New Census Estimates for the States

[muon2]

The US Census Bureau released (link) its estimates for the populations of the states for July 1, 2004. This data can be used to project the apportionment for 2010.

For each state I have calculated an annual rate of growth based on the 4 1/4 years between the decennial cencus on April 1, 2000 and this new estimate. I assume growth rates based on an annual percentage increase which is uniform over the period. This is the same as a financial institution would use to calculate the growth rate of an investment.

The annual growth rate is then applied for 10 years with annual compounding to the decennial census counts. This results in a projected population for each state on April 1, 2010. With this projection, the average CD would have 712.6 K people.

The apportionment of representatives is calculated in the correct manner. Each state starts with 1 seat. The priority vaule used to assign each subsequent seat is taken as geometric mean of the average population per seat and the average population per seat if an additional seat were assigned. Seats are assigned until 435 seats are apportioned.

The last few seats assigned (and next few not assigned) are:

#431 TX 35
#432 PA 18
#433 MN 8
#434 AL 7
#435 MI 15

#436 CA 55
#437 NY 28
#438 IL 19
#439 FL 28
#440 LA 7

The result of this apportionment would be the following changes:

AZ +1
CA +1
FL +2
GA +1
IL -1
IA -1
LA -1
MA -1
MO -1
NV +1
NY -2
OH -2
PA -1
TX +3
UT +1

[muon2]

I'm getting different results than you are for which states have seats 431 to 440.

#431  TX 35
#432  PA 18
#433  AL 7
#434  MN 8
#435  MI 15

#436  CA 55
#437  NY 28
#438  FL 28
#439  IL 19
#440  LA 7

We can cross-check our projected populations to see where a difference might lie. I'll list the populations in the following order, 2000, 2004, 2010, rounded to nearest 1000 (which could be our difference):


TX: 20904, 22490, 24829
PA: 12301, 12407, 12552
MN: 4926, 5101, 5348
AL: 4461, 4530, 4625
MI: 9956, 10113, 10329
CA: 33930, 35894, 38723
NY: 19005, 19227, 19531
IL: 12439, 12714, 13096
FL: 16029, 17397, 19435
LA: 4480, 4516, 4565

Those final populations give rise to these priorities. The priority number is the geometric mean of the present CD pop and the CD population if an additional seat is added:

#431 TX 35: 719.8
#432 PA 18: 717.5
#433 MN 8: 714.6
#434 AL 7: 713.7
#435 MI 15: 712.8
#436 CA 55: 710.7
#437 NY 28: 710.4
#438 IL 19: 708.1
#439 FL 28: 706.9
#440 LA 7: 704.4

If you have equivalent values I can see if rounding or some other effect caused our relative switches of MN and AL, and IL and FL.

[muon2]

How do you get those 2000 population numbers?
The April 2000 Census and the July 2000 estimates are both different.

I used the official apportionment populations from the April 1, 2000 census.

www.census.gov/population/cen2000/tab01.pdf

"The apportionment calculation is based upon the total resident population (citizens and noncitizens) of the 50 states. In Census 2000, the apportionment population also includes U.S. Armed Forces personnel and federal civilian employees stationed outside the United States (and their dependents living with them) that can be allocated back to a home state."

"Question: Are the overseas population counts used for redistricting?
Answer: No, the overseas counts are used solely for reapportioning seats in the U.S. House of Representatives. The home state data for the overseas population do not meet the substate geographical precision required to conduct redistricting (i.e., blocks)."

The apportionment data will be higher than the block-level state data due to overseas population. Yet the overseas population must be considered to get the apportionment estimates for 2010. A next level of precision would be to base the estimated rate off the in-state population only, then apply the rate to the total base including overseas population.

[muon2]

I wasn't using the apportionment population before, but even with correcting for that I'm still getting different results.

The states getting seats 431-440 remain unchanged, altho my pop numers are slightly different if I use the apportionment pop as my base pop instead of the estimate base pop as before.  I think we're using different multipliers.   Here's how I'm getting my number for each state:

1) Find the ratio between the July 1, 2004 estimate and the Apr 1, 2000 estimate base for that State.

2) Find the 17th root of that ratio to get the quarterly multiplier.

3) Raise that root to the 40th power to get the multiplier for 10 years (40 quarters).

4) Multiply that number by the base population to get an estimate for Apr 1, 2010.

I suspect the difference is in our compounding periods. I use the rate function on the spreadsheet (like your steps 1 & 2), but I used 4.25 periods to represent an annual basis. I then used the future value function (like your steps 3 & 4), but I used 10 periods since the rate was annualized.

[muon2]

The apportionment of representatives is calculated in the correct manner. Each state starts with 1 seat. The priority vaule used to assign each subsequent seat is taken as geometric mean of the average population per seat and the average population per seat if an additional seat were assigned. Seats are assigned until 435 seats are apportioned.

I'm a bit confused--could you please illustrate for seats 51-55?

The last few seats assigned (and next few not assigned) are:

#433 MN 10

Do you mean MN 8?

Thanks for that catch, I've editted my post to make the correction.

Your first question is a good one. As I noted the fifty states are each assigned a single representative seat. At that point the priority values for each state are equal to the square root of the product of their population (divided by 1) and their population divided by 2. This is the geometric mean.

For example AL has a projected population of 4625 K in 2010, so the priority value is sqrt[ (4625.1) * (4625.1/2) ] = 3270.4. AL maintains this priority value util a second seat is assigned to AL. At that point AL gats a new priority vaule for its third seat equal to sqrt[ (4625.1/2) * (4625.1/3) ] = 1888.2.

Each state has its own priority value, and the states with the highest population have the highest value. As each state is assigned another seat its proirity vaule is recalculated, and a new, lower, priority value is assigned.

Clearly CA has the highest value based on a projected population of 38733.3 K. Its priority value for the 51st seat is 27388.6 K. TX is next closest with a priority value of 17556.7 K for the 51st seat. So CA gets seat 51, and with 2 seats has a new priority value of 15812.8 K.

Seats 51 through 60 look like this (quoting pop in thousands):

#51 CA 2, priority value 27388.6, new value 15812.8.
#52 TX 2, priority value 17556.7, new value 10136.4.
#53 CA 3, priority value 15812.8, new value 11181.4.
#54 NY 2, priority value 13810.8, new value 7973.7.
#55 FL 2, priority value 13743.0, new value 7934.5.
#56 CA 4, priority value 11181.4, new value 8661.0.
#57 TX 3, priority value 10136.4, new value 7167.5.
#58 IL 2, priority value 9260.1, new value 5346.3.
#59 PA 2, priority value 8875.5, new value 5124.3.
#60 CA 5, priority value 8661.0, new value 7071.7.

Note how the large population of CA continues to allow CA to get seats ahead of other states.

[muon2]

The apportionment data will be higher than the block-level state data due to overseas population. Yet the overseas population must be considered to get the apportionment estimates for 2010. A next level of precision would be to base the estimated rate off the in-state population only, then apply the rate to the total base including overseas population.

The percentage of the (census-counted) overseas population varies among the states from 0.42% to 0.10% of the apportionment population.  If you use the apportionment population for the 2000 base of the projection, but use the 2004 census estimate for resident population, you are in essence estimatiing that the overseas population had moved away from each state between 2000 and 2004, and would project that about 150% more would move away between 2004 and 2010.

For example, Hawaii had a April 2000 resident population of 1,211,537; a April 2000 apportionment population of 1,216,642, and a July 2004 estimated resident population of 1,262,840.

If you use the resident population, the annual growth rate in the 4.25 years between April 2000 and July 2004 is 0.981%.  Compounded over 10 years results in a projected resident population of 1,335,725.  If we assume that the non-resident population remains constant, this would produce an apportionment population of 1,340,830.

If you base the projection on the April 2000 apportionment population and the July 2004 estimated resident population, you get an annual growth rate of 0.881%, and a 2010 projected population of 1,328,148, which is a difference of 0.955%.

In general, southern states have a larger share of their apportionment population overseas, while northeastern and midwestern states have a smaller share.  The overseas population includes US military and federal civilian employees and dependents living with them.  It does not include other non-resident US citizens.

One of the test censuses in 2004 tested the feasiblity of enumerating all overseas Americans.  The test countries were France, Mexico, and Kuwait.

It turns out that the effect of the overseas population on projecting the next apportionment is samll, and grows smaller as one gets farther from the census year. To test this I used the 2000 resident population as the base to determine the annual percentage increase in each state. I then applied that percentage increase over ten years to the 2000 apportionment population. This makes the assumption that the overseas population will grow at the same rate as the state's population as a whole. It correctly adds in overseas population to the apportionment projections.

Using this method I proceeded to find the projected number of seats given to each state in 2010. The only changes from my earlier projection is that AL and MN switch places for seats 433 and 434, and FL and IL would switch for potential seats 438 and 439. Neither of these swaps affect the total number of projected seats.

[muon2]

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The share of the overseas population in the apportionment population is small (0.1% to 0.4%).    I believe you may be too focused on the final priority list.  What would be the rate of growth needed for Florida to gain the 435th seat under the two projection methods (assuming that theother 49 states maintain their current estimated growth rate?

Your last question here is about sensitivity to the estimating variable. One can run trials where the estimates for any given state are slightly shifted and determine the effect. For instance if the 2004 estimate for FL were 0.24% higher (17439K vs 17397K) it would move to number 435. By comparison CA only needs an increase of 0.13% in its 2004 estimate to move up to #435. NY needs 0.17%.