Each morning before I drive to campus I make note of the remaining charge on my car. Between my 250 mile range and 45 mile commute, I need to have a pretty good idea of what my charge is to get back home in the evening and for the next day. I don’t know if this problem is unique to me (I don’t have a place to charge at home or conveniently on campus), or EV drivers in general, but I know I wasn’t checking my fuel level so intently when I drove a pickup truck.
The state of my charge, or how many miles I have left on the battery, would be considered a state variable. Each morning I wake up and face the result of my choices yesterday. That is, the state of my charge depends on decisions I made the previous day: how long did I charge for on the way back home, and how fast I drove (more speed means more air resistance which translates to less efficiency and less mileage leftover on the battery.) These decisions would be considered control variables.
The state of my battery also depends on things that I cannot control for like weather. I do not have as good efficiency in the rain (increased friction when the road is damp), and in colder weather as the battery needs to run a heater before starting up. I may have an idea about what the weather will be like, but it is an uncertain idea.
If I wanted to create a model for my battery charge over time, I might then utilize a Markov process. Instead of creating a model based on the entire history of my driving as well as the conditions I faced previously, the next state of my charge tomorrow only depends on what I carried forward to today. Utilizing a Markov process is powerful in its ability to simplify. It takes a very large problem of recording and recalculating probabilities based on a growing span of history through each period, and reduces it to just two periods. Today, and tomorrow.
To illustrate the point say my battery at time t is given by B(t). I can either consume my battery through driving or save it for tomorrow.
C(t) + B(t+1) = B(t)
Consumption plus savings equals what I had to start today. In macroeconomics, state and control variables manifest in models of consumption and capital. Instead, say I own a business which produces widgets according to a Cobb Douglas production function:
Y = z*k^a
Where widgets are “Y”, my factors of production solely capital “k” raised to some exponent “a” and multiplied by a productivity factor “z” which can take a value of 1.
Once I sell my widgets in the market I am now have some cash. I can either spend that cash in some sort of consumption, or save and invest it in the business for tomorrow.
So my consumption “C(t)” my savings plus my investments “k(t+1)” equal my production from today “k(t)^a”
C(t) + k(t+1) = k(t)^a
Here, capital is the state variable and consumption is the control variable. However instead of my battery sitting overnight not doing anything, capital overnight is assumed to turn into widgets, appreciating in value according to “a.”
Sometimes I still have nightmares about chemical engineering, which causes me to not completely forget my undergrad curriculum, and so I can’t help but make the connection to control systems here. I promise it isn’t that scary, in fact you may even know a simple “on/off” example of a control system- the heating system in your house turning on and off!
Rather than temperature, take for example a level control diagram:
Where the instrument on the right is the level controller, feeding a signal to the control valve where water is flowing into the tank, before then flowing out of the bottom to somewhere else.
I act as the level controller in the battery example, and the business owner in the representative household example. When aggregating to the macroeconomy, we might think of the level controller as the Federal Reserve.
Money is flowing into the economy via either direct money creation or government spending, and flowing out of the economy through taxes. It’s the Fed’s job to keep the tank from overflowing, and also to keep it from running empty. When the level in the tank is getting a little low, the Fed might send a signal to increase the money supply (through perhaps quantitative easing or loosening interest rates), and when the tank is close to overflowing it may do the reverse.
What’s great about the level control system is that it has hardly any uncertainty. The sensor is calibrated correctly, measurements are taken frequently, and it can respond to slight deviations and correct to the set level through an advanced PID (corrects for error terms from the set value using a proportional, integral, and derivative term) controller. PID is the type of control your cruise control uses which is why it works so well!
The Fed on the other hand, is at best only a proportional level control system. The are able to adjust interest rates proportionally according to the state of the economy against its 2% inflation target, but are not advanced enough to consider summation of errors and the direction of how errors are changing. Additionally, their actions operate with a lag, measurements are infrequent, and we don’t know that the Fed is calibrated correctly!
So it’s almost no surprise that the Fed is faced with an impossible job. It’s not well equipped for the job. You can see in the gif what how close you can get with just P level control compared to PID (virtually none.) But with more work, ingenuity, and innovation, maybe the price level could one day be PID controlled and we could all but forget about inflation since it would always be very close to its set point level of 2%.
For now, a Markov process seems to work well enough for something like a battery, but I suspect our consumption decisions around other things don’t simply depend on yesterdays decisions. Rather it may depend on a history of consumption decisions, perhaps discounted by the amount of time past, and expectations of future states and income. Additionally, peoples mindsets may be affected by life altering events. Victims of assault or domestic violence, racism, PTSD or misogyny may have had key events that stand out from the rest. Not simply based on the previous day. So maybe on the individual level a Markov is only a starting place.
My main message is that there are some variables in our lives that we can control, like who we choose to spend are time with and what we choose to spend our time on, while others are states like the political climate, climate change, and lending environment.
What are the state and control variables in your life?