INTRODUCTION
CLRM, GLRM and SUR models make the following assumption:
The error term is uncorrelated with each explanatory variable.
1) Omission of an important
explanatory variable
Three important sources
that produce a correlation
between the error term and
an explanatory variable –
A SEM is one which has
two or more equations with
one variable explained in
one equation appearing as
an explanatory variable in
other equation(s).
2) Measurement error in an
explanatory variable
3) Reverse causation
Purpose
Why SES?
 To investigate the importance
 Bi – directional connection
of FDI for economic growth in
India
 Time period: 1999-00 to 201112
between FDI and economic
growth
 Incoming FDI stimulates
economic growth and in its turn
a higher GDP attracts FDI
Model
1.
Growth = a1 + a2*(GCFC) + a3*(FDI) + a4*Export + a5*Labor
2.
FDI = b1 + b2*Growth + b3*GCFC + b4*(Wage)
3.
GCFC = c1 + c2*FDI + c3*Growth + c4*M3
4.
Export = d1 + d2*Growth + d3*EXRATE + c4*GCFC
Reference: FDI and Economic Growth - Evidence from Simultaneous Equation Models, G
Ruxanda, A Muraru - Romanian Journal of Economic Forecasting, 2010.
http://www.ipe.ro/rjef/rjef1_10/rjef1_10_3.pdf
Classification of Variables
 Endogenous : Growth rate of GDP, Gross fixed capital
formation, Exports, FDI
 Exogenous : Growth rate of labour, Wage, Exchange rate,
M3 money base growth
Identification
 M∆ ∆ - No. of excluded exogenous explanatory variables
 N * - No. of included endogenous explanatory variables
1.
First equation : M∆ ∆ - Wage, Exchange rate, Deviation of M3
N * - Gross fixed capital formation, FDI, Exports
M∆ ∆ = N * = 3 => Exactly Identified
2. Second Equation : M∆ ∆ - Labour growth, Exchange rate,
Deviation of M3
N * - GDP growth rate, Gross fixed capital formation
M∆ ∆ (3) > N * (2) and hence overidentified
3. Third Equation : M∆ ∆ - Labour growth, Exchange rate, Wage
N * - GDP growth rate, FDI
M∆ ∆ (3) > N * (2) and hence overidentified
4. Fourth Equation: M∆ ∆ - Labour growth, Deviation of M3,
Wage
N * - GDP growth rate, Gross fixed capital formation
M∆ ∆ (3) > N * (2) and hence overidentified
Estimation of the Model
 Why not OLS ?
 Correlation between the random error and endogenous variable
 OLS estimator biased and inconsistent
 One situation in which OLS is appropriate is recursive model
OLS Estimation
proc syslin data = sasuser.Consa 2sls reduced;
endogenous Growth GCFC FDI Export;
instruments Labor Wage M3 EXRATE;
First: model Growth = GCFC FDI Export Labor;
Second: model FDI = Growth GCFC Wage;
Third: model GCFC = FDI Growth M3;
Fourth: model Export = Growth EXRATE GCFC;
run;
GROWTH EQUATION
Variable Label
DF
FDI EQUATION
Parameter
Estimate
S.E
t Value
Pr > |t|
Intercept Intercept 1
-44.5762
13.301
-3.35
0.0016
GCFC
GCFC
1
14.28933
3.7473
3.81
0.0004
FDI
FDI
1
-0.62965
0.5258
-1.20
0.2372
Export
Export
1
0.99898
2.5920
0.39
0.7017
Labor
Labor
1
9.31565
9.0054
1.03
0.3062
Variable Label
DF
Parameter S.E
Estimate
t Value
Pr > |t|
Intercept Intercept 1
-8.81774
2.14
275
-4.12
0.0002
Growth
Growth
1
-0.03732
0.03
527
-1.06
0.2953
GCFC
GCFC
1
2.44840
0.71
752
3.41
0.0013
Wage
Wage
1
1.21112
0.31
025
3.90
0.0003
OLS Estimation
GFCF EQUATION
EXPORT EQUATION
Parameter
Estimate
S.E
t Value
Pr > |t|
Variable Label
Intercept Intercept 1
2.86500
0.2520
5
11.37
<.0001
FDI
FDI
1
0.08538
0.0221
3
3.86
Growth
Growth
1
0.02525
0.0053
6
M3
M3
1
0.23016
0.2041
4
Variable Label
DF
Parameter S.E
Estimate
t Value
Pr > |t|
Intercept Intercept 1
-2.68093
0.62
730
-4.27
<.0001
0.0003
Growth
1
0.00542
0.01
076
0.50
0.6170
4.71
<.0001
EXRATE EXRATE 1
0.01643
0.00
797
2.06
0.0447
1.13
0.2651
GCFC
1.33623
0.16
487
8.10
<.0001
Growth
GCFC
DF
1
Growth = -44.5762 + 14.28933*GCFC -0.62965*FDI + 0.99898* Export +
9.31565 * Labor
Methods of estimation
 Indirect Least Squares Estimation Method
 Two-stage least squares (2SLS) estimation Method
 Three-stage least squares (3SLS) estimation Method
 Instrumental Variable Method
 Limited Information Maximum Likelihood Method(LIML)
 Full Information Maximum Likelihood Method(FIML)
Assumptions
Limited Information
(Informational
assumption)
Full Information
(Informational
assumption)
Anything
(Distributional
assumption)
Normality(Distribution
al assumption)
ILS/ 2SLS/ IV
LIML
3SLS
FIML
2SLS
Step 1
Step 2
• Regress each right-hand side endogenous variable in the equation to be estimated on all
exogenous variables in the simultaneous equation model using the OLS estimator. Calculate
the fitted values for each of these endogenous variables.
• In the equation to be estimated, replace each endogenous right-hand side variable by its
fitted value variable. Estimate the equation using the OLS estimator.
SAS command:proc syslin data = sasuser.Consa 2sls;
endogenous Growth GCFC FDI Export;
instruments Labor Wage M3 EXRATE;
First: model Growth = GCFC FDI Export Labor;
Second: model FDI = Growth GCFC Wage;
Third: model GCFC = FDI Growth M3;
Fourth: model Export = Growth EXRATE GCFC;
run;
3SLS
Step 1
Step 2
Step 3
• The first stage involves obtaining estimates of the residuals of the structural equations
by two-stage least squares of all identified equations.
• The second stage involves computation of the optimal instrument, or weighting matrix,
using the estimated residuals to construct the disturbance variance-covariance matrix.
• The third stage is joint estimation of the system of equations using the optimal
instrument.
SAS command: proc syslin data = sasuser.Consa 3sls;
endogenous Growth GCFC FDI Export;
instruments Labor Wage M3 EXRATE;
First: model Growth = GCFC FDI Export Labor;
Second: model FDI = Growth GCFC Wage;
Third: model GCFC = FDI Growth M3;
Fourth: model Export = Growth EXRATE GCFC;
run;
Reduced Form
proc syslin data = sasuser.Consa 2sls reduced;
endogenous Growth GCFC FDI Export;
instruments Labor Wage M3 EXRATE;
First: model Growth = GCFC FDI Export Labor;
Second: model FDI = Growth GCFC Wage;
Third: model GCFC = FDI Growth M3;
Fourth: model Export = Growth EXRATE GCFC;
run;
proc syslin data = sasuser.Consa 3sls reduced;
endogenous Growth GCFC FDI Export;
instruments Labor Wage M3 EXRATE;
First: model Growth = GCFC FDI Export Labor;
Second: model FDI = Growth GCFC Wage;
Third: model GCFC = FDI Growth M3;
Fourth: model Export = Growth EXRATE GCFC;
run;
3SLS
2SLS
Intercept Labor
Wage
Growth
41.50672 -23.4773
0.473947 -6.93685
-0.47355
GCFC
3.502256 -0.75361
0.198071 0.42032
-0.0152
FDI
-4.62356
Export
3.369152 -2.68349
-0.48352
M3
EXRATE
Intercept Labor
Wage
M3
Growth
29.16422 -32.8265
-2.01741
1.898695 -0.36136
GCFC
4.177033 -1.31161
0.154508 -0.04627
-0.01444
1.592191 3.210914 -0.00975
FDI
0.420984 -1.96219
1.714074 -0.30895
-0.0216
0.232461 -0.16597
Export
3.021
0.014479 0.092038 0.003003
-0.00602
-3.84159
EXRATE
Covariance and Correlation
between Models
Cross Model Covariance
FIRST
SECOND
THIRD
FOURTH
FIRST
15.1202
0.82595
-0.2126
-0.1528
SECOND
0.8259
0.21683
-0.0322
0.00667
THIRD
-0.2126
-0.0322
0.00778
0.00152
FOURTH
-0.1528
0.00667
0.00152
0.02945
Cross Model Correlation
FIRST
SECOND
THIRD
FOURTH
FIRST
1
0.45616
-0.6198
-0.229
SECOND
0.45616
1
-0.7828
0.08341
THIRD
-0.61979
-0.7828
1
0.1003
FOURTH
-0.229
0.08341
0.1003
1
2SLS (First Stage)
proc syslin data = sasuser.Consa 2sls First;
endogenous Growth GCFC FDI Export;
instruments Labor Wage M3 EXRATE;
First: model Growth = GCFC FDI Export Labor;
Second: model FDI = Growth GCFC Wage;
Third: model GCFC = FDI Growth M3;
Fourth: model Export = Growth EXRATE GCFC;
run;
GROWTH EQUATION
FDI EQUATION
Variable
DF
Parameter Standard
Estimate
Error
t Value
Pr > |t|
Variable DF
Parameter
Estimate
Standard
Error
t Value Pr > |t|
Intercept 1
36.8228
7.75981
4.75
<.0001
Intercept 1
3.533211
0.31303
11.29
<.0001
Labor
1
-10.4448
5.61812
-1.86
0.0693
Labor
1
-1.43836
0.22663
-6.35
<.0001
Wage
1
2.33841
1.25136
1.87
0.0679
Wage
1
0.091367
0.05048
1.81
0.0767
M3
1
-3.88007
3.77901
-1.03
0.3098
M3
1
0.397645
0.15244
2.61
0.0122
EXRATE 1
-0.53717
0.1042
-5.16
<.0001
EXRATE 1
-0.01071
0.0042
-2.55
0.0142
2SLS (First Stage)
GCFC EQUATION
Export EQUATION
Variable
DF
Parameter Standard
Estimate
Error
t Value
Pr > |t|
Variable DF
Parameter
Estimate
Standard
Error
t Value Pr > |t|
Intercept 1
-6.10487
1.83106
-3.33
0.0017
Intercept 1
3.052623
0.50965
5.99
<.0001
Labor
1
-1.11909
1.32569
-0.84
0.4029
Labor
1
-2.51593
0.36899
-6.82
<.0001
Wage
1
1.355042
0.29528
4.59
<.0001
Wage
1
0.228051
0.08219
2.77
0.0079
M3
1
4.301012
0.89172
4.82
<.0001
M3
1
0.071137
0.2482
0.29
0.7757
-0.0001
0.02459
0
0.9966
EXRATE 1
-0.00608
0.00684
-0.89
0.379
EXRATE 1
2SLS (Whole Model)
proc syslin data = sasuser.Consa 2sls;
endogenous Growth GCFC FDI Export;
instruments Labor Wage M3 EXRATE;
First: model Growth = GCFC FDI Export Labor;
Second: model FDI = Growth GCFC Wage;
Third: model GCFC = FDI Growth M3;
Fourth: model Export = Growth EXRATE GCFC;
run;
GROWTH EQUATION
Variable
DF
Parameter
Estimate
S.E
t Value
FDI EQUATION
Pr > |t|
Variable
DF
Parameter
Estimate
S.E
t Value
Pr > |t|
Intercept
1
-193.83
92.3074
-2.1
0.0411
Intercept
1
-11.74
3.21839
-3.65
0.0007
GCFC
1
36.9322
18.67
1.98
0.0538
Growth
1
-0.0784
0.06579
-1.19
0.2391
FDI
1
-4.7038
2.81752
-1.67
0.1017
GCFC
1
3.45889
1.10956
3.12
0.0031
Export
1
23.4063
20.9007
1.12
0.2685
Wage
1
1.02143
0.35325
2.89
0.0057
Labor
1
96.3016
60.7713
1.58
0.1198
2SLS (Whole Model)
GFCF EQUATION
Variable
DF
Parameter
Estimate
S.E
t Value
EXPORT EQUATION
Pr > |t|
Variable
DF
Intercept 1
Parameter
Estimate
S.E
t Value
Pr > |t|
-3.6017
1.00783
-3.57
0.0008
1
0.07445
0.04816
1.55
0.1287
EXRATE
1
0.04529
0.02006
2.26
0.0285
GCFC
1
1.06574
0.44572
2.39
0.0208
Intercept
1
3.18121
0.33732
9.43
<.0001
FDI
1
0.12815
0.0374
3.43
0.0013
Growth
Growth
1
0.0323
0.00934
3.46
0.0011
M3
1
-0.068
0.26195
-0.26
0.7963
3SLS (Whole Model)
proc syslin data = sasuser.Consa 3sls;
endogenous Growth GCFC FDI Export;
instruments Labor Wage M3 EXRATE;
First: model Growth = GCFC FDI Export Labor;
Second: model FDI = Growth GCFC Wage;
Third: model GCFC = FDI Growth M3;
Fourth: model Export = Growth EXRATE GCFC;
run;
GROWTH EQUATION
Variable
DF
Parameter
Estimate
S.E
t Value
FDI EQUATION
Pr > |t|
Variable
DF
Parameter
Estimate
S.E
t Value
Pr > |t|
Intercept
1
-130.54
87.7701
-1.49
0.1436
Intercept
1
-16.796
2.23752
-7.51
<.0001
GCFC
1
29.2445
18.5152
1.58
0.1209
Growth
1
-0.1468
0.05802
-2.53
0.0147
FDI
1
-5.2962
2.68594
-1.97
0.0545
GCFC
1
5.21591
0.76458
6.82
<.0001
Export
1
13.3958
18.6372
0.72
0.4758
Wage
1
0.62866
0.30145
2.09
0.0424
Labor
1
31.9483
53.6044
0.6
0.554
3SLS (Whole Model)
GFCF EQUATION
Variable
DF
Parameter
Estimate
S.E
t Value
EXPORT EQUATION
Pr > |t|
Variable
DF
Intercept 1
Parameter
Estimate
S.E
t Value
Pr > |t|
-3.4908
1.00532
-3.47
0.0011
1
0.083
0.0481
1.73
0.0908
EXRATE
1
0.04811
0.02002
2.4
0.0202
GCFC
1
0.97501
0.44513
2.19
0.0334
Intercept
1
2.80296
0.27973
10.02
<.0001
FDI
1
0.11556
0.03682
3.14
0.0029
Growth
Growth
1
0.02972
0.00925
3.21
0.0023
M3
1
0.25544
0.2066
1.24
0.2223
Comparison - 2SLS and 3SLS
GROWTH
EQUATION
Variable S.E
(3SLS)
S.E
(2SLS)
Intercept 87.7701 92.3074
GCFC
FDI EQUATION
Variable
Intercept
S.E
(3SLS)
S.E
(2SLS)
2.23752 3.21839
18.5152 18.67
Growth
FDI
2.68594 2.81752
Export
18.6372 20.9007
Labor
53.6044 60.7713
GCFC
Wage
EXPORT
EQUATION
GFCF
EQUATION
Variable
S.E
(3SLS)
S.E
(2SLS)
Variable
S.E
(3SLS)
S.E
(2SLS)
Intercept
0.27973
0.33732
Intercept
1.00532
1.00783
FDI
0.03682
0.0374
Growth
0.0481
0.04816
Growth
0.00925
0.00934
EXRATE
0.02002
0.02006
M3
0.2066
0.26195
GCFC
0.44513
0.44572
0.05802 0.06579
0.76458 1.10956
0.30145 0.35325
Zellner and Theil’s Equivalence
 3 SLS on whole model= 3 SLS on OID equations (Zellner
and Theil’s, 1962)
 3SLS on EID= 2SLS+ linear equation of the OID
equations (Zellner and Theil’s, 1962)
3SLS (OID Equations)
GFCF EQUATION
proc syslin data = sasuser.Consa 3sls;
endogenous Growth GCFC FDI Export;
instruments Labor Wage M3 EXRATE;
Second: model FDI = Growth GCFC Wage;
Third: model GCFC = FDI Growth M3;
Fourth: model Export = Growth EXRATE
GCFC;
run;
Variable
DF
DF
Parameter
Estimate
S.E
S.E
t Value
Pr > |t|
Intercept
1
2.80296
0.27973
10.02
<.0001
FDI
1
0.11556
0.03682
3.14
0.0029
Growth
1
0.02972
0.00925
3.21
0.0023
M3
1
0.25544
0.2066
1.24
0.2223
FDI EQUATION
Variable
Parameter
Estimate
EXPORT EQUATION
t Value
Pr > |t|
Variable
Intercept
DF
Parameter
Estimate
S.E
t Value
Pr > |t|
1
-3.4908
1.00532
-3.47
0.0011
Growth
1
0.083
0.0481
1.73
0.0908
<.0001
EXRATE
1
0.04811
0.02002
2.4
0.0202
0.0424
GCFC
1
0.97501
0.44513
2.19
0.0334
Intercept
1
-16.796
2.23752
-7.51
<.0001
Growth
1
-0.1468
0.05802
-2.53
0.0147
GCFC
1
5.21591
0.76458
6.82
Wage
1
0.62866
0.30145
2.09
3SLS Comparison
(Whole vs OID Equation System)
FDI EQUATION
Whole System
Parameter
Estimate
S.E
GFCF EQUATION
OID Equations
Whole System
Parameter S.E
Estimate
Parameter
Estimate
S.E
OID Equations
Parameter S.E
Estimate
Intercept
-16.796
2.23752
-16.796
2.23752
Intercept
2.80296
0.27973
2.80296
0.27973
Growth
-0.1468
0.05802
-0.1468
0.05802
Growth
0.11556
0.03682
0.11556
0.03682
GCFC
5.21591
0.76458
5.21591
0.76458
GCFC
0.02972
0.00925
0.02972
0.00925
Wage
0.62866
0.30145
0.62866
0.30145
Wage
0.25544
0.2066
0.25544
0.2066
EXPORT EQUATION
Whole System
Parameter
Estimate
S.E
OID Equations
Parameter S.E
Estimate
Intercept
-3.4908
1.00532
-3.4908
1.00532
Growth
0.083
0.0481
0.083
0.0481
GCFC
0.04811
0.02002
0.04811
0.02002
Wage
0.97501
0.44513
0.97501
0.44513
3SLS(EID) vs 2SLS(EID)
GROWTH EQUATION (3SLS)
Variable
DF
Parameter
Estimate
S.E
t Value
GROWTH EQUATION(2SLS)
Pr > |t|
Variable
DF
Parameter
Estimate
S.E
t Value
Pr > |t|
Intercept 1
-130.54
87.7701 -1.49
0.1436
Intercept
1
-193.83
92.3074
-2.1
0.0411
GCFC
1
29.2445
18.5152 1.58
0.1209
GCFC
1
36.9322
18.67
1.98
0.0538
FDI
1
-5.2962
2.68594 -1.97
0.0545
FDI
1
-4.7038
2.81752
-1.67
0.1017
Export
1
13.3958
18.6372 0.72
0.4758
Export
1
23.4063
20.9007
1.12
0.2685
Labor
1
31.9483
53.6044 0.6
0.554
Labor
1
96.3016
60.7713
1.58
0.1198
Data
Variable in Model
Actual Variable Required
Denomination
Frequency
Growth Rate
GDP figures at Factor Cost and
Rupees
Quarterly
Gross Fixed Capital Formation
%age
Annual
Export
Rupees
Monthly
GDP figures at Factor Cost and
Rupees
Quarterly
Constant Prices
Gross Fixed Capital Formation as
proportion to GDP
Export as proportion to GDP
Current Prices
Labor Force Growth
Population
(millions)
Annually
Wage Growth
Inflation based on Consumer
%age
Monthly
Price Index
M3 Growth
M3 Money stock
Rupees
Monthly
Exchange Rate
Exchange Rate
Rupees vs Dollar
Monthly
Data
Actual Variable
GDP figures at Factor Cost and Constant Prices
Site
http://dbie.rbi.org.in/DBIE/dbie.rbi?site=home
GDP figures at Factor Cost and Current Prices
Reserve Bank of India
Export
Population
M3 Money stock
Exchange Rate
Inflation based on Consumer Price Index
http://labourbureau.nic.in/indexes.htm (Ministry of Labor)
Gross Fixed Capital Formation
http://www.indexmundi.com/facts/india/gross-fixed-capital-formation
Limitations
 Number of data points are small. (only 13 years)
 Lag Values ignored in each of the equation
 Proxy for labor(population), wage growth(CPI
inflation) were used which might not reflect the true
relation between the variables
 There are other factors which affect inflow of FDI but
are hard to quantify such as govt policies, economic
and political stabilities etc and hence are ignored in
current work.
Thank You!