DYNAMIC ESITMATION OF THE CONSUMER D E W D SYSI'EM IN POSlWAR JAPAN
Kozo Sasaki
I n s t i t u t e of S o c i o - E c o n o m i c P l a n n i n g , U n i v e r s i t y o f T s u k u b a , S u r a , I b a r a k i 305, J a p a n
Yoshihiro Fukagawa
M a t h e m a t i c a l S y s t e m s I n s t i t u t e , h c . , T o k y o , J a p a n
RR-84- 18 August 1984
INTERNATIONAI. INSTITUTE FOR A P P L E D SYSTEMS ANALYSIS Laxenburg, Austria
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Copyright @ 1984
International Institute for Applied Systems Analysis
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Understanding t h e n a t u r e and dimensions of t h e world food problem and t h e policies available t o alleviate it has been t h e focal point of t h e IIASA Food and Agriculture Program since i t began in 1977.
National food systems a r e highly interdependent, and yet t h e major pol- icy options exist a t t h e national level. Therefore, t o explore these options i t is necessary both to develop policy models for national economies and t o link t h e m together by t r a d e and capital transfers. For g r e a t e r realism t h e models in this scheme a r e being kept descriptive, r a t h e r t h a n normative. Eventually i t is proposed t o link models of twenty countries, which together account for nearly 80 percent of important agricultural a t t r i b u t e s such as area, produc- tion, population, exports, imports, and so on.
A description of consumer behavior is critically important in o u r policy models. This report on consumer demand estimation for Japan in the postwar period discusses t h e dynamic aspects of t h e demand s t r u c t u r e over t h e period 1951-80 and focuses on t h e specification of a proxy variable for changing tastes. Drs. Sasaki and Fukagawa report importarit findings with regard to t h e empirical implementation of their dynamic version of t h e linear expenditure system and on t h e varied s t r u c t u r e s of Japanese consumer demand. This is a f u r t h e r step toward t h e completion of a detailed agricul- tural policy model for Japan.
KIRIT PARIKH Program Leader National Agricultural Policies
ACKNOWLEDGMENTS
We would like t o thank Kirit Parikh, Eric Geyskens, and Hisanobu Shishido, and many other former colleagues in IIASA's Food and Agriculture Program for their valuable comments and suggestions. Many thanks are also due to Bonnie Riley for typing and editing earlier drafts of t h e report. We of course take full responsibility for any remaining errors.
SUMMARY
This report explores t h e dynamic demand relations operative i n Japan in t h e period 1951-80 in order t o elucidate t h e dynamic n a t u r e and characteris- tics of t h e varied structures of consumer demand. The analysis was con- ducted a t t h e subgroup level on t h e basis of time series of family budget data, using Powell's version of t h e linear expenditure system. A taste variable was incorporated into the expenditure functions and five alternative specifications of t h e t a s t e variable were utilized t o take account of recent structural changes in demand. The first two are based on c u r r e n t annual increase in income and on c u r r e n t annual r a t e of increase in income. The next two incorporate lagged annual increase in income and lagged annual rate of increase in income, and the last specification is based on t h e time trend.
The analysis was based on a 21-commodity breakdown and numerous individual segments of the total observation period were chosen for estimat- ing t h e dynamic model. The t a s t e variables had t h e effect of stabilizing the demand system as a whole and they considerably reduced t h e instability of important estimates, such as those for money flexibility, subsistence con- sumption levels, e t c . Consumption patterns in Japan are considered to have changed substantially toward more "Westernized" living and eating habits since t h e beginning of the 1960s. P e r capita consumption of rice and fish went down with t h e increase i n deflated income, whereas t h e consumption of animal protein food, fruit, beverages, and food away from home all increased rapidly. Owing to income and taste effects, transportation, recreation, and r e n t showed a notable upward shift in average s h a r e s , while rice consumption declined remarkably in t e r m s of its reduced marginal share.
Broadly speaking, estimated average substitution elasticity in Leser's model is inversely proportional to estimated money flexibility, which itself has a close relation to price elasticities. High values of money flexibility were obtained for t h e lower levels of per capita income in t h e early years of the period studied. For periods of more rapid economic growth, money flexibility estimates dropped to some extent, while for r e c e n t years they rose appreci- ably, reflecting t h e smaller response of consumer demand t o price changes.
CONTENTS
1 INTRODUCTION 2 METHOD
3 DATA AND ESTIMATION 4 ESTIMATION RESULTS
4.1 The Period 1951-61 4.2 The Period 1960-77 4.3 The Period 1958-80 4.4 The Period 1960-80
4.4.1 Use of Lagged Changes i n Income 4.4.2 Use of t h e Time Trend
5 INTERPRETATION OF THE REST-TLTS 6 CONCLUDING REMARKS
NOTES REFERENCES THE AUTHORS
DYNAMIC ESZllldATION OF
THE
CONSUMER DEMAND S Y m M IN POSlWAR JAPANKozo Sasaki and Yoshihiro Fukagawa
1 INTRODUCTION
This report explores the dynamic demand relations operative i n Japan in t h e period 1951-80. Consumption levels and patterns have shifted so drasti- cally over t h e last thirty years t h a t i t is of g r e a t interest to elucidate t h e dynamic n a t u r e and characteristics of t h e varied structures of consumer demand during t h e entire period. Special attention is given to t h e analysis of s t r u c t u r a l change in more recent years.
This study also aims a t evaluating empirical evidence of t h e dynamic s t r u c t u r e of consumer demand in t h e postwar period. It is a n extension of a previous study (Sasaki 1982) in which both static and dynamic models of t h e linear expenditure system were fitted to time series of family budget data for t h e period 1951-77.
The same method is adopted h e r e : a simplified version of t h e linear expenditure system extended by A. A. Powell for the sake of computational convenience. The expenditure and price data used in the earlier study were updated, adding t h r e e more years to t h e time series. Five alternative specifications of the taste variable were utilized here in order t o take due account of r e c e n t structural changes in consumer demand. The first two are based on c u r r e n t annual increase in income and on c u r r e n t annual rate of increase in income, which can be seen in some of t h e conventional demand analyses i n econometric models. The next two incorporate lagged annual increase in income and lagged annual rate of increase in income, and t h e last specification is based on t h e t i m e t r e n d .
The commodity definition used is described in more detail below. With respect to t h e previous study, t h e original 24 subgroups have been adjusted somewhat, yielding a 21-commodity breakdown for all t h e cases under con- sideration. Moreover, Inany individual segments of t h e total observation period were chosen for estimating t h e dynamic model. All these changes were made t o satisfy more closely t h e theoretical constraints imposed on t h e model and to obtain, as far a s possible, a good fit between t h e model and t h e empirical data.
We also felt i t was of some i n t e r e s t t o examine t h e stability of such important parameters a s money flexibility, subsistence consumption levels,
etc., when a particular specification of the taste variable is introduced into t h e expenditure functions.
The estimation results for many different cases could, in principle, be compared in various respects. However, this study concentrates on just four subperiods with fairly good results for detailed discussion. Note t h a t most of the statistical t e s t s used are implemented under linear least-squares postu- lates.
2 METHOD
A complete s e t of linear expenditure functions is used, explaining per capita expenditure on each commodity in t e r m s of all prices, per capita income, and the taste variable. Under the given assumptions, t h e estimating equation of Powell's system takes the form:
where
and
ut = m t - C p . ,tzj - ( i , j = 1 , 2 , . . . , N ) , ( t = 1 , 2 , . . . , T)
j
The notation used here is as follows: pi and xi are the price and quantity consumed per capita, m the per capita income, s the taste variable, and ci the e r r o r t e r m .
pi
is t h e sample mean of pi and ?ti is t h e ratio of the sample mean expenditure to t h e mean pricepi.
zi and u indicate substitution and income variables, respectively. The subscripts i and j a r e commodity indices, a n d t denotes time. The A, bi, and ci a r e unknown parameters. More specifically. A has t h e following properties:and
A = m -
C
pipi(Pi
= subsistence consumption level) i(3) where 13 is money flexibility, which is equivalent to the income elasticity of the marginal utility of income. p is called income flexibility and is the reciprocal of w'. Then A is interpreted as t h e supernumerary income. bi represents the marginal budget stlare and ci denotes the coefficient of the taste variable s t .
The taste variable st can be specified in a n appropriate way as t h e occa- sion requires. Leser (1960) noted t h a t i t is easy t o estimate a s e t of regres- sion equations with the same independent variables, b u t disregarding the zit variable, under least-squares assumptions.' In accordance with Leser's argu- ment, Powell's version of the linear expenditure system (Powell 1966) also contains a dynamic factor common to all equations, which allows for shifts in expenditure and demand functions.
In the present analysis, taste changes a r e represented by a single vari- able st in order to facilitate estimation by a systems least-squares method.
The dynamic model is fitted for various phases of t h e period studied, with alternative specifications of a proxy for t h e t a s t e variable. In the first place, two alternative expressions are taken into account: c u r r e n t annual increase in income and c u r r e n t annual rate of increase in income:
st = m t - mt-l and s t = ( m t - m t - l ) / m t - l (4) These expressions are applied uniformly to all cases involving different sample periods. For more recent periods, which t h e above specifications do n o t fit well, t h r e e different alternative expressions a r e incorporated separately into the estimating equation (1). These a r e written as:
't = mt-1 - and st = (mt-l - mt -2), mt-2 and
Equation (5) is the same as eqn. (4), except t h a t the former has a one- year lag. I t simply suggests t h a t , in r e c e n t years, t h e consumer has responded more slowly to either annual i n c r e m e n t s in or the annual growth r a t e of real income.
The dynamic model is assumed t o satisfy t h e homogeneity condition only a t the mid-point of t h e sample period. In cases where t h e model uses deflated expenditure and price data, however, all c u r r e n t (or nominal) expenditure functions are homogeneous of degree one in c u r r e n t prices, c u r r e n t income, and t h e General Consumer Price Index (hereafter referred to as t h e CPI). I t is apparent t h a t t h e corresponding demand Iunctions are homogeneous of degree zero in c u r r e n t prices and income.
3 DATA AND ESI'WI'ION
The data sources on per capita expenditures and prices are t h e Annual Reports published by the Office of t h e Prime Minister, Japan (1950-1980).
Data for all households in cities with a population of 50,000 or more are util- ized in this study, since long t i m e series a r e available on expenditures and prices in the postwiir period. Price indexes in t h e Laspeyres form are avail- able for all subgroups and these a r e taken as individual prices for each sub- group, with all of the 1970 indexes being s e t a t unity. Hence, the associated quantities represent expenditures in constant 1970 yen.
The commodity grouping on which t h e study is based is shown in Table 1 . In practice, a 21- r a t h e r than 24-commodity breakdown is generally employed here by combining several of t h e original subgroups into broader groups.
This results in two commodity lists, which differ slightly from each other as can be seen in some of t h e Iollowing tables. All t h e time series used cover the period 1951-80.
It should be noted t h a t both t h e expenditure and t h e price data are deflated by t h e CP1 so as to ensure t h a t consumer demand in t h e model does not respond to changes in nominal prices, b u t t o changes in relative prices.
TABLE 1 The 24 commodity groups employed in the study.
No. Commodity No. Commodity
1 Rice 13
2 Other cereals 14
3 Fish 15
4 Meat 16
5 Milk
+
eggs 176 Vegetables 18
7 Processed food 19
B Cakes 20
9 Fruit 2 1
10 Beverages 22
11 Food away from home (f.a.f.h.) 23
12 Rent 24
Repairs Water charges Furniture Fuel
+
Light ClothesPersonal effects Medical care Toiletries Transportation Education Tobacco Recreation
--
This analysis t a k e s into a c c o u n t t h e changes in prices and income relative t o t h e CPI. Given t h e values of t h e t a s t e variable, c u r r e n t (or nominal) expendi- t u r e functions a r e homogeneous of degree o n e in c u r r e n t prices. I t follows i m m e d i a t e l y t h a t t h e d e m a n d f u n c t i o n s a r e homogeneous of degree z e r o in a11 c u r r e n t prices.
We begin e a c h analysis with t h e e s t i m a t i o n of Leser's dynamic model, 2 a n d t h e nonlinear estimation of Powell's dynamic model is t h e n u n d e r t a k e n by a n i t e r a t i v e procedure. The e s t i m a t i o n criterion is t o m i n i m i z e t h e s u m of
s q u a r e d residuals over a11 commodities a n d all observed years u n d e r t h e a s s u m p t i o n of a simple e r r o r ~ t r u c t u r e . ~ The criterion of convergence for e s t i m a t e d p a r a m e t e r s m u s t b e d e t e r m i n e d so t h a t t h e i t e r a t i v e regression t e r m i n a t e s when t h e relative deviation of t h e p a r a m e t e r between two s u c - cessive r o u n d s is r e d u c e d t o below 0.01 p e r c e n t . This convergence: i s gen- erally fast, and i t is usuaIly r e a c h e d within 20 r o u n d s . However, convergence is n o t always a ~ h i e v e d . ~
As t h e sample period b e c o m e s longer, t h e a s s u m e d linearity of expendi- t u r e f u n c t i o n s t e n d s t o become unacceptably rigid. In particular, Engel c u r v e s would not r e m a i n linear for s o m e commodit.ies, as h a s been frequently pointed o u t in t h e ~ i t e r a t u r e . ~ As a m a t t e r of f a c t , a few commodities change f r o m being n o r m a l goods t o inferior goods and vice versa. A few o t h e r s a c t u - ally r e m a i n r a t h e r irresponsive t o i n c o m e c h a n g e s . Therefore, s a m p l e periods n e e d t o b e chosen carefully in accordance with p a r t i c u l a r phases of demand s t r u c t u r e development.
4 ESTIMATION RESULTS
First of all, t h e dynamic models were applied to n u m e r o u s sample periods using two related descriptions for t h e proxy of t h e t a s t e variable:
n a m e l y , t h e c - u r r e n t a n n u a l i n c r e a s e in deflateti i n c o m e a n d i t s c u r r e n t a n n u a l r a t e of i n c r e a s e . The whole period studied c a n be roughly divided into two p a r t s a s r e g a r d s t h e estimation of dynamic d e m a n d modc:ls. The first i s t h e 1950s, which r e p r e s e n t e d an e a r l y stage of t h e postwar period. The second p a r t consists of t h e 1960s and 1970s, which c a n b e designated a s a
TABLE 2 Estimates of t h e d e m a n d p a r a m e t e r s gin Ei, a n d for t h e period 1951-61. Taste variable: st = 9 - mt-*.
i Commodity g r o u p Marginal budget Coefficient of Multiple correlation Serial
s h a r e st variable coefficient correlation
coefficient
Ki It 1 r a t i o
4
It 1 r a t i o , R1 Rice ,0284 3.354 .0192* .377 .793 .918 .324
2 Other c e r e a l s -.0351 8.753 -.0129* .538 ,958 .948 .450
3 Fish ,0084 3.230 .0129* .827 .801 .912 .I69
4 Meat ,0365 19.893 .0038* .348 .99 1 .992 ,245
5 Milk
+
eggs .0494 26.856 -.0129* 1.169 ,995 .993 ,274 6 Vegetables-.
0057* 2.285 .0217* 1.459 .649* ,933 -. 101 7 Processed food .0526 14.527 -.0057* .265 .983 ,972 .261 8+9 Cakes+
f r u i t .0353 12.910 .0221* 3.343 ,981 .958 -.01710 Beverages ,0366 17.555 .0095* ,759 .989 .983 ,078
11 F.a.f.h. ,0490 18.433 -.0033* .206 ,990 .989 .469
12 Rent .0175 3.854 .0126* ,461 .832 ,965 ,084
13 Repairs .0237 7.728 -.0103* ,559 ,943 ,943 ,121
14 Water charges ,0045 8.287 .0025* .775 .954 ,973 ,230
15 F u r n i t u r e ,0932 10.549 .0093* .I75 ,970 .966 ,470
16 Fuel
+
light ,0363 12.521 .0095* .546 .978 ,985 ,40117+18 Clothes
+
.I496 19.643 .I514 3.313 .992 ,982 -.099personal effects
19 Medical c a r e .0372 20.582 -.0142* 1.312 .991 .981 .342
20 Toiletries .0264 11.949 -.0086* .495 .975 .979 .432
21 Transportation ,0233 15.466 -.0019* ,215 .985 .989 ,188
22 Education .03 14 8.886 -.0355* 1.675 ,954 ,975 .327
23+24 Tobacco
+
r e c r e a t i o n .3013 41.600 -. 1709 3.932 .998 ,998 .387 Insignificant at the 5-percent level (&, E,, %..,).All serial correlat~on coefficients are insignificant at the 5-percent level
TABLE 3 D e m a n d e l a s t i c i t i e s
(eii.6)
e s t i m a t e d f o r 2 1 s u b g r o u p s a a t t h e s a m p l e 1951-61.Price e l a s t i c i t i e s Fij
h c o m e e l a s t i c i t i e s
Budget s h a r e s Gj
a For a full list of t h e commodity groups i, j s e e Table 1.
Zij = e l a s t i c i t y of srlbgroup i with r e s p e c t t o t h e j t h price, calculated a t t h e s a m p l e m e a n s
Ej = i n c o m e elasticity of subgroup j, c a l c u l a t e d a t t h e s a m p l e m e a n s . G . J = budget s h a r e of s u b g r o u p j, calculated a t t h e s a m p l e m e a n s .
means of all variables and sample mean average budget shares (W,), for t h e period
more advanced stage from the viewpoint of economic development or in t e r m s of consumption levels and p a t t e r n s .
Estimation results for four subperiods 1951-61, 1960-77, 1958-80, and 1960-80 a r e selected here for detailed discussion. For t h e more r e c e n t years, t h e specification of t h e taste variable was modified. The commodity grouping used for earlier subperiods is also different from t h a t of r e c e n t subperiods.
Great efforts were made t o enhance t h e goodness of fit of t h e models and t o handle a s many normal goods as possible.
4.1 The Period 1951-61
For t h e earlier years studied, five subperiods between 1951 and 1965 were analyzed, with all of the subperiods starting in 1951.. Table 2 reports the estimates of demand parameters and relevant coefficients for t h e subperiod 1951-61. All commodities except o t h e r cereals and vegetables were found t o be normal goods (f.a.f.h. is a n abbreviation for food away from home). Other cereals a r e identified as a n inferior good, while vegetables hardly respond a t all t o changes in income.
The coefficient of t h e taste variable is positive for clothes and personal effects, negative for tobacco and recreation, a n d not statistically significant for t h e o t h e r commodities. The t a s t e variable is proxied by t h e c u r r e n t annual increase of deflated income. Multiple correlation coefficients6 a r e large on t h e whole, and those values indirectly calculated exceed 0.9. For- tunately, t h e r e is no significant first-order serial correlation in t h e residuals.
In connection with t h e goodness of fit, 231 ( N x T ) measures of fit were com- puted for all subgroups and all observation years t o conduct t h e interpolation t e s t within t h e sample period. Only two of t h e m h a d values of less than 80 percent. These measures indicate t h e ratios of estimated t o actual expendi- t u r e s , which a r e simply t h e ratios of estimated to actual quantities pur- chased. Therefore, the fitted system has a high predictive power in this early subperiod.
The inc_ome flexibility estimate a t t h e sample m e a n is derived from the p a r a m e t e r X and the sample mean income E . I t yields a value of -3.9 for t h e money flexibility G e . Even where t h e estimated money flexibility was this high, own price elasticities did not come o u t as low a s expected, since t h e r e are several subgroups with remarkably large income elasticities.
The e s t i m a t e d expenditure system can be conveniently expressed in elasticity form. The estimates of behavioral p a r a m e t e r s in Table 2, together with the observed data, provide a complete s e t of income and price elastici- ties, evaluated a t the sample means for all variables. Table 3 shows the demand elasticities and sample-mean average budget shares.
Income elasticity is particularly high for [urniture, Iood away from home (f.a.i.h.), milk a n d eggs, repairs, medical c a r e , and tobacco and recreation.
Owrl price elasticity is higher for these subgroups t h a n for
other^.^
One strik- ing feature is t h a t rice proved t o be a normal good, with a n income elasticity of 0.23 and a n own price elasticity oi -0.09. Fish a n d vegetables are also quite inelastic with respect to prices a s well as income. As for t h e average budget s h a r e s , rice, clothes a n d personal effects, and tobacco and recreation accountTABLE 4 E s t i m a t e d m o n e y flexibility 2jB by sample period i n t h e e a r l i e r y e a r s studied.
Period Taste variable
The subgroups of cakes and fruit, clothes and personal effects, and tobacco and recreation ere further aggregated here into three larger subgroups, respectively.
for 44 p e r c e n t of t h e total budget. The Engel. coefficient is still a s high a s 45 p e r c e n t on t h e average, a s will be illustrated later. This would s e e m to imply t h a t 1951-61 was a transitional period from a low s t a n d a r d of living to more comfortable living conditions.
Own price elasticities a r e all less t h a n 1.0 in absolute value for n o r m a l goods. This follows from t h e fact t h a t all e s t i m a t e s of
pit
a r e positive in sign.'pit
r e p r e s e n t s t h e subsistence consumption level, although t h i s interpreta- tion does n o t apply for inferior goods. Thepit
e s t i m a t e s for m o s t subgroups do n o t vary significantly within t h e sample period; nor does t h e subsistence cost.Table 4 p r e s e n t s t h e money flexibility estimates w" a t sample m e a n s , which have been calculated for each sample period and each alternative specification of t h e t a s t e variable. Most of t h e estimated money flexibilities lie within t h e range -2.1 to -4.0. As t h e sample period is lengthened t h e absolute value of money flexibility declines substantially. Obviously, i t fell with a rise in deflated income in those earlier years. Using t h e annual increase in income as a proxy for t h e t a s t e variable g e n e r a t e s more stable r e s u l t s a s regards t h e value of money flexibility t h a n does t h e u s e of a n n u a l r a t e s of increase in income.
Turning to t h e e s t i m a t e s of t h e average substitution elasticity in Leser's model,' m a n y of these were in t h e region 0.3 t o 0.4. This reveals t h a t , on t h e whole, substitutability between different subgroups of commodities i s limited t o a considerable e x t e n t . Extremely limited substitutability was particularly evident l o r t h e subperiods 1951-61 and 1951 -62.
After all of t h e
pit
values were calculated, t h e cost of living index1' and subsistence c o s t were estimated for every year in t h e subperiod 1961-61., despite t h e negative marginal budget s h a r e s for both o t h e r g r a i n s a n d veget- ables. These two subgroups comprise only a small portion of t h e t o t a l budget.The r e s u l t s a r e summarized in Table 5. Th.e cost of living index, deflated by t h e CPI, is less t h a n 100 for all years other t h a n the base year, 1951. This would appear t o be logical, because t h e deflator of t h e 1,aspeyres Index exceeds t h e t r u e index of cost of living in value. The subsistence c o s t is valued in 1970 y e n without modification by t h e cost of living index in Table 5.
TABLE 5 Estimates of the cost-of-living index and the subsistence cost by year for the period 1951-61, deflated by the CPI.
Year Cost-of-living index
1951 100.0
1952 99.6
1953 99.0
1954 98.7
1955 98.9
1958 99.2
1957 99.5
1958 99.1
1959 99.3
1960 99.2
1981 99.1
a Subsistence cost = z , p u
Bit
in 1970 yen.Subsistence costa
4.2 The Period 1960-77
This subperiod includes the 1960s, which saw a rapid growth of the Japanese economy during which consumer demand expanded greatly a s a whole and also became more diversified. It is noticeable t h a t a number of static and dynamic versions of t h e present expenditure system were fairly well suited for periods of about twenty years up until 1977. Selected results a r e briefly discussed here. Estimated demand parameters and related results are not, however, tabulated here because they a r e very similar t o those for t h e period 1958-77 reported previously (Sasaki 1982).
The sign of the marginal budget share of rice changed, and rice is now t h e only inferior good. Both other cereals and vegetables a r e now found to be normal goods. (Note t h a t t h e r e is little difference between t h e commodity classification used for this period and t h a t for 1951-61.) Estimates of margi- nal budget shares for Ash and education are not significant: in other words, per capita expenditures in constant prices on neither fish nor education varied significantly with income. The coefficient of the taste variable is significant for toiletries and for tobacco and recseation a t t h e 5-percent level, and is significant for clothes a t the 10-percent level. The taste variable is specified in t-he s a m e form as t h a t for t h e period 1951-61, namely as a c u r r e n t annual increase i n deflated income.
There are two subgroups, fish and education, with low multiple correla- tion coefficients for their estimating equations. Fortunately, again, t h e r e are few problems related to t h e serial correlation coefficients. Measures of fit computed to a t t e m p t the interpolation t e s t were very high. Only one of t h e 378 ( N x T ) point estimates failed to reach the 80-percent level. The estimated income flexibility $ increased, compared with the result in Table 2, and t h e corresponding money flexibility Ze was -2.5.
In t h e food category, t h e iricome elasticities for food away from home, beverages, fruit, and m e a t , e t c . , a r e each greater t h a n 1.0. Apart from other cereals and vegetables, however, most of Che income elasticities decreased compared to the earlier period. On the other hand, own price elasticity rose for beverages, cakes, and fruit. Turning to the nonfood category, t h e r e are
TABLE 6 Estimates of t h e demand parameters
gi,
Ei. and 5; for t h e period 1958-80. Taste variable: st = rnt-l - r n t - ~ . i Commodity group1 Rice
2 Other cereals 3 Fish
4+5 Meat, milk, etc.
6 Vegetables 7 Processed food 8 Cakes
9 Fruit 10 Beverages 1 1 F.a.f.h.
12 Rent
13+ 14 Repairs + water 15 Furniture 16 Fuel
+
light 17 Clothes18 Personal effects 19 Medical c a r e 20 Toiletries 2 1 Transportation 22 Education
23+24 Tobacco + recreation
Marginal budget share
b^,
It ( ratio -.0546 30.811.0035 5.838 -.0048 3.096 ,0626 19.950 ,0061 5.168 .0194 22.073 .0134 16.706 .0198 11.520 .0406 27.709 ,0462 27.864 ,0357 27.198 ,0139 12.373 .0683 18.648 ,0525 28.509 ,0794 22.238 ,0152 11.911 .0397 88.200 ,0195 24.745 ,1199 20.754 ,0062 2.700 .3973 45.287
Coefficient of st variable
Multiple correlation coefficient
Ei It 1 ratio
Serial correlation coefficient
*Insignificant a t t h e 5-percent level ( g i , 4, %.,,).
**Significact a t t h e 5-percent level (serial correlation coefficient).
TAEILE 7 Demand elasticities ( F i j ,
E,)
estimated for 21 subgroupsa a t t h e samplePrice e l a s t i c i t i e s Fij
h c o m e e l a s t i c i t i e s
Ej
Budget s h a r e s G,
a For %full list of t h e commodity groups i , j see Table 1.
G ,
E,. and Gj a r e as defined in Table 3.m e a n s of all variables a n d s a m p l e m e a n average budget s h a r e s (G,).*
quite a few subgroups whose income elasticities exceed 1.0. Demands for transportation, medical care, furniture, and recreation are all highly respon- sive to income changes. The absolute values of own price elasticity increased conspicuously for transportation, medical c a r e , recreation, and r e n t , and for fuel and light. Own price elasticities were all less t h a n 1.0 in absolute value, which s t e m s from the fact t h a t all of the
pit
estimates were positive.The average budget shares for rice and other cereals a r e much smaller than before. Those for food away from home, m e a t , milk and eggs, and bever- ages apparently went up. Of the nonfood subgroups, recreation and transpor- tation sharply expanded their shares of t h e total budget. Money flexibilities a r e found to be r a t h e r stable in t h e three subperiods 1958-77, 1959-77, and 1960-77, falling in t h e range -2.1 to -2.7. The estimates for 1958-79, how- ever, fell some distance outside this range. Moreover, t h e specification of t h e t a s t e variable used here does not seem to be suitable for more recent years.
This issue will be discussed l a t e r . Leser's elasticities of substitution were estimated a t between 0.6 and 0.7, except for t h e period 1951-77, for which t h e values were slightly greater than 1.0
4.3 The Period 1958-80
The specifications of t h e t a s t e variable described above did not prove suitable for estimating t h e dynamic model for more recent years. Moreover, t h e static model did not fit t h e latest data sets. Accordingly, another pair of t a s t e variables were implemented separately for the estimation of dynamic expenditure systems: namely, a lagged annual change in deflated income and a lagged annual r a t e of change in deflated income. For this purpose, a one- year lag was applied to t h e previous taste variables. The resulting, new t a s t e variables a r e predetermined variables in t h e expenditure system, and they produced good results for some cases covering more recent years.
Some examples of tht: results a r e shown in Table 6 in t e r m s of estimated demand parameters and related coefficients. The marginal budget share now takes a negative value for fish as well as for rice. The growth of expendi-ture i n constant prices on fish was so low in t h e past t h a t the income responsive- ness of fish consumption turned out to be insignificant for t h e period 1960-77. Over a longer period of time, such as the present subperiod, 1958-80, t h e income elasticity of fish declines t o a negative value. It is fre- quently said t h a t t h e reduction in fish consumption as a whole has been due t o t h e sharp increase in its price associated with changes in fish-supply con- ditions in recent years, changes in quality, and so on. All subgroups other than rice and fish are normal goods.
The coefficient of t h e taste variable is significantly different from zero a t t h e 5-percent significance 1t:vel for three subgroups: repairs and water, furni- t u r e , and tobacco and recreation. A t the 10-percent level, by comparison, i t is significant for five more subgroups as far as t h e t-ratio t e s t is concerned:
these a r e rice, cakes, fuel and light, clothes, and toiletries.
Multiple correlation coefficients are all significant, but nearly half of all t h e subgroups have positive serial correlation in t h e residuals. Measures of fit in t h e interpolation t e s t were mostly 80 percent or more. Of the 483 ( N x T)
TABLE 8 Estimated m o n e y flexibility 2js by s a m p l e period i n r e c e n t years.
Period Taste variable
st = nt - mt -Z st = (mi -1
-
mt -2)/ mi -21952-80 -1.320 -1.295
1958-80 -2.679 -2.528
1959-80 -3.225 -3.051
1960-80 -3.050 -2.919
1961-80 -3.083 -2.993
The subgroups of meat, milk, and eggs, repairs and water charges, and tobacco and recreation a r e further aggregated here into three larger subgroups, respectively.
TABLE 9 Estimates of t h e cost-of-living index a n d t h e s u b s i s t e n c e c o s t by y e a r for t h e period 1958-80, deflated by t h e CPI.
Year Cost of Subsistence Year Cost of Subsistence
living indexa costb living indexa costb
a Cost of living index in 1958 = 100.0. Figures in parentheses also indicate cost of living indexes but based on 1960-= 100.0.
Subsistence cost = z i p , * flu in 1970 yen.
point estimates for m e a s u r e s of fit, only five e s t i m a t e s were a t t h e 70-percent level and only t h r e e fell below 70 p e r c e n t . The value of income flexibility
5
decreased, and a money flexibility Ge of -2.7 was obtained.
Income and price elasticities were es?iinated and these a r e shown in Table 7. They a r e similar to t h e corresponding elasticities for t h e period 1960-77. Food away from home, beverages, fruit, a n d m e a t , etc., a r e elastic with respect t o income within food subgroups. In t h e nonfood category.
trarisportation, medical c a r e , f u r n i t u r e , and tobacco and recreation have very high income elasticities. Own price elasticities a r e rnostly lower t h a n t h e corresponding 1960-77 results.
Table 8 reports t h e estimates of money flexibilities for more r e c e n t sub- periods. The estimated money flexibility ranges from -2.5 t o -3.2, except for t h e 1952-80 e s t i m a t e s , which a r e given h e r e only for reference. The longer t h e sample period, t h e smaller t h e absolute value of money flexibility t e n d s t o be. Leser's elasticities of substitution were around 0.6 in t h e four
subperiods, while those for t h e 1952-80 period were close t o 1.0.
All
pit
estimates were found t o have positive values a n d t o change, to a g r e a t e r or lesser e x t e n t , from year t o y e a r . The cost of living index and sub- sistence cost by year, computed from e s t i m a t e d demand parameters and observed data, a r e presented i n Table 9. Incidentally, t h e s e results for t h e individual years between 1960 and 1977 were comparable with those obtained for the whole period 1960-77 and examined in Section 4.2.4.4 The Period 1960-80
For this period, two model formulations were employed. The first, and less successful approach used t h e lagged annual change i n deflated income for t h e t a s t e variable i n t h e s a m e way a s described in earlier sections. The second approach utilized a t i m e t r e n d a s a proxy for t h e t a s t e variable. The results for each method will now be briefly described.
4.4.1 Use of Lagged C h a n g e s in I n c o m e
The lagged annual change in deflated income was again found t o play a role in changes i n t a s t e s , although using t h i s kind of taste variable shed little light on t h e dynamic factors a t work. Rice and fish have negative marginal budget shares while all o t h e r subgroups have positive ones. Repairs and water, and furniture, have positive coefficients for t h e t a s t e variable while tobacco and recreation show a negative coefficient a t t h e 5-percent significance level. A t t h e 10-percent level, the coefficient of t h e t a s t e variable is positive for rice and cakes, but negative for fuel and light. These data a r e n o t tabulated here because they a r e very similar t o t h e results in Table 6 for t h e period 1958-80.
4 . 4 . 2 Use of the Zime T r e n d
Since none of t h e specifications of t h e t a s t e variable described earlier worked particularly well in. identifying dynamic factors affecti.ng t h e ex:pendi- t u r e system, a time trend. mechanism was incorporated in t h e model. This version of t h e model h a s been fitted to four data s e t s in r e c e n t years, and i t h a s been found t h a t t h e t i m e t r e n d serves r a t h e r well a s a proxy for t h e t a s t e variable over relatively long t i m e series.
The period 1960-80 is singled o u t h e r e for more detailed discussio.n, and t h e relevant data a r e given in the following two tables. Table 10 indicates t h a t t h e coefficient of t h e t i m e trend is statistically significant for two-thirds of all subgroups of commodities. The t r e n d variable exerts a significantly positive effect on four subgroups, including food away from home and trans- portation, and i t has a negative coefficient for t e n o t h e r subgroups. For the remaining subgroups i t does n o t s e e m t o have any significant influence.
Rice is certainly a n inferior good. All o t h e r commodities a r e normal goods except o t h e r cereals, food away from home, transportation, and educa- tion, which are irresponsive t o income change. The multiple correlation coefficients, whether or n o t they a r e adjusted for degrees of freedom, tend to be g r e a t e r and t h e serial correlation i n t h e residuals is m u c h less serious in Table 10 than in Table 6. The interpolation t e s t resulted in high measures of
TABLE 10 Estimates of t h e demand parameters
&.
I?=. and for t h e period 1960-80. Taste variable:st = t(-10.. . . , - 1 , O . l . . . . -10).
i Commodity group
1 Rice
2 Other cereals 3 Fish
4+5 Meat. milk. etc.
6 Vegetables 7 Processed food 8 Cakes
9 Fruit 10 Beverages 11 F.a.f.h.
12 Rent
13+14 Repairs
+
water 15 Furniture 16 Fuel+
light 17 Clothes18 Personal effects 19 Medical c a r e 20 Toiletries 21 Transportation 22 Education
23+24 Tobacco
+
recreationMarginal budget s h a r e
&
It 1 ratio-.
0292 2.985-.0030* .707
.0360 5.351
,1203 5.854
,0288 6.761
,0161 3.032
,0285 6.868
,0662 6.624
,0677 7.524
,0024' 2 8 9
,0277 3.040
.0372 6.917
,1552 7.844
,0201 2.958
,1762 16.660
,0224 3.169
,0427 10.939
,0273 5.297
-.0055* ,295
.0114* ,735
,1515 3.920
Coemcient of st variable
Multiple correlation coefficient
It
1
ratio 2.519 1.375 2.930 3.011 3.366 ,350 3.559 4.898 3.716 4.512 1.041 2.953 6.020 6.111 9.186 1.183 .779 1.505 7.303 .405 6.335Serial correlation coefficient
'Insignificant at the 5-percent level ( & , 4 , %.,,).
**Significant at the 5-percent level (serial correlation coefficient)
TABLE 11 Demand elasticities
( q j . 6 )
e s t i m a t e d for 21 subgroupsa a t t h e sample average budget s h a r e s(q),
for t h e period 1960-80.~-
2 3 4+5 6 7 8 9 10 11
Price elasticities
eij
Encome elasticities E,
Annual r a t e s of demand shift
[2 -/ F,. ]
x 100
Budget shares
a For a full list of the cornrnodity groups i , j s e e Table 1.
b - e ~ . E,, and Gj a r e as defined in Table 3; -/ a z .
3
= t h e a n n u a l r a t e of shift i n demand for atmeans of all t h e variables, annual rates of demand shift
[? -/ z. -,]
, and sample mean
subgroup j calculated a t the sample means
fit. Only two of t h e 4 4 1 ( N x T ) m e a s u r e s of fit were less t h a n 80 p e r c e n t . Table 11 presents t h e demand elasticities, a n n u a l r a t e s of demand shift, a n d average budget s h a r e s , calculated a t sample means. Fruits, beverages, f u r n i t u r e , a n d clothes have large income elasticities t h a t exceed 2.0.
Demand for these subgroups, however, shifts substantially downward year after year, o t h e r things being equal. On t h e other h a n d , demands for food away f r o m home, fuel and light, transportation, a n d recreation increase annually, while t h e i r income elasticities a r e quite low.
For t h e subperiods 1957-80, 1958-80, 1959-80, a n d 1960-80, e s t i m a t e s of money flexibility a t t h e mid-point were -2.5, -2.7, -2.8, a n d -2.4, respec- tively. The corresponding estimates for Leser's elasticity of substitution were 0.89, 0.76, 0.68, and 0.70. The estimated money flexibilities were r a t h e r stable.
As some pit estimates have negative values for the period 1960-80 and a s t h e r e a r e t h r e e subgroups with a negative marginal budget s h a r e , we do n o t propose to discuss h e r e t h e cost of living index or t h e subsistence cost for t h i s period.
5 INTERPRETATION OF THE RESULTS
Based on t h e estimation results for t h e above four subperiods, demand elasticities and average budget s h a r e s can be derived a t sample m e a n levels by subperiod for t h e two broad categories of food a n d nonfood. The demand elasticities a r e obtained from t h e e s t i m a t e s of income a n d price elasticities for 21 subgroups of commodities and t h e i r sample m e a n average budget s h a r e s , by using Engel aggregation, Cournot aggregation, and t h e homo- geneity condition.'' Table 12 shows t h e derived income a n d price elasticities and average budget shares for food and nonfood in t h e four sample periods.
For t h e period 1960-80 annual r a t e s of shift in d e m a n d a t sample m e a n s are also presented. The r a t e of shift for food is -1.9 p e r c e n t per a n n u m , while both income and price elasticities a r e appreciably higher t h a n expected.
The derived demand elasticities varied across the sample periods. On examination of t h e results for t h e flrst t h r e e periods, i t is clear t h a t income a n d price elasticities for food have been diminishing in absolute t e r m s over t i m e . This is reflected in t h e fact that. the average budget s h a r e of food (or Engel coefficient) declines as p e r capita income grows. The demand for food is m o r e susceptible to income and food price t h a n t o nonfood price. Cross price elasticities take negative values, satisfying t h e theoretical features of t h e linear expenditure system.12 This indicates t h a t t h e income effect of a change in price exceeds t h e substitution effect, a n d t h a t t h e e s t i m a t e s a t sample means a r e positive a n d can be interpreted as subsistence consump- tion levels.
According t o the analysis of t h e 21-commodity breakdown, all e s t i m a t e s of
pit
were positive in t h e first t h r e e subperiods, where own price elasticities were all less t h a n 1.0 in absolute value. Meanwhile, income elasticities were particularly high for such nonfood subgroups as transportation, medical c a r e , furniture, and recreation during t h e whole period studied. Rent, as well a s fuel a n d light, exhibited a n upward tendency i n i n c o m e elasticity. It isTABLE 12 Demand e l a s t i c i t i e s a n d average budget s h a r e s for food a n d nonfood, derived f r o m t h e r e s u l t s for 21-commodity breakdowns for f o u r different periods.
Period
- - - I " " I
1 2 Ei 1 2 Ei 1 2 4 1 2
G
1 Food -.36 -.20 .56 -.32 -.I5 .47 -.29 -.I5 .44 -.60 -.38 .98 -1.92
Demand elasticity matrix: (Fv
4);
(i. j = 1,2).o;j = elasticity of group i with respect to the j t h price calculated a t the sample means.
4
= income elasticity of group i calculated at the sample means.Gj = budget share of group j calculated at the sample means.
4 = annual rate of shift in demand for group i calculated a t the sample means.
beyond question t h a t larger and higher-quality housing continues t o be in g r e a t d e m a n d . At t h e same t i m e , beverages, food away from h o m e , f r u i t , and m e a t all exhibit high income elasticities.
I t is clear t h a t these commodity groups with high income elasticity have been rising in t h e i r relative position in total expenditure. Rice arid o t h e r cereals, which have a negative or low income elasticity, have dropped remarkably in t h e i r s h a r e of t h e consumer's budget. As a r e s u l t , income is considered t h e m o s t important factor in allocating t h e total budget between different commodities, always assuming t h a t annual i n c r e m e n t in income or t h e a n n u a l growth r a t e thereof is used for t h e t a s t e variable.
A brief illustration of t h e changes in prices and t h e i r influence on con- sumption p a t t e r n s m a y be useful a t this point. Over t h e period 1958-80, for instance, the c u r r e n t price increased 10 t i m e s for fish, 9 t i m e s for veget- ables, 6 times for other cereals, 5.7 times for food away from home, and 5 t i m e s for rice, whereas t h e r e was a 4.4-times rise in t h e CPI. Other subgroups of food commodities advanced relatively slowly in c u r r e n t price. Of t h e non- food subgroups, education and repairs each went up 8 t i m e s , and r e n t advanced 6 times in price during t h e period 1958-80. Increases in o t h e r prices were relatively small.
No s h a r p drop was observed i n t h e expenditures in c o n s t a n t prices on flsh, vegetables, food away from home, r e n t , or education, etc., whose prices jumped markedly during t h e period in question. This suggests t h a t consump- tion was affected more by income and probably by various dynamic factors t h a n by relative prices. Except for food away from home a n d r e n t , t h e l a t t e r subgroups s e e m t o have ceased to grow in t e r m s of per capita consumption.
As is widely recognized, money flexibility e s t i m a t e s are sensitive to differences i n the sample period, commodity classification, model specification, whether t h e model version is s t a t i c or dynamic, t h e type of proxy variable used for changing tastes, and so on. On t h e basis of results for t h e s a m e commodity classification and model specification, t h e r e is some indication t h a t t h e longer t h e sample period, t h e g r e a t e r t h e money flexibil- ity i n algebraic t e r m s . Since own price elasticities a r e closely related to t h e magnitude of money flexibility, t h e y are likely t o become larger i n absolute value over a longer period of time. Thus, money flexibility is t o a large e x t e n t associated with substitutability between commodities. For t h e s e reasons, we agree with t h e assertion t h a t too m u c h emphasis should n o t be placed on t h e welfare aspect of money flexibility.13
Several o t h e r notable characteristics of t h e demand p a t t e r n s in t h e 1950s c a n be singled out. Traditional Japanese di.etary habits prevailed, with a n increased per capita consumption of rice and fish a n d less consumption of barley a n d o t h e r miscellaneous grains. Food away from home a n d animal protein food like milk a n d eggs exhibited very high income elasticities. In view of t h e highly income-elastic demand for f u r n i t u r e a n d repairs (and equipment), i t is evident t h a t the Japanese h a d a growing i n t e r e s t in housing facilities.
In t h e 1960s and the 1970s, p e r capita consumption of rice dropped markedly while m e a t , fruits, beverages, and food away from home remained strongly i n demand. Other cereals t u r n e d into normal o r n e u t r a l goods a s bread, noodles, e t c . , became more deeply-rooted. i n dietary p a t t e r n s . Milk and
egg consumption ceased t o grow a t a rapid rate. Apart from food consump- tion, t h e r e was great demand for private cars with t h e advance of motoriza- tion into daily life. There was a noticeable rise in the income elasticity for r e n t , and later also in t h e demand for fuel and light, indicating a strong demand for more spacious and comfortable housing. Education was essen- tially inelastic with respect to income and prices.
The introduction of t h e taste variable into t h e expenditure functions made i t possible t o obtain a good fit in t h e regression of t h e linear expendi- t u r e system to long time series. The lagged increase in deflated income and the lagged r a t e of increase i n deflated income were both found t o be fairly effective in structuring a dynamic system of consumer demand, in particular for periods of slow and moderate economic growth when consumers adopt a more prudent attitude toward purchasing. However, time trends seem more suitable for describing changing tastes t h a n the other specifications of the taste variable utilized here.
6 CONCLUDING REMARKS
In this study, changing patterns of Japanese consumer expenditure and demand over t h e last t h r e e decades were analyzed. The analysis was con- ducted a t t h e subgroup level on the basis of time series of family budget data, using Powell's version of the linear expenditure system. The demand estima- tion problem was formulated as a complete systems approach within t h e clas- sical framework of consumer demand theory.
When analyzing the actual situation regarding consumer demand over a long period of time, i t is very important to identify t h e effects of dynamic fac- tors a s well a s those of income and price changes.14 For this reason, a proxy for changing tastes was incorporated into the expenditure system. The incor- poration of a taste variable led t o fairly good regression results and more stable demand and utility parameters were obtained. The taste variable in this study was generally formulated in three ways: as the annual increment in deflated income, as the annual r a t e of growth of deflated income, or as a time trend. For earlier subperiods t h e first two specifications were useful.
For later subperiods, a lagged annual increase in deflated income, a lagged annual r a t e of growth in deflated income, and a time trend were used separately; the time trend proved effective in achieving valid regression results. These approaches give a fairly plausible account of structural change in ccnsumer demand in recent years.
Consumption patterns a r e considered to have changed substantially toward more "Westernized" living and eating habits since t h e end of t h e 1950s and t h e beginning of the 1960s. With regard to per capita food consumption, rice and fish went down with increases in deflated income, whereas animal protein food, fruit, and beverages increased rapidly. Food away from home increased steadily throughout the period. Turning to nonfood consumption, private transportation practically became a daily necessity. There w a s a growing demand for more spacious and pleasant accommodation. It is also possible t h a t people's views of education have been changing slightly and t h a t they may be gradually diversifying in various ways.
