# Tim Miller (tmiller@demog.berkeley.edu)
# August 8, 2000
#
# Estimating the "immigrant stock" of the U.S.
# I have population estimates for the U.S. based on a closed-model
#  (assuming no immigration) from 1800 through 2000.
# I compare the actual population growth to that predicted by my
# closed-population model and assume the difference represents the
# impact of immigration.

# To do:  A much stronger case could be made if I included immigration 
#  in the model.  Currently, all the difference in population growth 
#  between actual and closed-population is atttributed to immigration.  
#  In fact, some part of this could be due to errors in the age-specific
#  rates or in the initial age distribution of the population.  
#  (For example, the actual age distribution in 1900 is probably younger
#  than that of a population closed to immigration since 1800.)
#  So, one reason why the closed-population model shows slower population
#  growth is that it start with a population with an older age structure.

# Attach Population Module
attach ("/home/davis/lee1/TIM.DATA/Splus.Data.Dirs/pop.module.usa",pos=1)
attach ("/home/davis/lee1/TIM.DATA/Splus.Data.Dirs/pop.module.functions",pos=2)


# Actual population size based on historical stats and 
#  most recent Census population clock
#  Series A 1-5, Hist. Stats of the US)

actual.pop.1800.2000 <- c(5.3,23,76,151,275) # in millions

# Population size in 2000 if no immigration occured over the
#  period in question (post-1800, post-1850, etc)
closed.pop.2000 <- actual.pop.1800.2000*
              (pop.size[2000-1800+1])/
               pop.size[(seq(1800,2000,50)-1800+1)]

# Percent of population in 2000 that could be attributed to 
#  immigration since 1800, 1850, ..., 2000
pct.due.to.immigration <- 
  1 - (closed.pop.2000/actual.pop.1800.2000[5])

# Attribute the current population to immigrant arrivals
# for time-periods:  pre-1800, 1800-49, 1850-99, 1900-49,
#  and post-1950


immigrant.stock <- -diff(c(1,pct.due.to.immigration))

names (immigrant.stock) <- 
  c("pre-1800", "1800-1849", "1850-1899", "1900-1949", "post-1950")

round (100*immigrant.stock)

 pre-1800 1800-1849 1850-1899 1900-1949 post-1950 
       33        12        26        12        17

# Let's try this for 1990

actual.pop.1800.1990 <- c(5.3,23,76,151,249) # in millions

# Population size in 1990 if no immigration occured over the
#  period in question (post-1800, post-1850, etc)
closed.pop.1990 <- actual.pop.1800.1990*
              (pop.size[1990-1800+1])/
               pop.size[(c(seq(1800,1950,50),1990)-1800+1)]

# Percent of population in 2000 that could be attributed to 
#  immigration since 1800, 1850, ..., 2000
pct.due.to.immigration.1990 <- 
  1 - (closed.pop.1990/actual.pop.1800.1990[5])

# Attribute the current population to immigrant arrivals
# for time-periods:  pre-1800, 1800-49, 1850-99, 1900-49,
#  and post-1950


immigrant.stock.1990 <- -diff(c(1,pct.due.to.immigration.1990))

names (immigrant.stock.1990) <- 
  c("pre-1800", "1800-1849", "1850-1899", "1900-1949", "post-1950")

round (100*immigrant.stock.1990)
 pre-1800 1800-1849 1850-1899 1900-1949 post-1950 
       34        12        27        13        13

# Compare this to Gibson (1992)
closed.pop.1990.gibson <- c(123.005,144.963,200.791,229.015,248.710)

pct.due.to.immigration.1990.gibson <- 
  1 - (closed.pop.1990.gibson/actual.pop.1800.1990[5])

# Attribute the current population to immigrant arrivals
# for time-periods:  pre-1800, 1800-49, 1850-99, 1900-49,
#  and post-1950

immigrant.stock.1990.gibson <- -diff(c(1,pct.due.to.immigration.1990.gibson))

names (immigrant.stock.1990.gibson) <- 
  c("pre-1800", "1800-1849", "1850-1899", "1900-1949", "post-1950")

round (100*immigrant.stock.1990.gibson)
 pre-1800 1800-1849 1850-1899 1900-1949 post-1950 
       49         9        22        11         8