Memento on Eviews output - Jonathan Benchimol

1 Memento on Eviews output Jonathan BenchimolyThis version: January 22, 2020 First version: February 10, 2008 AbstractRunning a simple regression in Eviews requires to satisfy several hypothe-ses. This paper explains Eviews outputs and results from standard econo-metric procedures. Simple examples and estimations are detailed to avoidspurious econometric interpretations, unfortunately, frequent in economic :stationarity, spurious regression, robustness, identi Classi cation:C13, C22, cite this paper as: Benchimol , J., 2020. Memento on Eviews output . Mimeo available This paper does not necessarily re ect the views of the Bank of Israel. I thank Michael Bell,Itamar Caspi, Guillaume Chevillon, Andr Four ans, and Ben Schreiber for their of Israel, Jerusalem, Israel. Email: IntroductionThis Memento intends to become a useful guide for Eviews users. It has beenused by researchers in various elds such as in Economics (Bong and Premaratne,2018), Operating and Maintenance (Chia, 2010), Finance (Bekale, 2015), and En-ergy (Bakhtiari et al.)

2 , 2015). Although incomplete, this paper is bene cial tounderstand fundamental econometric concepts and avoid spurious regressions Ordinary Least SquaresThe Ordinary Least Squares (OLS) method is one of the most used estimation tech-niques, both in research and industry. This linear least-squares method estimatesthe unknown parameters in a linear regression model: it chooses the parametersof a linear function of a set of explanatory variables by minimizing the sum of thesquares of the di erences between the observed dependent variable1in the givendataset and those predicted by the linear starting coding or writing, always ask this question: which research ques-tion do I want to answer? If the objective is to understand the connection andcausalities betweenxtandyt, which are two economic variables, the correspondingdata (time series) have to be available for your instance, how energy and consumer prices are related?

3 To answer this,we have to select the relevant data corresponding to the research question. Wechoose the Domestic Producer Prices Index (Manufacturing) for Israel (xt) and theConsumer Price Index Energy for Israel (yt) to analyze this analysesspan from August 1997 to May 2017, at a monthly StationarityIn order to use stationary time series without a ecting our results by seasonale ects, we compute the percentage growth of these two seasonally-adjusted3timeseries,dxtanddyt . Table 1 presents the stationarity tests based on Dickey andFuller (1979).Table 1 shows that our time series,dxtanddyt, are stationary. This propertyisessential4for OLS estimation, as we will see of the variable being includes electricity, gas and other fuels & fuels and lubricants for personal transportequipment. It excludes water. Energy is % of the CPI all items in adjust for seasonality by using X12-ARIMA(0,1,1).

4 4 Stationarity is even anecessarycondition for a non cointegration Root TestsNull Hypothesis:dxthas a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag=14)t-Statistic Prob.*Augmented Dickey-Fuller test critical values:1% *MacKinnon (1996) one-sided Dickey-Fuller Test EquationDependent Variable: (dxt)Method: Least SquaresSample (adjusted): 1997M10 2017M05 Included observations: 236 after adjustmentsVariableCoe cient Std. Error t-Statistic Mean dependent var R-squared dependent of Akaike info squared Schwarz Hannan-Quinn criter. Durbin-Watson (F-statistic) Hypothesis:dythas a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag=14)t-Statistic Prob.*Augmented Dickey-Fuller test critical values:1% *MacKinnon (1996) one-sided Dickey-Fuller Test EquationDependent Variable: (dyt)Method: Least SquaresSample (adjusted): 1997M10 2017M05 Included observations: 236 after adjustmentsVariableCoe cient Std.

5 Error t-Statistic Mean dependent var R-squared dependent of Akaike info squared Schwarz Hannan-Quinn criter. Durbin-Watson (F-statistic) : Augmented Dickey-Fuller unit root tests ( , stationarity tests) fordxt(left panel) anddyt(right panel). CausalityA pairwise Granger (1969) causality test is presented in Table 2 and shows thatwe cannot reject the hypothesis thatdytdoes not Granger causedxtbut we doreject the hypothesis thatdxtdoes not Granger causedyt. Therefore it appearsthat Granger causality runs one-way fromdxttodytand not the other CausalityLags: 2 Null Hypothesis:Obs F-Statistic not Granger Causedxt235 not Granger : Pairwise Granger causality tests other but more precise words, Table 2 shows thatdxtstatistically CorrelogramTable 3 presents the correlograms ofdxtanddyt. The autocorrelation of the seriesdxtis not very big at lag one, and quasi inexistent in the next lags.

6 The partialautocorrelation of the seriesdxtis quasi inexistent. However, the Ljung and Box(1978) Q-statistics and their p-values show that the series contains some autocor-relation at several orders. This correlogram could motivate the use of an AR(1)component to the next estimations, includingdxtas the variable to 3 shows there is no autocorrelation nor partial autocorrelation for and partial correlationIncluded observations: 237 Autocorrelation Partial CorrelationAC PAC Q-Stat ** **j1 * * * *j9 * * * *j18 * * * * * observations: 237 Autocorrelation Partial CorrelationAC PAC Q-Stat * *j1 * * * * * *j22 * * * : autocorrelation and partial correlation fordxt(left panel) anddyt(right panel).

7 Linear EstimationAssuming that related assumptions concerning the OLS regression are veri ed, theresults presented in Table 4 show a signi cant relationship betweendxtanddyt,with a good coe cient of determination5(Adjusted R2 around ) and withoutautocorrelation of order Energy: EstimationDependent Variable:dytMethod: Least SquaresSample (adjusted): 1997M09 2017M05 Included observations: 237 after adjustmentsVariableCoe cient Std. Error t-Statistic Mean dependent var R-squared dependent of Akaike info criterion squared Schwarz Hannan-Quinn criter. Durbin-Watson (F-statistic) : estimation ValidationOur OLS regression satis es all the linear regression assumptions presented belowand is signi cant according to statistics examined about the regression (AdjustedR2, Durbin-Watson, t-stat/p-values) as well as about the residuals (cf.)

8 Above).5 The coe cient of determination is explained in Section Durbin and Watson (1950, 1951, 1971) test is close to of Residuals051015202530-5-4-3-2-101234 Series: ResidualsSample 1997M09 2017M05 Observations 237 Mean Dev. : the skewness measures the asymmetry of the distribution relative to theaverage. While it di erentiates extreme values in one versus the other tail, kurtosismeasures extreme values in either Strict Exogeneity and Normality of the ResidualsFig. 1 shows that residuals are normally distributed with a quasi-zero Jarque-Bera test con rms residuals skewness and kurtosis match a Linear DependenceAccording to a simple cross-correlation between the two series (Table 5), there isno collinearity between our HomoscedasticityThere is no heteroscedasticity according to several heteroscedasticity tests presentedin Table AutocorrelationAccording to a correlogram of the residuals, there is no autocorrelation for all lagsconsidered.

9 This is also the case when testing the square of the residuals (notdisplayed).7 Table Cross-correlationsdxt,dyt idxt,dyt+ ** **j0 ** **j1 *j2 * : simple cross-correlation betweendxtanddyt. Correlations are asymptoticallyconsistent Generalized Method of MomentsThe starting point of the Generalized Method of Moments (GMM) estimation isa theoretical relation that the parameters should satisfy. The idea is to choosethe parameter estimates so that the theoretical relation is satis ed as closely aspossible. Its sample counterpart replaces the theoretical relation, and the estimatesare chosen to minimize the weighted distance between the theoretical and actualvalues. GMM is a robust estimator in that, unlike maximum likelihood estimation,it does not require information about the exact distribution of the disturbances. Infact, many common estimators in econometrics can be considered as special casesof theoretical relation that the parameters should satisfy are usuallyorthog-onality conditionsbetween some (possibly nonlinear) function of the parametersf( )and a set of instrumental variableszt:E f( )0Z = 0(1)where are the parameters to be estimated.

10 The GMM estimator selects parameterestimates so that the sample correlations between the instruments and the functionfare as close to zero as possible, as de ned by the criterion function:J( ) = (m( ))0Am( )(2)wherem( ) =f( )0 ZandAis a weighting TestsHeteroskedasticity Test: Breusch-Pagan-GodfreyHeteroskedasticity Test: HarveyHeteroskedasticity Test: Prob. F(1,235) Prob. F(1,235) Prob. F(1,234) * Prob. Chi-Square(1) * Prob. Chi-Square(1) * Prob. Chi-Square(1) explained SS Prob. Chi-Square(1) explained SS Prob. Chi-Square(1) Equation:Test Equation:Test Equation:Dependent Variable: RESID^2 Dependent Variable: LRESID2 Dependent Variable: RESID^2 Method: Least SquaresMethod: Least SquaresMethod: Least SquaresSample: 1997M09 2017M05 Sample: 1997M09 2017M05 Sample (adjusted): 1997M10 2017M05 Included observations: 237 Included observations: 237 Included observations: 236 after adjustmentsVariableCoe cient Std.