EE/GG 550
Develop a population cohort model to forecast the size of the Icelandic Population until the year 2020 using the cohort component method.
Base your model on the following data from the IDB database. If you are ambitious you can divide the population into males and females, but you must at least break the population into age-cohorts Ð the size of each cohort is up to you.
1. Births per 1,000 population = 15
2. Deaths per 1,000 population = 7
3. Life expectancy at birth (years) = 82.1
4. Infant deaths per 1,000 live births = 3
5. Total fertility rate (per woman) = 2.0
6. Emigration and immigration = 0. (my assumption to simplify things)
Midyear Population in the year 2000, by Age and Sex and Total.
------------2000-----------
AGE TOTAL MALE FEMALE
TOTAL 276,365 138,273 138,092
00-04 20,723 10,732 9,991
05-09 22,466 11,526 10,940
10-14 21,152 10,861 10,291
15-19 21,008 10,727 10,281
20-24 20,776 10,474 10,302
25-29 20,274 10,208 10,066
30-34 19,670 9,818 9,852
35-39 21,006 10,490 10,516
40-44 20,571 10,390 10,181
45-49 18,393 9,379 9,014
50-54 15,863 8,186 7,677
55-59 12,349 6,191 6,158
60-64 9,671 4,736 4,935
65-69 9,577 4,650 4,927
70-74 8,614 4,086 4,528
75-79 6,555 2,918 3,637
80-84 4,207 1,698 2,509
85+ 3,490 1,203 2,287
Please answer the following questions based on your model.
1. How big do you expect the Icelandic population to be in 2020?
2. Will the age structure of the population change substantially between 2000 and 2020?
In the process of model development, proceed along the following steps:
A) Select the state variables. Designate the condition for non-negativity of the state variables. Keep the number of state variables as small as possible. Purposely avoid complexity in the beginning. Record the units of the state variables.
B) Designate the controls (flows) . Note which state variables are donors and which are recipients with regard to each of the control variables. Note whether lagged effects should be included either in the controls or in the variables that compose the controls. Also, note the units of the control variables.
C) Select the parameters for the control variables. Note the units of these parameters and control variables. Ask yourself: Of what are these controls and their parameters a function? Do you expect some of these variables to be lagged or delayed functions of some of the other variables?
D) Check your model for compliance with any appropriate physical, economic or other laws; for example, the conservation of mass, energy, value; any continuity requirements. Also, check for consistency of units. Look for the possibilities of division by zero, negative values etc. Use conditional statements if necessary to avoid these violations. Fully document your parameters, initial values, units of all variables, assumptions and equations before going on.
E) Choose the time and space horizon over which you intend to examine the dynamic behavior of the model. Choose the length of each time interval for which state variables are being updated by reference to the space over which the dynamics occur, and mainly by reference to the fastest rate of change you expect in your model. Then choose the numerical computation procedure by which flows are calculated. Set up a graph showing the most important variables and guess their variation before running the model.
F) Run the model. Are your results reasonable? Are your questions answered?
G) Optional: Do a sensitivity analysis of key parameters. Try out these small changes singly and collectively within their reasonable extremes and see if the results in the graph still make sense.
H) Optional: Revise the parameters, perhaps even the model structure to reflect greater complexity and to meet exceptions to the experimental results, repeating steps A - G. Do the results of this model suggest a new set of questions?
Use these steps for the development of all your models.
I) Document your model by
a) Stating the question that the model is intended to answer (write: Question:...)
b) List the assumptions of your model Ð only those that you added to the list given in the lab (write: Assumptions:.)
c) Answer the questions asked and provide a brief discussion of your findings. (write: Result:...)
Additionally, remember to note the units of each variable within each variable's dialog box.