I I I I I I I I I 1 I I I 1 I I. Regional Economic Multipliers. A Consumer s Guide to. Cletus C. Coughlin and Thomas B. Mandelbaum

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1 Cletus C. Coughlin nd Thoms B. Mndelbum Cletus C. Coughlin is reserch officer nd Thoms B. Mndelbum is n economist t the Federl Reserve Bnk of St Louis. Thoms A. Pollmnn provided reserch ssistnce. A Consumer s Guide to Regionl Economic Multipliers ROPONENTS of mjor construction projects, such s stdium) irport or convention center, point to their potentilly lrge nd widespred benefits. Since these projects re costly nd my require public funds, estimtes of their economic benefits re used by the community to ssess their desirbility. Similrly, the closing of mjor mnufcturing fcility or lrge cutbck in its production is of interest throughout the community becuse of its nticipted dverse consequences. n hypotheticl, but relistic, exmple discussed lter in this pper, $50 million decline in ircrft sles by St. Louis mnufcturer is estimted to cuse $132 million reduction in output in the St. Louis economy nd the elimintion of 1,130 jobs. Upon hering such prediction, some bsic questions come to mind. Where do numbers such s these come from? How ccurte re they likely to be? Often, such numbers re obtined using regionl economic multipliers, which is stndrd wy to identify the potentil effects of mjor chnge in region s economy. These mesures estimte the chnges in output, income nd employment resulting from n initil chnge in spending. n this rticle, we provide n See Miller nd Blir (1985) for technicl discussion of input-output models. elementry discussion of regionl multipliers nd explin why they should be viewed with both cution nd skepticism. Our consumer s guide begins by discussing the bsics of n input-output model; such model identifies the reltionships mong different sectors in n economy nd, thus, is used to clculte regionl multipliers. We then describe different kinds of regionl multipliers nd discuss their mjor shortcomings. A NON-MATHEMATCAL LOOK AT MATHEMATCAL NPUT- OUTPUT MODELS An input-output model is mthemticl description of how ll sectors of n economy re relted. n lieu of technicl discussion of this topic, we describe the structure of input-output models using two pproches. n the text, we present n intuitive discussion; in the ppendix, the discussion hs more detil, but remins ccessible to reders comfortble with elementry lgebr.

2 20 ln constructing n input-output model, one begins by seprting economic ctivity in region (ny geogrphic re, such s country, stte or metropolis) into number of producing sectors. rhese sectors my be highly ggregted for exmple, mnufcturing, services, mining nd construction or firly disggregted utomobile production, hospitls, col mining nd new office construction. The vlue of products flowing from ech sector s producer to ech sector s purchser provides the essentil informtion for model. A model with steel nd utomobile sectors, for exmple, would include the dollr vlue of the steel produced in the region tht is sold to regionl uto mnufcturers, s well s the dollr vlue of the utomobiles produced in the region tht re sold to the region s steel industry. An industry s demnd for inputs from other industries is relted closely to its own level of output. For exmple, the utomobile industry s demnd for steel is relted closely to the number of utomobiles produced. Thus, steel sles re relted to utomobile production. ndeed, inputoutput models ssume tht, for ech industry in the region, there is constnt reltionship between the vlue of its output nd the vlue of inputs it purchses from ll other industries in the region. Suppose tht the vlue of utomobile production in given yer is $1 million nd the uto industry purchsed $200,000 of steel. f utomobile production were to double to $2 million, the input-output model then ssumes tht the uto industry s steel purchses would double s well, in this cse, to $400,000. n contrst, these models mke no explicit ssumption bout the reltionship between the vlue of the output nd purchses of inputs of groups other thn the region s industril firms. The demnd of these externl units is referred to s finl demnd becuse the outputs re leving the region s processing sectors. Finl demnd includes purchses by government, purchses by households nd firms from other regions nd, in some cses, purchses by households in the specific region under considertion. Thus, the vlue of totl output of ech industry in the region is divided into tht which is used in the production of other goods in the sme region (clled interindustry sles) nd tht which is purchsed by finl demnders. An input-output model, however, goes beyond describing the flows of goods nd services between sectors nd to finl demnd. t lso llows the user to determine the vlues for the gross output of ech industry necessry to meet these finl demnds. This informtion llows the clcultion of regionl multipliers. REGONAL MULTPLERS One primry use for n input-output model is the estimtion of the totl effect on n economy of chnges in the components of finl demnd for the goods nd services produced within the region. The term impct nlysis is used to chrcterize such study, prticulrly when the chnge is due to single event tht occurs within reltively short period of time. A chnge in finl demnd, like chnge in federl government demnd for ircrft, sets tegion s economy in motion, s productive sectors buy nd sell goods nd services from one nother. These reltionships cuse the totl effect to exceed its initil chnge in finl demnd. The rtio of the totl economic effect on regionl economy to the initil chnge is clled regionl multiplier.z The totl effect is mesured in terms of output, income or employment giving rise to output, income nd employment multipliers. An output multiplier of 1.66, for exmple, indictes tht, if firm s sles in one region to buyers in nother region increse by $100 million, totl sles throughout the region re expected ultimtely to increse by $166 million. The dditionl $66 million in regionl economic ctivity is generted becuse the $100 million chnge in spending, by ffecting production, income nd employment in the region, stimultes dditionl chnges in spending tht cuse further chnges in production, income nd employment in the region. Suppose the initil chnge in spending in regionl economy occurs s n pprel mnufcturer receives pyment for sles to wholesler 2 The regionl multiplier is nlogous to the stndrd Keynesin multiplier used in mcroeconomics: n initil increse in demnd leds to n even greter expnsion of regionl income, s the income received from this demnd is spent, creting income for others who spend nd crete dditionl income for still others. This process of respending comes to n end when the demnd increse is offset by lekges through sving, txtion nd imports.

3 21 Figure 1 The Mulfiplier Process b C d e i t in nother region. As figure 1 shows, for every such dollr of spending tht enters this hypotheticl region (column ), 40 cents is respent within the region (column b). n our exmple, this respending includes pyments to other firms within the region for inputs such s cloth, buttons nd electricity nd for services such s legl nd jnitoril services. The remining 60 cents of the initil dollr is considered lekge, s it is spent outside of the regionl economy. Lekges include pyments for inputs the mnufcturer buys from other regions, tx pyments to ll levels of government nd dividends distributed to stockholders in other regions. n the second round of respending (column c), 16 cents of the 40 cents is respent within the region, while the remining 24 cents is lekge. One exmple of locl respending would be purchses of regionlly ~Agiven sector s multiplier is smller for region thn for the ntion of which it is prt. This reflects the greter interindustry linkges t the ntionl level. A region s multiplier for specific sector tends to be smller produced goods by the suppliers of the pprel mnufcturer using the pyments they receive from the pprel mnufcturer. This process continues until ny dditionl spending within the region is inconsequentil. The chnge in totl business ctivity cn be clculted by dding the initil dollr to the totl respending within the region. n our exmple, this would totl $1.66 ($1 + $ $ $ $ SOUl). Thus, the pprel sector s multiplier indictes tht $1.66 of totl business ctivity is generted for ech dollr of dditionl externl sles by the region s producers.~conversely, for ech dollr reduction in finl demnd, totl regionl business ctivity is expected to decline by $1.66. nput-output models enble reserchers to clculte multipliers for vrious sectors of the economy. Ech sector hs unique multiplier becuse ech hs different pttern of purchses from firms in nd outside the region. Open nd Closed Models n prctice, the vlue of multipliers depends on whether households re considered prt of the interrelted processing sectors or component of finl demnd outside the regionl economy. The seprtion of households from processing sectors is rbitrry; households s consumers nd workers re enmeshed with the industril sectors. Households ern their incomes by providing their lbor services nd spend their incomes s consumers. Nturlly, the mount tht consumers spend is function of their incomes, which depend on the receipts of the sectors. f n input-output model clssifies households s prt of finl demnd rther thn prt of the region s productive economy, then income received by households is considered lekge, nd household respending does not contribute to the multiplier effect. f households re included in the interrelted processing sectors, the spending of income received by households within the region dds to the totl effect. Thus, multipliers derived from so-clled closed models, in which regionl households re included, re lrger thn those derived from open modbecuse, reltive to the ntion, region tends to purchse higher proportion of its inputs from other regions. n other words, lekges re greter.

4 els, which tret households s prt of finl demnd. 4 Output Multipliers An output multiplier for given sector is the totl vlue of sles by ll sectors of the regionl economy necessry to stisfy dollr s worth of finl demnd for tht sector s output. An importnt point is tht this vlue of totl business ctivity is lrger thn the mrket vlue of currently produced goods nd services becuse some of the respending in input-output models is for the purchse of intermedite goods nd services. The vlue of these inputs re counted gin when the finl goods they re used to produce re sold. Thus, Stevens nd Lhr (1988) conclude tht output multipliers re lmost lwys misleding becuse of this double-counting. A hypotheticl exmple my clrify how output multipliers re used. Tble 1 presents multipliers for the St. Louis Metropohtn Sttisticl Are (MSA) derived from one frequently used input-output system, the Regionl nput-output Modeling System (RMS ) developed by the U.S. Deprtment of Commerce. 5 Suppose the federl government cuts orders for militry fighter jets produced in the St. Louis re by $50 million. To estimte the totl output effect, the $50 million reduction of sles is multiplied by the totl output multiplier for ircrft, 2.64, resulting in totl chnge of $132 million. Thus, totl output in the St. Louis MSA would be expected to fll by $132 million becuse of the initil reduction in ircrft production. this totl multiplier effect is the sum of the output effects on ech of the sectors of the St. Louis economy. Not surprisingly, the trnsporttion equipment (except motor vehicles) industry, which includes ircrft production, is ffected the most. For every dollr chnge in finl demnd for ircrft, output of the trnsporttion equipment industry chnges in the sme direction by $1.09. As tble shows, the effects go 4 Multipliers derived from open models re referred to s Type or simple multipliers, while those derived from closed models re clled Type or totl multipliers. The sme distinction pplies to income nd employment multipliers. n ddition to households, other sectors cn be shifted from finl demnd to the region s productive sectors. Bourque (1969), for exmple, cretes multipliers for the Wshington economy tht ccount for the induced effects of stte nd locl government spending. 5 See U.S. Deprtment of Commerce (1986) for description of RMS. The St. Louis MSA includes the City of St. 22 beyond this industry. For exmple, for every dollr chnge in finl demnd for ircrft, output of the rel estte sector chnges by $0.09 nd the output of the retil trde sector chnges by $0.07. The output multiplier for households (industry 39) indictes $0.62 chnge in household ernings resulting from every dollr chnge in finl demnd for ircrft. The household ernings effect reflects the sum of ernings pid to households employed in the other 38 industries listed in the tble. n other words, some portion of the $1.09 multiplier effect listed for trnsporttion equipment is distributed s pyments to households. A similr sttement cn be mde bout the other industries. An estimte of exctly how much is distributed to households is listed in the column for the ernings multiplier, which is relted closely to the income multiplier discussed in the next section. ncome Multipliers ncome multipliers trnslte the effects of chnges in finl demnd into chnges in household income. Two kinds of income multipliers cn be constructed: those tht indicte regionl income chnges ssocited with n initil chnge in output nd those tht indicte income chnges ssocited with n initil chnge in income! The first pproch converts n initil $1 finldemnd chnge into the totl chnge in income. This conversion is strightforwrd. The $1 finldemnd chnge in specific sector cuses chnges in tht sector nd ll other relted sectors. These finl-demnd chnges led to chnges in household income in ech of these sectors. Summing the household income chnges over ll sectors yields the totl chnge in household income. The income multiplier is simply the rtio of the totl chnge in household income to the $1 chnge in finl demnd. Louis nd Frnklin, Jefferson, St. Chrles nd St. Louis counties in Missouri s well s Clinton, Jersey, Mdison, Monroe nd St. Chir counties in llinois. Prof. Fredrick Rines of Wshington University provided vluble ssistnce on the use of the RMS model for this exmple. income multipliers cn lso be distinguished on the bsis of whether households re considered prt of the interrelted processing sectors or component of finl demnd,

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6 24 The second pproch uses different denomintor in the clcultion of the income multiplier. A $1 chnge in finl demnd for specific sector s output initilly becomes $1 chnge in output by tht sector. n the first pproch, this dollr s worth of output is used s the denomintor in the income multiplier. The second pproch replces the denomintor with the initil dditionl income received by workers in the sector. The resulting multiplier indictes the totl chnge in income resulting from the initil chnge in income. Although the RMS model does not provide income multipliers, it does furnish closely relted ernings multipliers tht cn be pplied to the current exmple. (ncome generlly includes trnsfer pyments, dividends, interest nd rent in ddition to ernings.) Tble 1 shows tht the ernings multiplier for ircrft mnufcturing is , indicting tht for ech $1 chnge in output from the ircrft industry in St. Louis, ernings throughout St. Louis will chnge by pproximtely $0.62, other things equl. Approximtely $0.35 of this chnge occurs in the trnsporttion equipment (except motor vehicles) industry. Multiplying the hypothesized $50 million reduction by yields n estimted decline in regionl ernings of $31.15 million. Employment Multipliers n mny cses, citizens re s interested in employment s in output or income, tht is, the number of regionl jobs prticulr economic chnge is expected to generte or eliminte. f the reltionship between the vlue of sector s output nd its employment level cn be estimted, then employment multipliers cn be clculted. As with the discussion of income multipliers, there re employment multipliers tht trnslte initil output chnges into regionl employment chnges nd, using different pproch, employment multipliers tht trnslte initil employment chnges into regionl employment chnges. As Stevens nd Lhr (1988) note, most employment multipliers re estimted in terms of jobs rther thn full-time equivlent employees. Unfortuntely, the reltionship between jobs nd full-time equivlent employees is not the sme, either cross economic sectors or cross regions for the sme sector. Thus, not only re ll comprisons of employment multipliers suspect, but employment multipliers do not identify the mix of full- nd prt-time workers. Returning to our exmple, if the employment multiplier for St. Louis ircrft sector of 22.6 jobs per $1 million of finl sles, shown in tble 1, is pplied to the $50 million reduction in ircrft sles, the estimted regionl employment effect will be loss of 1,130 jobs. 8 n ddition to the reduction of employment in the trnsporttion equipment (except motor vehicles) industry of 450 (9 times 50), there re noteworthy employment effects in retil trde (120 jobs) nd resturnt services (85 jobs). To summrize, the estimted effects of the hypotheticl $50 million spending cut for ircrft would be: totl spending (output) declines by $132 million; ernings, by $31.15 million; nd employment, by 1,130 jobs. From different perspective, these results suggest tht, for ech job lost, regionl ernings will fll by $27,566 nd totl spending by $116,814. While the ernings per job figure seems resonble, the spending decline of $116,814 per job is of little prcticl vlue becuse this figure is not the loss in ctul output per worker. The region s output will fll by substntilly less thn totl sles losses. HOW ACCURATE ARE REGONAL MULTPLERS? MORE REASONS TO BE CAUTOUS The widespred use of input-output multipliers in regionl impct nlysis suggests tht mny economists, government officils, firms nd others hve found them useful. Yet, multiplier nlysis hs importnt limittions stemming from both the theoreticl bsis of input-output models nd mesurement problems. A few of these problems hve lredy been identified; more re discussed below. An wreness of these limittions is necessry to ccurtely interpret such multipliers. Trnsitory Effects Multipliers estimte short-term economic chnges; they do not tke into ccount regionl economy s long-term djustments. Thus, mny 8To be consistent with the St. Louis RMS model, the $50 million reduction is mesured in 1987 dollrs.

7 25 of the economic effects identified by multipliers re likely trnsitory. For exmple, while reduction in federl government purchses of ircrft will cuse reduction in regionl employment, t lest some of this reduction will be temporry s workers whose jobs were eliminted find new jobs in the region. Thus, multipliers my overstte the loss of jobs, if one looks beyond the immedite effects.b0 Recent reserch by Tylor (1990) stresses this trnsitory effect. Tylor estimtes tht ll 50 sttes would experience t lest smll reduction in employment in the short run if rel federl defense spending ws cut by 10 percent. n ll but 17 sttes, however, these losses would be more thn offset by the cretion of new jobs. Supply Constrints The input coefficients mesuring the interindustry flows between sectors re fixed in input-output models; in other words, t ny level of output, n industry s reltive pttern of purchses from other sectors is unchnged. When the initil chnge considered is n increse, this ssumption requires tht excess productive cpcity exists in regions in which inputs re purchsed. n ddition, sufficient surplus of lbor with dequte skills is lso ssumed to be vilble t unchnged wges. 2 f these ssumptions re invlid, producers will hve to lter their purchsing ptterns to increse production. For exmple, suppose region s uto ssembly plnt plns to increse its production nd sles to other regions by 50 percent. f the plnt s suppliers within the region were operting t, or ner, full cpcity, the ssembly plnt would hve to buy lrger proportion of its inputs from firms outside the Not ll displced workers, of course, will find lobs within the region, even in the hong run. The loss of such workers who leve for jobs in other regions will tend to retrd the region s growth. Yet, such restructuring ultimtely enhnces the ntion s economic performnce, by redistributing lbor resources to the industries nd regions where they re most needed. Someof the problems inherent in input-output models, including the mesurement of long-run impcts nd chnges in multipliers over time, re ddressed by linking inputoutput models to econometric models. Such models, however, re vilble for few regions. See Conwy (1990) nd srilevich nd Mhidhr (1990). Tylor (1990) uses U.S. input-output model to estimte the effects of the defense spending cuts on ech of the ntion s industries. A stte s short-run employment effects region, t lest until locl suppliers could expnd their production. n this cse, the input coefficients expressing the flows from ech regionl industry to the ssembly plnt would overstte the true short-run reltionship, nd multipliers derived from the model would lso be too lrge. f the supply of unemployed, dequtely skilled workers were insufficient, the ssembly plnt might substitute cpitl for lbor in its production or hire workers from other firms in the region. n this cse, estimted impcts bsed on erlier multiplier reltionships could overstte the ctul consequences. Of course, the mgnitude of this problem vries from cse to cse. t is more severe when considering substntil increse in output, especilly in smll nonmetropolitn region; it is less importnt when nlyzing lrger, more complex economies. Supply constrints in most industries lso re bigger problem closer to business cycle peks thn during recessions. gnoring nterregionl Feedbcks Multipliers exist becuse the expnsion of one sector s production cuses the region s other sectors to expnd s well; this, in turn, my induce further expnsion in the first sector. These feedbck effects operte not only between relted sectors within region, but lso between the economies of individul regions. Suppose, for exmple, s Missouri ircrft plnt expnds, it purchses tires produced in Tennessee. This could cuse the tire plnt to buy more industril chemicls from Missouri firms. n ddition, some of the incresed income tht Tennessee tire plnt workers receive might be spent purchsing consumer goods nd services produced in Missouri. Thus, the interreltions of the two stte economies would cuse were estimted by llocting ech U.S. industry s loss to stte bsed on its industril composition. A stte s hongrun rebsorption of lbor ws bsed on the ssumption tht its employment continued to grow t the historicl rte. 2 The fixed reltionship implies tht dditionl mteril nd lbor inputs re vilble t existing prices nd wge rtes, respectively. Tht is, the increse in the quntity demnded would not bid up input prices nd wges. Otherwise, n increse in production nd employment in one sector my result in n employment decrese in nother sector, nd the multiplier will overstte the ctul effect. This suggests nother use of multiplier nlysis: evluting the fesibility of n expnsion in light of existing regionl lbor pools.

8 lrger multiplier effect on the Missouri economy thn if the interregionl effects were ignored. Although they re not included in multipliers clculted from single-region models, these interregionl feedbcks re cptured by multipliers derived from interregionl nd multiregionl input-output models. Such models re rrely developed, however, becuse of their extensive dt requirements. How importnt is this omission for singleregion models? While the importnce vries from region to region, evidence suggests tht ignoring such feedbck effects does not substntilly ffect ggregte multiplier vlues. For individul industries, however, interregionl feedbcks could be quite importnt. Do Multipliers Chnge Over Time? The multipliers used in impct studies re often generted using dt bsed on trnsctions for period tht occurred five or more yers erlier. n mny cses, full survey to develop new input-output coefficients is costly, so existing models, often severl yers old, re used. Even if new survey is conducted, it my tke severl yers to complete the input-output tble. f the structurl reltionships indicted by regionl input-output model chnge significntly over these yers, the relibility of impct nlyses using the older model is diminished. 7 There re severl resons why input-output reltionships chnge considerbly over time. First, technologicl chnges nd inventions of new products lter mnufcturers input purchsing ptterns. Prtly becuse of technologicl chnges, for exmple, uto mnufcturers purchse more plstic nd robots nd less steel nd lbor per unit of output thn they did 10 yers go. Second, if producers in sector hve significntly expnded their output since the inputoutput tble ws constructed, the ssumed fixed Exmples include the nine-region interregionl model of Jpn (Jpnese Government, 1974), the three-region Dutch interregionl model (Oosterhven 1981) nd Polenske s (1980) muhtiregionb model of the 50 U.S. sttes nd District of Columbi. Multipliers, s shown by Stevens nd Lhr (1988), cn lso be derived from economic bse models. Such models generlly divide regionl economic ctivity into two sectors production for export nd production for locl use rther thn the mny sectors found in input-output models. This extreme ggregtion is the source of one of severl limittions of economic bse multipliers. See Richrdson (1985) for criticl review of these multipliers. 26 reltionship between the rtio of the vlue of input to output for ech input will no longer hold, For exmple, the costs of inputs tht re reltively insensitive to output levels, sy, purchses of ccounting services, could be spred over dditionl units of output s expnsion occurs, lowering some input coefficients. Furthermore, reltive price chnges cross commodities induce substitution of the reltively cheper inputs for the more costly ones. f oil prices rose reltive to col prices, for exmple, some mnufcturers might purchse more col nd less oil. Finlly, chnges in interregionl or interntionl trde ptterns perhps due to chnges in trnsporttion costs or exchnge rtes could substntilly lter ptterns of trde nd, thus, multiplier vlues. f obsolete vlues re used s input-output coefficients, the multiplier vlues nd impct estimtes derived from them will be inccurte. Conwy (1977) provided some insights into the importnce of chnging multiplier vlues by exmining three survey-bsed input-output models for the stte of Wshington. He found tht, on verge, simple output multipliers chnged by pproximtely 5 percent in ech of the , nd periods. Output multipliers for individul sectors chnged by s much s 17.7 percent in the period. The chnge in totl income multipliers ws somewht greter thn the chnge in output multipliers; on verge, they chnged by roughly 10 percent in the three periods. One sector s income multiplier fell by 33.3 percent between 1963 nd 1972, while nother s rose by 14.1 percent. Although these results re bsed on only one region, they suggest tht the use of multipliers bsed on n older model my be misleding, especilly given the drmtic chnges tht hve influenced the wy goods nd services hve been produced in recent decdes. These chnges include substntil fluctutions in oil 16 Miler nd Blir (1985), pp , found tht the verge error when interregionl feedbcks were ignored (verged over ll sectors in ll regions) ws less thn 3 percent in five models, 7 percent in one model nd 14.4 percent in nother. Also see Guccione, et h. (1988). ~Arelted problem rises if one ttempts to use inputoutput models for long-run regionl forecsting. Such cses require so-clled dynmic input-output models s described in Miller nd Blir (1985). pp , or combintion econometric-input-output models such s the one described by Conwy (1990).

9 27 1 prices, widespred technologicl innovtion, incresed use of services in production processes nd heightened foreign trde. Nobel Prize winner Wssily Leontief hs rised serious doubts bout the ccurcy of models bsed on the federl government s input-output tble of the U.S. economy. The frequently used RMS model, for exmple, ws derived from the 1977 U.S. input-output tble, so the underlying structurl reltionships hve hd more thn decde to chnge. For the sme reson, Leontief suggests tht, when the 1982 benchmrk U.S. input-output tble becomes vilble in erly 1991, it will be of only historicl interest. The Construction of Regionl nput-output Tbles Stevens nd Lhr (1990) stress n even more fundmentl problem: the lck of informtion on the reltionships mong producers within region mkes constructing n ccurte regionl input-output model very difficult. Since the pproprite coefficients re unknown, n nlyst must estimte them. One wy to do this is to ssume tht regionl input-output coefficients re the sme s the vilble, but dted, ntionl coefficients. This method is not used, however, becuse regionl production processes re seldom identicl to ntionl production processes nd, even if they were, firms within the region re more dependent on inputs from outside the region thn ntionl input-output coefficients would indicte. Another method is to conduct comprehensive survey of the region s firms; this, however, is rrely undertken becuse of its high cost. n most cses, regionl input-output coefficients re estimted using methods tht lter existing U.S. input-output models to better reflect regionl trnsctions. This ltertion is ccomplished by surveying key regionl sectors or by using recently published regionl dt. These methods re imperfect, however, nd the lck of ccurte informtion remins mjor obstcle in clculting regionl multipliers.20 The consumer of such multipliers is thus justified in wondering whether the vlue of multiplier is ccurte. See Leontief (1990). For description of five such models, see Brucker, et b (1987). For criticl review of nonsurvey nd prtil survey methods, see Miller nd Blir (1985), pp Hew- Clculting the Chnge in Finl Demnd Multipliers re used to estimte the totl effect on region s economy of n initil chnge in finl demnd; however, estimting the initil chnge is not simple exercise. Chnges in finl demnd hve finncil consequences. gnoring this fct cn result in estimtes of finl demnd chnges lrger thn re ctully wrrnted. To continue with our erlier exmple, ssume tht the reduction in defense expenditures for ircrft produced in St. Louis is ssocited with reduction in federl income txes. As result, St. Louis txpyers will py less in txes nd spend more on goods nd services, including those produced loclly, which would offset some of the negtive effects ssocited with the decline in ircrft expenditures. These offsetting effects re likely to be more pronounced in cses of loclly funded projects. For exmple, suppose tht city ws considering building sports stdium nd finncing it by rising locl txes. n generl, the lrger the burden of these txes on locl residents, the lrger the reduction in demnd for locl production. Thus, n nlysis tht looks t the demnd effects ssocited with spending on the stdium lone would overstte the multiplier effects of the project. Moreover, determining the initil chnge in finl demnd stemming from spending chnge is not lwys strightforwrd. n describing the use of RMS, for exniple, the U.S. Deprtment of Commerce (1986) illustrtes the importnce of determining the ctul finl demnd chnge in the context of tourist expenditures in Louisin. A first step ws to estimte the nticipted increse in tourist expenditures, n exercise subject to considerble error becuse of the difficulty of predicting the number of dditionl tourists s well s the chnges in their expenditure levels. n the Deprtment of Commerce exmple, for instnce, incresed expenditures on retil goods of $280 million were predicted. Given this figure, it ws necessry to determine how much of this mount reflected finl ings, srihevich nd Mrtins (1990) hve recently developed method tht might prove n improvement over pst pproches.

10 28 demnd for goods nd services produced in Louisin. The expenditure for retil goods is unlikely to be only for goods nd services produced in Louisin becuse this expenditure reflects chnges for the output of wholeslers, trnsporters, mnufcturers nd retilers. Assumptions must be mde bout the distribution of chnges mong these producers nd how much of the output of these producers tkes plce in Louisin. Thus, estimting finl demnd is subject to substntil error. Estimting the Regionl lmpct of New ndustry f regionl input-output model is vilble nd the mgnitude of the initil chnge in finl demnd is known, estimting the regionl impct of chnge in the finl demnd of n existing sector is strightforwrd. t is more difficult, however, to estimte the regionl impct of firm in n entirely new sector. Since the existing interindustry flows do not indicte such firm s reltionships with other sectors, the existing tble cnnot be pplied directly; dditionl informtion is needed. Detiled informtion is required on the new firm s sles to, nd purchses from, other regionl producing sectors nd other suppliers of inputs. Additionl informtion lso my be needed if new firm produces goods or services tht re substitutes for those previously produced outside the region. Suppose, for exmple, tht new firm produces n input tht mny regionl firms previously purchsed from other regions. The enhnced vilbility of the input from the new source will cuse some firms to purchse more of it from within the region. The chnge could lter purchses from firms outside of the region nd input coefficients to n extent tht more survey informtion or new estimtes of interindustry linkges would be required. A relted sitution would be the closing of firm tht is the sole producer of product. f the firm sells much of its output to other regionl sectors, the firm s elimintion would force them to import the good, ltering their externl nd interindustry linkges. CONCLUSON Economic multipliers re often used to estimte the totl regionl effect ssocited with n initil chnge in regionl economy, fter ccounting for ll the reltionships mong the economy s sectors. Multipliers used in regionl impct studies re usully bsed on single-region inputoutput models, which mthemticlly describe the industril structure nd linkges of the economy t one point in time. Numerous theoreticl nd mesurement problems, however, suggest tht estimtes bsed on these multipliers should be viewed with cution. The ccurcy of multipliers depends on how ccurtely the model describes the current regionl economy. f the structure of the economy hs chnged since the model ws developed or if the new development itself will substntilly lter the regionl economy s structure, multipliers will tend to be inccurte. n such cses, their ccurcy cn be improved by using dditionl informtion, n ddition, identifying the precise mgnitude of n initil chnge in finl demnd is not lwys strightforwrd. The finncing of prticulr expenditure cn offset n increse or decrese in demnd for loclly produced goods nd services. Further complictions cn rise in determining how much of chnge in expenditures is chnge in finl demnd. Despite their limittions, economic multipliers bsed on input-output models re populr nd will continue to be used in economic impct studies. Meningful nlysis using multipliers is not cler-cut nd mechnistic, but rther requires the exercise of creful judgment by n experienced nd knowledgeble nlyst. Such nlysis llows for degree of subjectivity nd therefore, possible bis to enter the nlysis, however. The consumer should be wre tht estimtes bsed on regionl multipliers my be subject to considerble error. REFERENCES Bourque, RJ. ncome Multipliers for the Wshington Economy, University of Wshington Business Review (Winter 1969), pp Brucker, Shron M., Steven E. Hstings nd Willim R. Lthm h. Regionl nput-output Anlysis: A Comprison of Five Redy-Mde Model Systems, The Review of Regionl Studies (1987), pp Conwy, Richrd S., Jr. The Stbility of Regionl nput- Output Multipliers; Environment nd Plnning A (1977), pp The Wshington Projection nd Simultion Model: A Regionl hnterindustry Econometric Model, nterntionl Regionl Science Review (Vol. 13, Nos. l&2, 1990), pp

11 1 Guccione, Antonio, Willim J. Gillen, Peter D. Blir nd Ronld E. Miller. nterregionb Feedbcks in nput-output Models: The Lest Upper Bound[ Journl of Regionl Science (August 1988), pp Hewings, Geoffrey JO., Philip R. bsrihevich, nd Edurdo Mrtins. The Construction of the llinois nd Chicgo nput-output Tbhes[ presented t the North Americn Meetings of the Regionl Science Assocition, Boston, November 9-11, Hewings, Geoffrey JO., nd Rodney C. Jensen. Regionl, nterregionl nd Muitiregionl nput-output Anlysis; in Peter Nijkmp, ed., Hndbook of Regionl nd Urbn Economics, Vol.1 (1986), pp srilevich, Philip, nd Rmmohn Mhidhr. Chicgo s Economy: Twenty Yers of Structurl Chnge, Federl Reserve Bnk of Chicgo Economic Perspectives (MrchlApril 1990), pp Jpnese Government, Administrtive Mngement Agency et l. The 1970 nput-output Tble of Jpn; (Tokyo, 1974). Leontief, Wssily. Federl Sttistics Are in Big Trouble; New York Times, October 1, Miller, Ronld E., nd Peter 0. Blir. nput-output Anlysis: Foundtions nd Extensions (Prentice-Hll, nc., 1985). Moghdm, K., nd K.R Bllrd. Smll Are Modeling of the ndustril Sector (SAMS): An ntegrted Econometric- nterindustry Approch[ Environment nd Plnning A (Vol. 20, 1988), pp Appendix Foundtions An input-output model is mthemticl description of the reltionships mong ll sectors of n economy. To construct such model, economic ctivity in region must be seprted into number of producing sectors. These sectors my be highly ggregted, or they my be identified in considerbly more detil. For exmple, regionl input-output model developed by the Deprtment of Commerce contins more thn 500 industries, 370 of which re specific mnufcturing industries. The mnufcture of household furniture contins six seprte ctegories: 1) wood household furniture; 2) wood television nd rdio cbinets; 3) upholstered household furniture; 4) metl household furniture; 5) mttresses nd bedsprings; nd 6) household furniture, not clssified elsewhere. The necessry dt for specific time period re the flows of products in monetry terms from ech of the sectors s producers to ech of the sectors s purchsers. A model with steel nd utomobile sectors, for exmple, requires See U.S. Deprtment of Commerce (1986) for dditionl detils. of nput~output Models 29 Oosterhven, Jn. nterregionl nput-output Anlysis nd Dutch Regionl Policy Problems (Aldershot, Hmpshire (U.K.): Gower Publishing Co., 1981). Polenske, Kren R. The U.S. Multiregionl nput-output Accounts nd Model (Lexington Books, 1980). Richrdson, Hrry W. nput-output nd Economic Bse Multipliers: Looking Bckwrd nd Forwrd; Journl of Regionl Science (Vol. 25, No. 4, 1985), pp nput-output nd Regionl Economics (John Wiley nd Sons, 1972). Stevens, Benjmin H., nd Michel L. Lhr. Regionl Economic Multipliers: Definition, Mesurement, nd Appliction; Economic Development Qurterly (Februry 1988), pp The Misclcultion, Misinterprettion, nd Misuse of Regionl Economic Multipliers; presented t the North Americn Meetings of the Regionl Science Assocition, Boston, November 9-11, Tylor, Lori L. Reduced Defense Purchsing: Anticipting the mpct on Stte nd ndustry Employment, Federl Reserve Bnk of Dlls Economic Review (November 1990), pp U.S. Deprtment of Commerce, Bureu of Economic Anlysis. Regionl Multipliers: A User Hndbook for the Regionl input-output Modeling System (RMS ) (GPO, My 1986). the dollr vlue of steel produced in the region tht is sold to regionl uto mnufcturers nd the dollr vlue of utomobiles produced in the region sold to the region s steel industry. An industry s demnd for inputs from other industries is relted closely to its own output. For exmple, steel sles re relted to utomobile production - n contrst, no explicit ssumption is mde regrding the reltionship between the vlue of sles to buyers outside the industril sectors (such s households, government nd buyers in other regions) nd the quntity they produce. Thus, the sles of specific industry re mde to other producers within the region, which re clled interindustry sles, nd to externl units, which is termed finl demnd. Assuming the economy consists of n sectors, the totl output of sector i, x 1, cn be written s:

12 where the z terms represent the interindustry sles by sector i to ech of the n sectors (including itself) nd yj is the finl demnd for sector i s output. There will be n eqution similr to (1) for ech sector of the regionl economy. The interindustry flows of goods re summrized in tble 1A. The entries in ech row re the sles of sector, such s sector 1, to itself (z,,) nd to ech other sector in the economy (z, z,~).these interindustry flows cn lso be considered from the perspective of ny sector s purchses: ech column in tble 1A expresses one sector s purchses of the products of the vrious producing sectors in the region. For exmple, the first column in tble ta indictes sector Vs purchses from itself (z 11 ) nd from ech of the other sectors (z 2, -. - A sector s purchses of inputs, however, re not restricted to purchses from itself nd other sectors. For exmple, lbor is n input tht must be purchsed. A purchse of lbor is n exmple of wht is termed vlue-dded. n ddition, sector my purchse rw mterils nd other mteril inputs from other regions. ncome nd Product Accounts The trnsctions in tble 1A re subset of complete set of income nd product ccounts for n economy. To illustrte complete set, tble ZA is flow tble for n economy with two industries. The z s re simply the interindustry sles between the two sectors. Finl demnd for the two sectors (Y, nd Y,) consists of three domestic components nd one foreign component. n the regionl context, domestic nd foreign refer to within nd outside of the Tble 2A Expnded Flow Tble for Two-Sector Economy 30 Tble 1A nput-output Tble of nterindustry Flows Purchsing sector - Selling sector n 1 z,. - 2~ 2, 2 z,. Z,, - 2? Z. 2, 2 2 n Z Regionl economy. The domestic demnd components re: C, consumer (household) purchses;, purchses for privte investment purchses; nd G, purchses by government within the region, The foreign demnd component is export sles (E) tht include sles of finished goods to ll consumers, investors nd governments outside of the region s well s sles of intermedite goods to producers in other regions. Thus, finl demnd for industry l s output cn be expressed s Y 1 = C, +, + G, + E 1 nd for industry 2 s output s = C 2 +, + + E 2. The pyments sector of tble 2A identifies three ctegories of pyments, two of which my be termed vlue-dded pyments. These pyments equl the vlue of the sector s output Processing Totl sectors Finl demnd output 1 2 Processing 1 Z ~.. E. X. seclors ~. G 7 E, L. L 2 L.. L, L, L 1 L Pyments sechor N, N N N. N~ N 1 N M. M M MMCMF Totl X C 0 E X outlys ~

13 31 minus the vlue of the inputs it purchses from other sectors. Vlue-dded pyments by the two processing sectors consist of pyments for lbor services (L, nd L 2 ) nd for ll other vlue-dded items, such s tx pyments for government services, interest pyments for cpitl services nd rentl pyments for lnd services (N, nd N 2 ). The finl component of the pyments sector is for purchses of imported inputs (M, nd M,). Regionl imports include ll purchses from beyond the region s borders. The entries in the intersection of the vluedded rows nd the finl demnd columns of tble 2A represent pyments by finl consumers for lbor nd other services. For exmple, Lc includes household pyments for domestic help, LG represents pyments to government workers nd Nc includes interest pyments by households. Lstly, the entries in the intersection of the imports row nd finl demnd columns represent purchses of imported items by households (Mc), privte businesses (M 1 ) nd government (MG). ME represents imported items tht re re-exported. Summing the entries in the totl output column yields the totl gross output (X) of the economy (2) X = X, + X 2 + L + N + M. Totl gross output my lso be found by summing cross the totl outlys row. Thus, (3) X = X, + X 2 + C + + G + Equting the two expressions for X, subtrcting X, nd X, from both sides nd rerrnging terms leves (4) L + N = C + + G + (E M). The left-hnd side, totl fctor pyments, is gross regionl income, while the right-hnd side, the totl spent on consumption nd investment goods, totl government purchses nd net exports, is gross regionl product. Thus, the eqution simply expresses the equlity of regionl income nd output. 2A secto(s output, sy j, cn lso be expressed s the sum of ech sector s purchses from other regionl sectors nd pyments for vlue-dded components nd imported inputs: X 1 = ~X~+ 2~ X 1... ~Xi-i ~ix~.i. where Wt is the sum of L~,N~nd M 1. The element, ~ An nput-output Model The preceding income nd product ccounts cn be trnsformed into n input-output model rther esily. Given the flow of inputs from sector i to sector j (zn) nd the totl output of j (X 1 ), the rtio of the vlue of the input to the output (tht is, z~/x 1 ) is known s n input coefficient or n input-output coefficient nd is denoted by jj. nput coefficients cn be clculted for ech interindustry flow nd re viewed s mesuring fixed reltionship between ech of regionl sector s inputs nd its totl output. For exmple, if one-qurter of sector 2 s output ws purchsed from sector 1, then,, = 025. This reltionship is clculted from the flows of inputs nd output for given period, often one yer. The fixed nture of the reltionship implies tht the rtio of the vlue of ech input to ech output remins unchnged irrespective of the level of output, reflecting n ssumption of constnt returns to scle in production. This mens tht n identicl percentge chnge in ll inputs will cuse n identicl chnge in output. For instnce, doubling ll inputs will cuse doubling of output. The fixed input coefficients llow the totl output of sector i, X~,to be written s: (5)X 1 =~X,+~,X, X~ ~ X,,+ Y 1. The input coefficients in the preceding eqution stte how much of sector i s output is needed per dollr of output in ech of the other sectors. Multiplying the input coefficients by the output of these sectors provides the dollr vlue of sector i s output tht is directed to these sectors. As before, Y 1 sttes how much of regionl sector i s output is used to stisfy finl demnd. For ech sector of the economy, there will be n eqution similr to (5). These equtions cn be solved to yield n nswer to the following question: if the finl demnds for ech of the n sectors were known, how much output from ech of the sectors would be necessry to supply them? Thus, vlues for the gross output of ech does not necessrily represent sector s j s totl purchses of input n, but only tht portion purchsed within the region. Production in j my lso require importing inputs from other regions or ntions, which re included in the pyments sector.

14 sector cn be determined given the input coefficients nd the finl demnds. Open nd Closed Models The described input-output model depends on the existence of sector distinct from the interrelted processing sectors. These finl demnds consist of consumption purchses by households, sles to government nd gross privte investment within the region s well s sles to the rest of the world. The seprtion of households from the processing sectors is rbitrry; households s consumers nd workers re enmeshed with the industril sectors. Households ern incomes by providing their lbor services nd, s consumers, spend their income in predictble fshion. Although households tend to purchse goods for finl consumption, the mount of their purchses is relted directly to their income, which depends on the outputs of the sectors. 32 n some input-output models, the household sector is shifted from finl demnd to the interrelted processing sectors. Such model is known s closed model with respect to households, while n open model keeps the household sector s prt of finl demnd. n the context of income nd product ccounts, household consumption (C, nd C, in tble 2A) is shifted to the processing sectors in closed model. A closed model requires seprte row nd column in tble A for the household sector. The row would show how the output of the household sector, its lbor services, is used s n input by the vrious sectors nd the column would show how the household sector s consumption purchses re distributed mong the sectors. Household input coefficients re clculted s other input coefficients re. The household sector s row entries re the vlue of lbor services sold to ech sector for given period divided by the vlue of the sector s totl output for the sme period. l he elements of the household purchses column re the vlue of household purchses from ech sector for given period divided by the totl output of the household sector.