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Questions tagged [generalized-moments]

generalized-moments stands for the econometric technique of "generalized method of moments", a method of quadratically combining multiple "generalized moments", or "estimating equations", to obtain parameter estimates, their standard errors, and test statistics in single and multiple-equation, cross-sectional, time-series, and panel data models.

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15
votes
3answers
23k views

When should one consider using GMM?

One of the things which makes econometrics unique is the use of the Generalized Method of Moments technique. What types of problems make GMM more appropriate than other estimation techniques? What ...
13
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1answer
2k views

Using generalized method of moments (GMM) to calculate logistic regression parameter

I want to calculate coefficients to a regression that is very similar to logistic regression (Actually logistic regression with another coefficient: $$ \frac{A}{1 + e^{- (b_0 + b_1 x_1 + b_2 x_2 + \...
12
votes
1answer
4k views

What is the difference/relationship between method of moments and GMM?

Can someone explain to me the difference between method of moments and GMM (general method of moments), their relationship, and when should one or the other be used?
11
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2answers
495 views

Explaining generalized method of moments to a non-statistician

How do I explain Generalized Methods of moments and how it is used to a non statistician? So far I am going with: it is something we use to estimate conditions such as averages and variation based ...
10
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0answers
1k views

Dynamic Panel/GMM in R with group:time fixed effects? [closed]

Is there a solution coded in R to estimate models of the form $$ y_{igt} = \alpha_i + P_{gt} + \beta_1y_{igt-1}+ \beta_2y_{igt-2} + X_{igt}'\gamma + \epsilon_{igt} $$ ? ...
9
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2answers
7k views

When to use Gaussian mixture model?

I am new to using GMMs. I was not able to find any appropriate help online. Could anyone please provide me right resource on "How to decide if using GMM fits to my problem?" or in case of ...
8
votes
1answer
258 views

Why are standard errors downward biased when considering weak instruments

I was wondering why standard errors are (severely) downward biased when you are using the (general) instrumental variable - estimator or the generalized method of moments (gmm) estimator.
6
votes
1answer
1k views

Elbow Test using AIC/BIC for identifying number of clusters using GMM

How to select number of clusters using GMM when the elbow test (AIC/BIC vs n_components) results in a graph like this?
5
votes
1answer
2k views

Forecasting unemployment rate with plm

Please see question for the background. Following the advice of @kwak and @Andy W, I have decided to use the package plm in R to fit my model. Here an excerpt of ...
5
votes
1answer
524 views

Dynamic panel data with large $T$

Given a data set with $N=2634$ and $T=92$, I want to estimate a dynamic model. My first though was to use a classic System GMM estimator, however digging through the literature it turned out that ...
4
votes
1answer
1k views

Principle of Analogy and Method of Moments

I am studying method of moments and GMM in the context of econometrics. Can someone explain on intuitive level, what does it mean to match moments? And how does this differ from the classical linear ...
4
votes
2answers
501 views

Is there an R package for MCMC estimation of Generalized Method of Moments?

I'm looking for an R package (or a combination of packages) that would allow me to perform MCMC estimation of a GMM model, with a user-specified moments function. I've looked at the CRAN Bayesian ...
4
votes
1answer
2k views

Could the covariance matrix of the moment conditions in GMM be ill-conditioned?

General question: In a generalized method of moments estimation could the covariance matrix of the moment conditions be ill-conditioned and therefore the inverse not computable? Background on my ...
4
votes
1answer
168 views

Possibility of solution in overdetermined system of moment conditions

Hayashi, in page 207-208 of his book Econometrics, ex.3 (see hint), discusses the possibility that when referring to the moment conditions that will determine the estimator formula, having an ...
4
votes
1answer
2k views

Generalized method of moments versus standard least squares estimation

I was thinking that in a very standard case such as a simple linear model with iid errors and no endogeneity, I would get the same results using the a simple least square estimate (such as provided by ...
4
votes
1answer
620 views

GMM estimation of linear regression with intercept restriction

Say I have a time series regression as follows: $$y_t = a_i + \beta_i x_t + \varepsilon_t^i \ \ ; \ \ t = 1, 2, \cdots, T \ \ \text{for each } i$$ Now say I impose the following restriction on the ...
4
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0answers
97 views

Identification Problem in Minimum Distance Estimation

I have the following problem with a system of minimum distance equations I want to solve. The objective is to estimate the parameters of the random variables in the following DGP: $$ x_t= \phi_t(\...
4
votes
0answers
107 views

Valid / invalid moments in Generalized Method of Moments (GMM)

I'm preparing to conduct an estimation procedure using GMM (Generalized Method of Moments), and I'm in the process of selecting my moments. This got me thinking, can I use non-statistical moments as ...
4
votes
0answers
963 views

How to properly use generalized method of moments (GMM) estimation with plm in R?

In the context of panel data analysis my key independent variable wage affects the response not immediately but rather over time. Therefore I would like to use some ...
4
votes
0answers
271 views

OLS standard error that corrects for autocorrelation but not heteroskedasticity

Question: By mapping the OLS regression into the GMM framework, write the formula for the standard error of the OLS regression coefficients that corrects for autocorrelation but not heteroskedasticity....
3
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1answer
1k views

Gradient in GMM estimation

I have a question that might be trivial but I have not much knowledge on that method: I want to estimate a structural model with GMM and my model works in the sense that it estimated the right ...
3
votes
1answer
2k views

How to make a GMM from a Histogram to give a probability?

I have a histogram that looks like the following: From the data, I can see that this histogram shows two obvious curves. If I make the claim that they are from two Gaussians, how can I make a ...
3
votes
2answers
2k views

Implementing Minimum distance estimation

Let $\mu$ and $\sigma$ be two parameters of interest characterising a normal distribution. From a theoretical model, I know that these two parameters are related to each-other according to $$\pi=\...
3
votes
1answer
51 views

Are analytical derivatives unambiguously superior to numerical derivatives in GMM?

I am estimating a non-linear GMM model. In both Stata and R, you need to specify the moment equations and the instruments, but there is no need need to provide analytical derivatives for the estimator ...
3
votes
1answer
176 views

Asymptotic variance of GMM with efficient instrument

This question emerged from reading Wooldridge's Econometric Analysis of Cross Section and Panel Data, second edition, section 14.4.3, where the asymptotic distribution of the GMM (Generalized Method ...
3
votes
1answer
2k views

Practical issues with dynamic panel data modeling

Unfortunately for me, I've got a situation where I need to control for the lag of a dependent variable as a robustness check against an alternative interpretation of my main regression. The baseline ...
3
votes
0answers
86 views

Limitation of number of features in GMM

I am new to GMM training. I could see from the link as below The main limitation of the GMM algorithm is that, for computational reasons, it can fail to work if the dimensionality of the problem ...
3
votes
0answers
93 views

Does diagnolizing higher-order cross-moment matrices lead to independent variables?

Diagonalizing the covariance matrix transforms multivariate data into uncorrelated variables, but does not make them independent necessarily. Does it follow from this that if I were to diagonalize ...
3
votes
0answers
1k views

HMM library, different length sequences training

I'm using the Kevin Murphy's HMM library in MATLAB(http://www.cs.ubc.ca/~murphyk/Software/HMM/hmm.html) There is a section called 'How to use the toolbox'. There is this example for GMM ouputs: <...
3
votes
0answers
670 views

Nonlinear GMM for Dynamic Panel Data

A friend of mine needs to estimate a non-linear GMM on Panel data. As I have checked, the softwares for Panel GMM only estimate linear forms (STATA gmm, xtabond, ...; R pgmm from plm package). How can ...
2
votes
1answer
171 views

How to implement the Generalized Method of Moments for the upper limit of a uniform?

Suppose $\{Y_1,\ldots,Y_n\}$ are iid uniform on $[0,\theta]$ where $\theta$ is the unknown parameter. I'm trying to understand how to create a GMM estimator for $\theta$ and I'm not really sure how. ...
2
votes
1answer
6k views

Fit measures for GMM Arellano-Bond estimator in R

A colleague and I have been working with difference GMM, i.e. the Arellano-Bond estimator, in R. Our option has been to use the pgmm command from the plm package. However, now I am struggling to test ...
2
votes
2answers
3k views

Linear regression with fat-tailed errors

I'm testing a linear model that explains stock returns with some contemporaneous factors; the model is assumed to satisfy OLS assumptions except that the errors (i.e., unexplained stock returns) have ...
2
votes
1answer
577 views

GMM Estimator of an Exponential Distribution

Suppose you have to calculate the GMM Estimator for $\lambda$ of a random variable with an exponential distribution. $$f(x) = \lambda \cdot \exp(-\lambda\cdot x)$$ with $E(X) = 1/\lambda$ and $E(X^2) ...
2
votes
2answers
2k views

Panel Data & IV

I have a panel data, and need to run an IV. I have only 1 endogenous variable. 1) Should I use a Two-stage least squares or a GMM? 2) I understand that GMM is only for dynamic panel data. What is a ...
2
votes
1answer
4k views

Two stage GMM estimator in Matlab

I am trying to create a simple GMM estimator for the mean of a normally distributed random variable using the first three odd central moments of a normal distribution (all of which should be zero ...
2
votes
2answers
36 views

What can I consider to choose between the same model but estimated with different estimators?

I estimated a standard regression equation with ML and GMM. The question is: how can I know which estimator provides the best estimate? (e.g., the GMM is more efficient if errors are not normally ...
2
votes
1answer
261 views

What are the (philosophical) assumptions behind GMM and Maximum Likelihood Estimation?

As stated in the question. In particular, how does a researcher know when to apply which estimation method and are there any examples that can show when one case is more appropriate than the other? ...
2
votes
1answer
79 views

A doubt on SUR model

On page 279, Hayashi begin by defining the SUR model. See picture below. If I compare with these slide-notes(slide number 34), we define the instrument vector $x_i$ equal not only to the union of all ...
2
votes
1answer
353 views

How to do model testing in Indirect Inference/Simulated/General Method of Moments

I have a model estimated via indirect inference, so I have a set of auxiliary moment conditions. What I am doing is very similar to Method of Simulated Moments. I want to do a couple of ...
2
votes
1answer
246 views

Question about a derivative of the 2nd-step moments in a two-step estimator as a joint GMM-estimators approach

I'm reading Newey & McFadden - Large sample estimation and hypothesis testing (in the Handbook of Econometrics, Volume 4, 1994, page 2176). In the model I'm interestend in has some former ...
2
votes
0answers
39 views

Why is uncorrelated(exogeneity) “good enough” for identification in regression?

Let the model $y=x+x^2-1$ be exactly correct, where $x\sim N(0,1)$, then $x^2\sim \chi^2_{(1)}$. Say we want to estimate the model $y=\beta x-1+\epsilon$ by least squares. Let $(y_i,x_i)_{i=1}^n\...
2
votes
0answers
41 views

Piecewise integration

I am trying to estimate residential demand for electricity in a country where electricity is sold (to all households (HH)) at an increasing two-part tariff. By choosing marginal prices as my key ...
2
votes
0answers
62 views

Murphy-Topel standard errors correction for GMM?

I employ a two-stage estimation routine: In the first stage, a large vector $\hat \theta_1$ (around 2000 elements) is estimated with maximum likelihood. In the second stage, I estimate $\hat \theta_2 (...
2
votes
0answers
2k views

Generalized method of moments estimation in R with plm and gmm

I am interested in using some of the additional features in the gmm package in R to estimate GMM in panel data. Specifically, I am interested in first estimating ...
2
votes
0answers
47 views

Can every identifiable model be estimated by GMM?

Assume a model with parameters $\theta$ is identifiable. Then that means that for every probability distribution over observable variables $p(x|\theta)$, there is a unique parameter value $\theta$. ...
2
votes
0answers
358 views

GMM Estimation and convergence problem

I try to minimize an unweighted moment function $G(\theta)$ given by $G(\theta) = \bar{g}(\theta)'\bar{g}(\theta) $. $g(\theta,x_i)$ contains the specified moment conditions, where we state $E(g(\...
2
votes
1answer
62 views

Estimating Equations for Treatment Model in Treatment Effects Estimation — How is this Equation Derived?

While reading the STATA 14 Treatment Effects Reference Manual (http://www.stata.com/manuals14/te.pdf), I'm having difficulty understanding how they arrive at the equation for the treatment model, that ...
2
votes
0answers
91 views

EM for GMM similar to KMeans

Can we get the value of the latent variable for each training example while fitting a Gaussian mixture model by performing kmeans on the data set ? Further can we then estimate the other parameters of ...
2
votes
1answer
637 views

Including time-varying regional fixed effects in Arellano-Bond estimation (R plm package)

I want to estimate a dynamic panel model with firm level time invariant fixed effects and time-varying regional fixed effects. I'm trying to implement this with R package ...