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.
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[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.
READER COMMENTS
Roger McKinney
Aug 6 2025 at 11:42am
Great points! I would add that Mises showed that persistent trade deficits are caused by monetary policies. In a pure gold standard, deficits would be temporary and self correcting.
But with credit money, banks can create more money than the nation wants to hold so they send it overseas by buying imports.
Also, the federal government needs to borrow more than citizens provide in saving, so it must borrow savings of foreigners. But for foreigners to get the dollars needed, they must sell us stuff. The federal debt causes the Fed to print more money than citizens want to hold.
Jon Murphy
Aug 6 2025 at 11:46am
Do you have a cite for this? I don’t recall reading that in Mises, but it’s also been a long time. I am not sure I agree with it, though.
That can be a mechanism, but I don’t think it applies to the US. Foreign holdings of government debt have been falling (in terms of % of total foreign lending) for a bit now. Foreigners want corporate investment, not government debt. Even if the Feds were to balance the books tomorrow and never run deficits ever again, I doubt the trade deficit would disappear, or even shrink that much.
Roger McKinney
Aug 8 2025 at 9:25am
Here’s the section from Human Action:
13. The Size and Composition of Cash Holdings
“The role money plays in international trade is not different from that which it plays in domestic trade. Money is no less a medium of exchange in foreign trade than it is in domestic trade. Both in domestic trade and in international trade purchases and sales result in a more than passing change in the cash holdings of individuals and firms only if people are purposely intent upon increasing or restricting the size of their cash holdings. A surplus of money flows into a country only when its residents are more eager to increase their cash holdings than are the foreigners. An outflow of money occurs only if the residents are more eager to reduce their cash holdings than are the foreigners. A transfer of money from one country into another country which is not compensated by a transfer in the opposite direction is never the unintended result of international trade transactions. It is always the outcome of intended changes in the cash holdings of the residents. Just as wheat is exported only if a country’s residents want to export a surplus of wheat, so money is exported only if the residents want to export a sum of money which they consider as a surplus.
If a country turns to the employment of money-substitutes which are not employed abroad, such a surplus emerges. The appearance of these money-substitutes is tantamount to an increase in the country’s supply of money in the broader sense, i.e., supply of money plus fiduciary media; it brings about a surplus in the supply of money in the broader sense. The residents are eager to get rid of their share in the surplus by increasing their purchases either of domestic or of foreign goods. In the first case exports drop and in the second case imports increase. In both cases the surplus of money goes abroad. As, according to our assumption, money-substitutes cannot be exported, only money proper flows out. The result is that within the domestic supply of money in the broader sense (money + fiduciary media) the portion of money drops and the portion of fiduciary media increases. The domestic stock of money in the narrower sense is now smaller than it was previously.” P 447
Of course, taxes, regulations, and unions increase imports. But ceris parabus, federal demand for loans forces the government to borrow overseas because US citizens don’t save enough. How will say the Chinese get dollars to loan them except by them or another country selling us stuff?
Currently, the Fed buys most new federal debt. But it does so by increasing the money supply. And it increases money more than what US citizens want to hold. We export the excess to other countries, such as China through buying their goods.
Jon Murphy
Aug 8 2025 at 10:00am
Thank you! It’s been close to a decade since I last read HA and I had forgotten about those passages.
Thomas L Hutcheson
Aug 8 2025 at 9:19am
“Mises showed that persistent trade deficits are caused by monetary policies.”
No, it is the underlying differences in saving and investment, especially fiscal defcits that monetary policy takes account of in setting values of policy instruments.
Roger McKinney
Aug 9 2025 at 12:03pm
I make that point above. US citizens don’t save enough for federal borrowing. But currently the Fed buys most of the new federal debt by expanding the money supply. That causes people to export excess money by buying imports.
David Seltzer
Aug 6 2025 at 2:18pm
Jon, Excellent, excellent post! Slightly off topic, from my experience learning econ and math, I’ve wondered why economics was more difficult than mathematics. I suspect econ seems harder because their models are parables. Figuring out what the equations mean and applying them is much tougher. More often it’s easier to analyze linearly, Qd= 10-2p, than quadratic nonlinearity employing differential equations. Good stuff!
Roger McKinney
Aug 8 2025 at 9:34am
Good points! Having studied Fed models, they seem simplistic. They must reduce the complexity of the economy enormously to make equations from it. Universities used to have much larger models with many equations, but they didn’t forecast better than the small models.
Part of the problem is a lack of relevant data. Part is poor data. But part is complexity. Decades ago a bunch of physicists met with economists to teach economists more sophisticated math. The physicists were astounded at the complexity of economics. They operated at the Santa Fe Institute for decades but never produced anything significant other than claiming to have created complex economics using chaos theory. But Mises and Hayek claimed complexity for economics almost a century ago.
David Seltzer
Aug 8 2025 at 12:15pm
Roger, thanks for your comment. When I was at UChicago, I was one of Fischer Black’s research grunts, programing the mathematics of the model in Fortran. Later, I went to the CBOE trading derivatives as a market-maker. Subsequent to that, I managed a hedge fund. I used all the elegant equations found in Taylor Series, Ito’s Lemma, Fractal Brownian Motion, CAPM…ad infinitum. My point; I knew those wonderful mathematical parables but I didn’t understand them until I applied them in a trading environment. My returns, adjusted for risk, matched markets returns. Simply stated, my alpha was zero. Not much better than a buy and hold strategy.
Brent Buckner
Aug 7 2025 at 8:29am
+1
I tried to make that point in a comment on Dr. Sumner’s “must stop using must” post. From the following comments clearly I failed. You’ve done so much better!
Knut P. Heen
Aug 7 2025 at 11:38am
I agree. 1 meter = 3.28 feet. That does not make Americans taller than Europeans.
Thomas L Hutcheson
Aug 7 2025 at 1:00pm
This is all true but sometimes it leads to the opposite mistake. If China decides to increase export subsides (backing that up with oher policies to increase net investment), that policy rippling through the global economy is likely to result in a more positive Chinese trade surplus and less positive surplus in the ROW. Whether that is “forcing” is pure nomenclature.
Jon Murphy
Aug 8 2025 at 10:03am
I disagree. It’s not merely a matter of nomenclature, unless we wish to totally invert the entire logic of economics and impute agency onto things that have no agency.
Let me ask you this: ceteris paribus, do lower prices force people to consume more, or to people consume more because prices are lower and thus marginally lower valued uses now become net-beneficial?
Mactoul
Aug 7 2025 at 11:49pm
Empirical relations need not be causal. Indeed, causality inheres not in the equations, empirical or not, but in the understanding.
For instance, empirically, you can plot obesity rate vs per capita sugar consumption. They are well-correlated. But, to say that sugar causes obesity is to make a controversial statement.
Jon Murphy
Aug 8 2025 at 7:34am
Correct. The model, which posits a causal relationship, is testable and falsifiable. The accounting identity, which has no causal relationship and is merely a definition, is not falsifiable. And then you have observations (like the correlation between sugar and obesity) which are neither.
Ike Coffman
Aug 9 2025 at 9:01am
One of the reasons people do not understand accounting identities is because they do not make sense to their own lives. For example, how is the equity I have in my house a liability?
Please. I would really like to know.
Jon Murphy
Aug 9 2025 at 12:54pm
Is it? I don’t think it is. I think it’s an asset. But I am not an accountant, so I am not 100% sure.
Warren Platts
Aug 9 2025 at 4:18pm
Jon, Ike is confused because “Assets = Liabilities” is not the correct equation; that is “Assets = Liabilities + Equities”. Say I buy a house for 100 fully financed by the bank. I’ve got an asset worth 100, but I’ve also got a liability of 100 thus I have zero equity; in this case, Assets does indeed equal Liabilities. However, I get it halfway paid off: I still got my asset worth 100 — that doesn’t change. But my liability is now only 50, thus I have equity worth 50. Finally, I pay the whole thing off. Now my liability is zero, I still have my asset worth 100, and thus equity of 100.
This actually raises an interesting point. It is often said that an accounting identity is an equality that must be true, by definition. Here is another accounting identity: S + I = -NX. Since it’s an accounting identity, it must be true, by definition, because I defined it as such. Thus if S+I=10, then since it must be true, then NX=-10; we have a trade deficit. Of course that’s perfect nonsense. But why is it nonsense? There’s certainly nothing wrong with it mathematically; it must be true in that sense. Nonetheless, it is nonsense because it does not correctly describe reality. Thus what makes the accounting identities we use in actual practice “true” is the fact they are empirical representations of reality; that is to say, they are not true in and of themselves.
Jon Murphy
Aug 9 2025 at 5:16pm
The full identity is “Assets = Liabilities + Owner Equity.” Of course, for simplification purposes, I just used “Assets = Liabilities.” That’s why I referred to it as the “simplified identity.” Whether one uses the simplified or full version, nothing really changes. I figured any reader would know what I meant. But if you are having trouble, then just assume Owner Equity = 0.
Your follow up example is unclear. Are you saying accounting identities are nonsensical? In what way do they not “correctly describe reality”? I mean, they are empirical representations of reality (unless one is literally just making up numbers). One can misunderstand what the accounts say (eg, that trade deficits are inherently bad), but that’s a failure on the part of the person, not the identity.
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