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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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Reparametrization trick in GMM

Assume I have two random variables, $X$ and $Y$. If $p(Y|X)=\mathcal{N}(Y;\alpha.X,\sigma^2\mathbb{I})$, I can calculate $Y$ by using reparametrization trick: $Y=\alpha.X+\sigma.\epsilon$, with $\...
Toan Le's user avatar
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Large $N$, small $T$ in SUR: workaround using system GMM

Consider a system of linear equations as in seemingly unrelated regression (SUR). If the number of equations $N$ is large relative to the sample size $T$, the weighting matrix in SUR (i.e. the error ...
Richard Hardy's user avatar
2 votes
1 answer
65 views

Why does system GMM fail due to computationally singular system in my setup?

I am estimating a system of seemingly unrelated regressions (SUR) with gmm::sysGmm in R. Each of the equations has one unique regressor and one common regressor. ...
Richard Hardy's user avatar
2 votes
1 answer
101 views

System GMM yields identical results for any weighting matrix

I am estimating a system of seemingly unrelated regressions (SUR) in R. Each of the equations has one unique regressor and one common regressor. I am using ...
Richard Hardy's user avatar
2 votes
1 answer
63 views

SUR estimated via `systemfit` vs `sysGmm`: different standard errors

I am estimating a system of seemingly unrelated regressions (SUR) in R. Each of the equations has one unique regressor and one common regressor. I have two alternative implementations: one via ...
Richard Hardy's user avatar
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0 answers
30 views

Two-Step GMM and Instrumental Variable

I am trying to run a regression in r using country-level panel data with female labour force participation rate as the independent variable and lnGDP, lnGDP^2, Trade (as % of GDP), Fertility, School ...
nomes's user avatar
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20 views

Within transformation vs. first differencing in the over-identified case

I have the following fixed effects model: $S_{it}=D_{it}'\gamma + \alpha_i + \epsilon_{it}$ My textbook says i can use first-differencing and derive a moment function that overidentifies $\gamma$ for ...
Katharina K's user avatar
5 votes
1 answer
393 views

How to derive the GMM estimator for the Covariate Balancing Propensity Score?

The covariate balancing propensity score (CBPS) described by Imai and Ratkovic (2014) involves fitting a logistic regression for the propensity score $\pi_\beta(\mathbf{X}) = P(T = 1\vert\mathbf{X})$ ...
Noah's user avatar
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1 vote
1 answer
43 views

Instrumental variable for panel data

I am trying to quantify the effect of financial sanctions on cross-border capital flows. I have built a dyadic dataset of sanctions and capital flows by country pair and year. My sample period spans ...
Loki5714's user avatar
3 votes
2 answers
75 views

Why can the method of moments be expressed as a minimization problem?

Generalized method of moments (GMM) estimation seems to be called generalized method of moments because the standard method of moments (MoM) is a special case, following the following logic. MoM is ...
Dave's user avatar
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momentfit::gmm4 model output interepretation

I specify my GMM routine ...
Mr Frog's user avatar
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How do I use GMM or LDV to handle a big problem with autocorrelation in a data frame spanning 1945-2018?

For an exam (results for this exam do not need to be entirely accurate and explain the all variations in our variable) I am doing an analysis of (all countries in the world) of whether parliaments ...
Felipe Branner's user avatar
3 votes
1 answer
68 views

Estimator for Dynamic Panels with Individual Specific Slopes

I'm working on some economic stuff and the objective is to conduct a panel data analysis. I assumed the following data-generating process: \begin{equation} y_{it} - y_{i,t-1} = \eta z_{i,t-1} + \...
Maximilian's user avatar
4 votes
1 answer
13 views

Incorporating idiosyncratic risk as a pricing factor with GMM

Originally I posted this on Quantitative Finance SE here but got no response. Months later, I am posting it here hoping for better luck. Suppose we are given a dataset with $T$ time periods and $N$ ...
Richard Hardy's user avatar
2 votes
1 answer
76 views

Clustered standard errors using pgmm()

I am estimating a system-GMM model using the pgmm function from the plm package in R: ...
Veronica Santana's user avatar
1 vote
0 answers
160 views

Number of instruments in GMM (using pgmm in R)

Number of instruments used in GMM model (pgmm function in R) I performed a GMM (Generalized Methods of Moments) analysis in R using the ...
Li4991's user avatar
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59 views

Sargan test results = 1 in system GMM

I am having difficulties understanding my diagnostic test results for my twoways effects two-step model system GMM, which I performed in R. The results of my Sargan test (test for overidentification ...
Li4991's user avatar
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1 vote
1 answer
90 views

Does PLM package (PGMM function) use Windmeijer-corrected cluster-robust errors? [closed]

I am performing a GMM analysis using the pgmm function in the plm package in R. I read a lot about different errors (nonrobust, ...
Li4991's user avatar
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0 answers
35 views

Problems with GMM (Generalized Methods of Moments) in R

I am interested in performing an analysis using a GMM model for a panel dataset. I am conducting the analysis in R, using the pgmm package. My code is the following:...
Li4991's user avatar
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1 vote
0 answers
33 views

How do deal with multicollinearity, endogeneity and interpret the interaction terms in a panel dataset?

The model ŷ = b0 + b1X1 + b2X2 + b3X1X2 ŷ =company financial performance metric X1 = carbon emissions X2 = carbon assurance X1X2 = interaction term The issues: Let’s say: • X1 + X2 are related (but ...
Reuben's user avatar
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2 votes
0 answers
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Dynamic panel data model with treatment

Consider a simple dynamic panel model with a single lag: $$y_{it} = \alpha_i + x_{it}'\beta + \rho y_{i,t-1}+\epsilon_{it}$$ Now assuming that $x_{it}$ is most ordinary covariates, this can be ...
user2958701's user avatar
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1 answer
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GMM and Instruments

I am using GMM for my research work. Previously, I have used ivreg command in stata in which we manually specify the instrumental variable for the endogeneous variable. I was just curious and ...
Researcher101's user avatar
0 votes
2 answers
109 views

How to understand the binary latent variable z in GMM model?

GMM(Gaussian Mixture Model) itself is a mixture of Gaussian with each having the proportion of $\pi_k$, $$\sum_{k=1}^{K}\pi_k=1$$this is easy to understand. But when introducing the latent, I don't ...
user3153824's user avatar
1 vote
1 answer
71 views

Proving uniform convergence of moment restriction score function in GMM asymptotic normality proof

I am asked in a homework question to prove asymptotic normality for the generalized method of moments estimator. The assumptions (which i think are necessary to solve this particular subproblem) given ...
Jeppe Pilgaard's user avatar
1 vote
0 answers
20 views

How to build the covariance matrix with different weighted moments via GMM [closed]

I have two sets of moment conditions, one is IV moment with N observations but the second moment only has N_1 observations, N_1<N. How to build the covariance matrix? Appreciate for any replies!
Nicolej's user avatar
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0 answers
195 views

Fitting a 3D GMM in a 3D space is equivalent to fit a gaussian in each 1D coordinate?

I have a 3D data set data represents positions in X,Y,Z space. The positions are generated by a Poisson model. I would like to filter out outlier positions, i.e., positions that are farther than the ...
MLggm's user avatar
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3 votes
0 answers
102 views

Clustered vs. GMM-based standard errors: which ones to use in asset pricing?

This question was posted on Quantitative Finance Stack Exchange a while ago. While it was received positively there and generated a reasonable amount of views, no answers have been posted. Thus I am ...
Richard Hardy's user avatar
5 votes
1 answer
798 views

Maximum likelihood vs generalized method of moments

I am trying to understand how maximum likelihood (MLE) and generalized method of moments (GMM) are related to each other. In particular, I often see people saying that MLE can be written in terms of ...
rick's user avatar
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0 answers
50 views

Central cross moments of independent random varibales

The central cross-moments of a random vector $[X_1, X_2,\dots, X_n]$ is $$ \mu_X(n_1,n_2,\dots,n_n) =E[(X_1-E[X_1])^{n_1}(X_2-E[X_2])^{n_2}\dots(X_n-E[X_n])^{n_n}]$$ I wish to know if $\mu_X(1,1,\dots,...
user1420303's user avatar
3 votes
1 answer
1k views

How do Measure "Robustness" in Statistics?

I am an MBA Student taking courses in Statistics. Our prof was comparing two different methods of estimating the parameters for a regression model: General Method of Moments (GMM) and Maximum ...
stats_noob's user avatar
1 vote
0 answers
124 views

Is there a formula for estimating confidence intervals for indirect inference estimates?

Indirect inference is usually deployed to estimate parameters $\theta$ of simulation models, i.e. models for which likelihood is unknown or intractable but that can be "run forward" ...
CarrKnight's user avatar
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0 answers
267 views

GMM panel data model in R - no individual effects

I need to estimate the coefficients of a particular dynamic panel data model. \begin{equation} \ln(y_{i,t})=\alpha_0+\beta ln(y_{i,t-1})+\theta_t+ \varepsilon_{i,t} \end{equation} Currently, I'm ...
user avatar
1 vote
1 answer
135 views

Regression specification: what if one regressor is function of another

Consider the following regression model $$ Y_i=D_{i}(\alpha_1+\beta_1 X_i)+(1-D_i)(\alpha_2+\beta_2 X_i)+\epsilon_i $$ where $D_i$ is a binary variable. Suppose the researcher has an i.i.d. sample $\{...
Star's user avatar
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0 votes
2 answers
1k views

Is using a fixed random seed in production okay?

I have a dataset and am trying to use GMM to cluster it. The algorithm works well but when I run it multiple times I get different results. While the clusters produced in each run are valid my users ...
M10000's user avatar
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1 vote
0 answers
75 views

ARSV model estimation with (constrained) generalized method of moments in R

I am trying to perform the estimation of the following Autoregressive Stochastic Volatility model $$ y_t=\sigma_t u_t = exp(w_t/2)u_t \\ w_t = \omega + \phi w_{t-1} + \eta_t $$ in R via the function <...
Mr Frog's user avatar
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2 votes
0 answers
142 views

Using the method of moments or GMM to estimate the parameters of a specific problem

Given $(X_t)_{t \in \mathbb{Z}}$ an AR(1) process: $$X_t = c+ \phi X_{t-1} + \epsilon_t, \quad \epsilon_t\sim WN(0,\sigma^2)$$ We can show that $E(X_t) = \frac{c}{1- \phi}$ and $E(X_t^2) = \frac{\...
user346481's user avatar
1 vote
0 answers
197 views

Covariance Matrix Estimation for the Generalized Method of Moments

I am solving and empirical exercise on the Generalized Method of Moments. It's a classical application/test of a famous model in Economics. There are 2 parameters $(\beta, \gamma)$ to be estimated ...
Raul Guarini Riva's user avatar
2 votes
1 answer
558 views

Efficiency of IV vs GMM

I am trying to understand how IV/just identified GMM and overidentified GMM compare when it comes to efficiency. The way I understand it, we are able to identify the vector of coefficients in IV and ...
Blo4d's user avatar
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2 votes
1 answer
217 views

Consistent but inefficient GMM

Consider the following linear model $$y_t = x_t' \beta +u_t$$ where $t =1,...,T$ and $x_t = (x_{1t} x_{2t} ... x_{kt})'$ , $ \beta$ is $k \times 1$ vector of unknown coefficients, $u_t$ is an iid ...
1190's user avatar
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1 vote
0 answers
66 views

Discuss that method of moment estimation is inefficient

Discuss that method of moment estimation is inefficient. Then model is Consider the following linear model $$y_t = x_t' \beta +u_t$$ where $t =1,...,T$ and $x_t = (x_{1t} x_{2t} ... x_{kt})'$ , $ \...
1190's user avatar
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0 answers
331 views

When is the Optimal weighting matrix in GMM singular?

currently I am trying to estimate a simple linear regression: \begin{equation} y_t = X \beta + \varepsilon_t, \end{equation} where I try to find 4 coefficients and one specific predictor is an ...
user326465's user avatar
3 votes
1 answer
182 views

Question on GMM

Consider the following linear model $$y_t = x_t' \beta +u_t$$ where $t =1,...,T$ and $x_t = (x_{1t} x_{2t} ... x_{kt})'$ , $ \beta$ is $k \times 1$ vector of unknown coefficients, $y_t$ is an iid ...
1190's user avatar
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1 vote
0 answers
1k views

What is the difference between GMM-style instruments and IV-style instruments in GMM estimation via xtabond2 or plm?

My question refers to the implementation of GMM estimators, e.g., in the package xtabond2 for Stata or package plm in ...
julia_rython's user avatar
1 vote
0 answers
74 views

Can the Arellano Bond model accommodate lags of explanatory variables?

The standard type of equation I've seen for the Arellano-Bond is y_it = r* y_it-1 + B*x_it + e_it. The endogenous variable y is a function of y at previous times, x at the current time, and an ...
Achintya Agarwal's user avatar
1 vote
0 answers
1k views

GMM regression and instruments count with xtabond2

I have to perform a difference GMM regression on my panel data. It's not important that it works, but if it does not I need robust motivation for why not. My panel data is divided in two bigger groups,...
bas's user avatar
  • 111
1 vote
1 answer
513 views

How to Remove Fixed Effects to Reduce Heterogeneity?

When discussing GMM estimation, Toni Whited and Luke Taylor suggest to reduce heterogeneity by ''eliminating fixed effects,'' see here on Taylor's slides (slide 36): My question: I'm not quite sure ...
Alex's user avatar
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0 answers
240 views

an alternative to GMM?

Dear StackExchange Users, I am currently working on my PhD thesis and one of the chapter deals endogeneity in the data. I have N the number of individual (here country) = 11 and T the time dimension = ...
Rémi Odry's user avatar
2 votes
0 answers
324 views

gmm function in R does not work due to singular variance-covariance matrix

We want to test the CAPM asset pricing models using the GMM procedure. The model is as follows: $$ R_{i,t} - R_{f,t} = \alpha_i + \beta_i(R_{m,t} - R_{f,t}) + \epsilon_{it}$$ The pricing errors at ...
Hans's user avatar
  • 21
4 votes
2 answers
4k views

Choice between static and dynamic panel regression

I have a panel dataset with countries as individuals observed per year. My analysis concerns a macroeconomic study and as often happens in these cases (I would not be wrong but they are commonly ...
UzbeKistaN's user avatar
1 vote
0 answers
120 views

Stopped by zero step from line search - R stops optimization early

I am trying to minimize an objective function, $J(\theta)$, with respect to $\theta$, a 19-dimensional parameter vector. $J(\theta)$ is a smooth nonlinear function so I have tried various gradient-...
EB727's user avatar
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