Nouriel Roubini and David Backus

Lectures in Macroeconomics

Chapter 5. Output and Real Interest Rates

We've seen, so far, that economies grow at different rates and experience short-term fluctuations that we've dubbed business cycles. We'd like to go beyond that, though, and say something about why we observe these things and what we might do to encourage better macroeconomic performance. What we need is a theoretical framework for thinking about these issues. Over the next few weeks we're going to examine two versions of a macroeconomic theory, labeled Classical and Keynesian, that emphasize different aspects of macroeconomic life. These models are often presented as competitors. I think you'll find instead that they are complementary, and provide different perspectives on the aggregate economy. Roughly speaking, the Classical theory is aimed at the long run (say, two years or longer) and the Keynesian theory at the short run (less than two years), though the distinction isn't that tight. You'll also find that the two theories share many common elements, so a lot of what we learn with the Classical theory applies to the Keynesian theory as well.

On Theory in Macroeconomics

By way of motivation, let me report the comment of a member of Stern's Board of Overseers, the CEO of a large corporation. He said: "Theory is power." What he meant by this, I think, is that people who understand how things work at a deep level will be able to influence and control those who do not. It's a personal advantage in your business and career. It's certainly been true of my career: my most marketable skills are my technical skills.

But back to our regularly scheduled programming. In this course I want to give you three complementary organizing devices: a long run "Classical" theory, a short run "Keynesian" theory, and an appreciation for accounting relations connecting seemingly different things. As I said, these are not alternatives, they're complements. Intuition comes in many forms, and these three aspects of economic life show up all the time. I think of them as the fundamentals of macro, with them you can do anything. More advanced economics simply puts more flesh on the same bones.

You'll notice as we go along that the theory has many elements. Perhaps that's not surprising: when you look at an entire national (or even world) economy, as we do when we look at growth and business cycles, there are a lot of aspects to it. There's simply no way around that. What we'll try to do, though, is distill the essential elements from the details, simplifying as much as possible. So here we go, starting with the Classical theory of the macroeconomy.

The Production Function Again

Y = A F(K,N),

where Y is output (real GDP), K is the stock of physical capital (buildings and machines), and N is labor (number and hours of people working). The letter A measures (total factor) productivity. We've seen that A might be influenced by, among other things, education and innovation, prices of imported raw materials (like oil), or even the weather (although this is generally small potatoes in industrial economies like the US, Germany, or Japan).

In many applications, we'll simplify the production function further. Over short time periods (a couple years, say) we can regard K as practically constant, since a year or two's worth of investment is a small fraction of the total stock of capital. To get a rough idea, the capital stock is about three times GDP and investment is, on average, about one-sixth of GDP, so a year's investment is only about 6 percent of the capital stock. Plausible short-run fluctuations in the rate of investment, therefore, have very little effect on K. Over longer time periods, however, changes in K can be critical, as we saw last week for Japan and the US between 1970 and 1985.

In the short run, then, we can regard K as approximately constant and express production as (approximately) a function of employment (which we know varies quite a lot in the short run) alone:

Y = A F(K,N),

where K denotes a constant value of K. This relation is an approximation since we are ignoring the small changes in K: all of the short run movements in Y, then, are attributed to A and N.

Now how would you expect output Y to vary as we change N, with fixed values of K and A? First, you would expect for a given level of productivity that more labor will lead to more output. That is, F is an increasing function. Second, you might also expect that diminishing returns to labor will set in as we use more and more of it. That is, the first unit of labor will generate lots more output, the next unit slightly less additional output, etc. What we're talking about is the slope of F, and the suggestion is that the curve will get flatter as we increase N; see Figure 1. This is exactly the kind of thing you've seen in microeconomics under the rubric diminishing marginal productivity. If you are comfortable with calculus, what we're saying is that the marginal product of labor,

MPN = dY/dN = A dF(K,N)/dN ,

is positive, but decreases as we increase N, for any given values of A and K. In the expression above dY/dN is the derivative of Y with respect of N, or the change in Y deriving from a small change in N. This derivative is positive and decreasing in N. The latter property is pictured in Figure 2.

All of this concerns the production function for fixed productivity A and capital stock K. If we change either of these variables we shift this curve. Suppose, for example, that the US (or any other) economy becomes more productive as a result of new product development that increases A. This is clearly an upward shift (in fact, a "twist") of the curve in Figure 1. Conversely, an increase in the price of imported oil results in a decline in A, and therefore a downward shift.

Changes in the capital stock have a similar effect. As we've seen, the Japanese capital stock has increased enormously over the postwar period. As a result, they can now produce much more output with the same number of workers. We can represent this by an upward shift of the curve in Figure 1. Similarly, the massive destruction of capital in Iraq and Kuwait during the Gulf War might be represented by downward shifts.

The essential similarity between changes in A and K is obvious in the particular production function we used last week. If

Y = A K^1/3N^2/3,

then changes in A and K are the same, except that the latter are attenuated by the exponent .33. With somewhat more abstract math, we could (but won't) show the same thing more generally.

There's a conceptual issue here that will come up again and again, so it's best to be clear about it at the start. Most of the relations we'll be dealing with concern more than two variables. In this case the relation is the production function and it involves four variables: Y, A, K, and N. What we've done is represent in two dimensions the changes in Y that result from changes in N, for given values of the other variables, A and K. Changes in Y resulting from changes in N are thus movements along the curve we drew in Figure 1. Changes in the given variables A and K, on the other hand, appear as shifts of the curve. You want to make sure you understand this distinction. (If you don't, this could be a long course.) What this means is that whenever we graph something, we have to keep in mind what variables are fixed behind the scenes, as it were. Changes in these variables will result in shifts of the curves.

The Labor Market

Labor demand. The demand for labor comes straight from the production function---or, rather, its close cousin the marginal product of labor, or MPN curve. We noted that the MPN declines as N increases. This showed up in the curvature of Figure 1 and the downward slope of Figure 2. Now think what a firm will do to maximize profits [you should remember this from micro]. For a marginal one-unit increase in labor input, the MPN tells us how much extra output we get. The value of the additional output is P times MPN, where P is the dollar price of each unit of output. The cost of the additional unit of labor input is W, the wage rate measured in dollars. A profit-maximizing firm will increase N until the cost and benefit of an additional unit of labor are equal at the margin: at lower levels of N the benefit exceeds the cost, at higher levels the reverse. Mathematically,

P x MPN = W,

or

MPN = W/P

That is, we can interpret the MPN curve as the (inverse) demand for labor: we replace the variable MPN with W/P, since the two are equal if firms are maximizing profits. In fact this is probably obvious after the fact: the labor demand schedule simply says that the higher is W/P the fewer workers firms will hire. We will refer to W/P as the real wage, since it measures the wage in units of goods. What this means, in essence, is that firms don't care what wages are in dollars, they care about how the wage compares to the price of their output. You may find it simpler to think of W/P as a single variable, even though we've represented it as two.

We've seen, then, that as we increase the real wage firms will demand less labor. But other variables can influence how much labor firms demand, and implicitly we've been holding them constant in Figure 2. [This is the distinction, again, between movements along the curve and shifts of the curve.] What other variables might be relevant? Here are some that come to mind. (i) Productivity A. If we increase A we increase the MPN at every level of N, hence shift the labor demand curve up and to the right (whichever you prefer, they're the same in practice). The assumption here, which is built into how I've expressed the production function, is that higher productivity not only increases the amount of output a given amount of labor produces, it also increases it at the margin: with higher A, an additional worker generates more additional output. Hopefully that will seem sensible to you. (ii) An oil shock is similar: if the price of imported oil rises, then A falls and the labor demand curve shifts down/left. (iii) Taxes and fringe benefits. One of the lessons of this course is that the tax system may have important influences on economic decisions. The demand for labor is an example of this. Suppose for every dollar of wages a firm must pay in addition a fraction f in taxes and fringe benefits. (The social security payroll tax is like this, as are some health benefits.) Then the cost to the firm of an additional unit of labor is (1+f)W, rather than W. The marginal condition for a profit-maximizing firm becomes

P x MPN = W(1+f),

or

MPN/ (1+f) = W/P.

In words, an increase in the payroll tax rate f is a downward (or leftward) shift (really, a twist) of the labor demand schedule.

For those who are comfortable with calculus, we can do all this a little more simply. A competitive firm chooses N to maximize

Profit = P Y - W N = P [A F(K,N)] - W N.

We get the answer by setting the derivative equal to zero:

d Profit / dN = P dYdN - W = P x MPN - W = 0.

As stated, the firm equates the marginal product of labor, MPN, with the real wage, W/P. For example, let

F(K,N) = K^1/3N^2/3.

Then the condition becomes

W/P = MPN = (2/3) A K^1/3N^-1/3.

If we solve this for N, we find that the demand for N declines with W/P:

N = [(2/3) A K^1/3/(W/P)]³ .

It's also clear that a firm will hire more workers at a given wage if it has more capital K or higher productivity A.

As practice, we can add the fringe benefits we just looked at to this relation. You should be able to see that the labor demand schedule becomes

N = {[(2/3) A K^1/3]/[(W(1+f)/P)]}³ .

Suppose we consider an increase in fringe benefits equal to 2% of the wage (eg, change f from 0.00 to 0.02). Then if W/P doesn't change, firms will demand, approximately, 6% less labor (the power 3 multiplies the real wage). Alternatively, labor demand will stay the same if the wage W falls by 2% (so that workers effectively pay for their own benefits) or prices P rise by 2% (firms pass fringe benefits on to consumers in higher prices).

Labor supply. The other side of the labor market is the people who are working. We're going to assume that at higher real wages people want to work more. It could go the other way (at higher wages people may find that they don't need to work as much to get the same income) but we'll assume it doesn't on the old-fashioned economic grounds that demand curves should slope down and supply curves slope up. The evidence, though, is that the labor supply curve is probably pretty steep. We've seen substantial increases in average wages over the last forty years, with little change in the number of hours worked per person. There's been a steady increase, though, in the number of people working, as (esp) more woman have entered the workforce. Once again the relevant price is the real wage W/P, since workers care not how many dollars they get but what those dollars will buy. That's why workers ask for cost-of-living adjustments in inflationary times.

Thus we can express the supply of labor as an upward sloping, and probably pretty steep, line in Figure 2 (draw it in if you like). Like the labor demand curve, the labor supply curve depends on a number of additional factors that we have ignored so far. Changes in any of these factors will result in shifts of the curve. Some that come to mind are: (i) Demographics. The number of people of working age, etc. There has been a marked tendency, for example, for the fraction of women in the labor force to increase over the postwar period in the US, which would show up as a rightward shift of the curve. Immigration and population growth have had qualitatively similar effects. (ii) Taxes again. We presume that people are interested in their after-tax income. If NS graphs the quantity of labor supplied at an after-tax real wage of (1-t)W/P for a tax rate t, then the labor supply curve (if we graph it with the pretax wage on the vertical axis) is related to the pretax wage by

W/P = NS/(1-t).

Then an increase in the marginal tax rate induces an upward shift in the labor supply curve. The closer this curve is to vertical, the less difference this makes.

Equilibrium. That gives us both sides of the labor market, which we combine in Figure 3. If we ignore the extra factors for the moment, we will assume (and remember, this is a theory of the medium to long term) that the real wage moves to equate supply and demand. Suppose the real wage is lower than this. Then firms demand more workers than they can get at that wage, and we would expect them to start bidding up wages. Eventually this process will lead to an equilibrium in which supply and demand for labor are equal. That gives us an equilibrium real wage (W/P)* and an equilibrium level of employment N*. You get this answer mechanically by simply taking the intersection of the two curves. But you lose something, I think, if you don't also tell yourself the story about how you get there.

If we combine the labor market with the production function, we have a complete theory of the quantity of output produced or supplied to the goods market. The labor market tells us how many people are working, in equilibrium. And once we know how many people are working, the production function tells us how much output is produced.

This equilibrium is changed if one of the underlying variables (the "curve shifters") changes. Here are some examples. (i) Increase income tax rate t. This is an upward shift in labor supply (workers require a higher before-tax real wage to compensate for the tax), which raises the after-tax real wage, lowers employment. The effect on employment will be small, though, if the labor supply curve is steep, which it seems to be. The biggest disincentives to work appear to be at the low end of the income distribution, since poor people who decide to work not only pay taxes, they may also be giving up welfare and health insurance. At the margin, the cost of working can be very high. Social security does the same thing to old people. (ii) The destruction of capital in Kuwait. This is a downward shift of both the production function and the labor demand curve. You'd expect it to lower wages and employment, since with less capital workers are less productive. It will also lower output, for two reasons: because fewer people are working and because each worker is less productive (the downward shift of the production function).

Application: The 1974-5 Oil Price Increase

1. Write down your initial reaction.
2. In the context of the theory, which curves are likely to shift?
3. Note the consequences of the shifts envisioned in Step 2. [Translation: let the curves do their work.]
4. Compare these consequences with your initial reaction. If the two differ, is there an important aspect of the situation that the theory leaves out? Or do you now find your initial reaction incomplete?

The situation. In 1974-5 we observed: real energy prices in the US rose 70 percent, productivity A fell 5.7 percent, real wages fell 9 percent, and profits output, and employment all fell. Can we make sense of this?

Using the 4-step procedure, you might guess, first, that this would be "bad" for the US economy, but it would be nice to be more specific than this. In Step 2, I would argue that this is captured by a downward shift in the production function (high oil prices are associated with low productivity, A). The decline in A also shifts the labor demand curve downward. The consequences are: lower output, lower real wage, and lower employment. All of this fits the situation pretty well, I think. [For details, not recommended for students, see Tatom, Carnegie-Rochester Conference Series on Public Policy, Volume 28, or Section 3.3 of Abel and Bernanke's Macroeconomics.)

Saving, Investment, and the Rate of Interest

Let me try to give you some intuition for why the real interest rate clears the "goods" market. We noted a couple weeks ago that purchases of goods can be decomposed into

GNP = Y + i NFA = C + I + G + CA,

or, in a minor variation,

S = S^p + S^g = I + CA.

or

S^p = I + Def + CA.

where

S^p= Y+ i NFA-T-C = private saving,

Def = G-T = - S^g = the government deficit = - government savings

and T is taxes collected by the government net of transfer payments and interest on the public debt. In this sense, the goods markets and capital markets are two sides of the same coin. A decision to consume more goods is also a decision to save less, which takes money out of the overall pool of financial capital. Both identities tell us, at least implicitly, where the goods go: to consumers, firms, government, or abroad. One nice thing about the second identity, though, is that its components have a natural interpretation as sources and uses of funds flowing through capital markets. Accordingly, it's natural to think of an interest rate equilibrating supply and demand in this market.

Our job, then, is to explain how much consumers save and how much firms invest. For the time being, we will ignore the rest of the world by setting CA= 0 and the government policies by setting G-T = 0 . These two simplifications allow us to focus on saving and investment. We'll consider both government deficits and foreign capital markets shortly.

Saving. A typical household has some assets, earns income, and expects to earn income in the future. This gives them some purchasing power that they can exercise now or later. Saving is essentially a decision to consume later, rather than now. What factors do you think would effect how much people save? (i) Current income. High current income can be spent now (consumption C) or later (saving S = Y-T-C). The relevant concept of income is after taxes, Y-T. (ii) Future income. If you know you have a lot of income coming in the near future, you might choose to consume more now and hence save less. (iii) Taxes and transfers, present and future, act much the same way. The consumer cares about the net, Y-T. Thus higher current taxes might lower consumption and saving. Higher expected future taxes might raise saving (you save to prepare for the future tax payments). (iv) Wealth. If you have a lot of assets, you might decide to consume more and save less than someone who doesn't.

(v) The real interest rate. I've saved one of the most important variables for last. If interest rates rise, you might decide to save more, since the return to saving is higher. You might also decide to save less, since a smaller amount of saving can produce the same future pool of wealth at a higher interest rate. This is another one of those things that can, in theory, go either way. The evidence seems to indicate that saving increases with the rate of interest, but whether by a little or a lot remains a matter of debate.

One of the key aspects of this relation is that we're talking about the real interest rate, r. The return on financial assets as reported in, say, the newspaper is measured in dollars. Thus, the January 17, 1991, twelve-month tbill rate was 6.2 percent, meaning 1 dollar put into tbills on 1/17/91 gets you 1.062 dollars a year later (on January 16, 1992, actually). We call this the nominal or money rate of interest, since it tells you how much money you get later for a dollar now. Label this rate of interest i The problem for a saver is that dollars probably won't buy as much next year as they do now, so the real return is less by the rate of inflation over the next year. As we've seen before, if we expect the rate of inflation to be p^e then the real rate is (approximately)

r = i - p^e .

If i = 6.2 percent and pi = 4.1 percent (a rough guess) then the real rate would be 2.1 percent, which doesn't sound nearly as good as 6.2 percent.

(vi) Taxes on interest. There's always a more complicated tax angle, and here's one that might be important. Since we have taxes on interest earnings (I'm thinking broadly of returns on investments, be they interest payments, dividends, or capital gains) the after-tax rate may be quite different from the real rate r. As a rule, we might expect taxes like this to lower saving since they lower the after-tax return. That's one of the reasons there's been discussion in Washington about indexing taxation of interest and capital gains to inflation.

We summarize our discussion of saving by relating saving to the real rate of interest in a diagram; see Figure 4. The other factors, then, lead to shifts in the curve. We'll postpone their discussion until we have specific applications, but you might ask yourself how changes in taxes, wealth, and expected future income would shift this curve.

Investment. The other component of our identity is investment: for the most part, purchases of new plant and equipment by firms. [What I have in mind with the qualifier "for the most part" is that investment in the national income accounts includes the change in inventories. In the short run inventory investment is highly variable, but over longer periods it's small potatoes relative to investment in physical capital, what we call "fixed investment." For that reason, I'm going to ignore inventory investment for now.] Among the factors that influence firms' decisions of how much to invest are: (i) Productivity of future capital. If productivity of capital is high, the return from investment will be high. Thus an innovation that raises future productivity will lead to more investment, other things equal. (ii) The real interest rate. We generally expect that at low rates of interest firms will want to invest more. Suppose firms finance investment through borrowing. Then the investment raises profits if the return is greater than the interest payments (technically, if the project has positive net present value). At high rates of interest fewer projects will be profitable, hence there will be less investment. (iii) Corporate taxes lower the after-tax return from investment projects, and thus reduce the amount of investment at any given rate of interest.

The negative relation between investment and the real interest rate is pictured in Figure 4. Once more, changes in other variables result in shifts of this curve.

Short-Run Equilibrium and Long-Run Dynamics

Short-run equilibrium. Given the tax environment and peoples' expectations of future income, profitability, etc, the real interest rate adjusts (in this theory) to reconcile saving and investment. To make things simple, let us ignore for the moment the foreign sector (set CA = 0) and start from a balanced government budget: G=T. See Figure 5. Suppose, for example that the interest rate is such that saving is greater than investment. That means that there is more capital flowing into financial markets than firms are using. As a result, this drives down the cost of funds, r. Eventually we reach equilibrium with S=I. Thus the real rate of interest is determined by a combination of consumers' willingness to postpone consumption and save, and by firms' desire to invest in new capital goods.

We can easily add government to this story and ask what happens when the government changes its policy. For each of these, you should try to tell yourself a story about how the change in policy leads to a change in the equilibrium of the economy. Eg: (i) Add government, G-T. Starting from G-T=0, what is the effect now of an increase in G? The interest rate rises and investment falls. We call the latter crowding out: the government has, to some extent, squeezed private investors out of the capital market. How much depends on the slope of the saving schedule. Story: government spends more money, finances it with debt (since T doesn't change, this has to happen). Increased government borrowing (demand for funds) results in higher rates of return. At higher rates of return, there is more private saving. But this increase is less than the increase in government borrowing (negative public savings), so total national savings are lower and private investment is lower in the new equilibrium (the S curve has shifted leftward to the curve S'). How much lower depends on the slope of S (which tells us how much additional private savings results from the higher rates). Although it's not explicit in the diagram, we can also say what happens to consumption: since Y and T do not change and private savings rise, consumption C must fall. [Recall: Y-T = C + S.]

(ii) I hope to avoid this, but just in case here's what's involved if we examine changes in tax revenue T. The resulting increase in public savings S^g shifts the S curve to the right by dT. But what about private savings S^p ? With smaller Y-T what happens to consumption? If consumption falls then private savings falls by less than the increase in taxes and the S curve shifts to the right on net. The result is that interest rates fall (there is less competition from the government for funds in financial markets) and investment rises. I know this is complicated, but this is the kind of thing that's involved in the current debate over the budget deficit.

Long-run dynamics. Such changes in government policy (as well as other changes in the economic environment) change the rate of investment I in new capital goods. Over longer time periods this will lead to changes in the amount of capital, which filters through the entire economy. By way of example, consider the increase in G outlined above. We've seen that immediate effect is to drive up the interest rate and lower the rate of investment. Over several years, this will result in less physical capital (K) for firms. That is, relative to the economy with lower G, the production function is lower (shift it down, see Figure 6). The decline in K also shifts downward the demand for labor. The reason, as we saw above, is that with less capital to aid them, workers are less productive at the margin. Thus the marginal product of labor, which is also the demand for labor, shifts down. The result in labor markets is lower wages and slightly less employment (remember, the labor supply schedule is steep). That means output is lower for two reasons: there are fewer people working and (most important) each person is less productive.

In short, there are important long-term effects on the economy of changes in government policy. Allocating resources to government means less for everything else, including fixed capital. We're ignoring, of course, government investments in infrastructure, R&D, and so on, which may raise output by increasing A. To the extent that such things are relevant, we need to combine the increase in G with simultaneous increases in A.

Application: Are Low Real Interest Rates Good for the Economy ?

A misleading view of real interest rates is that high real interest rates are bad because they choke off investment while low real interest rate are good as they stimulate investment. This view is fallacious since economic theory suggests that real interest rates will be high in boom times while they will be low during recessions. To see why high real interest rate may be a sign of a booming economy, note that the economy is a good place to invest during a boom. Booms can be seen as periods where the profitability of capital is high and firms want to invest a lot. The theory imbedded in our S/I diagram is that booms are associated with high demand for funds by firms represented by a rightward shift of the I schedule. Booms are also associate with an increase in private savings (as income is higher in a boom both savings and consumption increase) represented by a rightward shift of the S curve. Since investment demand is more cyclical than income and savings (it increases more than income and savings in booms), a boom period will be characterized by a rightward shift of the I curve that is larger than the rightward shift of the S curve. This is represented graphically in Figure 7. That leads, in the logic of the theory, to higher real interest rates, higher saving, higher investment in booms, all of which we see in the data for a typical boom.

Conversely, in a recession, there is low demand for funds by firms represented by a leftward shift of the I schedule. In a recession we also have falling private savings (as income is lower in a recession savings decrease) represented by a leftward shift of the S curve. Since investment demand is more cyclical than income and savings (it decreases more than income during a recession), a recession period will be characterized by a leftward shift of the I curve that is larger than the leftward shift of the S curve. This is shown graphically in Figure 8. Therefore, in a recession we will observe lower real interest rates lower savings and lower investment , all of which we see in the data for a typical recession.

For a more detailed discussion of the points above read the article in The Economist "How Low Low Can They Go?" (included in the Reading package).

Application: Voodoo Economics

Taxes enter many decisions, but the two most important are probably that they discourage work, since they lower the after-tax return from work, and they discourage saving and investment, since they lower after-tax returns. (A third, which we will not explore here, is that taxes distort investment decisions by taxing different types of capital unequally. Housing, for example, gets a free ride.) We know that the countries that invest the most (measured as the ratio I/Y) also grow the fastest, on average, so maybe this is important (or maybe the causality goes the other way, with the US investing less because it has fewer good opportunities). Whatever the case, let's examine the effect of taxes on wage and capital income.

A lower tax rate on wage income can be viewed, as we have seen, as a downward shift of the labor supply curve: any quantity of labor supply is associated with a lower before-tax real wage since taxes are lower. We would predict this to lead to a fall in the pretax real wage (what about after-tax?) and a rise in employment and output.

Now turn to saving. We would expect lower taxes on interest and capital gains, as well as tax-sheltered saving plans like IRAs and 401(k) plans, to make saving more attractive and lead to a rightward shift in the saving schedule [graph this]. In equilibrium, this will lower real rates of interest as more saving flows into capital markets, and raise investment. Over time this investment leads to higher capital, more productive labor, and higher output and wages. (This is the long-run dynamics we just talked about.)

That was the argument. While most economists would agree with the theoretical idea that lower taxes increase labor supply and savings, the crucial empirical question is whether the effects of cuts in tax rates on labor supply and savings are mall or larger. Most empirical evidence from a very large set of studies suggests that that the effect on labor supply is probably small, except on relatively poor workers whose marginal tax rate can be quite high (when they work, they may lose welfare and medical benefits, so the "opportunity cost" of working can be high). This may be an important aspect of social policy, but it probably does not have a large effect in the aggregate. In the graph, this would show up as a fairly steep labor supply curve, so that a shift up has little effect on employment.

The effect on saving, though, is thought by some to be substantial but there is wide disagreement on this issue as well. There is some question how responsive saving is to tax incentives, but a number of economists, including Martin Feldstein of Harvard, think the effect is important. Some argue that the saving rate S/Y in the US is smaller than in most other major economies, perhaps because US tax law is less friendly to saving than other countries'. One of the important policy questions is whether we should amend the tax system to make saving more attractive.

So why "voodoo" economics? There is some question about the magnitude of these effects, and the theory was way oversold at the time. Many "supply siders" argued that the incentive effects were so large that a reduction in tax rates would actually raise tax revenue, since the tax base would grow so much. There's no sign that this happened, and indeed most economists were pretty skeptical of this prediction at the time. Quite to the contrary, the budget deficits exploded in the 1980s after tax rates were cut by Reagan in 1981. The response of private savings and labor supply to the Reagan tax cuts was minimal so that, on net, revenues did not increase and the budget deficit became very large.

For a more detailed analysis of voodoo economics, see the home page on the controversy on Supply Side economics.

International Borrowing and Lending

CA = S - I

So how, is the current account determined ? Suppose that the country we are considering is small and open to international capital markets. This means that the country can borrow or lend in international capital markets at the exogenously given world rate of interest (say r). Then, suppose that at the given world interest rate, domestic savings are below domestic investment (this is represented in figure 9). Unlike the case of a closed economy where S= I, in an open economy where the country can borrow and/or lend, S can differ from I since S = I + CA. So, if domestic savings are below domestic investment, the country will run a current account deficit equal to S-I.

Application: Is a Trade Deficit Bad?

We won't provide a complete answer at this point, but you'll note that our approach so far has been to view the trade balance from the perspective of capital markets. What's missing is any mention of how our goods compete, and at what price and exchange rate, in markets for goods. To the extent you think prices and exchange rates matter, and I think they do somewhat, this theory is deficient. My judgment is that this is an extra feature to be put in, but that the classical theory works moderately well without it. Krugman (Age of Diminished Expectations, p 46) says in this regard: "Think of the US trade balance as an automobile. The exchange rate is not that car's engine---it is more like the drive shaft, with desired capital flows [KA] providing the motive power. In other words, changes in the exchange rate play a crucial role in translating changes in desired capital flows into changes in the trade balance, but the root cause lies elsewhere." That's not an argument, really, but it's clear he agrees with the gist of what I've said. I'll return to this later in the course.

There are at least some features of the data that make a lot of sense, I think, from this "capital markets" perspective. One of them is that countries tend to run trade deficits during booms, surpluses during recessions. Why is that? The idea is simply that the economy is a good place to invest during a boom, by foreigners as well as domestic residents. The theory imbedded in our S/I diagram is that booms are associated with high demand for funds by firms represented by a rightward shift of the I schedule and an increase in private savings (as income is higher in a boom savings increase) represented by a rightward shift of the S curve. Since investment demand is more cyclical than income, consumption and savings (it increases more than income in booms), a boom period will be characterized by a rightward shift of the I curve that is larger than the rightward shift of the S curve. This is represented graphically in Figure 10. That leads, in the logic of the theory, higher saving, higher investment and a current account deficit (higher foreign borrowing) in booms, all of which we see in the data for a typical boom.

Conversely, in a recession, there is low demand for funds by firms represented by a leftward shift of the I schedule. In a recession we also have falling private savings (as income is lower in a recession savings decrease) represented by a leftward shift of the S curve. Since investment demand is more cyclical than income, consumption and savings (it decreases more than income during a recession), a recession period will be characterized by a leftward shift of the I curve that is larger than the leftward shift of the S curve. This is represented graphically in Figure 11. Therefore, in a recession we will observe lower savings, lower investment and a current account surplus, all of which we see in the data for a typical recession.

I think we can understand this without mention of real exchange rates. I find this similar to what happens with firms: the firms that are borrowing the most are those that are expanding the fastest, and thus have productive uses for the borrowed capital (and can persuade investors of this).

A clear example of this is Mexico during the 1980s. If you recall the history, Mexico was booming in 1980, busted in 1982, then rebounded in the late 1980s. What happened to trade? In 1980-81, there was a large deficit, as investors poured money into Mexico. During the bust of 1983-87 there was a small surplus, as Mexico repaid some of its loans. Then as the economy has improved, triggered partly by anticipation of NAFTA, capital returned, reflected in a current account deficit on the order of 10 percent of GDP by 1994.

In short, trade deficits typically indicate that the country is doing well and is a good place to invest. In that sense a deficit is not a bad thing.

More, in general, running a current account deficit may be a good or a bad thing depending on what is the cause of the deficit. The discussion in Chapter 1 suggested that there is not anything inherently good or bad about a current account deficit. Like and individual or a firm that borrows funds, a country may be borrowing funds from the rest of the world for good or bad reasons. So a current account deficit and the ensuing accumulation of foreign debt may be good, sustainable and lead to higher long-run growth or may be eventually unsustainable and lead to a currency and debt crisis depending on what drives the current account deficit.

For a more detailed discussion of the determinants of the current account read the articles in The Economist "In Defence of Deficits" and "Global Capital Flows: Too Little, Not Too Much" (included in the Reading package) and the discussion about current account deficits in Chapter 1.

Application: Roots of the 1980s Trade Deficit

A quick look at Table 1 tells us that this explanation is partially correct: in the 1980s we had large budget deficits and large current account deficits even if the correlation between budget deficits and current account deficits is not perfect. Moreover, in the 1990s the improvement in the U.S. budget deficit has not been associated with an improvement of the current account of the same magnitude. We'll review both of these in greater depth later in the course. Note also that if the trade deficit is a reflection of the government deficit, we need a more complex theory to understand such links. We'll see some of the same issues in the next application.

Application: Real Interest Rates in the 90s

Our diagram gives us a useful framework for thinking about this question. Roughly speaking, we can produce a high real rate r either by shifting I to the right, or S to the left. Do any of these possibilities make sense when you look at them carefully?

Perhaps the most obvious suspect is the government. If we increase G-T, either through higher G or lower T, this reduce public savings and has the right effect on r. But what are the other implications? If we follow through the theory, it also implies a trade deficit (as we've seen), lower I, and lower C. We can compare this prediction with what happened; see Table 1. The trade deficit looks like what we got, at least temporarily, so that looks fine for this explanation until the late 80s, not so good recently. The other two variables go the opposite way as the theory. There's not much change in I, and C actually rose. So the government deficit can't be the whole story.

Another suspect is private savings: for unknown reasons, people decided to consume more and save less, a leftward shift of the S curve. This raises r and C, as we saw. It also leads to a trade deficit (roughly speaking, consumers are borrowing for consumption, and some of the borrowing comes from abroad). This is at least part of the story, and fits better with the timing: we've seen the saving rate recover in the 1990s and the trade deficit more or less dry up with it.

Where does that leave interest rates for the 1990s? In the US the reduction in budget deficits since 1992 has led to an increase in national savings (to levels that are higher than during the 1980s, but lower than most other countries) but the current account deficit is still with us even if it is improved relative to the 1980s.. On the international scene, Germany had a high demand for funds to develop the East in the early 1990s, and the emerging markets and transition economies continue to soak up foreign capital as their current account deficits require the excess savings (over investment) of the industrial world to be financed. However, one of the main net savers in the industrial world, Japan, witnessed a reduction of its current account surplus (as Japanese budget deficits have increased during the 1992-95 recession). The Japanese surplus used to finance the current account deficits of the US and other developing countries; therefore, its reduction could lead to higher world interest rates since the Japanese budget deficits imply a fall in world savings.

Application: Does Government Spending Raise Output?

I'll go through this with our 4-step procedure:

1. Guess (be my guest).
2. This shows up in the theory as a change in G, which shifts the S curve to the right.
3. The result is a lower interest rate, lower saving, and higher investment. Higher investment leads, eventually, to a higher stock of capital and thus higher output and real wages (this is the usual dynamic effect operating through the effect of K on the production function and labor demand).

In short, looks like there's no problem, as far as the theory is concerned.

4. One catch (we can call this step 4) is that there is likely to be a short term problem in moving large numbers of workers from military to other kinds of production. These transition problems are not something we thought about when we formulated the theory but may nevertheless be important. Another catch is that lower spending on infrastructure might lower output, but I don't buy this for military expenditures.

In summary, lower government spending G raises output Y (and, by analogy, high G lowers Y).

Summary

1. Theory is simplification of a complex reality, a filing system for organizing your thoughts. In this case the files are curves, or graphs, that tell us how different aspects of the macroeconomy fit together.
2. You should make sure you understand the distinction between movements along a curve and shifts of a curve.
3. Our theoretical economy consists of (i) a production function, (ii) a labor market, and (iii) a goods/capital market. Given taxes, productivity, government spending and so on, the theoretical model determines output, employment, the real wage, and the real interest rate. Within this structure, we can trace out the effects of changes in government policies and other variables on the economy.
4. In equations, the theory is: Y = A F(K,N), ND(W/P) = NS(W/P), S(r,Y-T)- (G-T)= I(r). Put "+/-" above each function to remind yourself of the function's slope.

Further Web Links and Readings

You can find Web readings and data on the topics covered in this Chapter in the home page on Macro Analysis and the page on Macro Data and Information.

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Figure 1. The Production Function

Figure 2. The Marginal Product of Labor

Figure 3. Labor Market Equilibrium

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Figure 4. Savings and Investment Schedules

Figure 5. Short-Run Equilibrium (Effect of An Increase in G)

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Figure 6. Long-Run Dynamics

Figure 7. High Real Interest Rates During an Economic Boom

Figure 8. Low Real Interest Rates during of a Recession

Figure 9. Determination of the Current Account

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Figure 10. The Current Account Deficit in a Boom

Figure 11. The Current Account Surplus in a Recession

Copyright: Nouriel Roubini and David Backus, Stern School of Business, New York University, 1998.