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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545 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 ...
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32 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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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(\...
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116 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
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0answers
983 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
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275 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....
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94 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 ...
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94 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 ...
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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: <...
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688 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
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1answer
35 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 ...
2
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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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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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75 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
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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 ...
2
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0answers
52 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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377 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
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1answer
64 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 ...
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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
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1answer
675 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 ...
2
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138 views

Question about Lagrangian Multiplier (Gradient) Statistic of constrained GMM

I am trying to derive the Lagrangian multiplier statistic (GMM version) under a restriction. The question is given below The quadratic form is given by $Q_n(\theta,\alpha)=[m(\theta)', (m^a(\theta)-\...
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55 views

How to model conditional moments using an additive model

Let's say that I have the data set $(X,Y)$ where $X$ is a p-dimensional variable and $Y$ is uni dimensional. I'm interested in the following model: $$ \theta_y = E(Y|X) \\ \theta_{y^2} = E(Y^...
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638 views

A special case of GMM estimation in R

I want to estimate the forward looking version of the Taylor rule equation using the iterative nonlinear GMM: I have the data for all the variables in the model, namely (inflation rate), (...
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32 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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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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40 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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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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334 views

For system GMM, do we need stationarity in levels or first-differences?

I'm trying to decide whether I should use a difference GMM or a system GMM. I have a panel of 50 states over 19 years. I know that system GMM has better finite sample properties when the series is ...
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1answer
62 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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85 views

Generalized method of moments (GMM): testing equality of parameters across subsamples

I estimate parameters of a panel data model with GMM using Stata. I specify the variance-covariance matrix assuming that the observations are correlated in the same period of time (...
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48 views

Using generalized method of moments (GMM) with partially overlapping expectational errors

I use GMM to estimate the log-linear Euler equation (using Stata). But I have autocorrelated error terms of the MA(q) form because of partially overlapping expectational errors. I'm a bit confused by ...
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0answers
166 views

Replication of an intercept only GMM SAS example in R

I try to replicate this SAS example in R: http://support.sas.com/kb/40/098.html I've done everything that's easy, but since I am not familiar with GMM, I am stuck with the last step. Reproducible ...
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57 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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180 views

GMM Estimator Problem

Suppose $X_i$ is uniformly distributed on $[v;c]$, where $v$ is the parameter of interest and $c$ is some constant. The task is to find a GMM estimator of $v$. I know that to derive a GMM estimator ...
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410 views

Cluster Robust Standard Errors vs GMM

I want to estimate a linear model on a panel data set using fixed effects and my dependent variable has positive serial correlation. I also have to address heteroskedasticity. I have read that two-way ...
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0answers
154 views

How to calculate the posterior probabilty of Gaussian Mixture Component

If the mean vector and the Covariance matrix of a Gaussian Mixture model are known, how could I calculate the posterior probability of each of the Gaussian Component in the mixture.
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0answers
411 views

Estimation parameters using Generalized Method of Moments and Generalized Empirical Likelihood with R

I have two density functions: $h_{1}(x)$, $h_{2}(x)$. I want to estimate parameters from one dataset using $ h_{1} $ and $ h_{2} $ andthe GMM estimator or the GEL : from the article "Computing ...
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0answers
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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15 views

ML Models for Speaker Identification

I am working on speaker identification problem using GMM (Gaussian Mixture Model). I have to just identify one user present in the given audio, as GMM model output log probability how to set the ...
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0answers
28 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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25 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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4 views

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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78 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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0answers
18 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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257 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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41 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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42 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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0answers
24 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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26 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 ...