Applied Multiplier and Structural Path Analysis

APPLIED MULTIPLIER AND STRUCTURAL PATH ANALYSIS

Andres F. Garcia DERG, University of Copenhagen

CIEM – DANIDA Project

July 2009 Contents

Introduction...... 3 Background...... 4 Economic Linkages, Multipliers, and Structural Path Analysis...... 6 Exercise 1: Calculating Round-by-Round Multiplier Effects...... 10 Exercise 2. Multiplier Decomposition in Stata...... 12 Exercise 3. Structural Path Analysis in Stata...... 16 Exercise 4. Structural Path Analysis Figures with NodeXL...... 19 Appendix 1. Theoretical Background...... 24 Appendix 2. Abbreviation List...... 30 Appendix 3. Main Stata Code for Multiplier Decomposition and Structural Path Analysis....31 References...... 34

2 Introduction

Using the 2003 Social Account Matrix (SAM) for Vietnam, this guide applied multiplier and structural path analysis. Multiplier analysis, under certain assumptions, measures the impact of changes in government spending, export demand, and investment demand on output, GDP, and income. Structural path analysis divides the multiplier effect into all of its components, showing how income moves across sectors, factors, and households. After completing this guide, you will be able to understand what a multiplier represents, calculate multipliers, and do a structural path analysis to show how income flows in the economy.

This guide is divided as follows. Before proceeding with the main topics of this guide, the concept and importance of a SAM will be explained in the background section. The second section introduces the concepts of economic linkages, multiplier effects, and structural path analysis. The next four sections are hands on exercises. The third section is an exercise in Excel, in which you will evaluate how economic linkages lead to multiplier effects. The fourth section is an exercise in Stata, in which a multiplier analysis is developed for a more detailed SAM. In the fifth and sixth sections, you will use Stata to calculate a structural path analysis and together with Excel, you will chart the paths of one of the multipliers calculated in the fourth section. Lastly, a theoretical background is provided in one of the appendixes, including all the formulas used in Stata to calculate multipliers and structural paths.

3 Background1

One way of depicting the economy is the circular flow diagram shown in Figure 1, which captures all transfers and real transactions between sectors and institutions. Production activities purchase land, labor and capital inputs from the factor markets, and intermediate inputs from commodity markets, and use these to produce goods and services. These are supplemented by imports (M) and then sold through commodity markets to households (C), the government (G), investors (I) and foreigners (E). In the circular flow diagram, each institution’s expenditure becomes another institution’s income. For example, household and government purchases of commodities provide the incomes producers need to continue the production process. Additional inter-institutional transfers, such as taxes and savings, ensure that the circular flow of incomes is closed. In other words, all income and expenditure flows are accounted for and there are no leakages from the system.

A Social Account Matrix (SAM) is also a representation of the economy. More specifically, it is an accounting framework that attaches actual numbers to the incomes and expenditures in the circular flow diagram. A SAM is laid out as a square matrix in which each row and column is called an ‘account’. Each of the boxes in the diagram is an account in the SAM. Each cell in the matrix represents, by convention, a flow of funds from a column account to a row account. For example, the circular flow diagram shows private consumption spending as a flow of funds from households to commodity markets. In the SAM it is entered in the household column and commodity row. The underlying principle of double-entry accounting requires that, for each account in the SAM, total revenue equals total expenditure. This means that an account’s row and column totals must be equal.

1 From Breisinger, Thomas and Thurlow (2009) 4 5 Figure 1: Circular Flow Diagram of the Economy

Factor earnings (value-added) Factor Domestic private savings markets

Indirect taxes Direct taxes Fiscal surplus

Productive Households Government Investment activities Intermediate demand Social transfers

Commodity Sales income markets Consumption Recurrent spending Investment spending (C) (G) demand (I) Exports (E) Imports (M)

Rest of world Remittances Foreign grants and Capital inflows loans

Source: Breisinger, Thomas and Thurlow (2009)

6 Economic Linkages, Multipliers, and Structural Path Analysis2

When we talk of ‘exogenous demand-side shocks’ to an economy we are referring to changes in export demand, government spending, or investment demand. The impacts of these shocks have both direct and indirect effects. Direct effects are those pertaining to the sector that is directly affected by the shock. So for example, an exogenous increase in demand for Vietnamese agricultural exports has a direct impact on the agricultural sector. However, it may also have indirect effects, which are the “knock-on” effects stemming from agriculture’s linkages to other sectors and parts of the economy. These indirect linkages can, in turn, be separated into production and consumption linkages. When we add up all direct and indirect linkages we arrive at a measure of the shock’s multiplier effect. In other words, by how much a direct effect is amplified or multiplied by indirect linkage effects.

Figure 2: Direct and Indirect Linkages

Direct effect Exogenous Consumption shock linkages Indirect Backward effects linkages Production linkages Forward linkages

Production linkages are determined by sectors’ production technologies, which are contained in the input-output part of SAM. They are differentiated into backward and forward linkages.

 Backward production linkages are the demand for additional inputs used by producers in order to supply additional goods or services. For example, when agricultural production expands it demands intermediate goods, like fertilizers, machinery and transport services. This demand then stimulates production in other sectors in order to supply these intermediate goods. The more input-intensive a sector’s production technology is, the stronger its backward linkages are.  Forward production linkages account for the increased supply of inputs to upstream industries. For example, when agricultural production expands it can supply more

2 Adapted from Breisinger, Thomas and Thurlow (2009) 7 goods to the food processing sector, which stimulates processed food production. So the more important a sector is for upstream industries, the stronger its forward linkages will be.

Stronger forward and backward production linkages lead to larger multipliers. Traditional input-output multipliers measure the effects of production linkages only. They do not consider consumption linkages, which arise when an expansion of production generates additional incomes for factors and households, which are then used to purchase goods and services. For example, when agricultural production expands it raises farmers’ incomes, which are used to buy consumer goods. Depending on the share of tradable and non- tradable goods in households’ consumption basket, domestic producers benefit from greater demand for their products. The size of consumption linkages depends on various factors, including the share of factor income distributed to households; the composition of the consumption basket; and the share of domestically-supplied goods in consumer demand. Evidence from developing countries suggest that consumption linkage effects are much larger than production linkage effects (i.e., they account for 75-90% of total multiplier effects in Sub-Saharan Africa and 50-60% in Asia) (Haggblade, Hammer and Hazell, 1991). SAM/accounting multipliers therefore tend to be larger than input-output multipliers, because they capture both production and consumption/income linkages.

Multiplier effects

Economic linkages are fairly static and are determined by the structural characteristics of an economy (i.e., sectors’ production technologies and the composition of households’ consumption baskets). Multiplier effects, on the other hand, capture the combined effects of economic linkages over a period of time. For example, as mentioned before, forward production linkages tell us that increasing agricultural production will stimulate production of processed foods by increasing the supply of inputs to this sector. This is the first round linkage effect between agriculture and food processing. However, in the second round, the increase in processed food production will have additional forward production linkage effects to other sectors, such as to the restaurant sector, which uses processed foods as an intermediate input. Similarly, in the third round, the expansion of the restaurant sector will generate more even demand for other sectors. This process continues over many rounds, as the effects of increasing agricultural production ripple throughout the economy, and eventually become small enough that they effectively cease.

SAM multipliers measure the value of all production and consumption linkage effects. They capture direct and indirect effects in the first and all subsequent rounds of the circular income flow. More specifically, multipliers translate initial changes in exogenous demand (e.g., increased agricultural export demand) into total production and income changes of endogenous accounts. Figure 3 illustrates this process.

8 Figure 3: Circular Flow of Income in the Multiplier Process

Increase in agricultural exports

Direct effect Indirect effects

A Increase in agricultural production

Production linkages

A B Tax leakage Increase in Increase in factor nonagricultural Government production incomes and employment

C Consumption Increase in Import leakage linkages household Rest of world incomes and consumption

Three types of multipliers can be distinguished from the figure. First, an output multiplier combines all direct and indirect (consumption and production) effects across multiple rounds, and reports the final increase in gross output of all production activities. In Figure 3 this is the combined increase in agricultural and nonagricultural production (i.e., the two boxes marked “A”). Secondly, a GDP multiplier measures the total change value-added or factor incomes caused by direct and indirect effects (i.e., the box marked “B”). Finally, the income multiplier measures the total change in household incomes (i.e., the box marked “C”).

The size of a multiplier depends on the structural characteristics of an economy. For example, a key determinant is the share of imported goods and services in households’ consumption demand. If households consume domestically-produced goods, then increasing household incomes will benefit domestic producers, and the circular flow of

9 income will lead to further rounds of indirect linkage effects. However, if households demand imported goods, then it is foreign producers that benefit and the indirect linkage effects will be smaller. Import demand is therefore a leakage from the circular flow of income. Similarly, when the government taxes factor incomes it limits how much of the returns to production are earned to households, and so reduces consumption linkages. Ultimately, these kinds of leakages make the round-by-round effects slow down more quickly and reduce the total multiplier effect.

These multipliers are calculated under a number of limiting assumptions. They assume that prices are fixed and that any changes in demand will lead to changes in physical output rather than prices. This in turn requires an additional assumption that the economy’s factor resources are unlimited or unconstrained, so that any increase in demand can be matched by an increase in supply. Finally, the multiplier model assumes that all structural relationships between sectors and households in the economy are unaffected by exogenous changes in demand. In other words, the input coefficients of producers and the consumption patterns of households remain unchanged (i.e., linkage effects are linear and there is no behavioral change).

After the SAM/accounting multipliers have been calculated, structural path analysis (SPA) indentifies the movement of income between origin and destination accounts. For example, we can find that 90% of the multiplier on rural household income from an external injection into the agricultural sector comes, not surprisingly, from a relatively direct path from agriculture to low skilled labor to rural households. The circular income flow presented in Figure 3 also determines the direction of paths in SPA. It is a means of identifying the paths through which structural relationships in an economy lead to ultimate effects on the economy. SPA is designed to provide a more detailed picture of the effects of shocks to exogenous accounts. SAM-multipliers measure the cumulative effects from a shock, while the path analysis decomposes these multipliers into direct and indirect components. The SPA decomposition is, in this context, useful in coming to grips with the nature and strength of linkages that work through the economic sector. Multiplier analysis, multiplier decompositions, and structural path analysis are attractive methodologies that can provide insights into a range of policy questions around government’s employment targets, stimulus policy, issues related to industrial policy and many other policy questions.

10 Exercise 1: Calculating Round-by-Round Multiplier Effects3

Please copy the provided folder called “MSPA_Training” to your C:\ drive. The path of the materials for this training should then be “C:\MSPA_Training\”.

In this exercise you are asked to calculate backward production linkage effects during each round of the circular flow of income. In this task you will use an aggregated 2-sector version of the Vietnam SAM so as to calculate input coefficients for the agricultural and nonagricultural sectors. Using these technical coefficients, you will then determine how downstream sectors benefit when agricultural production increases as a result of its use of intermediate inputs.

The Vietnam SAM and the flow chart (where you can complete this task) can be found in the file called “Exercises.xlsx”. Once you have completed the task you can check your answer by looking at the file called “Solutions.xlsx”.

Hints and tips

1. You are only asked to calculate backward production linkage effects. In this exercise we ignore forward production and consumption linkages. We’ll come back to these in later exercises. 2. Calculate input coefficients. It is good practice to link your calculations to the SAM entries, since this allows you to trace back the data used in your calculations. 3. The first round effect can be calculated by multiplying the direct increase in agricultural production (i.e., 10) by the respective input coefficients for each of the two sectors to derive the additional increase in production in the second round. 4. Then to calculate second round effects, repeat the process in Hint 2, but this time start with the production increase from the end of round 1. 5. The numbers in blue are the correct answers for the neighboring cell entry.

Discussion

This exercise demonstrates how sectors’ production technologies (i.e., input coefficients) determine the size of multiplier effects. For example, increasing agricultural production has a larger linkage effect on agricultural production, because the input coefficient on agricultural inputs (0.37) is much larger than the non-agricultural input coefficient (0.21). So at the end of the first round, the direct increase in agricultural production by 10 billion VND

3 Adapted from Breisinger, Thomas and Thurlow (2009) 11 leads to an indirect 3.73 billion VND increase in agricultural production, and a 2.06 billion VND increase in the non-agricultural production. This exercise also shows how indirect effects become smaller from round to round. For example, the direct impact of increased agricultural export demand was a 10 billion VND increase in agricultural production. In the first round there was a total increase in agricultural and nonagricultural production of 5.79 billion VND (3.73 for agriculture and 2.06 for non-agriculture). Similarly, in the second round the total increase was 3.46 billion VND, and in the third round it was 2.11 billion VND. If we were to continue calculating these linkage effects into subsequent rounds we would see their values declining until they are virtually zero. At this point we can say that the multiplier process resulting from the increase in agricultural export demand has effectively ceased.

The importance of technical coefficients and the fact that linkages diminish after each round are important features of the multiplier process. They still apply even when forward production and consumption linkages are included in the calculation of multiplier effects. This exercise has therefore explained the core concepts of the multiplier process and lays the foundation for calculating multipliers using matrix algebra, which is the objective of the next exercise.

12 Exercise 2. Multiplier Analysis in Stata4

In the previous exercise we saw how labor-intensive it is to calculate round-by-round multiplier effects. Moreover, we excluded in our calculations the effects of forward production and consumption linkages. In this section we use matrix algebra (Appendix 1) to calculate total multiplier effects (i.e., including all types of linkages and for all rounds). This also allow us to consider not just output multipliers but also GDP and income multipliers, which can reveal important distributional effects from external demand-side shocks. In other words, we will calculate SAM multipliers rather than just input-output multipliers.

In this exercise you are asked to construct an unconstrained SAM multiplier model using Stata. Your job is not to create a Stata code that uses matrix algebra. We will use the code from “Multiplier Decomposition and Structural Path Analysis in Stata”, created by the Development Economics Research Group of the University of Copenhagen. The code has been designed to manage SAMs up to 999 accounts. Very few edits are required to adapt the code to a new SAM. During this training you will make all of the necessary changes.

Hints and tips

1. Follow the instructions below. 2. Do not worry if you are not very familiar with Stata. The knowledge required for this exercise is very basic. However, if you are an advanced Stata user, you could fully understand how Stata can be used for data manipulation and matrix operations.

Instructions

1. Preparing SAM – in Excel. The interface between Stata and Excel is not perfect. Hence, we need to prepare the SAM into a format readable by Stata. a. Open the Excel file “2003 Vietnam SAM.xlsx” (for convenience this SAM has activities and commodities aggregated into single accounts). This spreadsheet has two sheets, one with the SAM, and the other with its legend. b. Column (A), which includes all account names for the rows, is empty, please type “name” in that cell (A1).

4 Adapted from Breisinger, Thomas and Thurlow (2009) 13 c. Make sure that the numeric values of the SAM are formatted as numbers, without the 1000 separator (,) and with 12 decimals as in the figure below.

d. Save the spreadsheet as presam.csv inside the MSPA folder. (C:\MSPA_Training\MSPA\presam.csv). e. Click Ok and then Yes in the following windows.

2. Preparing SAM – in Stata. The Stata program that calculates multipliers and structural path analysis requires the addition of two variables and renaming all account variables. a. Before opening Stata, using presam.csv, please complete the following table as you will need the row location of each of these blocks. Block Number Location Production accounts 15 1 - 15 Factors 5 16 - Institutions (households and enterprises) 3 Exogenous accounts 3 - 26 b. Open Stata c. Click on “New Do-file Editor” (Ctrl 8) d. Open the do file “dofiles/0multd_strp.do”. This is the master file that calculates the multipliers and the structural path for selected paths. e. Highlight the following section of the do file.

clear set mo off set matsize 250 14 cd "C"\MSPA_Training\MSPA\ f. Click Tools/Do (Ctrl D). The cd command should have the location where you saved the files for this training. g. Take a moment to read lines 1 - 56. As you can see, line 56 calls another do file, “dofiles/1samprep.do”. h. Open the do file “dofiles/1samprep.do” i. Look for the “EDIT” comments and make the necessary changes using the table from instruction a.

*EDIT: Add location of first exogenous account scalar exo = ?? * EDIT: Need to change ranges in all "forval" commands so as to match the location of such accounts. * Production forval x = 1/15 { * Factors forval x = ??/?? { * Institutions forval x = ??/?? { * Exogenous forval x = ??/26 {

j. While inside 1samprep and without highlighting any text, click Tools/Do (Ctrl D). Make sure that you do not get any errors. Some of the common errors come from not formatting the values as numbers in Excel or from writing the wrong location of the blocks in the forval commands. k. In the main Stata window, click on “Data Browser” or type “browse” in the command window. Make sure the prepared SAM looks okay. The last variable should be “exo26” as well as the last row. If you do have more variables and observations (usually with missing variables), go back to the “presam.csv” file and delete those rows/columns, which initially looked empty but Stata reads them as variables/observations. l. You have successfully prepared the SAM for a multiplier and structural path analysis.

3. Run the multiplier analysis in Stata. The matrix algebra Appendix 1 has been coded into a do file. As the equations change based on the number of blocks of endogenous variables, please select the correct do file. a. In this example, we have 3 blocks: production accounts, factors, and institutions (enterprise and households). Make sure that the do file for 3 blocks does not begin with “*” as shown below:

** MULTIPLIER DECOMPOSITION ** * The multiplier decomposition method in this program works for different blocks of endogenous variables

15 * Please select the multiplier decomposition do file for the corresponding number of blocks * i.e 3 blocks for production, factors, institutions

* 3 blocks do dofiles/1multdecomp3b * 4 blocks * do dofiles/1multdecomp4b * 5 blocks * do dofiles/1multdecomp5b

b. Highlight the line “do dofiles/1multdecomp3b” and click Tools/Do (Ctrl D). You have successfully calculated all SAM/accounting multipliers. c. However, it is useful to have formatted tables that can be easily used by Excel. The do file “dofiles/2tables_md” has been created for that purpose. Highlight the line “do dofiles/2tables_md” and click Tools/Do (Ctrl D).

* SUMMARY TABLES * The code below generates the following tables in output folder: * 1. Global Effects/Accounting Multipliers (M) - table_m.csv * 2. Closed Loop as a Share of Total Effects (N3/M) - table_n3m.csv * 3. Own and Open Loop Share of Total Effects ((N1+N2)/M) - table_n12m.csv * It also saves dta files in root folder with the same names as csv files do dofiles/2tables_md

d. As mentioned in the program, 3 tables were created inside the “MSPA/output/” folder. Open the accounting multipliers table “ table_m.csv” and answer the questions from the Exercise 2 sheet in the Exercises.xlsx file, which you were using in the previous Exercise. e. The code also calculates tables for multiplier decomposition which is not covered in this guide. The matrix algebra behind these matrices is included in Appendix 1 if you are interested.

Discussion

The file table_m.csv shows the SAM/accounting multipliers. The agricultural output multiplier is equal to 3.00. This means that a direct increase in exogenous agricultural demand by 1 billion VND, leads to a total increase in output by 3 billion VND once all linkages and round-by-round effects are taken into account. By contrast, the machinery output multiplier is only 1.85, even though the initial increase in exogenous demand is also 1 billion VND. These differences across sectors highlight the importance of taking multiplier effects into account when determining the overall impact of exogenous demand shocks. Notice also that the income multipliers for all sectors are lower than the output multiplier, due to various leakages from the circular flow of income (e.g., import and tax leakages).

16 Exercise 3. Structural Path Analysis in Stata

In the previous exercise we prepared the SAM before calculating the accounting multipliers. We found that agriculture and processed foods had the two of the largest output and income multipliers. Using structural path analysis we identify the components of those multipliers.

In this exercise you are asked to construct the structural path for two income multipliers. Your job is to specify in Stata, the origin and destination accounts for the paths of interest. In this case, we are interested in mapping the path between agriculture and both urban and rural households. You will also need to answer the questions in the exercises spreadsheet.

Hints and tips

1. Follow the instructions below. 2. The structural path analysis section of the code in Stata needs to be done in the same session as the multiplier section, as it uses matrices created during the multiplier calculations.

Instructions

1. Identify the origin and destination poles. a. In the previous exercise, the SAM was prepared using the do file “1samprep”. In that file, the codebook “samend.dta” was also created. b. The origin pole for this exercise is AGRI – Agriculture. Hence, you will need to change the origin account in the do file “0multd_strp”. The account needs to be entered in the value format that was assigned by the codebook, such as end001. In order to see the codebook, type the following in the command window (you may have to enter one line at the time).

use samend, clear browse

c. Enter the code for agriculture, rural household, and urban household in the table below (ignore the extra A for AGRI). names saccount end001 AAGRI end??? HHD_R end??? HHD_U

17 d. Now that you have identified the code used by Stata to recognize the origin and destination accounts (in column labeled “names”), edit the Stata code with the values identified in the table above.

* EDIT: Specify origin and destination poles in orig2 dest2 global macros. * The number of the account can be found in the codebook file (samend.dta) * Origin pole(s) global orig2 = "end???" * Destination pole(s) global dest2 = "end??? end???" e. We will use paths of up to 4 arcs in this exercise. Please select the corresponding do files (place “x” before the do file command for the arcs not included for this exercise, just as shown below).

* EDIT: Select the number of arcs. Traditionally 1-4 paths are okay for 3 blocks of endogenous variables * Need to run 1spa_arc1, all others are optional do dofiles/1spa_arc1 do dofiles/1spa_arc2 do dofiles/1spa_arc3 do dofiles/1spa_arc4 * do dofiles/1spa_arc5 do dofiles/2tables_spa f. Highlight the structural path analysis code, approximately from line 85 (** STRUCTURAL PATH ANALYSIS **) to line 115 (}).Click Tools/Do (Ctrl D). g. The structural path analysis code calculates the paths of all the possible combinations of origin and destination accounts. If you were interested in more accounts than the ones selected for this exercise, you could just add more, making sure they are all in between the semi-colons (“…”). h. As with the multiplier analysis, there is a do file that creates tables for Excel. Select the text for the summary tables (shown below) and Click Tools/Do (Ctrl D). You have now successfully created the tables required for this exercise and additionally, the data required for Exercise 4.

* SUMMARY TABLES * Tables are generated for a maximum of 20 observations, producing tables ready for reports (clean_`origin'.csv) * which can be opened in Excel * Furthermore, it produces a set of tables to be used in NodeXL (xnode_clean_`origin') * NodeXL files - set mo off do dofiles/2tables_spa_c clear

18 i. As mentioned in the program, tables were created inside the “MSPA/output/” folder. Open the table “spa_end001.csv”, which summarizes the structural path analysis where agriculture is the origin pole, and both rural and urban households the destination poles. j. Answer the questions in the Exercise 3 worksheet.

Discussion

The file spa_end001.csv shows structural path analysis for an exogenous increase in agricultural demand. The multiplier for rural households is equal to 0.661. This means that a direct increase in exogenous agricultural demand by 1 billion VND, leads to a total increase in rural income by 661 million VND. We also find that 53.11% (351 million VND) of that increase comes from low skilled labor hired in the agricultural sector. From the results we observe that rural households receive some income from labor hired in other sectors but only a very low proportion of their total income as a result of the income multiplier effect. The results from the structural path analysis can be overwhelming and hard to interpret, especially the sources of household income. The last exercise of this guide provides another alternative to better interpret the results.

19 Exercise 4. Structural Path Analysis Figures with NodeXL

In the previous exercise we generated the structural path for all the sources of rural household income from an exogenous increase in agricultural demand. The main sources of income were easily identified but the results were not as straight forward to visualize. This section uses a graphical approach for structural path analysis.

NodeXL is a template for Excel 2007 that can be used to graph structural path analysis. The objective of this exercise is to chart the structural path for 94.5% of the sources of rural household income from the previous exercise, which were identified by the top 20 paths.

Hints and tips

 Follow the instructions below.  NodeXL is only available for Excel 2007. It does not work with Excel 2003.  NodeXL is a very useful tool and the figures created can provide useful insights. However, this template can be confusing and “buggy” at times. Have patience, follow the instructions step by step, and if things do not seem to work, please restart Excel 2007.

20 Instructions

1. Extract arcs from structural path a. In the previous exercise, the Stata code also created the table (nodexl_end001.csv) needed for this exercise together with the structural path tables. This table is a modification of spa_end001.csv. All arcs were extracted in pairs together with their corresponding proportion of the total income multiplier effect. After the arcs were extracted, if the same arc was present more than once, their corresponding proportions were added into a new variable together with the number of paths where they appears into another variable.

b. Open nodexl_end001.csv. You can see that rural households received 56.67 percent of their income from unskilled labor, with a total of 10 paths passing by that arc.

2. Use NodeXL to chart the arcs a. Open the NodeXL template in Windows, not from Excel (Start, All Programs, Microsoft NodeXL, Excel 2007 Template). It may take a while for it to open. Once it opens, it should look like the image in the previous page.

b. Using nodexl_end001.csv, copy the accounts from pole1 and pole2 of the path AGRI. ~ HHD_R. (B2:C37) and paste them into Vertex1 and Vertex2 in the NodeXL template.

c. Select the NodeXL menu tab.

d. Using that menu, click Prepare Data, Merge Duplicate Edges. Click yes to the notice.

e. Using nodexl_end001.csv, copy the corresponding values for proportion and paste them into the Edge Weight column. Below you can see how NodeXL should look like.

21 f. In the NodeXL menu tab, click on Workbook Columns, and select labels. You will be taken to the worksheet “Vertices”. g. In the NodeXL menu tab, click on Schemes and select Weighted Graph Scheme, ticking the option to label each vertex… as shown below. Then click OK.

22 h. In the Vertices worksheet, copy the accounts from the Vertex column (A) and paste them into the Primary Label column (P). i. Repeat step i. j. Click on show graph if the figure does not appear in the Document Actions window. Select Sugiyama as the algorithm used to lay out the graph. This is the best fitting logarithm for structural path analysis. Select some other choices and see how the figure changes for different logarithms. k. Using the Sugiyama logarithm, the structural path figure should look similar to the one below (may not look exactly like it).

23 l. You can rearrange the account boxes by clicking on each box and dragging it to a more appropriate location. Zooming in and out is accomplished by scrolling your mouse or moving the Zoom bar. If you need to move the figure up or down, press and hold the space bar and move the figure with your mouse. m. In order to copy the image to another document, right click, and select Copy Image to Clipboard. You should have a figure like the one below after rearranging the account boxes.

24 n. Save the file as NodeXL_AGRI.xlsx. If you close this file and open it again, the figure will no longer be there. Once you refresh the graph or click on show graph, the figure will be as initially laid out. Thus, it is important to save a copy of the image that you previously created or you may have to rearrange the account boxes again.

o. You can now answer the question from the Exercise 4 worksheet.

Discussion

The figure created in NodeXL facilitates the interpretation of the structural paths. Remember that for some structural paths, the top twenty paths generated by Stata may not cover 100% of the multiplier effect. Nonetheless, the width of each arc that connects two poles/accounts represents the importance of that path, with the wider arcs representing a larger proportion of the accounting multiplier. In the exercise, most of the income that rural households receive comes from low skilled labor and land, which are both “hired” by the agricultural sector. Other important sources of income are enterprises where capital is invested from agriculture, and medium skilled labor.

With this exercise we have finished the multiplier and structural path analysis. Feel free analyze different scenarios and dig deeper into some issues that may be of your interest. Very few edits are required to import a more recent SAM once it becomes available.

25 Appendix 1. Theoretical Background

Multiplier Analysis

The multiplier analysis method presented here draws heavily on the work by Pyatt and Round (1979), Defourny and Thorbecke (1984), and Stone (1985). This method allows the measurement of the effect of injections from exogenous accounts into the economy represented by the endogenous accounts. It reveals the interaction between and across SAM categories as shown in Figure 4.

Figure 4. Interrelationship among SAM Accounts

Production activities

Consumption Value added expenditure

Households Production & Enterprises Factorial income factors distribution

Source: Adapted from Defourny and Thorbecke (1984)

Figure 4 represents the circular flow of income. Value added generated from production activities flows to production factors as factor payments (i.e. wages, land rents, capital returns). Thereafter, income is distributed to households and enterprises. Lastly, households and enterprises spend their income to purchase good and services from production activities.

SAM based multipliers provide a first-cut estimate of the effects of a policy or external shock (Round, 2003). For example, let’s assume that a government policy will lead to an increase in the demand of agricultural goods. This demand increase leads to a direct increase in agricultural activities. Indirectly, value added increases, increasing household income. The increase in household income leads to an induced effect as they now have more resources which may lead to an increase in expenditure.

The first step to compute the multipliers is to decide which accounts to designate as exogenous and endogenous (if all accounts were to be endogenous, multipliers could not be calculated as the matrix is not invertible). A SAM (S) usually includes production activities

26 (a), factors of production (f), institutions (i), government, capital, and the rest of the world. Normally, endogenous accounts include the production activities, factors, and institutions (enterprises and households). Conversely, the exogenous accounts (x) include government, capital, and the rest of the world.

Thereafter, average expenditure shares for each column are calculated. Submatrix ( ) only includes the shares for all endogenous accounts.

Accounting multiplier matrix are then calculated.

Multiplier Decomposition If a multiplier decomposition is needed, Matrix is then decomposed into Matrixes B and C where B is the partition that only includes interactions within each group of endogenous variables, and C, the interactions across groups.

If we denote the row totals for incomes received by endogenous accounts by y, and x for the expenditures by the exogenous accounts into endogenous accounts, we can then restate the rows of endogenous accounts in (S) as:

27 where

From equation (5), the accounting multiplier is decomposed into Matrixes , , and (assuming three blocks of endogenous accounts as the equations differ depending on the number of blocks).

captures the within account effects. For the production activities sector, represents the input-output multiplier. captures the cross/spillover effects, where the injection has an effect on another category with no reverse effects. Lastly, captures the between effects net of the within-account multipliers. completes the full circular effect.

As , , and enter the decomposition in a multiplicative fashion, is better expressed and understood in terms of additive components, where I is a matrix of injections.

Equation (9) can be represented as:

(10) where ,

represents the own-effects. It captures the within category effects, including the direct effects from an increase in exogenous demand and the interaction effects within categories (activities, factors, or households).

28 represents the incremental open loop linkages. It captures the between effects of endogenous variables and the resulting within category effects. It includes the effects from additional demand across categories. Additionally, it includes the indirect effect within categories.

represents the closed loop effects. It captures the additional feedback effects, which were not included, as N2 only included within categories indirect effects.

N1 and N2 together represent the part of the multiplier effects from exogenous demand increases and the adjacent spill-over into other categories. N3 represents the importance of the market for intermediate goods.

29 Structural Path Analysis

The following sections draw heavily on Defourny and Thorbecke (1984), who were the first to introduce the method. The average expenditure propensities aij, which were calculated for the accounting multipliers (the elements of Matrix A), are the only data requirements, limiting SPA to endogenous accounts only. These expenditure propensities represent the magnitude of the influence transmitted from account/pole i to account/pole j. SPA encompasses three types of influence: direct, total and global.

Direct influence

The direct influence of i on j is only the change of j induced by a unitary change in i. This influence can be measured along an arc (14) or along an elementary path p (15). An elementary path is a sequential group of arcs.

Total influence

Using the concept of total influence developed by Lantner (1974), the indirect effects within the structural path can be identified. These indirect effects induced by the adjacent circuits amplify the direct influence in the elementary path.

where is the direct influence along path p and Mp the path multiplier. The path multiplier captures the indirect effects on adjacent feedback circuits.

(17) where is the determinant of the matrix (I – A) and is the determinant of the structure excluding the poles (both rows and columns) constituting path p.

30 Global influence

Global influence measures the total effects on income or output of the destination pole j consequent to an injection of one unit of output or income in the origin pole i. Global influence corresponds to the j,i element of the accounting multiplier matrix (3). Global influence accounts for all direct and indirect influences transmitted by all elementary paths linking the origin and destination poles. Thus, the global influence can be decomposed into the total influences transmitted along all elementary paths between the origin and destination. (18)

31 Appendix 2. Abbreviation List

Production aagri Agriculture amine Mining anmet Non-metals achem Chemicals atext Textiles afood Processed foods awood Wood amach Machinery afuel Fuel acout Construction & utilities ahotl Hotels & tourism agovn Government services aosrv Other services atrad Trade atran Transportation

Factors flnd Factor- land flab-l Factor - low skilled labor flab-m Factor - medium skilled labor flab-h Factor - high skilled labor fcap Factor - capital

Institutions ent Enterprises hhd-r Household - rural hhd-u Household - urban

Other/exogenous gov Government s-i Savings-investment row Rest of the world total Column and row totals

32 Appendix 3. Main Stata Code for Multiplier Decomposition and Structural Path Analysis

0multd_strp.do

* Multiplier decomposition and Structural Transformation for Vietnam (2003). * Based on Defourny and Thorbecke (1984) and Stone (1985 - in Pyatt and Round) * Last modified on July 28, 2009 * by Andres Garcia, DERG, University of Copenhagen

* Citation: * Garcia, Andres. 2009. Multiplier Decomposition and Structural Path Analysis in Stata. * Development Economics Research Group. University of Copenhagen. clear set mo off set matsize 250 cd "C"\MSPA_Training\MSPA\

**------* INSTRUCTIONS: * This program can handle SAMs with a max of 999 accounts. Nonetheless, it is important to consider that * Structural Path Analysis generates all possible combinations, so the larger the SAM, the longer it takes for the * program to finish (days or weeks for SAMs with more than 200 accounts). Thus, it is recommended to work with an * aggregated SAM, which also facilitates the interpretation.

* Given the nature of multiplier decomposition and structural path analysis, activity and commodity accounts * are aggregated into single production accounts. This program assumes that you have already aggregated your SAM * and save it as "presam.csv" in the main folder, where the column that includes the name of the sam accounts becomes a * variable called "name".

* Importing the SAM * Once the presam.csv file has been created, the do file 1samprep.do will need to be modified (when using a new SAM). * This and the current do file are the only files needing changes when other SAMs are used. * Follow the instructions and identify the location of each block of endogenous accounts (i.e factors and institutions) * Specific details are indicated in the file.

* Multiplier Decomposition * Select the number of blocks of endogenous variables (there are do files already developed for 3, 4, and 5 blocks).

* Structural Path Analysis. * Multiple origin and destination poles can be calculated at the same time.

* In general, Look for "EDIT" labels and make the necessary changes.

* The following tables are saved in the output folder: * Tables: Multiplier Decomposition * - tablem.csv Accounting multipliers * - table_n3m.csv Closed Loop as a Share of Total Effects (N3/M) * - table_n12m.csv Own and Open Loop Share of Total Effects ((N1+N2)/M)

33 * Tables: Structural Path Analysis * - spa_òrigin-pole' Structural Paths from òrigin-pole' to all `destination-poles' * - nodexl_òrigin-pole' Tables to be used when using NodeXL to generate SPA charts

**------

** IMPORT AND LABEL SAM ** * EDIT: The do file needs to be edited as explained in it. * The following do file prepares the SAM, starting with a SAM saved as presam.csv, where the column that * includes the sam accounts is named "name". The file generates samdata.dta, which is used for the * Multiplier Decomposition and Structural Path Analysis. do dofiles/1samprep

**------

** MULTIPLIER DECOMPOSITION ** * The multiplier decomposition method in this program works for different blocks of endogenous variables * Please select the multiplier decomposition do file for the corresponding number of blocks * i.e 3 blocks for production, factors, institutions

* 3 blocks do dofiles/1multdecomp3b * 4 blocks * do dofiles/1multdecomp4b * 5 blocks * do dofiles/1multdecomp5b

* SUMMARY TABLES * The code below generates the following tables in output folder: * 1. Global Effects/Accounting Multipliers (M) - table_m.csv * 2. Closed Loop as a Share of Total Effects (N3/M) - table_n3m.csv * 3. Own and Open Loop Share of Total Effects ((N1+N2)/M) - table_n12m.csv * It also saves dta files in root folder with the same names as csv files do dofiles/2tables_md

**------

** STRUCTURAL PATH ANALYSIS **

* The method shown here creates paths of up to 5 arcs * Only need to specify origin and destination in lines below, the rest of the code * is automated and will produce a table for those paths. * Repeat for other poles.

* EDIT: Specify origin and destination poles in orig2 dest2 global macros. * The number of the account can be found in the codebook file (samend.dta) * Origin pole(s) global orig2 = "end???" * Destination pole(s) global dest2 = "end??? end???" foreach lorig of global orig2 { scalar orig = "`lorig'" * Set destination accounts * Don't use Enterprises as they don't seem to be connected to the economy foreach ldest of global dest2 { scalar dest = "`ldest'" * EDIT: Select the number of arcs. Traditionally 1-4 paths are okay for 3 blocks of endogenous variables * Need to run 1spa_arc1, all others are optional 34 do dofiles/1spa_arc1 do dofiles/1spa_arc2 do dofiles/1spa_arc3 do dofiles/1spa_arc4 * do dofiles/1spa_arc5 do dofiles/2tables_spa outsheet using output/table_spa_`lorig'`ldest'.csv, c replace ! cd output & copy table_spa_`lorig'*.csv `lorig'.csv } }

* SUMMARY TABLES * Tables are generated for a maximum of 20 observations, producing tables ready for reports (spa_`origin'.csv) * which can be opened in Excel * Furthermore, it produces a set of tables to be used in NodeXL (nodexl_`origin') * NodeXL files - set mo off do dofiles/2tables_spa_c clear

35 References

Breisinger, C., Thomas, M. and Thurlow, J.. 2009. Social Accounting Matrices and Multiplier Analysis: An Introduction with Exercises. IFPRI, Washington DC, USA.

Defourny, J. and Thorbecke, E. 1984. Structural Path Analysis and Multiplier Decomposition within a Social Accounting Matrix, Economic Journal, 94, 111-136.

Garcia, A. 2009. Multiplier Decomposition and Structural Path Analysis Using Stata. DERG, University of Copenhagen. Copenhagen, Denmark.

Haggblade, S. and Hazell, P. 1989. Agricultural Technology and Farm-Non-Farm Growth Linkages, Agricultural Economics, 3, 345-364.

Pyatt, G. and J.I. Round. 1979. Accounting and Fixed Price Multipliers in a SAM Framework, Economic Journal, 89, 850-873.

Round, J.I. (2003) ‘Social Accounting Matrices and SAM-based Multiplier Analysis’, Chapter 14 in F. Bourguignon, and L. A. Pereira da Silva (editors) Techniques and Tools for Evaluating the Poverty Impact of Economic Policies, World Bank and Oxford University Press.

Stone, J. R. N. 1985. The Disaggregation of the Household Sector in the National Accounts, G. Pyatt and J. I. Round (eds), Social Accounting Matrices: A Basis for Planning. The World Bank, Washington D.C.; 145-185.