PARTIALLY ENDOGENIZED CONSUMPTION: A NEW METHOD TO INCORPORATE THE HOUSEHOLD SECTOR INTO INPUT-OUTPUT MODELS

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1 PARTIALLY ENDOGENIZED CONSUMPTION: A NEW METHOD TO INCORPORATE THE HOUSEHOLD SECTOR INTO INPUT-OUTPUT MODELS Quaru Che 2 3, Erik Dietzebacher, Bart Los, Cuihog Yag 2 (. Uiversity of Groige, PO Box 800, 9700 AV, Groige, The Netherlads 2. Academy of Mathematics ad Systems Sciece, Chiese Academy of Scieces, Beijig, 0090, P.R.Chia 3. Graduate Uiversity of Chiese Academy of Scieces, Beijig, 00049, P.R.Chia) quaru.che@rug.l h.w.a.dietzebacher@rug.l b.los@rug.l chyag@iss.ac.c Abstract. The partially closed iput-output model with edogeous cosumptio is applied to may fields, both o atioal level ad regioal level, for it takes ito accout the likage betwee the household sector ad the productio sector. I our study, we fid that the household cosumptio behavior captured by this model is ot cosistet with the cosumptio theory, because i this model the curret cosumptio is oly determied by the curret icome. However, from the poit views of related cosumptio behavior hypotheses, such as the relative icome hypothesis ad the life cycle-permaet icome hypothesis, the household cosumptio is also determied by may other factors such as past cosumptio level ad future icome. I that case, the likage betwee the household sector ad the productio sector would be overestimated by this model. To address this problem, we proposed a ew method to icorporate the household sector ito the iput-output model, which ca recocile the iput-output aalysis with the cosumptio theory. The edogeous cosumptio coefficiets of eight categories of commodities i Chia from 989 to 2008 are estimated by the time varyig parameter method. Usig these results, we costruct our ew model, partially closed iput-output model with partially edogeized cosumptio, based o Chia s iput-output table of Fially employig our ew model, the short-term impact of the 4 trillio yua stimulus package aouced by the Chiese govermet o the GDP of Chia uder differet scearios is ivestigated.

2 . Itroductio The household sector plays a importat role i ecoomic activities. The household obtais icomes from the productio sector ad speds them o the products produced by the productio sector. Via this icome-cosumptio relatioship, the household sector is closely related to the productio sector. Hece, icorporatig the household sector ito the ecoomic system to accout for the icome-cosumptio relatioship betwee the household sector ad the productio sector is a importat ad sigificat work. Because of the advatages i idustry likages aalysis ad ecoomic structure study, the iputoutput model is a good startig poit to icorporate the household sector ito the ecoomic system. The Partially closed iput-output model with edogeous cosumptio, studied by may researchers such as Miyazawa (976), has become a prevalet method to icorporate the household sector ito the ecoomic system. I this model, the household sector is regarded as a edogeous sector by movig the household cosumptio ad labor iput to the iput-output itermediate delivery matrix. The household sector is liked to the productio sector by the labor iput coefficiet ad cosumptio coefficiet defied i this model. As may researchers (see Batey, Madde, ad Weeks, 987, 989; Cloutier, 994; Wakabayashi ad Hewigs, 2007; Miller ad Blair, 2009) poited out, there are some limitatios i this model, especially the costat cosumptio coefficiet ad igored cosumptio patters of differet households. These limitatios ca be alleviated by disaggregatig the household sector ito differet groups accordig to their characteristics. However, there is aother limitatio, which has bee paid little attetio to. We fid that the household cosumptio behavior captured by this model is ot cosistet with the cosumptio theory, because the household cosumptio is fully edogeized i this model, which implies that the curret cosumptio is totally determied by the curret icome. However, accordig to related cosumptio behavior hypotheses, such as the relative icome hypothesis ad the life cycle-permaet icome hypothesis, the household cosumptio is also determied by may other factors such as past cosumptio level ad future icome. I that case, if the household cosumptio is fully edogeized, the likage betwee the household sector ad the productio sector 2

3 would be overestimated by this model, ad further the results calculated from this model would be distorted. To address this problem, we try to develop a ew method to icorporate the household sector ito the iput-output model, which ca recocile the iput-output aalysis with the cosumptio theory. To implemet this method, a specific cosumptio decompositio formula is required. O the oe had, it ca take ito accout factors relevat to household cosumptio behavior. O the other had, it should facilitate decomposig the household cosumptio ito the edogeous cosumptio which is determied by the curret household icome, ad the exogeous cosumptio which is determied by other factors; oly the edogeous cosumptio flow should be closed ito the iput-output itermediate delivery matrix. Based o this method, our ew model, partially closed iput-output model with partially edogeized cosumptio, is developed. Compare to the traditioal model ad the partially closed iput-output model with edogeous cosumptio, the results calculated from our ew model would be closer to the realistic ecoomic activities. Because our ew model icorporates the relatioship betwee the household sector ad the productio sector ad at the same time captures a relatively comprehesive household cosumptio behavior. This idea ca also be geeralized to the social accoutig matrix (SAM) method, sice this method to icorporate the household sector is ot cosistet with the cosumptio theory either. We will show the performace of our ew model by ivestigatig the short-term impact of the 4 trillio yua stimulus package aouced by the Chiese govermet o the GDP of Chia. The remaiig cotet of this paper is orgaized as follows. Sectio 2 itroduces the partially closed iput-output model with edogeous cosumptio ad its limitatios. Sectio 3 describes our ew method to icorporate the household sector ito the iputoutput model. Sectio 4 takes Chia as a example to describe the procedure of costructig our ew model. Sectio 5 ivestigates the short-term impact of the 4 trillio yua stimulus package aouced by the Chiese govermet o the GDP of Chia uder differet scearios. Sectio 6 is our coclusio. 3

4 2. Partially Closed Iput-Output Model with Edogeous Cosumptio c ~ The traditioal iput-output model is x = ( I A) ( f + f ), where x represets the gross output vector; A represets the iput coefficiet matrix; f c represets the household cosumptio vector; ~ f represets the vector of fial demads other tha household cosumptio; I is a idetical matrix. I the traditioal iput-output model, household cosumptio is treated as a exogeous fial demad category, so there is o likage betwee the household sector ad the productio sector. I ecoomic activities, however, the household sector is closely related to the productio sector via a icomecosumptio relatioship. The household ears icomes from the productio sector ad speds them o the products produced by the productio sector. I that case, the Leotief iverse matrix ( I A ) calculated from the traditioal iput-output model does ot take ito accout the likage betwee the household sector ad the productio sector. To icorporate the icome-cosumptio relatioship ito the traditioal iputoutput model, may researchers such as Miyazawa have studied the partially closed iput-output model with edogeous cosumptio. I this model, the household sector is moved ito the itermediate delivery matrix ad treated as a edogeous sector. Its iputs are cosumptio commodities, ad output is labor. Curretly, the partially closed iput-output model with edogeous cosumptio has bee applied to may fields, both o atioal level ad o regioal level (see Batey, Madde, ad Weeks, 987; Cloutier 994; Hewigs et al., 999; Che, Guo ad Yag, 2005). Accordig to Miyazawa s formulatio (see Miyazawa, 976), the basic structure of the partially closed iput-output model with edogeous cosumptio is as follows: c ~ A h x f x () + =. r h 0 x+ f + x+ Where A = ( ) is a matrix of iput coefficiets; x ( ) is a vector of gross a ij = x i outputs of productio sectors; x + is the total household icome ; ~ f is a vector of fial demads other tha household cosumptio; f + is the exogeous icome of the c c r r household sector; h ( h ) is a vector of cosumptio coefficiets; h = ( h j ) is a = i 4

5 vector of labor iput coefficiets. The cosumptio coefficiet h c i is defied as c c hi = fi x +, where c f i is the commodity of sectori cosumed by the household sector. The labor iput coefficiet is defied as h r j = wj xj, where w j represets the wage ad salary of the household sector eared from sector j. Hereafter we call this model as the Miyazawa model. Previous studies have poited out that household cosumptio behavior is distorted i this model, because the cosumptio coefficiets are costat ad the cosumptio patters of differet households are igored (see Batey, Madde, ad Weeks, 987, 989; Cloutier, 994; Wakabayashi ad Hewigs, 2007; Miller ad Blair, 2009). First, the costat cosumptio coefficiets potetially assume that the household sector will sped the same proportioal ( h ) icome o correspodig commodities give ay additioal c i amout of household earigs. A approach to addressig this problem especially at regioal level is to divide the household sector ito established residet sectors ad ew residet sectors. For the established residets, the icome geerated from a icrease i the gross output would be a additioal icome to their curret icome, ad the a series of margial cosumptio coefficiets are eeded. For the ew residets who migrate to look for jobs, the icome geerated from a icrease i the gross output would be their total icome; hece, the cosumptio coefficiets defied above are reasoable. Secod, the cosumptio patters would vary over households with differet characteristics such as icome levels ad ages. For istace, the cosumptio patter of a household with a high icome level will be differet from that of a household with a low icome level. The model will thus lack cosumptio patter variatios if oly oe household sector is icorporated i it. A approach to addressig this problem is to disaggregate the household sector ito several groups accordig to their characteristics. For example, disaggregate the household sector by icome level: <$0000, $ , $ ad so o (see Cloutier, 994). The icome mobility should certaily be take ito accout i this situatio; i fact, due to the ecoomic developmet, some households may shift from oe icome level to aother. r I Miyazawa s model, h is a vector of value added ratios. Accordig to Miller ad Blair s descriptio o r Miyazawa s model, h is revised to a vector of labor iput coefficiets (see Miller ad Blair, 2009). 5

6 We fid aother limitatio of the Miyazawa model, which, however, has bee paid little attetio to. I the Miyazawa model, household cosumptio is fully edogeized, c c so the cosumptio coefficiet is defied as hi = fi x +. Trasformig it slightly c yields f = c i hi x+, which idicates that household cosumptio is oly determied by the curret icome. However, from the poit of views of related cosumptio behavior hypotheses, the curret cosumptio is ot oly determied by the curret icome but also determied by may other factors. For istace, accordig to Dueseberry s relative icome hypothesis (RIH), the curret cosumptio is also determied by the past cosumptio peak because cosumptio behavior is rather irreversible over time. It is difficult for a household to reduce its cosumptio level oce attaied; accordig to the life cycle/permaet icome hypothesis (LCPIH), developed by Modigliai, Friedma, ad Hall, cosumers are forward-lookig, so they ca advace or defer cosumig accordig to their plas ad expectatios to maximize their utilities i the log ru. Hece, the cosumptio behavior captured by the Miyazawa model is ot cosistet with the cosumptio theory. The fully edogeized household cosumptio ca lead to a overestimated likage betwee the household sector ad the productio sector. The the result calculated from the Miyazawa model will be distorted. This suggests that a ew model should be developed to recocile the iput-output aalysis with the cosumptio theory. To do that, the aggregate household cosumptio is required to be decomposed ito the edogeous cosumptio which is determied by the curret icome, ad the exogeous cosumptio which is determied by other factors. Closig the edogeous cosumptio ito the iput-output itermediate delivery matrix, we ca develop our ew model, amed the partially closed iput-output model with partially edogeized cosumptio. 3. Partially Closed Iput-Output Model with Partially Edogeized Cosumptio As we discussed i sectio 2, may excellet studies about disaggregatig the household sector ito differet groups have bee doe i the past years. Hece, this issue will ot be focused o i our paper. To facilitate our study, we assume that there is oly oe household i our model who is a represetative aget. This meas that the sum of all 6

7 the households decisios is mathematically equivalet to the decisio made by this represetative aget. 3. Framework The iput-output table provides data source for costructig iput-output models, ad its framework usually varies with the research issues. Table illustrates the framework for developig our ew model. <TABLE > I this framework, imports are excluded from the itermediate delivery matrix, household cosumptio, ad other fial demads. The d Z = ( z ij ) is the domestic delivery matrix; m j is the imported product used by sector j ; e c id is the domestic product of sectori edogeously cosumed by the household sector; c ex id is the domestic product of sectori exogeously cosumed by the household sector; c e m is the imported products edogeously cosumed by the household sector; c ex m is the imported products exogeously cosumed by the household sector; f id is the product of sectori used for domestic fial demads other tha household cosumptio; f m is the imported products used for domestic fial demads other tha household cosumptio; e i is the export of sector i ; x i is the gross output of sector i, iter alia, + x is the total household icome 2 ; h j is the edogeous icome of the household sector eared from sector j ; h is the exogeous icome of the household sector; v ~ j is other value added of sector j, ad it equals the value added of sector j ( v j ) mius h j ; v is the icome tax ad savig of the household sector, ad it equals the total household icome mius aggregate household cosumptio (both the edogeous cosumptio ad the exogeous cosumptio). I some researchers frameworks (see Cloutier, 994; Miller ad Blair, 2009), there are values i the shadow area of Table. They defie them as household purchases of labor services. However, we set them as 0 i our framework due to the fact that there is usually a specific sector to describe household services i iput-output tables. For 2 To be cosistet with the iput-output accoutig framework, all the icomes used i this paper refer to the gross icomes before tax. 7

8 istace, there is a sector amed household service ad other social services i Chia iput-output tables. Household purchases of labor services ca be captured i this sector s labor iput. I sectio 4, we will describe i detail how to costruct the row flows ad the colum flows for the household sector i our ew framework. Compared to Miyazawa s framework, besides distiguishig the edogeous cosumptio ad the exogeous cosumptio, aother differet poit i our framework is the defiitios of the edogeous icome ad the exogeous icome. I Miyazawa s framework, the value added is closed ito the itermediate delivery matrix to show the icome obtaied by the household sector from the productio sector. Hece, h r defied by Miyazawa (976) is a vector of value added ratios. Afterwards, Miller ad Blair (2009) revised h r to a vector of labor iput coefficiet. Pyatt (200) argued that the icome captured i the Miyazawa model is ot the istitutioal icome but the factorial icome such as icome for labor ad icome for capital; this is ot cosistet with the household icome ad will leave out some icome source especially whe the icome distributio issue is studied. Cosiderig this poit, we use the istitutioal icome istead of the factorial icome i our framework. Furthermore, we divide the household icome ito the edogeous icome ad the exogeous icome accordig to the icome source. The source of the household icome is very wide. For istace, i Chia the household icome basically comes from wages ad salaries, household operatios 3, properties, ad trasfers. Icomes from wages ad salaries as well as household operatios are directly related to the gross output, because they are geerated durig the productio process. The icome from wages ad salaries is the remueratio for household s labor service, so it directly relates to the gross output. The icome from household operatios is a retur of household s capital iput, so it also directly relates to the gross output; moreover, the icome from operatio o agriculture is a importat source of the rural household icome 4. I other words, these icome sources have a sigificat relatioship with the gross output, so we defie them as the edogeous icome. Oppositely, icomes from properties ad trasfers are basically geerated 3 Icome from household operatios refers to the icome eared by households as uits of productio ad operatio. For istace, a household operates a shop; the the beefit they gai from this shop is defied as icome form household operatio. 4 For example, i Chia, the share of icome from household operatios i rural household et icome is aroud 53%, iter alia, the share of household operatio o agriculture is aroud 42%. 8

9 outside the productio process ad ofte affected by may oproductio ifluecig factors. For istace, the icome from properties maily depeds o the fiace market coditio ad the amout of household s property such as savigs ad houses. The icome from trasfers is the result of icome redistributio ad usually depeds o istitutio s decisios o the household s welfare such as related govermet policies. Hece, we defie the icome from properties ad trasfers as the exogeous icome. From Table, we ca derive the followig accoutig equatios for the productio sector ad the household sector: (3) (4) (5) d e ex zij + cid + cid + fid + ei = xi j= ( i =,2K ), i= hj + h = x + j=, z + m + h + v% = x ( j =,2K ), d ij j j j j (6) e e ex ex cid + cm + cid + cm + v = x + i= i=. Equatio (3) expresses that the gross output ( x i ) of each sector flows to itermediate use ( z j= d ij ), edogeous cosumptio ( c e id fial demads ( ), exogeous cosumptio ( c ex id ), other domestic f id ), ad export ( e i ). Equatio (4) idicates that the sum of edogeous icome ( h ) ad exogeous icome ( h ) equals total icome ( x + ).Equatio (5) j= j idicates that the gross iput ( x j ) of each sector cosists of domestic itermediate iput d ( z ), imported itermediate iput ( m j ), ad primary iput ( h j + v~ j ). Equatio (6) ij i= idicates that the total household icome ( x + i= id m i= id m e e ex ex ( c + c + c + c ), ad icome tax ad savig ( v ). 3.2 Model ) flows to household cosumptio The partially closed iput-output model with partially edogeized cosumptio ca be derived from equatio (3) ad (4). First, we give some defiitios used i our d d model. A = ( ) a ij d d is a matrix of domestic iput coefficiets, where a = z x ; ij ij j 9

10 ' w = ( w j ) is a row vector of edogeous icome coefficiets, where wj hj xj d α i = ; d c = ( ) is a colum vector of the edogeous cosumptio coefficiets of domestic d e ~ ~ products, whereα i = cid x+. f = ( f i ) is a vector of the exogeous fial demads o ~ ex domestic products, where f = c + f + e. The Equatio (3) ad (4) ca be expressed as: i id id i (7) d d ax ij j + α i x+ + f% i = xi ( i=,2 K) j= wx j j + h = x+ j=. Matrix form: d d A c x f% x (8) + = 0 x + h x. ' w + Solvig Equatio (8) yields the fial model: (9) x = (I A ) f = L f, d d ~ A c x f where A = ', x =, f =, L = (I A ). w 0 x + h 3.3 Multipliers Some useful multipliers ca be obtaied by calculatig the exteded Leotief iverse matrix L. The solutio to L is d ' d ( + ' ) d ' d L l LI c wl Lc 2 wlc wlc (0) L = (I A ) = =, ' l2 l22 ' d ' d wl wlc wlc d where L = ( I A ). A vector of output multipliers m o) = [ m ( o), m ( o), K, m ( )] ca be derived based o L, which equals ' il 5. m j (o) ( 2 o idicates the total products of all productio sectors required to satisfy oe uit of exogeous fial demad of sector j. Similar to ' il, ' il 2 idicates the total products of all productio sectors iduced by oe uit exogeous icome of the household sector; we defie it as icome-drive output multiplier. If the household sector is disaggregated ito several groups, l 22 should be 5 I this paper, i ' = (,, K) deotes a summatio vector with coformable legth. 0

11 expressed as ( ) ' d I WLC. Miyazawa (978) defied it as the iterrelatioal icome multiplier, which describes the effect of a chage i oe group s icome o the icomes of all the groups. The j th elemet of the multi-sector icome multiplier vector l 2, which is defied by Miyazawa, idicates the total household icome (eared from all the productio sectors) iduced by oe uit exogeous fial demad of sector j. The value added multiplier matrix ca be obtaied by ˆ M() v = VL, where ˆV is a diagoal matrix ' trasformed from the value added coefficiet vector v = [ v x v x v x ] elemet mij ( v) i M( v), The idicates the total (both direct ad idirect) value added of sector i drive by oe uit exogeous fial demad of sector j. Fially, we give the edogeous cosumptio multiplier matrix M (ec), which ca measure the cosumptio of each sector iduced by oe uit exogeous fial demad of ay productio sector. Its formula is () d M( ec) = c l = ( I c w'l) I, d 2 d where agai L = ( I A ). The elemet m ij (ec) i M(ec) idicates the household cosumptio o sectori iduced by oe uit exogeous fial demad of sector j. 3.4 Cosumptio Decompositio The most importat step to develop our ew model is to decompose the household cosumptio ito the edogeous cosumptio ad the exogeous cosumptio. This requires a specific cosumptio decompositio formula. O the oe had, this formula ca take ito accout factors relevat to household cosumptio behavior. O the other had, it should facilitate decomposig the household cosumptio ito the edogeous cosumptio which is determied by the curret household icome, ad the exogeous cosumptio which is determied by other factors. Accordig to RIH, LCPIH, ad related studies, there are may other factors ifluecig aggregate cosumptio besides the curret icome, such as past cosumptio levels (the relative icome hypothesis proposed by Dueseberry), future icome (see Carroll, 994; Muellbauer ad Lattimore, 999; Luego-Prado ad Sørese, 2008), iterest rate (see Attaasio ad Weber, 993; Erladse ad Nymoe, 2008) ad demographic structures such as populatio age structure (see Erladse ad Nymoe,

12 2008) ad educatio structure. O the other had, related studies o cosumer preferece ad demad systems (see Clemets ad Selvaatha, 994; Barett ad Serletis, 2008) show that the commodity price ad cosumer s taste play importat roles i determiig the budget share of each commodity category. Whe attemptig to estimate the cosumptio decompositio formula for each commodity category, these two factors should also be take ito accout. The reaso for this is that they determie the cosumer s behavior to make choices amog differet commodities, give the budget. Cosiderig these factors, we specify the cosumptio decompositio formula as the followig form: (%,,,,...). (2) cit = αit e r d p λ x( + ) t + βici( t ) + εit Where ci is the aggregate household cosumptio of product i; αi is the edogeous cosumptio coefficiet of product i; x + agai is the total household icome. αit ( e%, σ, r, d, p, λ...) idicates that the edogeous cosumptio coefficiet depeds o the household s expectatio o his future icome e%, iterest rate r, demographic structure d, commodity price p, household s taste λ, ad other related factors. It implies that these factors affect the cosumptio by affectig the edogeous cosumptio coefficiet. I fact, if a icrease i icome occurs, a household with a optimistic expectatio o its future icome will spet a larger proportio of this icrease tha that with a pessimistic expectatio o its future icome. I the same sese, a household with a high depedecy ratio 6 ad other coductive demographic characteristics, ad a low real iterest rate will spet a larger proportio of a icrease i icome tha that with a low depedecy ratio, ad a high real iterest rate. With regard to a ordiary commodity, if its price decreases, the household sector will adjust its edogeous cosumptio o this commodity to a higher level, so that its cosumptio o this commodity will icrease eve if its icome holds fixed. A chage i the household s taste also affects the edogeous cosumptio coefficiets. If the household s taste chages to be fod of buyig commodity A, the the edogeous cosumptio coefficiet of commodity A will icrease, so that the cosumptio o commodity A will 6 The term depedecy ratio is defied as the umber of childre ad retired persos to those of workig age. Sice a idividual borrows whe they are youg, saves whe they are i workig age, ad dissave whe they are retired, a high depedecy ratio ca facilitate cosumptio. 2

13 icrease eve if the icome holds fixed. The edogeous cosumptio coefficiet α it is allowed to vary over time i our model, because its ifluecig factors usually chage over time. As we discussed i sectio 2, it is difficult for a household to reduce the cosumptio level oce attaied, so the past cosumptio peak is a importat determiat of the curret cosumptio. Sice the aggregate cosumptio is usually i growth, we use the cosumptio of the previous period c it ( ) as a measure of the past cosumptio peak. The past cosumptio shows the household s cosumptio habit or experiece. The effect of habit or experiece o cosumptio is usually hard to chage, so we deem that the coefficiet β i of the previous period cosumptio is ivariat over time. The estimatio of α it is the key to develop the cosumptio decompositio formula. As we discussed previously, the edogeous cosumptio coefficiets have may ifluecig factors. Some of the factors such as cosumer s taste are uobservable ad it is difficult to fid good proxy variables for them. Moreover, the fuctio form betwee the edogeous cosumptio coefficiet ad its ifluecig factors is also difficult to specify correctly, because it is ot clear how the household evaluates the chages i the ifluecig factors together. Cosiderig these difficulties, we assume that the household s decisio-makig process o the edogeous cosumptio coefficiet follows the radom walk process: αit = αit + μit, 2 μ ~ (0, σ ). This assumptio implies it NIID μ i that the household chages its decisio o α it oly whe it fids that the chages i the ifluecig factors e%, r, d, p, λ occur, ad the decisio chage at curret period is ot affected by those made at previous periods 7. 7 Before chagig his decisio o the edogeous cosumptio coefficiet, the household will cosider various chages i the ifluecig factors at curret period. Although the household may lear somethig about the curret situatio from the history, cosiderig ucertai chages i may factors ad the forwardlookig characteristic of the household, we thik that the household s decisio chage based o his evaluatio o the various chages i the ifluecig factors would be weakly depedet at each period. So, we thik that the household s decisio chage at curret period is maily based o the curret iformatio ad little affected by the decisio chage at previous periods. 3

14 Uder this assumptio, the edogeous cosumptio coefficiet α 8 t ca be estimated by the followig procedure. Suppose that ˆ αt = Et ( αt ) is a miimum mea square error (MMSE) estimator of αt based o all the iformatio up to periodt. The, the MMSE predictio of αt ad ct ca be obtaied by ˆ α ˆ tt = Et ( αt + μt) = αt ad c ˆ ˆtt = α tt x( + ) t + βc t. ˆtt α equals to the estimatio of α. However, this estimatio is oly based o the iformatio up to periodt, ad the t household may chage his decisio o the edogeous cosumptio coefficiet based o the iformatio at periodt. Hece, ˆtt α should be further adjusted. Whe the observatio of the household cosumptio at period t ( c t ) is available, we ca obtai the predictio error ˆ ε ˆ t = ct ctt. It cotais the iformatio about the chage iα. Based o this iformatio, ˆtt α ca be updated to a more precise estimatio ofα t : ˆ α ˆ ˆ t = αtt + f ( εt). This procedure ca be implemeted by usig the Kalma filter algorithm. The Kalma filter (see Harvey, 987; Hamilto, 994) is a recursive algorithm for updatig a oe-step ahead estimate of the state mea give ew iformatio. It has bee successfully applied to may empirical ecoomic issues to address time varyig parameter (TVP) model ad uobserved compoet models. Suppose that a uivariate TVP model is specified with a observatio equatio (3) ad a state equatio y = d + x β + z α + ξ, t =,2, K T ' ' t t t t t t (4) αt = rt + Tαt + ηt, t =,2, K T. Where y t is the depedet variable with a fixed observatio at timet ; αt is a state vector ( m ) with time varyig parameters of iterest; z t is a vector ( m ) with observed variables that affect the depedet variable; x t is a vector ( )with observed variables that affect the depedet variable whose coefficiet vector β is ivariat over time. T is a fixed matrix ( m m) which is specified based o prior iformatio; d t adr t are fixed scalar ad vector ( m ) respectively, which are also kow i advace; the 8 To be coveiet for our statemet, here the subscript i is dropped. It meas that the followig statemets are about ay commodity category. 4

15 disturbaces ξt ad η are white oise, with 0 meas ad variace σ 2 h, t respectively. ξt ad η t are assumed to be mutually serially idepedet. t 2 σ Q t Let αˆ t be the miimum mea square estimator of αt based o all the iformatio up to time t, ad let σ 2 Pt be the mea square error matrix of α ˆ t. Give ˆ t α ad Pt at time t, the miimum mea square estimator ofα t ad its mea square error matrix are: (5) αˆ ˆ tt = Tαt + r t (6) P = TP T + Q. ' tt t t Whe the ew observatio about y at time t is available, the estimator ad its mea square error matrix ca be updated by the followig formulas: (7) (8) αˆ = αˆ + P z ( y d xβ z αˆ )/( zp z + h) ' ' ' t tt tt t t t t t tt t tt t t P = P P zzp /( zp z + h ) ' ' t tt tt t t tt t tt t t Formula (5) ad (6) are referred as the predictio equatios, ad Formula (7) ad (8) are referred as updatig equatios. They together make up the Kalma filter. The cosumptio decompositio formula ca be estimated by applyig the maximum likelihood estimatio method with the Kalma filter o the followig TVP model: cit = αit x( + ) t + βici ( t ) + εit (9). αit = αit + μit It cosists of the observatio equatio cit = αit x( + ) t + βci ( t ) + εit ad the state equatioαit = αit + μ 9 it, i which ε it ad μ it are assumed to be Gaussia disturbaces, ad they are also mutually serially idepedet. Based o estimated results, we ca easily e obtai the edogeous cosumptio c = ˆ α x + ad the exogeous cosumptio c ex = c c e. it it it it it 9 By summarizig the Kalma filter related empirical results, Egle ad Watso (987) foud that whe the behavioral model is cocered, for may data sets the simple radom walk specificatio for the state equatio performs well. 5

16 4. Costruct Chia s Partially Closed Iput-Output Model with Partially Edogeized Cosumptio of Estimate Edogeous Cosumptio Coefficiets for Iput-Output Sectors The household s cosumptio preferece usually varies with differet commodity categories, such as food ad clothig, rather tha with differet iput-output sectors. It is because that the sectors i the iput-output table are pure sectors; amely, each sector produces a sigle product, ad each product ca be produced by oly oe sector. This implies that the products are i the same characteristic o mater what it is used for, as log as they are produced by the same sector. For example, scarf ad bed sheet are the same product produced by the textile goods sector i the iput-output table, however, the household s cosumptio preferece o them is differet. This suggests that we should divide the commodities ito several categories ad estimate their edogeous cosumptio coefficiets istead of directly estimatig the edogeous cosumptio coefficiets for iput-output sectors. The estimated edogeous cosumptio coefficiet of each commodity category ca be further distributed to the iput-output sectors by Formula (20). c = ( α i ) is a vector of edogeous cosumptio coefficiets of iputoutput sectors; c ( ) = α i m is a vector of edogeous cosumptio coefficiets of commodity categories; B = ( ) b ij m is the bridge matrix, where is the umber of iputoutput sectors ad m is the umber of commodity categories. (20) c= Bc. Chia Statistical Yearbook provides the data about per capita urba household icome, per capita rural household icome, ad eight categories of cosumptio commodities: food; clothig; residece; household facility, article ad service; health care ad medical service; trasport ad commuicatio; educatio, culture ad recreatio service; miscellaeous good ad service. Distiguishig domestic ad imported cosumptio products is required i our framework. However, these eight categories of cosumptio data do ot distiguish them. So, we decide to first estimate the edogeous cosumptio coefficiet for each commodity ( c ) ad the distribute it to those of correspodig iput-output sectors ( c ) by Formula (20). Fially, obtai the 6

17 edogeous cosumptio coefficiet for domestic products ( c d ) ad imported products by usig the share of imported products i the aggregate domestic demad. Before estimatig, the followig processes are made o the data. First, multiply the per capita urba household icome ad rural household icome with their correspodig populatios ad sum them to obtai the total household icome. Secod, deflate variables. Each category of commodity is deflated by its correspodig cosumptio price idex; the total icome is deflated by the geeral cosumptio price idex. Based o the processed data, the TVP model discussed i sectio 3 is estimated for each commodity category by the maximum likelihood estimatio method with Kalma filter. The Kalma filter yields the estimator of the state vector oly based o the available iformatio up to timet. We further used all the iformatio i the sample (T observatios i all) to provide smoothed estimate of the state vector α ˆ tt by fixed-iterval smoothig 0. The smoothed estimate ofα it ad the estimate of β i for each commodity category are listed i Table 2. <TABLE 2> Table 2 illustrates a picture of chages i the edogeous cosumptio coefficiets of the Chiese household from 989 to The edogeous cosumptio coefficiet of food maitaied decreasig from 989 to This is cosistet with the Egel s law; amely, as icome icreases, the budget share of food falls. As a kid of basic eeds, the edogeous cosumptio coefficiet of residece also presets a overall patter of decrease. The edogeous cosumptio coefficiets of household facility, article ad service, ad trasport ad commuicatio basically icreased over time. As the households icome icreases, more ad more people begi to sped a larger proportio of their icreased moey o commodities of high value such as appliaces, superior furiture ad sedas. Peoples pursuit of huma wats drives the icrease i the edogeous cosumptio coefficiets of these two commodity categories. The edogeous cosumptio coefficiet of clothig wet through three stages of chage, icreasig from 989 to 995, decreasig from 996 to 998, ad icreasig from The fixed iterval smoothig is a process of calculatig backward, startig with the fial Kalma filter estimates αˆ T ad P t. The smoothig equatios cosist of αˆ ˆ ˆ ˆ tt = αt + Pt ( αt+ T Tα t) ad PtT = Pt + Pt ( Pt+ T Pt+ t) P t ', ' where Pt = PTP t t+ t, t = T, T 2, K, with ˆ α ˆ TT = αt, PTT = PT. 7

18 to To a large extet, the decrease stage was caused by the sharply icreased clothig price from 994 to 997 durig which the clothig price icreased 7.%, 4.5%, 7.4%, ad 3% respectively. However, the respose seems to be somewhat lagged to the icreased price. The edogeous cosumptio coefficiets of health care ad medical service, ad educatio, culture ad recreatio service maitaied a relatively statioery patter i the recet years. Some importat evets also had a impact o the edogeous cosumptio coefficiets. For example, the SARS disease occurred i Chia ad caused a obvious impact o the cosumptio i Compared to 2002, almost all of the edogeous cosumptio coefficiets decreased, ad the aggregate edogeous cosumptio coefficiet decreased about 5.6%. The global fiacial crisis ad Wechua earthquake occurred i 2008 also led to a relatively large impact o the cosumptio. Beig affected by this, differet degree of declies i the edogeous cosumptio coefficiets of food, trasport ad commuicatio, educatio, culture ad recreatio service, ad miscellaeous good ad service were caused, ad the aggregate edogeous cosumptio coefficiet decreased about 4.2%. While the aggregate edogeous cosumptio coefficiet decreases due to the law of dimiishig margial propesity to cosume, accordig to Table 2, this degree of declie i 2008 is much larger tha that i the ormal year. I recet years, the cosumptio of each commodity category has grow with differet magitudes. Based o the estimated TVP model, we calculate the icrease i the cosumptio of each commodity category from 2000 to 2008 ad decompose it to the cotributios of edogeous cosumptio ad exogeous cosumptio by Formula (2). The results are preseted i Table 3. (2) c c = ˆ α x ˆ α x it ( + s) it it ( + s) ( + )( t+ s) it ( + ) t + ˆ βc ˆ βc i i( t+ s ) i i( t ) + ˆ ε ˆ ε it ( + s) it <TABLE 3> Accordig to Table 3, the cosumptio growth of each commodity category exhibits three types: exogeous growth domiat type, edogeous growth domiat 8

19 type ad duo type. The growth patters of most commodity categories, such as residece, trasport ad commuicatio, ad educatio, culture ad recreatio service, are exogeous growth domiat type. Namely, the cosumptio growth i these commodity categories is maily attributed to the icrease i the exogeous cosumptio. The exogeous growth domiat patter implies that the icrease i the cosumptio of these commodity categories maily depeds o the household s cosumptio habit or experiece; the cotiuatio or iertia of the household s cosumptio habit drives most part of the cosumptio growth i these commodity categories. The cosumptio growth patters of clothig, ad household facility, article ad service are edogeous growth domiat type. Namely the cosumptio growth i these commodity categories is maily attributed to the icrease i the edogeous cosumptio. This implies that the cosumptio of these commodity categories maily depeds o the household s curret icome ad his judgmet o the curret ecoomic ad social situatio. If his icome icreases ad his judgmet o the curret ecoomic ad social situatio is optimistic, he will prefer icreasig the cosumptio of these commodity categories. The duo patter is give to food ad health care ad medical service because the cotributios of the edogeous cosumptio ad the exogeous cosumptio to the cosumptio growth i these commodity categories are comparable. Next is to covert the edogeous cosumptio coefficiets of eight categories of commodities i 2007 listed i Table 2 to those of iput-output sectors by the bridge matrix B. The people who have compiled iput-output tables are supposed to hold more iformatio about determiig the bridge matrix. However, we oly have the followig iformatio: the matchig table betwee eight categories of commodities ad forty-two sectors i 2007 Chia iput-output table; the cosumptio data about each commodity category ad each iput-output sector. Based o the limited iformatio, we estimate B by the followig procedure. First, revise the household cosumptio i the iput-output table to be cosistet with the cosumptio of eight categories of commodities. The revised total household Some cosumptio items i the iput-output table are ot icluded i the eight categories of commodities. For istace, the fiace cosumptio, which is defied as the fiacial itermediatio service beefited by the household durig his activity of deposit ad loa, is ot icluded i the eight categories of commodities. 9

20 cosumptio i the iput-output table should equal to the total cosumptio of eight categories of commodities. Secod, geerate a crude estimatio of the matchig flow matrix R= ( r ij ) 42 8 betwee iput-output sectors ad eight categories of commodities. if sector i matches with commodity j, the c c rij = yi i ( j =, 2...8), otherwise r ij = 0. yi is the revised household cosumptio of sector i ; i is the umber of commodity categories that match with sector i. r ij represets the amout of cosumptio of sector i cotaied i commodity j. Third, balace the crudely estimated matchig flow matrix by meas of the RAS method 2 to make sure that the sum of each row ad each colum equal to the revised household cosumptio of correspodig iput-output sector ad the cosumptio of correspodig commodity category respectively. Fially, divide the elemet i each colum by the sum of correspodig colum to obtai the estimatio of B. The matchig table betwee eight categories of commodities ad forty-two sectors i 2007 Chia iput-output table, ad the estimated share of each iput-output sector i its correspodig commodity category are listed i the Appedix. After obtaiig the edogeous cosumptio coefficiet of each iput-output sector by the estimated bridge matrix, we further split it ito the edogeous cosumptio coefficiet of domestic product ad imported product accordig to the share of imported product i the aggregate domestic demad. Fially, based o the coverted edogeous cosumptio coefficiets of the iput-output sectors, the aggregate cosumptio ca be split ito the edogeous cosumptio ad the exogeous cosumptio by Formula (2). 4.2 Estimate Edogeous Icome Coefficiets for Iput-Output Sectors As we discussed i sectio 3, the icomes from wages ad salaries, ad household operatios are reasoable to be treated as the edogeous icome. The icome from wages ad salaries is a part of compesatio of employees which is a item i the iputoutput table. With regard to the icome from household operatios, it is difficult to distiguish the compesatio ad surplus from it, so the icome from household So, this part of cosumptio should be excluded from the household cosumptio i the iput-output table ad further regarded as the exogeous household cosumptio. 2 RAS is a popular method to recover the etries of a matrix from limited ad icomplete multisectoral ecoomic data. See Gola et al. (993) ad Dietzebacher (2009) for excellet discussio about this method. 20

21 operatio is usually aggregated to the compesatio of employees i the statistical data of Chia. The share of icome from wages ad salaries together with household operatios i the compesatio of employees is aroud 85.3% i These two icome sources domiate the compesatio of employees, so we assume that the structure of wage ad salary icome together with household operatio icome eared from each sector is the same as the structure of compesatio of employees obtaied from each sector. The latter structure is available i the iput-output table. We ca use the data about total wage ad salary icome ad household operatio icome collected from Chia Statistical Yearbook as a cotrol umber ad distribute it to each sector accordig to the share of each sector s compesatio of employees. The the edogeous icome flow is obtaied, ad the edogeous icome coefficiet of each sector ca further be calculated by dividig each sector s edogeous icome over gross output. Compared to the edogeous icome, the exogeous icome (cosistig of icome from properties ad trasfers) ca be easily obtaied, sice there is detailed data about property icome ad trasfer icome of household i Chia Statistical Yearbook. Up to ow, the preparatios o the ew features of our model have bee doe. Based o these preparatios, Chia s partially closed iput-output model with partially edogeized cosumptio of 2007 ca be expressed as the form of Formula (8). 5. The Impact of 4 Trillio yua Stimulus Package o the GDP of Chia i the Short Ru To alleviate the recessioary impact of global fiacial crisis o the ecoomic growth of Chia, the Chiese cetral govermet aouced a fiscal stimulus package i the fourth quarter of Accordig to this stimulus package, from the fourth quarter of 2008 to 200, a 4 trillio yua ivestmet scale will be formed i Chia by meas of govermet ivestmet ad absorbig private ivestmet. I this 4 trillio yua stimulus package, the cetral govermet ivestmet accouts for.8 trillio yua; the other ivestmet is afforded by the local govermet ad the private. The compositio of this stimulus package is listed i Table 4. Most of the items focus o ifrastructure costructio. <TABLE 4> 2

22 From the demad-side view, the ivestmet will directly stimulate the output of costructio idustry as well as the equipmet ad istrumet related idustries, ad further idirectly stimulate the output of other idustries via the idustry likages. I additio, due to the icrease i the household icome durig this stimulus process, the household cosumptio will be iduced ad i tur drive the outputs of the productio sectors. Hece, i the short ru this stimulus package will drive the GDP growth of Chia. O the other had, i a ope ecoomy this stimulus package will also icrease imports, sice both productio ad fial demad require imported products 3. I that case, the impact of this 4 trillio yua stimulus package o the GDP of Chia will be weakeed by the icreased imports. The iput-output model provides a approach for idustry level impact aalysis ad also has a advatage i ecoomic structure aalysis. Hece, i this sectio, we will ivestigate the impact of the 4 trillio yua stimulus package o the GDP of Chia by iput-output models. I these models, domestic products ad imported products are distiguished to take ito accout the ivolvemet of imports. We assume that the ivestmet items i this stimulus package will be accomplished before the ed of 200, ad our study will focus o this short-term. The adjustmet of price ad wage is usually sluggish i the short ru, so we further assume that the cetral bak will ot chage the iterest durig the implemetatio of this stimulus package. We thus do ot cosider the crowdig-out effect o the private ivestmet, which is always argued i the cotext of expasioary fiscal policy. The household cosumptio, however, may be affected by this stimulus package, if the household is forward-lookig. I the cotext of expasioary fiscal policy, the household would have a expectatio that the govermet may icrease the tax rate i the future to balace the fiscal deficit caused by the expasioary fiscal policy, ad the its future icome may be egatively affected. As we discussed i sectio 3, future icome is a ifluecig factor o the curret cosumptio ad it affects the curret cosumptio by affectig the edogeous cosumptio coefficiet, so i this sceario the edogeous cosumptio coefficiet may dimiish. 3 Accordig to Chia s iput-output table of 2007, the share of imported products (excludig products imported for processig export) i the aggregate domestic demad is aroud 9.3%. 22

23 Cosiderig the possibility of household cosumptio behavior chage, we first assume that the household has a very weak expectatio that the stimulus package will affect its future icome; amely, the household cosumptio behavior will ot chage uder this expasioary fiscal policy. I this sceario, we calculate the short-term impact of the stimulus package o the GDP growth by the traditioal iput-output model, the Miyazawa model, ad our ew model respectively ad make compariso amog them. Secod, we recalculate the short-term impact by our ew model based o the sceario that the household cosumptio behavior is affected by the expasioary fiscal policy. Before calculatig, we distribute the stimulus package to the fixed asset formatio vector i the iput-output table accordig to the ivestmet compositio i Table 4 ad the ivestmet matrix which cotais the iformatio about each idustry s ivestmet structure. We deote this icreased ivestmet vector as Δf 5. Impact Aalysis i the Absece of Household Cosumptio Behavior Chage We first cosider the assumptio that the household cosumptio behavior is ot affected by the stimulus package. Based o this assumptio, we predict the edogeous cosumptio coefficiets for 2009 ad 200 as the same value as those i By usig the value added multiplier matrix M () v derived from the traditioal iput-output model, the Miyazawa model ad our ew model 4, the value added of each sector drive by the stimulus package ca be calculated from M() v Δf. The result is listed i Table 5. <TABLE 5> At the ecoomy-wide level, Table 5 shows that the GDP drive by the 4 trillio yua stimulus package calculated from the traditioal iput-output model, the Miyazawa model ad our ew model are billio yua, billio yua ad billio yua respectively. Sice the traditioal iput-output model does ot take ito accout the effect of the household sector, its total multiplier is less tha those of the Miyazawa model ad our ew model. Due to the fully edogeized cosumptio i the Miyazawa model, its total multiplier is obviously larger tha that of our ew model. Because of the ivolvemet of imported products, the total multiplier of the traditioal iput-output model is less tha. The total multiplier of our ew model is also less tha, which 4 The value added multiplier of our ew model is derived i sectio 3. The deviatios of the value added multiplier of the traditioal iput-output model ad the Miyazawa model are similar. 23

24 implies that the domestic household cosumptio iduced by the stimulus package is less tha the imports drive by the stimulus package. O the cotrary, the domestic household cosumptio iduced by the stimulus package is overestimated by the Miyazawa model i a large degree ad is larger tha the icreased imports, so its total multiplier is more tha. At the idustry level, the result calculated from our ew model shows that the large icremet i ifrastructure costructio will most affect the costructio idustry (26); its icreased value added accouts for 23.5% of the total value added stimulated by the stimulus package. The idustries that have a close likage (direct ad idirect) with costructio idustry, such as ometal mieral products idustry (3), Metals smeltig ad pressig idustry (4), trasport ad warehousig idustry (27), wholesale ad retail trade idustry (30), electricity ad heatig power productio ad supply idustry (23), fiace ad isurace idustry (32), ad chemicals idustry (2), are also affected i a large degree. The icreased purchase of equipmet ad istrumet to meet the ivestmet requiremet will provide a opportuity for commo ad special equipmet idustry (6). Due to the relatively large edogeous cosumptio coefficiet of food commodity, the agriculture idustry () will beefit a lot from the iduced household cosumptio. 5.2 Impact Aalysis i the Presece of Household Cosumptio Behavior Chage The expasioary fiscal policy ca covey a expectatio o the icrease i tax rate i the future. I this situatio, if the household is forward-lookig, the household cosumptio will be egatively affected. This poit ca be usually foud i the ew Keyesia models used for fiscal policy aalysis (see Coga et al., 2009; Michal, 2009). Based o the sceario that the household will chage its cosumptio behavior to respod to the stimulus package, we assume that the edogeous cosumptio coefficiets decrease 5% ad 0% respectively. Uder this sceario, we recalculate the short-term impact by Formula (22) which is derived from our ew model. (22) M f M f M f () v Δ + [ () v () v ] Where Δf is the icreased 4 trillio yua ivestmet vector; f is the exogeous fial demad o domestic products i the framework costructed i Sectio 4. 24