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

11th National Convention on Statistics (NCS) EDSA Shangri-La Hotel October 4-5, 2010 INPUT-OUTPUT MULTIPLIER ANALYSIS FOR MAJOR INDUSTRIES IN THE PHILIPPINES by Madeline B. Dumaua For additional information, please contact: Author’s name Designation Affiliation Address Tel. no. E-mail Madeline B. Dumaua Statistician III Statistical Research and Training Center Quezon City +632-4260620 [email  protected] gov. ph INPUT-OUTPUT MULTIPLIER ANALYSIS FOR MAJOR INDUSTRIES IN THE PHILIPPINES1 by Madeline B. Dumaua2 ABSTRACT The study aims to assess the impact of the different major industries of the Philippines using Input-Output Multiplier Analysis. It attempts to do this by using the 2000 Input-Output Accounts of the Philippines (I-O Accounts), the most recently published tables by the National Statistical Coordination Board (NSCB). As the economic importance of the 11 major industries is growing among the policy makers and researchers, this study applied input-output technique in determining economic effects to gauge the significance of these industries in generating output, income and employment. Key sectors are identified in term of multipliers; the higher the multiplier, the stronger is the ability of the corresponding sector to create multiple impacts in the economy. The obtained multipliers showed that among major industries, the Manufacturing Industry showed the highest final demand-to-output multiplier; the Construction Industry gained the highest output-to-output multiplier; and Private Services Industry is found to have the highest income and employment multipliers. KEY WORDS: Input-output, Multiplier 1. Introduction Sectors of an economy are naturally interdependent. An input stimulates production in a sector directly, but it may also stimulate production in other sectors as well, where the intensity can be downgraded. The residual effect of an input beyond the intended sector is called multiplier that describes interrelationships among sectors of the economy. The multiplier effect provides a quantification of the direct and indirect effect on growth of the sector, possibly measured in terms of production output. Different economic multipliers like those for output, income, and employment can be used to determine economic effect for an industry. The Leontieff model 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 will assess the impact of the different sectors of the economy in terms of output, income and employment. Thus, Input-Output multiplier analysis 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 changes in final demand on the output of individual industries and the whole economy (Final Demand-to-Output Impact Multiplier) 1 2 One of the in-house research undertakings of the Research and Information Technology Division (RITD) of the Statistical Research and Training Center (SRTC) of the National Economic and Development Authority (NEDA) Statistician III, Res earch 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 impact of changes in each industry’s output on the total output (Outputto-Output Impact Multiplier) 3. find out the impact of changes in each industry’s output on household income (Household Income Multiplier) 4. determine the impact changes of output in an industry on employment (Employment Multiplier) 3. Significance of the Study In economics, the multiplier effect refers to the idea that the initial amount of money invested by government leads to an even greater increase in national income. In other words, an initial change in aggregate demand causes a change in ggregate output of the economy that is multiple of the initial. This measures the degree to which various businesses and households in an economy are interrelated. This measure the impact of a given external change, such as new inv estment, export expansion, start up of a new businesses, on total economic activity in a given community or country, through the respending of new dollars within that economy. The multiplier has been used to justify government spending or taxation relief that will stimulate aggregate demand. Many governments consider spending/tax break as instruments to stimulate aggregate demand. This is usually implemented during a period of recession or economic uncertainty. The money invested by a government is believed to create more jobs, which in turn 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 gross 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 not differentiate between consumption and investment spending. Examples of multipliers include I-O multipliers which are derived from I-O tables and show the impact of spending in certain industry 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 only uses I-O multiplier analysis in estimating multipliers. While I-O multipliers can be a rich source 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 w ill 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 assumed 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 reduce the validity of results 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 consideration of whether the economy has the capacity to incorporate the changes and whether changes in production are sustainable or cost competitive. Given 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 order to assess the economic effect of all major industries in the whole economy, the Input-Output Multiplier Analysis was used. The major industry groups used in the study include the following: For the employment multiplier analysis, 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) while data for the Gross Value-Added (GVA) was taken from 2000 Economic Accounts of the NSCB. Table 1. Major Industry Groups Major Industry Groups Code 01 Agriculture, Fishery and Forestry 02 Mining and Quarrying 03 Manufacturing 04 Construction 05 Electricity, Gas and Water 06 Transportation, Storage and Communication 07 Wholesale and Retail Trade 08 Finance 09 Real Estate 10 Private Services 11 Government Services 5. 1 Computation of Final Demand-to-Output Multiplier The step by step procedure in generating Final Demand-to-Output multiplier analysis is described below: 1. Get the column elements of the inverse matrix for all major industries. 2. Multiply 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 construction 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) Billion, multiply the 1billion increase to each employment multiplier where the result 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 Summary 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 Table 2 for details. Among the 11 major industries, the Manufacturing Industry yields the largest finaldemand to output multiplier of 2. 15. The Construction Industry and the Transportation, Communication and Storage Industry constitute the second and third most important output generating industries with both multipliers of around 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 used 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 Table 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 6Ãâ€"10-6. The second highest important sector in generating employment is the Trade (Wholesale and Retail) Industry with a multiplier of 6Ãâ€"10-5 followed by the Manufacturing and Real Estate Industries with both employment multipliers of around 6Ãâ€"10-5. 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 about 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 million 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 million 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. 7 Table 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 8 Table 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 constitutes 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 additi onal 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-u nit change in the industry’s 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 an industry’s output can impact on household income. To quantitavely determine the impact of changes in each industry’s 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 cha nge 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 Multipliers. 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. 0066 64 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 industry’s 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 industry’s 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 for 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 in put-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 Directions 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 content 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 quantify 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 strength 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). Th erefore, in order to satisfy the aforementioned objectives, the methodology employed in this paper in based on Leontief input-output techniques where structure of an economy is analyzed in terms of inter-relationships between economic sectors (e. . Miller and Blair, 1985). The inputoutput technique of a particular economy represents the flow 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 expressed 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: Supply = 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 i’s output needed to produce one unit (one peso) of sector j’s output; thus using the assumption of constant production coefficient, we get: a aij = qij Qi or qij = aij Q j This 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 known as Leontief inverse matrix. ? In equation (3), Q is the output vector; I is an identity matrix The general 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 zero 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 defined as the total value of pr oduction in all sectors of the economy that is necessary in order to satisfy a peso’s worth of final demand for sector j’s 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 peso’s 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 concept 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 ndustry’s output can impact on household income. To quantitatively determine the impact of changes in each industry’s 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 coefficient s, say e with the zij ’s, which are entries in the column under industry i in the Leontief inverse matrix tables. Row vector of income coefficients or e are referred to as salaries and wages (compensation) for each industry divided by the corresponding output. This gives us the following equation for income multiplier: ? ? I = e[I ? A] 9. 4 Employment Multiplier ? ?1 (4) Impact analyses are frequently preoccupied with employmentcreating effects of industrial expansion, because policymakers may be primarily and legitimately 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 follows: L = 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. Thijs 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