The Regional Economics Applications Laboratory (REAL) of the University of Illinois focuses on the development and use of analytical models for urban

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1 The Regional Economic Application Laboratory (REAL) of the Univerity of Illinoi focue on the development and ue of analytical model for urban and regional economic development. The purpoe of the Dicuion Paper i to circulate intermediate and final reult of thi reearch among reader within and outide REAL. The opinion and concluion expreed in the paper are thoe of the author and do not necearily repreent official poition of the Univerity of Illinoi. All requet and comment hould be directed to Geoffrey J. D. Hewing, Director, Regional Economic Application Laboratory, 67 South Matthew, Urbana, IL, , phone (217) , FAX (217) Web page: TYPOLOGY OF STRUCTURAL CHANGE IN A REGIONAL ECONOMY: A TEMPORAL INVERSE ANALYSIS by Yauhide Okuyama, Michael Soni And Geoffrey J. D. Hewing REAL 4-T-12 October, 24

2 Typology of Structural Change in a Regional Economy: A Temporal Invere Analyi 1 Yauhide Okuyama Regional Reearch Intitute, Wet Virginia Univerity, 511 N. High Street Morgantown, WV , USA Michael Soni Regional Economic Application Laboratory, Univerity of Illinoi, Urbana, IL , USA, and Bar Ilan Univerity, Irael Geoffrey J.D. Hewing Regional Economic Application Laboratory, Univerity of Illinoi, Urbana, IL , USA Abtract: Earlier tudie (Hewing et al., 1998, Okuyama et al., 22a, and Okuyama et al. 22b) invetigated the hollowing-out phenomenon of the Chicago economy, in which the manufacturing ector in Chicago have decreaed their intermediate dependency within the region while the ervice ector have increaed their dependency. In thi paper, a et of annual input-output table for the Chicago metropolitan economy during the period of wa again employed for a further invetigation of the tructural change, uing an alternative tool, the Temporal Leontief Invere Analyi (Soni and Hewing, 1998), which can ait in exploring trend and uncovering tendencie in individual ector or group of ector within the context of an economy-wide ytem of account. The reult are compared with the earlier tudie for examining the nature and detail of the hollowing-out phenomenon. 1. Introduction The analyi of economic tructure ha created a demand for technique that can invetigate both the nature and change of the tructure over time. Well-known technique include the familiar multiplicative decompoition aociated with the work of Pyatt and Round (1979) and of Round (1985, 1988) and interpretation uing tructural path analyi a in 1 The earlier verion of thi paper wa preented in the 14th International Conference on Input-Output Technique (22), the 4th Annual Conference of the Japan Section of Regional Science Aociation International (23), the 3rd Meeting of Brazilian Regional Studie (24), the 41 t annual meeting of the Japan Section of Regional Science Aociation International (24), and the author are grateful for the comment by the participant in thee conference.

3 Typology of Structural Change Page 2 Defourny and Thorbecke (1984). Thee approache were directed toward the evaluation of economie baed on the tructure of ocial accounting matrice. Narrowing to the change of the tructure over time, analyi of the evolution of interindutry relation ha become a major topic for economic analyi. The traditional approach, introduced by Chenery (1953) and Chenery and Watanabe (1958) wa further extended in variou tudie (for example, Carter, 197; Harrigan et al., 198; Deutch and Syrquin, 1989, among other). Recent empirical tudie on the Chicago economy (uch a Irailevich and Mahidhara; 1991, Hewing et al., 1998; Okuyama et al. 22a; and Okuyama et al. 22b) have indicated that the Chicago metropolitan economy ha experienced a hollowing-out phenomenon, in which the level of dependence on local purchae and ale i declining, epecially in the manufacturing ector. While thee tudie invetigated the Chicago economy employing variou analytical tool, further exploration focuing more on the tructural change over time may reveal not only the temporal path of change in interindutry relationhip acro ector but alo more comprehenive picture of hollowing-out effect. Thi paper utilize a new approach for invetigating the tructural change in the Chicago economy over the period of The analytical tool employed i the Temporal Leontief Invere, developed by Soni and Hewing (1998). One of the advantage of the temporal Leontief invere i the ability to implement and invetigate the role of tructural change in a time erie of input-output table. Another important feature of thi technique i it ability to provide a et of technique to explore the nature of the time erie and to ait in the extraction of important inight about the nature of technological change and/or of the change in trading patter (in the cae of regional and interregional ytem). Employing thi tool, impact and pattern of the hollowing-out effect acro ector are diplayed and analyzed. In the next ection, the concept of temporal Leontief invere i preented and dicued with other dynamic formulation of Leontief invere. Section 3 briefly decribe the derivation of Chicago input-output table uing the Chicago Region Econometric Input-Output Model (CREIM) and ummarized the previou tudie mentioned above. The fourth ection preent an analyi of the Chicago economy over the period of Thi paper conclude with ome ummary remark.

4 Typology of Structural Change Page 3 2. Methodology: Temporal Leontief Invere The Temporal Leontief Invere wa introduced (Soni and Hewing, 1998) a a tool to analyze and invetigate tructural change in an economy over time. Some of the earlier approache to the analyi of tructural change can be categorized into the following two: thoe, like Tiebout (1969), ued a comparative tatic approach; and the other, for example Leontief (197) and Miernyk et al. (197), who attempted to form a dicrete time-erie dynamic ytem. Tiebout approach involved a comparion of the tructure of a regional economy, A, at time t+n with another economy, B, at the preent time, t, borrowed the tructure from B a a firt etimator of the future tructure of region A economy. Although Tiebout idea wa ingeniou, hi method uffer mot from a dearth of comparative data. A dynamic verion of the input-output model wa firt introduced by Leontief (1953) and wa refined in hi 197 paper (Leontief, 197). Since Miernyk ytem i a derivative from Leontief (Soni and Hewing, 1998), only the latter will be dicued here. The dynamic inputoutput model aim to analyze and determine the tructural and the technological change of an economy (or economie) by including an intertemporal mechanim of capital accumulation. In hi firt model, Leontief formulated invetment a the rate of change in required capital tock a follow: where x x=ax+cx + f (1) i the vector of output, A i the matrix of input requirement on current account, C i the matrix of capital requirement, f i the vector of non-invetment final demand, and x i the time derivative of x. Leontief later (197) developed a dicrete approximation of model (1) uing a ytem of difference equation with dated technical matrice reflecting tructural change in an economy: x t =Atx t +Ct+1( xt+1-x t) +f t (2) where Ct+1 ( xt+1 -x t ) repreent the invetment requirement in addition to productive tock during t and t+1 in order to expand their capacity output from to x. Forming a ytem of interlocked balance equation over a period of m+1 year, the olution of thi ytem for unknown x in term of a given et of the c : xt t+1

5 Typology of Structural Change Page x-m G -m R-m R-3R-2G-1 R-m R-3R-2R-1G f -m -1-1 x -2 = R-2G-1 R-2R-1G f x-1 G-1 R-1G f-1 x G f (3) ( ) -1-1 where R =G C = I-A +C C. t t t+1 t t+1 t+1 The mathematical propertie of thi dynamic model have been tudied by many (for example, Zaghini, 1971; Schinnar, 1978; de Menard, 1992; and Guangzhen, 1993). However, the model ha been ued in few empirical work due to variou problem involved: firt, the implementation of the dynamic model require the aembly of capital requirement matrice that ditinguih between replacement and expanion of the capital; and econdly, the model could produce implauible reult due to it tructure. 2 Uing a different approach to introduce a dynamic tructure in the tatic input-output framework, a group of lagged input-output model with ditributed activitie were propoed. Concerning the time ued in the production proce and taking into account the time of labor market adjutment, among other thing, thee lagged input-output model aim to capture the proce of impact (or growth) from a production expanion within the input-output framework. The ditributed activity model developed by ten Raa (1986) i baed on the formulation of the Leontief dynamic input-output model, olving ome of the drawback in that framework, uch a ingular capital tructure, unbalanced growth, and different time profile of invetment, while preerving the formal tructure and implicity of the original Leontief dynamic model. ten Raa 2 Leontief (197) implemented hi dynamic model uing 1947 and 1958 US data, and it revealed the two major inherent drawback of the model, which could produce implauible reult. Leontief olved the model employing the backward-looking way--determine the final impact firt, and then olve the model for the requirement in previou year. Thi backward-looking olution i table, yet unrealitic, ince it aume that the economy ha a perfect foreight of the future. Although the forward-looking olution ha been tudied [Szyld (1985), Steenge (199a), Heeterman (199), and Steenge (199b)], it ha been found that a et of non-negative olution for exit only if the initial condition lie on the "balanced growth path". Thi drawback come from the aumption of full capacity utilization: the entire phyical productive capacity will be utilized. Another difficulty to derive the olution of the Leontief dynamic model i the ingularity of the capital matrix, C. A Duchin and Szyld (1985) pointed out, mot theoretical work have been carried out baed on the aumption that the C matrix i invertible, wherea the C matrix may be invariably ingular, with row of zero correponding to the ector not producing durable good. In order to overcome thee problem, Duchin and Szyld (1985) propoed the new formulation of the dynamic input-output model, and thi formulation wa ued in Leontief and Duchin (1986) tudy. x t

6 Typology of Structural Change Page 5 model i highly theoretical and aggregated, and few empirical application and analye baed on hi formulation have been implemented. Cole lagged-activity model (Cole, 1988 and 1989) are highly operational and are modeled on the empirical example of wetern New York and of Aruba. While Cole approach i highly practical for imulation-type analyi, in order for it to be ued for detailed analyi of tructural change, ome theoretical and modeling iue of the framework need to be further addreed. 3 A imilar approach to thee lagged model but with more emphai on production chronology, Romanoff and Levine (Levine and Romanoff, 1989; Romanoff, 1984; and, Romanoff and Levine, 1977, 1981, 1986, 199a, 199b, 1991, and 1993) introduced the Sequential Interindutry Model (SIM) in order to incorporate a more engineeringbaed flavor to the modeling of the production proce, uch a large contruction project where the effect on production and employment are tranitory. In the SIM, production i not imultaneou a in the tatic input-output model, but rather occur equentially over a period of time, with production procee categorized a either anticipatory or reponive production mode, depending on the repone to the tream of demand timuli. Thee dynamic framework on input-output ytem tend to place greater emphai on the modeling apect of tructural change, rather than on the analyi of tructural change per e. The temporal Leontief invere, introduced by Soni and Hewing (1998), i an alternative viion for time erie analyi of input-output ytem. The formulation include a conideration of the equence of direct input matrice for different period, A, A,, A, A,, exploit the notion of dicrete time change and correponding temporal multiplier, and propoe a temporal Leontief invere in lieu of the complexitie underlying the formal tructure of dynamic invere decribed in (3). A framework of the temporal Leontief invere can be hown in the following manner. Conider a equence of time period, t, t,, t, uch that in the initial 1 T 1 t t+1 period, t, there exit a matrix of direct input coefficient, A = a ij, and the aociated Leontief invere matrix, ( B = I-A ) -1. In each period, t, there i the matrix of change in direct input coefficient, E = e ij, uch that the matrix of direct input coefficient, A =, a ij and the Leontief invere matrix, ( B = I-A ) -1 will have the form: 3 Extenive dicuion were made regarding the theoretical underpinning and the formulation of Cole model in Jackon et al. (1997), Cole (1997), Jackon and Madden (1999), Cole (1999), and Ooterhaven (2).

7 Typology of Structural Change Page 6 A = A +E = A +E +E + +E B = ( I-A -E ) = ( I-A -E -E - -E ) Tranforming the latter relationhip to a multiplicative form, one can obtain: -1 ( ) ( )( ) ( ) -1-1 B = I-A -E = I-A I-B E = I-B E B ( ) ( )( ) ( ) -1-1 B = I-A -E = I-EB I-A =B I-EB (4) (5) The matrice, M = ( I-B E ) -1 and (, are called the left and right temporal L -1 multiplier. Obviouly: -1 M R = I-EB- 1) ( ) ( ) B =M B =B M ;M =B I-A ;M = I-A B (6) L -1-1 R L -1 R -1 Uing the left temporal multiplier, the following multiplicative decompoition of the temporal Leontief invere can be hown a follow: B =M B L -1-1 =MLML B-2 =MM MMB L L L L The multiplicative repreentation, model (6), of the Leontief invere, converted into the following additive decompoition: B (7), can be Uing the former relation: ( ) -1 ( ) B =M B =B + M -I B L -1-1 L B =B M =B +B M -I -1 R -1-1 R (8) Thi, D ( ) D =B -B = M -I B (9) -1 L -1, i called a the temporal increment, and thi, in turn, provide the additive decompoition of the temporal Leontief invere a follow:

8 Typology of Structural Change Page 7 Uing the left multiplier, M L B =B +D -1 =B +D +D -2-1 =B +D + +D +D =B +D +D + +D +D 1 2-1, one can tranform the relationhip (1) to the following form: (1) ( ) ( ) ( ) ( ) B = I+ B -I + ML -I B + ML -I MLB + + ML -I ML MLM B ( ) ( ) ( ) = B + ML -I B + ML -I MLB + + ML -I ML MLMLB ( ) ( ) = B 1 + ML -I MLB + + ML -I ML MLMLB L (11) = = B + M ( ) -I M M M B L L L L Soni and Hewing (1998) claim that thi repreentation provide for an interpretation of the temporal Leontief invere that hare a common feature with it dynamic couin; the invere depend on it evolutionary tail of change and thi dependence i highly non-linear. Together with temporal multiplier and temporal increment, thi form can erve a the bai for temporal analyi of an evolving input-output ytem. For example, if th period, the correponding gro output vector, x, can be derived a x = B f, and then can f i the final demand vector in the be decompoed into a um of the effect of the firt time period, the econd time period, through to the th time period increment, uing the relationhip (11), a follow: x =B f =f + ( ) + B -I f 1 ( L ) ( ) ( ) + + M -I Bf + (12) + M -I M B f 2 1 L L +M -IM MMBf L L L L More pecifically, thi formulation can decompoe the impact from the final demand change into the direct impact, f, the indirect impact at the bae year, ( B -I) f, the change (or the

9 Typology of Structural Change Page 8 1 deviation from the bae year) in indirect impact at the firt time period, ( ) ML -I Bf change (or deviation from the firt period) in indirect impact at the econd time period, ( L ) M -I M B f 2 1 L, the, and o forth. In thi way, how each year change contribute to the total impact in gro output change can be traced. 3. Data and Previou Finding In order to analyze tructural change of the Chicago economy, the Chicago input-output table are extracted from the Chicago Region Econometric Input-Output Model (CREIM), which conit of 36 indutrial ector (ee Appendix), during the period of Thi ytem of 25 equation include both exogenou and endogenou variable. Endogenou coefficient change erve a the mechanim to clear market in a quantity-adjutment proce (ee Irailevich et al., 1997, for more detail). The input-output coefficient matrix i not oberved directly; however, it i poible to derive analytically a Leontief invere matrix and, through inverion, the etimated direct coefficient matrix. An important aumption here i that the error term in the derived input-output coefficient from the CREIM are normally ditributed, and are independent and identically ditributed; thu, the coefficient, while not real obervation, can be treated a uch, ince they are derived by a quantity adjutment general equilibrium proce. Irailevich and Mahidhara (1991) and Hewing et al. (1998) ued a time erie of inputoutput table for the period , extracted from the CREIM, for invetigating the tranformation in the economic tructure of Chicago. While thee tudie employed the aggregated indutrial ector (7 and 9 ector, repectively), they explore the nature of the tructural change through examination of the change in the compoition of the Leontief multiplier and change in the economic landcape interpreted through the application of the multiplier product matrix. The reult of thee tudie, epecially in Hewing et al. (1998), revealed that intrametropolitan dependence ha been replaced by dependence on ource of upply and demand outide the region, indicating the evidence of a hollowing-out proce. In 4 In thi verion of CREIM, the price i fixed at 1987 million dollar.

10 Typology of Structural Change Page 9 addition, their analyi how a complex internal tranformation, a dependence on locally ourced manufacturing input i replace by dependence on local ervice activitie. One concern that might be raied i the degree to which the coefficient etimation i devolved to a bi-proportional adjutment proce. Uing the ame erie of input-output table for the Chicago economy, Okuyama et al. (22b) invetigated the way that the exogenou change included in CREIM are manifeted in the input-output coefficient and the degree to which thee input-output coefficient are predictable through the bi-proportional propertie of input-output table, under the uual condition aociated with the RAS technique. Aeing the time erie of direct input coefficient matrice, A, they found a greater volatility over time in the value of ubtitution effect, r, than in the entrie of fabrication effect, i t j, in the RAS procedure. In addition, ector with mall quantity of output tend to how greater variance over time wherea ector with large quantity of output eem to have larger number of r value, which are le than unity, than in the cae of j value. They concluded that thee reult coincide with the hollowing-out proce in the Chicago economy, reported by Hewing et al. (1998). In the hollowing-out proce, the level of dependence on local purchae and ale i declining, epecially between manufacturing ector. Therefore, the tendency of the ector with larger output to have r < 1 can be conidered a evidence of ubtitution, not acro ector, but in the location of purchae, ince the extracted Chicago input-output table are regional table. The maller volatility in the i j entrie indicate that the fabrication effect (technological change) i relatively inignificant. They alo found that ome of the interaction between manufacturing ector (a een in direct input coefficient, a, and Leontief invere coefficient, b ) have declining trend, implying that their interindutry relationhip within the Chicago region are weakening. In ummary, they claimed that, while the evidence of the hollowing-out proce in the Chicago economy i found, the general trend of bi-proportional propertie, baed on the direct input matrice over the period of , can be conidered a random movement. ij Uing a new analytical technique of Field of Influence 5, Okuyama et al. (22a) invetigated the tructural change of the Chicago economy with the ame et of input-output 5 The detail of field of influence analyi can be found in Soni and Hewing (1991) and Soni and Hewing (1992). i ij

11 Typology of Structural Change Page 1 table. They found that the Chicago economy exhibit little change in appearance by the economic landcape (multiplier product matrix); however, change in the hierarchy of forward and /or backward linkage illutrate ome underlying change in the tructure of the Chicago economy. In addition, by the cro-tructure of the direct (firt order) field of influence, the tability of ome Leontief invere coefficient and the intability of ome other coefficient are revealed. Moreover, their further analyi indicate that the trend and the type of change in forward and backward linkage differ coniderably acro ector. Thee reult indicate that the manufacturing ector have experienced ignificant tructural change in the period of , while the ervice ector have been rather table in term of field of influence; thi alo can be conidered a further evidence of the preence of a hollowing-out proce in the Chicago economy. In thi paper, the tructural change of the Chicago economy are further invetigated uing the technique of Temporal Leontief Invere, invetigating a time erie of invere matrice, Bt, intead of direct input coefficient matrice, A, employed in Okuyama et al. (22b). In thi way, the trend of ytem-wide tructural change in the Chicago economy can be evaluated over time. Furthermore, the decompoition of temporal invere can examine numerically in which year temporal change had more ignificant impact on the ytem-wide economic tructure than in other year, wherea the qualitative analyi of rank and hierarchie of interindutry relationhip were identified in Okuyama et al. (22a). Therefore, by uing the temporal invere, one can analyze change in the ytem-wide impact of the change in a particular ector a well a illutrate the trend of change in indirect impact. t 4. Analyi of Structural Change Uing Temporal Invere In thi ection, ome general obervation of temporal change in the Chicago economy are made and analyzed, followed by the analyi uing the temporal invere and the comparion with the finding ummarized in the previou ection.

12 Typology of Structural Change Page 11 General Trend of the Chicago Economy Figure 1 diplay the trend of total output of the Chicago economy and the top 1 ector with larget output in 198. The output of the top 1 ector, except Sector 2 (Electronic and Electric Equipment) and Sector 13 (Petroleum and Coal Product), increaed in real term over the period of The rate of growth among thee ector varie; for example, the larget output ector, Sector 27 (Wholeale and Retail Trade), ha a teady growth of output, mirroring the growth pattern of the total output of the region. On the other hand, the econd larget output ector, Sector 3 (Lodging, Buine, Engineering, Management, and Legal Service), had a ignificant increae between 1987 and 1988, and continuouly grew at the ame or lightly higher rate than that of total output, after Sector 19 (Indutrial Machinery and Equipment) ha a maller but till ignificant output increae between 1987 and 1989; however, the growth of the output in the other period appear rather flat. Sector 4 (Contruction), the fourth ranked in 198, ha growth trend almot parallel to the one of total output. The rank order among thee ector alo changed; Sector 4 (Contruction) moved up from fourth in198 to third in 1997; Sector 2 (Electronic and Electric Equipment) moved down from eighth to eleventh; more ignificantly, Sector 13 (Petroleum and Coal Product) moved down from ninth to 15th. <<Inert figure 1 here>> Temporal Invere Analyi A indicated earlier, equation (12) can be ued to analyze change in the impact path from the increae or decreae in final demand at a particular time period. Uing equation (8) and (9), equation (12) can be implified for numerical calculation a follow: x =B f = f + ( ) + B -I f + +D f + 1 +D f + 2 +D f (13)

13 Typology of Structural Change Page 12 Uing thi formulation of the temporal invere, an impact of final demand increae in 1997 to a pecific ector can be decompoed into the temporal impact (each year contribution to the total impact), o that tructural change in each year, in term of interindutry relationhip, can be traced. Three ector are choen to invetigate the characteritic of tructural change and the evidence of hollowing-out. Firt, final demand for Sector 27 (Wholeale and Retail Trade; having the larget output and econd larget final demand ector throughout the period) i increaed $1 million (1987 dollar). Figure 2 6 depict the trend of temporal indirect impact from the demand increae on the five aggregated ector (Reource [ector 1-3]; Contruction [ector 4]; Manufacturing (Non-Durable) [ector 5-15]; Manufacturing (Durable) [ector 16-23]; and Service [ector 24-36]) and of the ytem-wide impact. The ytem-wide temporal impact ha, on average, an upward trend, indicating increaing interindutry relationhip between Sector 27 and the entire ytem, with the negative value throughout the 198 (with an exception of 1987) and poitive value during mot of the 199. Thi upward trend appear to characterize each aggregated ector, except the Reource ector which ha a flat trend around the value of zero (meaning little change from the previou year). The mot notable change in value can be found with Manufacturing (Durable) ector, which ha large negative value in the early 198, ignificant upward hift in the late 198, and the teady poitive value during the 199. <<Inert figure 2 here>> In order to invetigate the relative change from the initial year (198) a the eroion of production lot (or the intenification of production gained), each year temporal indirect impact i integrated (accumulated) from the 1981 value. And, the trend are hown in figure 3. The ytem wide trend diplay the initial eroion of production lo during the 198, correponding to the negative value during the ame period in figure 2. Then, the trend become flatter in the early 199 with moderate increaing trend after 1993, regaining the value to ome extent. Thi alo reflect the poitive value after 1993 in figure 2. The trend of the aggregated ector, by and large, mirror the trend of the ytem-wide value. Both manufacturing ector (nondurable and durable aggregated ector) exhibit the teady decreae in the 198 and the flattened trend in the 199 without having any notable increae in the late 199. In um, Sector 27 f ( ) 6 Direct impact,, and the bae year (198) indirect impact, B -I f, are not included in thi and following figure in order to emphaize temporal change between 1981 and 1997.

14 Typology of Structural Change Page 13 appear to have gone through ome tructural change, with the growing trend with Contruction and Service ector and the moderately decreaing trend with both Manufacturing ector. <<Inert figure 3 here>> Another feature of the hollowing-out proce i that, epecially for manufacturing ector, the level of dependence on local purchae and ale i declining. In order to analyze the trend in one of the manufacturing ector in Chicago, a imilar timulu ($1 million increae in final demand) wa injected into Sector 19 (Indutrial Machinery and Equipment). Sector 19 output in 198 and 1997 wa ranked 6th over all and i ranked firt among manufacturing ector. Figure 4 how the trend of the temporal indirect impact to the entire ytem and to the aggregated ector. In contrat to the previou cae (figure 2), mot of temporal indirect impact in figure 4 have negative value, except ome mall poitive value in 1984, 1987, 1994, 1995, and 1997 for mot of the ector, indicating teady trend of weakening interindutry relationhip relative to the previou year. The general trend over the period can be conidered a lightly upward, but it i clearly flatter than the one in figure 2. In addition, the ytem-wide temporal impact have more fluctuation, wider variance, than for Sector 27. Manufacturing (Durable) ector, in which Sector 19 i, ha the larget negative value than other aggregated ector in mot year and tay negative, except only in a few year, while Sector 19 output appear to be increaing, epecially from 1983 to 1994 (figure 1). Thee finding ugget that the hollowingout proce ha been tranforming the manufacturing ector in Chicago to become more dependent on interregional trade. <<Inert figure 4 here>> Figure 5 how the trend of accumulated temporal change of Sector 19, a in figure 3 for Sector 27. During the 198, the trend of ytem-wide trend indicate a teady decreae throughout the 198 and continued until 1993, with a flattening after that point. The degree of decreae (eroion) in thi ector ha been much more evere than in the previou cae (Sector 27), indicating the coniderable decline in interindutry relationhip between Sector 19 and the ytem a a whole. Thi obervation alo reflect the trend that the value of temporal indirect impact are motly negative for thi ector, a hown in figure 4. In addition, the recovery trend

15 Typology of Structural Change Page 14 in the late 199 oberved for Sector 27 do not appear for Sector 19. A for the trend of the aggregated ector, both Manufacturing (Durable) and Service ector exhibit teady decline, while other aggregated ector (Reource, Contruction, and Manufacturing (Non-Durable)) how le ignificant change. Together with the obervation in figure 1, in which the trend of Sector 19 output indicate moderate but teady increae, thi reult document clearer evidence of the hollowing-out proce in thi particular ector with in the Chicago economy. While the output of a ector increae, the intermediate tranaction within the region decreae a a reult of interregional competition. <<Inert figure 5 here>> Hewing et al. (1998) found that Contruction (ector 4) in the Chicago economy exhibit ignificant change in the hierarchy of backward and forward linkage (page ), baed on their 9-ector model. In order to invetigate the temporal change of interindutry relationhip with Contruction ector, the temporal indirect impact are calculated uing a $1 million increae of final demand in Figure 6 diplay the trend in temporal indirect impact of ytem-wide and five aggregated ector. The general trend of temporal indirect impact look more like the one of Sector 27 (figure 2) than the one of Sector 19 (figure 4): the trend of the ytem-wide impact and of the five aggregated ector exhibit a light upward trend, flatter than of Sector 27 but teeper than of Sector 19, while the trend here tend downward during 1996 and A with the previou two cae, Manufacturing (Durable) ha the lowet value throughout the 198, but the trend turn to a teady increae after 1989 until Other aggregated ector have the very imilar trend to the one of Sector 27, except, again, with the downward trend during 1996 and <<Inert figure 6 here>> Figure 7 diplay the trend of accumulated temporal impact for Sector 4, a in Figure 3 and 5. The trend of the ytem-wide accumulated temporal impact appear very imilar to the one of Sector 27 (figure 3); the declining trend during the 198 and the early 199 and the regaining trend after The trend of five aggregated ector alo mirror the one of Sector 27, while the trend of Manufacturing (Durable) have a teeper decline than the one in figure 3, indicating evere eroion of interindutry relationhip between the Contruction ector and the

16 Typology of Structural Change Page 15 Manufacturing (Durable) ector. Conidering the output trend of the Contruction ector in figure 1 and Contruction ector output i trictly local, thi obervation alo ugget the hollowing-out proce in which Contruction ector ha come to rely more on the interregional trade for intermediate input and le on local purchae. <<Inert figure 7 here>> Typology of Trend of Accumulated Temporal Impact Baed on the finding of the previou tudie (Hewing et al. 1998; Okuyama et al. 22a; and Okuyama et al. 22b) and the obervation documented earlier, difference in trend of tructural change among ector appear prevalent; in addition, ome common type of tructural change may be created o that ector can be categorized into everal group of tructural change trend. In order to invetigate how a hollowing-out proce affect ector differently, a typology of ector baed on the hape of the trend of accumulated temporal impact to the entire ytem (ytem-wide trend in the above figure) wa developed. The reult are hown in Table 1. <<Inert table 1 here>> The typology of ector conit of four type: Tilted L, Flattened U, Flat, and Tilted J. The decription of each type i a follow: Tilted L (TL): thi type ha the hape of temporal impact trend that the accumulated impact decreae monotonically during all or mot of the period with a flat or lightly elevated tail (motly after 1993). Sector 19 in figure 5 ha the typical hape of the trend. Thi hape indicate that a ector in thi type ha conitently decreaed it intraregional interindutry relationhip with the ytem a a whole and with mot of the other ector. Thi tendency may be due to the increaing reliance on interregional trade for intermediate purchae, and thi i one of the feature of a hollowing-out proce. Included in thi category are: Food Product (5), Textile (7), Wood Product (8), Paper Product (1), Rubber Product (14), Primary Metal (17), Indutrial Machinery (19), Electronic (2), Tranportation Equipment (21), Intrument (22), Micellaneou Manufacturing (23), and Communication (25) ector. Thee ector are motly manufacturing ector (the only exception i Communication), from both Non-Durable and

17 Typology of Structural Change Page 16 Durable ub-categorie. Thi type coincide with the obervation found in the previou tudie that mot of manufacturing ector have decreaed the interindutry relationhip with the region and have increaed interregional trade for their production. Flattened U (FU): the hape of curve in thi type tart with moderate decreae during the 198, uually flatter than in TL, but tart to regain the lope upward in the 199. Sector 27 in figure 3 ha the typical hape of thee trend. A difference between TL lightly regaining tail and FU moderate recovery during the 199 i defined that the range of recovery (the difference between the lowet value and the 1997 (end of period) value) i greater than one third of the total decline (the difference between the highet value during the 198 and the lowet value). Thu, thi type ha the flattened U hape with more noticeable and larger recovery on the right hand ide (during the 199) than in TL that ha a much more modet recovery. Thi hape implie that the ector in thi type decreaed the interindutry relationhip within the region during the 198, but they regained them to ome extent during the 199. The ector in thi type include: Agricultural Product (1), Agriculture (2), Contruction (4), Furniture (9), Chemical (12), Leather Product (15), Stone Product (16), Fabricated Metal (18), Tranportation Service (24), Wholeale and Retail Trade (27), Entertainment (33), and State and Local Government (36). A mot of thee ector have increaed their output level continually and viibly during the period, thi hape may imply that during the 198 thee ector decreaed the interindutry relationhip within the region, imilar to the ector in TL, but their increaed output level may have neceitated to regain the intraregional interindutry relationhip in addition to the increaed interregional relationhip. In fact, the ector in thi type are a mixture of Reource, Contruction, Manufacturing, and Service ector. Flat (F): the name of the type decribe the hape of trend: flat, having few change over the period. The typical hape in thi type i hown in figure 8 for Sector 29 (Real Etate). The ector in thi type include: Mining (3), Tobacco (6), Printing and Publihing (11), Petroleum Product (13), Utility (26), Real Etate (29), and Auto Service and Parking (32). Thee ector have either very mall output level (Mining and Tobacco), or are trictly local activity (Utility, Real Etate, and Auto Service and Parking). Printing and Petroleum Product are the final two ector in thi group.

18 Typology of Structural Change Page 17 <<Inert figure 8 here>> Tilted J (TJ): the hape of thi type look like a vertical revere diplay of TL: initial decreae end by the mid 198, followed by the flat trend in the late 198 and the hape turn to upward throughout the 199, with the value in 1997 (end of the period) greater than any prior time point. The mot extreme cae of the hape i hown in figure 9 for Sector 28 (Finance and Inurance). In figure 9, the hape i motly upward after 1986 and the value of accumulated temporal impact turn poitive at 1992 and afterward. Sector 28 i the only ector having all poitive value with ytem-wide impact. Even with thi Sector 28, however, Manufacturing (Durable) ector ha negative accumulated value during the entire period. Thi obervation implie that Sector 28 increaed the interindutry relationhip within the region coniderably during the 199, except with the ector in Manufacturing (Durable) category. The ector in thi type are all Service ector, and thi reult i very much conitent with the finding in the previou tudie, in which Service ector increaed intraregional dependency. <<Inert figure 9 here>> In order to invetigate whether there i any relationhip between thi typology of ector and the growth rate of ectoral output and/or the change in rank, the comparion between the type and the growth and rank trend acro ector during the period of i made in table 2. For Tilted L (TL) type, the growth rate of ectoral output in thi type vary coniderably, from negative growth (-38% in ector 21) to trong increae (12% in ector 14), and the ditribution appear to be dipered without having a clear center. The change in their rank i either almot no change (ector 5, 7, 8, 1, 19, 22, 25) or decline (ector 17, 2, 21, 23), except ector 14 with a light gain. Flattered U (FU) type alo exhibit a imilar pattern: their output growth rate vary in a wide range, from -21% (ector 1) to 18% (ector 2); however, the ditribution of the growth rate tend more toward poitive value, although the hape of ditribution remain flat without any clear center with high frequency. The rank in thi type i almot unchanged for mot of the ector, except ector 9 (light decline) and ector 12, 16, 33 (gain). Flat (F) type alo ha a wide pread ditribution of growth rate, ranging from -48% (ector 3) to 1% (ector 32). In contrat with the FU type, the ditribution of growth rate for F type i rather kewed to the negative ide 4 out of 7 ector have negative value. The change

19 Typology of Structural Change Page 18 in rank in thi type how a wider variety of trend ignificant decline (ector 3, 13, 26) and ignificant gain (ector 32). The ector in TL and F are relatively mall in ize (with mall output hare); thu, their trend may be more volatile than the ector in other type (Okuyama et al., 22b). On the other hand, the ector in Tilted J (TJ) type appear more table or increaing in term of their growth trend and the change in rank. Their growth rate are all poitive value and relatively large, and the change in rank are all gain. Thee obervation ugget that the hollowing-out proce in the Chicago economy i very complex; uing only the trend of output growth rate and of rank to claify which ector i gaining (or loing) with in the regional economy may be mileading. For example, ector 14 increaed it output by 14% during , but the trend of interindutry dependence i declined a claified in TL. At the ame time, ector 34 increaed it output moderately, by 5%, while it alo increaed the interindutry relationhip within the Chicago economy over the period, a claified in TJ. It i clear that the reult from temporal Leontief invere analyi can provide additional and more detailed information of the hollowing-out proce. <<Inert table 2 here>> 5. Summary and Concluion In thi ection, major finding in thi paper are evaluated and compared to previou tudie. Some dicuion about the analytical technique and concluding remark are alo provided. Evaluation The reult in thi paper indicate that the evidence of different type of temporal change exit. With the typology of ector preented in the previou ection, it i quite clear that ector can be grouped into a few type, in which each type ha a ditinguihable path of tructural change. In thi regard, the finding in thi paper confirm the concluion of previou tudie that ued actual tranaction volume (Hewing et al., 1998); yearly analyi of Leontief invere matrix uing the field of influence technique (Okuyama et al. 22a); and the time erie (econometric) analyi of direct input coefficient matrice (Okuyama et al. 22b), over the

20 Typology of Structural Change Page 19 imilar period of time. The reult in thi paper can offer an analyi of temporal change in Leontief Invere, by which relative change in ytem-wide tructure of an economy can be traced and invetigated and thu may be een to complement and deepen the undertanding of the procee of tructural change in a regional economy. Combining thee reult, we now have a more complete picture of the hollowing-out proce in the Chicago Metropolitan economy: Manufacturing ector have experienced izable tructural change during the period of with weakening interindutry relationhip within the region and becoming more dependent on interregional trade, while Service ector have been rather table and increaing relative ignificance in interindutry relationhip within the region. The typology of ector created in thi tudy provide a more detailed view of the hollowing-out proce in Chicago, illutrating complex yet clearly divided trend of the tructural change among ector. Careful examination and comparion of the finding of the previou tudie may provide further depth in undertanding of the tructural change in an economy. Concluding Remark While the methodology and aociated propertie of the temporal Leontief invere do not provide the rich theoretical foundation that the Leontief dynamic ytem and it extended and modified model offer, the technique provide the capability for implementation and for exploration of the analyi of tructural change in a time erie of input-output table. Although the formal linkage between the methodologie remain to be developed, thi paper preented the uefulne and clear advantage of the temporal Leontief invere analyi and the evidence of the hollowing-out proce in the Chicago Metropolitan economy. If a greater number of data point (year) become available, the tatitical analyi of trend baed on thi type of analyi can be done for more robut invetigation of the difference in tructural change of an economy.

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