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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8 views

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 ...
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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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34 views

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 ...
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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 ...
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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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59 views

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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13 views

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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Difference GMM: is it possible to build valid instruments with X that is (mostly) time invariant?

I have a theoretical question regarding the estimation of Difference GMM (Arellano Bond). I have a panel with 90 countries and 27 years and am trying to estimate a model similar to the following $y_{i,...
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108 views

dynamic GMM (xtabond2) with interactions

I am trying to estimate a model using first difference GMM estimator with the xtabond2 command and I was trying to understand whether my logic was consistent. I ...
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34 views

Comparison of GMM and ML estimators for regression with correlated errors

Consider a linear model with normally distributed, autocorrelated errors \begin{aligned} y&=X\beta+\varepsilon \\ \varepsilon&\sim N(0,\sigma^2_{\varepsilon}) \text{ and autocorrelated.} \end{...
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40 views

Simultaneous GMM estimation: standard errors of common coefficients

So I am estimating a production function based on Wooldridge (2009) GMM adaptation of preexisting semi-parametric, 2-stage techniques. One of the upsides of GMM is simultaneous instead of sequential ...
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107 views

Use of Weighting Matrix (GMM)

While conducting estimation via the Generalised Method of Moments, or GMM, I understand that we need to minimise the following expression: $Q_n(\theta)=g_n(\theta)'W_ng_n(\theta)$ Where $g_n(\theta)$...
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39 views

Naming of mathematical elements in GMM?

I'm struggling with the naming of different elements in GMM. There doesn't seem to be consistency in the literature. What do we even call the moment integrand $g$? I take a stab below with help from ...
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19 views

OLS - Predeterminedness and moment condition

I'm having trouble validating if following procedure to test for predeterminedness is plausible. Given the linear model: $y_t=\beta_1+\beta_2x_{1t}+\beta_3x_{2t}+\epsilon_t$ Having $x_{2t} = y_{t+1|...
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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,...
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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 ...
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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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42 views

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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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 ...
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43 views

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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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\...
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130 views

Standard errors of *partial* two stage least squares coefficients

Here partial 2SLS (I coined this term and found it descriptive) is the approach that SAS uses for 2SLS. Compared to "ordinary" 2SLS which in the first stage projects all explanatory variables $X$ onto ...
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78 views

Using varimax – rotated PCA for clustering via Gaussian Mixture Model?

After extracting the Principle Components of my data, I apply Gaussian Mixture Models for clustering. I used a subset of the orthogonal basis of the Principle Components and projected my data onto ...
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148 views

Are Gaussian Mixture Models stochastic or deterministic?

Each time we generate a gmm model, we obtain slightly different clusters. Can we hence say gmm is stochastic? We obtain the same clusters if a random seed is set; does this mean given a random seed, ...
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1k views

R: GMM Estimators in a dynamic panel [closed]

I put up a fixed effects regression using panel data with a time lag of the dependant variable, so somthing like this: ...
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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 ...
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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?
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78 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 (...
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1answer
191 views

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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1answer
61 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 ...
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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 ...
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43 views

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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214 views

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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79 views

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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54 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 $\theta$. ...
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1answer
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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239 views

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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1answer
89 views

Some questions about the Generalized Method of Moments

Here are three (somewhat related) questions about the (Generalized) Method of Moments. I have only just today started studying this method. Concerning the following statement by Greene: Why is $...
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48 views

Book request on Generalized Method of Moments [closed]

I found a very basic but usefull chapter on GMM available here. Does anybody know the title and the author of the book containing this chapter?
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396 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(\...
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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 ...
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960 views

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 <...
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1answer
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 ...
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1answer
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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1answer
218 views

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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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 ...
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1answer
192 views

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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1answer
966 views

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 ...
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2k views

Robustness checks for Pooled OLS, Fixed Effects, and GMM

I am investigating conditional convergence across Indian states using panel data. I include the state name, year, SDP per capita, and a number of conditioning variables such as Public Expenditure, ...
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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 ...