Regression: What It Actually Does

You wake before dawn in Brasília on a Tuesday in October 2008. On your desk is a printout from the Ministry of Environment's research team, and it carries the weight of several hundred thousand square kilometers of rainforest.

The Amazon is burning. Between 2004 and 2008, Brazil lost an area of forest larger than Greece. International pressure is building. NGOs are publishing satellite images. The World Bank is threatening to pull financing. And now your team has handed you something that looks like an answer.

The printout shows a regression. The outcome variable is annual deforestation in each of Brazil's Amazonian municipalities. The key explanatory variable is access to rural credit, specifically the volume of agricultural credit flowing into each municipality from state-subsidized banks. The coefficient is positive and statistically significant: municipalities that received more rural credit in a given year cleared more forest the following year. The R-squared sits at 0.61, which your team describes as "strong."

The policy implication seems to write itself. Restrict subsidized rural credit to high-deforestation municipalities. Cut the financial lifeline to the ranchers and soy farmers who are clearing land. The regression says credit and deforestation move together, and you have the power to change the credit flows.

Your advisor, a quiet econometrician who has spent fifteen years at the Institute of Applied Economic Research in Rio, sets a coffee on your desk and says something you will not forget:

"The line fits the data beautifully. That is not the same thing as the line telling you the truth about what will happen when you pull the lever."

You have forty-eight hours before the interministerial meeting where a decision will be made. The regression is the best evidence you have. The question is what, exactly, it is evidence of.

This is not a hypothetical. Brazil did implement rural credit restrictions as part of its 2008 Action Plan for the Prevention and Control of Deforestation in the Legal Amazon. Deforestation rates did fall dramatically in subsequent years, dropping from roughly 12,000 square kilometers per year in 2008 to under 5,000 by 2012. But researchers spent the next decade arguing about how much of that decline the credit policy actually caused, and how much was driven by commodity price cycles, increased satellite monitoring, and federal law enforcement operations that happened simultaneously. The regression on your desk in 2008 could not tell you the answer. Understanding why is what this lesson is about.