Test for Autocorrelation and Time lagged variables

[John Marburg]

Hello i ve got following questions..


1. Is there a test for autocorrelation that fits with pooled ols and fixed effect model? Concrete, I’ve got the following two regressions:


reg TobinsQ SumHoldingsPct DebtTotalAssets RD Marketcap Dividend SalesGrowth QuickRatio ResidualsSumHoldingsPct i.year i.industry i.country, robust cluster(industry)

xtreg TobinsQ SumHoldingsPct DebtTotalAssets RD Marketcap Dividend SalesGrowth QuickRatio ResidualsSumHoldingsPct i.year i.industry i.country, robust fe




Using the Durbin Watson dwstat i get the following error massage.

"sample may not include multiple panels"




2. I also want to use a one timeperiod lagged dependent variable as additional dependent variable to reduce the autocorrelation.

Can this lead to wrong results and are there further things to check when using time lagged variables? or is my model suitable?

reg TobinsQ laggedtobinsq SumHoldingsPct DebtTotalAssets RD Marketcap Dividend SalesGrowth QuickRatio ResidualsSumHoldingsPct i.year i.industry i.country, robust cluster(industry)

xtreg TobinsQ laggedtobinsq SumHoldingsPct DebtTotalAssets RD Marketcap Dividend SalesGrowth QuickRatio ResidualsSumHoldingsPct i.year i.industry i.country, robust fe

[Joro Kolev]

1. You can test for autocorrelation
a) In pooled OLS by generating the residuals, including the lagged residuals, and testing that their coefficient is 0.
b) In fixed effects model, by running the firsts differenced regression, generating the residuals, then regressing the residuals on the lagged residuals and testing whether the autoregressive coefficients is -0.5 (see Wooldridge 2010, p.320).

2. Including lagged dependent variable makes everything more complicated, as this is a dynamic panel data model. The simplest estimator is the Anderson and Hsiao (1982).
More complicated estimators are implemented in -xtabond -- Arellano-Bond linear dynamic panel-data estimation- and are due to the mentioned authors.

[John Marburg]

Hello Joro, thank you for your multiple responses, which help me a lot.

I now tried the xtbond approach and if got some question. Maybe i should mention that my sample size is about 16000 observations including 4 countries over 20 years. My goal is therby to exaime relationship between instiutional owenship with sumholdingpct and TobinsQ .

my command is the following:

xtabond2 TobinsQ l.TobinsQ SumHoldingsPct Marketcap Dividend DebtTotalAssets QuickRatio SalesGrowth i.country i.year i.industry , gmm(TobinsQ SumHoldingsPct Marketcap Dividend QuickRatio SalesGrowth DebtTotalAssets i.industry, lag(2 4)collapse) iv(i.country i.year) twostep robust

Regarding literature i applied lag of 2 4. My results than only indicate significant relation only between Tobins Q l.TobinsQ if i omit l.TobinsQ. only market cap becomes significant. This result stands also if i change the time lags to (1 1) or (1 2 )
My results from Pooled OLS and fixed Effect models on the other side indicate relation between TobinsQ and most of the independent variables.

1. Now i am confused if i can trust this model and would be very glad for a response to evaluate if this method is appropriate ?

2. With xtbond and firm as group variable firm fixed effects are included?

3. I also read that i should evaluate only Ar2 and Hansen test results for model justification?

Group variable: firm Number of obs = 3505
Time variable : year Number of groups = 675
Number of instruments = 80 Obs per group: min = 1
Wald chi2(40) = 303.91 avg = 5.19
Prob > chi2 = 0.000 max = 19
---------------------------------------------------------------------------------
| Corrected
TobinsQ | . Coef. . Std Err z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------


L1 TobinsQ | | .4207326 .1152533 3.65 0.000 .1948402 .6466249

SumHoldingsPct | -.0040481 .0083311 -0.49 0.627 -.0203768 .0122805
Marketcap | .3248701 .2311921 1.41 0.160 -.1282581 .7779982
Dividend | 4.123281 4.729168 0.87 0.383 -5.145718 13.39228
DebtTotalAssets | .4059516 .9240692 0.44 0.660 -1.405191 2.217094
QuickRatio | -.0044627 .0997533 -0.04 0.964 -.1999756 .1910501
SalesGrowth | -.0783596 .1378419 -0.57 0.570 -.3485248 .1918056

------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -3.09 Pr > z = 0.002
Arellano-Bond test for AR(2) in first differences: z = 0.28 Pr > z = 0.777
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(39) = 116.20 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(39) = 30.47 Prob > chi2 = 0.834
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(32) = 25.11 Prob > chi2 = 0.802
Difference (null H = exogenous): chi2(7) = 5.36 Prob > chi2 = 0.617