# Questions tagged [method-of-moments]

A method of parameter estimation by equating sample and population moments then solving the equations for the unknown parameters.

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### 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" ...
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### Method of moments - what determines the number of moment conditions?

Given the following definition: What is the function $f$ here? For me, the method that is presented in the wikipedia article is very clear: https://en.wikipedia.org/wiki/Method_of_moments_(statistics)...
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### Compare quality of fit, MLE vs method of moments

I have many different datasets that presumably should follow the same distribution type (but with distinct parameters). I've identified one distribution type that seems to describe best the data (...
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### In a regression model, can we use $E(u)=0$ as the moment condition?

Consider the linear model with stochastic regressors: $$y_t = \beta_0^\prime x_t + u_t, \quad E(u_t | x_t)= 0$$ So that $E(u_t | x_t)= \beta_0^\prime x_t$. Using the e Law of Iterated Expectations (...
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### Two supposedly equivalent approaches to the method of moments

I am reading the book "An Introduction to Econometric Theory" by A. Ronald Gallant. In the section of the book on the Method of Moments, I get a little confused about the method as I know it....
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### Why Horvitz-Thompson Estimator is a type of Method of Moments?

I notice Donald Rubin once remarked the IPW estimator (resembling the Horvitz-Thompson estimator in sampling theory) in a conference: "Horvitz-Thompson is just glorified Method of Moments. We've ...
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### A description of the mean of the Geometric Distribution - is it unorthodox or just incorrect?

I have a homework assignment where I'm asked to propose an estimator for the mean of a geometric random variable. This seemed simple enough, given that I've always understood the mean of the geometric ...
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### Finding method of moments estimate for density function $f(x|\alpha) = \frac {\Gamma(2\alpha)} {\Gamma(\alpha)^2}[x(1-x)]^{\alpha - 1}$

Suppose that $X_1, X_2, ..., X_n$ are i.i.d random variables on the interval $[0,1]$ with the density function $$f(x|\alpha) = \frac {\Gamma(2\alpha)} {\Gamma(\alpha)^2}[x(1-x)]^{\alpha - 1}$$ where ...
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### 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 ...
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### Method of moments for symmetric mean zero distributions

When using the method of moments to fit a symmetric mean zero distribution, does it make more sense to fit higher order moments or lower order absolute moments? I could not find any resources which ...
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### What's special about moments that allows "method of moments" to work?

The idea behind Method of Moments (MOM) is quite intuitive: find the parameter values so that the population moments (which are functions of those parameters of interest) matches the sample moments. ...
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### 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 ...
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