The Ratio Technique• This technique utilizes historic population data for a larger geographic

area to project the population for a component subarea. Using this method we compare an individual county’s population trends with that of a larger area, referred to as a pattern area.

• Because population projections are usually available for these larger areas, planners often project a smaller area’s population based upon its projected share of the pattern area.

• The primary assumption of this technique is that the growth of a smaller area will emulate the growth of its pattern area because a similar set of factors affect both of these geographic regions.

• The usual set of comparisons:For Counties: 1) County to Region or 2) County to StateFor Cities: 1) City to County 2) City to Metro Area 3) City to State

• Two Basic Ratio Techniques:1) The “Simple Method” (Constant Share, Shift Share)2) The Extrapolation Method

The Ratio “Simple Method”• This method takes historical data for a county and compares it to

the pattern area by calculating a ratio. The ratio for each of the observation years is:

County Pop/Pattern Area Pop

• A visual analysis of the trends in this changing ratio provide the evidence for establishing a ratio for the projection time period.

• Then, using population projections for the pattern area and the projected ratio, population projections are generated for the county.

• A convention with the Ratio Technique is to calculate Low, Medium, and High population projections when possible. These different projections are usually taken from the projection set prepared for the pattern area.

• The Basic Procedure is:Step 1) Gather dataStep 2) Calculate observed ratiosStep 3) Project future ratios through qualitative analysis

Step 4) Project future population using ratios

• Constant Share Method: A smaller area’s share of the larger area’s population is held constant at some historical level.

• Shift Share Method: This method accounts for changes in population share over time. This assumes that changes in share between the Base Year and the Launch Year predict future changes in the share.

• Share-of-Growth Method: This method focuses upon population growth, not the share of growth. This method uses a smaller area’s share of growth as the primary means for predicting future populations.

The Ratio “Simple Method”

FLORIDA POPULATION PROJECTIONS 2010, 2020FL Actual FL Low FL Medium FL High

1980 9,746,324 1990 12,937,926 2000 15,982,378 2010 17,373,400 18,942,300 20,321,5002020 18,901,200 21,420,300 23,783,700

Ratio TechniqueLeon County to State Example

Florida Leon Ratio to State1830 34,730 6,494 18.70%1840 54,477 10,713 19.67%1850 87,445 11,442 13.08%1860 140,424 12,343 8.79%1870 187,748 15,236 8.12%1880 269,493 19,662 7.30%1890 391,422 17,752 4.54%1900 528,542 19,887 3.76%1910 752,619 19,427 2.58%1920 968,470 18,059 1.86%1930 1,468,211 23,476 1.60%1940 1,897,414 31,646 1.67%1950 2,771,305 51,590 1.86%1960 4,951,560 74,225 1.50%1970 6,789,443 103,047 1.52%1980 9,746,324 148,655 1.53%1990 12,937,926 192,493 1.49%2000 15,982,378 239,452 1.50%

Assuming a 1.50% Share, Leon County's Projected Population Would Be 1.50%

Actual Low Medium High2000 239,452 2010 260,601 284,135 304,823 2020 283,518 321,305 356,756

Constant Share MethodFlorida Leon Ratio to State

1960 4,951,560 74,225 1.50%1970 6,789,443 103,047 1.52%1980 9,746,324 148,655 1.53%1990 12,937,926 192,493 1.49%2000 15,982,378 239,452 1.50%2010 1.50%2020 1.50%

FLORIDA POPULATION PROJECTIONS 2010, 2020FL Low FL Medium FL High

2010 17,373,400 18,942,300 20,321,5002020 18,901,200 21,420,300 23,783,700

Shift Share MethodSHIFT SHARE METHODBase Year = 1990, Launch Year = 2000

State Actual Leon Actual Low Medium High1990 12,937,926 192,493 2000 15,982,378 239,452 2010 262,100 285,769 306,576 2020 287,116 325,382 361,283

Calculation of the Shift Share(1) Share 1990 1.4878%(2) Share 2000 1.4982%

(3) = (2)-(1) Shift 0.0104%(4) = (2)+(3) 10 Year Shift 1.5086%

(5) = (2)+2* (3) 20 Year Shift 1.5190%

(1)

(2)

(3)

Step 1: Calculate the Shift ShareStep 2: Project the Future ShareStep 3: Calculate the Population Projection

SHARE OF GROWTH METHODBase Year = 1990, Launch Year = 2000

State Actual Leon Actual1990 12,937,926 192,493 2000 15,982,378 239,452

Calculation of the Share of Growth(1) State Growth 90-00 3,044,452 (2) Leon Growth 90-00 46,959

(3) = (2)/(1) Leon's Growth Share 90-00 1.542%

STATE GROWTH PROJECTIONS 2010-2020State Actual Leon Actual Low Medium High

2000 15,982,378 239,452 2010 1,391,022 2,959,922 4,339,122 2020 1,527,800 2,478,000 3,462,200

LEON COUNTY SHARE OF GROWTHLeon Actual Low Medium High

2000 239,452 2010 21,456 45,655 66,929 2020 23,565 38,222 53,403

LEON COUNTY SHARE OF GROWTH POPULATION PROJECTIONSLeon Actual Low Medium High

2000 239,452 2010 260,908 285,107 306,381 2020 284,473 323,329 359,783

Florida Regional Planning Councils

West Florida Regional Planning CouncilEscambia, Santa Rosa, Okaloosa, Walton, Bay, Holmes, Washington

Apalachee Regional Planning CouncilCalhoun, Franklin, Liberty, Wakulla, Leon, Gadsden, Jackson, Gulf, Jefferson

North Central Florida Regional Planning CouncilAlachua, Union, Bradford, Gilchrist, Columbia, Dixie, Hamilton, Madison, Suwannee, Taylor, Lafayette

Northeast Florida Regional Planning CouncilBaker, Clay, Duval, Flagler, Nassau, Putnam, St. Johns

Withlacoochee Regional Planning Council Citrus, Hernando, Levy, Marion, Sumter

East Central Florida Regional Planning CouncilBrevard, Lake, Orange, Volusia, Osceola, Seminole

Central Florida Regional Planning CouncilDeSoto, Hardee, Highlands, Okeechobee, Polk Tampa Bay Regional Planning CouncilHillsborough, Manatee, Pasco, Pinellas

Southwest Florida Regional Planning CouncilCharlotte, Collier, Glades, Hendry, Lee, Sarasota

Treasure Coast Regional Planning CouncilIndian River, Martin, Palm Beach, St. Lucie

South Florida Regional Planning CouncilBroward, Dade, Monroe

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Apalachee Leon Leon RatioTotal County to AP Region

1830 18,608 6,494 34.90%1840 29,271 10,713 36.60%1850 39,476 11,442 28.98%1860 49,470 12,343 24.95%1870 53,774 15,236 28.33%1880 69,724 19,662 28.20%1890 72,505 17,752 24.48%1900 92,880 19,887 21.41%1910 110,824 19,427 17.53%1920 111,552 18,059 16.19%1930 125,041 23,476 18.77%1940 139,931 31,646 22.62%1950 162,741 51,590 31.70%1960 194,295 74,225 38.20%1970 219,915 103,047 46.86%1980 282,837 148,655 52.56%1990 337,522 192,493 57.03%2000 411,486 239,452 58.19%

SHIFT SHARE METHODBase Year = 1990, Launch Year = 2000

APAL Actual Leon Actual Medium1990 337,522 192,493 2000 411,486 239,452 2010 295,043 2020 349,708

Calculation of the Shift Share(1) Share 1990 57.031%(2) Share 2000 58.192%

(3) = (2)-(1) Shift 1.161%(4) = (2)+(3) 10 Year Shift 59.353%

(5) = (2)+2* (3) 20 Year Shift 60.514%

CONSTANT SHARE METHODAssuming a 59% Share, Leon County's Projected Population Would Be

Actual Medium2000 239,452 2010 293,289 2020 340,961

SHARE OF GROWTH METHODBase Year = 1990, Launch Year = 2000

APAL Actual Leon Actual1990 337,522 192,493 2000 411,486 239,452

Calculation of the Share of Growth(1) APAL Growth 90-00 73,964 (2) Leon Growth 90-00 46,959

(3) = (2)/(1) Leon's Growth Share 90-00 63.489%

APALACHEE GROWTH PROJECTIONS 2010-2020APAL Actual Leon Actual Medium

2000 411,486 192,493 2010 85,614 2020 80,800

LEON COUNTY SHARE OF GROWTH PROJECTIONSLeon Actual Medium

2000 192,493 2010 246,848 2020 298,148

LEON COUNTY SUMMARY OF POPULATION PROJECTIONSRATIO TECHNIQUES, MEDIUM SERIES

STATELeon Constant Shift SoG

1990 192,493 2000 239,452 2010 284,135 285,769 285,107 2020 321,305 325,382 323,329

APALACHEELeon Constant Shift SoG

1990 192,493 2000 239,452 2010 293,289 295,043 293,807 2020 340,961 349,708 345,107

The Ratio Extrapolation Method • This method is very similar to the previously discussed extrapolation

technique, except that instead of inputting observed population figures the method calls for the observed ratios to be the inputs.

• Another key thing to remember is that Inputs are a Ratio and the Outputs are a Ratio, so an additional step is required to turn the outputs into population projections that make sense.

• The extrapolation method utilizes all six curves and even uses the same set of evaluation techniques (CRV, ME, MAPE).

• However, some of the “rules” have changed:

1) In areas with declining ratios the asymptotic curves can sometimes be unable to calculate the “best fitting” curve.

2) In calculating the CRV, you do not multiply by 100.

3) Values for the Mean Error will be very low, but still should be compared.

Year Actual Data Projection1940 31,646 19,972 1950 51,590 52,094 1960 74,225 84,215 1970 103,047 116,337 1980 148,655 148,458 1990 192,493 180,580 2000 212,701 2010 244,823 2020 276,944

Y Int -6211595.9Slope 3212.14857

Leon County Linear Regression Projections

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50,000

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150,000

200,000

250,000

300,000

Year 1940 1950 1960 1970 1980 1990 2000 2010Year

Po

pu

lati

on

Actual Data

Projection

Ratio TechniqueLeon County-State Example

Even Number of Observations State LeonYear Actual Data Projection Population Proj Pop

1940 0.0167 0.01728 1,897,414 32,792 1950 0.0186 0.01674 2,771,305 46,398 1960 0.0150 0.01620 4,951,560 80,226 1970 0.0152 0.01566 6,789,443 106,337 1980 0.0153 0.01512 9,746,324 147,383 1990 0.0149 0.01458 12,937,926 188,658 2000 0.01404 15,524,500 217,990 2010 0.01350 17,942,300 242,249 2020 0.01296 20,420,300 264,676

Y Int 0.122065933Slope -5.40121E-05

FLORIDA Leon Ratio to State1940 1,897,414 31,646 1.67%1950 2,771,305 51,590 1.86%1960 4,951,560 74,225 1.50%1970 6,789,443 103,047 1.52%1980 9,746,324 148,655 1.53%1990 12,937,926 192,493 1.49%

LEON COUNTY-STATE EXAMPLEEvaluating the Various Curves

CRV ME MAPE Upper LimitLinear 5.629 0.0000000 4.63% NoneGeometric 5.234 0.0000278 4.51% NoneParabolic 6.654 0.0000000 4.35% NoneMod Exp* 1.503 -0.0001836 5.46% NoneGompertz* 1.482 0.0000022 4.62% NoneLogistic* 1.460 0.0000278 4.51% None

*UL = .05

LEON COUNTY-STATE EXAMPLEYear Actual Data Linear Geometric Parabolic Mod Exp* Gompertz* Logistic*

1940 31,646 32,792 32,724 33,158 32,828 32,788 32,760 1950 51,590 46,398 46,242 46,291 46,478 46,385 46,321 1960 74,225 80,226 79,936 79,461 80,374 80,198 80,077 1970 103,047 106,337 106,043 105,288 106,488 106,304 106,182 1980 148,655 147,383 147,278 147,007 147,440 147,371 147,327 1990 192,493 188,658 189,152 191,157 188,404 188,729 188,934 2000 217,990 219,591 226,384 217,147 218,234 218,901 2010 242,249 245,541 260,266 240,485 242,791 244,165 2020 264,676 270,369 297,012 261,577 265,687 268,061

*UL = .05

Evaluating the Ratio Technique• What are the advantages to this technique?

1) Takes into account regional or statewide factors driving local population changes.2) Regional or state trends are often much more stable than local trends (and stability aids predictability).3) This approach can “smooth out” local population trends, making them easier to fit these trends to the various curves.4) Can utilize high-quality projections developed for larger geographic areas (the pattern areas).5) Can utilize the various sets of pattern area projections to develop Low, Medium and High projections for the study area.

• The primary disadvantages are: 1) The continued assumption that past trends dictate future figures 2) The complexity of the techniques