# 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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### sklearn Gaussian Mixture Model chance of outlier belonging to any cluster?

Is there a way to determine the likelihood of a point belonging to ANY cluster given a Gaussian mixture model. For example if you have two clusters and you have a point very far away from both ...
29 views

### Why can a biased estimate still be statistically significant?

For example, I conduct an OLS regression and a regressor turns out to be statistically significant. When I conduct the same regression but with a GMM to account for serial correlation - I get a ...
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### What does the number of instruments in GMM mean?

I'm running a GMM estimation for panel data with lagged effects (so called dynamic panel data analysis) but I couldn't understand what does the number of instruments mean in the result. Example: I'm ...
105 views

### How to Test Linear Hypotheses about Parameters in Simulation-Based Indirect Inference

Setup: I have a model that produces a vector of aggregate outcomes, $\theta$, based on parameters, $\beta$. The relationship $\theta=\Theta(\beta)$ is stochastic and analytically intractable, but I ...
35 views

### Dynamic panel data model with AR(2) process in the errors

I set up the following dynamic panel data model: $$y_{it}=\alpha y_{it-1}+x_{it}^T\beta+v_{it}$$ Additionally, I have the process in the errors: $$v_{it}=\rho_1u_{it-1}+\rho_2u_{it-2}+\epsilon_{it}$$ ...
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### Singular covariance matrix in GMM?

I understand that typically the covariance matrix should not be singular (see e.g. this discussion here: Could the covariance matrix of the moment conditions in GMM be ill-conditioned?) But in the ...
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### System of equations GMM - time series (HAC) in RStudio [closed]

So I have a system of equations made up with some time series, to be estimated with a Generalised Moments Method model. Sth like: PREM[t] = phi_0+phi_1*PREM[t-1]+phi_2*IR[t-1]+phi_3*INAD[t-1]+phi_4*U[...
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### Estimation of variance in GMM

In GMM, the efficient weight matrix minimizes the asymptotic variance of the GMM estimator by setting: $$W_T^{opt} = S_T^{-1}$$ where $S_T$ is an estimator of the asymptotic variance of the moments,...
108 views

### What's the point in using identity matrix as weighting matrix in GMM?

What is the point of using the identity matrix as weighting matrix in GMM? GMM is the minimizer of the distance $g_n(\delta)'\hat{W}g_n({\delta})$, where $g_n = \frac{1}{n}\sum_ix_i\epsilon_i$. If we ...
288 views

### BIC score for Gaussian Mixture Model

I'm not sure how to compute a BIC score for multiple classes. For exmaple , I have a supervised problem with 3 classes.I fit 3 gaussian using MLE. Then, if I want to compute BIC score: I have to ...
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### Testing the equality of coefficients from two GMM models?

I run the same GMM model in two different samples (firms which have high imported input vs low imported input). I would like to test the coefficient estimates (particularly for fx) across the two ...
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### 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 ...
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### Lag regression independent variables in dynamic panel: which Explanation of the signs? [Resolved]

In the famous paper " Richard Blundell & Stephen Bond (2000): GMM Estimation with persistent panel data: an application to production functions, Econometric Reviews, 19:3, 321-34" the authors ...
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### Gaussian mixture models with constrained mixing proportions

I am fitting a Gaussian mixture model to multivariate data and my application suggests constraining the mixing proportions to lie in a pre-determined sub-space. I am curious if such an approach has ...
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### 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 ...
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### 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 ...
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### Dynamic vs. static model

I know that the decision between a dynamic and static model is mostly based on underlying theory. However, my supervisor asked me to estimate both and thereby distinguish between short and long run ...
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### System GMM while Dependent Variable lies within [0, 1]

Is it possible to utilise the system GMM estimator using xtabond2 when our dependent variable lies within the interval [0, 1]. Moreover, the mass point is at around 0. Thank you, Sagnik
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### Fixed Effects Logit Model with a Endogenous Binary Regressor

for a research project I am looking at a model to estimate a fixed effects logit model of the type $$y_{it} = \Lambda(x_{it}'\beta +w_{it}'\theta +a_i) .$$ Now I know that I would usually do that ...
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### 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 $\theta$. ...
120 views

### Is it a known phenomenon for the variance of a component (GMM) to increase without stopping?

I know it can happen for it to decrease dramatically as it overfits on a single datapoint. But I've never read about a component "taking everything over". See the following images (circles are stddevs)...
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### Minimization Method for GMM Estimates

Which minimization method is usually used for estimating the coefficients in a GMM setting? I.e. in the following: \begin{align*} arg min_b \ g_T(b)'Wg_T(b) \end{align*} Is there any dominating ...
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### 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 ...
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### How to calculate BIC and AIC for a gmm model in #R using #plm?

I originally posted this question here. But I think it is better suited for here. I am running Generalized Method of Moments (GMM) Estimation for Panel Data in <...
506 views

### Is there a way for gmm in R to return parameters even if the covariance matrix is numerically singular?

I'm trying to estimate a nonlinear GMM model with a large parameter space and a large data set. The numerical computation takes a extremely long time and I have been using small subsamples (which also ...
150 views

### Showing that the difference of two variance matrices should be positive semi-definite… or not

I am trying to prove a result: intuitively, the GMM estimator should have a larger variance under homoskedasticity than LS and vice versa under heteroskedasticity. We are working with various ...
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### Can anyone suggest me a book to study GMM estimator?

I need to learn GMM (Generalized Method of Moments) estimator to replicate a paper for my Research Workshop class. I have a very limited background in Econometrics and Statistics. Where should I ...
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### 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 ...
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### difference GMM with trending variables

I want to estimate a panel equation of the form $$y_{it}=ρ y_{i,t−1}+β_1 x_{1,t}+⋯+β_k x_{k,t}+ c_i+γ_t+ϵ_{it}$$ where $c_i$ are country specific effects, $γ_t$ period effects and $ϵ_{it}$ error ...
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### Forced alignment HMM

I am currently trying to understand what is involved to train a Hidden Markov Model (HMM) with Forced alignment. Forced alignment, as far I understand, is to align the audio file with the utterance ...