Stocks vs flows

Tell a level from a rate, and stop confusing debt with deficit.

Two headlines from the same week: the deficit has fallen for the fourth year running, and the national debt has hit a record high. Somebody in the comments will say one of them must be a lie. Neither is. The deficit is a rate and the debt is a level, and a falling rate still adds to a level for as long as it is above zero.

Levels and rates

A stock is an amount at a moment. You could photograph it. Debt, savings, , population, water in a reservoir, carbon in the atmosphere, people with jobs.

A flow is an amount per unit of time. It only exists over an interval. Deficit, income, hiring, emissions, rainfall, spending.

The relationship is a running total, and that is genuinely all it is. This period's level is last period's level plus what came in less what went out. Every result below is that one line applied honestly.

Watch them move apart

Bars are the flow. The line is the level, which is the running total of the bars. Nothing else is happening.

Deficit, a rate Debt, a level

Deficit fell in 7 of 8 periods. Debt rose in 7.

6 periods did both at once. The deficit falls every single year and the debt rises every single year. Only a surplus, a deficit below zero, takes debt down.

What leaves each period0Raise it past the bars and the level finally turns. Nothing else does it.

The bars come down every period in all four cases and the line goes up anyway. Then raise what leaves each period until it clears the bars, and watch the line finally turn. That is the only thing that does it.

The arithmetic is from the model on this page, which is a running total and is unit tested, including a case confirming the level turns only once the inflow drops below the outflow.

ConventionIn a company's filings the split is structural. The balance sheet is every stock: what is owned and owed at one instant, which is why it carries a date rather than a period. The income statement and cash flow statement are flows, covering a stretch of time. If you can tell which of the three a number came from, you already know whether it is a level or a rate.

Why the confusion is so persistent

Because the flow is what gets reported. A flow has a natural news cycle: this month's hiring, this quarter's deficit, this year's emissions. The level changes slowly and rarely produces an event, so it appears in headlines only when it crosses a round number.

The result is that people form opinions from the flow and hold them about the level. A month of slower hiring reads as job losses. It is not. Employment is still going up, just less steeply, and it only turns down when hiring falls below the number of people leaving.

What breaks

Comparing a stock to a flow. Debt to GDP is the most common instance in finance, and it divides a level by a rate, so the answer carries units of years and gets quoted as a percentage. It is still a useful ratio. It is not a percentage of anything, and treating it as one leads people to think that 120% means owing more than exists.

Expecting a policy to move the level as fast as it moves the flow. Flows can turn in a quarter. Levels built over decades take decades. A policy that changes the flow immediately and the level slowly is not failing, it is a tank draining.

Forgetting the drain. Every stock has one, and it is usually less visible than the tap. Savings has spending, employment has quitting and retiring, carbon has absorption, and a reservoir has evaporation. The level turns when the tap goes below the drain, which means you cannot answer the question without knowing both.

What to do with this

When a number moves, ask whether it is a level or a rate, and then ask what the other one is doing. Almost every confusing statistic clears up in that one step.

And when you want to change a level, work on the flow and be patient about the level. The arithmetic that makes a falling deficit disappointing on the debt is the same arithmetic that makes a small monthly saving turn into a balance. Small flows into a level, held for a long time, are how every stock anybody cares about was built.

Test yourself

01A company reports record revenue and files for bankruptcy the same quarter. How?

Revenue is a flow and cash is a stock. A company can sell more than ever and run out of money, because the money arrives after the costs go out. Pay your suppliers in 30 days, get paid by your customers in 90, and growing faster makes the gap larger rather than smaller.

This is the most common way a growing business dies, and it is why the cash flow statement exists as a separate document from the income statement. One tracks the flow and the other tracks what the flow did to the level.

02Emissions fall by 30%. Does the amount of carbon in the atmosphere fall?

No, it keeps rising, just more slowly. The level only falls when what goes in drops below what comes out, and what comes out is what the oceans and the forests absorb. Emissions have to fall below that number, not merely fall. This single distinction is behind a large share of the confusion in the public conversation about it, in both directions.

03Give the stock and the flow for: your career, a reservoir, and a reputation.

Career: the stock is your skills and relationships, the flow is what you learn and who you meet this year. Reservoir: the stock is the water in it, the flows are rainfall in and use out. Reputation: the stock is what people think of you, the flow is what you do this week. In all three, the level is built slowly out of small flows and it is the level that decides what you can do.

A tutor that knows this lesson. It asks before it explains, and it will not tell you what to do with your own money.

Educational material, not investment or policy advice. Figures are cited where they come from a filing or a statistical series, and labelled as illustrative where they do not.