# Economics 125 – Demographic Analysis and Forecasting, Spring 2021

Problem Sets
Assignment 1 (10 pts.)
1. Compute the doubling time using the exact method and approximation rule for selected cities in North Carolina using the 2010-2019 base period. (2 pts.)
2. Compute the projected 2045 total fertility rate for Alaska using the synthetic method based on the total fertility rate for the U.S. (1 pt.)
3. Compute the projected 2045 total fertility rate for Alaska using the targeting method for two alternatives:
a. Assume an 90% convergence by the year 2060 (1 pt.)
b. Assume a 50% convergence by the year 2060 (1 pt.)
4. Interpret the exact formula for doubling time for the cities of Wilson and Polkton (2 pts.)
5. Explain why the synthetic and targeting methods yield different total fertility rate projections in 2040 for Alaska. (3 pts.)
Assignment 2 (7 pts.)
1. Compute the 2014-2019 net migration number and rate by 5-yr. age groups for Woodbury County, Iowa females. (5 pts.)
2. What at-risk population did you use to compute the net migration rates and why did you choose it?
(2 pts.)
Assignment 3 (18 pts.)
1. Compute the 2024 projected population for Woodbury County, Iowa females using a net migration cohort-component model. (8 pts.)
2. Compute the 2019 to 2024 components of population change for Woodbury County females (2 pts.)
3. Calculate age-specific cohort change ratios between 2014 and 2019 and child-woman ratio for ages 0-4 in 2019 for Woodbury County females. (2 pts.)
4. Create a 2024 population projection by age for Woodbury County females using the Hamilton-Perry (HP) method. (3 pts.)
5. What is the difference in the 2024 total female population between the HP and CCM methods? What might explain the difference or lack thereof between these two projection methods? (1 pt.)
6. Explain results from Question 2. What are the factors contributing to the change in the female population of Woodbury County from 2019 to 2024? (2 pts.)

Problem Sets (Cont.)
Assignment 4 (20 pts.)
1. Using 2000 to 2020 as the base period, create 2055 total population projections for Ferndale, Washington using two complex extrapolation methods: 1) Linear model and 2) Exponential model. Use the recode value for time, include the CALIB term, and ignore the smearing correction in the Exponential model (some) (6 pts.) (Regression in Excel: http://www.wikihow.com/Run-Regression-Analysis-in-Microsoft-Excel)
2. Using 2000 to 2020 as the base period, create 2055 population projections for selected counties and balance of the State in California using five trend extrapolation methods: 1) Linear (LINE);
2) Exponential (EXPO); 3) Shift-Share (SHIFT); 4) Share of Growth (SHARE); and Constant Share (CONSTANT). (4 pts.)
3. Create a 2055 population projection for California for LINE and EXPO using the bottom-up method. (1 pt.)
4. Interpret the regression slopes from the complex Linear and Exponential Models. (2 pts.)
5. What are the key assumptions that underlie the Linear and Exponential models? (2 pts.)
6. Why was it necessary to have an independent projection for California for the SHIFT, SHARE, and CONSTANT methods? (1 pt.)
7. Describe why the 2055 projections in Question 2 vary for the California counties. Where appropriate, note specific geographic areas in the answer. (4 pts.)
Assignment 5 (10 pts.)
1. Determined the labor supply for Thurston County, WA in 2029 (3 pts.)
2. Determine the 2029 labor demand for Thurston County using the Shift-Share method (3 pts.)
3. Determine the net employment-related migration in Thurston County from 2019 to 2029 (1 pt.)
4. Determine the net employment-related migration in Thurston County from 2019 to 2029, assuming the U.S. adds on average 80,000 jobs per month from 2019 and 2029 (2 pts.)
5. What other migration components would need to be forecast to determine the total net migration for Thurston County from 2019 to 2029? (1 pt.)
Assignment 6 (20 pts.)
1. Using 15-year-horizon 2015 population forecasts based on extrapolation methods and cohort-component model for 39 counties within Washington State, calculate algebraic and absolute percentage errors for each county. (4 pts.)
2. Calculate the following summary measures of error: MALPE, MAPE, MEDAPE, and PRE for the MAPE and MALPE using the naïve forecast. (4 pts.)
3. Evaluate the precision, bias, shape of the error distribution, and utility of the forecasts based on extrapolation methods and cohort-component model. Which method or model does the best and worst? (8 pts.)
4. What would the MALPE value be for a 25-year forecast based on extrapolation methods for counties in Washington State? (2 pts.)
5. What would the MAPE value be for a 25-year forecast based on the extrapolation methods for counties in Washington State? (2 pts.)