1 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Projects 6 & 7: Generating 

Weighted Average Annual 

Education Expenditure and 

Standard Error
2 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Project 6

So far – we’ve only looked at sample estimates. 

Instead, we want to look at population estimates. 

We’ll calculate the education means based on the 

composition of the household 

In this project you will:

Learn about weighting in the CE

Calculate collection year population estimates

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3 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov 3

Weight – FINLWT21

 The sum of FINLWT21 each quarter equals the U.S. 

Population (in CUs).

 The sum of FINLWT21 for four quarters equals 4 

times the U.S. Population.

 FINLWT21 is the starting point for calculating 

expenditure weights and population weights
4 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov 4

Expenditure Weights

 Basic definition: The expenditure weight is 

the number of similar CUs that a CU 

represents in any given quarter. It is the 

weight used when aggregating to expenditure 

totals. 
FIRST LOOK: QUARTERLY WEIGHTS 

AND ESTIMATES
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Population

6

Quarter 1 Population: 24 CUs
7 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Sample

7

Quarter 1 Sample: 3 CUs
8 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Quarterly Estimates

8

CU Quarterly 

Expenditure

Weight Weighted 

Quarterly

Expenditures

Joness $3,500 8 $28,000

Browns $2,000 7 $14,000

Jenkins $8,000 9 $72,000

POPULATION 24 $114,000
9 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Quarterly Estimates

9

CU Quarterly 

Expenditure

Weight Weighted 

Quarterly

Expenditures

Joness $3,500 8 $28,000

Browns $2,000 7 $14,000

Jenkins $8,000 9 $72,000

POPULATION 24 $114,000
10 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Quarterly Estimates

10

POPULATION 24 $114,000

Weighted quarterly average: 

$114,000 / 24 = $4,750
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SECOND LOOK: ANNUAL 

WEIGHTS AND ESTIMATES
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Population

12

Annual Population: 27 CUs
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Sample

13

9

11 10 9

11

9 8
14 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Annual Estimates

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Quarter 1 Population Quarterly

weighted 

aggregate

Quarter 1 24 $114,000

Quarter 2 26 $110,400

Quarter 3 28 $116,200

Quarter 4 30 $125,000

9

11 8

11 10 9

9
15 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Annual Estimates

15

Quarter 1 Population Quarterly

weighted 

aggregate

Quarter 1 24 $114,000

Quarter 2 26 $110,400

Quarter 3 28 $116,200

Quarter 4 30 $125,000

Annual aggregate: 

114,000+110,400+116,200+125,000

=$465,600
16 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Annual Estimates

16

Quarter 1 Population Quarterly

weighted 

aggregate

Quarter 1 24 $114,000

Quarter 2 26 $110,400

Quarter 3 28 $116,200

Quarter 4 30 $125,000

Annual mean: 

Annual Aggregate / population

= $465,600 / ???
17 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Quarterly Estimates

17

Quarter 1 Population Quarterly

weighted 

aggregate

Quarter 1 24 $114,000

Quarter 2 26 $110,400

Quarter 3 28 $116,200

Quarter 4 30 $125,000

$465,400

Annual mean: 

Annual Aggregate / average population

= $465,400 ÷ ((24+26+28+30)/4)

= $465,400 ÷ 27 

= $17,237
18 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Calculating a Standard Error

 To compute actual standard errors, use all 44 

replicate weights (WTREP01-WTREP44) and 

FINLWT21.

 Use the same process just described for creating a 

mean, but do it 44 times, once for each replicate 

weight.

 Create a new variable that sums the squared 

difference between each of the replicate means 

(WTREP01-WTREP44) and the actual mean

 Calculate standard error

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19 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov 19

Project 6 Steps

1. Multiply quarterly education expenditures by FINLWT21 to obtain 

weighted aggregates (*NOT the annualized education expenditures!*)

2. Create population weights by dividing FINLWT21 by the number of 

quarters in our sample (4)

3. Aggregates: Sum the weighted estimates by each group

4. Populations: Sum the population weights by each group

5. Means: Calculate annual means for each of the group by dividing the 

aggregates by the populations

6. Create a new variable that sums the squared difference between each 

of the replicate means (WTREP01-WTREP44) and the actual mean:

7. Calculate the Standard Error 

n=44

difftotal = m1 − m0

 

2

 + m2 − m0 

2

 + m3 − m0 

2

 + m4 − m0 

2

 + ⋯

+ mn − m0

 

2

 

SE = 

difftotal

n
20 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Project 7

Calculate the calendar year education mean by 

the number of children in the household for the 

US population in 2018

In this project you will:

Learn about calendar year versus collection year 

in CE

Calculate calendar year population estimates 

using expenditure data from MTBI

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21 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Calendar Year Estimates

Two Main Differences:

 Use 5 quarters of data, but only select months 

that fall in the calendar year (Numerator)

 Population weights are adjusted based on the 

number of months in the calendar year the CU 

could report (Denominator)

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22 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov 22

Population Weights

 Need another adjustment to FINLWT21

Adjust weights based on the number of months that could have 

been included

MO_SCOPE: “Months in Scope”
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MO_SCOPE

Quarter 1 (FMLI181x)

Oct 

2017

Nov

2017

Dec 

2017

Jan

2018

Feb 

2018

March 

2018

0

X 1

X X 2

Quarter 5 (FMLI191)

Oct 

2018

Nov

2018

Dec 

2018

Jan

2019

Feb 

2019

March 

2019

X X X 3

X X 2

X 1
24 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov 24

Quarter 2 (FMLI182)

Jan 

2018

Feb

2018

March 

2018

April

2018

May

2018

June 

2018

X X X 3

X X X 3

X X X 3

Quarters 3 and 4 are analogous.

MO_SCOPE MO_SCOPE
25 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov 25

Population Weights

 Multiply FINLWT21 by MO_SCOPE / 3

 Still need to adjust to account for quarterly weights, so divide by 4. 

 ...wait – did you say 4?? But I’m using 5 quarters?!

Yes...but you’re really only using 1/3 of the first quarter and 2/3 of 

the fifth quarter. So, dividing by 4 is easier then saying divide by:

(1/3)*1 + 1 + 1 + 1 + (2/3)*1 = 4
26 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov 26

Quick Guide to Adjusting Population Weights

FMLI181x POPWEIGHT = FINLWT21 [(QINTRVMO-1)/3]/4 

FMLI182 POPWEIGHT = FINLWT21 (3/3) / 4

FMLI183 POPWEIGHT = FINLWT21 (3/3) / 4

FMLI184 POPWEIGHT = FINLWT21 (3/3) / 4

FMLI191 POPWEIGHT = FINLWT21 [(4-QINTRVMO)/3]/4
27 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov 27

Expenditures in Scope

 REF_YR

Identifies the reference year of the expenditure

 REF_MO

Identifies the reference year of the expenditure
28 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov 28

Project 9 Steps

1. Append all five quarters of MTBI data.

2. Create calendar year education expenditures:

 For each NEWID, create an EDUCA variable by summing the following UCC’s, if 

REF_YR = 2017:

• Tuition: 670110, 670210, 670410, 670901

• Test: 670903

• Books: 660110, 660210, 660410, 660901, 660902

• Other: 67092

3. Append all five quarters of FMLI data

4. Merge FMLI and MTBI

5. Create weighted expenditures by multiplying EDUCA by FINLWT21

6. Create population weights using months in scope (MO_SCOPE)

7. Aggregates: Sum the weighted expenditure by number of children

8. Populations: Sum the population weights by number of children

9. Means: Calculate annual means for each of the group by dividing the 

aggregates by the population weights by number of children