In Stata 14.2, we added the ability to use **margins** to estimate covariate effects after **gmm**. In this post, I illustrate how to use **margins** and **marginsplot** after **gmm** to estimate covariate effects for a probit model.

Margins are statistics calculated from predictions of a previously fit model at fixed values of some covariates and averaging or otherwise integrating over the remaining covariates. They can be used to estimate population average parameters like the marginal mean, average treatment effect, or the average effect of a covariate on the conditional mean. I will demonstrate how using margins is useful after estimating a model with the generalized method of moments. Read more…

For a nonlinear model with heteroskedasticity, a maximum likelihood estimator gives misleading inference and inconsistent marginal effect estimates unless I model the variance. Using a robust estimate of the variance–covariance matrix will not help me obtain correct inference.

This differs from the intuition we gain from linear regression. The estimates of the marginal effects in linear regression are consistent under heteroskedasticity and using robust standard errors yields correct inference.

If robust standard errors do not solve the problems associated with heteroskedasticity for a nonlinear model estimated using maximum likelihood, what does it mean to use robust standard errors in this context? I answer this question using simulations and illustrate the effect of heteroskedasticity in nonlinear models estimated using maximum likelihood. Read more…

We estimate the average treatment effect (ATE) for an exponential mean model with an endogenous treatment. We have a two-step estimation problem where the first step corresponds to the treatment model and the second to the outcome model. As shown in *Using gmm to solve two-step estimation problems*, this can be solved with the generalized method of moments using **gmm**.

This continues the series of posts where we illustrate how to obtain correct standard errors and marginal effects for models with multiple steps. In the previous posts, we used **gsem** and **mlexp** to estimate the parameters of models with separable likelihoods. In the current model, because the treatment is endogenous, the likelihood for the model is no longer separable. We demonstrate how we can use **gmm** to estimate the parameters in these situations. Read more…

We continue with the series of posts where we illustrate how to obtain correct standard errors and marginal effects for models with multiple steps. In this post, we estimate the marginal effects and standard errors for a hurdle model with two hurdles and a lognormal outcome using **mlexp**. **mlexp** allows us to estimate parameters for multiequation models using maximum likelihood. In the last post (Multiple equation models: Estimation and marginal effects using gsem), we used **gsem** to estimate marginal effects and standard errors for a hurdle model with two hurdles and an exponential mean outcome.

We exploit the fact that the hurdle-model likelihood is separable and the joint log likelihood is the sum of the individual hurdle and outcome log likelihoods. We estimate the parameters of each hurdle and the outcome separately to get initial values. Then, we use **mlexp** to estimate the parameters of the model and **margins** to obtain marginal effects. Read more…

**Starting point: A hurdle model with multiple hurdles**

In a sequence of posts, we are going to illustrate how to obtain correct standard errors and marginal effects for models with multiple steps.

Our inspiration for this post is an old Statalist inquiry about how to obtain marginal effects for a hurdle model with more than one hurdle (http://www.statalist.org/forums/forum/general-stata-discussion/general/1337504-estimating-marginal-effect-for-triple-hurdle-model). Hurdle models have the appealing property that their likelihood is separable. Each hurdle has its own likelihood and regressors. You can estimate each one of these hurdles separately to obtain point estimates. However, you cannot get standard errors or marginal effects this way.

In this post, Read more…

In a previous post I illustrated that the probit model and the logit model produce statistically equivalent estimates of marginal effects. In this post, I compare the marginal effect estimates from a linear probability model (linear regression) with marginal effect estimates from probit and logit models.

My simulations show that when the true model is a probit or a logit, using a linear probability model can produce inconsistent estimates of the marginal effects of interest to researchers. The conclusions hinge on the probit or logit model being the true model.

**Simulation results**

For all simulations below, I use a sample size of 10,000 and 5,000 replications. The true data-generating processes (DGPs) are constructed using Read more…