Population Forecasting

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Population Forecasting

• Time Series Forecasting Techniques

Wayne Foss, MBA, MAI Wayne Foss Appraisals,
Inc. Email wfoss_at_fossconsult.com
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Extrapolation Techniques

• Real Estate Analysts - faced with a difficult
  task
• long-term projections for small areas such as
• Counties
• Cities and/or
• Neighborhoods
• Reliable short-term projections for small areas
• Reliable long-term projections for regions
  countries
• Forecasting task complicated by
• Reliable, Timely and Consistent information

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Sources of Forecasts

• Public and Private Sector Forecasts
• Public California Department of Finance
• Private CACI
• Forecasts may be based on large quantities of
  current and historical data

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Projections are Important

• Comprehensive plans for the future
• Community General Plans for
• Residential Land Uses
• Commercial Land Uses
• Related Land Uses
• Transportation Systems
• Sewage Systems
• Schools

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Definitions

• Estimate
• is an indirect measure of a present or past
  condition that can be directly measured.
• Projection (or Prediction)
• are calculations of future conditions that would
  exist as a result of adopting a set of underlying
  assumptions.
• Forecast
• is a judgmental statement of what the analyst
  believes to be the most likely future.

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Projections vs. Forecasts

• The distinction between projections and forecasts
  are important because
• Analysts often use projections when they should
  be using forecasts.
• Projections are mislabeled as forecasts
• Analysts prepare projections that they know will
  be accepted as forecasts without evaluating the
  assumptions implicit in their analytic results.

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Procedure

• Using Aggregate data from the past to project the
  future.
• Data Aggregated in two ways
• total populations or employment without
  identifying the subcomponents of local
  populations or the economy
• I.e. age or occupational makeup
• deals only with aggregate trends from the past
  without attempting to account for the underlying
  demographic and economic processes that caused
  the trends.
• Less appealing than the cohort-component
  techniques or economic analysis techniques that
  consider the underlying components of change.

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Why Use Aggregate Data?

• Easier to obtain and analyze
• Conserves time and costs
• Disaggregated population or employment data often
  is unavailable for small areas

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Extrapolation A Two Stage Process

• Curve Fitting -
• Analyzes past data to identify overall trends of
  growth or decline
• Curve Extrapolation -
• Extends the identified trend to project the future

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Assumptions and Conventions

• Graphic conventions Assume
• Independent variable x axis
• Dependent variable y axis
• This suggests that population change (y axis) is
  dependent on (caused by) the passage of time!
• Is this true or false?

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Assumptions and Conventions

• Population change reflects the change in
  aggregate of three factors
• births
• deaths
• migration
• These factors are time related and are caused by
  other time related factors
• health levels
• economic conditions
• Time is a proxy that reflects the net effect of a
  large number of unmeasured events.

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Caveats

• The extrapolation technique should never be used
  to blindly assume that past trends of growth or
  decline will continue into the future.
• Past trends observed, not because they will
  always continue, but because they generally
  provide the best available information about the
  future.
• Must carefully analyze
• Determine whether past trends can be expected to
  continue, or
• If continuation seems unlikely, alternatives must
  be considered

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Alternative Extrapolation Curves

• Linear
• Geometric
• Parabolic
• Modified Exponential
• Gompertz
• Logistic

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Linear Curve

• Formula Yc a bx
• a constant or intercept
• b slope
• Substituting values of x yields Yc
• Conventions of the formula
• curve increases without limit if the b value gt 0
• curve is flat if the b value 0
• curve decreases without limit if the b value lt 0

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Linear Curve
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Geometric Curve

• Formula Yc abx
• a constant (intercept)
• b 1 plus growth rate (slope)
• Difference between linear and geometric curves
• Linear constant incremental growth
• Geometric constant growth rate
• Conventions of the formula
• if b value gt 1 curve increases without limit
• b value 1, then the curve is equal to a
• if b value lt 1 curve approaches 0 as x increases

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Geometric Curve
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Parabolic Curve

• Formula Yc a bx cx2
• a constant (intercept)
• b equal to the slope
• c when positive curve is concave upward
• when 0, curve is linear
• when negative, curve is concave downward
• growth increments increase or decrease as the
  x variable increases
• Caution should be exercised when using for long
  range projections.
• Assumes growth or decline has no limits

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Parabolic Curve
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Modified Exponential Curve

• Formula Yc c abx
• c Upper limit
• b ratio of successive growth
• a constant
• This curve recognizes that growth will approach a
  limit
• Most municipal areas have defined areas
• i.e. boundaries of cities or counties

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Modified Exponential Curve
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Gompertz Curve

• Formula Log Yc log c log a(bx)
• c Upper limit
• b ratio of successive growth
• a constant
• Very similar to the Modified Exponential Curve
• Curve describes
• initially quite slow growth
• increases for a period, then
• growth tapers off
• very similar to neighborhood and/or city growth
  patterns over the long term

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Gompertz Curve
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Logistic Curve

• Formula Yc 1 / Yc-1 where Yc-1 c abX
• c Upper limit
• b ratio of successive growth
• a constant
• Identical to the Modified Exponential and
  Gompertz curves, except
• observed values of the modified exponential curve
  and the logarithms of observed values of the
  Gompertz curve are replaced by the reciprocals of
  the observed values.
• Result the ratio of successive growth
  increments of the reciprocals of the Yc values
  are equal to a constant
• Appeal Same as the Gompertz Curve

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Logistic Curve
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Selecting Appropriate Extrapolation Projections

• First Plot the Data
• What does the trend look like?
• Does it take the shape of any of the six curves
• Curve Assumptions
• Linear if growth increments - or the first
  differences for the observation data are
  approximately equal -
• Geometric growth increments are equal to a
  constant

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Selecting Appropriate Extrapolation Projections,
cont

• Curve Assumptions
• Parabolic Characterized by constant 2nd
  differences (differences between the first
  difference and the dependent variable) if the 2nd
  differences are approximately equal
• Modified Exponential characterized by first
  differences that decline or increase by a
  constant percentage ratios of successive first
  differences are approximately equal

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Selecting Appropriate Extrapolation Projections,
cont

• Curve Assumptions
• Gompertz Characterized by first differences in
  the logarithms of the dependent variable that
  decline by a constant percentage
• Logistic characterized by first differences in
  the reciprocals of the observation value that
  decline by a constant percentage
• Observation data rarely correspond to any
  assumption underlying the extrapolation curves

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Selecting Appropriate Extrapolation Projections,
cont

• Test Results using measures of dispersion
• CRV (Coefficient of relative variation)
• ME (Mean Error)
• MAPE (Mean Absolute Percentage Error)
• In General Curve with the lowest CRV,ME and
  MAPE should be considered the best fit for the
  observation data
• Judgement is required
• Select the Curve that produces results consistent
  with the most likely future

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Selecting Appropriate Extrapolation Projections,
cont
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Housing Unit Method

• Formulas
• 1) HHg ((BPN)-DHUa)OCC
• 2) POPg HHg PHH
• 3) POPf POPc POPg
• Where HHg Growth In Number of Households
• BP Average Number of Bldg. Permits issued per
  year since most recent census
• N Forecast period in Years
• HUa No. of Housing Units in Annexed Area
• OCC Occupancy Rate
• POPg Population Growth
• PHH Persons per Household
• POPc Population at last census
• POPf Population Forecast

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Housing Unit Method Example

• Forecast Growth in Number of Housing Units
• 1) HHg ((BPN)-DHUa)OCC
• HHg ((1935)-00)95.1
• HHg 918
• Forecast Growth in Population
• 2) POPg HHg PHH
• POPg 918 2.74
• POPg 2,515
• Forecast Total Population
• 3) POPf POPc POPg
• POPf 126,003 2,515
• POPf 128,518

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So Thats Population Forecasting
Are there any Questions?
Wayne Foss, MBA, MAI, Fullerton, CA USA Email
waynefoss_at_usa.net