Input-Output Multiplier Analysis for Major Industries in the Philippines.Pdf

11th issue Convention on Statistics (NCS) EDSA Shangri-La Hotel October 4-5, 2010 INPUT-OUTPUT MULTIPLIER ANALYSIS FOR conduct INDUSTRIES IN THE PHILIPPINES by Madeline B. Dumaua For additional information, please contact Authors name Designation crosstie Address Tel. no. E-mail Madeline B. Dumaua Statistician III statistical search and Training Center Quezon metropolis +632-4260620 emailprotected gov. ph INPUT-OUTPUT MULTIPLIER ANALYSIS FOR MAJOR INDUSTRIES IN THE PHILIPPINES1 by Madeline B.Dumaua2 ABSTRACT The dissect aims to task the touch of the different major industries of the Philippines apply Input-Output Multiplier Analysis. It attempts to do this by using the 2000 Input-Output Accounts of the Philippines (I-O Accounts), the almost recently create t fitteds by the National Statistical Coordination circuit card (NSCB). As the economic importance of the 11 major industries is maturement among the policy makers and researchers, this study applied stimulant drug- turnout proficiency in determining economic outcomes to gauge the import of these industries in generating turnout, income and body of work.Key sectors atomic number 18 identified in term of multiplier factor factor factor factor factors the higher the multiplier, the stronger is the ability of the corresponding sector to create multiple partakes in the providence. The obtained multipliers showed that among major industries, the Manufacturing effort showed the highest final film-to- proceeds multiplier the turn constancy gained the highest turnout-to-output multiplier and mystical service exertion is found to have the highest income and employment multipliers. KEY WORDS Input-output, Multiplier 1. entrance Sectors of an parsimoniousness are natur altogethery interdependent.An input stimulates mathematical product in a sector coachly, but it may also stimulate production in other sectors as well, where the intensity quite a little be downgraded. The diff erence force play of an input beyond the intended sector is c eithered multiplier that describes inter kindreds among sectors of the economy. The multiplier solution provides a quantification of the direct and indirect effect on growth of the sector, possibly measured in terms of production output. disparate economic multipliers like those for output, income, and employment fag end be used to determine economic effect for an pains.The Leontieff regulate or the Input-Output model can be used to track the complex web of production linkages among industries in the country within the framework of interdependencies. This study exiting assess the bear upon of the different sectors of the economy in terms of output, income and employment. Thus, Input-Output multiplier psycho summary was performed to determine the effect of the different major industry groups. 2. Objectives of the Study The study aimed to measure the economic effects of the major industry groups using Input-Output Multiplier Analysis. Specifically, the study intended to 1. easure the multiplier effect of removes in final need on the output of individual industries and the intact economy (Final Demand-to-Output concussion Multiplier) 1 2 One of the in-house research downstairstakings of the Research and Information engineering Division (RITD) of the Statistical Research and Training Center (SRTC) of the National Economic and Development Authority (NEDA) Statistician III, Research and Information Technology Division (RITD) of the Statistical Research and Training Center (SRTC) of the National Economic and Development Authority (NEDA) 1 2. etermine the contact of kinds in for individually one industrys output on the number output (Outputto-Output have-to doe with Multiplier) 3. find out the intrusion of changes in severally industrys output on kinsfolk income (Household Income Multiplier) 4. determine the seismic disturbance changes of output in an industry on employment (Employ ment Multiplier) 3. Significance of the Study In economics, the multiplier effect refers to the idea that the initial arrive of money invested by organisation leads to an til now greater growing in national income. In other words, an initial change in aggregate beg causes a change in ggregate output of the economy that is multiple of the initial. This measures the degree to which various businesses and mobs in an economy are interrelated. This measure the impact of a precondition external change, such as new enthronisation, exportation expansion, start up of a new businesses, on thorough economic activity in a given community or country, through the re disbursal of new dollars within that economy. The multiplier has been used to justify governance spending or taxation relief that allow for stimulate aggregate demand. Many governments share spending/tax break as instruments to stimulate aggregate demand.This is normally implemented during a period of box or economic unce rtainty. The money invested by a government is believed to create more jobs, which in release will mean more spending that further fuel activities in various sectors of the economy. The idea is that the net increase in disposable income by different stakeholders throughout the economy will be greater than the original investment. As this happens, government can increase the staring(a) domestic product by an amount that is greater than an increase in the amount it spends relative to the amount it collects in taxes.Multiplier focuses on the relationship between spending and consumption. It is also referred as expenditure multiplier. The concept holds that a spending, whether initiated by the government, corporations or households, will trigger the national income. Expenditure multiplier does non differentiate between consumption and investment spending. Examples of multipliers let in I-O multipliers which are derived from I-O tables and show the impact of spending in certain indus try on various economic variable including GDP, employment, output and wages and salaries, etc. . Limitations of the Study The paper makes use of the 2000 Input-Output tables from the National Statistical Coordination Board (NSCB). It notwithstanding uses I-O multiplier analysis in estimating multipliers. While I-O multipliers can be a rich cite of information, they also have some limitations. These include I-O models treat all inputs as complements and exclude substitutes implying that increases in the demand for one input will only lead to demand increases for other inputs.The I-O model does not consider price-adjusting behavior or substitution effects. Because the model is entirely open, there is no scarcity of resources. The economy is sour to have limitless amounts of all the inputs it requires. 2 I-O models produce a snapshot of the economy at a given point in time. Structural changes in the economy over time will slim down the validity of way outs produced by I-O models. Analysis based on I-O models does not explicitly consider alternatives and tends to show only benefits of expenditures while ignoring costs.The impacts considered through the I-O model are short-term and at the margin there is no devotion of whether the economy has the capacity to incorporate the changes and whether changes in production are sustainable or cost competitive. stipulation these limitations, I-O multipliers can still provide a useful, but rough, initial indication of the economic impact of changes in spending in different industries. 5. Data and Methodology This study was primarily carried out based on the 2000 Input-Output Accounts of the Philippines (I-O Accounts), the most recently published tables by the National Statistical Coordination Board (NSCB).In vagabond to assess the economic effect of all major industries in the unit of measurement economy, the Input-Output Multiplier Analysis was used. The major industry groups used in the study include the succeedi ng(a) For the employment multiplier analysis, data for the total bod of persons employed in each industry was taken from the 2000 Census of Philippine Business and Industry (CPBI) of the National Statistics Office (NSO) while data for the Gross Value-Added (GVA) was taken from 2000 Economic Accounts of the NSCB. skirt 1. major Industry Groups Major Industry Groups Code 01 Agriculture, piscary and Forestry 02 Mining and Quarrying 03 Manufacturing 04 face 05 Electricity, gasoline and Water 06 Transportation, Storage and converse 07 Wholesale and Retail flip 08 Finance 09 accepted Estate 10 cloistered Services 11 presidency Services 5. 1 Computation of Final Demand-to-Output Multiplier The spirit by tone surgical process in generating Final Demand-to-Output multiplier analysis is expound below 1. become the column atoms of the opponent matrix for all major industries. 2. engender the column elements by the impact variable to get the specific impact on each industry. . Get the total of the column elements of the inverse matrix for all major industries. 4. Multiply the total column elements by the impact variable to get the impact on the entire economy. 3 5. 2 Output-to-Output Multiplier The step by step procedure in generating Output-to-Output multiplier analysis is described below 1. 2. 3. 4. Obtain the IO inverse matrix for all major industries. Divide each column by its diagonal element. Get the column sums of the output-to-output inverse matrix. The column sums are the output-to-output multipliers for each industry. 5. 3.Household Income Multiplier The step by step procedure in generating Household Income multiplier analysis is described below 1. Get the household income coefficients of all the major industries in the economy by dividing the compensation of employees by the total input of the corresponding industry. 2. Multiply the column elements of the inverse matrix of all major industries by all the household income coefficients. 3. Add all the products to get the household income multiplier. 5. 4 Employment Multiplier The step by step procedure in generating employment multiplier analysis is described below 1.Get employment coefficients of all industries in the economy by calculating the employment in each industry and dividing it by gross value-added (GVA). Data for the total number of persons employed in each industry was taken from the 2000 Census of Philippine Business and Industry (CPBI) of the National Statistics Office (NSO). Data for GVA was taken from 2000 Economic Accounts of the NSCB. 2. After getting the employment coefficients, get the employment multiplier. Employment multiplier is computed by multiplying employment coefficient with inverse matrix. This gives the individual effects of saying for each industry.If we sum up the multipliers, this somehow gives an effect of the construction industry in the economy. 3. In doing simulation, i. e. , government increases construction output by One (1) Bill ion, multiply the 1billion increase to each employment multiplier where the chair will provide possible additional jobs in every industry creating a corresponding effect in the whole. 4. These multipliers are additional jobs aside from the existing employment in the construction. In other words, the multiplier analysis assumes that from start to finish, these additional employments were generated already, or in place.The IO multiplier analysis cannot determine whether these additional jobs happened before, during or after the construction stages. 6. Results and Discussion 6. 1 unofficial of Multipliers Following the computation procedure presented above, the I-O multipliers were estimated for output, income and employment in the Philippine economy. An I-O model has the ability to identify the important sectors of an economy at a national (or even at a regional level). Key sectors are identified in term of multipliers the higher the multiplier, the 4 stronger is the ability of the corresponding sector to create multiple impacts in the economy.The sectoral multipliers are used in the impact analysis to estimate the impacts for policy change in all 11 sectors, see prorogue 2 for details. Among the 11 major industries, the Manufacturing Industry yields the largest finaldemand to output multiplier of 2. 15. The verbal expression Industry and the Transportation, Communication and Storage Industry constitute the second and third most important output generating industries with both(prenominal) multipliers of most 1. 93, respectively. However, output-to-output multiplier shows that the Construction Industry yields the highest multiplier of 1. 2, which means that a one-peso change in the output of the Construction Industry generates a 1. 92 pesos worth of additional output in the economy. This is followed by Transportation, Communication and Storage and the Private Services, with multipliers of 1. 85 and 1. 70, respectively. Output-to-output multipliers can be us ed to measure the impact of a change in output in a particular industry on the output of the whole economy. The Private Services Industry is the most important income generating sector with the highest income multiplier of 0. 39.The second most important sector is the Construction Industry in terms of income generation which is holding an income multiplier of 0. 36. The Agriculture, Fishery and Forestry ranks third among the income generating industries with an income multiplier of 0. 33. 5 defer 2. Summary of the Multipliers Final Demand-to-Output, Output-to-Output, Household Income, and Employment. Final OutputHousehold Total DemandOutput Income Employment Industry Description Output Multipliers Multiplier Multipliers Multipliers Agriculture, Fishery and Forestry 1. 466693 1. 321942 0. 336922 0. 000001 Mining and Quarrying 1. 702768 1. 647777 0. 235379 0. 00002 Manufacturing 2. 152964 1. 340648 0. 265802 0. 000004 Construction 1. 937681 1. 923491 0. 365889 0. 000003 Electricity, Gas and Water 1. 567449 1. 431400 0. 198316 0. 000002 Transportation, Communication and Storage 1. 937634 1. 859610 0. 256182 0. 000003 Trade 1. 658849 1. 611999 0. 265008 0. 000005 Finance 1. 654636 1. 636633 0. 244516 0. 000003 Real Estate 1. 197308 1. 194264 0. 05703 0. 000004 Private Services 1. 919238 1. 701126 0. 391793 0. 000006 Government Services 1. 533628 1. 533628 0. 080845 0. 000001 6 The number of employment generated for a given unit of expenditure/output can be estimated by employment multiplier.The result shows that the Private Services Industry has the highest employment multiplier of 610-6. The second highest important sector in generating employment is the Trade (Wholesale and Retail) Industry with a multiplier of 610-5 followed by the Manufacturing and Real Estate Industries with both employment multipliers of around 610-5. 6. 2 Final Demand-to-Output Multiplier Effect The final demand-to-output multiplier is used to measure the impact of a change in final demand on the output of individual industries and the whole economy.This tells us near the additional output generated in each industry given an impact increase in the investment in each industry (impact variable). Table 3 shows the impact of a 100 trillion peso increase the investments in the 11 major industries. Results showed that this spending has the greatest impact in the Manufacturing Industry with an additional generated output of 215 cardinal pesos. This is followed by the Construction Industry and the Transportation, Communication and Storage Industry with both an additional output of approximately 193 million pesos. 7Table 3. Final Demand-to-Output Multiplier Effect for a 100 Million Investment. Industry Output Multipliers Impact Agriculture, Fishery and Forestry 1. 466693 146,669,300 Mining and Quarrying 1. 702768 170,276,800 Manufacturing 2. 152964 215,296,400 Construction 1. 937681 193,768,100 Electricity, Gas and Water 1. 567449 156,744,900 Transportation, Communication and Storage 1. 937634 193,763,400 Trade 1. 658849 165,884,900 Finance 1. 654636 165,463,600 Real Estate 1. 197308 119,730,800 Private Services 1. 919238 191,923,800 Government Services 1. 533628 153,362,800 8Table 4 shows the inverse matrices of the 11 major industries, which is the direct and indirect effect of a one-peso change in final demand for a particular industry on the output of other industries and the economy as a whole. The sums of column elements of the inverse matrix for the 11 industries are called final demand-tooutput multipliers. The Manufacturing Industry yields the largest output multiplier of 2. 15 among the 11 major industries. Of its 2. 15 multiplier, the additional output generated in the Manufacturing itself for a peso change in the final demand for Manufacturing Industry is 1. 0 an additional output of 0. 19 in the Agriculture, Fishery and Forestry Industry and an additional generated output of 0. 13 in the Trade Industry. The Construction Sector, which con stitutes the second most important output generating industry, has a multiplier of 1. 93. This shows that a peso change in the final demand for the Construction Industry generates 1. 93 pesos worth of additional or incremental output in the economy. Moreover, of this total multiplier, a peso change in the final demand for the Construction Industry generates an additional output of 1. 00, 0. 53 and 0. 0 in the Construction, Manufacturing and in the Transportation, Communication and Storage industries, respectively. 9 Table 4. Final Demand-to-Output Impact Multipliers Code 01 02 03 04 05 06 01 1. 109499 0. 045780 0. 195436 0. 066634 0. 030540 0. 073292 02 0. 013579 1. 033373 0. 084080 0. 055157 0. 086973 0. 031180 03 0. 241695 0. 342875 1. 605913 0. 536138 0. 238312 0. 582694 04 0. 001967 0. 013762 0. 002122 1. 007377 0. 002711 0. 002136 05 0. 018788 0. 073066 0. 045204 0. 021301 1. 095046 0. 023748 06 0. 011616 0. 026676 0. 031898 0. 108802 0. 020999 1. 041957 07 0. 028925 0. 037978 0. 131903 0. 058128 0. 042323 0. 059100 08 0. 13211 0. 025827 0. 020688 0. 028335 0. 008581 0. 042086 09 0. 001723 0. 004155 0. 004100 0. 010400 0. 001524 0. 012501 10 0. 025690 0. 099276 0. 031620 0. 045409 0. 040440 0. 068940 11 Total 1. 466693 1. 702768 2. 152964 1. 937681 1. 567449 1. 937634 Source Input-Output Accounts of the Philippines 2000, NSCB. 07 0. 058268 0. 023337 0. 313948 0. 001075 0. 016836 0. 125663 1. 029063 0. 043095 0. 009477 0. 038087 1. 658849 08 0. 034172 0. 014104 0. 235991 0. 004210 0. 029420 0. 069130 0. 023819 1. 011000 0. 037840 0. 194950 1. 654636 09 0. 009747 0. 004625 0. 069402 0. 008938 0. 005641 0. 008494 0. 007558 0. 034009 1. 002549 0. 46345 1. 197308 10 0. 091426 0. 028537 0. 491699 0. 000990 0. 049594 0. 030003 0. 053011 0. 033758 0. 012004 1. 128216 1. 919238 11 0. 039646 0. 014503 0. 240350 0. 025834 0. 023496 0. 032847 0. 026221 0. 037171 0. 011392 0. 082168 1. 000000 1. 533628 10 6. 3 Output-to-Output Multiplier Effect In many instances, the impact on the economy comes from a change in output instead of a change in final demand. In this case, an output-to-output multiplier analysis is required. This gives us information that a one-peso or one-unit change in the industrys output will generate pesos worth of additional/incremental output in the economy.Table 5 shows the individual and total effects of a one-peso change in the output of a particular industry. Out of the 1. 92 multiplier for the Construction, the Construction, Manufacturing and the Transportation, Communication and Storage industries generated additional outputs of 1. 0, 0. 53, and 0. 10 respectively, for every peso change in the Construction output. 11 Table 5. Output-to-Output Impact Multipliers Code 01 02 03 04 01 1. 000000 0. 044302 0. 121698 0. 066146 02 0. 012239 1. 000000 0. 052357 0. 054753 03 0. 217842 0. 331802 1. 000000 0. 532212 04 0. 001773 0. 013318 0. 001321 1. 000000 05 0. 16934 0. 070706 0. 028148 0. 021145 06 0. 010470 0. 025814 0. 019863 0. 108005 07 0. 026070 0. 036751 0. 082136 0. 057702 08 0. 011907 0. 024993 0. 012882 0. 028128 09 0. 001553 0. 004021 0. 002553 0. 010324 10 0. 023155 0. 096070 0. 019690 0. 045076 11 Total 1. 321942 1. 647777 1. 340648 1. 923491 05 0. 027889 0. 079424 0. 217627 0. 002476 1. 000000 0. 019176 0. 038650 0. 007836 0. 001392 0. 036930 1. 431400 06 0. 070341 0. 029924 0. 559230 0. 002050 0. 022792 1. 000000 0. 056720 0. 040391 0. 011998 0. 066164 1. 859610 07 0. 056622 0. 022678 0. 305081 0. 001045 0. 016361 0. 122114 1. 000000 0. 041878 0. 09209 0. 037011 1. 611999 08 0. 033800 0. 013951 0. 233423 0. 004164 0. 029100 0. 068378 0. 023560 1. 000000 0. 037428 0. 192829 1. 636633 09 0. 009722 0. 004613 0. 069226 0. 008915 0. 005627 0. 008472 0. 007539 0. 033923 1. 000000 0. 046227 1. 194264 10 0. 081036 0. 025294 0. 435820 0. 000877 0. 043958 0. 026593 0. 046987 0. 029922 0. 010640 1. 000000 1. 701126 0 0 0 0 0 0 0 0 0 0 1 1 12 6. 4 Household Income Multiplier Effect Moreover, changes in a n industrys output can impact on household income. To quantitavely determine the impact of changes in each industrys output on household income, a household income ultiplier analysis is needed. This tells us about the additional household income in the whole economy due to a one-peso or one-unit change in final demand for each industry. Table 6 shows the individual and total effect of a one-peso change in the final demand for each major industry. Private Services Industry is found to be the most important income generating sector with the highest income multiplier of 0. 39. This means that a peso increase in final demand of private services implies an increase in household income by 0. 39. For individual effects, additional household income of 0. 29, 0. 02 and 0. 4 are generated in the Private Services itself, Manufacturing, and the Agriculture, Fishery and Forestry respectively, due to a one-peso change in the final demand for Private Services. 13 Table 6. Household Income Multipli ers. Code 01 02 03 04 01 0. 293397 0. 012106 0. 051681 0. 017621 02 0. 001810 0. 137770 0. 011210 0. 007354 03 0. 023844 0. 033825 0. 158427 0. 052891 04 0. 000478 0. 003347 0. 000516 0. 244972 05 0. 002275 0. 008849 0. 005475 0. 002580 06 0. 001532 0. 003519 0. 004207 0. 014351 07 0. 005075 0. 006664 0. 023145 0. 010200 08 0. 001846 0. 003608 0. 002890 0. 003959 09 0. 000043 0. 000104 0. 000102 0. 00259 10 0. 006621 0. 025587 0. 008150 0. 011704 11 Total 0. 336922 0. 235379 0. 265802 0. 365889 05 0. 008076 0. 011595 0. 023510 0. 000659 0. 132620 0. 002770 0. 007426 0. 001199 0. 000038 0. 010423 0. 198316 06 0. 019381 0. 004157 0. 057484 0. 000519 0. 002876 0. 137434 0. 010370 0. 005880 0. 000312 0. 017768 0. 256182 07 0. 015408 0. 003111 0. 030972 0. 000261 0. 002039 0. 016575 0. 180568 0. 006021 0. 000236 0. 009816 0. 265008 08 0. 009036 0. 001880 0. 023281 0. 001024 0. 003563 0. 009118 0. 004179 0. 141245 0. 000943 0. 050246 0. 244516 09 0. 002578 0. 000617 0. 006847 0. 002174 0. 000683 0. 001120 0. 001326 0. 04751 0. 024990 0. 011945 0. 057030 10 0. 024177 0. 003805 0. 048507 0. 000241 0. 006006 0. 003957 0. 009302 0. 004716 0. 000299 0. 290783 0. 391793 11 0. 010484 0. 001934 0. 023711 0. 006282 0. 002846 0. 004333 0. 004601 0. 005193 0. 000284 0. 021178 0. 080845 14 6. 5 Employment Multiplier Effect Changes in every industrys output can impact on employment. To quantitavely determine the impact changes of output in an industry on employment, an employment multiplier analysis is done. This shows us the additional/incremental employment in the whole economy due to a one-peso or one-unit change in each industrys output.Given a 100 Billion peso increase in the investment, the number of additional employment generated can be estimated by employment multiplier. The result shows that the Private Services Industry has the highest employment multiplier effect of 572, 637 additional employment in the whole economy due to a 100 billion change in the final demand fo r Private Services. The second highest important sector in generating employment is the Trade (Wholesale and Retail) Industry with a multiplier effect of 504, 821 followed by the Manufacturing Industry with additional employment of 430, 785. 15 Code 01 02 03 04 05 06 07 08 09 10 11 Total Table 7.Employment Multiplier Effect Due to a 100 Billion Investment. 01 02 03 04 05 06 07 35,541 1,467 6,261 2,135 978 2,348 1,867 1,108 84,309 6,860 4,500 7,096 2,544 1,904 51,498 73,057 342,175 114,236 50,778 124,156 66,894 194 1,359 209 99,452 268 211 106 1,553 6,039 3,736 1,761 90,508 1,963 1,392 1,758 4,036 4,826 16,463 3,177 157,656 19,014 10,921 14,338 49,800 21,946 15,979 22,313 388,519 2,324 4,542 3,639 4,983 1,509 7,402 7,579 589 1,420 1,401 3,554 521 4,273 3,239 9,651 37,294 11,878 17,058 15,192 25,898 14,308 115,136 227,861 430,785 286,088 186,005 348,762 504,821 08 1,095 1,151 50,283 416 2,432 10,460 8,993 177,811 12,933 73,234 338,807 9 312 377 14,788 882 466 1,285 2,853 5,981 342,644 17,410 387,000 10 2,929 2,328 104,767 98 4,099 4,540 20,014 5,937 4,103 423,823 572,637 11 1,270 1,183 51,212 2,550 1,942 4,970 9,900 6,538 3,893 30,867 114,325 16 7. Conclusion and Recommendation This paper quantified the multipliers of the 11 major industries for the Philippine economy using input-output technique. As the economic importance of the 11 major industries is growing among the policy makers and researchers, this study applied input-output technique to determine multipliers that will measure the significance of these industries in generating output, income and employment.The obtained multipliers showed that among major industries, the Manufacturing Industry showed the highest output multiplier Construction Industry yielded the highest output-to-output multiplier and Private Services Industry is found to have the highest income and employment multipliers. The results of the study will still have to be evaluated when the NSCB will release the latest I-O table. 8.Future D irections Since the study utilized a competitive type of I-O table wherein each cell element does not explicitly distinguish the domesticallyproduced from the imported, the study is bound to construct a noncompetitive or domestic type of IO table wherein the import conform to of each I-O transaction is netted out. After which, the Leontief inverse matrix will be re-estimated which will be used to calculate domestic multipliers for the major industries. This is important in order to be able to set correctly the impact of final demand on the various economic variables. 9. Appendices 9. Input-Output Analysis There are a number of methodologies developed to determine the multipliers. The most widely used approach is the input-output technique. The major intensity of the input-output analysis is that it provides detailed information on the direct and indirect effects of spending on all economic measures for different industries in the 17 local economy (Loomis and Walsh, 1997). Theref ore, in order to satisfy the same objectives, the methodology employed in this paper in based on Leontief input-output techniques where structure of an economy is analyse in terms of inter-relationships between economic sectors (e. . Miller and Blair, 1985). The inputoutput technique of a particular economy represents the work of goods and services among its different industries for a particular time period. In the framework of the input-output technique, the relationships between economic sectors can be described in a system of linear equations where total output produced by each sector is either consumed as an intermediate input by other sector, or, sometimes internally by the producing sector itself, or, by the final demand sector, or both. The presentation of the flow of goods and services could be denotative either by physical units or in money terms.To define, let there be an economy with n-producing sectors and a final demand sector. Total output of sector i will be try = Demand n Qi = ? qij + Fi j =1 (1) where Qi = gross output of industry i qij = the sales of industry i to industry j Fi = the final demand vector i = 1, , n. let ij be the technical (input) coefficient which represents the amount (value) of sector is output needed to produce one unit (one peso) of sector js output thus using the assumption of constant production coefficient, we get a aij = qij Qi or qij = aij Q jThis means that the total value of purchases of goods and services by sector j from sector i is aij Q j . Therefore, for a given target of final demand on goods and services, F, this relation defines how much each producing industry must produce in order to satisfy a particular bundle of final demand on goods and services, i. e. , Equation (1) in reduced matrix form can be written as 18 Q = AQ + F Solving the Equation (2) can be found as (2) (3) Q = I ? A F ? and I ? A is the total requirement matrix or mostly know as Leontief inverse matrix. ? In equation (3), Q is the out put vector I is an identity matrixThe usual solution of Equation (3) determines how much each industry of the economy must produce in order to satisfy a given level of final demand. It is mandatory that I ? A should be a equal to cryptograph to have a unique solution in the form of I ? A . When ? non-singular matrix meaning that the determinant of I ? A does not the Leontief inverse matrix is assumed to be I ? A? = Z, then zij s stand for the elements of the Leontief inverse matrix. Each element of the Leontief inverse matrix shows the direct and indirect requirements of output sector i per unit of final demand. . 2 Output Multiplier The final demand-to-output multiplier is used to measure the impact of a change in final demand on the output of individual industries and the whole economy. This will tell us about the additional output generated in each industry given an impact increase in the investment in each industry (impact variable). An output multiplier for sector j is define d as the total value of production in all sectors of the economy that is necessary in order to satisfy a pesos worth of final demand for sector js output.For the simple output multiplier, this total production is the direct and indirect output effect, obtained from a model in which households are exogenous. The initial output effect on the economy is defined to be simply the initial pesos worth of sector j output needed to satisfy the additional final demand. Then formally, the output multiplier is the ratio of the direct and indirect effect to the initial effect alone. 19 The output multiplier measures the sum of direct and indirect output requirements from all sectors needed to deliver one additional peso of output of i industry to final demand.It is derived by summing the zij s or the entries in the column under industry i in the Leontief inverse matrix tables. Although the output multiplier represents total requirements per unit of final output, it is not particularly useful con cept except as indicator of the degree of structural interdependence between each sector and the rest of the economy. In economic impact studies we are more usually concerned with income or employment generating effects, and these require income or employment multipliers. 9. 3 Income Multiplier Changes in an ndustrys output can impact on household income. To quantitatively determine the impact of changes in each industrys output on household income, a household income multiplier analysis is needed. This tells us about the additional household income in the whole economy due to a one-peso or one-unit change in final demand for each industry. The income multiplier is obtained by multiplying the row vector of income coefficients, say e with the zij s, which are entries in the column under industry i in the Leontief inverse matrix tables. haggling vector of income coefficients or e are referred to as salaries and wages (compensation) for each industry divided by the corresponding outpu t. This gives us the following equation for income multiplier ? ? I = eI ? A 9. 4 Employment Multiplier ? ?1 (4) Impact analyses are frequently preoccupied with employmentcreating effects of industrial expansion, because policymakers may be primarily and licitly concerned in forecasting jobs in a particular area.For this reason, it is often useful to be able to derive not only income multipliers from an I-O model, but as well as employment multipliers. 20 The following method was used to estimate employment multipliers. The employment coefficients, l , defined as employment per million pesos of outputs, was multiplied by the zij s, which are entries in the column under industry i in the Leontief inverse matrix tables, in order to obtain the multiplier. Mathematically, employment multi ? plier is expressed as followsL = l I ? A 10. References ? ?1 (5) Miller, Ronald E. and Blair, Peter D. Input-Output Analysis Foundations and Extensions. Englewoods Cliffs, N. J. Prentice Hall 1985. T hijs Ten Raa. The Economics of Input-Output Analysis. Cambridge University Press 2005. National Statistical Coordination Board. The 2000 Input-Output Accounts of the Philippines. Economics Statistics Office 2000. National Statistics Office. 2000 Census of Philippine Business and Industry. Presentation Material of Dr. Cid L. Terosa, UA&P Professor. 21