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General constrained OLS problem Recall that the OLS problem, subject to linear constraints can be written as $$ \begin{align} \arg\min_{\boldsymbol{\beta}}\boldsymbol{Y}'\boldsymbol{Y} - \boldsymbol{ …

You don't say what platform you are using. Stata makes this very easy to do using the margins, pwcompare command. For example, webuse nhanes2 logistic highbp sex##agegrp##c.bmi margins agegrp, pwcom …

You have a case of data-dependent truncated regression model, which is easily handled by the R package truncreg. …

The linear regression model is $$ \boldsymbol{Y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\varepsilon} $$ together with the conditional uncorrelatedness assumption $\mathbb{E}( \mathbf{X}\boldsymbol … Thus this cannot form the basis of a test for the unconditional uncorrelatedness assumption in the linear regression model. …

Here is a Python function to perform a t-test, as well as a z-test for the significance of the correlation coefficient between two series. import warnings import numpy as np import scipy as sp impo …

The Poisson regression model is $$ \begin{align} \mathbb{E}(Y_i \mid \boldsymbol{X}_i) &\equiv h(\boldsymbol{X}_i) \\ &= \exp(\beta_0 + \sum_{k=1}^K\beta_k X_{ki}) \\ &= \mathbb{V}(Y_i \mid \boldsymbol … There is however, nothing specific to the Poisson regression equation in your question. …

The filter function you want to run, from the base package stats -- stats::filter -- is being over-ridden by dplyr::filter, since you are probably also loading dplyr. You can either write stats::filte …

This is so because in the linear regression case, the regression coefficients are the marginal effects. … In the probit regression, there is an additional step of computation required to get the marginal effects once you have computed the probit regression fit. …

For example, assume that you are fitting a linear regression model with the upper set of variables $\mathcal{U} = \{X_1, X_2, X_3, X_4, X_5, X_6, X_7\}$, and lower set $\mathcal{L} = \{X_1\}$, and the …

You probably mean reverse causality. That is a form of endogeneity. For a nice discussion, see page 146 here. Broadly, you deal with it the same way you deal with endogeneity in general, using either …

There is indeed such a paper, written by some of the most eminent current econometricians. Econometrics: A Bird's Eye View by John Geweke, Joel Horowitz and Hashem Pesaran Don't think that this was …

The canonical reference for this kind of thing is White (2001). The model you have is $$ Y_i = \boldsymbol{X}_i'\boldsymbol{\beta}_0 + \varepsilon_i $$ together with the conditional exogeneity condi …

In your case, I am assuming that you are interested in the LM test for linear regression specification, in particular for testing for omitted variables in your model. … An auxiliary regression of the form you are attempting is a convenient way of computing the LM test statistic. …

To see this recall that endogeneity of a regressor $X_i$ in the simple regression model $$ Y_i = \beta_0 + \beta_1 X_i + \varepsilon_i $$ means that $\mathbb{E}(X_i\varepsilon_i) \neq 0$. …

more generally so that they read $$ \begin{align} \mathfrak{h}_0{}:{}\beta_1 &= \beta^0_1\\ \mathfrak{h}_a{}:{}\beta_1&=\beta_1^a \end{align} $$ Then, using standard machinery, and under the linear regression …