Money, inflation and interest

Unit of account. Money is the ruler prices are measured with. "R$ 69.90" is a length on that ruler, and like any measurement it is only meaningful next to the ruler it was taken with, on the day it was taken. Every price column in every dataset is in some unit of account, and the column header almost never says which date's version of it. That is the hidden column from Part 0, and it is the reason two years of prices in one table can be less comparable than they look.

Medium of exchange. Money is the token that lets a trade happen without a swap of goods. A seller of towels does not need to find a buyer who has exactly what the seller wants; they take money, which they do not want for itself, because everyone else will take it too. The value of money in this job is entirely that it is accepted. Nothing about the paper, the coin or the entry in a database matters except that the next person will take it.

Store of value. Money carries value from now to later. Sell the towels in January, hold the reais, buy stock in March. This is the job that fails first, because between January and March the ruler can shrink: the same reais buy less. It is also the job that has a price attached, because someone will pay you to let them hold your reais until March, and that payment is interest. The two facts, that the store leaks and that the store is charged for, are Parts 2 and 3 respectively, and they are about the same thing: time.

People reason in the unit they are shown. A 5 percent pay rise feels like a rise even in a year when the price of money fell 5 percent and nothing real changed; a price held flat for a year feels like a stable price even though it buys less of the seller's inputs than it did. That habit, treating the nominal number as the real one, is called money illusion, and it is not stupidity. It is the entirely reasonable strategy of a person who does not have the second table, the one that says what the ruler did, and so uses the only number they hold.

The data habit it gives you: a price column is a claim about a unit, not just a list of numbers. Before comparing any two prices from different dates, write down the unit and the date of each, and ask whether you have the second table. If you do not, the honest comparison is nominal and says so. That sentence, "these are nominal, and here is what it would take to make them real", is the one Part 2 writes for the marketplace data.

Nominal is the number on the tag. Real is what the tag bought. To get from one to the other you need the price of money on that date, which is what a consumer price index measures: a basket of ordinary purchases, priced every month, expressed as an index so that the ruler's length can be compared across dates. Divide a nominal price by the index for its month and you get a real price, one that can be compared with another month's real price. That is the whole arithmetic. A 5 percent rise on the tag in a year when the index also rose 5 percent is a real rise of zero; in a year when the index rose 3 percent it is a real rise of about 1.9 percent; in a year when the index rose 8 percent it is a real fall of about 2.8 percent. Those three index moves are invented for the arithmetic and the build-along works them through.

The honest sentence for the Olist data. Every price on every page of these sessions is nominal Brazilian reais, over 21 months from October 2016 to August 2018. To make them real you would need a Brazilian consumer price index, month by month across that span, and you would divide each product-month's price by the index for its month. That has not been done, and no inflation figure for Brazil is quoted here, because a number typed from memory is exactly the kind of number the source map refuses. What can be said without the index is this: the elasticity from Foundations session 2 was fitted with month effects as one of its variants, and month effects remove whatever part of a month's price move every product shared. A change in the price of money is precisely a move every product shares. The within-product slope was -1.788 without month effects and -1.854 with them, so whatever the ruler did across those 21 months, allowing for it moved the elasticity a little, not a lot.

Why the flip of view matters. "Prices went up 5 percent" invites the question "which prices". "The price of money fell" invites the right question: "then what did anything real do". A team that reports revenue growth across two years without the second table is reporting the ruler and the towels mixed together, and the mix is not separable after the fact without the index.

In a book review in the New York Times on 12 July 1987, Robert Solow wrote that "You can see the computer age everywhere but in the productivity statistics". The line is reported here from a secondary citation; the original review was not opened. It names a puzzle that has come back with every general technology since: the thing is visibly everywhere, and the measured output per hour, which is a real quantity, nominal output deflated by a price index, does not move for years.

The mechanisms are worth knowing because they are about measurement, not about the technology. The fixed cost comes first: Foundations session 3 said a large fixed cost is paid before the first unit; at the economy's scale that is years of spending that show up as cost before they show up as output. Complements are needed: a new tool pays only after the work around it is reorganised, and reorganising is slow. Quality is mismeasured: when a product gets better at the same nominal price, the index treats it as unchanged, so the real gain is invisible in the deflated number. The deflator itself lags: the basket is revised slowly, so a technology that changes what people buy is measured with last decade's ruler. None of these say the gain is not there. They say the real measure is a nominal number divided by a ruler, and both halves of that division can lag. Deep-dive session 7 returns to the point when it reads the task-level studies of AI at work.

Discounting is the price of time run backwards. If a year of waiting is priced at a rate r, then 100 due in one year is worth 100 divided by (1 + r) today, and 100 due in four years is worth 100 divided by (1 + r) four times over. Draw that for every year ahead and you have the discount curve: it starts at the full amount today and falls, and how fast it falls is the rate. Two things are visible in the figure and worth saying out loud. The curves start together, so the rate does not matter for money due now. And they part further with every year, so the rate matters more the further out the money is.

The flip. Offer A pays 100 in one year. Offer B pays 130 in four years. Both are constructed. At an invented 5 percent, A is worth about 95 today and B about 107, so B is the better offer. At an invented 20 percent, A is worth about 83 and B about 63, so A is the better offer. Nothing about the offers changed. The rate changed, and because B's money is further out, the higher rate charged it three extra years of waiting. Any comparison between a near payoff and a far one has a rate hidden inside it, and a person who says "B is obviously better because 130 is more than 100" has silently set the rate to zero.

Nominal and real rates. A rate written on a loan is nominal: it includes the lender's expectation of what the ruler will do. What is left after the expected change in the price of money is the real rate, the true price of a year of waiting in terms of things rather than reais. The arithmetic is the same division as Part 2, applied to the rate instead of the price. The three financial statements, cash against profit, and the funding gap that a slow-paying customer opens are a different subject with their own course, learn-finance-with-phoebe, and nothing here reads a balance sheet.

A central bank is the institution that sets one particular price of time: the rate at which ordinary banks borrow from it, or from each other, overnight. Every other rate in the economy is priced off that one with a margin on top, so moving it moves the price of a year of waiting for everyone. The bank's stated aim, in most countries, is a slow and predictable change in the price of money: a small, steady fall in what a unit buys each year, rather than a fast one or an unpredictable one. That target is the reason the two halves of tonight meet in one building.

The mechanism runs through Part 3's curve. When the price of money is falling faster than the target, meaning prices are rising faster than intended, the bank raises the price of time. Borrowing becomes dearer, spending that would have been financed by borrowing is postponed, and with less money chasing the same goods the fall in the price of money slows. When the price of money is falling more slowly than the target, the bank does the reverse. The effect arrives with a lag of many months, because the spending decisions it changes are decisions about the future, and that lag is why the bank is always acting on a forecast and why its critics always have last year's numbers on their side. No rate, no target figure and no official is named here on purpose: all three change, and the mechanism does not.