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Economics 1: U.C. Berkeley: Fall 2010: September 27 Government Deficits and Debts Lecture


Economics 1: U.C. Berkeley: Fall 2010: September 27 Government Deficits and Debts Lecture

The Dynamics of the Debt-to-GDP Ratio: Last time we talked about fiscal stability and about the danger that the government's promises would unravel completely--that you would wind up in some "Mad Max Beyond Thunderdome" scenario in which nobody trusts the government and its monetary system. We saw that happen in the past decade in Zimbabwe.

Last week, however, I skipped over one part of the analysis of the sustainability of government deficits: the debt equation, the equation for how to calculate what's happening to a country's debt-to-GDP ratio, the ratio of government debt D to annual GDP Y.

(D/Y)t = (1 + (r-g))(D/Y)t-1 + d


Here is how you think about it: You take the previous year's debt-to-GDP ratio; (D/Y)t-1. Start by noting that if nothing changes the debt the next year will be the same as the debt this year--that is the "1" in the debt equation. Plus you have got to pay this year's interest on last year's debt. That is the "r" in the debt equation. But even if the debt is growing the debt-to-GDP ratio will be shrinking if the economy is growing faster than the debt, so you have to include a term for the percentage rate of growth of GDP: that is the "g" in the debt equation. Even a rapidly-growing debt is perfectly consistent with a stable debt-to-GDP ratio if the economy is growing rapidly too. For it is not what is happening to the debt but rather what is happening to the debt-to-GDP ratio that determines whether a government's promises to pay back its debt are going to be credible or not. Last you have to add in this year's primary deficit: the excess of spending on programs over revenues. That is the lower-case "d" in the debt equation.

The deficit reported in newspaper headlines around the country is not the primary but the total deficit. Why do I focus, instead, on the primary deficit? Two reasons. First, the primary deficit is what the arithmetic wants: it is the primary deficit that shows up in the debt equation. Second, the government controls the primary deficit. It does not get to choose what the interest rate on government debt is: the market gets to choose that. The primary deficit is the quantity that government policy controls.


Now let us ask our debt equation a question: what must be the case for the debt-to-GDP ratio to be stable? What must be happening if this year's debt-to-GDP ratio is the same as last year's? To see the answer, we expand our equation out:

(D/Y)t = (D/Y)t-1 + r(D/Y)t-1 -g(D/Y)t-1 + d

We set (D/Y)t equal to (D/Y)t-1 and cancel terms:

0 = r(D/Y)t-1 -g(D/Y)t-1 + d

We move the lower-case "d" to the left-hand side:

-d = r(D/Y)t-1 -g(D/Y)t-1

And we divide through:

-d/(r - g) = (D/Y)t-1

And let us denote this stable value of the debt-to-GDP ratio by a star:

-d/(r - g) = (D/Y)*

This is our answer: You take that level of the primary deficit. You attach a minus sign to it. You then divide it by the difference between the interest rate on government debt and the growth rate of the economy. That tells you where the debt-to-GDP ratio can balance.

The first lesson to get from this final equation is that if g > r you do not have a problem: if g > r your debt-to-GDP ratio is heading for zero if you are running a primary surplus--if d is less than zero--and is headed for some well-defined and stable number if you are running a primary deficit.

But what if--as is more likely--r is greater than g? The a stable long-run debt-to-GDP ratio requires that you run a steady primary surplus. And if your primary surplus gets too small---if when divided by r - g it is less than your current debt-to-GDP ratio, you are in big trouble: your debt-to-GDP ratio is then primed to grow without bound. If you don’t want to want primary surpluses or run a large enough primary surplus--well, either people believe that policies are about to change and you are about to start running a large-enough primary surplus, or you are headed for the Mad Max scenario.


At the moment in the U.S. r is less than g. This debt equation thus tells that there is not any big problem now. The government can run a primary deficit and then over time the economy will grow faster than the interest rate and so even a big deficit now will gradually shrink over time as a share of GDP so that in the long run will be able to pay it off without much trouble.

Does that mean we should not worry about the government deficits the United States is now running? No. r is less than g now, but it would be very foolish to believe that r will be less than g over the long run.

This ends the piece of last week's lecture that I did not have time for.

The Government Budget and "Depression Economics": Now let us move on to the government budget in the less-than-long run. We already covered situations of "depression economics." In situations of "depression economics," boosting government spending puts cyclically-unemployed people to work directly and also increases the supply of safe savings vehicles that people can hold. Thus it has a direct and may have an indirect stimulative effect--if the cause of the downturn is not a shortage of money per se but rather a shortage of bonds or a shortage of safe assets. There is a presumption in situations of "depression economics" that the government should spend more and tax less in the short term.

The Government Budget at Other Times": Suppose, however, that we are not in a situation of "depression economics." And suppose that there are no worries that the government will not pay back its debts in the long run. We still have an unanalyzed question: what happens in the medium run if the government runs a larger or a smaller deficit?

We are going to assume the level of production and employment in the economy is pretty much equal to the economy's productive capacity, that real GDP Y is equal to potential output Y*. Remember that back in our income-and-spending framework we had GDP Y divided into four components: consumption spending by households C, plus investment spending by businesses I, plus government purchases G, plus the balancing net exports term.

Y = C + I + G + NX


And remember our consumption function: a part of consumption that depended on the confidence consumers had about the future and a part that depended on their incomes today:

C = c(0) + c(y)Y.

We can substitute our little consumption function in for C in our income-and-spending equation and we can replace the level of GDP Y by potential output Y* to get:

Y* = c(0) + c(y)Y* + I + G + NX

We can move all terms with Y* to the left and group them:

(1 - c(y))Y* = c(0) + I + G + NX

The potential output of the economy multiplied by the marginal propensity to save, by the difference between one and the marginal propensity to save--that is going to be equal to investment spending, plus government purchases, plus next exports plus that part of consumption spending that depends on household confidence.

The reason to do this algebra is that when we look at this equation, we notice that--unless we are in a "depression economics" situation--the left-hand side is going to be very close to a fixed number. The level of potential output Y* is not going to change quickly by much. Neither is the marginal propensity to consume.


This tells us that if government purchases go up and G rises--or if tax cuts make consumers feel flush and boost c(0)--then investment spending I or net exports NX or both are going to go down.

Do we like having investment spending and net exports go down? Investment spending is one of our major sources of economic growth, and we like economic growth. Diminish the amount that the economy is devoting to adding to its capital stock and you're going to diminish its rate of economic growth and make the future poorer. We probably do not want to do that. If net exports go down--if they turn large and negative--then we owe a bunch of money to people in foreign countries. When we pay that money back it will diminish our wealth. Large external foreign debts have been a common source of financial crises and episodes of depression economics over the past two centuries. Moreover, we do think that it is important for economic growth to maintain a certain productive capabilities inside the United States. We like having Applied Materials located in Silicon Valley: it is a major source of technological innovation, and if you have technological innovation in one place that tends to make for a whole bunch more technological innovation around that and makes everyone in the whole region if not the country richer. There are powerful external benefits from being at the forefront of technological progress


Crowding Out: Our conclusion that government spending crowds out investment and net exports, however, is just math. The math tells us that if government purchases go up and if we are not in a depression economics situation then you can bet that net exports and investment spending have to go down.

But that math does not really tell us why this happens. That is the problem with mathematical arguments in economics. They get you to a place. Often they get you to the right place. But you do not understand how or why you got there, or what it means.

So how is it that when government purchases rise--and when we are not in a depression economics situation--investment spending or net exports or both fall?

Government purchases rise. The government is thus running a larger budget deficit. The government must issue more bonds in order to raise the financing to pay for its extra spending. And as the government issues more bonds, bond prices fall: it is supply and demand.

When bond prices go down, interest rates go up. That is accounting. That is what a high interest rate means: that you can purchase a bond cheaply and thus get a lot of interest payments in return for your initial outlay.


When interest rates go up, foreigners take a look at the potential profits from investing in the United States. More foreigners who had just sold us imports decide that they don’t want to buy American exports but instead they want to buy United States bonds to get the high interest rates those bonds pay. Thus their spending on U.S. exports drops, and net exports falls.

Alternatively, businesses thinking of issuing their own bonds to finance investment projects take a look at the low prices they would have to accept to sell their bonds given the low prices of Treasury bonds--a substitute investment. They decide that given the high interest payments they would have to incur, it is not worth undertaking their investment projects, and so investment spending falls.

So the conclusion; if we don’t want investment spending or net exports to fall when government purchases rise--in this scenario in which there is no depression economics and in which there is no fear of lack of credibility in the government's promises, at least--we would need to do something to consumer confidence. We need to do something to c(0) so that its decline would offset the expansion of government purchases G.

How do you diminish The parameter c zero? You need to make households feel poor and so want to spend less. What measures can the government take to make households feel poor and want to spend less? Increasing taxes. Increase taxes and, yes. indeed people have less money because their paycheck goes down. This tends to disturb them: they tend to feel poor. Congratulations! you have raised government purchases without diminishing investments spending or net exports. That is a big win on the macroeconomic balance sheet.


However, it is also likely to be a big loss on the political balance sheet if you are a politician. Voters do not like governments that make them feel poor. Hence politicians really do not love to increase taxes.

Nevertheless, if we want to stay far away from Mad Max-like scenarios--and we do--we do have to do the tax increases. As Milton Friedman liked to say: "to spend is to tax." Once you have decided to spend you have also then decided to tax. You can then tax stupidly or you can tax smartly, but to complain about the taxes once you have done the spending--well that is just stupid. And if you tax smartly, and balance your spending increases with tax increases, you can avoid the falls in investment and net exports that slow economic growth that happen if you tax stupidly.

Dysfunctional America: Alas! America today seems prone to tax stupidly. You can postpone taxes until later. Postpone them until the next presidential administration, or until you have retired from Congress or become a lobbyist and are happily riding around in your limousine. Then it is your successor sitting in the seat who has to take the blame.

And indeed there can be good reasons to postpone tax increases: remember our discussion of depression economics that a cyclical deficit is a good thing to have when unemployment is high.

But if we're not in depression economics, postponing our tax increases is likely to be a bad idea.

Five Rules for Public Finance: And so now we have arrived at five rules for public finance:

(1) The government must do whatever is necessary in order to make sure that people have confidence it will pay back its debts.

(2) You really ought to have budget balance over the business cycle. It is fine to run cyclical deficits in times of high unemployment, but you really should balance them with surpluses when the economy is in a boom.

(3) That implies Milton Friedman's Pay-as-You-Go principle that he set out in his late 1940s framework for fiscal and monetary stability: whenever the government takes on a mission to do some long term spending program, it also needs to match that by imposing some tax large enough to fund the spending. Changes in government spending plans over time should be accompanied by changes in taxes so that when politicians make decisions and when voters evaluate politicians there is no gaming the system.

(4) You need to keep plenty of headroom in your debt capacity in normal times. In normal times you should aim to keep your debt-to-GDP ratio fairly low. There will come emergencies and opportunities during which you will want to increase your debt-to-GDP ratio. Remember 1803: Thomas Jefferson was president and Napoleon I was about to become Emperor and was willing to sell French "rights" to the entire Louisiana territory. The United States had plenty of debt capacity and could easily afford to borrow--and Jefferson did. Thus we have a United States that doesn’t end at the Mississippi river but instead continues all the way on from the Atlantic to the Pacific Coast. The War of 1812, Civil War, World War I, World War II--in all of them we were very grateful that we started with a low national debt-to-GDP ratio. The government wanted to fight these wars for reasons that it thought were sufficient. It was able to borrow in order to build the armies and navies and air forces to fight them, It could not have done that if the debt to GDP ratio was really high. The Great Depression and the current Great Recession--we want to respond to them by deficit spending as well.

And then there are the other foreign policy missions: after World War II--even though we'd already run up a large debt during World War II--we decided it was to the world's advantage to undertake a remarkably large aid program to Western Europe to help rebuild it under the three headings of the UNRRP, the United Nations Relief and Rehabilitation Program; the MSA, Mutual Security Assistance, and the ERP, the European Recovery Program better known as the Marshall Plan. (Who, you ask, was Marshall? Wasn't Truman the president? Yes, the president was Truman. George Marshall was the ex-general who was the Secretary of State. Truman decided to call it the Marshall Plan: "Can you imagine how low its chances of passage would be in an election year with a Republican majority Congress would be if we called it th Truman plan?" he said. Smart man, President Truman.)

One more digression. Most of you were... barely born when the Cold War came to an end at the start of the 1990s. I remember a whole bunch of us economists--besides me I remember Barry Eichengreen, Rudy Dornbusch from MIT, Larry Summers then at the World Bank, Joe Stiglitz, a whole bunch of people--saying this: We had just spent what would be $8 trillion at today's prices over the previous generation preparing to resist the military threat of the Soviet Union. Shouldn’t we be willing to spend an eighth of that--$1 trillion--on a Marshall Plan for Eastern Europe and the former Soviet Union to help shape their transitions away from really-existing communism to a more normal political system? We made the argument. We were shot down because the debt-to-GDP ratio was then on rising trajectory because of Ronald Reagan's budget deficits. The view of the politicians then was the U.S. government could not take on another large additional commitment given the instability of its long run finances.

I think we would be living in a better world now if we had found the extra trillion to disburse to countries that elected leaders friendly to democracy to move Eastern Europe and the Soviet Union in the direction of a normal political-economic configuration. The current state of Russia--where it settled without that large push from us--disturbs me greatly. But we could not find the resources to do it.

The fact that you are going to face emergencies and opportunities that involve large-scale government spending programs is a powerful argument for keeping your debt-to-GDP ratio low in normal times.

(5) But that does not mean that countries should not borrow except in emergencies. It is perfectly okay for a government to borrow and run up its debt when it is undertaking projects that are going to primarily benefit future generations.Taxing the citizens of the East Bay and San Francisco right now to pay for the entire reconstruction of the Bay Bridge seems unfair--the new Bay Bridge will still be there and be earthquake-safe 50 years from now. People who are going to move into the San Francisco area 40 years from now will benefit from the bridge. They should pay some part of the cost. Thus you should finance infrastructure projects that build up productive capacity through borrowing and debt.

You should also finance current spending through borrowing and debt if you think the future is going to be a lot richer than the present. If everyone in 2070 is going to have five personal robots capable of taking care of their every need, while we each have zero, perhaps we should run up the debt-to-GDP ratio and spend some of what their robots are going to produce on ourselves--for it will be little skin off their nose if they were taxed extra so that they had to divert the production of one of their robots to debt service and only had four personal robots capable of taking care of their every need.

If I had here a wormhole time machine with the other end in 2070, the people in 2070 might respond to that by sending us one of their killer robots to say:

Aren’t you already doing this? Aren't you imposing huge costs on us in your future by changing the climate with your carbon emissions? Right now you are melting the north polar ice cap as on hors d'oeuvre. You have no idea what you are ordering for an entree--but we are going to have to deal with all the floods and typhoons your actions are bringing to the people of the Genghis Delta in what is your future but our present.

If you weren't selfish dorks, you would right now be reducing your debt-to-GDP ratio now because we're going to need all the resources we can find to deal with global warming.

That's an argument.

That's the kind of argument you have to think about in thinking about what your plicy for the debt-to-GDP ratio should be. Which arguments should you find most convincing? I think you should pay very close attention to arguments made by people who can deploy wormhole time machines and killer robots..

So here we have our five rules for public finance.


A Right-Wing Conclusion: I want to close this lecture by making a right wing argument that these five rules are inconsistent and we have to drop one of them.

This right-wing argument is one that back when I was your age I pooh-poohed as nonsensical and simply silly. But it is 30 years later. I at least feel a little bit wiser. It's not that I believe this right-wing argument completely. But it has much more force with me than it did 30 years ago.

The argument comes from Nobel Prize-winning James Buchanan. He pointed out two generations ago that he didn’t think that these rules were politically sustainable. If you try to enunciate the principal that cyclical deficits in downturns are good and permanent structural deficits are bad--that is just too complicated for the political system to process.If you tolerate and approve of cyclical deficits to fight downturns, Jim Buchanan argued, then you're setting the political stage for permanent structural deficits because politicians will be eager to grab the argument that the deficits that they want to run are actually good for the economy.

Allow cyclical deficits, and you make permanent large structural deficits likely. They will slow growth by crowding out investment. They might eventually lead to an erosion of confidence in the government's ability to pay back its promises--and so lead you down the road to Mad Max.

Thus, Buchanan argued, the risks run by undertaking deficit spending in a downturn are too great. The only prudent course is to enunciate the principle: "always balance the budget, no matter what." 30 years ago I thought this was of course complete nonsense: to say that counter-cyclical deficits are good and structural deficits are bad did not seem to be an argument that was too complicated for the American political system to understand.

Today? Today I have to say that I just don’t have that confidence any more.

How many people have read George Orwell's Animal Farm? Oh, excellent--it is part of our common culture!


How many people remember the one-sentence slogan that is the basic principle of animalism? It is:

Four legs good, two legs bad.

That is the basic principle of animalism: four legs good, two legs bad.

(Note, by the way, that a wing is properly classified as an organ of locomotion. The wing properly understood is a leg and not an arm--and it is certainly not a hand. So even though chickens and geese have only two legs, they are not properly classified as Enemies of the Animals.)

The pigs and chickens and dogs and horses of Animal Farm can understand: "four legs good, two legs bad." Why can’t the senators at Congressmen of Washington understand the principle: "counter-cyclical deficit good, structural deficit bad"?

I have a much harder time believing in the rationality and the intelligence and the honesty of the politicians we tend to elect than I had thirty years ago. Right now we have a Republican party that's just set out its platform for the fall 2010 election. As best as I can see, the one sentence summary of its platform is: deficits are bad, so let's take steps to cut taxes and make them bigger.

Since 1980 I have seen all kinds of people--most of them but not always Republicans--attempt to permanently unbalance the U.S. federal government budget over the long run with all kinds of truly astonishing and falacious arguments. I have seen economists I had a lot of respect for--the likes of Eddie Lazear, Marty Feldstein, Glenn Hubbard, and Greg Mankiw--fall in line at the dictates of their political masters and argue for budget policies that they know are long-run economic disasters. So I would like to inoculate you against some of these fallacious ideas.

On the Laffer Curve: The idea you will hear more often is the idea of the Laffer Curve--the claim that cutting taxes is actually increasing taxes because if you cut tax rates you will increase tax revenues. Why? Because the cut in tax rates will produce such a huge outburst of extra economic activity and prosperity.


To immunize you against this I want to say that this Laffer Curve argument really does work in three but in only three situations.

  1. The Laffer Curve argument can work in "depression economics" situations. Because business investment depends on how large business profits are, a cut in taxes that boosts consumption spending can also boost business sales by enough to raise profits enough that investment grows enough that the government-deficit multiplier is large enough your cut in tax rates while unemployment is high actually improves government finances and lowers the debt-to-GDP ratio. In times of very high unemployment you should at least think about whether cutting taxes and raising spending might put the government finances on a sounder basis. I think that that is definitely the case for Ireland today. Ireland embarked upon a policy of fiscal austerity, of cutting back spending and increasing taxes in order to reduce its deficit and restore confidence in the government. What did they find happened? They just pushed one of their biggest banks over the edge into bankruptcy. The cost of keeping it from bringing down the entire Irish financial system into a complete crash will be in the order of five times as large as the improvement in the deficit they got by increasing taxes and cutting spending.

  2. The Laffer Curve generally works with tariffs--taxes on imports, on international trade. Taxes on trade are extremely damaging in the sense that you raise remarkably little money for the economic activity you discourage. Indeed, one of my jobs when I worked for the Clinton administration was to make Laffer Curve arguments about how tariff cuts were in fact likely to produce much more benefits in terms of expanded economic growth by letting people who would make things more cheaply in different parts of the world make them. And I still stand behind those arguments.

  3. The Laffer Curve works when tax rates are nearly 100%--whether through the tender mercies of the likes of Kim Jong-un or Fidel Castro or just through complete corruption. Under those situations cutting "tax rates" on enterprise is something you surely want to do.

But if you have the relatively honest governments of the North Atlantic with their effective tax systems, and if you have our remarkably well-functioning Internal Revenue Service successfully making people pay what taxes they owe by threatening them with random terror if they underreport their incomes--then your Laffer coefficient is one-tenth rather than one. You should think that if you cut tax rates, then you will find that you have induced some people to shift some of their income into taxable forms and you won't lose all of the tax revenue that you had initally calculated you would lose--but you will lose 90% of it.