(Stata13): How to Interpret GMM Output

[@CrunchEconometrix]

Beloved guest/subscriber, you have discovered my amazing KZbin Channel tailored specifically for you and other beginners and intermediate users. Please do not keep me to yourself (lol). Kindly share my videos and links with your students, colleagues and academic community so that they too can SUBSCRIBE and learn with ease….and for the global community to be aware that applied econometrics can be simplified. My teaching approach is very practical. I adopt a do-as-I-do style. Many thanks to those who have supported me by telling others. Once again, CrunchEconometrix loves to teach, support my Channel with your subscription, likes, feedbacks and sharing my videos with your cohorts. Follow me on Facebook, Twitter and Reddit. Love you all, greatly!!!😍

[@purnachandrapadhan8734]

Very nice lecture... Thanks you very much Mam... Look forward to watch more from you... Thanks fro sharing this knowledge...

[@CrunchEconometrix]

Thanks for the encouraging feedback, Purna. Deeply appreciated! Please may I know from where (location) you are reaching me?

[@purnachandrapadhan8734]

I am from India

[@salmilou]

Hello, I have a short panel model that I used PANEL GMM. I found the value of the lagged dependent variable coefficient to be 0.24 when estimating Diff GMM with Lag 1 for all variables. However, its value is 0.22 in OLS and 0.13 in the fixed-effects model. Did I use Diff GMM or Sys GMM? Please help. Note: I did not use the command xtanond2.

[@CrunchEconometrix]

Hi Sal, kindly watch my video on "Deciding between DIFF and SYSTEM GMM". You will find it helpful. Thanks.

[@barnonamondol5032]

Thank you for your video. Can you please answer me that the 5.09 minutes of the video when you presented the values of the variable on the table, are those values are coefficients ? or the p>t value ?

[@CrunchEconometrix]

Barnona, please refer to the Stata output to confirm this.

[@tsehayzeleke9743]

i am doing my thesis paper on minerals and i found very important concepts from your different videos thank you Crunch!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[@AlLitu-p1q]

Dr. What abiut sargan test? Its less than 5 percent so what may i do? Also my ar1 is significant. But hansen,ar2 is good. What should i do?

[@CrunchEconometrix]

I use Hansen not Sargan.

[@oluwatobiogunnusi8377]

How do I specify interaction variables in system GMM? I have a model that i wanted to look at the significance of two interaction variables.

[@CrunchEconometrix]

Same way you to include interaction terms in any equation. You may want to watch some of my videos where I used interaction terms.

[@zuzekandovela3872]

Good day Crunch fam. I would like to ask, how was 0.1675 obtained? and all other interpreted values?

[@CrunchEconometrix]

Ruralbarbie, kindly watch the video to see what was done.

[@khalilelbachiri9977]

Hello teacher, First of all, I would like to thank you for your videos which help us a lot. Please I have a question for you: I would like to estimate a dynamic model by applying the GMM for a number of individuals which is equal to 12 and T=5, is this feasible? If not, is there another method that I can apply for this case? Thanks in advance.

[@CrunchEconometrix]

Hi Khalil, GMM technique is applicable if you have N>T panel data structure.

[@oisebenson5398]

Hi there, your videos are super helpful! I got all my data from the World Bank, a reliable dataset, and I ran a system GMM regression and all the results but one came out insignificant? This is very stressful, what should I do?

[@CrunchEconometrix]

Hi Oise, if only one coefficient is NOT significant, I'm wondering how using the GMM technique is stressful?

[@oisebenson5398]

@@CrunchEconometrix Thanks so much for replying and for all your videos, they're very helpful. I'm doing my dissertation and it's due on Thursday but I'm having issues with my GMM regression. Sorry I meant to say only one came out significant, but it didn't even matter anyways as for every GMM analysis I do, the number of instruments is greater than the number of groups and I don't know how to solve this issue. I really need help from a Stata professional, is there any way I could have your email to discuss further? My paper is investigating the impact of FDI on the economic progress of African countries...

[@CrunchEconometrix]

Oise, use the COLLAPSE option. I explained that in the GMM videos.

[@hafidhahmadrizqipratama7608]

Thank you fot your explanation! Thank you so much!

[@CrunchEconometrix]

You are so welcome :)

[@jiran1234]

Dear Professor can we have negative value for the estimate of the lag dependent variable. We have a result run using the first difference data of the original variable (first difference because to make the variables stationary) and the estimate of the lag dependent variable is coming out as negative, is this okay. Thank you in advance.

[@CrunchEconometrix]

Hi Meitei, you can have negative sign for the lag dependent variable. It implies there's no persistence in the variable.

[@jiran1234]

@@CrunchEconometrix thank you so much.

[@AlLitu-p1q]

Hi dr. I am in a problem. My AR1 is significant/p value is 000 but AR2 IS INSIGNIFICANT. ALSO SARGAN TEST IS SIGNIFICANT AT P VALUE 000. BUT HANSEN IS GOOD AND INSIGNIFICANT. NOW I HAAVE TO REPORT MY REAULT IN THESIS. BUT AR1 AND SARGAN ALso.I HAVE TO INCLUDE. NOW,WHAT TO DO? HOW TO REPORT AS AR1 SHOULD BE INSIGNIFICANT BUT MY ONE IS SIGNIFICANT. SARGAN SHOULD BE INSIGNIFICANT BUT I HAVE SIGNIFICANT. WHAT MAY I DO?PLEASE HELP dr

[@CrunchEconometrix]

I use Hansen.

[@mahabubrahman9432]

Thank you very much your very easy to follow videos on GMM. All the GMM videos are the best among all the videos available in youtube. I wonder if you have any plan to make more videos on panel data models such PCSE, FGLS, fixed effect, ramdom effect model Thanks again

[@CrunchEconometrix]

Hahahaha, thanks for the excellent pass. Yes, I have videos on RE, FE and Hausman test. ...if i understand the PCSE, FGLS procedures, I'll definitely do videos on them. I'll so much appreciate if you can share my videos, I need to reach more people...thanks!!!😍

[@barnonamondol5032]

Hello, Thank you for your video. Can you please explain the F statistics value interpretation?

[@CrunchEconometrix]

Hi Barnona, the F-stat has the natural interpretation of testing for joint significance of the regressors on the depvar. Thanks.

[@brendasolis70]

Thank you so much for your videos! What if my number of groups is around 3,000 and my instruments are around 300 without collapse. Do you consider that i have instrument proliferation problem? if i use collapse then i have problems with Hansen test

[@CrunchEconometrix]

Hi Brenda, from your info, you have a large panel. Instrument proliferation occurs when N>Z, if Hansen is 1.000 or returns with a dot (.). Otherwise, you need not worry. May I know from where (location) you are reaching me?

[@vaishnavibalaji6811]

Sir may I please know why pvalue of AR(2) must be greater than 0.05? And AR(1) less than 0.05

[@CrunchEconometrix]

Please read any of the articles listed at the end of the clip for detailed knowledge about your question. Thanks.

[@naeemkhan4246]

Hello, if the probability of J stat is insignificant, what it means ? how to interpret it in my research thesis?

[@CrunchEconometrix]

I responded to you on this on a different thread.

[@harwinderkaur3142]

it's always wonderful to watch your videos. great knowledge. can we apply GMM in the short panel. with n=10 and T= 6

[@CrunchEconometrix]

Thanks for the encouraging feedback, Harwinder. The response to that is YES!

[@yayapouakone9006]

Hello Madame and thanks for what you've been doing for the scientific community. Please I've a concern. In the course of effectuating the two system GMM, my Wald chi2 keeps giving me a very high value. I don't know how to solve this problem reason why I seek for your help. Regards

[@CrunchEconometrix]

Thanks for the kind words about my KZbin Channel. Deeply appreciated! Focus on the Hansen stat. More important.

[@jingguan1493]

Hi Professor, thank you very much for these great videos. They are really helpful. I am currently running a two-step system GMM model, however, my F statistics, and AR(2) are both missing. I am using 4-year panel data. Can you please kindly let me know how could I deal with this issue? Thank you in advance!

[@CrunchEconometrix]

Jing, the time span is too short. Increase to at least 8 years and re-estimate.

[@jingguan1493]

@@CrunchEconometrix Thank you so much for your quick response.

[@benedictarthur8311]

Thank you very much. This is very help. please can we use interactions terms in GMM ?

[@CrunchEconometrix]

Yes Benedict, absolutely!

[@sobiyahanif3295]

HI Ma'am! I have a query, can the coefficient of lagged dependent variable be negative? or it must be positive in all the regressions?

[@CrunchEconometrix]

Yes, it can. Your interpretation follows analogously.

[@sobiyahanif3295]

@@CrunchEconometrix thankyou so much, my dependent variable is gross savings (% of Gdp) in differce gmm estimation lag value of dependent variable is negative. How can i justify it. Can you plz explain it?

[@CrunchEconometrix]

Sobiya, the best approach is to download and read related publications and adapt their interpretation. I have always admonished reading in addition to watching my videos. Thanks.

[@sobiyahanif3295]

@@CrunchEconometrix ok. Thankyou ma'am

[@emmy6874]

Thanks a lot it is very clear. You are a good teacher

[@CrunchEconometrix]

Compliments well-taken, Enouga!...may I know from where you are reaching me?😀

[@emmy6874]

Sénégal 🇸🇳 but i am cameroonian

[@CrunchEconometrix]

@@emmy6874 Good to know, Enouga...kindly share my videos with your students and academic community in both countries. I'm sure that they will learn a few analytical skills. Thanks! 💕

[@charithkrish]

Hi.. do you have Arellano Bond implementation in R? because Hansen test is not found in R results. thanks

[@CrunchEconometrix]

Not at all, Charith.

[@jdisira]

You videos are extremely helpful. It give us way to understand econometric and software application in very lucid manner. Keep posting your great work. I have one comment regarding the interpretation video. In the previous videos you have done around fifty simulation in total and I find difficult to follow interpretation regarding the thumb rule/criteria to interpret "Hansen test statistics". I request you to help me with that.

[@CrunchEconometrix]

Jdisira, if the p-value of the Hansen statistic is >0.05, it implies the model is correctly identified.

[@diegoroldan2290]

Thank you for your videos

[@CrunchEconometrix]

You are very welcome, Diego.

[@vaishnavibalaji6811]

Sir can you please tell how to check model for using System GMM method. Is there any values that we can take to identify model fit in System GMM method.

[@CrunchEconometrix]

Vaishnavi, use the model diagnostics. AR(2), Hansen stat, and Instruments/Groups. I explained all these in my videos. When you watch them, you will be better informed.

[@vaishnavibalaji6811]

@@CrunchEconometrix thank you Sir

[@maheenmuhammadsali7254]

Hello, How to check the validity of instruments used in GMM estimation. Thanks for your videos

[@CrunchEconometrix]

Hi Maheen, observe the Hansel statistic. I emphasized that throughout my GMM videos.

[@ubahjeremiah2149]

Is using year dummies mandatory

[@CrunchEconometrix]

Yes Jeremiah, to control for variation of the dependent variable over time.

[@ubahjeremiah2149]

@@CrunchEconometrix is there a way of generating them automatically or do you need to plot using excel Dr.

[@CrunchEconometrix]

I generate in Stata using: tab year, gen (y)

[@ubahjeremiah2149]

@@CrunchEconometrix thank you so much 😊. I love your channel and God would bless you abundantly

[@CrunchEconometrix]

Amen!!!!

[@shannonmurray747]

Hi, thank you so much for your videos they are the only reason I have been able to get through my dissertation :))) I’m stuck on some interpretation and was hoping you could possible help? My main explanatory variable is significant but the coefficient seems far too high to be economically possible , was wondering what your thoughts are on this? What would be a reason for this- everything else in my model seems to check out and I’m stuck on a justification or what this means for my model/results :( thanks again!! X

[@CrunchEconometrix]

Estimate with the log forms of the variables and compare the coeffs.

[@UpaznabornofChrist]

I have a question about interpreting coefficients. I have inflation as an explanatory variable and my dependent variable is in log. My inflation variable is converted from percentage form to decimal numbers in the data. 16% to 0.16 and this is the form in which I entered it to the data. How would I interpret it’s coefficients if it’s 2.24 and dependent variable is in log in the situation that my rate variables are not in percentage form but rather in decimal number form?

[@CrunchEconometrix]

I will refer you to Wooldridge. Look up the Chapter on Functional Forms for proper understanding. Thanks.

[@jasmijn5629]

Thank you for your videos. They are super helpful. I have implemented a system GMM model. Using the outputs, I have to interpret the sum of two coefficients to measure the total impact of FDI on inequality. Seperately, one of these coefficients is significant, while the other is insignificant. The sum of the two coefficients is also insignificant. Do I therefore conclude FDI has NO impact on inequality?

[@CrunchEconometrix]

Jas, if you sum negative and positive coeffs, you interpret your result based on the sign of the summed coeff. May I know from where (location) you are reaching me?

[@Lost11385]

Hello ma'am. Many many thanks for your helpful videos. I have a query regarding endogeneity. There is a problem of heterogeneity and auto-correlation in my data, but no endogeneity. Can i still go ahead with GMM.

[@CrunchEconometrix]

Hi Esha, kindly watch "Understanding GMM" and jot some notes while at it. Pay attention to the things GMM controls for. Thanks.

[@marycoaquira9072]

Hello professor, thank you so much for sharing this content. I have been working with a GMM model and the outcome is that my regresors coefficients are all significant (using GMM, 2 steps GMM, more or less lags/instruments, using the collapse command, etc.) BUT the tests (Hansen and AR(2) ) p-values are near 0 in all cases. Which I would understand means the instruments are poor. Does this mean that the whole model is wrong even though regresors are significant? or the regressors can still be valued despite the instruments used? I would extremely appreciate yours or someone else reading to help me.

[@CrunchEconometrix]

Hi Javier, thanks for the encouraging feedback. Deeply appreciated! GMM diagnostics are as crucial as the coefficients. Good instruments (Hansen stat) give the confidence that endogeneity is corrected and 2nd-order serial correlation (AR2) must be removed. Reviewers check all GMM output to certify if the outcomes can be used for inferences.

[@yayapouakone9006]

Hello Madam, Endless thanks for the incredible job you're doing. I for one never had a good knowledge about GMM method of estimation, but after watching nine of your vedeos on this method i can claim of having a reasonable knowledge on it. I am analysing the influence of Public spending on agriculture in SSA from 2000-2018 and i've come accross a problem While applying a two-step sytem GMM, public spending which permits me to take into account the possibility of non-linearity in the relationship between Public spending and agricultural production presents some signs of collinearity and i've try to resolve this but no way reason why i come towards you to seek for solution.

[@CrunchEconometrix]

Hi Yaya, thanks for the encouraging feedback on my GMM videos. Deeply appreciated! On linearity are you a log-log model? How did generate the square of public spending?

[@yayapouakone9006]

@@CrunchEconometrix Greatful for the quick response. It makes your followers feel honored. I multiplied it by itself before Generating the log.

[@yayapouakone9006]

@@CrunchEconometrix I've multiplied public spending by itself before linearising the model. Regards

[@CrunchEconometrix]

I'm doing my best. It's a lot of work though (lol). Maintaining a 97% response rate is no joke😊... Yeah, I thought as much. Your multiplication will yield collinearity. The correct way is: lnpub*lnpub. Learnt that from experience.

[@CrunchEconometrix]

Wrong approach. Read my response to this on your separate thread.

[@MikeArthas]

Hello Madam, I really love your videos! One question: What should I do if the coefficients I obtained from GMM is 'quite' different from fixed effects least-squares model? This is what I have, robust standard errors are reported in brackets beta_GMM = -1.16 (0.4095) beta_LS = -0.1104 (0.0465) Thanks!

[@CrunchEconometrix]

Hi Mike, thanks for the warm commendation about my videos. Deeply appreciated. Of course the results will differ because the estimators are different. You need to stick with the one you intend using for your analysis or serve as robustness for one another. Please may I know from where (location) you are reaching me?

[@MikeArthas]

@@CrunchEconometrix Thank you very much for your reply Madam. I am a PhD student in London. I also share you videos with other students!

[@CrunchEconometrix]

@@MikeArthas You're awesome!

[@nurehh2271]

Thank you for your smart videos!

[@CrunchEconometrix]

U're welcome, Nur. I hope you were able to gain something from these series😀

[@shikhabhurtel9337]

Thank you for all these videos on GMM. It has been super helpful as I write my capstone paper. I do have one question. You have emphasized creating a year dummies. I am a bit unclear on why is this necessary. Maybe I missed some things in the videos. Will you please help me understand this? Thank you for your time.

[@CrunchEconometrix]

Hi Shikha, thanks for the encouraging feedback. Deeply appreciated. Please watch my video on "GMM Year Dummies" answers your query.

[@chahinebergaoui1402]

I estimated the two-step GMM and I found the number of instruments equal to the number of cross sections what can I do

[@CrunchEconometrix]

Hi Chahine, it appears you skipped the prerequisite videos. Kindly watch them to know what to do. Regards.

[@dorstellgh6238]

Hello Dr, please what will you do if your number of instruments is larger than number of groups

[@CrunchEconometrix]

Use the collapse option. I explained this in all the videos.

[@MrKiaeeha]

First: thank you for your great video. One question: should we report and explain about DIffernece-in-Hansen test?

[@CrunchEconometrix]

HI Kiaeeha, thanks for the positive feedback on my videos, deeply appreciated. Unless you are interested in the statistic, otherwise no need for it. I only showed how it can be derived...may I know from where (location) you are reaching you?

[@MrKiaeeha]

Thank you for explanation. I am currently living in Malaysia. @@CrunchEconometrix

[@CrunchEconometrix]

Awesome, Kiaeeha! Kindly spread a word about my KZbin Channel to your students and the academic community in Malaysia...thanks!

[@MrKiaeeha]

SURE, your channel is great.@@CrunchEconometrix

[@vaishnavibalaji6811]

Sir can u please tell how to interpret Sargan and Hansen test. What must be the p values for a Sargan and Hansen test to be considered as a good model. Please explain sir

[@CrunchEconometrix]

Vaishnavi, I explained this in my GMM videos starting from the introductory video. I suggest you watch these videos in SEQUENCE. Both Hansen and Sargan have the same interpretation and qualifying statistics.

[@vaishnavibalaji6811]

​@@CrunchEconometrix Thank you Sir

[@hamanmahamataddi8600]

Thank you Mam for your videos. I'd like to know if it is possible to run a GMM model when N is less than T. If no, which other estimation (except the pooled OLS) might be suitable. Thank you .

[@CrunchEconometrix]

Hi Human, GMM is not appropriate. Increase T to 30 years or more and execute 3 comparative time series models. Hope this is helpful.

[@hamanmahamataddi8600]

I would like to increase T but due to lack of complete data, I think it would be better to increase N and run GMM.

[@CrunchEconometrix]

@@hamanmahamataddi8600 Yes, better. Ensure that N is sufficiently larger than T.

[@franco7273]

hi, i have a question: For DIFF GMM is the same interpretation of coefficientes (initial model in levels) ? or we treat regressors like if they were expressed in differences (transofrmed model)? Thanks a lot for your videos, regards.

[@CrunchEconometrix]

Hi Trajano, same short-run interpretations. Thanks for the positive feedback on my videos. Deeply appreciated. May I know from where (location) you are reaching me?

[@franco7273]

@@CrunchEconometrix i'm from Argentina and honestly is too hard to find a video related to gmm thematic so i say thank you for helping me, your videos are useful

[@CrunchEconometrix]

Good to know, Trajano...I'll also appreciate if you help share my videos with your colleagues and academic community in Argentina...gracias!!!

[@gasparjuico9528]

Hello. May I ask what it means if the lagged dependent variable is not significant? Is it a miss specification?

[@CrunchEconometrix]

Hi Gaspar, it is not a miss-specification but try to run some simulations by augmenting the instruments set to see if the significance of the lagged depvar will improve. You can also use the 2nd lag of depvar. May I know from where (location) you are reaching me?

[@advaithsuresh9131]

Hello Professor, thank you so much for the GMM series. It has helped me immensely. I just wanted to ask for clarification regarding interpretation. My dependent variable is log(GDP per capita) and explanatory variable is life expectancy and the coefficient is 0.0403. Would that mean that a one year increase in life expectancy leads to a 4.03% increase in per capita GDP? Thank you once again!

[@CrunchEconometrix]

Yes, I'd give it that interpretation. But check the interpretation from similar papers online to be very sure.

[@imancharming]

Hi Dear, Can you please explain me the concept of forward orthogonal deviations with the help of some example? I mean as first differences work as "current minus previous value", how do forward orthogonal deviations work? Also, can you please reassure that both difference and system estimates are short run estimates? Thank you.

[@CrunchEconometrix]

Hi Iman, the concept of "orthogonal deviation" is complicated for me to break down so I will refer you to the references listed at the end of the videos. Or better still read (Roodman, 2004, 2009). And yes, GMM estimates are short-run estimates. I'll also refer to Roodman for better conviction. Hope these are helpful, thanks.

[@jumpjoshii]

First of all I'd like to thank you for your insightful videos, they are helping me tremendously with my Master's thesis! Two questions on coefficient interpretation still remain though: how do you interpret the coefficient on the lagged dependent variable? Also, I am using both differenced and undifferenced explanatory variables (by undifferencing them before running the system GMM as proposed by Roodman). How does that change the interpretation? Again, thanks a lot for your videos and greetings from Switzerland :)

[@CrunchEconometrix]

Thanks, Jaylord for the encouraging feedback. Deeply appreciated! Lags interpretation is very straightforward. Simply relate discussions to the period in question. Differenced variables are short-run variables and should be interpreted as such. For undifferenced, the usual interpretation holds.

[@jumpjoshii]

@@CrunchEconometrix Alright, thanks a lot for your answer! Do I understand correctly then, that if I create long-term coefficients after System GMM on differenced variables, should that yield the same result as if I did system GMM on the undifferenced variable?

[@CrunchEconometrix]

Read my response again.

[@mubasherzaman6988]

Kindly share how to interpret the value of AR1, AR2 and Hansen Statistics

[@CrunchEconometrix]

Hi Mubasher, I interpreted these in the course of the videos. The Ho for AR (1) and (2) is that there is no 1st and 2nd order serial correlation. For Hansen, no over-identifying restrictions. You may need to watch them again and also read Roodman (2004).

[@mustanggemini2156]

Dr. Do you have a video on how to construct interaction term using system gmm? Thank you Dr

[@CrunchEconometrix]

Hi Khairul, it is the same way you create them in other models. Create and include in the GMM model.

[@mustanggemini2156]

CrunchEconometrix thank you Dr👌

[@maminoo93]

Hello madame, I wanted to know the best way to add an interaction term into the model. Should i put this term at the same xtabond2 command with the other variables or should i test them without an interaction term and then i write another xtabond2 command containing only the interaction term? for example, i have this model: y= x+z+ (x*z). in this case, is it right to write the xtabond2 command like that assuming that the variables or endogenous/ predetermined: xtabond2 y l.y x z x*z , gmm( l.y , lag( ) collapse) gmm( l.x , lag( ) collapse) gmm( l.z, lag(1 1) collapse) gmm( l.x*z , lag( ) collapse) iv() twostep?

[@CrunchEconometrix]

Ok, I've never tried GMM with interaction terms but you can attempt it. I'll suggest that you simplify the syntax, yours have too many gmm instruments. See the syntax I used and adapt accordingly.

[@maminoo93]

@@CrunchEconometrix Thank you so much madame

[@CrunchEconometrix]

@@maminoo93 U're welcome GusTun...keep watching, keep sharing! 💕

[@alishariffkabaraphd427]

we are very happy and grateful with all your videos on GMM series. Its quite educative and well articulated. Pls, is their any difference when it comes to the interpretation of regressor's p-value of z instead of t ? Best regards Ali

[@CrunchEconometrix]

Not at all Ali, the regressors retain their interpretation given the significance of the pvalues.

[@alishariffkabaraphd427]

@@CrunchEconometrix Fully satisfied Dr. Best wishes

[@CrunchEconometrix]

@@alishariffkabaraphd427 Same here Ali, please let others know about my Channel...kindly share my link with your students and academic networks! 💕

[@alishariffkabaraphd427]

@@CrunchEconometrix sure All the best

[@sabastineakongwale1944]

Please what does a Hansen J test values of 0.999 imply in terms of test for over identification or not

[@CrunchEconometrix]

Hi Sabastine...model is not good. To get a better understanding of G

[@sabastineakongwale1944]

@@CrunchEconometrix Thanks Ma'am. So what is the solution? Are there any further test I need to run?

[@CrunchEconometrix]

@@sabastineakongwale1944 There's no shortcut to your query. You mean you haven't watched these videos as advised? Take advantage of the information. The solutions are discussed therein.

[@AGhulam73985]

Just three words I love you mam

[@CrunchEconometrix]

Hahahaha, love you too, Aribah! Thanks for the positive feedback...deeply appreciated. May I know the country from where you are reaching me?

[@abujad4226]

8:10 if log is not used ,,, I mean the number is it is. How the interpretation would be ?

[@CrunchEconometrix]

Hi Abu, interpretation will be in the the unit of X on Y. The unit will be the measurement of X. That's why using the natural logarithm is preferred. It simplifies interpretations.

[@arindambandyopadhyay3896]

Sargan test interpretation is missing

[@CrunchEconometrix]

I use Hansen stat.

[@shamimiizzati1975]

I FEEL LIKE MY AUNTIE ARE TEACHING ME MATHEMATICS

[@CrunchEconometrix]

Glad to hear you find this helpful...thanks!