Hi Thao.

I do a lot of work with panel data and I have been in your situation. I also use GRETL.

My opinion: you have strong evidence that Pooled OLS should not be employed. According to Wooldridge (2010), pooled OLS is employed when you select a different sample for each year/month/period of the panel data. Fixed effects or random effects are employed when you are going to observe the same sample of individuals/countries/states/cities/etc. If the tests showed that pooled ols is inadequate, I infer you are observing the same sample along different periods of time.

In both the fixed effects and the random effects in the docx you posted, the R-squared of the models is so low. Again, according to Wooldridge (2010), in chapters 13 and 14, it is important to include dummy variables for each studied year/period you are observing. The effects of time (my teacher once said: "the inertia of the time passage") are really strong.

If you are not observing the same sample through time, you can try adding these time dummies to pooled ols and aplying Breusch-Pagan and F-test again. Maybe then the model will pass these tests and keep the relevant variables significant while also geting a higher R-squared. I know R-squared is not a very important statistic, but it can be used as a clue for where are the problems in the models.

If you are using the same sample along all periods, than your results are correct by now and Fixed or Random effects models are recommended. But you should execute Hausman test on the data to see which of the is the right one. If p-value is higher than 0,05, than you do not reject nule hypotesis: random effects. If p-value is low, tha you can reject the nule hypotesis and assume the data follows a fixed effects model. You will then know for sure which of them is right even if the varibles are not significant: you can calibrate the model incluiding another variables. I also advise you again to include the dummies of period and Hausman-test the dummies model again.

Brief summary of my answer to you - what to do?

1- Are you observing the same sample along different period of time?

If you do, that's why pooled ols is not working. The fixed or random effect models are probably correct. Their R-squared is very low, so you can include variables or dummies of time to correct heteroskedacity or innertial effects that are at play.

If you don't (which means you are using different samples along each periods), include the dummies of time and test for Breusch Pagan and F again. Probably, the significant variables will remain significant and the model with dummies will pass the tests.

2- If you are using the same sample along all periods, use Hausman test to verify if fixed or random effects are to be used as a model. Nule hypotesis: random effects. Alternative hypotesis: fixed effects. For p-value > 0,05: random effects. Test it with and without time dummies and see the results. See if the relevant variables are significant or not.

3- If none of it helped: see if there are no relevant variables being ignored, check if there are no heteroskedacity factors (as spatial correlation in the variables, for example). The book I mentioned if "Introductory Econometrics: A Modern Approach" by Jeffrey M. Wooldridge, published in 2012. It is very easy to find it in internet.

This video explains how to chose between Pooled, FE and RE, also shows how to apply Hausman test: https://vimeo.com/150635443

Sorry for: the lenght of this explanation and eventual problems with my english.

I hope this is useful for you. Best wishes with your research.

You need to describe what you are trying to estimate. What is your dataset? What is the question you are trying to answer?

Hi Thao.

I do a lot of work with panel data and I have been in your situation. I also use GRETL.

My opinion: you have strong evidence that Pooled OLS should not be employed. According to Wooldridge (2010), pooled OLS is employed when you select a different sample for each year/month/period of the panel data. Fixed effects or random effects are employed when you are going to observe the same sample of individuals/countries/states/cities/etc. If the tests showed that pooled ols is inadequate, I infer you are observing the same sample along different periods of time.

In both the fixed effects and the random effects in the docx you posted, the R-squared of the models is so low. Again, according to Wooldridge (2010), in chapters 13 and 14, it is important to include dummy variables for each studied year/period you are observing. The effects of time (my teacher once said: "the inertia of the time passage") are really strong.

If you are not observing the same sample through time, you can try adding these time dummies to pooled ols and aplying Breusch-Pagan and F-test again. Maybe then the model will pass these tests and keep the relevant variables significant while also geting a higher R-squared. I know R-squared is not a very important statistic, but it can be used as a clue for where are the problems in the models.

If you are using the same sample along all periods, than your results are correct by now and Fixed or Random effects models are recommended. But you should execute Hausman test on the data to see which of the is the right one. If p-value is higher than 0,05, than you do not reject nule hypotesis: random effects. If p-value is low, tha you can reject the nule hypotesis and assume the data follows a fixed effects model. You will then know for sure which of them is right even if the varibles are not significant: you can calibrate the model incluiding another variables. I also advise you again to include the dummies of period and Hausman-test the dummies model again.

Brief summary of my answer to you - what to do?

1- Are you observing the same sample along different period of time?

If you do, that's why pooled ols is not working. The fixed or random effect models are probably correct. Their R-squared is very low, so you can include variables or dummies of time to correct heteroskedacity or innertial effects that are at play.

If you don't (which means you are using different samples along each periods), include the dummies of time and test for Breusch Pagan and F again. Probably, the significant variables will remain significant and the model with dummies will pass the tests.

2- If you are using the same sample along all periods, use Hausman test to verify if fixed or random effects are to be used as a model. Nule hypotesis: random effects. Alternative hypotesis: fixed effects. For p-value > 0,05: random effects. Test it with and without time dummies and see the results. See if the relevant variables are significant or not.

3- If none of it helped: see if there are no relevant variables being ignored, check if there are no heteroskedacity factors (as spatial correlation in the variables, for example). The book I mentioned if "Introductory Econometrics: A Modern Approach" by Jeffrey M. Wooldridge, published in 2012. It is very easy to find it in internet.

This video explains how to chose between Pooled, FE and RE, also shows how to apply Hausman test: https://vimeo.com/150635443

Sorry for: the lenght of this explanation and eventual problems with my english.

I hope this is useful for you. Best wishes with your research.

Dear Thao,

Please check following:

1. The appropriateness of the choice of method considering the number of cross-section and Time in your data set.

2. If yes, you need to use Hausman test as well as BP Lagrange Multiplier test to choose the right method.

3. If you have selected the right method and not getting significant results, then it is your finding and contribution.

4. However, if you are interested in getting the significant results, i suggest using different proxies and measurements of your variables.

Hope it helps.

Best wishes,

Atif

Thank all for your supports,

My goal is to explore the effects of Budget Deficit, GDP, Effective Interest Rate and Exchange Rate on the Public Debt related to the South East Asia (SEA) and the East Asia (EA) countries. The data of 10 SEA and 5 EA countries during 2007-2017 are collected. I notice that when applying the mentioned models for only 10 SEA countries, the REM model is the best (Hausman test has been performed) and all variables are statistical significance. However, when I insert only one EA country, in particular Japan, to the current data, the result now has no significance. I also notice that the pairwise correlation between variables of SEA are different from EA countries.

If you believe that these variables are sufficient in explaining the Public Debt, then you can use random effects. In this case, your model will be probably explaining mainly variation across countries.

However, if you believe that there are some unobservable factors (which is usually the case) that are influencing Public Debt, then you should use fixed effects. In this case, variation across countries will be explained by fixed effects, and your estimated coefficient will have the following interpretation:

"For a given country, how much will public debt increase if the explanatory variabe increases by one unit?"

Hi Thao,

Something you said called my attention: when Japan is included, the significance of variables is changed.

Although REM model is very less likely to present heteroskedacity (because it is a specific type of Generalized Least Square method, which is used to address heteroskedacity when it is known), it seems like you face spatial correlation here.

Your variables are correlated to where the countries are located, and this effect must be addressed by the model. Othewise, this effect will be in the unknown factors and there will be correlation between variables and unknown factors and the hypotesis of zero conditional mean will be violated: not only significance will be affected, but also you estatistic will be biased.

To me, the easiest way of addressing it is including a dummy variable of space: EA = 1 for countries in East Asia and = 0 otherwise, for example.

Self and Grabowski (2006) once tried a simple OLS with 75 countries and agricultural and macroeconomic variables. To address the heteroskedacity, they used 3 dummies representing each continent: SSA for Subsaharian Africa, LAT for Latin America and ASIA for Asian countries. When all these 3 dummies are zero, the country in question belongs to other continent, such as Europe or Oceania.

Pay attention to multicolinearity while using dummies, okay?

Self and Grabowski reference paper: Economic Development and the Role of Agricultural Technology, 2006.

Seems like I'm obsessed with dummies, hahahaha.

Thanks for your attention and best luck with your research,

Bruna.