Samuel Clark Department of Sociology, University of Washington Institute of Behavioral Science, University of Colorado at Boulder Agincourt Health and Population Unit, University of the Witwatersrand Basic Concepts & Measures

1 Overview  Population  Balancing Equation  Demographic Rates  Period Rates & Person Years  Principal Period Rates  Crude Growth Rate  Concept of a Cohort

2 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.

3 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

4 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 …

5 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  … … …

6 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.

7 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

8 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

9 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

10 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

11 Structure of Demographic Rates  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)

12 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

April 4, Structure of Demographic Rates  Life Lines – Population G – Birth  Death – Event of type E

April 4, 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

April 4, Period Rates & Person Years Individual life lines Total population over time

April 4, Period Rates & Person Years  Summing the length (duration) of individual life lines:  Summing the total population over time:

April 4, 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

18 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

19 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

20 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 1 st employment cohort of 2001”  Most common is “birth” cohort  A cohort rate restricts counting to members of a cohort