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Your clue to figuring this out should be that the parameter estimates from the scikit-learn estimation are uniformly smaller in magnitude than the statsmodels counterpart. This might lead you to belie …

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. …

The formulae for these can be found in any intermediate text on statistics, in particular, you can find them in Sheather (2009, Chapter 5), from where the following exercise is also taken (page 138). …

Let us first work through some definitions of identification, isolating the exact form of identification that applies to nonlinear regression models, where only the conditional mean, and not the entire … identification in the exponential regression model. …

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{ …

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 …

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. …

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 $\mathbb{E}(X_i\varepsilon_i) \neq 0$. …

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 first thing to note is that your notation is quite inconsistent, and you do not specify your exogeneity assumptions. The model you have is the following $$ \begin{align} Y_{it} &= \alpha_i + X_{ …

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. …

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 …

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 …

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 …