Presentation on theme: "presented by Dipl. Volkswirt Gerhard Kling"— Presentation transcript:
1presented by Dipl. Volkswirt Gerhard Kling A short introduction to applied econometrics Part D: Panel Data Analysispresented byDipl. Volkswirt Gerhard Kling
2Advantages of panel analysis More observationsMore degrees offreedomReducedmulticollinearityPooling of cross sectional and time series dataEspecially a problem in distributed lag modelStems from more observations Improved efficiency (unbiased estimator with smallest variance for all possible true parameter values)
3Advantages of panel analysis Wider range ofproblemsCausalitydiscussionDynamics of change e.g. labor market participationTime structure facilitates discussionyou can test new hypothesis on individual behavior or policy changes that affect several entities
4The importance of the data structure Example: 11 countries over 10 yearsGeneral note: cross-sectional dimension should be larger than time dimensionBut: many new models currently developedVery fertile field for research!I prefer the following data structure
5The importance of the data structure First cross-sectional unitTime dimensionmissing
6Pooled regression Combine both dimensions in one data set Neglect time and cross-sectional structureRun following regression with POLS/SOLSThereby, i...countries, t...years
8AutocorrelationNow time dimension; hence, correlation among successive residuals possibleThis affects t and p-values – violates assumption E(eiteit-j)=0 for all j0How can we test for this problem?What can we do if we detect autocorrelation?
9Autocorrelation Stata should know that the data set is a panel Command: tsset (i) yearnote: i=cross-sectionNormal test commands for autocorrelation do not work; hence, develop own test (several procedures!)
10Test for Autocorrelation Run the following regression and estimate residualsInsert lagged residuals in regressionRun t-test for autocorrelation coefficientH0: =0 – if rejected autocorrelationNote: AR(1) and assumption of strict exogenity!
11Hint: Construction of Lags with Panel Data After regress command – predict r, residThen construct lagged residual– gen r1=r[_n-1]Problem: Panel structure; thus, replace lagged values for first year (1990 in our case) – replace r1=. if year==1990Note: t-value reaches 4.62!
12Robust Estimation Procedure We estimate a so called long-run variance using the Newey-West (1987) procedureEstimation of variance-covariance matrix is now robust against heteroscedasticity and autocorrelationCommand: newey2 gdp pop sav, lag(5)Number of lags = truncation (can be determined!)
13Robust Estimation Procedure Note: point estimates are the same!
14GLS Estimation Procedure Make assumptions regarding heteroscedasticity and autocorrelationNote: often called FGLS – feasible!Command: xtgls – then different specifications possibleCan also be used to test for specific heteroscedasticity using log-likelihood ratio testsNote: If structure too complicated – loss of degrees of freedom!
16Pitfalls of GLSSpecification of form of autocorrelation and heteroscedasticity importantIf specification bad – estimates are biasedGeneral: I would prefer this procedure for larger samples because more parameters need to be estimatedCan be used to test for instance panel-level heteroscedasticity!
17Fixed Effects Regression Assumption: partial impact (slope) stays constant over time and across countriesDifferent methodsInsert time dummies into regressionInsert dummies for cross-sectional unitsInsert both types of dummiesNote: Sometimes dummies are not reported if too many!
19Fixed Effects Regression: Joint F-tests indicate that neither time nor country dummies are relevantBut: For a few countries dummies might be usedGeneral: You have to estimate lots of additional coefficientsBut: Widely applied and easy to interpretNote: Time dummies do not eliminate problems that may arise from stochastic trends!
20Random Effects Regression We assume the following regressionIndividual effects are randomEstimation with GLS or maximum likelihood procedureAfter estimation: Breusch-Pagan (1980) test or likelihood ratio test whether random effects should be assumed
22Which Procedure should we use? Neither fixed nor random effects are superiorLittle evidence that individual effects matterHence: stick to POLS/SOLS pooled regressionMaybe: use dummies for extreme countriesCheck stability of coefficients over time (goes beyond the scope of the course!)
23The Causality IssueNote: We assume that current saving rate and population growth rate affect GDP growth rateBut: Possible that causality goes the other way round!Solution: VAR model – test for Granger causalityResult: Savings and population growth rate Granger cause GDP growth rate and not vice versa!
24Additional Issues Stochastic trends in panel data Spurious regressionsUnit-root tests – panel based; thus, more observationsFirst differencing or deviation from common trendsLong-term equilibriums and cointegration