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Import prices and the distribution of personal income
European Economic Rcviec 12 (lY79) 171 179. @ North-Holland
Publishing Company
J. Neil1 FORTUNE*
Receited October 1977, final version received September 1978 An indirect translog utility function is esttmated for U.S. expenditure on domestically produced non-durables. durables, services and consumer imports. Empirical tests le;td to the rejection of homogeneity and linear logarithmic utility as valid functional forms. Estimates of expenditure elasticities indicate that imported varieties of consumer goods are luxuries. An exogenous decrease in the price of these goods, which would occur when tariff barriers are relaxed. would be especially beneticial to upper income consumers. Finally. a redistribution of expenditure from upper income consumers to lower income consumers will increase expenditure on domestically produced goods and reduce expenditure on consumer imports.
1. introduction
The conventional approach to the estimation of demand functions for consumer imports employs a double logarithmic relationship and, as a result. implicitly assumes that the utility function is separable between consumer imports and domestically produced goods (i.e., domestic goods can be aggregated). Such separability implies that consumers make their decisions on expenditure on consumer imports independently of their decisions on the allocation of expenditure among domestically produced goods. In this manner, the conventional procedure places arbitrary restrictions on consumer behaviour. Jorgenson and Lau (1975) have derived direct and indirect translog utility functions which do not impose separability as a maintained hypothesis. Indeed, these utility functions are suffkiently flexible that they can in-’ corporate a form in which no hypotheses are maintained. Moreover. the imposition of restrictions enables the testing of hypotheses about various functional forms. Jorgenson and Lau (1975) have performed such tests fol *The author would like to thank, without implicating, A.V. Dcardorff, W.J. Gillen. R.M. Stern, two referees and members of the research seminar at the Graduate Institute of International Studies (Geneva) for constructive comments on earlier drafts. Financial support was gratefully received from the Canada Council.
the United States using :\ three commodity breakdown of pcrsonal
c011~11111c’1’
cspditiire. The
indirect
translog utility function is used in this study to dcrivc the domestic demand in the U.S. for domestically produced consumer nondurables ( 1 ), durables (2), services (3), and final wnsumcr imports (4). Tests of hypotheses about functional forms are performed using these foul commodity groups1 as arguments in the urility function. The indirect utility function corresponds to the direct demand function since quantity consumed i?; a function of price. Quantities are endogt’nous. wfiik prices are exogenous. The indirect utility function allocvs expenditure shares to wry with the Icwl ol’ prices and cxpcnditure. Price and cxpcnditurs tz!asticitics cm be readily deriled without imposin g the restriction of scparabilitj. Inipk~~tions ;~lwut the cffccts of cliaiqcs in import prices cm 1x2 ohtaiiid from cstiwitc‘c; of these elasticities. If consmner imports are expenditure elastic, these imported wric‘ties of consumer goods are luxuries. which Alec preferred by upper income cmsumers. The tariff discriminates against thcsc Iusury goods. Under these circumstances. mi esogeiimis decre;w in coiisimt’r import prices. whkh would occw when tariff barriers NT lowred.’ will be pa-t icularly bencfici;il to upper incomc consuint’rs. 2. The espcnditurc share equations
Jorgenson and Lau ( 1975) dcfiiic
fhc
Iranslog
indirt
iltility
fimclioil
lvhere pj is the price of the .jth conmodit~. ;mci ,IJ is the \uluc of consumer expendit we. The lo,(Tform of Roy’s identity ih
;b
pc~wmd
173
where /Jfi = x/rii. TIN twrtnalizatiot~ In the present GISC 111 =4. Since
Cli
= - I is required for cstitn;ttion.
tlic expenditure shares sum to unity.
tlit‘
parameters of any one equation GUI hc obtained frotn the other t11ree. The cquatiun for consumer imports is obtained in this manner. Following Jorpctison and Lrtu (1975. p. 561, the hypothesis of utility tii~tsitnizatioti is taken 1o bc 3ti assutnptioti r;tther than an hypothesis 10 bc tcstcd’. L’tility maximiation implies that the parameters satisfy fourtam cqu;tlily atid sj mmctry rcstrictiotis. -rhcse restrictions reduce the. tiumbcr 01‘ utiktiowi patwiictcrs t’rotii twenty-scwti 1o thirtecn.3 Restriction5 017 the I;vm o!’ the utilit! I‘unction arc tcstcd wthcr than imposed. A stochastic spccitkatiotl is added to the cxpcnditurc sharc equ;:tion~ and I,‘,,-, must t&c Ihc S;IIIW wluc~ tight cqualit~ restrictions. The imposition rcstrictiwis 011 tilt patwiictcrs:
/I \I .+
and
in all three equations. Thcrc arc of qmtnctry entails fhc foll~~~~ ing
Estiinatss of the parameters of the indirect tramlog utility function.” ___ _ .- _ -_ --- --- -I ._ _.. __-- - -_-- _-_----. ._ ____ _ - .._- .-_. ... . Equalily and synimetry Pa rantctcrs -~1_5_------_._-Iw_w __ _ _ _._-_______--_-
- 0.430933
- 0.0766S3 (0.02 I 6 I 5
- 0.0 164S6 (0.036797
-0. I37093 (0.0036S2 )
%;
- O.390552 ciu~l7oxz
- 0.303935 (0.029572
- 0.4 I 0 I 60 (0.004~32 )
72
I .96X037
2.05540 I
I .978 I Hh
Ii ! !
- 0.330139 (0.043870
- 0.3 I9248 (0.095766
1;: z
0.10575l (@.o?3lcz,
10.02062s) 3:
/G:;
0 101’1’
u_w29679 I
(iO&25
14.:
-0.101210
lk
-0.121’1~17 to.:i39701 )
1;: :.
- 0.01 MS I
0. I 1600-l
(0.0 3ZZlS)
t0.060902 1
0.15 1064 - 0.17S9H6 (O.OS? I64 k
R’
0.9999
0.9093
SSR
0.0000093i2
O.~H)C~5hWh
._-_-_-__
(0*005t(3~)
0.166972 (0*0tc025c,
- wxC79
- --. ---.___a-_-
-
Linear logarithmic Honwpeneit~ utility ._--_-----__-__ ---__ _______ _-_- _______
- 0.633970 (O.~W~S5)
- iMMx402
2,
.
__- _ _ __--__.______._ ____.--
0.9s97
..
i).ooS4~wh _
“Standard tmors in parent hew.
the corresponding durables personal durables are used
current
dollar
expenditure
figures
on non-durablcs
and
(domestically produced and imported) in order to obtuin datu on domestic consumer expenditure on domestically produced INW and-durables in current dollars. Implicit price deflators ( 19% = 100) in order to obtain constant dollar values of personal domestic
consumer expenditure The constant dollar
on domestically value of total
produced non-durables and durables. consumer imports is obtained by
175
subtracting the sum of the constant dollar values of personal domestic consumer expenditure on domestically produced non-durables. durablcs and services from the constant dollar value of personal domestic consumer expenditure. An implicit price deflator for consumer imports is obtained by dividing current dollar consumer imports by constant dollar consumer imports. The requisite figures for the value of consumer imports of nondurables and durables are obtained from the Survey of Current Business. Data on the wustm~t dollar value of consumer imports of non-durables and durables. and their implicit price dellators are not available. Hence, it is not possible to disaggregate consumer imports into non-durablcs and durablcs in the translog utility function. The assumption of utility maximization is imposed by estimating4 a ‘stacked’ regression’ in which the parameters satisfy equality and symmetry res~ricfiws. ‘Stacked’ regressions are also estimated to test the validity of the homogeneity and linear ic,garithmic utihty restrictions. The resulting loss 01 fit from imposing these restrictions will be significant or not according to whether the constrained (e.g.. by homogeneity) estimating equation differs Ggnificantlc from the unconslrained equation.” There are fifteen observations for each expenditure share equation. so there are forty-five observations wailablc for the ‘stacked’ regressions. The equalit) and symmetry estimates of ?Ge indirect transiog utilit> function arc prcscnlcd in the first column of tablt: I. The &maws under thy’ humc,gcnei t j* and linear logarithmic utility rwric’tions ;trt’ @wn in the . sc’wiid uiid third cohiiiiiih rwpccti\ ciy. I-lypothcscs about 111~’ form of the’ Nilit>, functions are fc3tt’d b> niwl3 01’ ;~ii F 4a\istic:
176
Under the linear logarithmic form of the utility function, all expenditure proportions are constant for all values of prices and expenditure. If the homogeneity restriction is maintained, linear logarithmic utility can be tested. Wkn the linear lugarithnk utility restrictim is iqmsed on the indirect utility function, the calculated F statistic with 6 and 36 degrees of freedom is 82.54, while the critical value of F is 3.35 at the one percent level of significance. Consequently the hypothesis of linear logarithmic dtility is rejected. Since homogeneity and linear logarithmic utility have been rejected, the subsequent analysis of consumer preferences refers to the equality and symmetry estimates. However, the satisfaction of the regularity conditions is a prerequisite for this analysis. The equality and symmetry estimates are used to test these conditions. Since the indirect utility function is a decreasing function of the ratios of each prkz to personal consumer expenditure, the monotonicity conditions are valid. Moreover. the estimation of the matrices of elasticities of substitution indicates that the curvature conditions are satisfied for the indirect utility function.
3. Consumer preferences
.
In the indirect utility function, quantities are endogenous while prices are exogenous. The parameters of the indirect utility function can be used to determine whether an exogenous decrease in the price of consumer imports provides greater benefits to upper or lo~r income consumers. An exogenous decrease in consumer import prices would occur for instrmcc when tariff barriers are relaxed. A reduction in the price of consumer imports will be especially advantageous to upper income consumers if these goods are expenditure elastic. as one would expect of luxury ite‘ms. Estimation of the magnitudes of the expenditure elasticities of dome& demand for domestically produced goods and for consumer imports will determine the preferences of upper and lowe! income consumers for these goods. Expenditure elasticities for domestically produced non-durahles. durubles. services and consumer imports Ei,ZI(i = 1.2.3.4) arc derivable from the expenditure share equations corresponding to the indirect utility function :
where kf: refers to the share of expenditure allocated to good i. The formulr~
177
EItimatcd
cxpcnditure clasticitics (L, ,, 1. marginal propen&ies consume ( .ZIPt‘, ) and import price elasticities 11:~~ ).
- --- --___
-_ - .---
_-_--.__--__I_____ -----l_l_l
195K
1965
0.793922
I:1\I 1s.J v (:A21
O.t(21857 I AI7427 I .0492x0 1.525478
MPC, .W’C~ .CfPC, .I1PC.,
0.385697 0.17H902 0.409009 0.02639 1
0.34106Y 0.2033 13 0.42X7hS 0.026893
* --- _.-T--e--__ .- -.. -_I.- - ._-.-------_1.1rf
i:IJ
--
-
1.Y 10603
-- __ __ -.
10
1.392554
1.(I558 11
1.4673Y5
_ -. -_
- I.779162
1972
.--_. -_- --_. -_ _-_ ___
- ._. _ _ _. _
0.768 101 1.36221% I .0632 10 I .370666 (Lw37x4 I). 1Y6977 0.3-534,cY 0.04~7x0
-1 ..qPl51 _ _
.-
for this elasticity is obtained from Christensen and %l;n~3- ( 1977. p_ 51 j.The margina) propensity to consume each good out of an additional dollar . of total expenditure is q~,~~. Thus ‘&,Lt; = 1. The responsiveness of domestic consumers to an exogenous decrease in the price of consumer imports is measured by the own-price elasticity of consumer imports I:~~. Christensen and Manser (1977. p. 5) dcrke the formula for this elasticity from the expenditure &arc tzquations of the indirect translop utility function.
The parameters of the indirect translop utility function art’ used to dt’rk estimates of expenditure elasticities for domesticaily produced non-durables ( 1). durables (2). services (3). and consumer imports (4) for 19%. 1965 and W72. These estimates, which are presented in table 2. IWJ~ in *accordance with Ehgd’s Irrw. The Engel curves arc ct.nca\*e from ;tho~ for domcst.ic;lll~ producc’d Jurubks ;md consumer imports (d;i\I > 1 ). concaw front bt~lo~vfoi domestically produced non-durables ((;i,, < 1 1, and approximately ;i straight line for scrviccs (q,, 4 1). Thcsc EngtA cur\cs h;tvc t hc ad\~antage tl:at fhq NC obtuincd from budget shc\re cyuations in which prices arc included along with pcrsonul consumer expenditure. Owr the puiod 19% 72. all of tllc cxpcnditure Asticitics except those for services declined. This dcclinc is consistent with previous cvidt‘na?’ indicating a iicgatiw relationship o\ cr a
.“;vide range of commodities between expenditure (income) elasticities and total expenditure (income). Declining expenditure elasticities prevent the cqenditure share of kuries from cotttinuously increasing leading ultimately &I the vio&ion of the budget constraint. Thr;oughout the period 1958-72, the estimates of the expenditure elasticities for consumer imports were greater than the estimates for the domestically produced goods. These relative magnitudes indicate that the preferences of upper income consumers are for imported varieties of consumer goods, which are deemed to be luxuries. Corroboration for the inference that consummer imports are composed of luxury goods can be obtained from an examinaGon of the marginal propensities to consume &WC out of an additional dollar of personal consumer expenditure over the period 195% 72. As personal consumer expenditure in the United States has increased over the period. the MPC for domestically produced non-durables has declined. the .WPC for domestically produced durables and services have increased slightly, white the MPC’ for consumer imports has increased substantially. This evidence indicates that consumers in the United States view domestically produced non-durabtes as necessities, domestically produced durabtes and services as moderate luxuries and imported varieties of consumer goods as luxuries. The imported varieties are preferred by upper income consumers. Therefore. an exopcnous decrease in consumer import prices, which would occur when tariff barriers arc lowered. will be particularly beneficial to upper income consumers. The magnitude of the price elasticities of demand for consumer imports I:~~ (table 2) indicates the response of consumers to such a decrease in import prices. The estimates of these elasticities are higher than those obtained from most previous studies. By imposing separability between consumer imports and domestically produced goods, these studies have caused the estimates of the price elasticity of demand for consumer imports to be biased downward, 4. conciasions A translog indirect utility function has been estimated usinp U.S. data fog domestically produced consumer non-durables, durables. services and consumer imports. The results obtained from the equality and symmetry estimates of this utility function indicate that consumer imports ure cxpenditure elastic as one would expect of goods that are luxuries. An exogenous decrease in consumer import prices occurring wl~cn tariff barriers are reduced rvili. be especially advantageous to upper income consumers. Alternatively. food stamp programs. rent subsidies, medicare and other welfare schemes. which act to redistribute total personal consumer expenditure from upper income to lower income consumers. wilt increase expenditure on domestically
produced paribus.
goods
and
reduce
cxpenditurc
on consumer
imports.
cctoris
Bcrndt, E.R. and L.R. C’hristcnsen. 1973. The translog function and the substitution of equipment, structures, and labor in U.S. manufacturing 1929 68. Journal of Econometrics I. xt 113. Bcrndt, E.R., W.E. Diewcrt and M.N. Darrough. 1977, Flcxi!& functional forms and qwndidemand functions. International ture distributions: An ;qplication to Canadian conwrwr
C’hri~tcnscn. L.R. and M.E. Manscr. 1977. !!stimating U.S. conaumr prcfcrcnccs for meat Mill1 ;i flexible utility function, Journal of Eco&,wwtrics 5, 37 53. Cioldbcrgcr. AS. and T. G~tmaletws. 1970. A crew-country comparison 01‘con~~1111cr cxpcnditurc pat terns. European Economk Rcb iw I. 357 J(H). Houthakkcr. H.S.. 1957. An internationul comparison of houachoid expenditure pattt‘rns commcmcwating the wnttlnary of lGigcl’3 Ia. lkonomctrica 25. 533 551. Jqcnson. D.W. and L.J. Lau. 1075. The htructure of consumer prcfcrcnccs. ,Annals 01 Exx~n~mic and Social Moaawcment 4. 49 101.
Publishing Company
J. Neil1 FORTUNE*
Receited October 1977, final version received September 1978 An indirect translog utility function is esttmated for U.S. expenditure on domestically produced non-durables. durables, services and consumer imports. Empirical tests le;td to the rejection of homogeneity and linear logarithmic utility as valid functional forms. Estimates of expenditure elasticities indicate that imported varieties of consumer goods are luxuries. An exogenous decrease in the price of these goods, which would occur when tariff barriers are relaxed. would be especially beneticial to upper income consumers. Finally. a redistribution of expenditure from upper income consumers to lower income consumers will increase expenditure on domestically produced goods and reduce expenditure on consumer imports.
1. introduction
The conventional approach to the estimation of demand functions for consumer imports employs a double logarithmic relationship and, as a result. implicitly assumes that the utility function is separable between consumer imports and domestically produced goods (i.e., domestic goods can be aggregated). Such separability implies that consumers make their decisions on expenditure on consumer imports independently of their decisions on the allocation of expenditure among domestically produced goods. In this manner, the conventional procedure places arbitrary restrictions on consumer behaviour. Jorgenson and Lau (1975) have derived direct and indirect translog utility functions which do not impose separability as a maintained hypothesis. Indeed, these utility functions are suffkiently flexible that they can in-’ corporate a form in which no hypotheses are maintained. Moreover. the imposition of restrictions enables the testing of hypotheses about various functional forms. Jorgenson and Lau (1975) have performed such tests fol *The author would like to thank, without implicating, A.V. Dcardorff, W.J. Gillen. R.M. Stern, two referees and members of the research seminar at the Graduate Institute of International Studies (Geneva) for constructive comments on earlier drafts. Financial support was gratefully received from the Canada Council.
the United States using :\ three commodity breakdown of pcrsonal
c011~11111c’1’
cspditiire. The
indirect
translog utility function is used in this study to dcrivc the domestic demand in the U.S. for domestically produced consumer nondurables ( 1 ), durables (2), services (3), and final wnsumcr imports (4). Tests of hypotheses about functional forms are performed using these foul commodity groups1 as arguments in the urility function. The indirect utility function corresponds to the direct demand function since quantity consumed i?; a function of price. Quantities are endogt’nous. wfiik prices are exogenous. The indirect utility function allocvs expenditure shares to wry with the Icwl ol’ prices and cxpcnditure. Price and cxpcnditurs tz!asticitics cm be readily deriled without imposin g the restriction of scparabilitj. Inipk~~tions ;~lwut the cffccts of cliaiqcs in import prices cm 1x2 ohtaiiid from cstiwitc‘c; of these elasticities. If consmner imports are expenditure elastic, these imported wric‘ties of consumer goods are luxuries. which Alec preferred by upper income cmsumers. The tariff discriminates against thcsc Iusury goods. Under these circumstances. mi esogeiimis decre;w in coiisimt’r import prices. whkh would occw when tariff barriers NT lowred.’ will be pa-t icularly bencfici;il to upper incomc consuint’rs. 2. The espcnditurc share equations
Jorgenson and Lau ( 1975) dcfiiic
fhc
Iranslog
indirt
iltility
fimclioil
lvhere pj is the price of the .jth conmodit~. ;mci ,IJ is the \uluc of consumer expendit we. The lo,(Tform of Roy’s identity ih
;b
pc~wmd
173
where /Jfi = x/rii. TIN twrtnalizatiot~ In the present GISC 111 =4. Since
Cli
= - I is required for cstitn;ttion.
tlic expenditure shares sum to unity.
tlit‘
parameters of any one equation GUI hc obtained frotn the other t11ree. The cquatiun for consumer imports is obtained in this manner. Following Jorpctison and Lrtu (1975. p. 561, the hypothesis of utility tii~tsitnizatioti is taken 1o bc 3ti assutnptioti r;tther than an hypothesis 10 bc tcstcd’. L’tility maximiation implies that the parameters satisfy fourtam cqu;tlily atid sj mmctry rcstrictiotis. -rhcse restrictions reduce the. tiumbcr 01‘ utiktiowi patwiictcrs t’rotii twenty-scwti 1o thirtecn.3 Restriction5 017 the I;vm o!’ the utilit! I‘unction arc tcstcd wthcr than imposed. A stochastic spccitkatiotl is added to the cxpcnditurc sharc equ;:tion~ and I,‘,,-, must t&c Ihc S;IIIW wluc~ tight cqualit~ restrictions. The imposition rcstrictiwis 011 tilt patwiictcrs:
/I \I .+
and
in all three equations. Thcrc arc of qmtnctry entails fhc foll~~~~ ing
Estiinatss of the parameters of the indirect tramlog utility function.” ___ _ .- _ -_ --- --- -I ._ _.. __-- - -_-- _-_----. ._ ____ _ - .._- .-_. ... . Equalily and synimetry Pa rantctcrs -~1_5_------_._-Iw_w __ _ _ _._-_______--_-
- 0.430933
- 0.0766S3 (0.02 I 6 I 5
- 0.0 164S6 (0.036797
-0. I37093 (0.0036S2 )
%;
- O.390552 ciu~l7oxz
- 0.303935 (0.029572
- 0.4 I 0 I 60 (0.004~32 )
72
I .96X037
2.05540 I
I .978 I Hh
Ii ! !
- 0.330139 (0.043870
- 0.3 I9248 (0.095766
1;: z
0.10575l (@.o?3lcz,
10.02062s) 3:
/G:;
0 101’1’
u_w29679 I
(iO&25
14.:
-0.101210
lk
-0.121’1~17 to.:i39701 )
1;: :.
- 0.01 MS I
0. I 1600-l
(0.0 3ZZlS)
t0.060902 1
0.15 1064 - 0.17S9H6 (O.OS? I64 k
R’
0.9999
0.9093
SSR
0.0000093i2
O.~H)C~5hWh
._-_-_-__
(0*005t(3~)
0.166972 (0*0tc025c,
- wxC79
- --. ---.___a-_-
-
Linear logarithmic Honwpeneit~ utility ._--_-----__-__ ---__ _______ _-_- _______
- 0.633970 (O.~W~S5)
- iMMx402
2,
.
__- _ _ __--__.______._ ____.--
0.9s97
..
i).ooS4~wh _
“Standard tmors in parent hew.
the corresponding durables personal durables are used
current
dollar
expenditure
figures
on non-durablcs
and
(domestically produced and imported) in order to obtuin datu on domestic consumer expenditure on domestically produced INW and-durables in current dollars. Implicit price deflators ( 19% = 100) in order to obtain constant dollar values of personal domestic
consumer expenditure The constant dollar
on domestically value of total
produced non-durables and durables. consumer imports is obtained by
175
subtracting the sum of the constant dollar values of personal domestic consumer expenditure on domestically produced non-durables. durablcs and services from the constant dollar value of personal domestic consumer expenditure. An implicit price deflator for consumer imports is obtained by dividing current dollar consumer imports by constant dollar consumer imports. The requisite figures for the value of consumer imports of nondurables and durables are obtained from the Survey of Current Business. Data on the wustm~t dollar value of consumer imports of non-durables and durables. and their implicit price dellators are not available. Hence, it is not possible to disaggregate consumer imports into non-durablcs and durablcs in the translog utility function. The assumption of utility maximization is imposed by estimating4 a ‘stacked’ regression’ in which the parameters satisfy equality and symmetry res~ricfiws. ‘Stacked’ regressions are also estimated to test the validity of the homogeneity and linear ic,garithmic utihty restrictions. The resulting loss 01 fit from imposing these restrictions will be significant or not according to whether the constrained (e.g.. by homogeneity) estimating equation differs Ggnificantlc from the unconslrained equation.” There are fifteen observations for each expenditure share equation. so there are forty-five observations wailablc for the ‘stacked’ regressions. The equalit) and symmetry estimates of ?Ge indirect transiog utilit> function arc prcscnlcd in the first column of tablt: I. The &maws under thy’ humc,gcnei t j* and linear logarithmic utility rwric’tions ;trt’ @wn in the . sc’wiid uiid third cohiiiiiih rwpccti\ ciy. I-lypothcscs about 111~’ form of the’ Nilit>, functions are fc3tt’d b> niwl3 01’ ;~ii F 4a\istic:
176
Under the linear logarithmic form of the utility function, all expenditure proportions are constant for all values of prices and expenditure. If the homogeneity restriction is maintained, linear logarithmic utility can be tested. Wkn the linear lugarithnk utility restrictim is iqmsed on the indirect utility function, the calculated F statistic with 6 and 36 degrees of freedom is 82.54, while the critical value of F is 3.35 at the one percent level of significance. Consequently the hypothesis of linear logarithmic dtility is rejected. Since homogeneity and linear logarithmic utility have been rejected, the subsequent analysis of consumer preferences refers to the equality and symmetry estimates. However, the satisfaction of the regularity conditions is a prerequisite for this analysis. The equality and symmetry estimates are used to test these conditions. Since the indirect utility function is a decreasing function of the ratios of each prkz to personal consumer expenditure, the monotonicity conditions are valid. Moreover. the estimation of the matrices of elasticities of substitution indicates that the curvature conditions are satisfied for the indirect utility function.
3. Consumer preferences
.
In the indirect utility function, quantities are endogenous while prices are exogenous. The parameters of the indirect utility function can be used to determine whether an exogenous decrease in the price of consumer imports provides greater benefits to upper or lo~r income consumers. An exogenous decrease in consumer import prices would occur for instrmcc when tariff barriers are relaxed. A reduction in the price of consumer imports will be especially advantageous to upper income consumers if these goods are expenditure elastic. as one would expect of luxury ite‘ms. Estimation of the magnitudes of the expenditure elasticities of dome& demand for domestically produced goods and for consumer imports will determine the preferences of upper and lowe! income consumers for these goods. Expenditure elasticities for domestically produced non-durahles. durubles. services and consumer imports Ei,ZI(i = 1.2.3.4) arc derivable from the expenditure share equations corresponding to the indirect utility function :
where kf: refers to the share of expenditure allocated to good i. The formulr~
177
EItimatcd
cxpcnditure clasticitics (L, ,, 1. marginal propen&ies consume ( .ZIPt‘, ) and import price elasticities 11:~~ ).
- --- --___
-_ - .---
_-_--.__--__I_____ -----l_l_l
195K
1965
0.793922
I:1\I 1s.J v (:A21
O.t(21857 I AI7427 I .0492x0 1.525478
MPC, .W’C~ .CfPC, .I1PC.,
0.385697 0.17H902 0.409009 0.02639 1
0.34106Y 0.2033 13 0.42X7hS 0.026893
* --- _.-T--e--__ .- -.. -_I.- - ._-.-------_1.1rf
i:IJ
--
-
1.Y 10603
-- __ __ -.
10
1.392554
1.(I558 11
1.4673Y5
_ -. -_
- I.779162
1972
.--_. -_- --_. -_ _-_ ___
- ._. _ _ _. _
0.768 101 1.36221% I .0632 10 I .370666 (Lw37x4 I). 1Y6977 0.3-534,cY 0.04~7x0
-1 ..qPl51 _ _
.-
for this elasticity is obtained from Christensen and %l;n~3- ( 1977. p_ 51 j.The margina) propensity to consume each good out of an additional dollar . of total expenditure is q~,~~. Thus ‘&,Lt; = 1. The responsiveness of domestic consumers to an exogenous decrease in the price of consumer imports is measured by the own-price elasticity of consumer imports I:~~. Christensen and Manser (1977. p. 5) dcrke the formula for this elasticity from the expenditure &arc tzquations of the indirect translop utility function.
The parameters of the indirect translop utility function art’ used to dt’rk estimates of expenditure elasticities for domesticaily produced non-durables ( 1). durables (2). services (3). and consumer imports (4) for 19%. 1965 and W72. These estimates, which are presented in table 2. IWJ~ in *accordance with Ehgd’s Irrw. The Engel curves arc ct.nca\*e from ;tho~ for domcst.ic;lll~ producc’d Jurubks ;md consumer imports (d;i\I > 1 ). concaw front bt~lo~vfoi domestically produced non-durables ((;i,, < 1 1, and approximately ;i straight line for scrviccs (q,, 4 1). Thcsc EngtA cur\cs h;tvc t hc ad\~antage tl:at fhq NC obtuincd from budget shc\re cyuations in which prices arc included along with pcrsonul consumer expenditure. Owr the puiod 19% 72. all of tllc cxpcnditure Asticitics except those for services declined. This dcclinc is consistent with previous cvidt‘na?’ indicating a iicgatiw relationship o\ cr a
.“;vide range of commodities between expenditure (income) elasticities and total expenditure (income). Declining expenditure elasticities prevent the cqenditure share of kuries from cotttinuously increasing leading ultimately &I the vio&ion of the budget constraint. Thr;oughout the period 1958-72, the estimates of the expenditure elasticities for consumer imports were greater than the estimates for the domestically produced goods. These relative magnitudes indicate that the preferences of upper income consumers are for imported varieties of consumer goods, which are deemed to be luxuries. Corroboration for the inference that consummer imports are composed of luxury goods can be obtained from an examinaGon of the marginal propensities to consume &WC out of an additional dollar of personal consumer expenditure over the period 195% 72. As personal consumer expenditure in the United States has increased over the period. the MPC for domestically produced non-durables has declined. the .WPC for domestically produced durables and services have increased slightly, white the MPC’ for consumer imports has increased substantially. This evidence indicates that consumers in the United States view domestically produced non-durabtes as necessities, domestically produced durabtes and services as moderate luxuries and imported varieties of consumer goods as luxuries. The imported varieties are preferred by upper income consumers. Therefore. an exopcnous decrease in consumer import prices, which would occur when tariff barriers arc lowered. will be particularly beneficial to upper income consumers. The magnitude of the price elasticities of demand for consumer imports I:~~ (table 2) indicates the response of consumers to such a decrease in import prices. The estimates of these elasticities are higher than those obtained from most previous studies. By imposing separability between consumer imports and domestically produced goods, these studies have caused the estimates of the price elasticity of demand for consumer imports to be biased downward, 4. conciasions A translog indirect utility function has been estimated usinp U.S. data fog domestically produced consumer non-durables, durables. services and consumer imports. The results obtained from the equality and symmetry estimates of this utility function indicate that consumer imports ure cxpenditure elastic as one would expect of goods that are luxuries. An exogenous decrease in consumer import prices occurring wl~cn tariff barriers are reduced rvili. be especially advantageous to upper income consumers. Alternatively. food stamp programs. rent subsidies, medicare and other welfare schemes. which act to redistribute total personal consumer expenditure from upper income to lower income consumers. wilt increase expenditure on domestically
produced paribus.
goods
and
reduce
cxpenditurc
on consumer
imports.
cctoris
Bcrndt, E.R. and L.R. C’hristcnsen. 1973. The translog function and the substitution of equipment, structures, and labor in U.S. manufacturing 1929 68. Journal of Econometrics I. xt 113. Bcrndt, E.R., W.E. Diewcrt and M.N. Darrough. 1977, Flcxi!& functional forms and qwndidemand functions. International ture distributions: An ;qplication to Canadian conwrwr
C’hri~tcnscn. L.R. and M.E. Manscr. 1977. !!stimating U.S. conaumr prcfcrcnccs for meat Mill1 ;i flexible utility function, Journal of Eco&,wwtrics 5, 37 53. Cioldbcrgcr. AS. and T. G~tmaletws. 1970. A crew-country comparison 01‘con~~1111cr cxpcnditurc pat terns. European Economk Rcb iw I. 357 J(H). Houthakkcr. H.S.. 1957. An internationul comparison of houachoid expenditure pattt‘rns commcmcwating the wnttlnary of lGigcl’3 Ia. lkonomctrica 25. 533 551. Jqcnson. D.W. and L.J. Lau. 1075. The htructure of consumer prcfcrcnccs. ,Annals 01 Exx~n~mic and Social Moaawcment 4. 49 101.