Global COE Hi-Stat Discussion Paper Series 295

Research Unit for Statisticaland Empirical Analysis in Social Sciences (Hi-Stat)

Estimating Upward Bias in
the Japanese CPI Using Engel's Law

Hi-Stat Discussion Paper

Kazuhito Higa

April 2013

Hi-Stat
Institute of Economic Research
Hitotsubashi University
2-1 Naka, Kunitatchi Tokyo, 186-8601 Japan
http://gcoe.ier.hit-u.ac.jp

Estimating Upward Bias in the Japanese CPI
Using Engel’s Law
Kazuhito Higa∗
Graduate School of Economics, Hitotsubashi University

Abstract
The Japanese Consumer Price Index (CPI) is considered to be upwardly
biased. This paper estimates the Engel curve based on National Survey of
Family Income and Expenditure data to measure the bias. The estimatedannual bias for the period 1989 to 2004 is 0.5 percentage points. Correcting
the bias leads to a lower inﬂation rate of 0.14 percent per year, against theoﬃcial inﬂation rate of 0.65 percent during the period. A demographic analysis
shows that a household with a pre-school child faces a smaller bias suggestingthat the opportunity cost of shopping determines the size of the bias.
Keywords: consumer price index bias; Engel’s Law
JEL Classification Numbers: C10 E30 D12∗ I appreciate comments from Daiji Kawaguchi, Naohito Abe, Miki Kohara, and attendance of

7th Applied Econometrics Conference. The data used in this paper are provided by ResearchCentre for Information and Statistics of Social Science Institute of Economics Research, Hitotsubashi University. This study is supported by Global COE project of Hitotsubashi University.

11 Introduction
The general consumer price index (CPI) represents the cost of living and general
inﬂation, and many policies are index-linked to the CPI. However, the CPI has
been criticized for overstating the cost of living and, therefore, as being upwardly
biased. Because of CPI bias, welfare policies become ineﬀective if the beneﬁciaries
are overcompensated. This leads to excess government spending.
Several studies have estimated the bias of the Japanese CPI. Shiratsuka (1999)
estimated that the size of the overall bias is 0.9 percentage points per year. Ariga andMatsui (2003) concluded that the CPI is upwardly biased by at least 0.5 percentage
points per year. Measuring the bias of the Japanese CPI based on the calculation
methodology and bias estimates of the US CPI, Broda and Weinstein (2007) concluded
that the Japanese CPI overstates the cost of living by around 1.8 percentage points
per year.
This paper, following a diﬀerent approach from previous studies, applies the Engel
curve method suggested by Hamilton (2001) and Costa (2001) to estimate bias in
the Japanese CPI. The Engel curve method exploits the fact that the change offood expenditure share represents the change of real income after accounting forthe change of relative food price. Then, if the CPI correctly represents the cost ofliving and household preference is stable, the CPI-deﬂated Engel curve should be2

stable across diﬀerent periods after the relative price change in food and household
characteristics are controlled for. In this approach, a shift of the Engel curve fromone year to another indicates CPI bias. Several previous studies rely on this method(Beatty and Larsen, 2005; Barrett and Brzozowski, 2010; Chung et al., 2010). In
contrast to previous studies in which the CPI bias is analyzed in terms of its causes,
this approach estimates the overall CPI bias.
In addition, this paper analyzes the cause of bias from the point of the opportunity
cost of shopping. Aguiar and Hurst (2007) and Abe and Shiotani (2012) analyzed
the relationship between prices that households face and the frequency of shopping.
Both studies suggested that households, such as the elderly, who have enough time
to ﬁnd lower prices for commodities face a lower inﬂation. Based on the same idea,
therefore, This paper estimates bias between the households with and without preschool children. A household with enough time would be able to seek out low-priced
or discount goods and substitute them for expensive goods. As a result, the household
might face a larger upward bias.
This paper obtains the following results. The overall bias between 1989 and 2004
is 0.5 percentage points per year. If CPI bias is corrected, the inﬂation rate would be
0.14 percent rather than the oﬃcial inﬂation rate of 0.65 percent between 1989 and2004. In addition, from an analysis based on household characteristics, households
without pre-school children face an upward bias of 0.66 percentage points per year,3

larger than the bias of 0.36 percentage points per year for households with pre-school
children. Thus, households without pre-school child face a lower inﬂation.

2 ModelThis paper follows the approach of Hamilton (2001) and Costa (2001) to estimate
the Japanese CPI bias. This method depends on several assumptions. First, theincome elasticity of food is assumed to vary from unity. This assumption assures thatthe food share declines as real income increases and allows an inference of the real
income from the food share. Second, food has no durability so that food expenditure is
identical to food consumption. This implies that food expenditure in a period cannot
produce a ﬂow of food consumption to another period. Third, the food component
can be separated from the non-food component in a utility function. This assumes
that CPI bias of non-food items does not aﬀect the food share through an unexpectedmechanism. Fourth, household preference is stable over time. This condition ensuresthat the shift of the Engel curve is caused only by CPI bias.
An Engel curve is derived from the Almost Ideal Demand System by Deaton andMuellbauer (1980), and it can be written as a linear function of the food share andthe log of real income:ωit = ϕ + γ(ln Ptf − ln Ptnf ) + β(ln Yit − ln Pt ) + X ′ θ + uit ,4(1)

where ωit is the food-income ratio of a household i at time t and Y is the nominal
household income. The vectors P f , P nf , and P are true but unobservable priceindices of food, non-food items, and all goods, respectively. The vector X represents
the household characteristics, and u is the error term. Here, I assume that the true
price index of all goods is the weighted average of the true price indices of food andnon-food items:
ln Pt = α ln Ptf + (1 − α) ln Ptnf .

(2)

In addition, I assume that each true price index is obtained by removing the error
from the observed price index:′

ln PtG = ln Pt G + ln(1 + EtG ),(3)

where P ′ is the observed price index and G represents food, non-food items, and all
goods. The term Et is the percent cumulative measurement error in the cost of living
index from time 0 to t. In this paper, the term Et represents the cumulative CPI
bias. By deﬁning y ≡ ln Y , π ≡ ln P ′ , and ε ≡ ln(1 + E) and substituting two priceassumptions, I get the Engel curve to be estimated:ωit = ϕ + γ(πtf − πtnf ) + β(yit − πt ) + X ′ θ + γ(εft − εnft ) − βεt + uit= ϕ + γ(πtf − πtnf ) + β(yit − πt ) + X ′ θ +

T
∑
t=1

5

δt Dt + uit ,(4)

where Dt represents the year dummy and δt = γ(εft − εnft ) − βεt . Then, assuming
the relative bias between food and non-food items is constant over time, εft = εnf
t , I
have
εt = ln(1 + Et ) =

−δt
.
β

(5)

Therefore, I can calculate the cumulative percentage point of the CPI bias at time t(
BIASlinear= 1 − exp
t

−δt
β

)
.

(6)

Costa (2001) applies the quadratic functional form of the Engel curve.

The

quadratic form of the Engel curve can be written as follows:ωit = µ + γ(πtf − πtnf ) + β1 (yit − πt ) + β2 (yit − πt )2 + X ′ θ +T∑δt Dt + vit .

(7)

t=1

I then calculate the cumulative bias as follows:(
BIASquad= 1 − exp
t

β1 ±

)
√
β12 + 4β2 δt
.
2β2

(8)

3 DataThis section introduces the data set used in this study and explains the constructionof the analysis sample. The cross-sectional data set used in this paper is from the
National Survey of Family Income and Expenditure, published by the Ministry of In-

6ternal Aﬀairs and Communication. This survey was conducted to collect comprehensive data on family income, expenditure, saving, debt, durable consumer goods, andassets. The survey started in 1959 and has been conducted every ﬁve years thereafter.
It covers more-than-two-person households and one-person households. The survey ofmore-than-two-person households is conducted for three months, from September toNovember. One-person households are surveyed in October and November. A household is requested to ﬁll in the household accounts, household questionnaire, consumer
durables questionnaire, and annual income and saving questionnaire. This paper uses
80% re-sampled and anonymized data sets for 1989, 1994, 1999, and 2004, focusing on
the sample of more-than-two-person households. Each data set contains almost 45,000
households in each year. I restrict the sample to households headed by persons aged
20 to 59 years. I eliminate households that produce food for personal consumption,
speciﬁcally households headed by persons falling under farmer and ﬁsher categories.
In addition, I exclude expenditures on housing, alcohol, and food eaten out.
The food share, obtained by dividing food expenditure by living expenditure, is used
as a dependent variable that takes a value between zero and one. The exclusion of
alcohol and food eaten out produces negative food expenditure and living expenditurevalues.*1 Thus, I restrict the sample to food shares between zero and one. To exclude*1 Some households reported zero for expenditure,

food expenditure, or income even if theyreported non-zero annual income, food consumption, rent, or saving. For unknown reasons,
respondents did not expend during the sample period.

7

observations where food demand might be unusual, the sample is trimmed at the 3rd
and the 97th percentile values of the cross-sectional distributions of food share andreal living expenditure for each survey year. Without the trimming, the Engel curve
predicts that the food share takes a negative value at some expenditure levels.
The description of the independent variable is as follows. The independent variable
includes the real living expenditure, the relative price of food and non-food items,
family characteristics, year dummy variables, and region dummy variables. The realliving expenditure is deﬂated by the oﬃcial Japanese CPI. The demographic controls
are as follows: the number of adult family members aged 18 to 59 years, the numberof elderly people, that is, family members aged 60 years and more, the number ofpre-school children, the number of elementary-school-going children, and the numberof children going to junior high or high school. Control variables also include dummy
variables of being employed, which takes one if a household head is employed, job
type of household head, and age of household head. Industry dummy variables thatindicate the industry of household head’s job are included. The industry category
includes mining, construction, manufacturing, electricity, gas, heat supply, and water,transport and communication, wholesale and retail trade, ﬁnance and insurance, realestate, service, government, and others. The year dummy variables are for 1989, 1994,
1999, and 2004. The region dummy variable takes one if a household lives in an urban
area.
8The construction of price indices is as follows. I use the oﬃcial 2010-base priceindices reported by the ministry: the Japanese CPI, the food price index, and thenon-food price index. Since the deﬁnition of urban area in the analysis sample contains
small cities around the main big cities and is diﬀerent from that in the price indicessample, nationwide price indices are used for households living in rural areas; priceindices of cities with a population of more than 50,000 are used for households living
in urban areas. I constructed three price indices, excluding alcohol, food eaten out,
and housing.*2

4 Empirical Analysis
4.1 Analysis of Summary Statistics
Table 1 shows summary statistics of the food share and the real living expenditure
per month for each sample period. The food share decreased by 15 percent during
the sample period, from 25.9 percent in 1989 to 22.0 percent in 2004. The decreaseof the food share implies the improvement of living standard and necessitates theincrease of real living expenditure. However, the real living expenditure decreased
by 4.6 percent during the sample period, from 243,600 yen in 1989 to 232,400 yen in
2004.*3 The twisted relationship suggests the underestimation of CPI deﬂated real
*2 The calculation method is explained in Appendix A.
*3 The National Health and Nutrition Survey showed the trend in nutrient intake of energy

between 1990 and 2004 dropped by 124 kilocalories (6 percent). This suggests a decrease in9

living expenditure because of upward bias in the CPI.
Table 2 shows the summary statistics for household characteristics: job type ofhousehold head, age of household head, rate of home owners, and proportion of households living in the urban area. The table shows that job types of almost half of thehousehold heads are manufacturing and service. The share of manufacturing jobs
decreased by 4.5 percentage points from 1989 to 2004, in contrast to a 3.7 percentage
point increase in service jobs. In this data set, household heads aged 20 to 24 years
constitute less than 1 percent of the total. Most household heads are more than 30
years old.
Table 3 shows the changes in the numbers of children.*4 The table shows the
proportion childless households increases over time. Almost 30 percent of households
in 1989, and 40 percent in 2004, have no children. Although the proportion of singlechild households is stable during the sample period, that of households with twochildren declines by about 10 percentage points.
Figure 1 shows Engel curves, speciﬁed as quadratic functions of the real living
expenditure, for each year. If the Japanese CPI accurately corresponds to the changes
in the true cost of living, the Engel curve is stable across diﬀerent periods. However,the ﬁgure shows the curves shift downward in diﬀerent periods. This implies the CPI
the importance of food. However, if this results in higher expenditure on other goods, it might
imply that living standards have increased.
*4 The deﬁnition of children includes pre-school children and those who go to elementary schooland junior high or high school.

10

is potentially upwardly biased.

4.2 Analysis of Overall Bias
Estimating the Engel curve, I regressed the food share on the log of real living
expenditure, year dummy variable, log of relative price, and dummy variables of family characteristics- being a home owner, living in urban areas, being employed, job
type of household head, age of household head, and number of adults, elderly people,
pre-school children, children in elementary school, and children in junior high or highschool. Regressing the quadratic Engel curve, I included the quadratic term of thelog of real living expenditure as an independent variable. Table 4 shows regression
results for the linear and quadratic Engel curves. With the linear model, the coefﬁcient of the log of real living expenditure is statistically signiﬁcant even at the 1
percent signiﬁcance level. The result shows the food share declines as the real living
expenditure increases. A 1 percent increase in real living expenditure results in a 0.17
percent decrease in the food share. With the quadratic speciﬁcation, the coeﬃcientof the quadratic term is statistically signiﬁcant at the 1 percent signiﬁcance level.
This result shows the quadratic Engel curve nests the linear speciﬁcation and is more
appropriate.*5 This implies that the linear Engel curve might overestimate the bias.
*5 Unayama (2008) estimated the quadratic almost ideal demand system for food and other goods

using the Japanese Family Income and Expenditure Survey from 1982 to 2000. The paper did
not obtain evidence of a signiﬁcant quadratic form for food. The paper focused on householdswith two married adults but no child, living in their own houses. The dissimilar results might

11

The income elasticities of the two speciﬁcations are about 0.440, evaluated at the
sample means of the food share and the log of real living expenditure.
The crucial variable of this study is the year dummy variable. Again, if the Japanese
CPI is not biased and corresponds to the true cost of living, the Engel curve would
be stable across the sample period. If so, the parameters of the year dummy variables
would not diﬀer from zero. However, regression results from both the linear andthe quadratic models show that the dummy variables, dummy-94, dummy-99, anddummy-04, are statistically signiﬁcant. This evidences an upward bias in the oﬃcial
Japanese CPI.
Estimates of the annual bias are reported in Table 5.*6 The overall upward bias
between 1989 and 2004 based on the linear Engel curve is 1.7 percentage points
per year. The annual bias increases every ﬁve years: 1.6 percentage points during
1989-1994, 2.0 percentage points during 1994-1999, and 2.5 percentage points during
1999-2004. Based on the quadratic Engel curve, the overall bias is 0.51 percentage
points per year from 1989 to 2004-a lower size of the bias compared to the linear
model. In addition, the bias increases in later periods, although it is much lower
compared to the linear model: 0.4 percentage points for 1989-1994, 0.5 percentage

be due to sample construction diﬀerences.
*6 The annual bias is calculated as follows:1

annual bias = ((1 + BIAS) period − 1) ∗ 100
where BIAS is as deﬁned in equation 6 or 8.

12points for 1994-1999, and 0.7 percentage points for 1999-2004.
The 1.7 percentage point annual bias based on the linear Engel curve is larger
than the 0.9 percentage points estimated by Shiratsuka (1999), but is close to the 1.8
percentage points reported by Broda and Weinstein (2007). On the other hand, the 0.5
percentage point estimate based on the quadratic Engel curve is much lower comparedto the previous two studies. This estimate is similar to the lower bound reported by
Ariga and Matsui (2003). As the regression result shows that the quadratic term
is statistically signiﬁcant, the estimated annual bias from the linear model could beoverestimated.
Estimates of annual bias indicate that the oﬃcial Japanese CPI and the inﬂation
rate might not be measured correctly. Figure 2 shows the oﬃcial Japanese CPI andthe revised CPI. The revised CPI is obtained from Equation 3 and the estimatedannual bias. The ﬁgure shows the oﬃcial CPI is placed above the revised CPI. In
2004, the cumulative bias amounts to almost 7 percentage points. The revised CPI
implies lower inﬂation and more serious deﬂation. It shows moderate inﬂation from1992 to 1998 and severe deﬂation, more acute than suggested by the oﬃcial CPI,
thereafter. The inﬂation rate based on the oﬃcial CPI is 0.65 percent from 1989 to
2004. This contrasts with the 0.14 percent inﬂation rate for the same period based on
the revised CPI. However, bias correction suggests severe deﬂation after 1998. After
1998, the deﬂation rate is 0.95 percent based on the corrected CPI and 0.36 percent
13according to the oﬃcial CPI.

4.3 Demographic Analysis
The above discussion shows that the CPI is upwardly biased and presents thedegree of bias across the sample period. This subsection examines the cause of bias byexamining the diﬀerence in bias across demographic groups that presumably represent
the diﬀerence in the opportunity costs of shopping time.
The Ministry of Internal Aﬀairs and Communications survey, in principle, corrects
normal retail prices or normal service charges. Thus, outlet or discount sale prices are
excluded. However, compared to households with pre-school children, those without
pre-school children have more time to seek out low-priced or discount goods andsubstitute them for expensive goods. This results in a larger upward bias for them.
Table 6 shows bias estimates for households with and without pre-school children.
Households with pre-school children faced an overall bias of 0.36 percentage points
per year from 1989 to 2004, compared to 0.66 percentage points for those without
pre-school children. Thus, households with pre-school children presumably have lessshopping time, resulting in lower upward bias. A household without a pre-school childcan spend more time looking for cheaper goods and faces lower inﬂation, resulting ina larger CPI bias for the household.

14

5 Summary and Conclusion
In this paper, I estimated the upward bias of the Japanese CPI based on Engel’slaw, using National Survey of Family Income and Expenditure data. The estimatedoverall bias was 0.5 percentage points per year between 1989 and 2004. This estimate
is close to the lower bound reported by Ariga and Matsui (2003), but lower than the
result reported by Shiratsuka (1999) and Broda and Weinstein (2007).
The 0.5 percentage point upward bias implies that the oﬃcial CPI overstates thetrue cost of living. Consequently, the bias-corrected annual inﬂation rate from 1989
to 2004 was estimated to be 0.14 percent, whereas the oﬃcial inﬂation rate was 0.65
percent during the same period. The deﬂation during the period was severe, especiallyafter 1998, when the rate of deﬂation was 0.95 percent compared to 0.36 percent basedon oﬃcial statistics. These results suggest that government policy payments indexlinked to the Japanese CPI, such as pension, might overcompensate the recipients.
A demographic analysis showed that, compared to households with pre-school children, those without pre-school children faced a larger bias and lower inﬂation since
they presumably have enough time to visit diﬀerent stores and can seek out low-costgoods. The result oﬀers suggesting evidence that the ignorance of sales, discount orbrand substitution is an important source of CPI bias.

15

References[1] Abe, Naohito and Kyosuke Shiotani, ”Who faces higher prices? -An empiricalanalysis based on Japanese homescan data-.” Research Center for Price Dynamics
Working Paper Series, No. 3, 2012.
[2] Aguiar, Mark and Erik Hurst, ”Life-Cycle Prices and Production.” American
Economic Review, Vol. 97(5), pp. 1533-1559, 2007.
[3] Ariga, Kenn and Kenji Matsui, ”Mismeasurement of the CPI.” Structural Impediments to Growth in Japan, University of Chicago Press, pp.89-154, 2003.
[4] Barrett, Garry F. and Matthew Brzozowski, ”Using Engel Curves to Estimate
the Bias in the Australian CPI.” Economic Record, Vol. 86, Issue 272, pp. 1-14,
2010.
[5] Beatty, Timothy K. M. and Erling Roed Larsen, ”Using Engel Curves to Estimate
Bias in the Canadian CPI as a Cost of Living Index.” Canadian Journal of
Economics, Vol. 38(2), pp. 482-499, 2005.
[6] Broda, Christian M. and David E. Weinstein, ”Deﬁning Price Stability in Japan:
A View from America.” Monetary and Economic Studies, Institute for Monetaryand Economic Studies, Bank of Japan, vol. 25(S1), pp. 169-206, 2007.
[7] Chung, Chul, John Gibson, and Bonggeun Kim, ”CPI Mismeasurements andTheir Impacts on Economic Management in Korea.” Asian Economic Papers,
16

Vol. 9(1), pp. 1-15, 2010.
[8] Costa, Dora L., ”Estimating Real Income in the United States from 1888 to
1994: Correcting CPI Bias Using Engel Curves.” Journal of Political Economy,
Vol. 109(6), pp. 1288-1310, 2001.
[9] Deaton, Angus S. and John Muellbauer, ”An Almost Ideal Demand System.”
American Economic Review, Vol. 70(3), pp. 312-326, 1980.
[10] Hamilton, Bruce W., ”Using Engel’s Law to Estimate CPI Bias.” American Economic Review, Vol. 91(3), pp. 619-630, 2001.
[11] Shiratsuka, Shigenori, ”Measurement Errors in the Japanese Consumer Price
Index.” Monetary and Economic Studies, Vol. 17(3), pp. 69-102, 1999.
[12] Unayama, Takashi, ”Measuring the substitution bias in Japan: the demand system approach and a superlative index.” Applied Economics, Vol. 40(14), pp.
1795-1806, 2008.

17

AppendixA Price Data
Since this analysis eliminates the eﬀect of alcohol, food eaten out, and cost of
housing, the data of the Japanese CPI, the food price, and the non-food price arecalculated as follows:
For CPI,CPI =pT × wT − pA × wA − pO × wO − pH × wH.
wT − wA − wO − wH

For food price,
food-price =pF × wF − pA × wA − pO × wO.
wF − wA − wO

For non-food price,

non-food-price =pT × wT − pF × wF − pH × wH.
wT − wF − wH

The variables pT , pF , pA , pO , and pH are the price indices of total, food, alcohol, foodeaten out, and cost of housing. The variables wT , wF , wA , wO , and wH represent theweights of these variables.

18

Table1 Summary Statistics 1
Year
Observations
Food share (%)

1989
29,59226.0(10.8)
246.4(108.8)

Real living expenditure per month (1000 yen)

1994
28,73923.3(10.4)
246.7(118.5)

1999
26,726
22.7(10.8)
236.9(117.7)

2004
23,81922.1(10.9)
231.0(120.5)

Source: National Survey of Family Income and Expenditure.
Notes: The food share is obtained by dividing the food expenditure by the real living expenditure.
The real living expenditure per month is deﬂated by the oﬃcial 2010-base CPI.
Standard deviations are in parentheses.

Table2 Summary Statistics 2

Variable
Employed
MiningConstruction
Manufacturing
Electricity, gas, heat supply and waterTransport and IT
Wholesale and retail trade
Finance and insurance
Real estate
Service
Government
OthersAge 20-24
Age 25-29
Age 30-34
Age 35-39
Age 40-44
Age 45-49
Age 50-54
Age 55-59
Home owner
Living in urban area

1989
Percent
98.00
0.32
12.54
25.55
1.29
9.07
15.58
3.56
0.78
18.46
10.78
2.06
0.75
5.05
11.45
18.47
20.63
17.73
13.75
12.17
70.4
40.6

Source: National Survey of Family Income and Expenditure.

19

1994
Percent
98.18
0.22
12.44
24.45
1.43
9.12
15.34
3.66
0.81
20.14
10.55
1.85
0.79
4.69
11.16
15.18
19.44
19.29
16.58
12.87
65.7
42.4

1999
Percent
97.47
0.17
13.05
23.37
1.29
8.56
14.71
3.38
0.93
21.38
10.57
2.57
0.84
5.18
10.80
14.02
16.68
18.29
18.08
15.97
67.8
42.7

2004
Percent
97.28
0.18
12.29
21.52
1.48
9.36
14.41
3.22
0.99
21.98
11.79
2.78
0.63
4.32
10.39
14.13
16.04
17.20
18.29
18.85
70.3
40.9

Table3 Summary Statistics 3

Total children
0
1
2
3
4
5

1989
Percent

1994
Percent

1999
Percent

2004
Percent

27.87
21.96
36.04
13.07
0.99
0.07

33.69
22.13
31.37
11.95
0.80
0.07

37.31
21.79
29.28
10.59
0.97
0.06

38.82
22.88
27.91
9.49
0.76
0.14

Source: National Survey of Family Income and Expenditure.

Table4 Results of Selected Regression Coeﬃcients

Constant
Log (real living expenditure)

Linear model coeﬃcient
2.432∗∗∗(0.008)-0.171∗∗∗(0.001)(Log (real living expenditure))2
Dummy-94
Dummy-99
Dummy-04
sample size
Adjusted R2-0.015∗∗∗(0.001)-0.034∗∗∗(0.001)-0.058∗∗∗(0.001)
108,876
0.394

Quadratic model coeﬃcient
5.783∗∗∗(0.173)-0.718∗∗∗(0.028)0.022∗∗∗(0.001)-0.015∗∗∗(0.001)-0.034∗∗∗(0.001)-0.059∗∗∗(0.001)
108,876
0.396

Note: The results are obtained by regressing the food share on the log of the real living expenditure,
the log of the relative price, and dummy variables of home owner, living in the urban area, employed,
job types, ages, adults, elderly people, pre-school children, children in elementary school, children injunior high or high school, and year dummy variables.
The robust standard errors are in parentheses.
Nonlinear least-squares estimation is used.
∗ ∗ ∗: Signiﬁcant at the 1 percent level20

Table5 Annual Bias (percentage point)

LinearQuadratic

1989-2004
1.70(0.02)
0.51(0.02)

1989-1994
1.61(0.09)
0.42(0.03)

1994-1999
1.99(0.09)
0.52(0.03)

1999-2004
2.52(0.08)
0.67(0.03)

Source: National Survey of Family Income and Expenditure.
Note: Standard errors from 500 bootstrap replications are in parentheses.

Table6 Annual Bias by Demographics (percentage point)
Householdswith pre-school children
Households
without pre-school child

1989-2004
0.36(0.01)
0.66(0.05)

1989-1994
0.32(0.03)
0.53(0.04)

1994-1999
0.38(0.03)
0.65(0.06)

1999-2004
0.42(0.04)
0.92(0.09)

Source: National Survey of Family Income and Expenditure.
Note: The results are obtained by regressing the food share on the log of the real living expenditure,
the quadratic term of the log of the real living expenditure, the log of the relative price, and dummy
variables of home owner, living in the urban area, employed, job types, ages, adults, elderly people,
and year dummy variables.
Standard errors from 500 bootstrap replications are in parentheses.

21

50

1994
2004

10

20

Food Share (percent)
30
40

1989
1999

0

200
400
600
Real Living Expenditure Per Month (1000 yen)

800

Figure1 Engel curves
Source: National Survey of Family Income and Expenditure.

CPI and revised CPI
95
100

105

Note: The lines are simple Engel curves for each year.

revised CPI

90

official CPI
1990

1995

2000

2005

year

Figure2 CPI and revised CPI
Source: 2010-base Oﬃcial CPI statistics. Revised CPI ﬁgures are based on author’s calculation.

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