14
votes
Accepted
Principle of Analogy and Method of Moments
Least squares estimator in the classical linear regression model is a Method of Moments estimator.
The model is
$$\mathbf y = \mathbf X\beta + \mathbf u$$
Instead of minimizing the sum of ...
- 60.8k
6
votes
Accepted
Elbow Test using AIC/BIC for identifying number of clusters using GMM
Welcome to CV!
This plot shows how the AIC and BIC change as a function of the number of clusters. While the AIC continues to decrease with a larger number of clusters, you can see that the BIC stops ...
- 14.3k
6
votes
Accepted
How to implement the Generalized Method of Moments for the upper limit of a uniform?
The sample equivalents of your moment conditions are
$$
g_1 = \frac{1}{n}\sum_{i=1}^n \left(Y_i - \frac{\theta}{2}\right)
$$
and
$$
g_2 = \frac{1}{n}\sum_{i=1}^n \left(Y_i^2 - \frac{\theta^2}{3}\right)...
- 1,632
6
votes
Accepted
What's the point in using identity matrix as weighting matrix in GMM?
Yes, getting a first step estimator is the canonical use. Of course, the error terms in $$S = \frac{1}{n}\sum_i\epsilon_i^2x_ix_i'$$ are not observable, so that you need to replace them with something ...
- 34.8k
6
votes
What are the "moment conditions" in the GMM method? Also: GMM vs IV vs 2SLS?
The moment condition is the exogeneity condition $\mathbb{E}(u_i x_i) = 0$. ($\mathbb{E}(u_i | x_i)=0$ is not a moment condition. It is an equality of random variables.)
OLS is a special case of ...
- 3,378
5
votes
Accepted
How to make a GMM from a Histogram to give a probability?
This example is demonstrated using Matlab. It can be easily adapted into Python or R.
Let's assume that your data contains a mixture of two underlying Gaussians, $\mathcal{N}(m_1, s_1)$ and $\mathcal{...
- 3,602
4
votes
Accepted
R: GMM Estimators in a dynamic panel
Dynamic panels are usually dealt with using GMM. Check pgmm in plm. It should be quite straightforward to follow.
https://www.jstatsoft.org/article/view/v027i02/v27i02.pdf
- 279
4
votes
When to use Gaussian mixture model?
In my opinion, you can perform GMM when you know that the data points are mixtures of a gaussian distribution. Basically forming clusters with different mean and standard deviation. There's a nice ...
- 159
4
votes
Accepted
Why are standard errors downward biased when considering weak instruments
See slides 8 and 9 of these notes. In a simplified setting,
$$y=\beta_{0}+\beta_{1}x + u$$
where $\text{Cov}(x,u) \ne 0$ but $z$ is a valid instrument for $x$, the estimated variance for $\hat{\...
- 321
4
votes
Accepted
How to Remove Fixed Effects to Reduce Heterogeneity?
Regarding the meaning, on the same slide 36, they claim an assumption:
"Common identifying assumption: Parameter values are constant across
all firms and years within the sample."
Because ...
- 323
4
votes
Why can the method of moments be expressed as a minimization problem?
To expand on @Glen_b’s comment, consider the function $f : \mathbb R \to \mathbb R$, and suppose that we want to find the set of all $x \in \mathbb R$ such that $f(x) = 0$.
It may be the case that ...
- 5,180
4
votes
Accepted
How to derive the GMM estimator for the Covariate Balancing Propensity Score?
Let $$\begin{align*}\Sigma(\boldsymbol T,\boldsymbol X) &= N^{-1}\sum_{i=1}^N\begin{pmatrix} s_{\beta}^{~}(T_i, X_i)s_{\beta}(T_i,X_i)^\top & s_{\beta}^{~}(T_i, X_i)w_{\beta}(T_i,X_i)^\top \\ ...
- 399
3
votes
Selection of weighting matrix in GMM estimation
in general you do not need much assumptions in order to define a proper weighting matrix. The weighting matrix $W$ must be positive (semi)definite as a minimum condition. However, the power of GMM ...
- 1,478
3
votes
What's the point in using identity matrix as weighting matrix in GMM?
This second answer, based on exposition from Hayashi, Econometrics, addresses the question posed in the comment to the first answer as to why the specific choice of $W$ results in an efficient GMM ...
- 34.8k
3
votes
Accepted
Use of Weighting Matrix (GMM)
Each estimated moment is a random variable with unequal variances, and, usually, non-zero cross-moment covariances. Using the inverse of the covariance matrix re-weights the moments, so that you ...
- 38.3k
3
votes
How to Test Linear Hypotheses about Parameters in Simulation-Based Indirect Inference
You don't have independent obsevations, so the factor $\sqrt{n}$ with which one usually scales the likelihood ratio/other test statistics would make your test oversized. I know this is not much, but ...
- 331
3
votes
Choice between static and dynamic panel regression
My analysis concerns a macroeconomic study and as often happens in these cases (I would not be wrong but they are commonly called "macro-panel" or "wide-panel").
I have never ...
- 6,454
3
votes
Why does system GMM fail due to computationally singular system in my setup?
The main reason is that your moment matrix is badly conditioned. This is specific to your dataset. Using momentfit, we can try to see what happens if we compute the ...
- 116
2
votes
Implementing Minimum distance estimation
You need to change the initial value of sigma. Default is zero, so you're dividing by zero and get missings at your initial values, as your error message indicates.
- 54
2
votes
Accepted
Forced alignment HMM
For better understanding of the complex subject it is better to read the book instead of random sources on the web.
A book like Rabiner, Juang. Fundamentals of Speech Recognition will give you much ...
- 570
2
votes
Are analytical derivatives unambiguously superior to numerical derivatives in GMM?
I can't speak about your model specifically, but in general, no.
This is part of the reason why analytical (i.e. symbolic) derivatives are not used for large models in machine learning. (Instead, ...
- 2,284
2
votes
System GMM while Dependent Variable lies within [0, 1]
GMM does not impose distrubutional assumptions on the errors, so you can estimate the model and the standard errors; interpreting the model for testing and inference might be tricky.
- 21
2
votes
Minimization Method for GMM Estimates
It entirely depends on the form of the moment conditions! You can end up with everything from a simple, quadratic programming problem to some horrible, non-convex objective. (As a side note, a key ...
- 23k
2
votes
Minimization Method for GMM Estimates
It certainly is problem specific. E.g., for linear GMM estimators, we can find an analytical solution to the problem (using the notation from Hayashi's book, i.e., instruments $x$, regressors $z$, ...
- 34.8k
2
votes
Accepted
Book request on Generalized Method of Moments
The book is called:
Econometrics: A Modern Introduction, by Michael P. Murray
- 100
2
votes
Accepted
GMM Estimation and convergence problem
To be precise, it is the second moment that you get wrong. The first first one is on spot. In your case, given that the moment conditions are correct (but the criterion function looks very messy to be ...
2
votes
R: GMM Estimators in a dynamic panel
there is a "pgmm" option: estimation of generalized method of moments models for panel data in "plm" package. It should be a corresponding function in R to xtabond2 from Stata (see CRAN and Author's ...
- 21
2
votes
Accepted
Question on GMM
The restrictions you gave are linear and so we will find that this GMM specification is equivalent to restricted OLS as is most natural. We can express the restrictions as,
$$R\beta = r$$
Where $r = \...
- 2,557
2
votes
Efficiency of IV vs GMM
Hayashi's exercise mentioned in the comments (see http://fhayashi.fc2web.com/hayashi_econometrics.htm) is a good reference, yes. He considers the case where the set of instruments $x_i$ consists of ...
- 34.8k
2
votes
Maximum likelihood vs generalized method of moments
To expand on what I wrote in the comment, suppose we have data $\{X_i\}_{i=1}^n$ which have some distribution $F$ whose density $f_{\theta}(x)$ is known up to some parameters $\theta \in \Theta \...
- 549
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