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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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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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1answer
182 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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32 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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26 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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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 ...
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1answer
636 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 ...
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182 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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2answers
843 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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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 ...
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36 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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1answer
32 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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1answer
43 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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15 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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6k views

Granger Causality Testing With Panel Data

I'm trying to apply a Granger Causality test to panel data. I've found enough literature to understand that topic. However, I've been unable to find and R package to carry out that analysis. I'm ...
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10 views

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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1answer
71 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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40 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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37 views

GMM: can a constrained regression perform better than an unconstrained regression?

I have one linear regression with a set of explanatory variables and an other set of instrument variables. In my constrained regression, one of the coefficient for a given variable is constrained to ...
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22 views

GMM panel data estimation for a nonlinear response with a binary endogenous variable

I'm interested in potentially using Poisson panel Generalized Method of Moments to hopefully gain consistent estimates for my parameters of interest. However, I have an endogenous binary variable (a ...
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25 views

Bootstrap confidence interval for just-identified IV estimator

Assume we have a regression model \begin{equation} y_{i} = z_{i}' \delta + \epsilon_{i} \end{equation} with dependent variable $y_{i}$, L regressors $z_{i}$ and K instruments $x_{i}$, and assumptions ...
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1answer
42 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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34 views

Moments of the Generalized Dirichlet distribution

I have been trying to solve the following integral. $ \int\theta_j \sum_{k=1}^K \theta_k \beta_{k,w} \prod_{k=1}^K \frac{\Gamma(\alpha_k + \beta_k)}{\Gamma(\alpha_k)\Gamma(\beta_k)} \theta_k^{\...
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1answer
92 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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2answers
178 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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66 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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55 views

How can I scale the $k$-th moment of a time series to a different time frequency?

I have a time series, let's say N daily log-returns. I want to study the moments (possibly the distribution) of the weekly returns. I have two ways: 1) Using the time-additivity property of ...
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1answer
121 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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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 ...
4
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1answer
619 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 ...
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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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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?
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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
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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 (...
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1answer
166 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 ...
3
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1answer
50 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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2answers
494 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 ...
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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 ...
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1answer
60 views

Dimensionality of GMM Estimation

So in my class today we discussed GMM estimation and how we can derive OLS using GMM. I am struggling with the matrix algebra with GMM (from Summations to Matricies) $$g(x,\theta)=\frac{1}{n}\sum_{i=...
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0answers
38 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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78 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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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 $\theta$. ...
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1answer
105 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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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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2answers
174 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
75 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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1answer
44 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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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 ...
2
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0answers
356 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(\...