Visualization of Economic Input-Output Data - CMU
Visualization of Economic Input-Output Data Octavia Juarez Espinosa, Chris Hendrickson Ph.D., James H. Garrett Jr. Ph.D. Civil and Environmental Engineering Department, Carnegie Mellon University, Pittsburgh, PA Abstract
following four matrices: make matrix, use matrix, total requirements and direct requirements matrix. This research contributes a new way of resolving this problem by doing visualization of input-output data.The visualization was created as part of an interface for users doing disaggregation of input-output data. Disaggregation is the breaking of an industrial sector into two or more rows and columns in each matrix. In order to perform this operation, users need to manipulate the make and use tables to regenerate the total requirements data. A visual presentation of the data matrix might improve the navigation and the understanding of the input-output data. The design of the graphics and interaction techniques was based on the task analysis of users. The input-output data is explained in more detail in the following sections.
In this paper, visual techniques used to present economic input-output data are described. These techniques were created because the size of the data matrices and the screen limitations complicate data navigation. These techniques allow users to ask questions about detailed and global information. The techniques were designed based on the user tasks. The graphic techniques are combined with direct manipulation techniques to improve the ease and efficiency with which users interact with the system. The software prototype uses I992 US economic data.
1. Introduction
2. Input-Output Data
For many users, it is difficult to perform analysis of data used to support economic input-output analysis. This is particularly true for users who are not familiar with this data. Both the size of the matrices and the limitations of the screen size used to display the information complicate the users ability to navigate the data set from the complete view to detailed information. This results in users using the input-output data without analyzing the data in detail. The quality of input-output analysis could be better if a user were more familiar with the data being used. Input-output is a framework developed by Leontief in the late 1930’s [2]. The purpose of input-output analysis is to study the interdependencies between industries in one regional economy. It is also used as an underlying model in some forms of environmental life-cycle assessment (LCA) PI. Input-Output data includes sets of matrices which can not be displayed completely on the computer screen. Only matrix regions can be displayed on the screen. Current interfaces for the input-output data use only text to display the information. The user interaction with the data is minimal. For example, a user can extract a row or a column of a matrix. Input-output data consists of the
The information contained in an input-output analysis includes flows of products from producers to consumers which are stored in matrices. The goods produced are outputs (sales) and the goods consumed are inputs (purchases) [2]. Data and models are available for many regions and most countries, at levels of detail from 20 to 500 sectors. Matrices are used because the input-output model consists of a set of n equations and n unknowns. An example with two elements will be used in this section to explain the model. The set of equations has the following form: (X, = Zll +z*2 + Y,)
While elements zl, and z21 (column 1) represent the purchases made in sector 1, elements z,, and z,~ (row 1) represent the sales of sector 1 to other sectors. X, represents the total output for sector 1 and Y, represents the final demand for sector 1. The matrix that describes the sectors transactions consists of sellers represented by rows and buyers represented by the columns.
496 O-7695-0210-5/99 $10.00 0 1999 IEEE
(1)
(X2 = =21 + 222 + Y,)
The direct requirements matrix is computed based on the use matrix and the total output. The matrix coefficients are computed using equation (3).
The system of equations presented in (1) needs to be augmented with rows representing the value added, consisting of employee compensation, government services, interest payments, and land. The same system represented in (1) is augmented with extra columns representing the final demand that consists of household purchases, government purchases, private purchases, and sales abroad or exports.
au = zij/X
(3)
Where z,/ is the quantity of commodity i used by industryj, X, is the vector industry total output, and a,, is the dollar value of commodity i needed to produce a dollar of industry j. The total requirements matrix contains the direct and indirect interactions between industrial sectors and is equal to (I- A))’ .
3. The User Tasks Common tasks performed by users when using inputoutput data are described in this section. The tasks include questions about the following three levels of information: elementary level, intermediate level, and overall level. The elementary level deals with the matrix cells, the intermediate level works with information subsets such as rows and columns, and the overall level deals with the whole matrix. Figure 1: Direct and indirect suppliers to the steel industry 3.1. Looking for the interaction of two sectors Equation (2) represents the relation between the total output represented by X and the final demand represented by Y. I is the identity matrix which contains l’s in the diagonal and O’s out of the diagonal, and A is the direct coefficient matrix that represents the interaction between industrial sectors.
To find the coefficient of interaction of two economic sectors, the user looks in the total requirements, direct requirements, or use matrices. A user looks for a sector name in the rows and a sector name in the columns to obtain the coefficient in the intersection.
X = (I-A)-’ . Y
3.2. Labeling a data point
To obtain the total requirements matrix, represented by (I- A)-’ , the use matrix, the make matrix, and the direct requirements matrix are used. These matrices are described in the following paragraphs. Figure 1 shows a section of the supply chain of the steel industry. The first level in the chain consists of the direct suppliers. The matrix of direct coefficients (A ) only contains values for the first level of suppliers. The following chain levels are included in the total requirements matrix. The sectors in the levels higher than 1 are the indirect suppliers of a product. The use matrix represents the interindustry activity and describes the commodity inputs to an industrial production process. This matrix includes the value added rows and the final demand columns. The make matrix describes the commodities produced by industries. However, this matrix does not consider the interaction between industries.
In this task, a user selects a point in the matrix to obtain the coefficient value. The two sectors that interact in that cell are obtained from the row and column labels. This is the inverse task to the previous one. 3.3. Magnifying a matrix area In this task, a user wants to see in detail a region because he/she has identified an interesting pattern. To do that, a user changes the ranges and the scales used to plot the data.
3.4. Comparing two industries based on the commodities produced In the make matrix, a user wants to create a comparative chart with the commodities produced for two indus-
497
4.1. Use Matrix
tries. To create the chart, a user gets the two industries data from the matrix, sorts them, and creates the chart.
This use matrix for the US has 491 rows and 538 columns [3]. Figure 3 shows the use matrix that contains the interactions between industries. It is larger than the other matrices because it includes extra rows consisting of wages and salaries as well as profits. This matrix also includes extra columns for final demand, consisting of households, government, and others.
3.5. Comparing two sectors based on the coefficient values Users want to compare two industrial sectors in the use matrix or in the total requirements matrix. The sectors compared are selected and displayed to see the similarities and differences between them.
3.6. Looking for patterns in the matrix Users search for patterns of interaction between sectors. For example, in the total requirements matrix, the diagonal is a pattern with values larger than one.
3.7. Modifying values and recomputing the total requirements matrix Users sometimes want to change values in some cells of the use and make tables to see the effects in the direct and total requirements.
3.8. Geographic visualization of economic activity A user wants to see where the economic activity takes place. This information completes the picture captured by the input-output data.
Figure 2: Visualization framework
4. Visualization Techniques
This matrix has 498 rows and 498 columns and represents information about commodities produced in 1992 by US industries [3]. Figure 4 shows that the diagonal has the highest values. Elements in the diagonal are primary products. The elements out of the diagonal represent secondary products. Figure 3 enables the user to see that an industry produces more than one commodity. However, only one of the commodities is considered to be a primary product.
4.2. Make Matrix
The matrices are completely displayed in a window using a pixel for each cell. By screen limitations, the information is encoded with color instead of writing the text for each cell. While the matrix rendered is displayed in a window, regions of the matrix can be rendered in another window. The values in the visualized matrix are divided into five categories. A color is assigned to each cell based on its category. Figure 2 shows the total requirements matrix. The larger window contains the matrix while the window in the bottom contains detailed information. The left window defines the data to be visualized. The numbers to the right of the matrix represent the ranges of values in the matrix. Users can update the values. The detailed window, shown in Figure 2, displays an area of 7 by 7 cells with a label for the sector code.
4.3. Total Requirements Matrix The total requirements matrix is shown in Figure 2. This matrix represents the interaction between industrial sectors. The total requirements matrix represents direct and indirect interactions. Figure 2 shows patterns consisting of horizontal lines in the bottom of the matrix. These lines represent patterns of the sales of industrial sectors. The diagonal members are the highest values. Users can change the color map to see other patterns.
498
4.4. Direct Requirements Matrix The direct requirements matrix is obtained from the use and make matrices. The values are lower than the values in the total requirements matrix because the matrix values only include direct components. Patterns similar to those observed in Figure 2 are observed in the direct requirements matrix. -.
4.5. Geographic Visualization The economic data for 1992 includes geographic information [4]. An input-output estimation can be rendered in a map showing the economic impacts as can be seen Figure 5. The data is rendered at the state level and the information is presented for each industrial sector. Figure 5 maps the total value of shipments for one industrial sector.
0
Figure 3: Geographic View of the data
Finding a Point in the Matrix. A user can search for a specific point in the matrix. To search for the point, a user types the names of two industrial sectors and the system displays the point with its neighbors labeled in the detail window.
5. Interaction Operations Viewing the Coefficients for a Row or Column. A user can view the coefficients of an economic sector. Figure 6 shows a chart with the coefficients of the matrix TOW. Also a user can compare two TOWS or two columns by creating several charts. While Figure 6 shows the total requirements coefficients for steel, Figure 7 represents the direct requirements coefficients. These two charts allows to see the difference between direct and total requirements.
The software prototype to visualize and manipulate these matrices provides operations to interact with the system. There are operations to interact with matrices and maps. Users modify the visualization by using the operations to better understand the encoded information.
5.1. Matrix Operations The matrix operations allow users to ask questions at different levels of detail. These operations consist of changing the color map, labeling cells in the detail window, finding a point in the matrix, viewing the coefficients for a row or column, and reading a cell value.
Reading a Cell Value. A user is able to read the exact value of a cell displayed on the detail window. To display the names and the values attached to a particular cell, a user selects the cell rendered in the detail window. Then the information is displayed in a dialog box.
Changing the Color Map. This operation allows users to ask questions about patterns in the matrix. Some of the user choices consist of: . select a different set of colors and different ranges for every category, and . select only some of the range categories.
5.2. Map Operations Maps are generated based on the value of the industrial sector the user wants to visualize. In addition, a user can move the map and zoom in particular regions. Also a user can move the map to focus attention on a very specific area. The map operations consist of changing the industrial sector and viewing the state information.
Labeling Cells in the Detail Window. It is not practical to label every cell in the matrix view because the screen size limits the number of labels displayed. To view the labels, users select a cell to display on the detail window.
Changing the Industrial Sector. The map can be modified by changing the name of the industrial sector to be displayed.
499
Use M atrix 1992
7969.000000 2000.000000 1000.000000 20.000000 -4000.000000
Figure 4: Use Matrix
Make
M atrix 1992
n 8092.000000 n 100.000000 n 15.000000 n 3.000000 -2642.000000
Figure 5: Make Matrix
500
l
l
Edit values in the matrix. Users modify values on the make and use tables and then recompute the direct and total requirements matrices. Visualize effects after the disaggregation of industrial sectors.
ACKNOWLEDGMENTS We thank Carnegie Mellon’s Green Design Industrial Consortium for the support received for this research. We also thank the Department of Energy, Office of Energy research, EPA cooperative Agreement # CR825188-01-2 NSF/EPA Grant # BES-9873582 for the support received for this research. We thank Julia Gardner Deems for her comments.
Figure 6: Total requirements coefficients for Blast Furnaces and Steel Mills
I. References
Viewing the State Information. The state information can be displayed by clicking on the right polygon.
[‘I
6. Conclusions and Future Research v-1
The visualization techniques used in this research were created based on user tasks and data characteristics. These techniques allow naive and experienced users to navigate through the data. While naive users can learn about inputoutput data by just using the mouse and selecting areas on the screen, experienced users can perform detailed analysis.
[31 [41 [51
Figure 7: Direct requirements coefficients for Blast Furnaces and Steel Mills
The geographic view complements the input-output information and gives information about states that are directly impacted by the production of a product. In the near future, usability testing will be conducted with users to refine the techniques used to visualize the input-output data. These visualization techniques will be used as an interface for input-output data disaggregation. The main tasks to be performed with this interface consist of:
501
Hendrickson, C., S. Joshi and L.B. Lave, “Economic Input-Output Models for Environmental Life Cycle Analysis,” Environmental Science & Technology, April, 1998. Miller, R., Blair, P. “Input-Output Analysis: Foundations and Extensions,” Prentice-Hall, Inc., 1985. U.S. Department of Commerce, “1992 Benchmark I-O Six-Digit,” Bureau of Economic Analysis, 1998. U.S. Department of Commerce, “1992 Economic Census CD-ROM,” CD-EC92-1 J, 1998. Bertin, J. “Graphics and Graphic Information Processing,” Walter de Gruyter, 1981.
following four matrices: make matrix, use matrix, total requirements and direct requirements matrix. This research contributes a new way of resolving this problem by doing visualization of input-output data.The visualization was created as part of an interface for users doing disaggregation of input-output data. Disaggregation is the breaking of an industrial sector into two or more rows and columns in each matrix. In order to perform this operation, users need to manipulate the make and use tables to regenerate the total requirements data. A visual presentation of the data matrix might improve the navigation and the understanding of the input-output data. The design of the graphics and interaction techniques was based on the task analysis of users. The input-output data is explained in more detail in the following sections.
In this paper, visual techniques used to present economic input-output data are described. These techniques were created because the size of the data matrices and the screen limitations complicate data navigation. These techniques allow users to ask questions about detailed and global information. The techniques were designed based on the user tasks. The graphic techniques are combined with direct manipulation techniques to improve the ease and efficiency with which users interact with the system. The software prototype uses I992 US economic data.
1. Introduction
2. Input-Output Data
For many users, it is difficult to perform analysis of data used to support economic input-output analysis. This is particularly true for users who are not familiar with this data. Both the size of the matrices and the limitations of the screen size used to display the information complicate the users ability to navigate the data set from the complete view to detailed information. This results in users using the input-output data without analyzing the data in detail. The quality of input-output analysis could be better if a user were more familiar with the data being used. Input-output is a framework developed by Leontief in the late 1930’s [2]. The purpose of input-output analysis is to study the interdependencies between industries in one regional economy. It is also used as an underlying model in some forms of environmental life-cycle assessment (LCA) PI. Input-Output data includes sets of matrices which can not be displayed completely on the computer screen. Only matrix regions can be displayed on the screen. Current interfaces for the input-output data use only text to display the information. The user interaction with the data is minimal. For example, a user can extract a row or a column of a matrix. Input-output data consists of the
The information contained in an input-output analysis includes flows of products from producers to consumers which are stored in matrices. The goods produced are outputs (sales) and the goods consumed are inputs (purchases) [2]. Data and models are available for many regions and most countries, at levels of detail from 20 to 500 sectors. Matrices are used because the input-output model consists of a set of n equations and n unknowns. An example with two elements will be used in this section to explain the model. The set of equations has the following form: (X, = Zll +z*2 + Y,)
While elements zl, and z21 (column 1) represent the purchases made in sector 1, elements z,, and z,~ (row 1) represent the sales of sector 1 to other sectors. X, represents the total output for sector 1 and Y, represents the final demand for sector 1. The matrix that describes the sectors transactions consists of sellers represented by rows and buyers represented by the columns.
496 O-7695-0210-5/99 $10.00 0 1999 IEEE
(1)
(X2 = =21 + 222 + Y,)
The direct requirements matrix is computed based on the use matrix and the total output. The matrix coefficients are computed using equation (3).
The system of equations presented in (1) needs to be augmented with rows representing the value added, consisting of employee compensation, government services, interest payments, and land. The same system represented in (1) is augmented with extra columns representing the final demand that consists of household purchases, government purchases, private purchases, and sales abroad or exports.
au = zij/X
(3)
Where z,/ is the quantity of commodity i used by industryj, X, is the vector industry total output, and a,, is the dollar value of commodity i needed to produce a dollar of industry j. The total requirements matrix contains the direct and indirect interactions between industrial sectors and is equal to (I- A))’ .
3. The User Tasks Common tasks performed by users when using inputoutput data are described in this section. The tasks include questions about the following three levels of information: elementary level, intermediate level, and overall level. The elementary level deals with the matrix cells, the intermediate level works with information subsets such as rows and columns, and the overall level deals with the whole matrix. Figure 1: Direct and indirect suppliers to the steel industry 3.1. Looking for the interaction of two sectors Equation (2) represents the relation between the total output represented by X and the final demand represented by Y. I is the identity matrix which contains l’s in the diagonal and O’s out of the diagonal, and A is the direct coefficient matrix that represents the interaction between industrial sectors.
To find the coefficient of interaction of two economic sectors, the user looks in the total requirements, direct requirements, or use matrices. A user looks for a sector name in the rows and a sector name in the columns to obtain the coefficient in the intersection.
X = (I-A)-’ . Y
3.2. Labeling a data point
To obtain the total requirements matrix, represented by (I- A)-’ , the use matrix, the make matrix, and the direct requirements matrix are used. These matrices are described in the following paragraphs. Figure 1 shows a section of the supply chain of the steel industry. The first level in the chain consists of the direct suppliers. The matrix of direct coefficients (A ) only contains values for the first level of suppliers. The following chain levels are included in the total requirements matrix. The sectors in the levels higher than 1 are the indirect suppliers of a product. The use matrix represents the interindustry activity and describes the commodity inputs to an industrial production process. This matrix includes the value added rows and the final demand columns. The make matrix describes the commodities produced by industries. However, this matrix does not consider the interaction between industries.
In this task, a user selects a point in the matrix to obtain the coefficient value. The two sectors that interact in that cell are obtained from the row and column labels. This is the inverse task to the previous one. 3.3. Magnifying a matrix area In this task, a user wants to see in detail a region because he/she has identified an interesting pattern. To do that, a user changes the ranges and the scales used to plot the data.
3.4. Comparing two industries based on the commodities produced In the make matrix, a user wants to create a comparative chart with the commodities produced for two indus-
497
4.1. Use Matrix
tries. To create the chart, a user gets the two industries data from the matrix, sorts them, and creates the chart.
This use matrix for the US has 491 rows and 538 columns [3]. Figure 3 shows the use matrix that contains the interactions between industries. It is larger than the other matrices because it includes extra rows consisting of wages and salaries as well as profits. This matrix also includes extra columns for final demand, consisting of households, government, and others.
3.5. Comparing two sectors based on the coefficient values Users want to compare two industrial sectors in the use matrix or in the total requirements matrix. The sectors compared are selected and displayed to see the similarities and differences between them.
3.6. Looking for patterns in the matrix Users search for patterns of interaction between sectors. For example, in the total requirements matrix, the diagonal is a pattern with values larger than one.
3.7. Modifying values and recomputing the total requirements matrix Users sometimes want to change values in some cells of the use and make tables to see the effects in the direct and total requirements.
3.8. Geographic visualization of economic activity A user wants to see where the economic activity takes place. This information completes the picture captured by the input-output data.
Figure 2: Visualization framework
4. Visualization Techniques
This matrix has 498 rows and 498 columns and represents information about commodities produced in 1992 by US industries [3]. Figure 4 shows that the diagonal has the highest values. Elements in the diagonal are primary products. The elements out of the diagonal represent secondary products. Figure 3 enables the user to see that an industry produces more than one commodity. However, only one of the commodities is considered to be a primary product.
4.2. Make Matrix
The matrices are completely displayed in a window using a pixel for each cell. By screen limitations, the information is encoded with color instead of writing the text for each cell. While the matrix rendered is displayed in a window, regions of the matrix can be rendered in another window. The values in the visualized matrix are divided into five categories. A color is assigned to each cell based on its category. Figure 2 shows the total requirements matrix. The larger window contains the matrix while the window in the bottom contains detailed information. The left window defines the data to be visualized. The numbers to the right of the matrix represent the ranges of values in the matrix. Users can update the values. The detailed window, shown in Figure 2, displays an area of 7 by 7 cells with a label for the sector code.
4.3. Total Requirements Matrix The total requirements matrix is shown in Figure 2. This matrix represents the interaction between industrial sectors. The total requirements matrix represents direct and indirect interactions. Figure 2 shows patterns consisting of horizontal lines in the bottom of the matrix. These lines represent patterns of the sales of industrial sectors. The diagonal members are the highest values. Users can change the color map to see other patterns.
498
4.4. Direct Requirements Matrix The direct requirements matrix is obtained from the use and make matrices. The values are lower than the values in the total requirements matrix because the matrix values only include direct components. Patterns similar to those observed in Figure 2 are observed in the direct requirements matrix. -.
4.5. Geographic Visualization The economic data for 1992 includes geographic information [4]. An input-output estimation can be rendered in a map showing the economic impacts as can be seen Figure 5. The data is rendered at the state level and the information is presented for each industrial sector. Figure 5 maps the total value of shipments for one industrial sector.
0
Figure 3: Geographic View of the data
Finding a Point in the Matrix. A user can search for a specific point in the matrix. To search for the point, a user types the names of two industrial sectors and the system displays the point with its neighbors labeled in the detail window.
5. Interaction Operations Viewing the Coefficients for a Row or Column. A user can view the coefficients of an economic sector. Figure 6 shows a chart with the coefficients of the matrix TOW. Also a user can compare two TOWS or two columns by creating several charts. While Figure 6 shows the total requirements coefficients for steel, Figure 7 represents the direct requirements coefficients. These two charts allows to see the difference between direct and total requirements.
The software prototype to visualize and manipulate these matrices provides operations to interact with the system. There are operations to interact with matrices and maps. Users modify the visualization by using the operations to better understand the encoded information.
5.1. Matrix Operations The matrix operations allow users to ask questions at different levels of detail. These operations consist of changing the color map, labeling cells in the detail window, finding a point in the matrix, viewing the coefficients for a row or column, and reading a cell value.
Reading a Cell Value. A user is able to read the exact value of a cell displayed on the detail window. To display the names and the values attached to a particular cell, a user selects the cell rendered in the detail window. Then the information is displayed in a dialog box.
Changing the Color Map. This operation allows users to ask questions about patterns in the matrix. Some of the user choices consist of: . select a different set of colors and different ranges for every category, and . select only some of the range categories.
5.2. Map Operations Maps are generated based on the value of the industrial sector the user wants to visualize. In addition, a user can move the map and zoom in particular regions. Also a user can move the map to focus attention on a very specific area. The map operations consist of changing the industrial sector and viewing the state information.
Labeling Cells in the Detail Window. It is not practical to label every cell in the matrix view because the screen size limits the number of labels displayed. To view the labels, users select a cell to display on the detail window.
Changing the Industrial Sector. The map can be modified by changing the name of the industrial sector to be displayed.
499
Use M atrix 1992
7969.000000 2000.000000 1000.000000 20.000000 -4000.000000
Figure 4: Use Matrix
Make
M atrix 1992
n 8092.000000 n 100.000000 n 15.000000 n 3.000000 -2642.000000
Figure 5: Make Matrix
500
l
l
Edit values in the matrix. Users modify values on the make and use tables and then recompute the direct and total requirements matrices. Visualize effects after the disaggregation of industrial sectors.
ACKNOWLEDGMENTS We thank Carnegie Mellon’s Green Design Industrial Consortium for the support received for this research. We also thank the Department of Energy, Office of Energy research, EPA cooperative Agreement # CR825188-01-2 NSF/EPA Grant # BES-9873582 for the support received for this research. We thank Julia Gardner Deems for her comments.
Figure 6: Total requirements coefficients for Blast Furnaces and Steel Mills
I. References
Viewing the State Information. The state information can be displayed by clicking on the right polygon.
[‘I
6. Conclusions and Future Research v-1
The visualization techniques used in this research were created based on user tasks and data characteristics. These techniques allow naive and experienced users to navigate through the data. While naive users can learn about inputoutput data by just using the mouse and selecting areas on the screen, experienced users can perform detailed analysis.
[31 [41 [51
Figure 7: Direct requirements coefficients for Blast Furnaces and Steel Mills
The geographic view complements the input-output information and gives information about states that are directly impacted by the production of a product. In the near future, usability testing will be conducted with users to refine the techniques used to visualize the input-output data. These visualization techniques will be used as an interface for input-output data disaggregation. The main tasks to be performed with this interface consist of:
501
Hendrickson, C., S. Joshi and L.B. Lave, “Economic Input-Output Models for Environmental Life Cycle Analysis,” Environmental Science & Technology, April, 1998. Miller, R., Blair, P. “Input-Output Analysis: Foundations and Extensions,” Prentice-Hall, Inc., 1985. U.S. Department of Commerce, “1992 Benchmark I-O Six-Digit,” Bureau of Economic Analysis, 1998. U.S. Department of Commerce, “1992 Economic Census CD-ROM,” CD-EC92-1 J, 1998. Bertin, J. “Graphics and Graphic Information Processing,” Walter de Gruyter, 1981.
