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TUTAR, E. (2005), “Üniversitelerin Yerel Ekonomiye Katkısı: Niğde Örneği”. Ankara: Detay. APPENDIX A Linear regression model is X t = b + cY t where X t = EX t = Final Consumption Expenditure of Resident Households, Y t = GDP t = Real Gross Domestic Product, c = Marginal Propensity to Consume, b = Autonom Consumption Expenditure. Seasonally adjusted data in regression model and short run model both was taken quarterly in number of periods between 2002Q4 and 2012Q3. Because of seasonal variations in GDP and EX it might not be easy to detect a trend. Census X12 ARIMA in E-Views was used to deseasonalize (seasonally adjust) GDP and Final Consumption Expenditure of Resident Households (EX). To validate the automodel choice by X12 ARIMA, Ljung-Box(LB) statistics was conducted on the residuals. There was no significant autocorrelation among the residuals. Gross Local Output (GDP) and Final Consumption Expenditure of Resident Households (EX) both increases as time increases. Time series EX and GDP do not have a constant mean and variance. Therefore, EX and GDP are not stationary, but they have a constant and trend. Before ADF test is applied to make them stationary, it is important to read the graphs for the assumptions. The same can be discussed for EXSA and GDPSA. In our study to test the hypothesis whether EXSA and GDPSA have a unit root or not, ADF test is applied to both EXSA and GDPSA series at level. Results given on Table A1 shows at level ADF test values are greater than McKinnon critical values. Therefore, H hypothesis could not be rejected which implies both EXSA and GDPSA series were not stationary at level. To make EXSA and GDPSA stationary first difference was taken for each and ADF test values were found to be less than McKinnon critical values. Therefore, the first differenced series both DEXSA and DGDPSA became stationary.
Table A1. ADF test t-statistics, ( ):McKinnon 5% critical values Series Level 1st Difference EXSA 254127 (-2.910860) -760135 (-2.912631) GDPSA 719017 (-2.912631) -179232 (-2.912631) So EXSA~ I(1) and GDPSA ~ I(1). This means that variables EXSA and GDPSA both are integrated of order 1. Since they were integrated of the same order, we could run
Johansen Cointegration test with lag 1 to check for the number of cointegrating equations using Trace Statistic and Maximum Eigenvalue Statistic. Table A2 shows that both statistics indicated 1 cointegrating equation at the 5% level. The two variables EXSA and GDPSA were cointegrated and this suggested that they had a long run relationship. Table A2. Johansen Cointegration Test Lag 1 Results at 5% Hypothesis Statistic 5% critical values # of CE* equations p-value H : No CE* rejected H : At Most 1 CE* not rejected Trace 94809 87760 49471 84147 1 0.0031 0.1706 H : No CE* rejected
H : At Most 1 CE* not rejected Max-Eigen 07049 877601 26460 84147 1 0.0036 0.1706 *CE means Cointegration Equation The linear regression model was used to generate the residual series and then residuals were tested for stationarity using ADF test and residuals were stationary at level. Results are given on Table A3 below. Table A3. ADF Residual Test Results at 5% None Hypothesis t-statistic McKinnon Critical Value Level H : Residual is not stationary (rejected) -815368 -1.946654 Since residuals were stationary we could conclude that the variables in regression model had long run relationship and they were cointegrated. Regression model was estimated by OLS method and corrected to remove serial correlation (autocorrelation).
Regression Model: X t = 1646 + 0.70Y t + 0.36AR(1) X t = EXSA t and Y t =GDPSA t Constant coefficient was not significant. Long run coefficient of GDPSA, marginal propensity to consume, was highly significant. ADF results of the regression model are given below. Residuals of the regression model were not serially correlated (had no autocorrelation) by Breusch-Godfrey Serial Correlation LM Test, monoskedastic by Breusch-Pagan-Godfrey Heteroskedasticity Test and normally distributed by Jarque-Bera probability test. All implies that the regression model X t = 1646 + 0.70Y t + 0.36AR(1) is a good model. Table A4. ADF Results of the Regression Model Variable Coefficient p-value C 1642 0.3744 R 2 0.998221 GDPSA 0.702092 0.0000 Durbin-Watson 986084 AR(1) 0.361712 0.0248 Akaike 38016 F-statistic 0.0000 SHORT RUN MODEL
Correlogram and LB statistics were also used to check for autocorrelation. DEXSA and DGDPSA had no autocorrelation. Null Hypothesis H : DGDPSA is stationary was accepted. Since the two variables were cointegrated, using E-Views we could run Error Correction Model (ECM) to estimate marginal propensity to consume (c). ECM model: ∆X t = b + c∆Y t +d*u t-1 From Table 5 below, ECM short run model is ∆X t = 335 + 0.70∆Y t – 0.64*u t-1 Since the coefficient of error correction term u t-1 was negative (-1< u t-1 < 0) and significant, it validated long run equilibrium relationship between X t and Y t in our linear regression model. In the ECM model constant coefficient was not significant, but short run coefficient of ∆Y t which is marginal propensity to consume was highly significant. Marginal propensity to consume was estimated 0.702157 and approximated to be 0.70 in our study. Table A5. Short Run Model Variable Coefficient p-value C 32745 0.6037 R 2 0.655178 DGDPSA 0.702157 0.0000 Durbin-Watson 951602 U(-1) -0.638101 0.0006 Akaike 42431 F-statistic 0.0000