth rates can be used for:– Estimating population between two censuses

– Projecting population based on constant growth rateassumption

Final word on growth rates



Final word on growth rates

• If r is the rate of population growth, then apopulation will double in

ln(2)/r years!

Population Projections and Forecasts



Population Projections and Forecasts

• Clarify some definitions, keeping consistency withCensus Bureau:– Estimate: indirect measurement of population for the

past, between Censuses, based on births, deaths andmigration figures.

• Released for July 1st of previous year

• Projections: estimates of population for futureyears.

Projections and forecasts



Projections and forecasts

• How “accurate” do I have to be?– What is the cost of being wrong? Is the “error

function” symmetric?

– What is the cost of acquiring additional information andanalysis to produce a more accurate projection?

• All estimates, projections and forecasts aresubject to potential error. Open Excel sheet:“forecasting.xls”

Population Projections



Population Projections

• Two basic types– Top-down

• Applying constant rates

• Curve-fitting/extrapolation techniques

– Bottom-up

• Cohort-component model

• Distributed housing unit method

• There are also regression and structural models, notcovered in this class, but of use in many applications

Top down projections




• Constant rate projections:– 1. Calculate average annual growth rate, using most

recent data. (e.g. 1990-2000).

– 2. Apply growth rate to future years.

– Incidentally, this is also called a “geometric” curve




Top-down projections

• Constant increment projections:– 1. Calculate total number of people added per year.

– 2. Apply constant increment to future years.

– Also called “linear” curve

Curve-fitting/extrapolation




• Idea is relatively straightforward:– 1.Plot the data

• In this case, population from previous time periods

– 2. Fit a curve to the data• Made easier in Excel with “insert trendline”

• Problem: “insert trendline” has limited options

– 3. Derive the equation of the fitted curve

– 4. Use the equation to calculate future values.




• Step 1. Plot the data.

US Population

0

50

100

150

200

250

300

1790 1810 1830 1850 1870 1890 1910 1930 1950 1970 1990 2010

Year

P e r s o n s ( m i l l i o n s

Curve-fitting



Curve fitting

• Step 2. Fit a curve.

• Types of Curves:The most commonly used curvesin population analysis are:

– Linear, Geometric, Exponential, Modified Exponential,n-degree Polynomial, Logarithmic, Logistic, andGompertz.

– The number of possible curves is virtually limitless!

“Curves”



Curves

• No, not the fastest growing women’s fitnesschain….

• A “curve” is simply a mathematical formula whichdescribes the shape of the relationship betweendata points.

• Characterized by at least 1 parameter.• Given x, tells you what y equals.

• Let’s look at: “Population ProjectionsWorksheet.xls” on class server

Curves



Curves

• 1. Linear

bxa y +=

a=intercept, b=slope

Curves



Curves

• 2. Geometric

x

ab y =We can do a logarithmic transformation to get:

b xa y lnlnln +=

Curves



Curves

• 3. “Power” (so called in Excel)

bax y =

Again, a logarithmic transformation can make this moreestimable

xba y lnlnln +=

Curves



Curves

• 4. Polynomial

2cxbxa y ++=

Called a 2nd degreepolynomial because

highest exponent is 2

Can create an n-th degree polynomial:

n xexdxcxbxa y α ...432 +++++=

Curves



Cu es

• 5. Exponential

• 6. Modified Exponential

bxae y =

x

abc y +=

Curves



• 7. Gompertz

xb

ca y=

Curves



• 8. Logistic

xabc y

+

=1

Fitting curves to data



g

• See examples on Population ProjectionsWorksheet, “fittingcurves” with population datafrom US.– Graph data

– Fit curve

– Get equation

– Extrapolate

Bottom-up projections



p p j

• The most commonly used in planning is the“cohort-component” method

• Cohort=age group

• Component=the three components of

demography (fertility, mortality, migration)

The Master Demographic Equation



•Put all three components together:

onOutmigratin Inmigratio Deaths Births POP POP t t −+−+=+1

Cohort Component Technique



• Step 1. Get age-sex data• Step 2. Acquire “vital records” data

– Birth rates

– Death rates

• Step 3. Calculate survival rates.• Step 4. “Age the survivors” – move to next bin

for next period

• Step 5. Calculate births

Cohort Component Technique



• 6. Allocate births to males/females• 7. Project Population

• 8. Model migration as residual.– -problem is we rarely have age-specific migration rate

AGE MALES FEMALES MALES FEMALES0 to 4 579 504

5 to 9 753 666 574 504

10 to 14 694 747 753 661



10 to 14 694 747 753 661

15 to 19 662 589 694 747

20 to 24 347 316 642 589

25 to 29 384 414 347 316

30 to 34 530 578 384 414

35 to 39 676 753 530 578

40 to 44 808 868 671 753

45 to 49 846 917 793 863

50 to 54 823 834 841 907

55 to 59 627 657 808 834

60 to 64 458 462 593 637

65 to 69 404 418 448 452

70 to 74 358 422 366 418

75 to 79 215 308 324 402

80 to 84 134 192 178 25285 plus 87 190 113 223

“Age” each population after applyinga survival rate

Cohort-Component Technique



•Go to Excel spreadsheet:

New_and_Improved_Cohort_Component_Model.xls

• Gives you an examples of the technique with and withoutmigration.

• Caution: Example is a PA Township, but townships aregenerally too small for accurate modeling without otherassumptions

• Generally, model larger areas such as counties or regions

Migration as a residual



• Recall the master demographic equation:

• Can be rewritten as:

onOutmigratinInmigratioDeathsBirthsPOPPOP t1t −+−+=+

Migration NetDeathsBirthsPOPPOP t1t +−+=+

Migration as residual



• In our cohort component technique, we haveprojected populations based on births, deaths,and age-cohorts.

• The only “unexplained” component is netmigration

• Can assume net migration is the difference foreach age cohort between the projected andactual.

Migration as residual



• For example, take 1990 data to project (usingcohort-component) 2000 data

• Compare each age-cohort, 2000 actual and 2000predicted

• Difference is net migration, 1990-2000• Apply net migration data (either constant

increment or constant rate) to cohort componentmethod to project future (2010) population

Migration in cohort-component



• Problems: Migration is cyclical so past rates arepoor estimates of future rates.

• Modeling migration as residual might actuallyreflect model error or variation

• Is the best available technique, however, for thetype of data currently available

Migration Data



• Alternatives exist: acquire detailed migration data fromCensus or othersources:http://www.census.gov/population/www/cen2000/migration.html

• Problem: no internet sources of migration by age-cohort for small-areas. Census released “Migration

DVD” on October 30,2003 for $70, but some datadisclosure/confidentiality issues

• Pennsylvania State Data Center has files available as of October 2003 at the county level. See:http://pasdc.hbg.psu.edu/pasdc/products_and_services/Publications/migration/Migration_Flow_Tables_2000.ht

ml



Census Bureau



• Paper on Population Projection Techniques,recommended reading for further methodology:

• “Methodology and Assumptions for thePopulation Projections of the United States: 1999to 2100.” Population Division Working Paper No.38, US Census Bureau.

• On class server.

Census Bureau – sub-county populationestimates and projections



• Distributed Housing Unit Method

• Utilize Building Permits Data, mobile home shipment data,and estimates of housing loss to provide intercensalestimates of housing units.

• Then apply occupancy rates and average persons per

household (PPH) to derive population estimates, usingcounty population estimates as controls.

• County population estimates conducted through the“administrative records” method.



Distributed Housing Unit Method



• Continuous updating of housing unit counts through“GUSSIE” (Geographic Update System to SupportIntercensal Estimates)…..wow!

• From the time of the last census, Census estimates(through a complicated methodology) residentialconstruction, mobile home placement, and housing loss…using building permits data, Survey of Construction, andapplying “loss rates” from the “Components of InventoryChange Survey” (1993)




• Before controlling for county population changes, theformula is quite simple:

Where POP is the estimated population, HU is the estimatednumber of housing units, OCC is the occupancy rate, andPPH is people per household

PPH OCC HU POP t t **=

Yeah, so what…who cares



• Why do we care so much about the method theCensus uses to estimate sub-countypopulations???

• Estimates are used in Federal and State fundingallocations….its all about the $$




• How accurate are these estimates/projections?• Source: “Evaluation of 2000 Subcounty Population

Estimates” Greg Harper, Chuck Coleman and JasonDevine, Population Estimates Branch, Population Division,U.S. Census Bureau. 2002

• Census used to estimate sub-county populations withadministrative record-component method until 1996, butreplaced with Distributed Housing Unit Method in 1996,presumably because more accurate.




• Mean Absolute Percent Error (MAPE) is much higher forsmaller areas.

• Mean Absolute Percent Error (MAPE) is much higher forareas with more rapid growth/decline rates

• Many municipalities in the Philadelphia suburban region

are either fast growing or relatively small.• Mean Absolute Percent Error for Pennsylvania is 7.8

percent, below national average of 12.4 percent.







Demographic Projections



• All projections and estimates are subject to errors

• How important is it to get it “right”?

• Every method has its strengths and weaknesses.

• Every method makes assumptions.

• Demographic projections, in the “textbook” world,feed into the land use planning and needsanalysis

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