Vector Autorregresive (VAR) models are very popular in economics because they can model a system of economic variables and relations. Bayesian VARs are receiving a lot of attention due to their ability to deal with larger systems and the smart use of priors. For example, in this old post I showed an example of large Bayesian VARs to forecast covariance matrices. In this post I will show how to use the same model to obtain impulse response coefficients and perform structural analysis. The type of estimation was based on Bańbura et al. (2010) and the empirical application is from Barboza and Vasconcelos (2019). The objective is to measure the effects of the Brazilian Development Bank on investment. Therefore, we will measure how the investment respond to an increase in loans over the time.
Let us begin with a brief explanation about Benford’s law and why should it work as a fraud detector method. Given a set of numbers, the first thing we need to do is to extract the first digit of each number. For example, for (121,245,12,55) the first digits will be (1,2,1,5). Perhaps our intuition would say that for a large set of numbers, each first digit, from 1 to 9, would appear in equal proportion, that is for each digit between 1 and 9. However, Benford’s law shows us that this is not true. In fact, smaller digits will have larger probabilities. If you want to see a very didactic explanation of why this happen just watch this video https://www.youtube.com/watch?v=XXjlR2OK1kM&t=460s . We could not give a better explanation.
By Gabriel Vasconcelos & Yuri Fonseca
This post is the second of a series of examples of the BooST (Boosting Smooth Trees) model. You can see an introduction to the model here and the first example here. Our objective in this post is to use the derivatives of the BooST to obtain prices that maximize the profit for a given set of products. We will use a very simple setup that we know the true optimal prices to compare with the estimated prices. The tricky thing here is that the demand functions we defined are for substitute products. Therefore, if we increase the price of product A it will affect positively the demand for product B.
This will be a short post about a simple, but very important concept that can drastically increase the speed of poorly written codes. It is very common to see R loops written as follows:
v = NULL
n = 1e5
for(i in 1:n) v = c(v, i)
This seems like a natural way to write such a task: at each iteration, we increase our vector v to add one more element to it.
This is the first of a series of post on the BooST (Boosting Smooth Trees). If you missed the first post introducing the model click here and if you want to see the full article click here. The BooST is a model that uses Smooth Trees as base learners, which makes it possible to approximate the derivative of the underlying model. In this post, we will show some examples on generated data of how the BooST approximates the derivatives and we also will discuss how the BooST may be a good choice when dealing with smooth functions if compared to the usual discrete Regression Trees.
By Gabriel Vasconcelos and Yuri Fonseca
We are happy to introduce our new machine learning method called Boosting Smooth Trees (BooST) (full article here). This model was a joint work with professors Marcelo Medeiros and Álvaro Veiga. The BooST uses a different type of regression tree that allows us to estimate the derivatives of very general nonlinear models. In other words, the model is differentiable and it has an analytical solution. The consequence is that now we can estimate partial effects of a characteristic on the response variable, which provide us much more interpretation than traditional importance measures.
The (Artificial Counterfactual) ArCo package is now fully described in a paper in the R Journal (click here). There you can find details about the model, examples and applications on simulated and real data and a comparison with the Synthetic Control.