March 19, 2012 Clemons Chapter 6

EXTRAPOLATION AND FORECASTING Method of predicting the value of something in the future Underlying assumption what happened in the past will repeat itself in the future. Formula of Extrapolation Estimated Population (or any other value) = Population in a chosen base year + (the average growth increment between time periods x selected time periods) Source: Clemens and McBeth (2000)

EXTRAPOLATION AND FORECASTING 1960: chosen base year Average growth increments between time periods = (15, , ,500) / 4 decades = 6,375 YearPopulation of Boondocks , , , , , ? 2020? Source: Clemens and McBeth (2000)

EXTRAPOLATION AND FORECASTING POPULATION ESTIMATE FOR 2010 Estimated Population = Population in a chosen base year + (the average growth increment between time periods x selected time periods) Population in a chosen base year (1960) = 25,000 Average growth increment between time periods = 6,375 Selected time periods (from 1960 to 2010)= 5 P2010 = 25,000 + (6,375 x 5) = 25, ,875 = 56,875 YearPopulation of Boondocks , , , , , ? Source: Clemens and McBeth (2000)

EXTRAPOLATION AND FORECASTING POPULATION ESTIMATE FOR 2020 Estimated Population = Population in a chosen base year + (the average growth increment between time periods x selected time periods) Population in a chosen base year (1960) = 25,000 Average growth increment between time periods = 6,375 Selected time periods (from 1960 to 2020)= 6 P2020 = 25,000 + (6,375 x 6) = 25, ,250 = 63,250 YearPopulation of Boondocks , , , , , ? Source: Clemens and McBeth (2000)

EXTRAPOLATION AND FORECASTING Calculate the projected population for 2010 and 2020 by using 1970 as the base year Source: Clemens and McBeth (2000)

EXTRAPOLATION AND FORECASTING Calculate the projected population for 2010 and 2020 by using 1970 as the base year 1970 population = 40,000 Average growth increment = 2, =10,500/3=3,500 Projected population 2010 = 40,000 + (3,500 * 4) = 54,000 Projected population 2020 = 40,000 + (3,500 * 5) = 57,500 Source: Clemens and McBeth (2000)

EXTRAPOLATION AND FORECASTING The table compares the findings of using 1960 as the base year and 1970 as the base year Q: In our reports to the mayor on the new pool, which one should we use for 2020? 2010 projection 2020 projection 1960 as the base year 56,87563, as the base year 54,00057,500 Source: Clemens and McBeth (2000)

EXTRAPOLATION AND FORECASTING A: We should mention both (Be honest, resist the manipulative impulses of elected officials!). Our client may decide to use one vs. the other depending on whether s/he is in favor of the new pool projection 2020 projection 1960 as the base year 56,87563, as the base year 54,00057,500 Source: Clemens and McBeth (2000)

EXTRAPOLATION AND FORECASTING Problems with extrapolation Its assumption that the future will resemble the past Does not account for the changes in the broader context (changes in economy, culture, etc. that may affect the population growth) Subjectivity of the selection of the base year (1960 in this case) Data related problems, such as Increase in population between 1960 and 1970 could be because of annexation (if this is the case, use 1970 as the base year) Source: Clemens and McBeth (2000)