The benefit relative to linear regression is that it allows more flexibility in the probabilistic relationships between variables.

Here we illustrate maximum likelihood by replicating Daniel Treisman's (2016) paper, [Russia's Billionaires](http://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.p20161068), which connects the number of billionaires in a country to its economic characteristics.

Here we illustrate maximum likelihood by replicating Daniel Treisman's (2016) paper, [Russia's Billionaires](https://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.p20161068), which connects the number of billionaires in a country to its economic characteristics.

The paper concludes that Russia has a higher number of billionaires than

economic factors such as market size and tax rate predict.

```

Now let's replicate results from Daniel Treisman's paper, [Russia's

Billionaires](http://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.p20161068),

Billionaires](https://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.p20161068),

mentioned earlier in the lecture.

Treisman starts by estimating equation {eq}`poissonreg`, where:

parameters of a Poisson model.

`statsmodels` contains other built-in likelihood models such as

[Probit](http://www.statsmodels.org/dev/generated/statsmodels.discrete.discrete_model.Probit.html)

[Probit](https://www.statsmodels.org/dev/generated/statsmodels.discrete.discrete_model.Probit.html)

and

[Logit](http://www.statsmodels.org/dev/generated/statsmodels.discrete.discrete_model.Logit.html).

[Logit](https://www.statsmodels.org/dev/generated/statsmodels.discrete.discrete_model.Logit.html).

For further flexibility, `statsmodels` provides a way to specify the

distribution manually using the `GenericLikelihoodModel` class - an

example notebook can be found

[here](http://www.statsmodels.org/dev/examples/notebooks/generated/generic_mle.html).

[here](https://www.statsmodels.org/dev/examples/notebooks/generated/generic_mle.html).

## Exercises