Gestão de Sistemas Energéticos 2015/2016 Energy Analysis: Input-Output Prof. Tânia Sousa taniasousa@ist.utl.pt

Input-Output Analysis: Motivation Energy is needed in all production processes Different products have different embodied energies or specific energy consumptions How can we compute these?

Input-Output Analysis: Motivation Energy is needed in all production processes Process Analysis Methodology To compute embodied energies or specific energy consumptions of different products To compute the impact of energy efficiency measures in the specific energy consumptions of a product Input-Output Methodology

Input-Output Analysis: Motivation Energy is needed in all production processes Process Analysis Methodology To compute embodied energies or specific energy consumptions of different products To compute the impact of energy efficiency measures in the specific energy consumptions of a product Input-Output Methodology To compute the embodied energies for all products/sectors in an economy simultaneously (no need to consider specific consumption of inputs equal to zero) To compute the impact of energy efficiency measures across the economy

Input-Output Analysis: Motivation Input-Output Methodology To compute energy needs for different economic scenarios because it allow us to build scenarios for the economy in a consistent way

Input-Output Analysis: Motivation Building a scenario for the economy in a consistent way is difficult because of the interdependence within the economic system

Input-Output Analysis: Motivation Building a scenario for the economy in a consistent way is difficult because of the interdependence within the economic system a change in demand of a product has direct and indirect effects that are hard to quantify Example: To increase the output of chemical industry there is a direct & indirect (electr. & refined oil products) increase in demand for coal Refinery Power Plant Chemical Industry Coal Mine

Input-Output Analysis: Motivation Portuguese Scenarios for 2050: http://www.cenariosportugal.com/

Input-Output Analysis: Basics Input-Output Technique A tool to estimate (empirically) the direct and indirect change in demand for inputs (e.g. energy) resulting from a change in demand of the final good Developed by Wassily Leontief in 1936 and applied to US national accounts in the 40’s It is based on an Input-output table which is a matrix whose entries represent: the transactions occurring during 1 year between all sectors; the transactions between sectors and final demand; factor payments and imports.

Input-Output Portugal Input-Output matrix Portugal (2008) PRODUCTS (CPA*64) R01 R02 R03 RB R10_12 Products of agriculture, hunting and related services 954,9 18,4 0,0 4275,2 Products of forestry, logging and related services 103,4 Fish and other fishing products; aquaculture products; support services to fishing 38,4 40,5 Mining and quarrying 0,5 152,7 10,6 Food products, beverages and tobacco products 1284,7 0,1 3,9 1,1 3012,0 R13_15 Textiles, wearing apparel and leather products 21,1 4,0 5,3 1,2 R16 Wood and of products of wood and cork, except furniture; articles of straw and plaiting materials 30,4 1,8 58,5 R17 Paper and paper products 8,2 1,3 2,2 304,3 R18 Printing and recording services 0,3 4,3 49,5 R19 Coke and refined petroleum products 224,8 14,3 38,6 144,3 99,4 R20 Chemicals and chemical products 225,9 10,2 0,8 31,8 106,5 R21 Basic pharmaceutical products and pharmaceutical preparations 6,3 12,1

Input-Output: Basics For the “Tire Factory” Output from sector 1 to sector 2 Output from sector 1 to final demand Total Production from sector 1 Individual Consumers Tire Factory Automobile Factory

Input-Output: Basics For the “Tire Factory” x1= z11+ z12+… + z1n+ f1 Output from sector 1 to sector 2 Output from sector 1 to final demand Total Production from sector 1 Individual Consumers Tire Factory Automobile Factory

Input-Output: Basics For the Electricity Sector: xi= zi1+ zi2+… + zii+… + zin+ fi

Input-Output: Basics For the Electricity Sector: xi= zi1+ zi2+… + zii+… + zin+ fi Output from sector i to sector 2 Output from sector i to final demand Total production from sector i Individual Consumers Electricity Sector Automobile Factory

Input-Output: Basics What is the meaning of this? For the Electricity Sector: xi= zi1+ zi2+… + zii+… + zin+ fi Output from sector i to sector 2 Output from sector i to final demand Total production from sector i Individual Consumers Electricity Sector Automobile Factory

Input-Output: Basics Electricity consumed within the electricity sector: hydraulic pumping & electric consumption at the power plants & losses in distribution For the Electricity Sector: xi= zi1+ zi2+… + zii+… + zin+ fi Output from sector i to sector 2 Output from sector i to final demand Total production from sector i Individual Consumers Electricity Sector Automobile Factory

Input-Output: Basics For all sectors: zij is sales (ouput) from sector i to (input in) sector j (in ? units) fi is final demand for sector i (in ? units) xi is total output for sector i (in ? units)

Input-Output: Basics For all sectors: zij is sales (ouput) from sector i to (input in) sector j (in money units) fi is final demand for sector i (in money units) xi is total output for sector i (in money units) The common unit in which all these inputs & outputs can be measured is money Matrix form?

Input-Output: Basics For all sectors: i is a column vector of 1´s with the correct dimension Lower case bold letters for column vectors Upper case bold letters for matrices

Input-Output: Matrix A of technical coefficients Let’s define: What is the meaning of aij? zij is sales (ouput) from sector i to (input in) sector j xj is total output for sector j

Input-Output: Matrix A of technical coefficients Let’s define: The meaning of aij: aij input from sector i (in money) required to produce one unit (in money) of the product in sector j aij are the transaction or technical coefficients

Input-Output: Matrix A of technical coefficients Rewritting the system of equations using aij:

Input-Output: Matrix A of technical coefficients Rewritting the system of equations using aij: How can it be written in a matrix form?

Input-Output: Matrix A of technical coefficients Rewritting the system of equations using aij: In a matrix form:

Input-Output: Matrix A of technical coefficients The meaning of matrix of technical coefficients A:

Input-Output: Matrix A of technical coefficients The meaning of matrix of technical coefficients A: What is the meaning of this column?

Input-Output: Matrix A of technical coefficients The meaning of matrix of technical coefficients A: Column i represents the inputs to sector i Inputs to sector 1

Input-Output: Matrix A of technical coefficients The meaning of matrix of technical coefficients A: Column i represents the inputs to sector i The sector i produces goods according to a fixed production function (recipe) Sector 1 produces X1 units (money) using a11X1 units of sector 1, a21X1 units of sector 2, … , an1X1 units of sector n Sector 1 produces 1 units (money) using a11 units of sector 1, a21 units of sector 2, … , an1 units of sector n Inputs to sector 1

Production Functions: a review Production functions specify the output x of a factory, industry, sector or economy as a function of inputs z1, z2, …: Examples: Produces x units using z1 units of sector 1, z2 units of sector 2, … , zn units of sector n Cobb-Douglas Production Function Linear Production Function

Production Functions: a review Production functions specify the output x of a factory, industry or economy as a function of inputs z1, z2, …: Examples: Which of these productions functions allow for substitution between production factors? Cobb-Douglas Production Function Linear Production Function

Production Functions: a review Production functions specify the output x of a factory, industry or economy as a function of inputs z1, z2, …: Examples: Which of these productions functions allow for substitution between production factors? Cobb-Douglas and Linear production functions Cobb-Douglas Production Function Linear Production Function

Production Functions: a review Production functions specify the output x of a factory, industry or economy as a function of inputs z1, z2, …: Examples: Which of these productions functions allow for scale economies? Cobb-Douglas Production Function Linear Production Function

Production Functions: a review Production functions specify the output x of a factory, industry or economy as a function of inputs z1, z2, …: Examples: Which of these productions functions allow for scale economies? Cobb-Douglas (if b+c >1) Cobb-Douglas Production Function Linear Production Function

Input-Output: Matrix A of technical coefficients The meaning of matrix of technical coefficients A: Production function assumed in the Input-Output Technique Sector 1 produces X11 units (money) using X1 a11 units of sector 1, X1 a21 units of sector 2, … , X1 an1 units of sector n Is there substitution between production factors? Are scale economies possible? Inputs to sector 1

Input-Output: Matrix A of technical coefficients The meaning of matrix of technical coefficients A: Production function assumed in the Input-Output Technique Sector 1 produces X11 units (money) using X1 a11 units of sector 1, X1 a21 units of sector 2, … , X1 an1 units of sector n Leontief which does 1) not allow for substitution between production factors and 2) not allow for scale economies Inputs to sector 1 Leontief Production Function

Input-Output: Matrix A of technical coefficients The meaning of matrix of technical coefficients A: Production function assumed in the Input-Output Technique Sector 1 produces X11 units (money) using X1 a11 units of sector 1, X1 a21 units of sector 2, … , X1 an1 units of sector n Leontief which does not allow for 1) substitution between production factors or 2) scale economies Matrix A is valid only for short periods (~5 years) Inputs to sector 1

Input-Output Analysis: The model Intermediate inputs: intersector and intrasector inputs Final Demand: exports & consumption from households and government & investment The input-ouput model Intermediate Inputs (square matrix) Final Demand Total output Outputs Inputs Sectors

Input-Output Analysis: The model Intermediate inputs: intersector and intrasector inputs Final Demand: exports & consumption from households and government & investment Primary inputs? The input-ouput model Intermediate Inputs (square matrix) Primary Inputs Final Demand Total output Outputs Inputs Sectors

Input-Output Analysis: The model Intermediate inputs: intersector and intrasector inputs Final Demand: exports & consumption from households and government & investment Primary inputs: payments (wages, rents, interest) for primary factors of production (labour, land, capital) & taxes & imports The input-ouput model Intermediate Inputs (square matrix) Primary Inputs Final Demand Total output Outputs Inputs Sectors

Input-Output Analysis: The model Intermediate inputs: intersector and intrasector inputs Final Demand: exports & consumption from households and government & investment Primary inputs: payments (wages, rents, interest) for primary factors of production (labour, land, capital) & taxes & imports The input-ouput model Intermediate Inputs (square matrix) Primary Inputs Total Inputs or Total Costs Final Demand Total output Outputs Inputs Sectors

Input-Output Analysis: The model The input-ouput model Intermediate Inputs (square matrix) Primary Inputs Total Inputs or Total Costs Final Demand Total output Outputs Inputs Sectors

Input-Output Analysis: The model Lines & columns are related by: The input-ouput model Intermediate Inputs (square matrix) Primary Inputs Total Inputs or Total Costs Final Demand Total output Outputs Inputs Sectors

Input-Output Analysis: Leontief inverse matrix How to relate final demand to production?

Input-Output Analysis: Leontief inverse matrix How to relate final demand to production? is useful for which types of questions?

Input-Output Analysis: Leontief inverse matrix How to relate final demand to production? is useful for which types of questions? If final demand in sector i, fi, (e.g. automobile industry) is to increase 10% next year how much output from each of the sectors would be necessary to supply this final demand?

Input-Output Analysis: Leontief inverse or total requirements matrix 2nd Indirect effects intersectorial needs to produce the following intersectorial needs 1st Indirect effects intersectorial needs to produce these cars Direct effects cars for final demand

Input-Output Analysis: Leontief inverse or total requirements matrix Leontief inverse matrix which can be obtained as: Total Output is: If accounts for the final demand in total output (e.g. cars consumed by households) – direct effects Af accounts for the intersectorial needs to produce If (e.g. steel to produce the cars) – 1st indirect effects A[Af] accounts for the intersectorial needs to produce Af (e.g. coal to produce the steel) – 2nd indirect effects

Input-Output Analysis: Leontief inverse or total requirements matrix Impacts in output from marginal increases in final demand from f to fnew:

Input-Output: Multipliers If sector 1 is paints and sector 2 is cars what is the meaning of l12? Total output is:

Input-Output: Multipliers Total production of paints Total output is: Production of paints required directly and indirectly for 1 unit of final demand of cars

Input-Output: Multipliers Total output is: lij represents the production of good i, xi, that is directly and indirectly needed for each unit of final demand of good j, fj What about lii? x1 needed for one unit of f2 xn needed for one unit of f1

Input-Output: Multipliers Total output is: lij represents the production of good i, xi, that is directly and indirectly needed for each unit of final demand of good j, fj lii > 1 represents the production of good i, xi, that is directly and indirectly needed for each unit of final demand of good i, fi x1 needed for one unit of f2 xn needed for one unit of f1

Input-Output: Multipliers Total output is: lij represents the production of good i, xi, that is directly and indirectly needed for each unit of final demand of good j, fj What is the meaning of the i column sum? x1 needed for one unit of f2 xn needed for one unit of f1

Input-Output: Multipliers Total output is: lij represents the production of good i, xi, that is directly and indirectly needed for each unit of final demand of good j, fj Multiplier of sector i: the impact that an increase in final demand fi has on total production (not on GDP) x1 needed for one unit of f1 xn needed for one unit of f1

Input-Output: Multipliers Multipliers change over time and over regions because they depend on: the economy structure, size, the way exports and sectors are linked to each other and technology “Ripple effect” - Analogous of the impact of a stone in the water, bigger in the point of entry and smaller outward.

Input-Output: Multipliers Multipliers change over time and over regions because they depend on: the economy structure, size, the way exports and sectors are linked to each other and technology Where do you expect the multiplier of the wind energy sector to be higher: in a country that imports the wind turbines or in a country that develops and produces wind turbines? “Ripple effect” - Analogous of the impact of a stone in the water, bigger in the point of entry and smaller outward.