INTRODUCTION CLRM, GLRM and SUR models make the following assumption: The error term is uncorrelated with each explanatory variable. Three important sources that produce a correlation between the error term and an explanatory variable – 1) Omission of an important explanatory variable 2) Measurement error in an explanatory variable 3 ) Reverse causation 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).

Purpose Why SES? To investigate the importance of FDI for economic growth in India Time period: to Bi – directional connection 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,

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 GROWTH EQUATION VariableLabelDFParameter Estimate S.Et ValuePr > |t| Intercept GCFC FDI Export Labor FDI EQUATION VariableLabelDFParameter Estimate S.Et ValuePr > |t| Intercept Growth GCFC Wage 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;

OLS Estimation GFCF EQUATION VariableLabelDFParameter Estimate S.Et ValuePr > |t| Intercept <.0001 FDI Growth <.0001 M EXPORT EQUATION VariableLabelDFParameter Estimate S.Et ValuePr > |t| Intercept <.0001 Growth EXRATE GCFC <.0001 Growth = *GCFC *FDI * Export * 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 Anything (Distributional assumption) Normality(Distribution al assumption) Limited Information (Informational assumption) ILS/ 2SLS/ IVLIML Full Information (Informational assumption) 3SLSFIML

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; Step 1 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. Step 2 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. 2SLS

3SLS Step 1 The first stage involves obtaining estimates of the residuals of the structural equations by two-stage least squares of all identified equations. Step 2 The second stage involves computation of the optimal instrument, or weighting matrix, using the estimated residuals to construct the disturbance variance-covariance matrix. Step 3 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 3SLS InterceptLaborWageM3EXRATE Growth GCFC FDI Export 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; 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; 2SLS InterceptLaborWageM3EXRATE Growth GCFC FDI Export

Covariance and Correlation between Models Cross Model Covariance FIRSTSECONDTHIRDFOURTH FIRST SECOND THIRD FOURTH Cross Model Correlation FIRSTSECONDTHIRDFOURTH FIRST SECOND THIRD FOURTH

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 VariableDFParameter Estimate Standard Error t ValuePr > |t| Intercept <.0001 Labor Wage M EXRATE <.0001 FDI EQUATION VariableDFParameter Estimate Standard Error t ValuePr > |t| Intercept <.0001 Labor <.0001 Wage M EXRATE

2SLS (First Stage) GCFC EQUATION VariableDFParameter Estimate Standard Error t ValuePr > |t| Intercept Labor Wage <.0001 M <.0001 EXRATE Export EQUATION VariableDFParameter Estimate Standard Error t ValuePr > |t| Intercept <.0001 Labor <.0001 Wage M EXRATE

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 VariableDFParameter Estimate S.Et ValuePr > |t| Intercept GCFC FDI Export Labor FDI EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept Growth GCFC Wage

2SLS (Whole Model) GFCF EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept <.0001 FDI Growth M EXPORT EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept Growth EXRATE GCFC

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 VariableDFParameter Estimate S.Et ValuePr > |t| Intercept GCFC FDI Export Labor FDI EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept <.0001 Growth GCFC <.0001 Wage

3SLS (Whole Model) GFCF EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept <.0001 FDI Growth M EXPORT EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept Growth EXRATE GCFC

Comparison - 2SLS and 3SLS GROWTH EQUATION VariableS.E (3SLS) S.E (2SLS) Intercept GCFC FDI Export Labor FDI EQUATION VariableS.E (3SLS) S.E (2SLS) Intercept Growth GCFC Wage GFCF EQUATION VariableS.E (3SLS) S.E (2SLS) Intercept FDI Growth M EXPORT EQUATION VariableS.E (3SLS) S.E (2SLS) Intercept Growth EXRATE GCFC

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) 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; FDI EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept <.0001 Growth GCFC <.0001 Wage GFCF EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept <.0001 FDI Growth M EXPORT EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept Growth EXRATE GCFC

3SLS Comparison (Whole vs OID Equation System) FDI EQUATION Whole SystemOID Equations Parameter Estimate S.EParameter Estimate S.E Intercept Growth GCFC Wage GFCF EQUATION Whole SystemOID Equations Parameter Estimate S.EParameter Estimate S.E Intercept Growth GCFC Wage EXPORT EQUATION Whole SystemOID Equations Parameter Estimate S.EParameter Estimate S.E Intercept Growth GCFC Wage

3SLS(EID) vs 2SLS(EID) GROWTH EQUATION (3SLS) VariableDFParameter Estimate S.Et ValuePr > |t| Intercept GCFC FDI Export Labor GROWTH EQUATION(2SLS) VariableDFParameter Estimate S.Et ValuePr > |t| Intercept GCFC FDI Export Labor

Data Variable in ModelActual Variable RequiredDenominationFrequency Growth Rate GDP figures at Factor Cost and Constant Prices RupeesQuarterly Gross Fixed Capital Formation as proportion to GDP Gross Fixed Capital Formation%ageAnnual Export as proportion to GDPExportRupeesMonthly GDP figures at Factor Cost and Current Prices RupeesQuarterly Labor Force GrowthPopulation(millions)Annually Wage Growth Inflation based on Consumer Price Index %ageMonthly M3 GrowthM3 Money stockRupeesMonthly Exchange Rate Rupees vs DollarMonthly

Data Actual VariableSite GDP figures at Factor Cost and Constant Prices Reserve Bank of India GDP figures at Factor Cost and Current Prices Export Population M3 Money stock Exchange Rate Inflation based on Consumer Price Indexhttp://labourbureau.nic.in/indexes.htmhttp://labourbureau.nic.in/indexes.htm (Ministry of Labor) Gross Fixed Capital Formationhttp://

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.

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