Article Heterogeneity and cross section dependence in panel data mod...

Heterogeneity exists in cross section studies while time series studies have serial correlation problem. If you choose the sample size carefully or transform the variables to avoid the heterogeneous problem you can minimize the problem. Second generation panel unit root and cointegration tests that take account of possible cross-section dependence in the data have been developed, see the recent surveys by Choi (2006) and Breitung and Pesaran (2007). Perhaps you can follow up on the papers by the papers by Hsiao, Shen, Wang and Weeks, Pedroni and Serlenga and Shin as they attempt to control for heterogeneity for empirical research with panel data methods.

Thank you very much for your answer, Sir. However, "If you choose the sample size carefully or transform the variables to avoid the heterogeneous problem you can minimize the problem" What did you mean? Can you explain it more broadly?

I'll begin by building on the helpful reply of Chung Tin Fah. Analysis of panel or longitudinal data has the potential to take us much closer to being able to identify causal relationships than can analysis of either time-series or cross-sectional data. However, variation in two dimensions also brings potential problems in two dimensions: potentially both serial correlation and heteroskedasticity. Diagnosing and addressing these problems is all too often ignored in panel analysis, even though a range of diagnostic tests is available. This applies even more to cross sectional dependence, which is endemic in panel data but, until fairly recently, tended to be ignored by economists. I assume that you have tested for cross-sectional dependence in the errors and have found it. The first step to address this problem is to specify your model with a complete set of period dummies. If quarterly dummies completely saturate your model - i.e. explain nearly all of the variation in your dependent variable - or (very likely) make the model impossible to estimate, then specify your model with annual dummies. In either case, the effects of period-specific, systematic shocks (i.e. otherwise unmodelled influences affecting all of the banks in your sample at more or less the time) are removed from the error term and put into the estimated part of your model. This should remove - or at least greatly attenuate - cross-sectional dependence. Of course, even if otherwise unmodelled period-specific shocks - e.g. recession - are controlled for by the inclusion of period dummies, it is always possible that the reactions of banks may differ and thus give to complicated patterns of error cross-correlation. However, the degree of cross-correlation should be considerably reduced even if not completely eliminated. You should check this by retesting. One final comment: the effects of period-specific shocks will probably not be confined to particular quarters, in which case, annual dummies should be adequate.

If you still find evidence that your model suffers from error cross correlation even after inclusion of period dummies, then you will will have to make your modelling decisions in accord with trade offs; in this case, there is no uniformly preferred model. For example, the "second generation" cointegration tests - the Common Correlated Effects Mean Group (CCEMG) and Augmented Mean Group (AMG) estimators - in comparison to the MG and PMG estimators have the advantages that they (i) take account of possible cross-section dependence and (ii) yield a cointegrating vector for each group (although the MG approach also does this); but they also have several disadvantages, including (to the best of my knowledge) (i) not allowing for the identification and measurement of error-correction, (ii) not allowing for the identification and measurement of short-run dynamics, and (iii) not allowing potential endogeneity to be addressed. So, my advice as a practitioner is that if you find evidence of cross-group error correlation even after specifying your model with period dummies, then estimate your model using different approaches and compare the results. This robustness checking of your results with respect to estimation approach is good practice in any case.

Finally, on the issue of the use of information criteria and the Hausman test. I suggest that your model selection should always first and foremost be based on model diagnostics, which establish whether or not your model is an adequate description of the statistical generating mechanism giving rise to your data. Then and only then worry about "fit". By all means use the Hausman test to help decide between the MG and PMG approaches; but better might be to decide on theoretical grounds whether or not a single representative long-run equilibrium is reasonable on economic grounds.

I have added a set of lecture notes that might help. See slide 61, in particular.

Thank you very much, Mr. Pugh. Your answers are thin, meticulous and very deep, like a spider's web. Each of your answers has been a guide for researchers. In your answer, you suggested that I should use quarter or annual dummy variables to avoid the problem of cross sectional dependence. In that case, do I have to use my entire dataset annually?

Comparing using CCEMG, AMG, or even DCCE methods can be very convenient. But I have a problem here:

(I) in some of the models I have used, my dependent variable becomes stationary at the level I [0]. Therefore, I am afraid that I will make a mistake because methods such as CCEMG, PMG,MG, AMG and DCCE are based on error correction. Moreover, it is argued that even for the PDOLS method to be used, the dependent variable must be stationary at the I [1] level. In this case, there is a possibility that I can only use the method of GMM, OLS and fixed effects.

I also used time series methods in part of my research. So I used ARDL/NARDL methods. But in some of my models, my dependent variables become stationary at the I[0] level. So I have the same concerns here. Because ARDL / NARDL methods are also based on error correction models such as PMG-ARDL, CCEMG and AMG, I think I can take criticism that dependent variables should be stationary at the I [1] level. I've already started a separate discussion about it. I'll share your link below.

https://www.researchgate.net/post/Is_it_necessary_that_the_dependent_variables_used_in_the_ARDL_NARDL_method_are_stationary_at_the_level_I_1

And thank you, Mr. Pugh, for the document you shared. It's a great resource.

You write: "In your answer, you suggested that I should use quarter or annual dummy variables to avoid the problem of cross sectional dependence. In that case, do I have to use my entire dataset annually?" No. There is no reason why you should not estimate using quarterly data and specify your model with a set of year dummies. In principle, you might prefer quarterly dummies; however, in practice, as I noted, you might find it difficult to estimate an iterative model specified with a full set of quarterly DVs. Specifying with yearly DVs is an acceptable workaround.

Moving on. If your dependent variable is I(0) (i.e. stationary) then any cointegration model is not appropriate. (The wrong tool for the job.) In this case, transform any non-stationary independent variables that are integrated at a higher order into I(0) variables and estimate a dynamic linear regression model. With your relatively large number of quarterly observations, you should get reasonable results from FE estimation, Nickell bias notwithstanding. Maybe try bias-corrected FE estimation as a robustness check. If you follow this procedure, then estimating FE models is (i) methodologically sound and (ii) will avoid a lot of complication. By the way, Difference- and System-GMM estimation is for panels with (very) large N and small T; these approaches are not suitable for your dataset, which has the opposite characteristics (small N and relatively large T).

Thank you so much for your help, Mr. Pugh. The answers you give will be useful not only for me, but also for many people who conduct research on this issue.

Hikmet Akyol Tq for your queries and also the detailed answers provided by Geoffrey Thomas Pugh , which I find interesting, illuminative and educational. By transforming the data, I mean the use of log or ratio to reduce the wide heterogeneity of some variables if you are measuring them. For example per capita GDP is a better measure than GDP or financial ratios in the case of banking statistics might be better than the asset/liabilities figures, if you are measuring banks. The sample size comprises the banks, which you can group them by their size (asset). The use of dummy variables is one way that Geoffrey Thomas Pugh indicated.

Thank you very much, Mr. Tin Fah. I also used the methods you recommended. For example, I first took the Industrial Production Index, representing real activity. When I couldn't get results, I took the natural logarithm of the Industrial Production Index and then the ratio to GDP. When this variable did not solve my problem, I used the natural logarithm of GDP and then the percentage change rates. I used the same thing for banking data. I took Financial rates as variable.

I even used different indicators that represent variables. For example, I used stock returns instead of volatility, representing the individual risks of banks (Laeven et al (2014); Dreyer et al (2018))). But converting some variables was very difficult. For example, I received the SRISK(million dollars) variable from NYU V-Lab, representing systemic risks. The SRISK variable contains very small negative values and very large positive values. Therefore, I could not find any transformation for this variable. The natural logarithm of negative directional variables is not taken. And the percentage change rates are wrong. Getting your cube leads to similar challenges. The worst part is, I have encountered very large coefficients in models where the SRISK variable (million dollars) is the dependent variable. These are also very difficult to interpret.

If cross sectional dependence is detected in a panel, I think conventional estimation techniques like PMG, GMM, FMOLS, become biased, since they do not account for Cross sectional dependence.

Firstly, I think the author should consider using second generation test like that account for cross sectional dependence..

Secondly,, I propose the author should employ the estimation techniques like CCE of Pesaran (2006). If dealing with a static model ,, or the DCCE technique of Chudik and Pesaran (2015) for dynamic model. Another estimation technique that can be considered is the Driscoll-Kraay standard errors approach, which equally account for cross sectional dependence.

Thank you very much for your answer, Mr. Dinga. Pedroni (2001) mean group dynamic least squares method is also useful in the case of cross-sectional dependence.

In response to colleagues urging the use of particular estimation approaches, including "second generation" ones, I emphasise the implications of my April 4th post. Recognise that there are trade-offs involved in your choice of estimator; i.e. each one has both advantages and disadvantages. Accordingly, there is (as far as I know) no universally preferred approach. Instead, consider (i) what you want to achieve and (ii) the properties of your data. For example, if you are not concerned with adjustment mechanisms (e.g. error-correction) and cross-group error correlation persists even when estimating with period dummies, then a second-generation approach may be appropriate. Conversely, if you want to investigate the dynamics of your model and cross-group error correlation can be addressed by period dummies, then mean group or pooled mean group estimation may be preferable. In all cases, use alternative approaches to robustness check your estimates.

Thank you, Mr. Pugh, for your answer. As you have stated, Although there are common uses, it is impossible to use a universally valid method. What is important is the purpose of the researcher and the nature of the data he used. Third, keep our prejudices under control. These three factors prevent researchers from proposing a universal method. Therefore, it would be more accurate to use estimators that accurately serve our purpose and match the property of the data we have. In doing so, we need to accurately calculate what the advantages and disadvantages of the methods we use are.

Another aspect here is that we researchers sometimes focus more on the econometric methods we use than on the nature of the data. In fact, sometimes focusing on data transformations can make the path to our goal easier.

Hello ,

can we use cross section data (Questionnaire data - primary data ) by applying ARDL model ? if possible how it ?

regards

Hikmet Akyol I hope now you have finished your research. I know that we have to do a cross-sectional dependence test before even unit root test because while first-generation unit root tests assume cross-sectional independence the second generation considers cross-sectional dependence. Once cross-sectional dependence is found, given the nature of stationarity is it is for ARDL, there will be a model considering the cross-sectional dependence in the error terms developed by Chudik, Mohaddes, Pesaran, and Raissi.

My question is which method of cross-sectional dependence test did you use?

if the dataset is is in such a way that N >T one shall use Pesaran CD test, if N

Hi Tasfaye , to test cross section dependence of a panel data in stata I used the command: xtcd 'variable name' for my study, if the p-value of Pesaran 2004 CD test is less than 0.05 your data is cross sectionally dependent.

Hope I'm on the right path, and you get a convenient answer.