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

The Flow of Services from Owned Vehicles

in Consumer Expenditure Interview Surveys

Caleb Cho and Dominic Smith

Division of Price and Index Number Research

March 18, 2022
2 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Consumption Measure of Motor Vehicles

 Measuring living standards for households

 Frequent and expensive long-lived goods

 Consumption vs. spending

o zero spending ≠ zero consumption
3 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Key Concept: 

Depreciation of Motor Vehicles

 An effort towards a full user cost approach

1) Value of service received during the reference period

2) Smooth out consumption

3) Measures at consumer unit level
4 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Service Flow From Owned Vehicles

SSit=∑jj=1

JJ (rt

+δδa(j))∗(1−δδa(j))

yyjj

∗Pjo

where

SSit: service flow from all vehicles at time t of CU i

rt : inflation adjusted annual yield on long-term security at time t

δδa(j): age specific depreciation rate

Pjo: purchase price for vehicle j

yj : owned years since purchasing

J: number of vehicles owned by CU i
5 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

CE Interview Survey, 1996Q1-2019Q4

 Over 1 million motor vehicles

Include cars, SUVs, trucks (85%)

Exclude boats, kayaks, aircrafts, RVs, other unknowns, etc. 

(15%)

 40% purchased as new vs. 60% purchased as used

 23% price reported (11% news cars, 12% used cars)
6 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

CE Interview Survey, 1996Q1-2019Q4

CE Variables Description

FAMID, NEWID Consumer unit ID 

SEQNO Sequence number

ALCNO Allocation number

QINTRVYR, QINTRVMO

Interview year, Month

VEHICYR Vehicle model year 

VEHPURYR, VEHPURMO Purchase year and month

NETPURX

Net purchase price after discount, trade-in, or rebate 

including destination fee

TRADEX Amount of trade-in allowance

MKMDLY Vehicle Make and Model code (4 digit #)

MKMODEL Vehicle Make and Model

MKMDESC Vehicle make and model description

VEHNEWU Was it new or used when acquired?

FINLWT21 Calibration final weight for the full sample
7 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Regression Model

 Regression model

Log (Pjt) = β0 + βa* aget + make + model + year + ujt

Constant geometric depreciation include vehicles of all ages

Non-parametric depreciation include only new vehicles and 

vehicles of specific ages from 1 through 20.
8 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Construction of Subsamples for 

Depreciation Estimation

 Purchase prices are reported and >$300 in 1983 dollars

 Variables make, model, modelyear are all available
9 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Annual Depreciation Rates (δδa)

 Age specific depreciation rate

δδa =1-exp(βa)

 Current market value 

CMVjt =Pj0 * (1- δa)y

 Service flow received during the reference period

SSjt= (rt+δδa ) * CMVjt
10 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Depreciation Rate (δδa)
11 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Motor Vehicle Consumption vs. Spending

Quarterly Average of All Consumer Units 
12 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Consumption and Spending

at Consumer Unit Level

0

20

40

60

80

100

P

erc

ent

0 20000 40000 60000

Spending

0

5

10

15

P

erc

ent

0 2000 4000 6000 8000

Consumption

2019Q4
13 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Consumption and Spending

at Consumer Unit Level

2019Q4 (>$0)

0

2

4

6

8

P

erc

ent

0 20000 40000 60000

Spending

0

2

4

6

8

P

erc

ent

0 2000 4000 6000 8000

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

Consumption and Spending at Consumer Unit Level

Consumption = 888 + 0.05*Spending

0

2000

4000

6000

8000

0 20000 40000 60000 80000

Spending

Consumption

2019Q4
15 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Conclusion

 Depreciation based approach

Correlated with spending measure 

Reliable and smoothed estimates at CU level

 Next step: adding in other expenditures

Maintenance & repairs

Operating expense

Gas & fluids

Vehicle insurance
16 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Appendix 

2018 Non-parametric

depreciation

Constant geometric

depreciation Difference

Average 0.93 0.89 0.04

 Ratio of CE predicted price to NADA value for given 

make/model/age

 Non-parametric prices more similar to NADA prices than 

constant geometric prices

Coefficient of simple regression: NADA price = CE predicted price (no intercept)
17 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Contact Information

Caleb Cho (cho.caleb@bls.gov)

Dominic Smith (smith.dominic@bls.gov)

Division of Price Index Number Research

Bureau of Labor Statistics