SERIAL CORRELATION. In Panel data. Chapter 5(Econometrics Analysis of Panel data -Baltagi) Shima Goudarzi

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1 SERIAL CORRELATION In Panel data Chapter 5(Econometrics Analysis of Panel data -Baltagi) Shima Goudarzi

2 As We assumed the stndard model: and (No Matter how far t is from s) The regression disturbances are homoscedastic with the same variance across time and individuals. 2

3 This assumption cannot be always true For example in Investment, Consumption a shock affects the behavioral relationship for at least the next few periods. Using the routine solution results in: consistent but inefficient estimates of regression coefficients and biased standard errors. 3

4 Serial Auto regression AR(1) in ν it (Willis- Lillard 1978) They generalized the error component model to the serially correlated case, by assuming that lρl<1 4

5 Baltagi and Li (1991) applied the Prais-Winstten transformation matrix,to transform disturbances into serially uncorrelated classical errors. 5

6 First step :They suggest estimating from Within esiduals it as : -for large T -for small T 6

7 Second step: Estimating, by substituting OLS residuals in this equation: Then, Estimating and From Where 7

8 Empirical Application AR(1) Lillardand Weiss(1979) used the panel earnings data on American scientists over the decade to analyze the covariance structure of earnings over time. Ln Y it = X it β+ U it Y it : real annual earnings of the i th person in the t th year x : dependent variables like,experience,gender, employment in private industry. 8

9 μ i Represents unmeasured characteristics such as ability and work on the relative earning of scientists (individual effects). Represents the effect of omitted variables which affect the growth of earning like learning ability. Transitory but serially correlated differences, represents the rate of deterioration of the effect of random shock ε it on which persists over a year. 9

10 They used the Maximum likelihood to estimate the parameters of the residual and then applied GLS to estimates β. By comparing the actual and predicted covariances, we see that their specification is quite successful in predicting the pattern. 10

11 Serial Auto regression AR(2) in νit The transformation can allow also for AR(2) process on the ν it where 11

12 The matrix C defined The first step is transforming the data by the C Matrix And then obtain GLS on model by computing. 12

13 Unequally Spaced Panels with AR(1) Disturbances (Baltagi 1991) Sometimes panels cannot be collected every period due to lack of resources or cut in data. Panel daily data from stock market that is unequally spaced when the market closes on holidays. Housing resale data when the pattern of resale for each house occurs at different time periods. In this paper Baltagi and Wu tried to estimate an unequally spaced panel data regression model with Random effect and AR(1)disturbances. 13

14 Random Effect(GLS) Random Effect GLS with AR(1) β1 0.11(0.011) 0.095(0.008) β (0.017) 0.32(0.026) 14

15 Random Effect and AR(1) and locally best invariant test(lbi - The Baltagi Wu LBI statistics: Durbin-Watson for :

16 Jointly test of Serial Correlation and Individual Effects Remainder disturbances AR(1) process or MA(1) process 16

17 Other extensions include Extensions The fixed effect model with MA(q)Remainder disturbances and also the treatment of Autoregressive moving average ARMA(p,q) case on the ν it. Extension to the two-way model with serially correlated disturbances Chamberlain (1982, 1984) allows for arbitrary serial correlation and heteroskedastic patterns by viewing each time period as an equation and treating the panel as a multivariate. 17

18 Refrences: -Becketti, S.,W. Gould, L. Lillard and F.Welch, 1988, The panel study of income dynamics after fourteen years: An evaluation, Journal of Labor Economics 6, Berry, S., P. Gottschalk and D. Wissoker, 1988, An error components model of the impact of plant closing on earnings, Review of Economics and Statistics 70, Baltagi, B.H. and Q. Li, 1995, Testing AR(1) against MA(1) disturbances in an error component model, Journal of Econometrics 68, Econometric Analysis of Panel Data, 4th Edition,Badi H.Baltagi,2008,Wiley - 18

Econometrics. Week 4. Fall Institute of Economic Studies Faculty of Social Sciences Charles University in Prague

Econometrics. Week 4. Fall Institute of Economic Studies Faculty of Social Sciences Charles University in Prague Econometrics Week 4 Institute of Economic Studies Faculty of Social Sciences Charles University in Prague Fall 2012 1 / 23 Recommended Reading For the today Serial correlation and heteroskedasticity in