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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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835 views

How to derive the GMM log-likelihood formulation in the eigenvoice modeling technique?

Given a GMM with mean $M=[M_1, M_2, ..., M_C]$ and covariance $\Sigma=[\Sigma_1, \Sigma_2, ..., \Sigma_C]$ (where $C$ is the number of mixtures), many papers on eigenvoice modeling states that the ...
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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 ...
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1answer
410 views

Selection of weighting matrix in GMM estimation

As stated in the title. Are there any assumptions or restrictions behind in selection of weighting matrix in doing the estimation? Does it exist a form which is suitable in most cases?
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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
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1answer
172 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. ...
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1answer
1k views

How can I compute the GMM in STATA without having any instrumental variables, just the underlying assumptions?

I am trying to find the coefficients of a linear model using the gauss-markov assumptions but since I am not experienced in Stata I do not know the code and was looking for the generic recipie: using ...
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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
964 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 ...
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275 views

How to select “moments to match” in simulated method of moments (SMM)?

Unlike DSGE model ,which indicates which moment to match explicitly (this paper), the standard of "moment selection" in quantitative econ model is ambiguous. Certain parameter can influence more than ...
8
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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.
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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 ...
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0answers
84 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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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=\...
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46 views

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

I'm new to GMM, so sorry in advance for maybe stupid question. 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 ...
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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 ...
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161 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 ...
2
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1answer
578 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
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1answer
639 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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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
186 views

How to get the determinant of a covariance matrix from its diagonal elements

I am trying to implement a speaker recognition system in MATLAB. I am using Gaussian Mixture Models (GMM) for speaker modelling and maximizing the posterior probabilities for classification. The ...
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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 ...
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0answers
175 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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1answer
1k views

Can anyone help me with R code for the two-step generalized method of moments (GMM) [closed]

I am new to R and need to do a 2 step Generalized Method of Moments estimation. Can anyone help me with an example code. Thanking you.
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2answers
112 views

Generalized Method of Moments

I was looking for a book that could explain me well the Generalized Method of Moments, its mathematical nuances, and even have a look to the empirical side, maybe with some guided exercises with Stata ...
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1answer
385 views

GMM-IV or 2TSLS for small sample?

I only have 23 obervations. I heard that GMM-IV is usually for large sample. Hence should I use GMM-IV or 2TSLS? Besides the sample size, what should I also consider when deciding between GMM-IV and ...
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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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2answers
756 views

What does “special case of GMM” mean?

I was researching purchasing this text book: http://www.amazon.com/dp/0691010188/ref=wl_it_dp_o_pd_nS_ttl?_encoding=UTF8&colid=2QTISO1Y8TYVW&coliid=I3FUEFWL47AC4L In its description it talks ...
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1answer
1k views

Can someone explain 2SLS - GMM?

I believe I have a dynamic relationship within my panel dataset, with heteroscedasticity and autocorrelation. I've been instructed to look into GMM as it is the solution. What is it and how can I do ...
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1answer
77 views

Textbook GMM/Convergence Question

Consider a binary random variable X that satisfies: $Pr(X = 0) = \theta \ \ \ $ and $Pr(X = 1) = 1−\theta $ for $\theta \in (0, 1)$ an unknown parameter. Suppose an i.i.d. sample of size $n$ ...
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1answer
3k views

How to deal with weak instrument with GMM estimator?

I use the two-step system GMM estimator (panel data) and I get the following results: ...
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0answers
402 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 ...
1
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1answer
988 views

Moment Conditions for Stochastic Discount Factor (SDF)

Following extract has been taken from Computing Generalized Method of Moments and Generalized Empirical Likelihood with R, the Vignette of gmm R package. In some ...
2
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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? ...
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1answer
185 views

Deriving a restricted efficient GMM estimator with common coefficients

I'm having a bit of trouble in doing exercise 3. For us to compare with Pooled OLS, and Random effects model, it seems that we must assume that we're under conditional homoskedasticity, and the set of ...
2
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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 ...
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1answer
140 views

Typos in Hayashi Econometrics? How to understand this 2SLS as an IV estimator

Below are a few passages of Hayashi's Econometrics. According to the notation there, $X$ the matrix of instruments, $Z$ the matrix of original regressors, and $Y$ vector of dependent variable. A few ...
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0answers
153 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.
4
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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 ...
3
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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
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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 ...
4
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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
272 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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0answers
130 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)-\...
2
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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 ...
1
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1answer
3k views

Unit roots and GMM estimation

I want to estimate panel models of the following structure: $y_{it} = \rho y_{i,t-1} + \beta_1 x_1 + \dots + \beta_k x_k + c_i + \gamma_t + \epsilon_{it}$, where $c_i$ are time constant country ...
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1answer
5k views

J stat problem, GMM

I have recently performed a GMM estimations, my problem is that all the J-stats are 0.0000. It means that the IV are overrefined right or the model is not well specified. I used one-period lags of the ...
2
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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 ...
4
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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 ...
3
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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 ...
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 $$ y_{igt} = \alpha_i + P_{gt} + \beta_1y_{igt-1}+ \beta_2y_{igt-2} + X_{igt}'\gamma + \epsilon_{igt} $$ ? ...