Basic Concepts & Measures

1. Basic Concepts & Measures

2. Overview • Population • Balancing Equation • Demographic Rates • Period Rates & Person Years • Principal Period Rates • Crude Growth Rate • Concept of a Cohort

3. Population • Population • 1a. All of the people inhabiting a specified area. • b. The total number of such people. • 2. The total number of inhabitants constituting a particular race, class, or group in a specified area. • 3. The act or process of furnishing with inhabitants. • 4.Ecology All the organisms that constitute a specific group or occur in a specified habitat. • 5.Statistics The set of individuals, items, or data from which a statistical sample is taken.

4. Population • Demographers typically define populations on: • Time • Geo/political area • Sex • Age • Population in a general sense refers to dynamic collectivity of people that endures through time • The population of Seattle without further qualification is the collection of people living in the Seattle area about now, including new births, those who die, immigrants and emigrants

5. Population • Core of Demographic Analysis concerned with the attributes and dynamics of the population: • Overall size • Sex, age, … -specific structure • Changes in size and composition (dynamics) • Consequently Demography is also concerned with: • How these aggregate-level attributes and processes reflect on (average) individuals • How individual-level behavior aggregates to create population-level attributes and dynamics • Demography is concerned with both micro and macro-level and attempts to connect them …

6. Population • Everyone who shares some attribute(s) within a defined geographic region at a defined time; either a point in time or a period of time • Attributes: • Sex • Age • Educational attainment • Marital status • … … …

7. Balancing Equation • Can ENTER a population through • Birth • In-migration (immigration) • Loosely, “attainment” of some status: • “lives within”, • “married”, • “high school graduate” • EXIT a population through • Death • Out-migration (emigration) • Loosely, “relinquish” some status: • “lives within”, • Etc.

8. Balancing Equation • The size of a population at any given point in time is the size of the base population at time 0 plus the sum of cumulative births and in-migrations minus the sum of cumulative deaths and out-migrations • Called the BALANCING EQUATION: Example 1

9. Balancing Equation • Four fundamental flows: • Births • Deaths • In-migrations • Out-Migrations • Start with an initial population of known size, add the cumulative flows between time 0 and time T and you have the size of the population at time T • Fundamental population accounting IDENTITY • In reality one can never measure the flows with enough precision to be absolutely accurate

10. Structure of Demographic Rates • Changes in population size broken down into four flows in the balancing equation • Three of these can be related to at least one individual in the population when the flow event takes place: • Birth, death, out-migration • A demographic RATE relates the number of occurrences of an event to the size of the population that produces the events

11. Structure of Demographic Rates • Demographic rates are occurrence/exposure rates • The number of events occurring within a population is affected by: • The total size of the population, how many people there are at risk of the event • The duration of time over which the individuals in the population are exposed to the risk of the event • An occurrence/exposure rate therefore takes into account both dimensions the risk of occurrence: population size and time

12. The numerator is a count of the number of events The denominator is a count of the number of person-years exposed to the risk of the event in the population Both the count of events and the person-years refer to a specified period of time (a duration with a start or stop date/time) Structure of Demographic Rates

13. Structure of Demographic Rates • A Person-year is: one year lived by one person • An individual can contribute from 0 to 1 person-years during one calendar year • The total person years lived by a population is what goes into the denominator, must be summed up • Person-years are not directly observed; must be calculated

14. Life Lines Population G Birth  Death Event of type E Structure of Demographic Rates

15. Period Rates & Person Years • A period rate limits the counts of events and person-years exposed to a specified period of time, say January 1, 2000  July 1, 2001

16. Period Rates & Person Years Individual life lines Total population over time

17. Period Rates & Person Years • Summing the length (duration) of individual life lines: • Summing the total population over time:

18. Period Rates & Person Years • A rate defined with respect to Person-years is an annualized rate • Keep in mind the difference between calendar years and annualized rates: • Can calculate person years over a single month, a quarter or any arbitrary period of calendar time • Can also calculate Person-days, Person-weeks, Person-months etc. • Demographic Rates express number of occurrences of an event per exposure to the event; exposure measured in Person-time

19. Principal Period Rates in Demography • Crude Birth Rate: CBR • Crude Death Rate: CDR • Crude Rate of In-Migration into the population: CRIM • Crude Rate of Out-Migration out of the population: CROM

20. Crude Growth Rate • Subtracting the initial population N(0) from both sides of the balancing equation and dividing by the Person-years exposed between time 0 and T yields an expression for population change between times 0 and T called the Crude Growth Rate (CGR): Example 2

21. Concept of a Cohort • Cohort = An aggregate of all units that experience a particular demographic event during a specific time interval • “Seattle birth cohort of 2000” • “UW sociology department graduate student cohort of 2004” • “South African male 1st employment cohort of 2001” • Most common is “birth” cohort • A cohort rate restricts counting to members of a cohort