It is often argued that the GMM approach is a second best identification strategy compared to IV approach in case of endogeneity of the explanatory variables. Sometimes, it is also hard to believe that the dependent variable lagged one period can be included as additional explanatory variable. GMM is a more of an econometric trick than a proper solution for endogeneity. Is that argument valid?
Well Yes, You are right. GMM is just another econometric trick. You can play with data as much as you like and obtain the results that you desire.
so in the case of using a panel data model with a lagged dependent variable, is there any way to avoid using GMM?
As far as I know, GMM is the most commonly tool used when you have endogeneity between the dependent variables and want to instrument them with a lagged dependent variable...
The problem is that today everybody is talking about endogeneity. GMM is one of the instrumental variable technique, so why not ?
GMM is just a class of estimator; an estimator that happens to be naturally well suited to deal with potential endogeneity issues. GMM is just an econometric trick in the sense that a hammer is just a tool trick. A hammer doesn't really solve the problem of nails sticking out. Now, carefully applying the hammer to said nails, that is how you solve the problem.
Andres, GMM is often used to account for dynamics in the model. When there are changes in one explicative variable, they impact the dependent variable but it adjusts over time to that impact towards its long run equilibrium.
Jorge
I do not like GMM for many reasons. I prefer to specify the endogenoues varaibles inside a simultaneous equation model.
Well as Rossi mentioned, when you have valid (external) instruments, you may not need GMM. This is because you can work with the simultaneous equation model. However, in most socio-economic research getting valid (external) instruments both from theorectical and empirical point of view is very difficult. Hence, GMM becomes a handy tool.
I agree with Antonio. In case your independent variable (One of many) is supposed to be determined by a list of other determinants, you need to use a model which corrects for the bias you will get into the estimated coefficients of Independent variables. So Instrumental Regression model if not feasible in its simplest case, will lead you to use GMM based estimator.
Well in my case that I worked with productivy analisys don´t any problema because we use the DEA Frontier approach, so the differences benefits with GMM I think that it depend od the aim of it research.
In general to correct for the correlation between explanatory variable(s) and the error term. Examples: measurement error and endogeneity.
Hi Antonio. As some have mentioned, GMM is just one estimation strategy along with the others. It is a form of Instrumental variable approach (IV), which is supposed to be more efficient because it use a richer set of instruments. It should not be associated exclusively to the cases where the lagged dependent variable is included among the regressors. Yet, whenever it is the case, GMM is preferable. For instance, dynamic panel models (those containing the lagged dependent variable) cannot be estimated by OLS, which in those cases is biased. Instead, you should employ GMM. Indeed, in some models you must include the lagged dependent variable as a regressor (e.g. in order to take into account inflation inertia, consumption smoothing, interest-rate smoothing etc.).
More generally, whenever you have the problem with endogenous regressors (as often would be the case), again, you cannot use OLS, but you should use either IV or GMM. The choice is yours, though many argues that GMM is a more efficient estimator.
Regards,
At the end of the day, GMM is just an instrumental variable approah to avoid endogeneity. However, it is very powerful and flexible. Especially in its GMM-SYS version, it uses lagged values of both levels and differences until orthogonality is reached. Moreover, LM, Sargan nd Hansen tests alert you about the feasibility/realibility of the adopted instrumental approach. In this perspectice, it is still the major econometric advance in dealing with microdata over the past decades.
I agree with your response. But in many empirical applications is not even justified the inclusion of the lagged dependent variable
I am not sure looking at GMM and IV as either/or is an appropriate way to think about econometric techniques. Exogenous instruments are obviously pretty hard to come by (natural experiments are perhaps one of the only ways in social sciences to achieve identification), and orthogonality conditions through GMM might offer a way out in those circumstances (which must be built on sound theory). So if your theory leads you to GMM as the right technique, use it; if not, look for the appropriate econometric tool.
I think it would first help to recognize that GMM is a class of estimators that include OLS and 2SLS. That is, there is a way to construct a GMM estimator that is equivalent to the OLS estimator.
With OLS, the number of moment restrictions equals the number of unknown parameters, E[Xe]=0, so this falls into the subset of MM estimators. 2SLS where the number of endogenous variables equals the number of instruments would be another example of an exactly identified GMM estimator using the moment restriction E[Ze]=0, and thus also called MM.
But, you could have more instruments than endogenous variables. Now your system is over-identified with more moment restrictions than parameters to estimate. This is GMM in the fullest sense, though it will lead to the same estimation as typing IVREG in STATA.
Thus, the dichotomy of IV versus GMM is a false one. The AB estimator is both IV and GMM. In AB, the instruments (or in GMM speak--moment restrictions) follow algebraically from assumptions about how the dependent variable is related to the unobservable and time-series properties of the unobservable. The number of instruments is greater than the number of unknown parameters because lagged (and twice-lagged and thrice-lagged) values will tend to be weak instruments, so a large set is often necessary.
The issue then is not some inherent property of IV or GMM, but rather whether the authors have adequately argued for why the lagged value is correlated with contemporaneous value (ok, that is pretty easy) and why the time structure of the unobservables imply the exclusion restriction is actually valid (it will not be if the unobservable is MA or if fixed-effects are involved).
You should pay attention to the question of
under what circumstances the efficient GMM estimator takes the form of an instrumental variables estimator.
While MoM estimators such as OLS and 2SLS are unbiased & consistent, GMM estimators are consistent but NOT unbiased, and thus may suffer from finite-sample problem. If heteroskedasticity exists, you can use GMM, Huber-White SEs, etc.. If serial correlation is a problem, you can pick between time-series analysis, GEE, or GMM. If you have two or more IVs, and you want to use all of them, the only thing you can do is to use GMM.
GMM is a well suited method when you use a dynamic micro Panel data, basically firm data, to control for Endogeneity problems. This is not the case when you deal with macro panels (countries) where variables are not stationary and you may have some time invariant variables in the model. So Estimating the model with first differences is not an optimal solution. So you need to implement Pooled Mean Group, Dynamic OLS or Fully modified Ols estimation rather than GMM.
Hello,
There is a brief summary on Wikipedia at:
http://en.wikipedia.org/wiki/Generalized_method_of_moments
You can also refer to Hansen's book as well, which is very good. You can also find freely available mimeos on the web such as
www.ssc.wisc.edu/~bhansen/econometrics/Econometrics.pdf
Lag augmentation is one way to deal with endogeneity (which generates the well known second order bias: misestimation of asymptotic distributions and also of model parameters) but fully modified versions of econometric models (that account directly for endogeneity issues) also exist.
Regards.
In that case, it could be a possibility if AR(1) component is added into your panel data which in most cases will control for the issues in your model.
This is not an answer to your question but a comment on the dependent variable lagged one period. As someone working in applied econometrics for some forty years, I have learned that the prediction of human behavior depends heavily on properly measuring the degree of habituation. There are a variety of mathematical approaches to measuring habituation, but the fundamental logic includes the notion that my behavior last period has an influence of my behavior this period. When I was a graduate student in the late 60's, economics and econometrics avoided incorporation of strong findings among the psychological professions. Unfortunately, this still appears to be the case. You cannot predict the vast majority of real world behavior without the help of psychologists.
The GMM Approach is a very general large sample estimator and can deal with potential endogeneity. Hansen (1982) showed that all instrumental variables estimators, in linear or nonlinear models, could be interprated as a GMM estimator.. In practice the most important step in applying GMM is finding good instruments (Instruments that are valid and srtrong). For a good explanation see Murray, M. P. Avoiding Invalid Instruments and Coping with weak Instruments, 2006, JoEP 20(4), 111-132
In empirical IO, models of the random-coefficient logit style may not be able to be estimated using standard IV, due to non-linearity in your model. In this case, you will need to use GMM or other simulation based estimators. It's not a question of choice, so much as a question of necessity. The famous Nevo (2000) paper describes this issue well.
GMM methods also allow us to specify moment conditions from different data sets that have different units of observation. For example, Petrin (2002) uses CEX microdata on consumer choices of vehicles to compliment market-level vehicle sales data. The difference between model predictions of vehicle sales and the "known" values from the CEX can be turned into moment conditions. Remember that in GMM, we're trying to find parameter estimates that minimise the moment conditions. So GMM allows us to easily incorporate more "known" information. Bayesian methods provide another approach to the same ends.
I agree with Savage, so it is more consistents when we use panel data.
In the current literature of econometrics as exhibited in widely circulated (even advanced) text books GMM is presented as a separate estimation procedure without explicit connection to other estimating procedures. In effect GMM is a procedure that produces ``efficient" estimators. At a basic conceptual level it is the fusion of two very basic notions in inference (a) instrumental variable estimation and (b) the fact that {\bf for any random vector with a nonsingular distribution} there exists a transformation that yields another vector whose elements are uncorrelated. For example if $u$ is T-element random vector with mean zero and positive definite covariance matrix $ \Sigma $, the transformation $ \Sigma ^{-1/2}u = v$ yields the random vector $v$ which has mean zero and covariance matrix $I_{T}$.\footnote{As a parenthetical note the well known moments condition in GMM is none other that the statement that there exists a matrix of observations, say $Z$ (or a set of variable $z$) containing variables that are relevant to the estimation problem, which is not correlated with the vector of structural errors, $u$, whose observations are contained in the matrix $U$.}
If viewed in this context, when the errors of a general linear model (GLM) have a nonstandard covariance matrix whose parameters are consistently estimable, GLS is a GMM procedure. If $y$ and $X$ are observations on a single endogenous variable and the predetermined variables, respectively, 2SLS {\bf is} a GMM estimator {\bf in the context of that equation alone}, since the parameters may be obtained by applying least squares on the transformed variable $(X^{\prime }X)^{-1/2}y$. However {\bf it is not a GMM estimator in the context of the entire system of equations because in such a system, even under the usual standard assumptions, the system’s covariance matrix is not diagonal!}
The situation does not change if we are dealing with a system of equations which are nonlinear in the parameters {\bf but linear in the error terms, i.e. the error terms enter each equation as an addition to its nonlinear part.}
\vskip .15in \noindent
By way of a historical note the so called method of moments (MM) estimator, as far as I know, was first used in the 1920’s to derive the Yule-Walker equations (for estimating the parameters of a stable auto-regression). However Yule and Walker should also be credited with the first use of IV (instrumental variables) methods. One should also note that the method they used is in effect is identical to least squares.
It is generally not helpful to think of IV methods as limiting the instruments to precisely the number of parameters to estimate. Certainly Theil, who ca. 1955 invented 2SLS, used IV methods and added another step to it.
Also in the literature of GMM there is an important omission in stating the conditions under which we operate. If in a GLM $X$ is the matrix of the explanatory variables, while $Z$ is the instrumental matrix, it is not enough to impose the ``moment" condition $EZ^{\prime }u = 0$, we also need to impose the condition $EZ^{\prime }X \neq 0$, or at least its probability limit is non-null and of sufficient rank. Failure to appreciate that in the labor econometrics literature has led to the futile examination of the issue of ``weak" instruments.
This presentation of what has come to be called the GMM estimator appeared first in Dhrymes, P.J. (1969) ``Alternative Asymptotic Tests of Significance and Related Aspects of 2SLS and 3SLS Estimated Parameters", {\it Review of Economic Studies}, 213-236, Dhrymes, P.J. (1970), {\it Econometrics: Statistical Foundations and Applications}, New York: Harper and Row, 183ff, and Dhrymes, P.J. (1994), {\it Topics in Advanced Econometrics: vol. II Linear and Nonlinear Simultaneous Equations}, New York: Springer-Verlag, 27-41, 354-67,368-77.
If you require the pdf let me know and I'll email it.
Having posted the previous answer I read some of the other responses. I was sad to see how the existing computer programs must be very confusing to potential users, even if they have a good working knowledge of econometric theory.
Remember, GMM is nothing more than an OLS procedure applied to a suitably transformed version of the model whose parameters you are trying to estimate.. The transformation involved is simply an IV transformation, followed by premultiplication by the square root of the inverse of the covariance matrix of the errors in the IV- transformed system.
Dear Prof Dhrymes thank you very much for your clear and detailed explanation. Is there any way or texbook where GMM is nothing more than an OLS procedure applied to a transformation of the model. I wanna read the proof.
Dear Professor Andres:
I don't know if any of the currently circulating textbooks do that. In part this is due to the fact that most textbook writers do not assimilate the material they report in their texts. They merely repeat what the particular paper that inspired the context asserts. This means that no insight is provided and the poor reader is led to perceive of econometrics as a very diffficult and complicated subject. In fact classsical econometrics is little more that variations on OLS (least squares). This is what I attempted to do in my writings, but I am afraid it did no have sufficient appreciation; perhaps because many people found my mathematics forbidding.
At any rate responding directly to your question, I believe I gave some references in my earlier response, but here it is again. On p. 368 of my book "Topics in Advanced Econometrics: vol. II Linear and Nonlinear Simultaneous Equations" , 1994 pulished by Springer-Verlag, there is a 2 page restatement of Hansen's paper (who incidentally was recently awarded the Nobel Memorial Prize in Economics [for this paper] for reasons that are not clear to me) which is far more understandable. The matrix Z therein is the matrix of instruments and the so called weighting matrix W_{T} is nothing more than the covariance matrtix of the error process in the nonlinear simultaneous equations system, with addditive errors. The fact that a general matrix W was used rather than the inverse of the covariance matrix is an empty generality that may possibly have some pedagogical value, but not any substantive significance since the efficient parameter estimator needs to use the inverse of the covariance matrix.
When you read this if you have any problem with the math let me know.
The statement that GMM is simply least squares applied to a transform system is evident in equation (6.110). If the equation vector model in g is linear in theta, we have simple least squares; if it is nonlinear in theta we have nonlinear least squares.
What many instructors fail to make clear to their students is that nonlinearity in the parameters presents only minor mathematical problems, if the errors of the system enter additively. The very serious problems arise when the errors enter the system nonlinearly.
Dear Professor Andres:
In rereading my original answer I discovered a minor misprint: the relevant sentence should read "2SLS is a GMM estimator in the context of that structural equation alone since it is obtained as $(X^{\prime }X)^{-1/2}X^{\prime}y$. However {\bf it is not a GMM estimator in the contex......".
thank you very much for your detailed response. I will try to get a copy of your textbook asap. Many students are asking me about the GMM method and they are using a panel data model. But they do not even understand what is an İV approach maybe because their supervisors are ignorant and they belıeve that publıcation is much easier using fancy methods.
But you don't need prior distribution assumptions in least square and many other procedures,except for maximum likelihood.
Dear Professor Antonio,
I fully agree with the Prof. Dunn.
Bevcause is still the better way to deal with the endogeneity of the lagged dependent variable, the inclusion of which is often necessary to model autoregressive dynamics such those of employment, technological change, inequality and so on so forth.
Dear Professor Mansour Zarra-Nezhad
I would like to know two things (1) if we estimate system of equation using GMM in Time Series Context, does GMM takes into account Error Correlation across Equations? (2) would you please tell me the tests to check error correlation across equations in Time series context as we have Cross sectional dependence test in Panel data. It would be nice of you if you refer articles or book also. Thanks
First a general comment. The introduction of GMM with much fanfare in the middle 80s has served to obsfuscate matters and has led to a great deal of confusion. Despite its claims GMM is not a new estimation technique that includes as special cases many others that preceded it. It is simply what we used to call generalized least squares; it is simply a way of getting "efficient" estimators when in models with additive error terms the covariance matrix of the error is not a scalar matrix. This was first observed by the British statistician Aitken in the first third of the twentieth century. His idea was that if we knew the covariance matrix we could transform the data so that the in the transformed context the error has a scalar covariance matrix and thus least squares is BLUE by the Gauss-Markov theorem. This is the Aitken estimator, when the initial covariance matrix is known. Since it is rarely known the Aitken estimator is infeasible. But if we could estimate it consistently, which is possible in a large number of cases common in empirical practice, we could use this instead. When we do so we have a feasiable Aitken estimator. This appears in my book Econometrics: Statistical Foundations and Applications published in 1970. In tjhe statistical literature this same procedure has been referred to as generalized least squares for some time now. Enter GMM in the 80s. What is GMM? It is simply weighted least squares. Specifically we look at the vector of differences between the observations on the dependent variable and the linear or nonlinera combination of the predetermined or exogenous variables that our model uses to "explain" or "forercast" the dependent variable within the sample plus some weighting matrix. This might be a generalization if the weighting matrix led to interesting choices that suggests useful estimators previously uknown. But all it does is to tell you that if you chose the weighting matrix to be the inverse of the covariance matrix of the error you get efficient estimators, i.e. it tells you nothing that you didn't know from the previous literature. Nonlinearity of parameters is not a serious econometric issue; it has mathematical repercussions in that the existence (and uniqueness) of solutions for the equations defining the estimator(s) is more complicated, but given that the econometric properties continue to hold.
To get to Mr. Eberle's question, it is not clear why the weighting matrix is singular. If this reflects the singularity of the model's error covariance matrix, then this is the canonical way of dealing with such issues. To this end see Deffinition 12.23 and Remark 12.23 p. 539 of the attached chapter. There are very few places in the literature of econometrics where this is discussed and is quite likely not widely known.
The implication of this definition and convention is that test statistics invlving singular distribution entail the use of the generalized inverse of the covariance matrix. An instance of the use of this is found in "A Comment on LR, Lagrange Multiplier and Wald Statistics" which I recently upload in Researchgate.
I do not understand what is meant by "two step GMM is far from ideal".
If we just move away from GMM which only serves to confuse, you are dealing with something like
(y-Xbeta)^{'}Sigma^{-1}(y-Xbeta).
Usually two-step means you first estimate consistently Sigma, then you instert in the minimand and then minimize with respect to beta. Under many circumstances the estimator of beta resulting from this operation has the same asymptotic distribution as that resulting when you estimate beta and Sigma simultaneously. It is analogous to 3SLS and full information maximum likelihood estimators in simultaneous equations.
Your last inquiry about robustness to autocorrelation etc: obtaining the efficient estimator confers no immunity against complications involving the violation of some of your assumptions regarding the error term. Both the two step as I have defined it, and the efficient (one step) estimators will suffer if such violation occurs.
If some points are not clear feel free to ask follow-up questions.
Thanks for this thread, I am using GMM to estimate a model at different wavelet scales. It so happens that at higher scales Stata can't do the estimations. After reading this I realized that it is because at high wavelet scales, wavelet coefficients become smoother and smoother, and the variance of the disturbance tends to zero. As a result the matrix of the error becomes singular, and therefore impossible to inverse in order to get the weighting matrix.RIP Professor Phoebus Dhrymes, you are sadly missed.
I am wondering if my dependent variable has many zeros, can i use GMM ?
The Literature supports the superiority of the GMM methodology over pooled OLS and fixed effects models to treat classical econometric problems that arise when dealing with dynamic panel data and socio-economic variables, such as the endogeneity of explanatory variables, simultaneity and unobserved heterogeneity of the sampled companies.
Seb Ako Right, you have other choices as the dynamic panels will not be a good fit for your data with so few years of observations. You have other choices but that will depend on what is your specific type of endogeneity issue. For example, if you are referring to self-selection bias, you can use the Heckman model. If you deal with observables another choice will be PSM. Good luck.
Omar A Esqueda dear can you provide more explications about this " If you deal with observable another choice will be PSM." and what is the cases that we can use propensity score matching ?!
Omar Al-Bataineh Sure, PSM or other matching methods are useful to address endogeneity due to self-selection. For example, measuring the performance of firms that (decide to) cross-list versus non-cross-listed: running the model Y=α+βX+ε will be biased since the Decision to cross-list must be taken into account, using the equation: D=ϒZ+η. This is since D and ε are correlated. So the matching methods assume that you can observe the vector of Z variables (the factors affecting the decision to cross-list). Hope that helps. I am attaching a related paper.
Second best? Multistep GMM actually allows you to chose a weighting matrix for your moment restrictions. And then (when you have more instruments than end. variables) it leads to more efficient estimates. Simple IV requires exact identification, while with overidentification you will have 2SLS which is less efficient than a 2 step GMM.
But GMM is no cure for weak identification, so even if xtabond2 does not report weak iv tests, one should definitely use then. And this usually does not happen.
Can we use GMM for time series analysis? Actually i am doing analysis for a single country.. Can I use GMM or is it specifically a panel data technique?
dears colleagues, i estimated GMM panel for 25 banks for the period 2010-2018 . in the estimation results J statistic equals to 23.32 andp value of j statistic equals to 0.44 is that normal? any one can help me with GMM Panel i will appreciate it. thank you
dear colleagues, if i have panel data for 10 countires for the period 2004 to 2018, and i am using simultaneous equation , first i used 3SLS, and then i found i have autocorrelation and Heteroscedasticity problem. can i use GMM in this case to solve the endogeneity problem as well as autocorrelation and Heteroscedasticity ?
@Omar A Esqueda how to determine the specific type of endogeneity issue? Can you clarify this?
Peter Foldvari Does that mean that the use of GMM cures endogeneity in the independent variables other than the lagged dependent variables, in a dynamic panel environment? Or do you require additional solution to the endoegenous covariate?
A question for all GMM experts, is it possible to fiddle with instruments and get the result you desire? My time with GMM was fraught with great parameter fluctuation
Have a look at https://stats.stackexchange.com/questions/27736/when-should-one-consider-using-gmm
https://www.jstor.org/stable/2696518?seq=1
http://conference.iza.org/conference_files/pada2009/kiviet_j5163.pdf
more preferred when you suspect the problem of endogeneity among your variables.
Yes, more preferred when you suspect the problem of endogeneity among your variables.
@
In real world, its very hard to find pure exyogenius variables! All variables are related in one way or another! We are aware of things that we are in control of it.
We purposely control endogeneity ( simultaneously bias) to avoid confounding, and other variables omitted bias in regression analysis.
We cannot include all related variables in one model, since these variables are interdepe
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Nothing wrong with econometric “tricks” once you recognize that “tricks” are just techniques or tools (see above) useful for solving problems.
Not at all, instrumentation by lagged values is much more legitimate than weird instrumentations which are totally invented and out of the reference thoery.
I totally agree with Marco Vivarelli. Nothing is more closely related to a variable than the variable itself. As a result, the best and most direct instruments are lagged variables. Other types of instruments are a real problem for practitioners; they are difficult to find and inefficient. When I read papers and the researchers used clumsy instruments that had nothing to do with the model or the analyzed variable, I was always frustrated. GMM is a useful tool rather than a trick.
Dear Antonio,
A valid instrument must fulfill two conditions:
(1) Relevance. The IV must be strongly correlated with the endogenous variable. In this respect, a lagged value is usually strongly correlated with the current value of the variable. There are recent research suggesting that we should be even more conservative that we have usually been (https://arxiv.org/abs/2010.05058).
(2) Exogeneity. This is not directly testable. At most, one can carry out indirect tests, which would depend on each case. Overall, one needs to argue why the IV does not affect the left-hand-side variable of your equation, apart from its effect on the endogenous variable. In this respect, it is very unlikely one can convince the reader about the fact a lagged variable affect the current variable but not the left-hand-side variable one assumes is affected by the current value. There are many reasons suggesting that it could affect: dynamic effects (the value of the endogenous variable in t-1 might affect the outcome in t), serial correlation across time (the value of the endogenous variable in t-1 is correlated with the value of the variable in t) and even the correlation of the variable with unobservable factors that are correlated over time.
Furthermore, GMM often implies a massive use of IVs and we have compelling evidence that it is better to use one instrument than many ones (Angrist & Pischke , 2008, Mostly harmless Econometrics). We know also that a bad instrument makes more harm than good (https://doi.org/10.1111/j.1542-4774.2010.tb00544.x).
The use of IVs is quite controversial ("Friends don't let Friends do IV"), particularly, if one does not a convincing one (e.g., random lottery). In practice, in many cases, researchers just claim that the results are robust to the use of IV and the results are similar to those obtained used OLS. This is debatable, but this is an actual practice. Nevertheless, from my point of view it is hard to convince anyone that you can remedy endogeneity using GMM based on lags. Keep in mind that (1) is testable; (2) is not testable and you have to convince the reader about exogeneity and the burden of the proof is on the author.
Well, gmm is just another way to take reliable estimation on your population parameters either when your data violates gauss markov assumptions or when you just want to further reassure that your estimators do not suffer from endogeneity.
Regarding, your difficulty "to believe that the dependent variable lagged one period can be included as additional explanatory variable"..I will give you an example..
Lets say you measure the daily temperature for the month March...Do you think, among others, the temperature you will measure at the 15th of March will be totally independent than the temperature you measured at the 14th of March??In other words, keeping all the other circumstances constant, if I get out of my bed at 14th of March and is sunny will i expect the next day to snow or at least be as warm as today (+-)???If i get up at 8 o clock in the morning and its sunny, well i can say with a great confidence that at 8:01 o clock of the same morning will still be the same sunny day...Thats why we alsp take into consideration lagged dependent variable as regressor.You definately cant totally explaine the variance of your dependent variable but surely you can count on its historical values to make an estimation for the future.
GMM generalizes the method of moments (MM) by allowing the number of moment conditions to be greater than the number of parameters. Using these extra moment conditions makes GMM more efficient than MM. When there are more moment conditions than parameters, the estimator is said to be overidentified.
GMM approach is used when an estimated coefficient of a lagged dependent variable (e.g, 0.87) is close to or below the fixed effect model,
Yes this argument is true "GMM is quite good in solving model with endogeneity issues".
GMM generalizes the method of moments (MM) by allowing the number of moment conditions to be greater than the number of parameters. Using these extra moment conditions makes GMM more efficient than MM. When there are more moment conditions than parameters, the estimator is said to be overidentified.
- Badges
- Science topic
- Similar topics
- Instrumentation Engineering
- Instruments