Imagine a tank of water that has a pipe in and a pipe out.

As water flows in, water also flows out. Ignore the flow rates on this diagram, and just think for a minute — if the water level in the tank is rising, what can we say about the inflow and outflow?

The only way the water level rises is if the water flowing in is greater than the water flowing out. The only way the water level sinks is if it flows out faster than it flows in.

This may seem obvious, and frankly, a bit useless. Why should you care about the dynamics of water tanks? But, in fact, understanding the relationship of these three variables — inflow, stock, and outflow — is one of the quickest ways to hone your statistical literacy.

Here’s one example — Between 1995 and 2000 almost 2 million Mexicans came into the U.S. Between 2005 and 2010, about 1.4 million Mexican came into the U.S.

That’s a drop, but that’s still a lot more people in this country, right? Can the U.S. handle this level of Mexican immigration?

Except those numbers, though correct, give the wrong impression. Those numbers represent only the inflow of immigrants from Mexico. What they don’t take into account is the outflow — the number of people moving or returning to Mexico. When we look at the outflow, our entire perception changes:

In fact, it appears that in the past five years more people moved back to Mexico than came to the U.S.  But, until recently, the only numbers you would hear on the news are the inflow numbers — and inflow, by itself, tells us very little.

Arrest/Conviction Rates or Length of Sentence?

As we’ve noted in other places, the U.S. has the largest per capita prison population in the world. If you were to ask the average person why that is, they would probably look at you like you were nuts. The answer is obvious — the prisons are full because we send a lot of people to jail.

But again, this is only the inflow side of the equation. There’s the outflow to consider as well. In the case of prisons, various laws enacted in the 1980s and 1990s dramatically increased the length of prison sentences. This has a profound effect on outflow — if you imagine that water tank up top there, what happens if we keep the same amount of water flowing in, but slow the water flowing out to a trickle? The water rises, just like our prison population has risen.

This isn’t to say that much (maybe even most) of the rise isn’t due to a higher inflow, but because outflow has such an impact, any effort that focuses on reducing population only through reducing the amount of people we put in jail is incomplete. Even if we didn’t arrest a single person for the next five years, at the end of five years we’d likely *still* lead the world in prison population, because the sentences we have in place are much longer than in most countries.

In fact, there is a school of thought, influenced by research in behavioral psychology, which posits that effective policy would put a lot of people in prison, but that it would keep them there for very short periods of time, since most criminals don’t really consider how long they might be imprisoned — only if there’s a chance of them being sent to prison at all. A detailed inflow/outflow analysis might show that such an approach would dramatically shrink our prison populations with no impact on public safety.

Other Examples

 (Stock::Flow)

i. World population :: Birth Rate

ii. Unemployment Rate :: Jobs Created per Month

iii. Disease prevalence :: disease incidence

iv. Wealth :: Income

Inflows matter….

We can see the national deficit/surplus as a stock with inflows (taxes and revenue) and outflows (spending). Obama has dramatically increased the deficit. But it doesn’t mean he has dramatically increased spending – in a recession, taxes (the inflow) collapse due to reductions in employment, income, and return on investment. Inflow reduction accounts for much of the increase in the deficit.

But Outflows matter too…

A killer disease will have less prevalence than a chronic one – when people die quickly, that’s an outflow. As the disease becomes treatable, prevalence will rise, not fall. This is the case with diabetes now – the survival rates for diabetes have dramatically improved, so now more people have it (there are other major reasons for the diabetes increase too, but survival rates play a role).