Post on 13-Jan-2016
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