Back when I was growing up, I was always quite good at math, but as I got older, I hated doing proofs, so a career as a mathematician didn't really appeal to me. Applied math, however, was fascinating because I could use my math skills to solve useful practical problems, which is why I decided to go to Stanford and become an engineer. After my freshman year, I got a job at Honeywell as an intern and started learning about control theory right away, since the group I got assigned to studied aerospace control systems. I loved control theory because I thought it was a fascinating way to approach problems where you had a complicated dynamic system and wanted to achieve a specific goal. Ultimately, I decided not to pursue engineering because I thought my rational problem solving skills could be used to better ends by pursuing public policy, which is how I ended up with a bachelor's degree in electrical engineering and a bachelor's degree in public policy coming out of Stanford.
Eventually, I realized economics was a useful way to use my skills in applied math, which is why I decided to get a PhD at Berkeley, and always wondered if all my knowledge about control theory might come in handy there. Macroeconomics and monetary policy is the most obvious application, since policymakers are trying to manage a complex dynamic system (through interest rates) in order to achieve a specific desirable outcome (low inflation and low unemployment). At one point, I thought it would be useful to take the most important advances in control theory (like robust control, which deals with models with a lot of uncertainty) and apply them to the problem of macroeconomics. As it turns out, someone already did this, namely Nobel Prize winner Lars Peter Hansen, so there was not much for me to do on top of what was already done.
Then I eventually realized that the whole debate on whether the Federal Reserve should target inflation rates or price levels when managing the economy is basically a problem that has been well studied in engineering. One of the first things you learn when studying control theory is PID control, which stands for proportional (P), integral (I), and derivative (D) control.. In monetary policy, proportional control is just targeting the inflation rate, and targeting the price level is considered integral control, because price level targets worry about all the errors in the inflation rate added up over the entire past (an integral) while targeting the inflation rate only worries about errors in the immediate present. The way this works in practice is if inflation comes in too low, say at 1% with a 2% target, then an inflation rate target will try for 2% in the following year, while a price level target will try for an amount somewhat more than 2% for a while in order to make up for the past differences from the target.
What engineering tells us is that you normally want to start with proportional control, but that sometimes it is useful to add integral control to make sure your system is more precise over the long term. What ends up happening is that targeting the inflation rate gets you fewer errors over the short term, but targeting the the price level in addition gets you fewer errors over the long term. This means that the whole debate about whether to target the inflation rate or the price level is really a false choice since the Federal Reserve should probably be doing both. The trick is to weigh the price level target relatively lightly so you do not get wild swing in inflation over the short term, say by trying for a target close to 2% over the short term, but also an average of 2% over say 5 years. That means if inflation came in 1% too low for a year, then the Fed would target inflation at 2.2% for the following five years to make up the difference.
I describe this in a little more detail in one of the research ideas on my website, and would like to figure out how to turn this into an academic paper, since I do think it sheds some light on an extremely complicated debate that can be difficult to get your mind around.
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