Teaching the Fallacy of Composition: The Federal Budget Deficit

SUMMARY: One of the most important concepts to be taught in economics is the notion of the fallacy of composition: what might be true for individuals is probably not true for society as a whole. The most common example is the paradox of thrift: while an individual can save more by reducing spending (on consumption), society can save more only by spending more (for example, on investment). Another useful and very topical example involves the federal government’s budget deficit. Politicians and the media often argue that the government must balance its books, just like a household. If a household were to continually spend more than its income, it would eventually face insolvency; it is thus claimed that government is in a similar situation. However, careful examination of macroeconomic relations will show that this analogy is incorrect, and that it would lead to improper budgetary policy. This example can drive home the fallacy of composition.

One of the most important concepts we teach in economics, and most importantly in macroeconomics, is the notion of the fallacy of composition.

Students and others who haven’t been exposed to macroeconomics naturally extrapolate from their own individual situation to society and the economy as a whole.

This often leads to the problem of the fallacy of composition. Of course, that isn’t just restricted to economics. While a few people could exit the doors of a crowded movie theatre, all of us could not.

The macroeconomics example of the fallacy of composition most often used is the paradox of thrift. Any individual can increase her saving by reducing her spending—on consumption goods. So long as her decision does not affect her income—and there is no reason to assume that it would—she ends up with less consumption and more saving.

The example I always use involves Mary who usually eats a hamburger at Macdonald’s every day. She decides to forego one hamburger per week, to accumulate savings. Of course, so long as she sticks to her plan, she will add to her savings (and financial wealth) every week.

The question is this: what if everyone did the same thing as Mary—would the reduction of the consumption of hamburgers raise aggregate (national) saving (and financial wealth)?

The answer is that it will not. Why not? Because Macdonald’s will not sell as many hamburgers, it will begin to lay-off workers and reduce its orders for bread, meat, catsup, pickles, and so on.

All those workers who lose their jobs will have lower incomes, and will have to reduce their own saving. You can use the notion of the multiplier to show that this process comes to a stop when the lower saving by all those who lost their jobs equals the higher saving of all those who cut their hamburger consumption. At the aggregate level, there is no accumulation of savings (financial wealth).

Of course that is a simple and even silly example. But the underlying explanation is that when we look at the individual’s increase of saving, we can safely ignore any macro effects because they are so small that they have only an infinitely small impact on the economy as a whole.

But if everyone tries to increase saving, we cannot ignore the effects of lower spending on the economy as a whole. That is the point that has to be driven home.

We can then again return to the notion of the multiplier, and show that the way to increase aggregate saving is by increasing spending, specifically, nonconsumption spending—spending on investment, spending by government, or spending by foreigners on our exports.

I don’t want to go into that particular example any further. Another example that is less frequently used concerns unemployment.

The view shared by most of my undergraduate students is that unemployment is caused by laziness or lack of training. The argument they often use is that “I can get a job, therefore all the unemployed could get jobs if only they tried harder, or got better education and training”.

The way I go about demonstrating that fallacy is a dogs and bones example. Say we have 10 dogs and we bury 9 bones in the backyard. We send the dogs out to find bones. At least one dog will come back without a bone.

We decide that the problem is lack of training. We put that dog through rigorous training in the latest bone finding techniques. We bury 9 bones and send the 10 dogs out again. The trained dog ends up with a bone, but some other dog comes back without a bone (empty-mouthed, so to speak).

The problem, of course, is that there are not enough bones and jobs to go around. It is certainly true that a well-trained and highly motivated jobseeker can usually find a job. But that is no evidence that aggregate unemployment is caused by laziness or lack of training.

We could also go into the common belief that minimum wages cause unemployment. It is at least partly true that for an individual firm, higher wages reduce the number of workers hired. But we cannot extrapolate that to the economy as a whole. Higher wages mean higher income and thus higher consumption spending, which induces firms to employ more labor. So the truth is that economic theory does not tell us that raising minimum wages will lead to more unemployment, indeed, theory tells us it can go the other way—raising the minimum wage could increase employment.

Again, the reason we can reach the wrong conclusion in all of these cases when we aggregate up from the micro level to the macro is because we ignore the impacts that behavior of individuals or firms has on other individuals or firms. That can be OK for the case of the individual firm or household, but is almost certainly incorrect for firms and households taken as a whole.

Let me move on to a more important fallacy of composition. We hear politicians and the media arguing that the current federal budget deficit is unsustainable. I have heard numerous politicians refer to their own household situation: if my household continually spent more than its income year after year, it would go bankrupt. Hence, the federal government is on a path to insolvency, and by implication, the budget deficit is bankrupting the nation.

That is another type of fallacy of composition. It ignores the impact that the budget deficit has on other sectors of the economy. Let me go through this in some detail, as it is more complicated than the other examples.

We can divide the economy into 3 sectors. Let’s keep this as simple as possible: there is a private sector that includes both households and firms. There is a government sector that includes both the federal government as well as all levels of state and local governments. And there is a foreign sector that includes imports and exports; (in the simplest model, we can summarize that as net exports—the difference between imports and exports—although to be entirely accurate, we use the current account balance as the measure of the impact of the foreign sector on the balance of income and spending).

At the aggregate level, the dollar spending of all three sectors combined must equal the income received by the three sectors combined. Aggregate spending equals aggregate income. But there is no reason why any one sector must spend an amount exactly equal to its income. One sector can run a surplus (spend less than its income) so long as another runs a deficit (spends more than its income).

Historically the US private sector spends less than its income—that is it runs a surplus. Another way of saying that is that the private sector saves. In the past, on average the private sector spent about 97 cents for every dollar of income.

Historically, the US on average ran a balanced current account—our imports were just about equal to our exports. (As discussed below, that has changed in recent years, so that today the US runs a huge current account deficit.)

Now, if the foreign sector is balanced and the private sector runs a surplus, this means by identity that the government sector runs a deficit. And, in fact, historically the government sector taken as a whole averaged a deficit: it spent about $1.03 for every dollar of national income.

Note that that budget deficit exactly offsets the private sector’s surplus—which was about 3 cents of every dollar of income. In fact, if we have a balanced foreign sector, there is no way for the private sector as a whole to save unless the government runs a deficit. Without a government deficit, there would be no private saving. Sure, one individual can spend less than her income, but another would have to spend more than his income.

While it is commonly believed that continual budget deficits will bankrupt the nation, in reality, those budget deficits are the only way that our private sector can save and accumulate net financial wealth.

Budget deficits represent private sector savings. Or another way of putting it: every time the government runs a deficit and issues a bond, adding to the financial wealth of the private sector. (Technically, the sum of the private sector surpluses equal the sum of the government sector deficits, which equals the outstanding government debt—so long as the foreign sector is balanced.)

Of course, the opposite would also be true. Assume we have a balanced foreign sector and that the government runs a surplus—meaning its tax revenues are greater than government spending. By identity this means the private sector is spending more than its income, in other words, it is deficit spending. The deficit spending means it is going into debt, and at the aggregate level it is reducing its net financial wealth.

At the same time, the government budget surplus means the government is reducing its debt. Effectively what happens is that the private sector returns government bonds to the government for retirement—the reduction of private sector wealth equals the government reduction of debt.

Now let us return to the Clinton years when the federal government was running the biggest budget surpluses the government has ever run. Everyone thought this was great because it meant that the government’s outstanding debt was being reduced. Clinton even went on TV and predicted that the budget surpluses would last for at least 15 years and that every dollar of government debt would be retired.

Everyone celebrated this accomplishment, and claimed the budget surplus was great for the economy.

In the middle of 2000, I wrote a contrary opinion (“Implications of a budget surplus at mid-year 2000, CFEPS Policy Note 2000/1). I made several arguments. First, I pointed out that the budget surplus meant by identity that the private sector was running a deficit. Households and firms were going ever farther into debt, and they were losing their net wealth of government bonds.

Second, I argued that this would eventually cause a recession because the private sector would become too indebted and thus would cut back spending. In fact, the economy went into recession within half a year.

Third, I argued that the budget surpluses would not last 15 years, as Clinton claimed. Indeed, I expected they would not last more than a couple of years. In fact, the budget turned around to large and growing deficits almost immediately as soon as the economy went into recession.

And of course we still have large budget deficits. No one talks any more about achieving budget surpluses this decade; almost everyone agrees that we will not see budget surpluses again in our lifetimes—if ever.

The question is whether the US government can run deficits forever. The answer is emphatically “yes”, and that it had better do so. If you look back to 1776, the federal budget has run a continuous deficit except for 7 short periods. The first 6 of those were followed by depressions—the last time was in 1929 which was followed by the Great Depression. The one exception was the Clinton budget surplus, which was followed (so far) only by a recession.

Why is that? By identity, budget surpluses suck income and wealth out of the private sector. This causes private spending to fall, leading to downsizing and unemployment. The only way around that is to run a trade or current account surplus.

The problem is that it is hard to see how the US can do that—in fact, our current account deficit is now rising toward 7% of GDP. All things equal, that means our budget deficit has to be even larger to allow our private sector to save. Given our current account balance, the budget deficit would have to reach 9% of GDP to allow our private sector to have a surplus of 2% of GDP.

I don’t want to give the impression that government deficits are always good, or that the bigger the deficit, the better. The point I am making is that we have to recognize the macro relations among the sectors.

If we say that a government deficit is burdening our future children with debt, we are ignoring the fact that this is offset by their saving and accumulation of financial wealth in the form of government debt. It is hard to see why households would be better off if they did not have that wealth.

If we say that the government can run budget surpluses for 15 years, what we are ignoring is that this means the private sector will have to run deficits for 15 years—going into debt that totals trillions of dollars in order to allow the government to retire its debt. Again it is hard to see why households would be better off if they owed more debt, just so that the government would owe them less.

There are other differences between the federal government and an individual household. The government is the issuer of our currency, while households are users of the currency. That makes a big difference, and one explored in many other CFEPS publications. However, the purpose of this particular note is to explain why we cannot aggregate up from the individual household situation to the economy as a whole. The US government’s situation is not in any way similar to that of a household because its deficit spending is exactly offset by private sector surpluses; its debt creates equivalent net financial wealth for the private sector.

32 responses to “Teaching the Fallacy of Composition: The Federal Budget Deficit

  1. Oh! Those pesky adding-up constraints! Thank you Randall. I've been trying to explain this to a friend of mine (a right-leaning economics student). I'll send this along. I think the Willem Buiter's explanation of the zero-bound on interest rates may have cracked the conservative skull ice already…Maybe this will cause a full-blown thaw.

  2. So the earth is flat huh? I've been in the economics and finance arenas for a long time, and while I've hears some argue that the minimum wage may not decrease employment, I've never never heard an argument for it increasing employment. What a joke.

  3. To Anonymous Coward: You must have been around those arenas for so long that a simple google search is beyond you, as that would certainly have revealed to you that people have been arguing about the effects of minimum wage increases since Card and Kreuger (1992).

  4. I can't believe somebody like this is allowed to teach economicsThere is no "paradox" of thrift. Give it up.Please learn economics: http://mises.orghttp://mises.org/story/3194 —> this should cure your totalitarian urge

  5. Stephen L, do you take serious that it's possible to isolate the impact of a single variable in a system as complex as the US economy? There were no exogenous forces pushing employment one way or another in C&K's study? Has it really come down to relying on 1 paper, quoted ad nauseum by defenders of the minimum wage, to try and defend an indefensible theory?Here's a model that seeks to eliminate the impact of any exogenous variables, as C&K were so mastefully able to do:1. As the price of a good rises, demand falls2. The minimum wage increases the price of a good called labor3. Demand for labor fallsThat must have failed the fallacy of logic…

  6. Anonymous coward should stay anonymous, lol.Raising the minimum wage has an obvious first-order effect of decreasing employment, as for example when businesses close or lay off workers who aren't worth the new, higher wages. Call this E.The second-order effects are, of course, legion:- (a.1) a moderate redistribution of income away from employers and towards minimum wage earners (as ceteris paribus the money that's now going towards those higher wages is coming out of profits, at least temporarily)- (a.2) a moderate redistribution of income away from minimum wage earners (those who are now out of work) back towards employers (those who were previously employing the now-jobless)- (b.1) a corresponding increase in consumption, as minimum wage earners have a higher marginal propensity to consume than their employers, and thus the still-employed spend more of the redistributed income than its previous recipients (their employer)- (b.2) a corresponding decrease in consumption, as the out of work minimum wage earners have less income (and the corresponding income is shifted into the hands their previous employers, who have lower propensity to improve)- (c.1) an increase in employment in firms that witness the increase in consumption (eg mcdonalds, payless, etc.)- (c.2) a decrease in employment in firms that experience the decrease in consumption (eg ruth's chris, aldo, etc.)…and so it goes.To decisively conclude that the higher-order effect of a minimum wage increase is to decrease employment you'd of course want to be able to claim that:c.2 + E > c.1probably by working up some model explaining how a1 and b1 -> c1 and a2 and b2 -> c2, etc., but that's either a problem of multivariate analysis or an empirical question; the latter approach is clearly beyond you and I'd suspect the former is, also.You'd have the same problem trying to decisively conclude that raising the minimum wage increases employment, which is why there's a still a debate about what the actual effects are; The point here is that once you get beyond the a grade-school level of reasoning nothing is as simple as it appears; what you find is that the ideologically committed use first-order reasoning when it arrives at the conclusion they want and start some hand-waving about higher-order effects when the first-order approach doesn't get the answer their pet theory tells them is right.The blog host is to be flattered for taking an honest approach, and seeing where things take them (including into the land of "no conclusions possible without more data").

  7. It seems to work well for Utah to balance their budget every year, including this year. I rather think a deficit spending mindset will catch up with a person, state, or country eventually.

  8. Hi Professor Wray,Thank you for sharing you insights. I am a computer science major and these ideas are very new to me. I still don't understand why the following identity must be true. Can you clarify?"At the aggregate level, the dollar spending of all three sectors combined must equal the income received by the three sectors combined. Aggregate spending equals aggregate income."To help me think I further simplified your example. Let's assume there are only 2 sectors. One is the private sector and the other is the government. Let's ignore the foreign sector and just assume that it is always balance. Furthermore, let's eliminate currency and assume the society is based on bartering.Let's say the private sector are all farmers and they produce 100lb of grain a year. Each year, the private sector turns over 30lb of grain to the government as tax. Furthermore, the private sector only consumes 60lb a year and save 10lb of grain in a warehouse. The government consumes 25lb a year and saves 5lb in the warehouse. Here both the private sector and the government are net savers every year. Both are increasing in wealth as measure by lbs of grains in the ware house.I don't see why everything a society produces must be spent by the private sector or the government sector. What am I missing?

  9. It would be fine if we were only exchanging government wealth for private sector wealth because the wealth/debt of the government is the wealth/debt of the private sector. The problem is that both the government AND the private sector are running deficits and it's no known how much longer the foreign sector will support this and largely the money was used for consumption and not investment.

  10. If I understand you correctly, and A,B and C are the imbalances in each of the 3 sectors then A+B+C=0You appear to be saying that if trade is balanced then C=0 and A=-B. In other words, public deficit equals private surplus.But why should C be zero? Why not aim for an export surplus (a deficit for the foreign sector, so C is negative), in which case both the public and private sectors can be in surplus?

  11. "I don't see why everything a society produces must be spent by the private sector or the government sector."Careful, you're mixing up the real ("what a society produces") with the financial ("what can be spent"). This always leads to trouble.In your example, you are talking about grain stockpiles, which like every real asset is "single entry": my house is an asset to me, and a liability to no one. But a financial asset is, by definition, a relationship between two parties: the mortgage on my house, for example, is a debt to me and an asset to the bank.What the professor is saying is an accounting identity: all money spent must be someone else's income. It has to be, since the act of spending is the transfer of money from one party to another.

  12. Anonymous Mises-ian,The true tragedy is that so many, like yourself and like the author of the link you provided, continue to base their analysis on a monetary framework (loanable funds and such) that is entirely flawed and could only actually apply in a gold standard or similar system.

  13. Yes, it is true that government deficits represent private savings. Thank you for explaining that again in such clear and simple terms.More generally speaking, government surpluse3s or deficits perform an important equilibrating function and are needed to enable macroeconomic equilibrium.Further, an accumulation of government deficits means that people get richer and spend more. This reduces the necessity for running government deficits, seehttp://epub.uni-muenchen.de/2143/for an analysis.

  14. Sorry, the link should have beenhttp://epub.ub.uni-muenchen.de/2143/

  15. Oh, I guess I'm another one of those pesky conservative dolts…Like one of the Anonymous pople above, I'd refer any thoughtful people to mises.org for some intellectual food. You really need it.Or, just read a classic from Hazlitt, Economics in One Lesson. It deals (extensively) with the pervasive logical 'fallacy of composition', which basically is a tendency of most thinkers to oversimplify the 'micro' effects and then perform a simple sigma summation to derive the 'macro' and then apply further reasoning from there. The true 'macro' has many unseen effects.Or, go back to Bastiat's broken window. Or, go to William Graham Sumner's forgotten man. Google them if you don't know…The Liberal Statist Left suffers from hubris, in thinking that their collective reasoning is sufficient to account for all the forgotten men, that their collective reasoning is sufficient to perform a sigma summation with accuracy to the whole. This is simply hubris, nothing more.The only solution to such complex problems is the collective reasoning of the many forgotten men in their own self-interest. The sigma summation of this massively iterative process is the only rational calculus to the multitude of 'macro' problems out there. From this process ALONE does the 'micro' in economics rationally produce the 'macro.' From this process ALONE does the 'macro' become efficient, logical, and fair.

  16. Razorback, thank you for pointing to mises.org and other recommended reading (that I knew before, however). I had a look at the site and found, at first glance, neither an analysis of the fallacy of composition nor an analysis of the paradox of thrift. Please be more precise, such that I can educate myself. A general reference to mises.org is approximately as helpful as a reference to amazon.com.

  17. Yes, one must be thankful for the smashing Misesian analysis that if you don't manufacture televisions, you won't have any televisions to sell to people who demand them, ergo supply precedes demand. Which is why America's enormous television industry keeps adding to the billion-television stockpile, erm, hold on, no it doesn't, does it?It's amazing that these people's "intellect" is sufficient to find their shoelaces in the morning, let alone work a computer well enough to be able to post this nonsense.

  18. I got here a year late, but I am curious – what happens to all that saved burger money? You know the money formerly spent at 'Macdonald's'. Is it burned? Buried in the yard? Mattressed? Or banked and loaned to others, increased in amount by a banking multiplier, which others then hire people? Or invested in equities so that, sometimes through a long chain, the money is again multiplied and used to … wait for it… here it comes…hire others. Badda, bing.How can one trust a poster so inattentive to detail that he twice mis-spells 'McDonald's', and does so with the same separate errors both times?Jeez, I dunno.

  19. Now, it is not as hard to create a job as it is to create a 10th bone, because you really don't create them that easily… jobs can be created much more easily. You first get people to agree that they will exchange with you at some point. Then, you, the 10th dog or worker, create a business for yourself. Do SOMETHING. And then sell it to those people who you agreed to sell to and buy from. That is at least a start in the right direction.

  20. What if several burger buyers got layed-off (or even fired, et cetera) recently, and simply cannot afford the burger anymore? They did not pursue thift deliberately in this case. This is… paradox of downsizing? (it needs to be called that. This does.)

  21. If a person can't compete against a corporation, and can't find a job, bones can be created quite easily.The bank that the burger-saver invests that saved money in, and the company they lend that money to, depend on the government's bonds for their base rate. No deficit, and that base rate falls to 0. The banks' interest rates must lower their rates on loaned money. They will not loan if they cannot charge interest. So, they sit on that money, until interest rates climb to where it's profitable again to lend. That's where the current capital glut is coming from.von Mises is just a purveyor is the fallacy debunked above. Sumner recanted his naive blustering later in life.

  22. Your analysis on the fallacy of composition and the effect of minimum wages, while correct overall, ignores one possible reaction from the employers: to absorb a loss of profit. (Note that I am not attaching any value judgment to this).Further, increased wages could be (and often are) tied to increased productivity.

  23. Great piece, although this seems a little antiquated at this moment in time:"No one talks any more about achieving budget surpluses this decade; almost everyone agrees that we will not see budget surpluses again in our lifetimes—if ever."But I think that's a sign of the insanity of the times rather than a bad analysis.

  24. "A+B+C = 0; therefore everything is okay. Q.E.D."Am I missing something?If A + B = 0, and A and B are on the same side(private sector and government sector of the same nation), this is just as well.If A + B + C = 0, and C is a third party competitor of A and B, the net neutrality of the forumla is irrelevant! Woo, money isn't broken. Money owed by someone is a credit to someone else.Explain to me why (-)A + (-B) + (+)C = 0, is in any way a source of solace when America is A and B.I get the fallacy of composition component of this (that the federal gov't being stingy with stimulus funds will come at the cost of private sector saving, and possibly even federal income tax). But none of that answers to the fact that C is amassing both HUGE savings (as A and B go into debt together, irregardless of their relationship to each other), which it's reinvesting in itself.

  25. >Explain to me why (-)A + (-B) + (+)C = 0, is in any way a >source of solace when America is A and B.Follow the money. Using China as the (+)C, assume China nets ~$250 Billion in a year from exports to the US. According to the equation, that means A + B must equal (-)$250 Billion, i.e., either the public, private, or both sectors are running a deficit. That is exactly what has been happening for 10+ years.But what does China do with that money? It has large sums of American Dollars. In fact, it has so much that it cannot effectively use it because there is only one market player large enough to consume $250 Billion a year: The US Government Bond market.But the US Government Bond market is not a true market… it is an economy manipulation device for controlling US interest rates. US Government Bonds cannot truly be called government debt. At any point in time, they could effectively be negated by issuing new currency. Of course, doing this suddenly would upset many nations… however, doing it slowly, in a period of "economic crisis" could be overlooked… Make no mistake, we are in the midst of an economic war.

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  28. The paragraph on minimum wage implies that there exists an optimal minimum wage that maximizes employment. In other words, a minimum wage above or below the optimum would reduce employment.

    This assertion would benefit from the presentation of a formal model, but a thought experiment is helpful. A wage of zero attracts no labor and thus results in no employment. If wages rise high enough that firm profits go to zero, then additional wage increases simply result in equivalent price increases in order to avoid nominal costs exceeding nominal revenue. Once negative profit is reached, there is a disincentive to increase output (even if all firms were “nonprofits”). (In practice disincentives to investment and output creep up as margins shrink toward zero.) Thus, there is an output and employment maximizing wage level.

  29. “while an individual can save more by reducing spending (on consumption), society can save more only by spending more (for example, on investment)”

    Isn’t the individual who reduces spending and saves in a bank by definition investing? Ergo I see no reason for the existence of the “paradox” of thrift since micro savings = macro investment. An individual can decrease consumption and increase savings, allowing for greater consumption in the future. On aggregate, a society can decrease consumption and increase investment, leading to an increase in future productivity which allows for an increase in future consumption. Nothing paradoxical there; net spending doesn’t change. Furthermore there is no composition fallacy. What does change is the structure of employment as interest rates drop, making long-term capital investments and bonds less financially risky.

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  31. “On aggregate, a society can decrease consumption and increase investment, leading to an increase in future productivity which allows for an increase in future consumption. Nothing paradoxical there; net spending doesn’t change.”

    Because it is not an example of the paradox.