# INTRODUCTION CLRM, GLRM and SUR models make the following assumption: The error term is uncorrelated with each explanatory variable. Three important sources.

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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: 1999-00 to 2011- 12 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, 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 GROWTH EQUATION VariableLabelDFParameter Estimate S.Et ValuePr > |t| Intercept 1-44.576213.301-3.350.0016 GCFC 114.289333.74733.810.0004 FDI 1-0.629650.5258-1.200.2372 Export 10.998982.59200.390.7017 Labor 19.315659.00541.030.3062 FDI EQUATION VariableLabelDFParameter Estimate S.Et ValuePr > |t| Intercept 1-8.817742.14 275 -4.120.0002 Growth 1-0.037320.03 527 -1.060.2953 GCFC 12.448400.71 752 3.410.0013 Wage 11.211120.31 025 3.900.0003 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 12.865000.2520 5 11.37<.0001 FDI 10.085380.0221 3 3.860.0003 Growth 10.025250.0053 6 4.71<.0001 M3 10.230160.2041 4 1.130.2651 EXPORT EQUATION VariableLabelDFParameter Estimate S.Et ValuePr > |t| Intercept 1-2.680930.62 730 -4.27<.0001 Growth 10.005420.01 076 0.500.6170 EXRATE 10.016430.00 797 2.060.0447 GCFC 11.336230.16 487 8.10<.0001 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 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 Growth41.50672-23.47730.473947-6.93685-0.47355 GCFC3.502256-0.753610.1980710.42032-0.0152 FDI-4.62356-0.483521.5921913.210914-0.00975 Export3.369152-2.683490.232461-0.16597-0.00602 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 Growth29.16422-32.8265-2.017411.898695-0.36136 GCFC4.177033-1.311610.154508-0.04627-0.01444 FDI0.420984-1.962191.714074-0.30895-0.0216 Export3.021-3.841590.0144790.0920380.003003

Covariance and Correlation between Models Cross Model Covariance FIRSTSECONDTHIRDFOURTH FIRST15.12020.82595-0.2126-0.1528 SECOND0.82590.21683-0.03220.00667 THIRD-0.2126-0.03220.007780.00152 FOURTH-0.15280.006670.001520.02945 Cross Model Correlation FIRSTSECONDTHIRDFOURTH FIRST10.45616-0.6198-0.229 SECOND0.456161-0.78280.08341 THIRD-0.61979-0.782810.1003 FOURTH-0.2290.083410.10031

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| Intercept136.82287.759814.75<.0001 Labor1-10.44485.61812-1.860.0693 Wage12.338411.251361.870.0679 M31-3.880073.77901-1.030.3098 EXRATE1-0.537170.1042-5.16<.0001 FDI EQUATION VariableDFParameter Estimate Standard Error t ValuePr > |t| Intercept13.5332110.3130311.29<.0001 Labor1-1.438360.22663-6.35<.0001 Wage10.0913670.050481.810.0767 M310.3976450.152442.610.0122 EXRATE1-0.010710.0042-2.550.0142

2SLS (First Stage) GCFC EQUATION VariableDFParameter Estimate Standard Error t ValuePr > |t| Intercept1-6.104871.83106-3.330.0017 Labor1-1.119091.32569-0.840.4029 Wage11.3550420.295284.59<.0001 M314.3010120.891724.82<.0001 EXRATE1-0.00010.0245900.9966 Export EQUATION VariableDFParameter Estimate Standard Error t ValuePr > |t| Intercept13.0526230.509655.99<.0001 Labor1-2.515930.36899-6.82<.0001 Wage10.2280510.082192.770.0079 M310.0711370.24820.290.7757 EXRATE1-0.006080.00684-0.890.379

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 1-193.8392.3074-2.10.0411 GCFC 136.932218.671.980.0538 FDI 1-4.70382.81752-1.670.1017 Export 123.406320.90071.120.2685 Labor 196.301660.77131.580.1198 FDI EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept 1-11.743.21839-3.650.0007 Growth 1-0.07840.06579-1.190.2391 GCFC 13.458891.109563.120.0031 Wage 11.021430.353252.890.0057

2SLS (Whole Model) GFCF EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept1 3.181210.337329.43<.0001 FDI1 0.128150.03743.430.0013 Growth1 0.03230.009343.460.0011 M31 -0.0680.26195-0.260.7963 EXPORT EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept 1 -3.60171.00783-3.570.0008 Growth1 0.074450.048161.550.1287 EXRATE1 0.045290.020062.260.0285 GCFC1 1.065740.445722.390.0208

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 1-130.5487.7701-1.490.1436 GCFC 129.244518.51521.580.1209 FDI 1-5.29622.68594-1.970.0545 Export 113.395818.63720.720.4758 Labor 131.948353.60440.60.554 FDI EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept 1-16.7962.23752-7.51<.0001 Growth 1-0.14680.05802-2.530.0147 GCFC 15.215910.764586.82<.0001 Wage 10.628660.301452.090.0424

3SLS (Whole Model) GFCF EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept12.802960.2797310.02<.0001 FDI10.115560.036823.140.0029 Growth10.029720.009253.210.0023 M310.255440.20661.240.2223 EXPORT EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept 1-3.49081.00532-3.470.0011 Growth10.0830.04811.730.0908 EXRATE10.048110.020022.40.0202 GCFC10.975010.445132.190.0334

Comparison - 2SLS and 3SLS GROWTH EQUATION VariableS.E (3SLS) S.E (2SLS) Intercept 87.770192.3074 GCFC 18.515218.67 FDI 2.685942.81752 Export 18.637220.9007 Labor 53.604460.7713 FDI EQUATION VariableS.E (3SLS) S.E (2SLS) Intercept 2.237523.21839 Growth 0.058020.06579 GCFC 0.764581.10956 Wage 0.301450.35325 GFCF EQUATION VariableS.E (3SLS) S.E (2SLS) Intercept0.27973 0.33732 FDI0.03682 0.0374 Growth0.00925 0.00934 M30.2066 0.26195 EXPORT EQUATION VariableS.E (3SLS) S.E (2SLS) Intercept 1.00532 1.00783 Growth0.0481 0.04816 EXRATE0.02002 0.02006 GCFC0.44513 0.44572

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 1-16.7962.23752-7.51<.0001 Growth 1-0.14680.05802-2.530.0147 GCFC 15.215910.764586.82<.0001 Wage 10.628660.301452.090.0424 GFCF EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept12.802960.2797310.02<.0001 FDI10.115560.036823.140.0029 Growth10.029720.009253.210.0023 M310.255440.20661.240.2223 EXPORT EQUATION VariableDFParameter Estimate S.Et ValuePr > |t| Intercept 1-3.49081.00532-3.470.0011 Growth10.0830.04811.730.0908 EXRATE10.048110.020022.40.0202 GCFC10.975010.445132.190.0334

3SLS Comparison (Whole vs OID Equation System) FDI EQUATION Whole SystemOID Equations Parameter Estimate S.EParameter Estimate S.E Intercept -16.7962.23752-16.7962.23752 Growth -0.14680.05802-0.14680.05802 GCFC 5.215910.764585.215910.76458 Wage 0.628660.301450.628660.30145 GFCF EQUATION Whole SystemOID Equations Parameter Estimate S.EParameter Estimate S.E Intercept 2.802960.279732.802960.27973 Growth 0.115560.036820.115560.03682 GCFC 0.029720.009250.029720.00925 Wage 0.255440.20660.255440.2066 EXPORT EQUATION Whole SystemOID Equations Parameter Estimate S.EParameter Estimate S.E Intercept -3.49081.00532-3.49081.00532 Growth 0.0830.04810.0830.0481 GCFC 0.048110.020020.048110.02002 Wage 0.975010.445130.975010.44513

3SLS(EID) vs 2SLS(EID) GROWTH EQUATION (3SLS) VariableDFParameter Estimate S.Et ValuePr > |t| Intercept 1-130.5487.7701-1.490.1436 GCFC 129.244518.51521.580.1209 FDI 1-5.29622.68594-1.970.0545 Export 113.395818.63720.720.4758 Labor 131.948353.60440.60.554 GROWTH EQUATION(2SLS) VariableDFParameter Estimate S.Et ValuePr > |t| Intercept 1-193.8392.3074-2.10.0411 GCFC 136.932218.671.980.0538 FDI 1-4.70382.81752-1.670.1017 Export 123.406320.90071.120.2685 Labor 196.301660.77131.580.1198

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 http://dbie.rbi.org.in/DBIE/dbie.rbi?site=home 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://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.

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