semibruin
• Member for 8 years, 6 months
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• Los Angeles, CA

First, in the Roy model, $\sigma_{\varepsilon}^{2}$ is normalized to be $1$ for identification reason (c.f. Cameron and Trivedi: Microeconometrics: methods and applications). I will maintain this ...

Chris Genest has another introductory paper "Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask".

This is a variation of the selection model in econometrics. The validity of the estimates using only the selected sample here depends on the condition that $\Pr\left(Y_{i}=1\mid X_{i},D_{i}=1\right)=\... View answer Accepted answer 5 votes Throughout my answer, the usual conditional mean independence$\mathbb{E}(\varepsilon_{i}\vert X_{i},Z_{i})=0$is maintained. It is instructive to consider a concrete example. Let$X_{i}$be a dummy ... View answer Accepted answer 4 votes Simply put: the simple OLS estimator will be inconsistent when$U_{1}$or$U_{0}$is not mean indepent with$\varepsilon$, i..e$\mathrm{E}\left(U_{1}\mid\varepsilon\right)\neq0$or$\mathrm{E}\left(...

Here is a counter example. Let $X_{n}$, $n=1,2,\ldots$, be a sequence of random variables, whose distributions are defined as follows, $$X_{n}=\begin{cases} 0, & \mbox{with probability }\frac{n-1}... View answer Accepted answer 3 votes The following code implemented the practice of putting interaction between Female dummy and year. The F test at the bottom test your null \beta_{Female} = \beta_{Male}. The t-statistic from plm ... View answer Accepted answer 3 votes The intuition is that it is possible that the pair (Y,Z) or (Y,W) cannot determine X; but (Y,Z,W) together can determine X. The following counter example is constructed from this intuition. ... View answer Accepted answer 3 votes Let me rephrase your question a little bit. The original regression (1) is$$ Y=\beta_1 X +\beta_2M+\beta_3XM+\varepsilon, $$where \varepsilon is the error term. To study the partial effect of X... View answer 2 votes I may prove it under the assumption that \mathrm{E}\left|Y\right|<\infty. In order to prove X_{n}\rightarrow_{d}X, we wish to show that \mathrm{E}f\left(X_{n}\right)\rightarrow\mathrm{E}f\left(... View answer 2 votes Your question is indeed asking for the finite sample distribution of r_{N}. To address your question, let me rephrase it in terms of linear regressions. So a linkage between r_{N} and the ordinary ... View answer Accepted answer 1 votes Yes and no. If x and w are correlated, the endogeneity of w will bias the estimation of \beta, partial effect of x. Let Y, X, \hat{X} and W be the matrices by stacking the ... View answer Accepted answer 1 votes For n = 2, p(\gamma(x) = 1) = p(x_{1} - x_{2} > 0). Let z_{1,2} = x_{1} - x_{2}. Obviously, z_{1,2} \sim N(\delta_{1} - \delta_{2}, 2). Hence, p(\gamma(x) = 1) = 1 - \Phi((\delta_{1} - \... View answer 1 votes We have \sqrt{h_n} = o_p(1). Note that \sqrt{h_n}O_p(1) = O_p(\sqrt{h_n}). Using the result that o_p(1)O_p(1)=o_p(1). We have the conclusion that O_p(\sqrt{h_n}) = \sqrt{h_n}O_p(1) = o_p(1). View answer 1 votes For notational simplicity, I drop the subindex i in the sequel. Observe that \mathbb{E}\left(vx\right)=0 implies that$$ \mathbb{E}\left\{ \left(z-x\delta\right)x\right\} =0. $$Hence, we have \... View answer 1 votes I think the main difference between fixed and random effects is that the unobserved individual effect \alpha_i is purely random in the random effect paradigm in the sense that its distribution does ... View answer Accepted answer 1 votes I did not see the rationale of using your "group BIC/AIC". Your proposed group BIC/AIC is comparing a different pair of models. Let f(\mathbf{x}_i \mid \alpha) and g(\mathbf{y}_i \mid \beta) be ... View answer Accepted answer 0 votes For simplicity, consider y_{i,t} = \rho y_{i,t-1} + a_{i} + e_{i,t}. Let \hat{\rho} be the Arellano-Bond or any consistent estimator of \rho. We have$$ \hat{e}_{i,t} \equiv y_{i,t} - \hat{\rho}...