PyIO: Input-Output Analysis with Python. Suahasil Nazara, Dong Guo, Geoffrey J.D. Hewings and Chokri Dridi. REAL 03-T-23 October 2003

Transcription

1 The Regioal Ecoomics Applicatios Laboratory (REAL) is a cooperative veture betwee the Uiversity of Illiois ad the Federal Reserve Bak of Chicago focusig o the developmet ad use of aalytical models for urba ad regioal ecoomic developmet. The purpose of the Discussio Papers is to circulate itermediate ad fial results of this research amog readers withi ad outside REAL. The opiios ad coclusios expressed i the papers are those of the authors ad do ot ecessarily represet those of the Federal Reserve Bak of Chicago, Federal Reserve Board or Goverors of the Uiversity of Illiois. All requests ad commets should be directed to Geoffrey J.D. Hewigs, Director, Regioal Ecoomics Applicatio Laboratory, 607 South Mathews, Urbaa, IL , Phoe (27) , Fax (27) Web page: PyIO: Iput-Output Aalysis with Pytho By Suahasil Nazara, Dog Guo, Geoffrey J.D. Hewigs ad Chokri Dridi REAL 03-T-23 October 2003

2 PyIO (read: pai-o) Iput-Output Aalysis with Pytho Suahasil Nazara, Dog Guo, Geoffrey J.D. Hewigs, Chokri Dridi Regioal Ecoomics Applicatios Laboratory, Uiversity of Illiois at Urbaa-Champaig 2

3 Cotets. Itroductio 2. Gettig started 3 2. About Pytho ad its istallatio Settig up the PyIO Iputtig a iput-output dataset Ruig PyIO: A typical example Iput-output balace check 9 3. Table operatios 3. Aggregatio of iput-output tables 3.2 Updatig matrix: regioal supply percetage, locatio quotiet Updatig matrix: RAS method 5 4. Basic iput-output aalysis 6 4. Leotief ad Ghoshia iverse matrices Impact aalysis Multiplier aalysis: output, icome, employmet, iput 8 5. Advaced iput-output aalysis Key sector aalysis Output decompositio aalysis MPM aalysis Extractio method aalysis Push-pull aalysis Field of ifluece 28 Referece 28 Appedix: PyIO usig fuctios 30 3

4 PyIO: Iput-output Aalysis with Pytho Suahasil Nazara, Dog Guo, Geoffrey J.D. Hewigs, Chokri Dridi Regioal Ecoomics Applicatios Laboratory, Uiversity of Illiois at Urbaa-Champaig. Itroductio This ote outlies the use PyIO, a Pytho module for iput-output aalysis. It is hoped that this module will be the first i a series of modules that address differet ad more complex methods of aalysis based o iput-output, social accoutig ad computable geeral equilibrium models. What are icluded i the curret module are fuctios to perform basic operatios ad aalysis with iput-output models. The module does ot provide the capability for assemblig or geeratig a iput-output table; the program assumes that the user has a iput-output table available for maipulatio. Further, the program assumes familiarity with the basics of iputoutput aalysis; readers eedig to refresh their recollectio of iput-output models are referred to Miller ad Blair (985). I the ear future, this maual will be liked to a more extesive text o iput-output aalysis that is earig completio (Sois ad Hewigs, 2004). The applicatios i this module are derived from iput-output aalysis coducted by colleagues at the Regioal Ecoomics Applicatios Laboratory (REAL), Uiversity of Illiois at Urbaa- Champaig. The calculatios i a iput-output framework typically comprise a set of routies. This poit warrats the use of fuctios i the iput-output aalysis. For a specific aalysis, e.g., a extractio method, the computatio steps will be idetical regardless of iput-output of differet years or of differet dimesios. Pytho is chose as the basis for this module for several reasos. First, Pytho is easy to lear ad has great computatioal capability. It is also possible to build a graphic user s iterface which frees the user from ay requiremet to kow aythig about Pytho itself. At some poit, the maual will accompay a program that will be prepared i poit-ad-click form. Secodly, the core of Pytho is free. Oe ca dowload, as well as distribute, all files eeded to ru this module freely from the iteret. This is of great advatage to may, especially to users i developig coutries where legal access to software such as Matlab or Stata is limited for various reasos. This ote will outlie several fuctios related to iput-output aalysis, which are categorized i three parts below:

5 . Table operatios Aggregatio of iput-output tables o Aggregatig sectors i oe regio (atioal) or iter-regioal iput-output tables o Aggregatig regios i a iter-regioal iput-output table Updatig matrix: regioal supply percetage, simple locatio quotiet Updatig matrix: RAS method 2. Basic I-O aalysis Leotief ad Ghoshia iverse Impact aalysis Multiplier aalysis: output, icome, employmet, ad iput 3. Advaced I-O aalysis Key sector aalysis Output decompositio aalysis Multiplier Product Matrix (MPM) aalysis Extractio method aalysis Push ad pull aalysis Field of Ifluece Besides for the iput-output aalysis, iputtig iput-output data is a very importat part i this pytho module. For the sake of programmig efficiecy, PyIO developed at this stage allows oly iput from a ASCII text file. This decisio was take to facilitate accessibility to all users of computer. The geeral structure is that users eed to iput the iformatio about iputoutput as a text file. Whe the computatio results are ready to be preseted, the users will be asked whether they wat those writte i Microsoft Excel. If so, Excel eeds to be properly istalled, ad the results will be show i a worksheet that is automatically opeed. If users do ot wat the output i Excel format, the the results will be automatically writte i a pre-amed text file. Aside from the poit-ad-click eviromet, it is hoped at a later stage the module would be able to read the data from wider variety of spreadsheet software. As a object orieted programmig laguage, Pytho has that capability. At preset, the curret module is also capable oly to receive a fairly aggregate iput-output structure, i.e., oe vector of fial demad ad primary iput, each. The ext versio of this module will have greater capability of multiple types of fial demads ad primary iputs. As the fial ote, the use of this module agrees to the followig licese ad disclaimer: This software is distributable uder the terms of the GNU Geeral Public Licese (GPL) v2, the text of which ca be foud at Istallig, importig or otherwise usig this module costitutes acceptace of the terms of this Licese. Disclaimer: This software is provided "as-is. There are o expressed or implied warraties of ay kid, icludig, but ot limited to, the warraties of merchatability ad fittess for a give applicatio. I o evet shall the writer of this code or Regioal Ecoomics Applicatio Laboratory be liable for ay direct, idirect, icidetal, special, 2

6 exemplary or cosequetial damages (icludig, but ot limited to, loss of use, data or profits, or busiess iterruptio) however caused ad o ay theory of liability, whether i cotract, strict liability or tort (icludig egligece or otherwise) arisig i ay way out of the use of this software, eve if advised of the possibility of such damage. Also, we expect users of PyIO to quote this maual (as the REAL Discussio Paper) as a referece. This maual is structured as follows. Sectio 2, followig this itroductio, outlies five thigs eeded to get started. First will explai about the istallatio of Pytho ad related extesios eeded to ru PyIO. Secodly, it will show how to set up PyIO. The third sub-sectio will discuss how iput-output data are iputted ito PyIO. The computatio of a impact aalysis will be show as a example. Fourth sectio will show a typical example of a PyIO sessio. The last sub-sectio here will discuss the balace check i iput-output data. Sectio 3 to 5 discusses the fuctioal capabilities of PyIO. The discussio is framed withi the three mai PyIO fuctios: table operatio, basic iput-output aalysis, ad advaced iput-output aalysis. 2. Gettig started 2.. About Pytho ad its istallatio Pytho is a geeral-purpose ope source computer programmig laguage, optimized for quality, productivity, portability, ad itegratio (Lutz 200: xix.) It is easy to lear, eve as the first programmig laguage. While we are aware that Pytho is frequetly updated at the momet this maual is writte, versio 2.3 (beta) is the latest i we suggest users to use Pytho versio 2.2. We were actually iformed that PyIO also works fie with the versio 2.3, but o thorough test is doe for that. The istallatio of Pytho should be doe i the three steps as the followig:. Istall Pytho versio 2.2. For Widows user, you should dowload Pytho exe ad double click this file to istall Pytho versio Istall the Widows Extesio for Pytho versio 2.2. Dowload Mark Hammod s Pytho for Widows Extesios ( which for Pytho versio 2.2 is amed wi32all-52.exe. 3. After the above two files are properly istalled i your computer, you should also istall the Numerical Pytho (Numpy), a module for umerical array computatio. Widows user should istall Numeric-23.0.wi32-py2.2.exe. Oce agai, Numpy should be istalled oly whe you have the first two files properly istalled i your computer. Havig istalled all of the three files, you are ready to use PyIO. You ca start by double clickig ru_pyio.py. 3

7 What hardware is required? Ay Petium-level computer should be able to ru Pytho ad PyIO. The limit is more o the software. The curret versio of PyIO is iteded oly for Widows user. We are really sorry that we caot accommodate Mac ad Liux users. All of the fuctios i PyIO offers a output i Microsoft Excel format. If you wat this, aturally the Microsoft Excel should be properly istalled i your computer. For those who do ot wat Excel output, PyIO will automatically write the results i a ASCII text file Settig up the PYIO Oce Pytho, the Widows extesio ad Numpy are properly istalled i your computer, you ca dowload the pyio.zip from REAL website ( There are four files i this zip file: pyio.py, ru_pyio.py, PyIOMaual.pdf, ad data.zip. The first two files are eeded for the PyIO sessio ad may be put i your workig directory, PyIOMaual.pdf is the electroic versio of this maual, ad data.zip cotais the data text files used i this maual. Users ca copy the two files pyio.py, ru_pyio.py to ay directory i their computer. You ca start your PyIO sessio by double-clickig ru_pyio.py. Three widows will pop up. The first is a blak widow with a title tk o the upper left corer. I all of PyIO applicatio, you ca always igore this widow. The secod widow is a welcomig page of PyIO, which looks like oe show i figure below. The third is a verificatio widow. I there, you will be show your curret workig directory, ad asked if you wat to chage the curret workig directory. Whe you have all of your data files (to be explaied later) i the same workig directory with the two PyIO files, the there is o eed to chage the workig directory. You may wat to chage the workig directory if the data files are located elsewhere i your computer. Figure. Scree drop to chage the workig directory If you wat to chage your workig directory, for example to c:\work, the write it o the prompt as show above. If you do ot wat to chage the workig directory, the the PyIO mai meu will appear, as show below. 4

8 Figure 2. Scree drop of the PyIO mai meu Now, users are ready to do iput-output aalysis. There are three choices for aalysis ad a exit. You ca start the aalysis by eterig the umber of your choice (o 2 i the above scree drop) ad press eter Iputtig a iput-output dataset Before goig further with aalysis, it is importat to uderstad how a dataset is iputted i PyIO. This will be explaied i this sectio. For illustratio, we will use the followig hypothetical iput-output structure. It comprises eight sectors with a aggregate fial demad ad value added. Table. A hypothetical iput-output table Sector Fial demad Total Output Value added Total iput

9 Let s say that we wat to put the above matrix ito a iput-output dataset called datafile.txt. This file is a ASCII file cotaiig the iput-output dataset with a particular sequece as follows:. First digit is the umber of regios 2. Secod digit is the umber of sectors 3. Iteridustry trasactio matrix 4. Output or iput values 5. Total fial demad values 6. Total primary iput values The first two digits serve as idetifiers of the iput-output table. These idetifiers play a importat role i ay subsequet aalysis as it determies the type of matrix ad, hece, its correspodig maipulatios. A example of a datafile.txt is show i figure 3 below. The above iput format allows oe to iput both atioal (or sigle-regio) iput-output tables as well as iterregioal iput-output (IRIO) tables. To iput a atioal or sigle regio iput-output table, eter i the first digit (look at figure 3 below). The ext set of umbers is the iteridustry trasactios. PyIO reads the umbers i by each lie to the right. Therefore, from the datafile.txt below we kow that z = 6, z 2 = 5, z 3 = 24, etc., where z is the trasactio across sectors. The values of output or iput, fial demad, ad primary iput, must be iputted i the same sectoral sequece with the oe i the trasactios matrix. Number of regio Number of sector Trasactio matrix Output or iput Primary iput Primary iput Figure 3. Structure of datafile.txt To eter a iterregioal iput-output table, put the appropriate umber of regios ad sectors as the idetifiers. The regioal-sectoral sequece is such that the sectoral idex rus faster 6

10 tha the regioal idex. If the iput-output dataset show i Figure 3 were actually from a iterregioal iput-output with two regios ad four sectors, the the first two digits would have bee 2 ad 4, respectively. Ad, the four sectors i regio are preseted as the first four rows/colums followed by the four sectors i regio 2. The first three items i the datafile.txt are required, i.e., PyIO ca read a text file that oly cotais the two idetifiers ad the trasactio matrix. The output, fial demad, ad primary iput values are basically optioal. However, differet iput-output aalysis may require oe or all of the last three items. For example, calculatig Leotief iverse matrix requires the trasactio matrix ad output values. O the other had, the extractio method requires all of the trasactio, output, fial demad ad primary iput values. As show i Table, the absece of a trasactio betwee two sectors should be iputted as a value 0. Do ot leave a blak to deote a zero value, sice the fuctio actually couts the umber of umbers iputted. For example, sice the above datafile iputs all items, it has to have 90 umbers. If the fuctio detects less tha that, a error message will appear. If the dataset does ot iclude primary iput values, the the text file should have 82 umbers, ad so o Ruig PyIO: A typical example This part will show a typical PyIO sessio. For a illustratio, we will do a impact aalysis usig the datafile.txt show above, calculatig the output impact of differet scearios of fial demad. These scearios should also be iputted to PyIO ad they should be regarded as additioal iformatio eeded to coduct the aalysis. Differet iput-output aalysis may require differet additioal iformatio, which should be structured i a ASCII file i a particular structure. Regardless of the differet structures, all of the additioal iformatio files should cotai the first two idetifiers, which must be idetical to oes i the primary iput-output text file (i our example here is datafile.txt). Whe the idetifiers i the primary iput-output file ad i the additioal iformatio file are ot idetical, a error message will pop up. Let s show how a impact aalysis is coducted i PyIO. Assume that we have three ecoomic scearios that we wat to check. These scearios are stored i a text file called sce.txt, each lie i the file represets a sceario. A more detail requiremets for this sceario file will be discussed later i sectio 3. Here, the mai purpose is to show how a sessio works. Havig uploaded the PyIO, users will see the mai meu as show i figure 2 above. The impact aalysis is listed uder the Basic I-O Aalysis, so eter umber 2 ad press eter. The, we eter the Basic I-O Aalysis meu. The impact aalysis is listed there as oe of the aalysis. So, eter umber 3 ad press eter agai. Users will be asked to iput the primary iput-output data. Write: datafile.txt ad press eter. Note that the file ame should be iputted fully, icludig its txt extesio. The, users will be asked to iput the additioal iformatio file. Thus, write: sce.txt. The widow would seem like figure 4 below. 7

11 Figure 4. Typical PyIO sessio At this poit, whe PyIO caot fid the two files datafile.txt ad sce.txt i the workig directory, PyIO will close itself automatically. Users will have to upload the sessio by doubleclickig ru_pyio.py agai. Alteratively, whe everythig works fie, users will be asked whether the computatio results should be prited i Microsoft Excel. If so, the the Microsoft Excel should be properly istalled i the computer. For this impact aalysis, the Excel output is give below (figure 5). The Excel report typically cotais the title of, ad some backgroud iformatio about, the type of iput-output (atioal or iterregioal), the umber of sectors ivolved, ad the file ames of the primary iput-output data ad the additioal iformatio, if ay. Figure 5 Typical Excel report i PyIO If Excel output is ot preferable, the computatio result will be stored i a text file. This text file will be automatically give a ame, typically i accordace to the type of aalysis, stored i the workig directory. The iformatio i this text file is typically similar to the oe preseted i Excel output. 8

12 The Pytho computatio is fast. However, writig the results to Excel may take some sigificat amout of time, especially whe the aalysis ivolves a iput-output of larger dimesios. For a illustratio, it takes about 45 secods to write elemets of a 30x30 Leotief iverse matrix (i.e., 900 cells) i Excel usig a Petium IV 2. GHz. O the other had, writig dow results to a text file (i.e., sayig o to the questio whether output should be prited i Excel), is doe also very fast. Therefore, for some aalysis, users may alteratively wat to save the results first i a text file, ad ope this text file i Excel. For some very large iput-output aalysis, this alterative sequece may save time. Whe all computatio ad writig results (either to Excel or to a text file) is doe, a Well-doe widow will appear, followed by aother widow askig whether users would like to exit the Basic I-O aalysis. If o, users will stay i the Basic I-O aalysis meu, ad aother PyIO sessio ca be started. If users choose to exit the Basic I-O aalysis, users will be checked whether they wat to exit PyIO. If so, the the PyIO will stop. Otherwise, users will be brought back to the mai meu (see figure 2), ad aother PyIO aalysis ca be executed Iput-output balace check A importat part of PyIO capabilities is the iput-output balace check, i particular whe the iput-output iputted ivolves the fial demad ad/or primary iput vectors. The balace checkig, i essece, evaluates whether the iputted output (i.e., the output data as writte i the iput-output text file) is idetical to the computed output (i.e., the output data as computed usig trasactios, fial demad ad primary iput vectors.) This balace check is carried out every time PyIO opes a iput-output text file with fial demad ad/or primary iput vectors. Whe the iputted ad computed output data are idetical, the PyIO will move o with the desigated computatio. Whe the two are ot the same, a warig widow will pop up. Users the ca choose whether to cotiue or halt the computatio. Importat ote: whe users choose to move o with the aalysis, PyIO will use the iputted (ad ot the computed) output i the computatio. I either case, i.e., cotiuig with or haltig the computatio, PyIO will write a text file cotaiig detail iformatio about the ature of ubalace data. For a illustratio of this capability, let s make two chages i the correct (balaced) iputoutput data as show by figure 3. These chages are:. The output set from sector to sector 4 is chaged to 0 (from the correct oe 0). 2. The output set from sector 2 to sector is chaged to 7.2 (from the correct oe 7). We kow exactly that this will create a ubalace iput-output data sice we do ot chage the rest of the values. Let s call this ew data data.txt, ad use this file to geerate the Leotief iverse matrix. This aalysis is listed as the first aalysis i the Basic I-O Aalysis. Havig etered umber 2- from the mai meu, users will be asked to iput the ame of iput-output text file. Eter data.txt here, ad you should have a widow similar to figure 6(i) below. Sice the iput-output data cotaied i data.txt are ot balace, the a error widow pops up, as show i figure 6(ii). 9

13 (i) (ii) Figure 6. (i) PyIO sessio for Leotief iverse; (ii) Ubalace data prompt Regardless whether users wat to stop or cotiue with computatio, a text file cotaiig the detail of the error is created ad amed after the primary iput-output data. I this example, this error iformatio is automatically amed data_err0.out. Clickig Yes i the warig widow will get PyIO to cotiue the computatio of the Leotief iverse matrix, ad users ca see the error file data_err0.out later. Clickig No will stop the computatio of the Leotief iverse matrix. Figure 7 Cotets of error iformatio file 0

14 The error report starts with the title ad the ame of iput-output text file beig examied. The ubalace criterio deserves some attetio here. PyIO ackowledges that the criterio should ot be based o the level of differeces betwee the iputted ad computed outputs, because oe iput-output table may have etries i the viciity i thousads, others may have oes i the viciity of millios. Thus, a differece i a magitude of ca mea oe thousad or oe millio, depedig o the iput-output table at had. Therefore, PyIO chooses differet criterio: the ratio of the differeces (betwee the iputted ad computed outputs) to the total output, for each sector. There is still aother problem. Some sectors may be markedly differet i magitude from others. I the real iput-output, some sectors may have output at a 7-digit magitude while others, because they are ot so coected to the rest of the ecoomy, may be oly at 3-digit magitude. I order to demote this problem, PyIO takes the average umber of (output) digits from each of the sectors, deote this as k, ad uses 0 -k as the bechmark. That is, the ratio betwee the differece (betwee the iputted ad computed outputs) ad the total output should ot be greater tha 0 -k. I the above example, all of the outputs are at 3-digit magitude. Thus, the criterio is that the differece, as the ratio to the actual output, should ot be more tha 0-3, or The actual reportig of differeces, by sector, follows. Note that the error file reports the actual differeces, ad ot the ratio. The differece is positive (egative) whe the iputted is greater (smaller) tha the computed values. A asterisk is put to the right of the differece (either colum or row), whe it actually exceeds the bechmark. I the above example, the first chage results i a differece greater tha the bechmark, while the secod chage does ot. 3. Table operatios 3.. Aggregatio of iput-output tables The aggregatio of iput-output tables is a commo procedure i iput-output aalysis. I the case of a atioal table (or oe regio table), aggregatio of iput-output tables ca be coducted betwee sectors, while i the case of iter-regioal iput-output both sectoral ad regioal aggregatios ca be cosidered. Suppose we wat to aggregate a -sector iput-output table ito a k-sector specificatio, where is greater tha k. A crucial elemet i the aggregatio procedure is the costructio of a aggregatio matrix S that is of k dimesio. For example, to aggregate sector 2 ad sector 3 i a 4-sector iput-output table, the aggregatio matrix will be: S = 0 0 () The ew trasactio matrix, total output, fial demad for the aggregated table ca be accomplished by multiplyig the aggregatio matrix S with the origial trasactios matrix. Let

15 NT ad T be the ew trasactio matrix ad old trasactio matrix respectively, NX ad X be the ew ad old total output, NF ad F be the ew ad old fial demad. NT = STS NX = SX NF = SF ' (2) Note that to aggregate sectors or regios i the iter-regioal iput-output table a similar procedure is followed to sectoral aggregatio scheme except for the differet structure of the aggregatio matrix. The table aggregatio requires a file cotaiig the aggregatio iformatio, i.e., how sectors are aggregated together. Note that each lie i this aggregatio ifo file will form a ew sector. Let s show a example whe we wat to aggregate the iput-output table show i table, from a 8-sector to a 4-sector classificatio. Suppose that we ame the aggregatio ifo file as agg_ifo.txt. Figure 8 below shows a typical aggregatio criterio ad its correspodig agg_ifo.txt. Note that the aggregatio ifo text file does ot require the usual two idetifiers about the umber of regios ad umber sectors. A valid agg_ifo.txt has several requiremets. First, each of the old sectors must oly be used oce i the ew sector structure. Secod, the agg_ifo.txt file should have o blak lies. PyIO will retur a error i either case. New sector Old sector,6 2 2,3,4 3 5,7 4 8 Figure 8. Aggregatio ad agg_ifo.txt Whe prompted by PyIO, users should iput the file ames of the primary iput-output text file ad the aggregatio iformatio file. Results ca be writte either i Microsoft Excel or text file. I Excel file, there will be two worksheets: oe amed aggregated table describes the aggregated table, the other oe amed agg_ifo shows that correspodig aggregatio iformatio betwee the ew table ad the old oe. The text file of the results cotais the same iformatio as the Excel file, with a ame of agg_ beig a prefix,.out beig the suffix of data file. PyIO automatically creates a ew iput-output text file for the ewly aggregated table. Sice the primary iput-output is amed datafile.txt, the aggregated iput-output text file is amed datafile_ew.txt. The cotets of this ew text file deped o the cotets of the primary iput-output table. If the primary file cotais output, fial demad ad primary iput, the the ew text file will also do so. 2

16 Fially, aggregatio ot oly ca be doe i terms of sectors, but also i terms of regios. Usually this procedure is applied to a iterregioal iput-output table. The aggregatio iformatio file will the pertai to the umber of regios, rather tha umber of sectors. I the regioal (or spatial) aggregatio, the compositio of sectors is itact. Aggregatig a iterregioal iput-output table i terms of sectors ad regios ca thus be doe i two steps Updatig a iput-output table Updatig techiques are widely used i iput-output aalysis to overcome the expesive cost of producig ew tables from surveys. Updatig a iput-output ca be doe usig either osurvey or partial-survey methods. At this poit, the program icludes two fuctios to update a iput-output table usig o-survey methods: oe employs the locatio quotiet, ad the other uses the regioal supply percetage. These two fuctios will be elaborated i this sectio. A partial-survey method, kow as the bi-proportioal or RAS method, is elaborated i the subsequet sectio. The regioal supply percetage ad locatio quotiet are commoly used to regioalize a atioal iput-output table. This techique is frequetly used whe the oly available iputoutput data is the atioal table supplemeted by regioal data, such as gross output or employmet by sector. R The regioal supply percetage i regio R i each sector i ( p i ) ca be computed as the followig: p R R X E = X E + M R i i i R R R i i i (3) where X, E ad M respectively deote output, export ad import. The magitude of the regioal supply percetage lies betwee 0 ad, with the higher ed correspodig to regioal selfsufficiecy i sector i. To adjust the atioal table, each row of the atioal A matrix will be RR multiplied by the appropriate percetage. I matrix otatio this is writte as A = PA, ˆ where RR A is the regioal iput coefficiet matrix, ˆP is the -elemet vector of regioal supply percetage, ad A is the atioal iput coefficiet matrix. The locatio quotiet also measures some degree of self-sufficiecy at the regioal level. Here we will use the simple locatio quotiet, which for regio R ad sector i is defied as SLQ X / Σ X / Σ X R R R i i i i = N N X i i i (4) where the superscript R ad N, respectively, deote regioal ad atioal data. The updatig criteria are give as the followig: 3

17 a N R R aij ( SLQi ) if SLQi < = aij if SLQi RR ij N R (5) The additioal iformatio required to compute the regioal supply percetage (ad also the simple locatio quotiet) should be iputted i a separate ASCII text file. This file, as usual, should cotai idetical idetifiers with the primary iput-output data file. Suppose that we wat to update the iput-output table as show datafile.txt. Let s say that datafile.txt is a atioal iput-output table, ad we wat to geerate a regioal iputoutput for regio R usig the regioal supply percetage method. Thus, the iformatio to calculate the RSP for regio R should be iputted i aother text file, let s ame it regio_r.txt. This file should cotai the values of exports, imports, ad output (exactly i that sequece) for each sector i the ecoomy. Thus, this file should cotai exactly 2+3d umbers, where d is the umber of sectors. Differetly, suppose we wat to update datafile.txt to geerate a regioal iput-output table for regio S usig the simple locatio quotiet method. The iformatio eeded is the atioal ad regioal dataset to compute the locatio quotiet. Agai, this iformatio should be iputted i aother text file, for example let s ame it regio_s.txt. I additio to the usual idetifiers, this regio_s.txt should cotai values of atioal ad regioal sectoral variables (exactly i that sequece). This file should oly cotai 2+2d umbers, where d is the umber of sectors. Note that users ca use ay kid of atioal-regioal dataset to compute the locatio quotiet. Amog those variables that are of commo iterest are output, employmet or icome. Havig iputted the appropriate file ames of the primary iput-output data ad the updatig iformatio file, users will be asked whether they wat to create a ew datafile based o the ew regioal iput coefficiet matrix. This datafile may be used for subsequet iput-output aalysis i PyIO. The ew datafile will be a text file (.txt) with the same ame as the earlier updatig ifo file plus a suffix _RSP whe the updatig uses regioal supply percetage method, ad _SLQ whe the updatig uses the simple locatio quotiet. I our example above, the ew data file for regio R will be amed regio_r_rsp.txt, ad that for regio S would be regio_s_slq.txt. This ew data file will oly cotai the usual idetifiers, trasactio matrix ad output. To use this ew datafile i PyIO aalysis that requires more data (i.e., fial demad ad primary iput), users eed to eter them maually usig a text editor. To create a ew data file usig SLQ method, users eed to iput aother text file cotaiig the regioal output. This text file is eeded, because usig SLQ, o iformatio is give about the extet of regioal output. This file, as usual, eeds to cotai the usual two idetifiers ad the sectoral regioal output. This file should cotai 2+d umbers, where d is the umber of sectors. This regioal output text file is ot eeded for the RSP method. The reaso is because the regioal output data has bee earlier iputted i the updatig iformatio text file. PyIO takes the regioal output data directly from this file. The example for this regioal output text file ca be see i file output_s.txt. As usual, the ew regioal iput coefficiet matrix ca be prited i Microsoft Excel. If users do ot wat the output i Microsoft Excel format, a output text file will be created. It will be amed 4

18 usig the datafile ame, plus a suffix _SLQUpdate.out or _RSPUpdate.out. I the output text file, oly the ewly updated A matrix is preseted RAS method A widely used partial survey method to update a iput-output table is the bi-proportioal or RAS method. This method is commoly used to update a iput-output matrix over a short period of time as well as to adjust a atioal table i order to derive a regioal matrix. A legthy expositio of this techique ca be foud i Chapter 8 of Miller ad Blair (985). The method fids a ew iput coefficiet matrix A i, for period t give the prior A matrix i period 0, ad some additioal iformatio for period t. The period t iformatio eeded are sectoral allocatio of itermediate output (U), sectoral allocatio of itermediate iput (V) ad sectoral output (X). The geeral structure of the RAS method is = [ ] (0)[ ] 2 A R R A S S (6) where A (0) is the prior matrix to be adjusted usig series of adjustmets coefficiets represeted i [ R R ] ad [ S S ]. I the actual computatio, the method ivolves a series of iteratios up to the poit where the absolute differece betwee the row (ad colum) sums of trasactio (i.e., AX ) matrix ad the values of U (ad V) are less tha This covergece criterio should be good eough for ay reasoable applicatio of RAS method. I the case that the iteratios do ot get to satisfy the covergece criteria, PyIO will stop at the 50 th iteratio, ad the A matrix obtaied at that step will be used i the reportig. I PyIO applicatio, the RAS method actually updates the iput coefficiet A matrix. I several applicatios, the user may wish to update the trasactios matrix rather the iput coefficiet. This ca be easily doe by iputtig the trasactio matrix i the iput-output data file, ad put values of as output values. The updatig iformatio vectors U, V ad X should be iputted i a separate text file. The structure of this ASCII text file follows the stadard format with two usual idetifiers i the begiig. The rest must be sequeced as follows: sectoral allocatio of itermediate output (U), sectoral allocatio of itermediate iput (V) ad sectoral output (X). Let s suppose this file is amed time_t.txt, as show below. Users will be prompted to decide whether to specify a ew datafile based o the updated regioal iput coefficiet matrix. This ew datafile may further be used for subsequet computatio of Leotief iverse, impact aalysis or other aalysis i PyIO. To use this ew datafile i PyIO aalysis that requires more data (i.e., fial demad ad primary iput), users eed to eter them maually usig a text editor. 5

19 Number of regio Number of sector U data V data X data Figure 9. Structure of time_t.txt The ew data file will be a text file (.txt) with the same ame as the earlier iput-output data file, plus a suffix _RAS. This ew data file oly cotais the usual idetifiers, trasactio ad output. To use this ew datafile i fuctios that requires more data (i.e., fial demad ad primary iput), users eed to put them maually usig a text editor. As usual, the ew regioal iput coefficiet matrix ca be prited i Microsoft Excel. Otherwise, a text file will be created. Give the file ames above, this output text file will be amed time_t_rasupdate.out. 4. Basic iput-output aalysis 4.. Leotief ad Ghoshia iverse matrices The geeratio of multipliers from iput-output models may be cosidered as oe of the most popular uses of the modelig system. Impact aalysis (illustrated i sectio 4.2) provides isights ito the way i which chages i oe sector of a ecoomy affect all other sectors; the magitude of these impacts, the stregths of the likages betwee sectors, the size ad complexity of the ecoomy all combie to produce a rage of multiplier values. I this sectio, multipliers geerated from the Leotief ad Ghoshia iverses will be preseted; i additio to their use i impact aalysis, these multipliers also appear as part of key sector aalysis itroduced i sectio 7. The Leotief iverse is practically the most widely derived matrix from a iput-output table. While the Leotief iverse is based o the iput requiremet matrix A = [ a ij ], the Ghoshia iverse is based o the output allocatio matrix A = [ a ij ]. The elemets of these matrices are computed i the followig way: 6

20 a ij z = ij X j ad a = ij z ij X i (7) where z ij is the iput from i required i the productio of j (or i Ghoshia structure is the output of i set to the productio to j), ad X is the total iput or output. I practical terms, the iput requiremet matrix is obtaied by dividig each cell i the trasactio matrix with its correspodig iput i each colum; while the output allocatio matrix is obtaied by dividig each cell i the trasactio matrix with its correspodig output i each row. The Leotief iverse matrix is the computed as ( I A ), while the Ghoshia iverse is the obtaied by ( I A ). I PyIO, the computatio of these iverses requires a iput-output text file that cotais at the miimum the trasactio ad output data. Users will also be prompted to idicate whether Microsoft Excel format is preferred. If so, a Microsoft Excel worksheet will be opeed, ad the Leotief or Ghoshia iverse matrix will be writte. If users do ot wat the Microsoft Excel format, the output will be preseted i a ASCII text format, placed i the same workig directory. For our datafile.txt the output text file of Leotief iverse will be amed datafile_leotiv.out ad that of Ghoshia iverse will be datafile_ghoshiv.out. The maximum umber of sectors (or combiatio of regio-sector) that a iput-output dataset ca have is limited by the fact that a Excel worksheet oly has 256 colums. If you are dealig with a iput-output dataset with greater umber of dimesios, do ot sed the output to Pytho whe prompted by the fuctio. Istead, sed it to a output text file, ad you ca easily ope this file i Excel spreadsheet Impact aalysis Impact aalysis is oe area where iput-output is widely used; applicatios here typically require the aalyst to prepare a estimate of the impact of a chage i oe or more sectors o the ecoomy as a whole or o idividual sectors. The aalysis computes a ew set of output if the ecoomy is give ew hypothetical values of fial demad. I particular, the usual formula is X= ( I A) F where X is output, ( I A ) is the Leotief iverse, ad F is fial demad. The impact aalysis requires the scearios to be iputted i a separate text file. This text file should cotai the two idetifiers ad fial demad sceario(s). Earlier i sectio 2.3 we have see typical scearios iputted i a file amed sce.txt. As show, PyIO is capable of hadlig multiple scearios of fial demads. Practically, there is o limitatio o the umber of scearios, for which output impact, that PyIO ca compute at oe shot. More limitatio is put by the Excel spreadsheet, because the output impact of each sceario is reported i Excel colum. Sice a Excel worksheet oly cotais 256 colums, the this is the maximum umber of sceario that sce.txt ca cotai, if users wat the output i Excel file. If output will be later stored i a output text file, this limitatio does ot apply. 7

21 As before, the code will read sce.txt file by lie to the right. Therefore, it does ot really matter if the scearios are stacked to the right, istead of lie by lie. What really matters is the fact that the sectoral sequece of each sceario must coform to oe i the datafile.txt. As before, the fial demad sceario i the iterregioal iput-output framework is easily costructed usig the two idetifiers i the begiig of this sceario text file. The regioalsectoral sequece of the scearios must also coform to the regioal-sectoral sequece i the iterregioal trasactio matrix. If oe chooses to have the output i Microsoft Excel format, the PyIO will ope a Microsoft Excel file. Two worksheets will be writte: Fial Demad Scearios ad Output Impact. The Fial Demad Scearios worksheet will rewrite the scearios give i sce.txt, ad the Output Impact worksheet will produce the correspodig output impact. Each fial demad structure ad its correspodig impact are arraged i each colum. If users choose ot to have the output i Microsoft Excel format, the a output text file is automatically created. Give that the scearios above is cotaied i sce.txt, the the output text file is writte to a file amed sce_impact.out Multiplier Aalysis Followig Miller ad Blair (985), there are four types of multipliers that are possible to calculate from a iput-output matrix: output multiplier, icome multiplier ad employmet multiplier. The output multiplier is calculated as the colum sum of the Leotief iverse. Give that B = [ b ij ] as the Leotief iverse matrix, the the output multiplier for sector j, deoted by O j, is give by = O b (8) j i= ij where is the umber of sectors. The computatio of icome multiplier requires the use of wage vector (i the primary iput table) to calculate the household iput coefficiet. This coefficiet makes up the (+) th (household) row that is used i closig the model with respect to households, idicatig household icome received per dollar s worth of sectoral output (Miller ad Blair, 985: 05.) Deotig this coefficiet with a +, i, it is defied as a+, i = z+, i / X i where z is trasactio ad X is output. Give the Leotief iverse B, the household icome multiplier is formulated as = H a b (9) j +, i ij i= The employmet multiplier would require the use of sectoral employmet to calculate the labor iput coefficiet. This coefficiet w +, i is give as w+, i = ei / X i, where e is the employmet. The employmet multiplier for sector j is the give by the followig formula 8

22 = E w b (0) j +, i ij i= Fially, the iput (or supply) multiplier is computed from the Ghoshia iverse. The actual computatio is idetical to the output multiplier, give a Leotief iverse matrix. Therefore, if B= [ ] = ( I A), the the iput (or supply) multiplier is give as b ij O j = b ij i= () As should have bee clear, the computatio of iput or output multiplier does ot require ay iformatio other tha the primary iput-output text file. However, the computatio of icome, or employmet multiplier does require additioal iformatio. Icome multiplier requires data o icome, which are typically iputted as parts of the primary iput matrix. This iformatio should be iputted i a separate text file, that cotais the usual two idetifiers ad the sectoral total icome values. I the iput-output applicatio, icome is typically geerated by the wages ad salaries. More broadly, oe may also assume that icome comprises wages, salaries, operatig surplus (profit) ad iterest paymet. I ay case, the icome data iputted i this iformatio file to compute icome multiplier should be the total icome. This file should oly cotai 2+d umbers, where d is the umber of sectors i the iput-output data. A example of this file ca be see i icome.txt. O the other had, the computatio of employmet multiplier requires additioal text file cotaiig the umber of employmet by sectors. This data is ot a part of the iput-output table, so they should be elsewhere foud. Agai, this file oly cotais 2+d umbers, where d is the umber of sectors i the iput-output data. A example of this file ca be see i employ.txt. As usual, users will be asked whether output i Microsoft Excel is preferred. The output i Microsoft Excel will also cotai the type of iput-output model beig employed (atioal or iterregioal) with its correspodig dimesios. The reportig format i Excel for each multiplier allows for a very large dimesio of iput-output. At this momet, the maximum umber of Excel rows is more tha 65,500 lies, which practically puts o limit o the iputoutput dimesio for the multiplier aalysis. If Microsoft Excel is ot preferred, a output text file will be automatically created. The ame of this output text file will be take from the ame of primary iput-output text file, plus a suffix _[type]mult.out where [type] ca be Out for Output, Ic for Icome, Emp for Employmet multiplier, ad Ip for Iput multiplier. For example, the output multiplier of the earlier datafile.txt will be writte to a text file amed as datafile_outmult.out. 9

23 5. Advaced iput-output aalysis 5.. Key-sector Aalysis Key sector aalysis is widely used i iput-output aalysis. It aims to idetify those sectors whose ecoomic activity exerts a greater tha average ifluece o the whole ecoomy. Policy makers iterested i idustrial targetig, govermet officials cosiderig icetives for ew idustry, or school officials axious to estimate the fiscal impact of the closure of a major firm or govermet istallatio are all users of key sector aalysis. I essece, the search for key sectors is based o a assumptio that some activities i a ecoomy have the potetial to geerate greater growth ad through their backward ad forward likages, spur the growth of the rest of the ecoomy. The idea has always bee cotroversial; may authors have claimed that the methods used to idetify key sectors are based o ex post relatioships ad provide o idicatio of the future prospects for these sectors. Further, the idea that all sectors are iterdepedet ad yet a subset of these are key sectors may appear to be cotradictory; the o key sectors may be the glue that holds the ecoomy together. Two other methods are closely associated with key sector aalysis the extractio method (described i sectio 2) ad cluster aalysis. The methodology for cluster aalysis will be icluded i a future volume of the software. I this sectio, key sectors are idetified by calculatig backward ad forward likage proposed by Rasmusse (956) drawig o etries i the Leotief iverse. Let B= ( I A ) = [ b ij ] be the Leotief iverse matrix ad let B j ad Bi be the colum ad row multipliers of this Leotief iverse. The sector j s backward likage ( BL ) ad forward likage ( FL ) are defied as: j i BL 2 b b B j V 2 B ij i= j j = = = ij i, j= V ad FL i = 2 b b Bi V 2 ij j= = = ij i, j= Bi V (2) where, B j = b ij i=, B i = b ij ad V j= = b ij i= j=. BL j >, a uit chage i fial demad i sector j The usual iterpretatio is to propose that, if will geerate a above-average icrease i activity i the ecoomy. Similarly, for FL i >, it is asserted that a uit chage i all sectors fial demad would create a above average icrease i sector i. Thus, a key sector is idetified as oe havig both idices greater tha. As usual users will be prompted whether results i Microsoft Excel is preferable. If so, a Microsoft Excel file with two worksheets will be opeed. The first worksheet, amed Key Sectors, shows the usorted backward ad forward likages. The secod worksheet, amed Likages idicators, presets the sorted backward ad forward likages. If output i Microsoft Excel is ot preferable, the the output will be writte i a output text file amed after the 20

24 primary iput-output text file. I our example usig the datafile.txt, the output file for the key-sector aalysis will be datafile_keysector.out Decompositio of output chages The decompositio techique aalyzes differeces i two-period sectoral output ito three differet parts. The techique is based o Sois et al. (996), where they ote that the output chage X ca be stated i the followig way: X= B f B f t t 0 0 = ( B + B)( f + f) B f = B f + Bf + B f 0 0 = X + X + X f B Bf (3) where X is output, B is the usual Leotief iverse, ad f is fial demad, subscripts 0 ad t deotes two time periods. The decompositio results i three differet compoets. The first compoet ( X f ) is the part of output chage that is due to chages i fial demad. The secod compoet ( X B ) pertais to the output chage that is due to techological progress (i.e., due to chages i the Leotief iverse matrices), ad the last part ( X Bf ) is the part due to syergistic iteractio betwee fial demad ad techological chage. Further, the decompositio ca be made to trace the output chages by determiig whether they origiated from the sector itself or from other sectors i the ecoomy. The two compoets are referred to as self-geerated ad o-self-geerated chages, respectively. For a certai sector i, self-geerated chages ca be obtaied by usig b ii, f i, ad their chages through time. If s X represets self-chage of output, s X represets o-self-chage of output, the self-chage ad o-self-chage of each part i will be: f s X = b ii f ; s X = X s X i i f f f i i i B s X = b ii f ; s X = X s X i i B B B i i i Bf s X = b ii f ; s X = X s X i i Bf Bf Bf i i i For the PyIO sessio, the two IO data files, with idetical idetifiers, should have the miimum iformatio of trasactios, output ad the fial demad. After the decompositio is preformed, the user will agai be prompted to choose whether output i Microsoft Excel format is preferred. If users do ot wat the output i Excel the the output will be automatically writte i a output text file at time-t with suffix _Decomp.out. I these reports, ie parts of the above f B Bf decompositio are reported: X, X, X are deoted as Decom_, Decom_2 ad f B Bf Decom_3; s X, s X, s X are deoted as SelfCh_, SelfCh_2, ad SelfCh_3, ad i i i 2

25 s X f, s X B, s X Bf are deoted as NoSelfCh_, NoSelfCh_2, ad NoSelfCh_3, i i i respectively MPM Aalysis The structure of ecoomies chage over time; users iterested i providig a visual appreciatio of structural chages ca easily accomplish this with use of a simple method to be preseted here. If the iterest is i comparig the structure of two ecoomies at the same poit i time, the the same methodology will be of value. The iput-output multiplier product matrix (MPM) is a visualizatio techique derived from the Leotief iverse matrix. The MPM matrix, M, is defied as (see Sois et al. 997): B B2 M = m ij = Bi B j = ( B B 2 B ) (4) V V B = ij where B [ b ] is the Leotief iverse, V is the grad sum of rows ad colums of B or = V b, i= j= ij B ii = b ij ad Bi j= are the same as those from the Leotief iverse matrix: j = b ij. Note that the colum ad row multipliers from MPM i= m = B B = B ij i j i j= V j= ad m = B B = B ij i j j i= V i= (5) Thus, the MPM structure is essetially coected with the properties of sector backward ad forward likages. The rows ad colums of matrix M ca be rearraged alog the magitude of the values of backward ad forward from the largest to the smallest to provide the hierarchy of backward (for colums) ad forward (for rows) likages. Usig the MPM matrix, it is possible to costruct ecoomic ladscapes to provide a summary view of the ecoomic structure. Oe use of the MPM is to trace the structural chage over time. Sois et al. (997) suggested to freeze the orderig of rows ad colums at oe poit i time, ad to use this orderig to compare the ecoomic ladscapes from differet time periods. The aalysis highlights the extet to which the structure has remaied stable or chaged over time. If the hierarchy is the same, the structure has ot chaged; disruptios to the hierarchy at subsequet periods provide a sese of the magitude of the chages. Detailed sector-by-sector aalysis ca thus focus o the sector(s) i which the domiatig chages have bee observed. Whe the MPM Aalysis is chose (o. 3 i the Advaced I-O Aalysis), users will be prompted to several questios. First asks the umber of years ivolved i the aalysis. Secod asks the year which is goig to be used as the bechmark year. Note that i PyIO the umberig of years starts with (ot 0). For example, if users wats to do a MPM aalysis 22

26 ivolvig two-period iput-output ad uses the first year as the bechmark, the they will aswer the first questio with 2 ad the secod questio with. Followig those two questios, user will the asked to iput the ames of iput-output text files for the MPM aalysis. See figure 0 o the left. Naturally, each period iputoutput should be iputted i a text file. I the example here, suppose that the two iputoutput text files are data.txt & data2.txt. Figure 0. Scree drop of MPM Aalysis i PyIO The results will be writte either as Excel or text file upo users prefereces. I Excel, the umber of worksheets will be (2 umber of years + ). For our example, sice the aalysis ivolves two years of iput-output, the there are 5 worksheets writte. See the scree drop below (figure ). The first two are amed as MPM- ad MPM-2 cotaiig MPM results writte i the sector order of its ow time. See that the sectors are raked, ad these raks are differet for time- ad time-2. The ext two worksheets amed MPM (ordered)- ad MPM (ordered)-2 show the MPM results i the sector order of time- (i.e., the bechmark year). The last worksheet is Datafiles listig two files correspodig to time- ad time-2. Figure. Scree drop of Excel results of MPM 23

27 If results writte i text file are preferred, there will be a warig message to tell users that the results will be saved as a text file i the workig directory. Give the above file ames, this output text file will have ame data2_mpm(2,).out. The umbers i paretheses pertai to the umber of years ad the bechmark year (i.e., aswers to the first two questios i the PyIO sessio of MPM) Extractio Method The extractio method i iput-output system was iitially suggested by Strassert (968) ad Schultz (976, 977). The method aalyzes the importace of a sector or regio by hypothetically extractig that particular sector or regio from the iput-output system what would happe to the structure of the ecoomy if the sector disappeared. The output differeces betwee the with ad without that regio or sector are the aalyzed, ad are geerally cosidered as the importace of the extracted elemet. Several measures have bee proposed i the literature to actually quatify the output differeces (e.g., Cella 984, Clemets 990, Dietzebacher et al. 993, ad Dietzebacher ad va der Lide 997). The code preseted here computes the backward likage ad forward likage of the extractio method as outlied i Dietzebacher et al. (993). The importace of a sector or regio is preseted i terms of the backward ad forward likages betwee a system with ad without the extracted elemet. Further, the backward likage is computed i terms of the Leotief iverse while the forward likage is obtaied usig the Ghoshia system. The output differece betwee the full ad the extracted system ca be estimated from the followig equatio (Dietzebacher et al. 993): R x x L L ( I A ) 0 f x x = = R R R RR RR R x x L L 0 ( I A ) f (6) where x deotes output, L is the Leotief iverse matrix, A is the iput requiremet matrix, f is the fial demad vector, superscript ad R deotes the extracted regio or sector ad the rest of the system, respectively. The above measure pertais to the backward likage of the impact. I terms of the forward likage, the differece is as follows R G G ( I B ) 0 = R RR RR G G 0 ( I B ) R ( x x ) ( v v ) (7) where v deotes the primary iput vector, G is the Ghoshia iverse, B is the output allocatio matrix, ad the rest is as previously defied. See Dietzebacher et al. (993) for further elaboratio of the extractio method. The extractio method i PyIO requires a iput-output text file with complete iformatio, i.e., cotaiig idetifiers, trasactios, output, fial demad ad primary iput. Whe the iput- 24

28 output file cotais a atioal (or oe-regio) iput-output matrix, the fuctio will do sectoral extractio: extractig oe sector at a time to compute the extractio impact of that sector. If the iput-output data is actually a iterregioal iput-output table, the fuctio will do regioal extractio: extractig oe regio at a time to compute the extractio impact of that regio. Note oce agai that the iterregioal iput-output dataset should be iputted i such a way that the sectoral idex moves faster tha the regioal idex. For this extractio method, results ca oly be see i Excel. So, users eed to say yes for output i Excel. Two Excel worksheets will be loaded: oe for backward likage ad the other for forward likage computatios. I the header of these two worksheet is writte some backgroud of the iput-output, i.e., whether it is a atioal (or, oe-regio) or iterregioal iput-output ad the umber of sector/regios i the data. The structure of output should be read i the followig way. Let us use the atioal iput-output table as is iputted by datafile.txt. See the scree drop below: Figure 2. Scree drop from extractio method Each of the colums o the above matrix provides the sectoral impact if the sector i that colum is hypothetically extracted from the iput-output system. However, the first row idicates the impact o its ow sector. This result has a direct lik to the equatio (6), where the extracted sector is placed as the first elemet i the impact matrix x x. I this sese, the sector # give i the leftmost colum should be read cautiously. The first colum gives the output impact whe sector is hypothetically extracted from the system. Thus, is the impact to sector whe that sector is hypothetically extracted. Dietzebacher et al (993) called this the feedback effect. Also, i the first colum idicates the impact to sector 2 whe sector is extracted. Likewise, the secod colum gives the sectoral impact if sector 2 is extracted from the iput-output system. The first elemet i this colum is the impact to sector 2 whe sector 2 itself is extracted from the system. The ext elemet, is the impact to sector whe sector 2 is extracted, ad the ext elemet is the impact to sector 3 whe sector 2 is extracted ad so forth. 25

29 The result for the forward likage computatios should be read i a similar maer as the backward likage computatios. The same cautios should also be used whe dealig with this aalysis whe applied to a iterregioal iput-output dataset. As metioed earlier, i the iterregioal framework, the extractio works by each regio, ot by sector. Therefore, the output impact will comprise r colums, where r is the umber of regios i the system; ad d rows, where d=r* is the umber of iput-output dimesio. The first rows of the matrix pertai to the ow-regio impact of extractig the regio from the iterregioal system Pull-push aalysis Pull-push aalysis is a flow decompositio method, based o the superpositio priciple, that examies the degree to which the structure of flows might be decomposed ito a set of subflows (Sois 980; Jackso et al. 989), each of which acts accordig to extreme tedecies. That is, a give flow matrix Y ca be rewritte as a weighted sum of some extreme tedecies matrices: Y= px = px + p X + + p X (8) i= i i 2 2 where 0 p < p2 < < p ad i= p = i I this fashio, each extreme tedecy ca be writte as a biary matrix describig the itersectoral relatioship i the hierarchy of decompositios. I the cotext of iput-output, pull aalysis ca show the backward likage patters i a ecoomy, while push aalysis reveals the patters of forward likage patters. I PyIO, the push-pull aalysis requires a iput-output data that cotais at the miimum the two idetifiers ad trasactio matrix. As usual, users will be prompted whether output i Microsoft Excel is preferable. If so, a Microsoft Excel file will be automatically opeed. For the illustratio below, we will use the datafile.txt i the push-pull aalysis. For each aalysis, they will be writte i four worksheets. Figure shows the example of these worksheets for pull aalysis (the Microsoft Excel results for push aalysis follows exactly the same structure.) The first worksheet i the Excel file is amed Flow matrix showig differet decomposed flow matrices accordig to the data set. The weight of each decomposed flow is writte uder each decomposed flow matrix together with its cumulative weights (CP). The maximum of each colum i each decomposed matrix are preseted i dash-bordered cells i the matrix, ad the miimum of the maximum (miimax) of the whole matrix is marked as cells i red. The secod worksheet is the X-tedecies matrix showig the correspodig extreme tedecy matrix for the decomposed flow matrix. Note that differet decomposed extreme tedecy matrices are marked by differet colors. The third worksheet deoted as Cumulative X is the cumulative extreme tedecy matrix, which is also colored accordig to differet decomposed levels. The fourth worksheet is weights (p), showig all the weights of the decomposed extreme tedecy matrices. 26

30 Figure 3. Scree drops from pull aalysis If users do ot prefer the Microsoft Excel results, the all of the results will be writte i a output text file. The structure of this output file will be similar to the above descriptio. 27

31 5.6. Field of ifluece The uderlyig idea of the field of ifluece is to assess the chages i the Leotief iverse matrix resultig from the chage i oe or more direct iput coefficiets i the iverse Leotieof matrix (i.e. total requiremets matrix), research o the fields of ifluece applied to Iput-Output models was iitiated by M. Sois ad G.J.D. Hewigs i the series of publicatios started from 988. At this stage of developmet, PyIO computes oly the first order field of ifluece. The first-order field of ifluece deals with a sigle chage i oe elemet of the coefficiet matrix A. For example, say that the chages take place at the elemet a ij. The first order field of ifluece F[( i, j )], of the icremetal chage e ij is a x matrix geerated by a multiplicatio of the j-th row of the matrix B with the i-th colum (Okuyama et al. 2002): b i F ( i, j) = ( bj bj) (9) b i I the PyIO, after iputtig the ame of iput-output text file, users will be asked to iput the row ad colum associated with the source of chage. Note that the umber of row ad colum, for this purpose, starts from (ot 0). Users will also be prompted whether Excel output should be writte. Otherwise a output text file will be created. If the primary iput-output is amed datafile.txt ad the field of ifluece is computed for cell (3,8), the this output text file will be amed datafile_foicell(3,8).out. Referece: Cella G (984). The Iput-Output Measuremet of Iteridustry Likages, Oxford Bulleti of Ecoomics ad Statistics 70: Clemets BJ (990). O the Decompositio ad Normalizatio of Iteridustry Likages, Ecoomics Letters 33: Dietzebache E, va der Lide JA, Steege AE (993). The Regioal Extractio Method: EC Iput-Output Comparisos, Ecoomic Systems Research 5: Dietzebacher E, va der Lide JA (997). Sectoral ad Spatial Likages i the EC Productio Structure, Joural of Regioal Sciece: Feldma SJ, McClai D, Palmer K (987). Sources of structural chage i the Uited States : a iput-output perspective, Review of Ecoomics ad Statistics 69: Jackso RW, Hewigs GJD, Sois M (990). Decompositio Approaches to the Idetificatio of Chage i Regioal Ecoomies, Ecoomic Geography: Lutz M (200). Programmig Pytho. O Reilly 28

32 Miller RE, Blair PD (985). Iput-Output Aalysis: Foudatios ad Extesios. Pretice-Hall Okuyama Y, Hewigs GJD, Sois M, Israilevich P (2002). Structural chages i the Chicago ecoomy: A field of ifluece aalysis. I: Hewigs GJD, Sois M (eds.) Trade, Network ad Hierarchies: Modelig Regioal ad Iterregioal Ecoomies, Spriger Verlag, pp, Rasmusse P (956). Studies i Iter_Sectoral Relatios. Copehage, Eiar Harks Sois M (980). Locatioal Push-Pull Aalysis of Migratio Streams, Geographical Aalysis 2: Sois M, Hewigs GJD, Guo J (997). Comparative aalysis of Chia's metropolita ecoomies: a iput-output perspective. I: Chatterji M, Kaizhog Y (eds.) Regioal Sciece i Developig Coutries. Basigstoke, Macmilla Press:47-62, (996). Sources of Structural Chage i Iput-output Systems: A Field of Ifluece Approach, Ecoomic Systems Research 8:5-32 Sois M, Hewigs GJD (2004). Evolvig Spatial Ecoomic Structures: Iput-Output Aalysis Perspectives (web-based mauscript i preparatio) Strassert G (968). Zur Bestimmug Stretegischer Sektore mit Hilfe vo Iput-Output- Modelle, Jahrbucher fur Natioalokoomie ud Statistik 82:

33 Appedix: PyIO usig fuctios PyIO ca also be used i the programmig eviromet provided by Pytho. There are several of these eviromets. Two easily accessed eviromets are the PythoWi ad IDLE. Users iterested i usig these eviromets ca fid further iformatio about these i Pytho documetatio that are provided upo its istallatio. Here we will assume that users have had sufficiet backgroud o these eviromets. This eviromet is suitable for more advaced programmers who wat to explore PyIO at a techical level. Oe of the advatages of usig the programmig eviromet is the possibility to (eedless to say) program. Oe useful applicatio is, for example, if oe has series of tasks o the iput-output aalysis. Rather tha executig the aalysis oe by oe through the ru_pyio.py, oe ca istead write aother Pytho code that automatically execute the whole tasks at oce. This makes the whole aalysis more efficiet. PyIO comprises a set of fuctios, writte i the pyio.py file. The IDLE eviromet is easily accessed by right clickig this file, ad the click Edit with IDLE. Of course, Pytho must be properly istalled for that optio to appear by right clickig. Two widows will appear, ad the active oe will show the Pytho code. Users ca ru this code by clickig Meu Ru Script or simply by pressig Ctrl-F5 simultaeously. Havig doe that, the secod widow will become active, ad users are ready to use PyIO fuctios at the prompt. We will discuss these fuctios below, after showig how the other eviromet, i.e., PythoWi, ca be called. Oce the Pytho is successfully istalled, oe ca call PythoWi ico i the Widows Start meu. Oce it is loaded (look at the scree drop below i figure A.), there are several ways to load the PyIO module: () Ru the module by clickig File-Ru commad meu as show; (2) Ru the module by pressig Ctrl-R; or (3) Click the ru ico (a perso o the ru) o the meu bar. I all of these three ways, you will eed to browse to the directory where the PyIO is located, the same directory where you should put all of your iput-output data files for aalysis. Detailed descriptios of the fuctios cotaied i PyIO are give i the subsequet sectio. A typical example of a PyIO sessio usig fuctios ca be see below. Let s replicate the example show i sectio 2.4, calculatig the output impact aalysis. The same aalysis ca be doe by iputtig the followig commad i the PythoWi (or IDLE) prompt: >>> ImpactAalysis( datafile.txt, sce.txt ) Havig etered the commad, users will be prompted if they wat the results prited i Excel. Whe all result writig is doe, users ca see that a array is retured i PythoWi widow. The array is the result of computatio. Give there are eight sectors ad three fial demad scearios i sce.txt, the ImpactAalysis fuctio returs a array of dimesio 3x8. Look at figure A.2. below. 30

34 Ru butto Figure A.. Opeig Pythowi ad uploadig (or, ruig) a module Figure A.2. Typical sessio usig PyIO fuctios 3