Accounting Identities and Economic Theories

The relationship between accounting identities and economic models is frequently misunderstood. An accounting identity is an equality that must be true, by definition. It is tautology. It is meant to categorize and organize relationships between variables. For example Assets = Liabilities is an identity. Regardless what “assets” equals, “liabilities” must be the same amount. We have defined it this way. There is nothing causal about this statement. It tells us nothing about the behavioral relationship between the various factors.

Furthermore, an identity is not testable and falsifiable. It is always and necessarily true. We cannot test to see if an increase in consumption increases GDP; it always and everywhere will. If an increase in consumption decreases GDP, then you made a math mistake.

Conversely, economic models describe causal, behavioral relationships. Rather than being defined a certain way, models take simplifying assumptions and observed behaviors to posit cause and effect. Take a simple model of demand: Quantity demanded = 10–2P. This is a model of the causal, behavioral relationship between quantity demanded and price: as price falls, quantity demanded rises by 2 (and vice versa). Quantity demanded does not equal 10–2P by definition. That is based on observed behavior and various simplifying assumptions. Quantity demanded could be quadratic, it could be locally upward-sloping, it could take on many different shapes! This is a relationship that was discovered and is limited to this use.

Furthermore, a model is testable and falsifiable. We can test to see if a change in price influences quantity demanded by 2. Say, we observe that instead, a marginal change in price changes quantity demanded by 3. Our model is falsified!

The misunderstanding might come from the fact that identities and models look similar. They are both mathematical equations. But to properly appreciate what they tell us, one must understand the difference. A model describes a theoretical causal relationship. An identity is a description, a definition. Further, an accounting identity only tells us what happened in the past.

Michael Pettis, a Carnegie Fellow and professor of finance at Peking University in Beijing, is perhaps the most prominent (though not the only) offender who confuses the two, since he writes often in large, international outlets. Brian Albrecht, chief economist at the International Center for Law & Economics, has an excellent blog post in which he shows how a little Econ 101 reasoning exposes the weaknesses, contradictions, and hidden assumptions in Pettis’s arguments.[1] (My co-blogger Scott Sumner has similar comments.)

Pettis frequently argues that mercantilist policies of other governments, in particular China, force America to run a trade deficit. His argument falls out of the accounting identity that, in a closed economy, Savings = Investment. If planet Earth is a closed economy (and it is, at least until we uncover sentient alien life), then a nation like China increasing savings must mean that another nation is investing more, leading to a trade deficit. Taking Pettis’s argument on its own terms betrays a fundamental misunderstanding of how accounting identities work. Accounting identities are not mind control. They are a record of transactions. In other words, they tell us what has occurred, not what will occur. Only transactions that have occurred show up in the accounts. Accounting is only a description of what has occurred. The accounting of past events tell us nothing about future transactions.

Take the simplified accounting identity Assets = Liabilities. If a firm buys an asset on credit, the firm’s assets go up and the firm’s liabilities go up by the same amount. As the firm pays off the debt, its assets go down, and so do the liabilities by the same amount. That must be true because that’s simply the purpose of these categories. But the changes in assets and liabilities reflect transactions that have occurred, not future transactions. As a matter of course, when a purchase occurs both assets and liabilities adjust—if the transaction occurs. If the transaction does not occur, it never appears in the ledger.

To bring this to the international stage, the accounting identity Investment = Savings – Balance of Trade is merely accounting for (describing formally) transactions that occurred in the previous time period. If some investment occurred, it must have been funded by some combination of domestic and international savings. But it does not track the countless investments (and savings) that did not occur because they didn’t make sense at the available interest rate. Because they didn’t happen, they can’t be described, and so those transactions do not show up at all! Again, the accounting identity only tells us what has occurred, not what will occur.

For another example, say you have an extra $200,000 and decide to save it. You open a Certificate of Deposit savings account at the local bank and deposit the money there. The bank’s assets have risen (its reserves increased by the amount you deposited) but so have its liabilities (account holders can demand their deposits back). The deposited funds are now available for investment, but nothing about your deposit says investment must rise. No one wakes up the next day and says, “I must buy a house and borrow $200,000 now!” The bank will try to entice borrowers with interest rates, but there is no compulsion going on, and nothing about the definition says it has to happen. Indeed, if the bank cannot lend out the money, it stays in bank reserves and never shows up in GDP at all. Even though a savings account has increased, without corresponding investments, the transaction does not appear in GDP.

Once we understand that accounting identities record transactions that have occurred and have no power to compel future transactions, the logic of Pettis’s (and other mercantilists’) argument falls apart. Increasing Chinese savings does not compel Americans to run a trade deficit. Of course, all else held equal, increased savings (loanable funds) would reduce interest rates, which in turn would increase the quantity demanded of loans, increasing US GDP (through increased consumption, investment, or government spending) and the trade deficit, it is true. But that does not follow from the accounting identity, but from Econ 101 supply-and-demand framework. If there were no appetite to borrow, no mutually beneficial transactions to occur, then no amount of increased savings will compel Americans to borrow.

—

[1] As Brian points out, Pettis would argue that Econ 101 doesn’t apply. But that’s just another weakness in his argument. If you have to toss out scientific laws to make your case, your case isn’t very good.