APPLIED MULTIPLIER AND STRUCTURAL PATH

ANALYSIS

Andres GarciaDERG, University of

Copenhagen

CIEM – July 29, 2009

Overview

Economic linkages, multipliers, and structural path analysis.

Exercise 1: Calculating round-by-round multiplier effects in Excel.

Exercise 2: Multiplier decomposition in Stata.

Exercise 3: Structural path analysis in Stata.

Exercise 4: Structural path analysis figures in NodeXL.

ECONOMIC LINKAGES, MULTIPLIERS, AND STRUCTURAL PATH ANALYSIS

Circular flow diagram of the economy

Factor markets

Commodity markets

GovernmentProductive activities

Rest of world

Households Investment

Recurrent spending (G)

Consumption spending (C)

Exports (E)

Imports (M)

Investment demand (I)

Direct taxes Fiscal surplus

Social transfers

Intermediate demand

Domestic private savings

Factor earnings (value-added)

Sales income

Remittances Foreign grants and loans

Capital inflows

Indirect taxes

Source: Breisinger, Thomas, and Thurlow (2009)

Direct and indirect linkages

Direct effects

Indirect effects

Consumption linkages Exogenous

shock

Production linkages

Backward linkages

Forward linkages

• Exogenous demand-side shocks: Changes in export demand, government spending, or investment demand.• Total impact of an exogenous demand shock = Direct effects + Indirect effects

Source: Breisinger, Thomas, and Thurlow (2009)

Circular income flow in the multiplier process

Increase in agricultural

exports

Increase in agricultural production

Increase in nonagricultural

production

Increase in factor

incomes and employment

Increase in household

incomes and consumption

Direct effect

Production linkages

Consumption linkages

Indirect effects

Import leakage

Government

Rest of world

A

A B

C

Tax leakage

A: Output multipliers

B: GDP (value-added) multiplier

C: Income multiplier

Source: Adapted from Breisinger, Thomas, and Thurlow (2009)

Structural path analysis

Increase in agricultural

exports

Increase in agricultural production

Increase in nonagricultural

production

Increase in low skilled

labor

Increase in rural household

income

Increase in medium

skilled labor

60%

15%

Multiplier0.66

Exogenous increase in Exports1 billion VND

99 million VND

396 million VND

660 million VND

Key assumptions for multipliers1. Fixed prices2. Unconstrained supply3. Fixed technology and consumption

patterns

EXERCISE 1: CALCULATING ROUND-BY-ROUND MULTIPLIER EFFECTS IN EXCEL

Exercise: Multiplier effects

2003 SAM for Vietnam with 2 sectorsUnits: Billions of VND

Tr-Margins Factors Other accountsaagri anoag cagri cnoag tr factor hhd gov s-i row total

aagri 553,959 18,071 86,985 659,016anoag 13,752 1,986,661 14,178 2,014,591cagri 245,764 55,172 210,238 15,835 174,155 701,164cnoag 135,950 1,217,897 211,554 348,453 197,592 424,893 704,246 3,240,585tr 40,442 171,113 211,554factor 277,015 720,994 998,008hhd 989,861 121,720 67,779 58,624 1,237,984gov 286 20,529 34,840 90,896 8,147 157,021 265,924 51,955 4,187 633,785s-i 299,389 86,656 90,804 476,848row 58,171 973,844 1,032,015total 659,016 2,014,591 701,164 3,240,585 211,554 998,008 1,237,984 633,785 476,848 1,032,015

Activities Commodities

SHOCK ROUND 1 ROUND 2 ROUND 3

agragr 0.52

nagragr

3.73agr

nagr

nagragr 0.4710

agragr

0.06 nagrnagr

2.06agr

nagr

nagr0.75

SAM legendaagri Activity – agricultureanoag Activity – non-agriculturecagri Commodity – agriculturecnoag Commodity – non-agriculturetr Trade marginsfactor Factors – labor, land, and capitalhhd Households – rural, urban, and enterprisesgov Governments-i Savings/investmentrow Rest of the worldtotal Column and row total

EXERCISE 2: MULTIPLIER DECOMPOSITION IN STATA

Exercise 2. MD in Stata

*Calculate identity matrix I - uses size from matrix C

mat I = I(r(N))

*Calculate matrix D

mat D = inv(I-B)*C

*Calculate matrices M1, M2, and M3

*These matrices are calculated for 3 blocks of endogenous variables (n=3)

*M1 remains constant

*M2 = I + sum(D^(n-i)), for all i between 1 and n-1

*M3 = inv(I-D^n)

mat M1 = inv(I-B)

mat M2 = I+D+D*D

mat M3 = inv(I-D*D*D)

*Calculate total multiplier matrix M

mat M = inv(I-A)

*Calculate matrix N1, N2, and N3

mat N1 = M1

mat N2 = (M2-I)*M1

mat N3 = (M3-I)*M2*M1

Total multiplier effects by type of multiplierCalculate the total multiplier effects by type of multiplier for all production accounts

AGRI CHEM COUT FOOD FUEL GOVN HOTL MACHOutput 3.00 2.11 2.91 3.20 1.60 2.88 2.48 1.85GDP 1.23 0.47 0.88 0.95 0.32 1.09 0.80 0.32Income 1.32 0.55 1.03 1.06 0.38 1.21 0.93 0.37

EXERCISE 3: STRUCTURAL PATH ANALYSIS IN STATA

Exercise 3. SPA in Stata

Origin Destination Global Influence Path Direct

InfluencePath

MultiplierTotal

Influence Proportion Accumulated Proportion

AGRI. HHD_R. 0.661 AGRI. FLAB_L. HHD_R. 0.2070 1.6968 0.3512 53.11 53.11AGRI. FLND. HHD_R. 0.1111 1.6370 0.1819 27.51 80.62AGRI. FCAP. ENT. HHD_R. 0.0178 1.6908 0.0301 4.54 85.16AGRI. FLAB_M. HHD_R. 0.0179 1.6696 0.0298 4.51 89.67AGRI. CHEM. FLAB_L. HHD_R. 0.0035 2.1379 0.0075 1.14 90.81AGRI. TRAD. FLAB_L. HHD_R. 0.0021 1.7283 0.0037 0.56 91.36AGRI. FOOD. FLAB_L. HHD_R. 0.0016 1.9667 0.0032 0.48 91.85AGRI. TRAN. FLAB_L. HHD_R. 0.0017 1.7265 0.0029 0.44 92.29AGRI. CHEM. FCAP. ENT. HHD_R. 0.0009 2.1300 0.0020 0.30 92.58AGRI. COUT. FLAB_L. HHD_R. 0.0010 1.7631 0.0018 0.26 92.85AGRI. FUEL. FLAB_L. HHD_R. 0.0009 1.7419 0.0015 0.23 93.08AGRI. OSRV. FLAB_L. HHD_R. 0.0007 1.8213 0.0013 0.19 93.27AGRI. FLAB_H. HHD_R. 0.0008 1.6571 0.0013 0.19 93.46AGRI. TRAN. FCAP. ENT. HHD_R. 0.0007 1.7189 0.0012 0.17 93.64AGRI. MACH. FLAB_L. HHD_R. 0.0005 2.2406 0.0011 0.17 93.80AGRI. CHEM. FLAB_M. HHD_R. 0.0005 2.1063 0.0011 0.16 93.97AGRI. TRAD. FCAP. ENT. HHD_R. 0.0006 1.7221 0.0009 0.14 94.11AGRI. FOOD. FCAP. ENT. HHD_R. 0.0004 1.9599 0.0008 0.11 94.22AGRI. TRAD. FLAB_M. HHD_R. 0.0004 1.7016 0.0006 0.09 94.32AGRI. COUT. FCAP. ENT. HHD_R. 0.0003 1.7556 0.0006 0.09 94.41

AGRI. WOOD. FLAB_L. HHD_R. 0.0003 1.9469 0.0006 0.09 94.50

Direct influencemat DI_1 = A[dest, mid2]mat DI_2 = A[mid2, mid1]mat DI_3 = A[mid1, orig]mat DI = DI_1*DI_2*DI_3scalar sDI = el(DI,1,1)

*Required conditionif sDI>sMDI & mid1~=mid2 {

*Path multiplieruse matrixa, cleardrop if names==orig |names==dest | names==mid1 | names==mid2drop names varnxpose, clear vdrop if _varname==orig | _varname==mid1 | _varname==mid2 | _varname==destdrop _varnamexpose, clearmkmat v*, matrix (A12)mat I12 = I(r(N))mat PM = det(I12-A12)/det(I-A)mat TI = DI*PM

EXERCISE 4: STRUCTURAL PATH ANALYSIS FIGURES IN NODEXL

Exercise 4. SPA Charts with NodeXL

Questions?

Thank you