Use panel data

Yes! Panel Data is more appropriate method.

thank you for your response,

I'm familiar with panel data econometric, but one of my goal in this project is obtaining coefficients and significance for each variable in each cross-section that is not possible in standard fixed and random effect models.

What is your N and T size

Dear Yasmine,

thank you for your response.

N------> 30

T-------->8

You say:

"I want to obtain coefficients and significance for each variable in each cross-section that is not possible in standard fixed and random effect models"

I think this is possible - think about the LSDV panel specification with interaction terms:

y=b0+b1*x+c2*d2+...+c2*d30+ m2*(d2*x) +...+m30(d30*x)+u

Interaction terms will give you "premiums" to the marginal effect b1 for each cross-sectional unit 2,...,30 as compared to unit1 - and t-tests for significance of these premiums.

If you estimate 30 equations to get 30 different coefficents for each IV with only T=8 datapoints, most likely you will not have any significant effects.

Hoping this will help.

What is your research about and what do you want to achieve?

Rethink your problem as estimating a single regression with eight data points and then combining across 30 regressions. Practically OLS estimates are asymptotic and eight points are too few. Even if you discovered parameters that were statistically significant, I would not believe the test statistics. You need cross-equation restrictions. Njuguna asks the correct question: What is the research question?

If I understand the question correctly, what you want to achieve is to generate a robust standard error estimator so as to do statistical tests. The first thing to know is that cross-sectional dependence will not lead to biased estimation of the coefficient itself. However, traditional estimator of standard error can be biased. For cross-sectional data, we could use the White standard error to adjust for this problem. And the corresponding estimator for panel data is Newey-West standard error.

I hope this would help.

my research question is

1) is variable X significance affecting factor for Y?

-------> hypothesis

2) If it's so, are coefficients differ from one cross-section to another?

I'm thinking about estimating the below equation:

Y=a+bX+cX2+ control variables

if I estimate standard fixed or random effect, I will know a general status of the presence of my hypothesis and shape of it.

at the second stage, I wanna know the presence and shape of the hypothesis in each cross-section.

If I had enough time series data for all variables, could simply estimate the separate equation using time series econometric, but unfortunately I don't have.

in one case, I studied bootstrap panel Granger causality approach that made it possible to the estimation of the coefficients of X (not x2 and control variables) for each cross-section.

I want to know is it possible to get coefficients and their significance level for all of the variables of the equation in each cross-section or not?

If YES, which model is suitable?

If your concern is whether the coefficients differ from one cross-section to another - If I get you correctly - you want to test whether the cross sections are homogenous or not then I believe this can be determine when you do a "poolability test" that is if you accept Ho that intercept coefficients are not different then you can simply used pooled panel data model. And if you reject then the variable intercept is your alternative. Somebody suggested that if you are interested with all the coefficients then you can estimate LSDV if coefficients are found to be different. Please check the consistency requirements whether as N goes to infinity the estimates are consistent as suggested by William.

Use panel dynamic GMM estimator as your T is small. Check https://www.researchgate.net/post/What_is_the_syntax_for_Xtabond2

T=8 and N=30 - this makes 240 panel observations, which allows you to "sacrify" 60 degrees of freedom in order to estimate LSDV with interaction terms (which I have suggested 3 days ago). You can inform yourself about this matter, for example, from J.Wooldridge (Introduction to Econometrics), the chapter about "Interactions Involving Dummy Variables", difference in slopes. You want to see slope coefficients for 30 cross-sectional units - that would be possible if you explicitly estimate them - one for the reference units, combined with a "premium" parameter for each other unit that you add to the base parmeter .

If somehow you can define an ordering on the the set of your N individual variables, you can define Lags so you can use cross-section type regression otherwise panel data would be more appropriate. however, more generally I will suggest you to plot the error term of your regression and track the trend and heterogeneity in both first and second conditional moments and get some hint regarding the adequacy of your model. you might need to detrend and dememorize your variables prior to any statistical inference.

You can use Cross Correlated Effects Models that take into account cross sectional dependence. If you want to see different coefficients do a Random Coefficient Model with cross correlated effects. Check Swamy Random Coefficient Model and Hsiao Random Coefficient Model for two-level panel data. Also, there is for three level panel data in the Book the Econometrics of Multidimensional Panel Data

Dear Ehasan

Have a look on it, especially methodological part.

I explained your question in detail.

Hope it will work.

Good luck

https://www.researchgate.net/publication/322635350_The_European_union%27s_technological_and_economic_growth_A_study_of_renewable_energy

You have T=8 and N=30. So, if you run cross-sectional regressions, you have 8 regressions using only 30 observations per regression. The first problem you are likely to encounter is loss of degrees of freedom. Similarly, with a panel of 240 observations, I do not understand your intuition of wanting to run cross-sectional regressions whereas a panel regression would be a better use of your data since it accounts for heterogeneity in the N units.