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4 votes
2 answers
135 views

Markov-type functions

I'd like to have some informations about Markov-type functions (or Cauchy-type): \[ f(z)=\int_{\Gamma} \frac{\mathrm{d}\gamma(\xi)}{\xi-z}.\] $\gamma$ is a positive measure with compact support $\...
Thomas's user avatar
  • 41
2 votes
0 answers
193 views

How to find moment condition for generalized method of moments?

Consider a scalar system with $2K$ outputs and $K+2$ unknowns: $y_{k,1}=x_ka_1+n_{k,1} \quad y_{k,2}=x_ka_2+n_{k,1}$. The variables $n_{k,\ell}$ are zero mean noise variables. To estimate $a_1$ and $...
Jonathan's user avatar
0 votes
0 answers
185 views

Why does the OLS estimator simplify as follows for the single regressor case?

I was reading in "A Guide to Econometrics" that given $Y = X \beta + \epsilon$, the variance covariance matrix of $\beta^\text{OLS}$ is given by $\sigma^2 (X' X)^{-1}$ where $\sigma^2$ is the variance ...
Palace's user avatar
  • 1