The Macroeconomy—Private Choices, Public Actions, and Aggregate Outcomes

Michael McElroy (©2005)

CHAPTER TWELVE CONSUMPTION, SAVING, & INVESTMENT 12.1 Introduction

ith the economic news so strongly focused on government policies -- how spending, taxes, deficits, and the money supply are causing or curing various economic problems -- it is

easy to forget that what provides the real power to the U.S. economy is the multitude of "this or that?" and "now or later?" choices by individuals and businesses. While the media focus our attention on public sector actions, Figure 12.1 shows that four-fifths of total output comes from private consumption spending by households and private investment spending by firms.1 Private investment, though only about 15% of total spending, is particularly volatile and is a key factor in the cyclical swings of the economy. Its jagged time series profile, shown in Figure 12.2, contrasts sharply with the much smoother stream of consumption.

Figure 12.1

1

How do we find the percentage of total spending (y=c+i+x+g) accounted for by each category when one, net exports, is negative? Negative net exports tells us that the totals for consumption, investment, and government spending include some expenditures on foreign goods in addition to the spending on U.S. output. To adjust for this, we've made the simple assumption that each category of domestic spending (consumption, investment, and government) is overstated by the same amount; in other words, that our negative net exports occur uniformly by type of spending. This approximation is sufficient for present purposes, which is to get a general picture of the relative importance that consumption and investment play in U.S. economic activity.

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Part IV Long-Run Dynamics: Saving, Investment, and Growth 2

We've seen that an understanding of changes in private consumption and investment spending is central to an explanation of the trends and cycles in overall economic activity. Our model macroeconomy (AD/AS and its "expectations-augmented" variation, AD/ASe) is built around theories of these components. Consumption -- represented by the "consumption function" c=c0+c1(y-t) -- was assumed to vary directly with after-tax income (y-t). The strength of this relationship is represented by the size of the coefficient c1. The multitude of other factors that can and do affect total consumption spending -- from gradual demographic change to stock market gyrations or altered expectations of future events or policies -- are lumped together in the "autonomous consumption" term c0.

Figure 12.2

Investment spending—captured in the "investment function" i=i0-i2r—was assumed to

move inversely to changes in the real rate of interest (r). The magnitude of this relationship is given by the size of the estimated coefficient i2. Anything else that causes firms to alter their investment expenditures—from changes in product lines due to changing consumer tastes to technologically-induced changes in production processes or expected changes in the tax system—goes into the "autonomous investment" term (i0). Autonomous investment is presumed to be independent of other variables within this model, at least for the relatively short time period for which the "no growth" AD/AS analysis is designed.

Consumption and investment spending, then, have played the same crucial roles in our model as we think they play in the "real world" that the model seeks to mimic. Consumption, in particular, forms a symbiotic relationship with income through the two-way causality described by y=c+i+x+g and c=c0+c1(y-t). A change in one is transmitted to the other, starting a continuing but diminishing sequence of events (∆y⇔∆c). This interaction—the heart of the demand-side multiplier—plays a key part in the process by which the impact of a change in one variable spreads throughout the macroeconomy. Investment plays a less obvious but still important role, since both the volatility of its autonomous component (±∆i0) and its sensitivity to changes in the real interest rate lead to changes in total income (y=c+i+x+g), which are then

Chapter 12 Consumption, Saving, and Investment 3 magnified through the multiplier process. All this is built into the workings of our model, allowing it to capture quite complicated economy-wide interactions and repercussions from many different events and policies.2

But so far we have viewed consumption and investment as largely independent entities, done by different decision-makers responding to different influences. This is a reasonable and useful simplification for understanding short run issues. But it leaves out a deeper relationship between consumption and investment—a connection through saving and capital markets—that lies at the heart of the process of economic growth. To see this, let's start with a simple closed economy (x=0) with no government sector (g=t=0) and assume it is always at full employment. In this setting all income goes either to consumption or saving (y*=c+s, since t=0) and all output is divided between private consumption and private investment (y*=c+i, since x and g are both zero). At full employment, investment will always be limited by saving since c+i=y*=c+s, hence i=s. Though obviously much simplified, this structure helps us see the vital consumption-saving-investment linkage to economic growth, while avoiding details that complicate but don't alter the story.

Within this setting, each of us must decide how much of our current income to consume (c) and how much to leave for future consumption via saving (s). What we consume now cannot be used to feed the investment (s=i), capital formation (i=∆k), economic growth (∆k⇒∆PPF & ∆AS*) process. These connections are illustrated in Figure 12.3, which shows the long run implications of a consumption-investment choice at point Q. This sends enough resources through saving (sQ=y*

0-cQ) to support current net investment of iQ which, in turn, increases the total capital stock and shifts out both the production possibilities and aggregate supply curves.

2

There is much, much more that can be said about the specific determinants of consumption and investment spending in the context of stabilization policy and the AD/ASe model -- issues of definition, measurement, and forecasting. For example, the high level of aggregation that we have used obscures features of different kinds of consumption (consumer durable goods, non-durable goods, and services) and investment (plant and equipment, inventories, residential housing, research and development, education) that can be important for particular questions. Such detail is not needed for the general understanding of macroeconomic interactions that is the goal of this book. For a more detailed look at consumption and investment spending as determinants of economic fluctuations, see Robert J. Gordon, Macroeconomics, Fifth Edition (HarperCollins, 1990), Chapter 18 "Instability in the Private Economy: Consumption Behavior" and Chapter 19 "Instability in the Private Economy: Investment." A more complete and advanced presentation of the intertemporal approach of this chapter is available in Jeffrey D. Sachs and Felipe Larrain, Macroeconomics in the Global Economy (Englewood Cliffs, N.J.: Prentice Hall, 1993).

Part IV Long-Run Dynamics: Saving, Investment, and Growth 4

Figure 12.3 Capital Connections: Consumption/Saving/Investment/Growth

From a given initial real income (y0* = c0 + i0) the choice between consumption and saving y0* = c0 + s0), reflected at (1), determines how many resources are available for investment at (2). Because iQ > 0 means an increase in the capital stock (+∆k), this is also an outward shift in PPF (3) and in AS* (4). Movements up this PPF from Q would quicken the rate of growth at the cost of less current consumption, i.e., -∆c → +∆i → +%∆k → +%∆PPF & +%∆AS*.

Incorporating this connection between our consumption-saving choice and the investment-capital formation outcome finally brings economic growth inside our analysis. Figure 12.3 shows that we can have faster growth but only at the cost of cutting current consumption and moving up the PPF. It requires a cut in current consumption (and increased saving) which moves more resources into current investment. This, in turn, accelerates the growth of the capital stock and causes PPF and AS* to shift out at faster rates. This is a simple but essential point, first made back in the Chapter One -- economic growth is determined, in part, by how we choose between consumption and saving. It involves the inescapable tension between "consume now" or "consume more later" that, whether we are conscious of it or not, underlies each and every economic choice we make. These three chapters (12-14) will develop an analytical structure that incorporates the "now or later?" choice into the connection between consumption and saving—through capital markets—to investment and economic growth. 12.2 Choosing the ‘Best’ Consumption Path

e have seen that "scarcity", so obvious yet so often surprising in the breadth of its reach, means that decisions made today have consequences for our well-being one year and ten

years from now. By the same reasoning, the options we face today reflect choices that we (or others) made one year or ten years ago. In other words, our basic condition is one in which every choice exists in a "web of time" that hampers our desires to change the economic present or future. We need to understand these intertemporal linkages before we can know whether we're making promises that we can't or won't keep—privately through our college loans or home mortgages, publicly through continued government deficits or off-budget commitments to pay for future retirement and medical care programs.

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Chapter 12 Consumption, Saving, and Investment 5

This connection between our current decisions and our future options was illustrated in Figure 12.3. It showed, rather clumsily, that the level of current consumption influences the rate at which AS* and PPF shift over time. The two key determinants of the size of these shifts are:

(1) how much of our current income we don't consume now (s=y-c), allowing us to put additional resources into capital formation through the saving-investment channel (s=i=∆k), and

(2) the real rate of return on additional capital (r=∆y*/∆k, hence ∆y*=r∆k) that tells us how much additional output the new capital produces.

This way of posing the "now or later" issue comes from the ingenious "two period diagram" introduced and developed decades before Keynes' General Theory by American economist Irving Fisher.3 While Fisher's framework is a marvelous simplification, it requires some patience to get accustomed to the notation now that each variable has a "time period" attached to it.

3

Irving Fisher, The Nature of Capital and Income (New York: Macmillan, 1906); The Rate of Interest, (New York: Macmillan, 1907), and The Theory of Interest (New York: Macmillan, 1930).

Part IV Long-Run Dynamics: Saving, Investment, and Growth 6

Using a single graph and temporarily continuing our earlier assumptions (full employment and no government or foreign sectors), we can portray an individual's intertemporal consumption options in a revealing way. Suppose we know that our income in two time periods—0 and 1—will be some specific values given by y0

E and y1E. This particular income

path over periods 0 and 1 is usually called the initial endowment (E). Suppose also that there is a given real interest rate (the "rate of return" on capital) at which we can either borrow or lend. Given our initial endowment and the real interest rate and recognizing that consuming more now means less later, how much should we consume now? To get a handle on this intertemporal optimization problem, let's examine the constraints on what we can and cannot do. This requires us to identify which consumption paths are attainable.

Figure 12.4 The Wealth Constraint in the Two-Period Model

For a consumer with a given endowment (income path) of (y0E,y1

E) facing a given rate of interest (r), any point on (or inside) the wealth constraint (line FEG) is an attainable consumption path. We begin with the arithmetic of "compounding" and "discounting". If we have $100 now

and the interest rate is 10%, this can be transformed into $110 in the next period if we save/invest it all. We can express this intertemporal relationship by saying that $100 now is equivalent to $100+r⋅$100 or $100⋅(1+r) next year.4 So if we could go without consuming any of our current income (y0

E), we could transform it into the amount y0E⋅(1+r) by saving for one year.

That means that if we starve ourselves now, next year's total consumption will be y0E⋅(1+r) plus

next year's income y1E.

This accumulated value of both periods' incomes (plus interest on the first period) is a

4

This return grows exponentially over time (compounds) as we get interest on previous interest as well as on the principal. Its value in period n is given by $100(1+r)n.

Chapter 12 Consumption, Saving, and Investment 7 measure of total "wealth" as of next period -- W1=y0

E⋅(1+r)+y1E. This value, plotted along the

vertical axis of Figure 12.4, represents the maximum value we could consume next period out of our given endowment (y0

E, y1E) if we took the miserly "always tomorrow, never today" approach

and consumed nothing this period. Thus point F represents a consumption path in which current consumption is zero while consumption next period is the amount W1.

Another possible consumption path is simply to consume at point E, the initial endowment of income. This choice forgoes any manipulation of the consumption stream through saving or dissaving (borrowing). It's a sort of "easy come, easy go" strategy in which we spend all our income on consumption each period. So a consumption path at point E is identical to the income path, hence c0=y0

E and c1=y1E.

The final step in mapping available consumption paths (for our given income endowment

and given interest rate) is to "discount" future income back to the present. Suppose we entirely ignore the future and decide to maximize our consumption now. In this "life's short, grab for all the gusto" approach we consume all our current income (y0

E) plus all we can borrow on next period's income as well. What is the present value of y1

E? We saw above that $100 now is worth $100⋅(1+r) next period so, turning it around, the present value of next year's $100⋅(1+r) must be $100 or $100⋅(1+r)/(1+r). Just as we compound (multiply by (1+r)) to get from this period to next, we discount (divide by (1+r)) to get back to the present.5 So the present value of next year's y1

E is y1E/(1+r) and the maximum we can consume now (leaving nothing for next

period) is given by y0E+y1

E/(1+r0)=W0. Thus W0 is simply our current wealth or, more precisely, the present value of our

endowed income path at interest rate r. This value, plotted on the horizontal axis at point G in Figure 12.4, represents another possible consumption path. The line FEG connecting these three points shows all the attainable consumption time paths ("now/later" combinations) for someone with the given income endowment (y0

E, y1E) facing a constant real interest rate of r.

It's called the intertemporal budget constraint or, more simply, the wealth constraint.

The slope of the wealth constraint, ∆c1/∆c0=-W1/W0=-(1+r), is of particular importance because it is an intertemporal exchange rate, representing the terms on which we can trade "consumption now" for "consumption later" and vice versa. It's a "minus" because more later means less now. It's greater than one since giving up $1 in consumption now returns principal plus interest later. For example, if the interest rate is 10% the slope (-1.10) tells us that every $1 that we don't consume now will be worth $1.10 next period. Equivalently, every $1 that we consume this year lowers next year's potential consumption by $1.10. Hence the haunting implication that every dollar we've ever spent has reduced our attainable consumption this year by that dollar plus accumulated interest. This is the above-noted "web of time" with which scarcity binds our every choice.

The wealth constraint defines the boundary between attainable and unattainable consumption paths. But which point on (or inside) this constraint should we pick? Which balance between "now" and "later" should we strike?6 Should we consume all our income in

5

Discounting $100 n periods from now back to the present gives a present discounted value of $100/(1+r0)

n.

6Presuming that more consumption is preferred to less in any period, any

Part IV Long-Run Dynamics: Saving, Investment, and Growth 8 each period, staying at the endowment E? Or should we save and move toward point F or borrow and move toward G? In Chapter One's brief discussion of the "rate of time preference" we saw that any such choice is inevitably a matter of preference that will differ across individuals. Suppose that person A, with initial endowment E, selects the consumption pattern (c0

A*,c1A*) at point A* in Figure 12.5. Her optimal consumption path is for consumption now to

exceed her current income, requiring her to borrow against future income. In other words, her preference is to consume beyond her current income even though it will cost her that amount plus interest --(1+r)⋅(c0

A*-y0E) -- in reduced "consumption later".7

Figure 12.5

With endowment E, individual A chooses consumption path A* with coA*, c1

A*. She

choice inside the budget line will be less desirable than another feasible combination on the line. This allows us to limit our attention to points along the wealth constraint, W1W0 in Figure 12.4.

7If you've had intermediate microeconomic theory, you're familiar with the

notion of an indifference map as a way to describe our subjective preferences between "this" or "that". We could use this device in our two-period model, as Irving Fisher originally did, to describe individual preferences between "now" and "later". Superimposing the family of indifference curves on the budget line, we could then locate the "intertemporal optimum" (i.e., the best consumption path) by finding the (single) point at which an indifference curve is tangent to the given intertemporal budget constraint. This joining of preferences (the indifference map) and possibilities (the budget constraint) portrays the solution to the "choice under scarcity" problem in a way that most economists find elegant and satisfying. The presentation here forsakes elegance and simply proclaims an optimum point (implicitly, the point of tangency) without actually drawing in the indifference map. The justification is an economic one -- the time and effort to learn this technique adds little to our understanding of the basics of macroeconomic issues.

Chapter 12 Consumption, Saving, and Investment 9

chooses to borrow now (c0A* - y0*e) and repay later (y1

E – c1A*) = c0

A* - y0E)(1+r).

Another person with exactly the same wealth constraint (initial endowment and interest

rate) might make a very different choice. For example, suppose individual Z selects the consumption path (c0

Z*,c1Z*), shown at point Z* in Figure 12.6. His choice, compared to A's,

reveals a stronger preference for future over present consumption. Z is said to have a lower "rate of time preference" than A, since he's more patient with respect to when he consumes. Though both have the same income path (and wealth constraint), Z's intertemporal preferences have induced him to "save now, consume (more) later", while A chooses to "borrow now, repay (more) later".

Figure 12.6

A VERY patient consumer, with a low rate of time preference, might choose a consumption path like Z*. he would “save now” and “enjoy later,” moving consumption from present to future at the rate (1+r). Relative to consumer A’s choice (A*), he puts a higher value on his future consumption.

Neither choice can be said to be "better" than the other; they each reflect a balance

between now and later that suits two different persons. The role of the capital market (next chapter's subject) is to link Z's saving with A's borrowing, making both better off by allowing them to move from their initial endowments (both at E, in our example) to their individually preferred consumption paths at A* and Z*, trading consumption across time at the rate -(1+r). 12.3 How Far Ahead Do We Plan?

his two-period framework offers a relatively easy way to portray the impact of current decisions on future well-being. We saw in Figure 12.5 that A's decision to borrow and T

Part IV Long-Run Dynamics: Saving, Investment, and Growth 10 consume beyond her first period's income, affected her consumption in the next period. While the use of just two periods is very artificial, it is a simple way to portray a crucial point -- our current actions have future consequences. You might think this so obvious that it hardly needs saying, much less the addition of another economic model. But it's one of those simple/subtle points that can get lost in the discussion of difficult issues such as the workings of the macroeconomy. For example, the belief that government borrowing (b>0) necessarily means a falling standard of living in the future is a failure to examine how the borrowed funds were begin used. Another example is that our assumption of zero growth in previous chapters means that even the elaborate 10-equation AD/ASe analysis ignored the fact that more consumption now means less later.

Figure 12.7

(a) Myopic Response (b) Forward-looking Response E → E’ and A* → A’ E → E’ but ∆A* = 0

Now that we have a workable framework to connect present with future, the obvious

question is the degree to which consumers actually consider these future outcomes in making their consumption/saving choices.8 How far ahead do we plan? Before discussing the empirical evidence on the length of our economic horizon, let's sharpen our view of the issue by returning to the two-period model. While this intertemporal framework can be used to examine many different events and policies, for our purposes the analysis can be restricted to a very specific

8

We ventured into this territory in our earlier discussion of rational expectations in the context of the AD/ASe model. But we only looked at part of the issue -- how mis-information in the "short run" could create an upward-sloping aggregate supply curve. The demand side role of expectations was ignored. In addition, we lacked a multiperiod framework (like the two-period model) that could reveal the connection between current decisions and future outcomes. Instead we substituted categories (self-financing, consumption-smoothing, consumption-draining) that could describe but not analyze intertemporal relationships.

Chapter 12 Consumption, Saving, and Investment 11 situation.9 Suppose that A's initial endowment happens to change in a particular way -- her current income drops while her future income rises and the relative sizes of these changes just happen to move her to a new point on the same wealth constraint as before.

This hypothetical and coincidental change is illustrated in the movement from E to E' in the two graphs in Figure 12.7. Though she's lost income now (-∆y0

E), she's gained enough income later (+∆y1

E) to offset that loss plus interest and remain on the same intertemporal budget line.10 The question is whether this change in the timing of her income, leaving her "lifetime" wealth unchanged, will lead her to change the timing of her consumption. In other words, will the movement from E to E' cause her to move her preferred consumption path away from her earlier choice of A*? The answer to this question reveals the extent to which her consumption/saving choices are forward-looking.

Suppose her response is to adjust her consumption path to A' as shown in Figure 12.7a. By cutting consumption in reaction to the decline in her current income, she is doing just what our basic consumption function described. But we now see this as myopic behavior because it ignores the fact that the drop in this period's income is exactly offset by next period's increase, leaving her wealth (present value) unchanged. The move from A* to A' in response to a change in the timing but not the present value of her income path, reveals a decision-maker so trapped within the confines of the current period that she ignores anything that lies beyond it. Such extreme myopia is probably unusual. In varying degrees we look beyond the arbitrary boundaries defined by calendars (grounded in the motions of the solar system rather than the economy) and consider our longer term prospects when making current choices.

What would A's response be if she was forward-looking and understood that this

specific change in the timing of her income didn't change its present value (as defined by the intertemporal budget line W1W0)? Since she chose A* as her preferred consumption path before, there's no reason for her to change now. Put another way, when her endowment was E she could have chosen the path A' but didn't. She decided that A* was the most desirable consumption path along her budget line. Since this budget line hasn't changed, she can still reach A* from her new income path (at E') by increasing her current borrowing. Hence the forward-looking response to this altered income stream is to leave her consumption stream unchanged, as shown in Figure 12.7b.

Which of these two options best describes the consumption behavior of the actual people living in the real economy, not the hypothetical decision-makers of abstract models? Will a change in the income path that doesn't alter our total wealth (like E to E' in Figure 12.7) cause people to change the timing of their consumption? No doubt we could find some consumers whose behavior fits the nearsighted mold and others who behave with all the 9

For example, we could look at how an increase (or decrease) in the initial endowment (income path) shifts the wealth constraint out (or in), leading to a new optimal consumption path. Or, with the income path unchanged, we could see how a change in the interest rate alters the "intertemporal price ratio", thereby rotating the wealth constraint around point E and having differential effects on savers and borrowers.

10For this change in the timing of income to leave the wealth constraint

unchanged, her future income must have increased by r% more than her current income fell. Algebraically, ∆y1=-∆y0(1+r) so that ∆y1/∆y0= -(1+r) which defines a movement along the curve, leaving its intercepts (W1W0) unchanged.

Part IV Long-Run Dynamics: Saving, Investment, and Growth 12 foresight of the forward-looking model. But remember that macroeconomics works with bulky aggregates, combining all individual responses -- the thoughtful and the thoughtless alike -- into a single average. So the issue is one of determining an average time horizon that describes the degree to which consumers are forward-looking.

Aggregate consumption behavior has been among the most thoroughly tested of all macroeconomic relationships over the past fifty years. Initial studies of the static Keynesian consumption function -- c=c0+c1(y-t), where we're back to the notation in which c0 and c1 are the parameters defining the relationship between current income and consumption -- confirmed that current after-tax income was an important explanatory variable. But they also uncovered a steady growth in autonomous consumption (+∆c0) that was having a major influence on total consumption spending over time. Because this equation lumps everything but after-tax income into the c0 term, it gives us no clues as to just what is causing it to grow systematically over time. Beginning in the 1950s, research turned to finding an expanded theory that could account for this "upward drift" in the standard consumption function. Which of the multitude of excluded determinants of consumption was responsible for this continuing change?

Many hypotheses were proposed and tested and it soon became clear that a key element missing from earlier studies was a measure of the income path. This was discovered independently in classic studies by Franco Modigliani and Milton Friedman, among others.11 The explanations of these two Nobel Laureates-to-be -- Modigliani's "Life Cycle Hypothesis" and Friedman's "Permanent Income Hypothesis" -- were both grounded in an intertemporal framework. Both replaced current after-tax income as the independent variable with a measure that incorporated current and future elements of the income path. Modigliani added a measure of financial wealth while Friedman used a "permanent income" concept that represented lifetime average income discounted back to the present. And both hypotheses provided an explanation for the upward drift of the static consumption function that was broadly consistent with the statistical evidence.

Decades of refinement in theory and econometric technique have largely reinforced the basic insights of these early models of Modigliani and Friedman, both inspired by Irving Fisher's work with the two-period model. But testing hypotheses at the aggregate level inevitably leaves many details in the dark and often raises new questions as it answers old ones. There's little doubt that aggregate consumption responds to changes in both current and expected future income, confirming the commonsense notion that consumers are forward-looking in their consumption-saving decision. But the evidence also suggests that current income has a larger influence on current consumption than predicted by the life cycle hypothesis, the permanent income hypothesis, or their more recent extensions.12

11

F. Modigliani and R. E. Brumberg, "Utility Analysis and the Consumption Function: An Interpretation of Cross-Section Data," in K. K. Kurihara, ed. Post-Keynesian Economics (New Brunswick, New Jersey: Rutgers University Press, 1954), pp. 383-436; A. Ando and F. Modigliani, "The Life-Cycle Hypothesis of Saving: Aggregate Implications and Tests," American Economic Review, Vol 53 (March 1963), pp. 55-84; and Milton Friedman, A Theory of the Consumption Function, (Princeton, New Jersey: Princeton University Press, 1957).

12Important studies include Robert E. Hall "Stochastic Implications of the

Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, Vol. 86, December 1978 and Marjorie Flavin, "The Adjustment of Consumption to Changing Expectations about Future Income," Journal of Political

Chapter 12 Consumption, Saving, and Investment 13

This finding can have a variety of explanations and continues to draw much research attention. It may be that it reflects measurement errors. Measuring consumption is not as easy as it might seem, as will be discussed in Chapter Fifteen. Another problem is that trying to estimate the influence of the expected income path leads us into the many difficulties associated with measuring expectations. So it's possible that consumers are more forward-looking than our studies reveal because problems of measurement are biasing our statistical tests. Or it may be that some consumers are forward-looking while others are not and that the aggregate results simply reflect a mixture of near-sighted and far-sighted responses. Still another possibility is that consumers are liquidity constrained because of imperfections in capital markets. As explained in the next section, this condition can make it look like consumers are behaving myopically even if they're as supremely forward-looking as presumed in the most abstract of models.

But the diversity of explanations for the apparent overly-large influence of current income on consumption should not be allowed to obscure the main finding. The simple Keynesian consumption function of the AD/AS model offers only a partial explanation of aggregate consumption spending and it's clear that, in some degree, people are forward-looking in their consumption choices. Fisher's two-period model offers us a relatively uncomplicated avenue into the complex dynamics underlying the "consumption-saving-investment-economic growth" linkages in the macroeconomy. Any attempt to understand the strengths and limitations of fiscal policy, the workings of capital markets, and the dynamics of economic growth must incorporate these connections across time. 12.4 Fiscal Policy When Consumers are Forward-Looking

o far our intertemporal analysis has looked only at the private sector. Still assuming a closed economy (x=0), we move to a more realistic setting by adding government spending,

financed by taxes or borrowing. This creates a relationship between current income and spending as given by c+i+g=y=c+s+t. Let's start with the assumption that consumers are forward-looking (as described by the two-period model), so that in making their current consumption-saving choice they look beyond current after-tax income (y-t) to the anticipated after-tax income path that, along with the interest rate, defines their wealth constraint.

Does such an intertemporal setting with forward-looking consumers alter our understanding of the role of fiscal policy in the macroeconomy? In the most basic sense, our situation remains much the same. Bound by scarcity, we still have to contend with competing uses (c+i+g, private consumption, private investment, or public spending) for limited resources. Political rhetoric notwithstanding, we know that public goods and services use up resources just like their private counterparts and that every dollar of government spending will be paid -- now or later, directly or indirectly -- by taxes. Looking beyond these basics, however, we discover that the use of fiscal policy to stabilize output and employment ("smoothing the business cycle") loses some of its potency as consumers become more forward-looking. The reason is quite straightforward. If our consumption spending depends on our wealth rather than just our current income, policies that have only short run effects on income will have relatively little impact on

Economy, Vol. 89, October 1981.

S

Part IV Long-Run Dynamics: Saving, Investment, and Growth 14 consumption.

For example, when a fiscal stimulus is used to speed the return to full employment (by shifting the IS and AD curves to the right), the impact is primarily on income over a few quarters or, at most, a year or two. However welcome this quicker recovery may be, consumers with long horizons will respond less vigorously than those who focus all their attention on the here and now. Since this reduced response diminishes the strength of the multiplier process that propels fiscal changes through the economy (∆FP⇒∆y⇔∆c), the result is a weakening of fiscal policy's ability to cause short run changes in output and employment. An economy populated by forward-looking decision-makers operates more like a large oil tanker than a small sailboat. Its greater stability tends to keep it closer to the desired course in the presence of adverse conditions. But when a correction is needed it takes considerably more time and effort to accomplish.

Is there evidence to support this hypothesis? For example, have fiscal changes that were expected to be temporary had less impact on current economic activity than those that were expected to be longer lasting? The answer is about as clear a "yes" as we ever get in a discipline that, in the absence of controlled experiments, must try to sift clues from highly aggregated data in which many things are changing simultaneously. The empirical results reinforce and overlap with those cited in the previous section, portraying an "average" consumer who looks beyond the present but not quite so far or so clearly as the hypothetical far-sighted consumer of our two-period model.13 Thus the actual impact of fiscal change on the macroeconomy is smaller than predicted in the basic, but shortsighted, AD/ASe model. This is an important finding because it implies that our ability to manipulate aggregate demand through fiscal changes is more limited than is widely believed.

But we can't leave this area without re-examining what has been one of the most contentious topics in macroeconomics of recent decades -- the "tax cut/tax postponement" issue first raised back in Chapter Five (Fiscal Policy). Suppose there is a cut in taxes without any reduction in government spending, the difference being made up through deficit financing (g=↓t+b↑). Scarcity ordains that if we keep government spending unchanged, there must be higher taxes in the future. This is just the familiar "no free lunch" result and is uncontroversial among economists. But the tax discounting hypothesis goes a step further and asserts that consumers are aware of the time path of their tax liabilities and that they take this into account in making their current consumption-saving decision.14 13

For evidence that the temporary tax surcharge imposed in 1968 (to restrain inflationary pressures from the Vietnam war spending) had almost no impact on consumption, see Alan Blinder and Angus Deaton, "The Time Series Consumption Function Revisited," Brookings Papers on Economic Activity, 2, 1985. Also see John Campbell and N. Gregory Mankiw, "Consumption, Income, and Interest Rates: Reinterpreting the Time Series Evidence," NBER Macroeconomics Annual, 1989.

14Tax discounting is often called "Ricardian equivalence" in recognition of

similar insights by British economist David Ricardo in the early 19th century. Its modern incarnation begins with the article by Robert Barro, "Are Government Bonds Net Wealth?", Journal of Political Economy, Vol. 82, November/December 1974. Additional references include Martin Feldstein, "Government Deficits and Aggregate Demand," Journal of Monetary Economics, January 1982; Douglas Bernheim, "Ricardian Equivalence: An Evaluation of Theory and Evidence", NBER Macroeconomics Annual, 1987; James Poterba, "Are Consumers Forward Looking?

Chapter 12 Consumption, Saving, and Investment 15

In other words, "tax discounting" asserts that we are forward-looking in terms of our

after-tax income path so that a transfer from tax to deficit-financing (-∆t but +∆b) will not make us feel richer. We'll perceive that deficit-financing is essentially the government borrowing in our name and we'll treat it as our future liability, just as if we'd borrowed privately. Therefore such a tax "cut" in a world of tax discounters is clearly seen as a postponement, not a lasting reduction, and will not lead to increased consumption. The bottom line is that tax discounting behavior implies that tax changes do not shift the IS and AD curves and therefore have no power to expand a stagnant economy or to subdue an inflationary one. This reinforces the ideological predispositions of Non-Activists and presents a challenge to the Activist case for the use of discretionary fiscal changes to keep the economy close to full employment.

Before turning to historical evidence, let's look at tax discounting in terms of the two-period model. In Figure 12.8 we return to individual A, whose initial income path is given at E, which she transforms into her preferred consumption path at A* by borrowing now and repaying later. If A is a far-sighted tax discounter then a cut in current taxes (assuming government spending unchanged) will have no impact on her consumption-saving choice. She will realize that this tax postponement has only altered the timing of her after-tax income path (E to E'), not its present value (W0), so she'll stay with her preferred balance between "now and later" at point A*.15 The increased deficit reduces her private borrowing, leaving her total borrowing unchanged. In other words, to a tax discounter public and private borrowing are equivalent and are therefore perfect substitutes. For individual A, changes in the current tax-deficit mix are offset by changes in her private saving, leaving consumption spending (hence IS and AD) unaffected.

Evidence from Fiscal Experiments," American Economic Review, vol 78, May 1988; and John J. Seater, "Ricardian Equivalence" Journal of Economic Literature, Vol. XXXI (March 1993), pp. 142-190.

15As in our earlier analysis, since A* was previously chosen over all other

points on the budget line, then another point on the line (like A') must be regarded as less desirable.

Part IV Long-Run Dynamics: Saving, Investment, and Growth 16

Figure 12.8 Full Tax Discounting

A deficit-finance tax ‘cut’ moves A’s after-tax endowment from E to E’ along her given wealth constraint. If she’s a ‘tax discounter’ her consumption path will remain unaltered at A*.

In contrast, Figure 12.9 shows the behavior of M, a well-known "tax myopic" we'll assume. When a tax cut increases M's current after-tax income (E to E'), he gives no thought to its implications for his future after-tax income. Instead, the (temporary) rise in his take-home pay leads him to increase his current consumption, moving from M* to M'. As a tax myopic, he thinks his wealth constraint has shifted out. We, of course, know he's in for an unpleasant surprise in the next period when he discovers that his after-tax income and hence consumption will be less than he expects (by the amount of the current deficit plus interest).

Chapter 12 Consumption, Saving, and Investment 17

Figure 12.9 A Tax Myopic Response

The same tax ‘cut’ (postponement) will cause M to increase his consumption now (forcing him to reduce it later) if he is ‘tax myopic.’

Are most consumers tax discounters or tax myopics? A pure tax discounter would be

such a meticulous and calculating person as to be boring beyond belief. They're probably a rare breed. But what about those who, however casually, do plan ahead and who consider current deficits as a potential drain on their future consumption? It is likely that their current saving will be higher than if the government were running a balanced cash flow budget. This sort of casual tax discounting is probably fairly common. In deciding how much to save or borrow now, most of us look beyond our immediate circumstances and formulate some estimate, however rough, of our future after-tax income path. To that extent, we're displaying tax discounting behavior. Just because we're not as farsighted as eagles, doesn't mean we behave like ostriches. There are many possibilities between the two extremes.

The tax discounting issue is not about whether deficit-financed tax postponements (tax cuts without spending cuts) need to be repaid in the future. In a world of scarcity there's no doubt that they do. The real issue is the extent to which consumers, consciously or otherwise, take this future obligation into account in deciding how much to consume now. The more forward-looking they are on taxes, the less impact changes in the tax/deficit balance will have on aggregate demand, limiting its use for macroeconomic stabilization. What does the historical evidence reveal? Where does the average consumer fall in the spectrum between pure tax discounting and total tax myopia? Are we eagles or ostriches when it comes to government deficits?

Statistical tests of tax discounting using aggregate data run into an array of measurement and conceptual difficulties leaving us in the undesirable but not uncommon situation in macroeconomics where several quite different hypotheses are consistent with available evidence. The result has been very sharp disagreement over the importance of "tax-

Part IV Long-Run Dynamics: Saving, Investment, and Growth 18 discounting" and a tendency for ideology to take over where empirical evidence is inconclusive. Not only has this slowed our progress in understanding the issue but has also used up an inordinately large amount of time of many of the best research economists.

After two decades, however, it appears that a middle ground has emerged that has drawn a majority of economists away from the extreme positions of "complete" versus "zero" tax-discounting. This alternative offers an explanation that is consistent with statistical findings that tax cuts without spending cuts do have some impact on current consumption. But it doesn't require us to accept the hypothesis that the same consumers who we find to be somewhat farsighted with respect to future earnings are virtually blind when it comes to future taxes. This realignment comes from dropping the implicit assumption of perfect capital markets and introducing a liquidity constraint that prevents some consumers from borrowing as much as they would like.

Let's look at how a liquidity constraint can alter the predictions of the two-period model. One of the many simplifications we have made in this model was the assumption of a given interest rate at which individuals could borrow or lend in order to achieve a consumption path different from their endowment. This assumption of "perfect capital markets" is certainly not realistic, since for most of us the rate at which we can lend is less than the rate we have to pay to borrow.16 Adding this "imperfection" to the analysis (which puts a kink in the wealth constraint at the endowment point) can change some of our previous conclusions, particularly when there are some consumers who can't borrow on their future earnings at all.

Before turning to the two-period diagram, let's work through this situation intuitively. Suppose that L is a forward-looking, tax-discounting, but liquidity-constrained consumer with a low income now but very good reasons to expect much higher earnings in the future. Rather than to also have low consumption now and high later, her preference is to smooth her consumption path by borrowing now and repaying later. But if we assume she is unable to borrow on her future income, then her current consumption can be no more than her current take-home pay. Now suppose that a deficit-financed tax cut is enacted that increases L's after-tax income. This tax-postponement allows her to increase her consumption just as if she had borrowed privately. In essence the government has provided a loan to L, allowing her to pay part of her current tax bill later and enabling her to move toward her desired consumption path.

To an outside observer, L's increase in consumption in response to a tax postponement might look like myopic behavior. But what's at work here is the liquidity constraint, not tax myopia. Public borrowing has acted as a substitute for imperfect private capital markets. If there are a number of such liquidity-constrained consumers, the outcome of a pure tax postponement will still be to increase current consumption spending. The presumption that fiscal policy retains its ability to expand or contract the economy in an intertemporal setting is therefore not tantamount to assuming exceedingly shortsighted consumption behavior.

The impact of a tax cut on someone who is liquidity constrained is shown geometrically in Figure 12.10. Whether done in words or graphs, the importance of the liquidity constraint hypothesis is that it offers an alternative to tax myopia for explaining why a tax cut (without a 16

For example, those without equity in something tangible (like a home) or a track record of steady earnings generally pay much higher rates of interest for unsecured loans.

Chapter 12 Consumption, Saving, and Investment 19 spending cut) can stimulate current consumption (and thereby shift out IS and AD). In so doing, it is consistent with what most, but certainly not all, macroeconomists believe is revealed by the data.17 Fiscal policy appears to have more influence on demand than predicted for a pure forward-looking, tax-discounting, two-period world. Some combination of "tax myopia" and "liquidity constraint" seems to be at work here. Additional analysis and further testing are needed before we will be able to bring this hazy picture into sharper focus. Those adopting extreme views (decision-makers are all eagle or all ostrich) may turn out to be correct, but they're going beyond what current evidence can support.

Figure 12.10 Adding a Liquidity Constraint

Suppose L is “liquidity-constrained,” unable to borrow to move to her preferred consumption path at L*. The closest she can come to L* is her initial endowment point E so her de facto wealth constraint is, therefore,W1EW0. A tax ‘cut’ (postponement), shown in the right graph, moves her endowment to E’, allowing her to move closer to L* by spending the entire tax cut on current consumption. This tax postponement effectively expands the wealth constraint of someone who is liquidity constrained.

12.5 What Determines the Rate of Capital Formation?

17

Important studies of the role of liquidity constraints in aggregate consumption behavior include Marjorie Flavin, "Excess Sensitivity of Consumption to Current Income: Liquidity Constraints or Myopia?" Canadian Journal of Economics, Vol. 18, February 1985; Fumio Hayashi, "The Effect of Liquidity Constraints on Consumption: A Cross-Sectional Analysis," Quarterly Journal of Economics, Vol. 100, February 1985; and Stephen P. Zeldes, "Consumption and Liquidity Constraints: An Empirical Investigation," Journal of Political Economy, vol. 97, April 1989.

Part IV Long-Run Dynamics: Saving, Investment, and Growth 20

o briefly review, out of current (after-tax) income we must make a joint consumption-saving decision -- what we don't consume is, by definition, saved. Consuming beyond our current

income means borrowing or dissaving. The intertemporal setting of our two-period model shows how current saving is connected to future consumption. It reveals the important fact that our current consumption-saving choice is really about the timing of consumption or the "consumption path." Saving (and dissaving) enables current consumption to escape the boundaries of current income by encroaching on the expected income of the future. Put another way, the act of saving frees our consumption decision from the tyranny of some arbitrary accounting period. The "terms of trade" between consumption now and consumption later are defined by the real rate of interest, which in this sense can be thought of as the "price of time".

But for the economy as a whole to move consumption from now to the future, it's not enough to just save. This saving must then find its way (via capital markets, the subject of the next chapter) into investment activities that increase the capital stock in order to produce the consumption goods of the future. "Plowing" current output back into the production process provides the compost for future crops. To be specific, we can increase our full employment level of output -- y*=F(n*,k,inst) -- with investment activities that increase the quality of the labor force (+∆n* through education and training), increase the quantity and quality of capital (+∆k by investment in plant and equipment or research and development), or improve the efficiency of the institutional structure (+∆inst through political reforms and various public investment activities). This section presents a broad overview of the factors underlying such investment decisions. We move beyond the simple i=i0-i2r relationship of the earlier model to get more detail on (1) what determines the level of investment spending that underlies +∆n*, +∆k, and +∆inst; (2) why this spending is so volatile, and (3) how policy changes can alter it.

Suppose a corporation is trying to decide how much capital it needs to maximize profits.18 For the overall economy we'll call this the optimal capital stock and represent it by k*. The basic optimization rule tells us to keep expanding as long as this adds more to revenues than to costs. This process of equating costs and benefits "at the margin" leads, under many conditions, to profit maximization. Without getting involved in the details, let's examine how this can be applied to a firm's capital spending decision.

18

Though presented here in terms of business investment, this framework is equally applicable to households and governments, and to physical capital as well as financial capital decisions.

T

Chapter 12 Consumption, Saving, and Investment 21

Figure 12.11 Optimal Capital Stock, k*

The optimal capital stock (k*) is defined by the equality of the marginal product of capital (mpk) and the user cost of capital (uck).

On the benefit side, we know from the production function—y*=F(n*,k, tn, inst)—that

adding another unit of capital (+∆k) increases the maximum production level (+∆y*). This relationship, defined by the ratio of the change in output to the change in the input (∆y*/∆k), is called the marginal product of capital (mpk). In most situations the marginal product of capital is positive (more capital means more output) and diminishing (as we add more capital, output grows but by smaller and smaller amounts). This relationship between the amount of capital and its marginal product is represented by the downward-sloping mpk curve in Figure 12.11.

Knowing how much an increase in capital increases this year's output is half the story. The other half is how much it increases this year's costs. We can divide the relevant costs into three categories.

1. Because a capital good, by definition, lasts for many years we don't want to attribute its entire cost (pk, for its "real price" or money price adjusted for the price level) to the year of purchase. So we have to depreciate this cost through "capital consumption allowances" that reflect its expected loss of value over time.19 If the real purchase price is pk and the yearly rate of depreciation is δ (where 0<δ<1 and assumed constant), then the annual depreciation cost of an extra unit of capital is δpk.

2. Another important cost of purchasing this additional unit of capital is its opportunity cost -- the return this firm could have gotten by spending the money

19

So the cost of a $100 million plant that lasts 20 years will be spread over those years, in a particular pattern that depends on standard accounting procedures and tax laws.

Part IV Long-Run Dynamics: Saving, Investment, and Growth 22

on its next best alternative. Let's suppose this opportunity cost is what it could have earned by investing at the going real rate of interest, r. The annual foregone interest cost of this extra unit of capital is rpk.

3. A final cost to be considered in the investment decision is taxes. A portion of the marginal product of this additional unit of capital will be taxed away by the corporate income tax, which we'll represent by a constant rate tk. An increase in this tax can be thought of as lowering the after-tax marginal product of the dditional capital or, equivalently, as raising the annual cost of this capital. Either way the firm keeps only the fraction (1-tk) of the returns to any new capital it puts into production.

Combining these three ingredients gives us the amount an additional unit of capital would add to annual costs, known as the real user cost of capital (uck): uck = pk(r+δ)/(1-tk). The next step is to compare these additional costs of adding more capital with the additional benefits. If another unit of capital adds more to benefits than to costs (mpk>uck), then profits will rise by undertaking this investment. If it adds more to costs than to benefits (uck>mpk) then it will reduce profits and should not be carried out. The optimal capital stock (k*) for this firm is therefore the level at which changing it would add the same amount to benefits as to costs (mpk=uck). Thus the optimal level of capital is achieved when the firm accumulates capital up to the point at which: mpk=pk(r+δ)/(1-tk). This is illustrated in Figure 12.11 at the intersection of the user cost and marginal product curves.

As you can tell from the graph, anything that increases user cost (+∆pk, +∆r, +∆δ, or +∆tk) will shift uck upwards and lead to a lower optimal capital stock (a process of disinvestment). Similarly, decreases in any of these four components will raise the desired level of capital (through the investment process). Increases in the marginal product of capital (through technological change, for example) shift the mpk curve to the right, thereby increasing k* and stimulating increased investment.20

Now that we've seen what factors influence the firm's optimal capital stock, there's one last step needed to turn it into a theory of investment. Suppose this firm discovers that its optimal capital (k*) is much larger than its existing capital stock (k0) and moves to close the gap by undertaking net investment spending (that is, investment over and above that needed to replace depreciating capital). How quickly should it make this adjustment, i.e., at what rate should it invest in new capital? Should it do it all at once so that this year's net investment will be i=k*-k0? Or will it be better to spread the adjustment over several years? Closing the gap

20

Note that buried in here with these new relationships is a familiar one -- a drop in the real rate of interest lowers user cost and leads to an increase in the desired capital stock and hence investment spending (↑i=i0-i2r↓).

Chapter 12 Consumption, Saving, and Investment 23 between the actual and desired capital stock quickly can be expensive. For example, getting a new plant built in a rush brings the higher costs of paying overtime to the contractors and subcontractors. So the rate at which the actual capital is adjusted to the desired level may be quite gradual.

Thus the rate of investment spending depends on both (1) the optimal capital stock and the existing capital stock (specifically the gap between them, k*-k0, and all the underlying ingredients of user cost and marginal productivity of capital discussed above) and (2) a determination of the optimal rate at which to close this gap by equating the costs and benefits of adjustment at the margin.

We can express this very generally as: i* = h(k*-k0) or where k* is determined by mpk=pk(r+δ)/(1-tk), as shown in Figure 12.11, and the general functional relationship h(⋅) has the property that the firm will close this gap gradually over time. For example, a specific functional form might be: i* = λ(k*-k0), where λ is a constant between 0 and 1. With an adjustment coefficient λ of .7, the firm will close 70% of the remaining gap each period.

Statistical testing of this theory of investment spending (known as the "neoclassical model of investment spending") requires quantification of all these variables, a challenging undertaking.21 While there is much we can't explain, the results generally confirm the broad picture that is our concern -- aggregate investment spending varies inversely with the real interest rate (r), the real price of capital goods (pk), the rate of depreciation (or obsolescence) of capital (δ), and the rate at which the resulting returns are taxed (tk).

This treatment of investment has identified factors that were hidden in the autonomous

investment term (i0) of our previous formulation. From a policy perspective, an important instrument is the rate at which the returns to capital are taxed.22 By lowering the tax on capital (-∆tk) and raising the tax on income (+∆t1), for example, the government would be taking a pro-growth strategy. If the tax changes were balanced so that their expansionary/contractionary impacts on IS and AD canceled out, the long run (full employment) result would be a change in the consumption-investment composition of output that increases the capital stock and hence potential output. This is one way that fiscal policy can be used to alter the consumption- 21

There are a variety of approaches to the empirical estimation of an investment function. Among these are the accelerator model, the adjustment cost model, and "Tobin's q". See Jeffrey D. Sachs and Felipe Larrain, Macroeconomics in the Global Economy (Englewood Cliffs, N.J.: Prentice Hall, 1993), Chapter 5, for an excellent presentation of the details of alternative investment models.

22While lowering the corporate income tax would serve to reduce tk, a more

common approach is to give a specific "investment tax credit" that lowers a company's tax liability depending on how much investment they undertake that year. "Accelerated depreciation allowances" are another way that essentially lowers the tax on capital and shows up in our analysis as -∆tk.

Part IV Long-Run Dynamics: Saving, Investment, and Growth 24 investment mix, but don't forget that the resulting increase in economic growth is no "free lunch". In a fully-employed economy, the inevitable cost of this increased investment (+∆i) and the resulting economic growth (+∆y* through +∆AS* and +∆PPF) must be lower current consumption (-∆c).

Neither this nor any of the several other models of investment spending has been very successful at predicting the large and sudden jumps in real investment spending that constitute an important component of the business cycle. Hopes of significantly reducing the unpredictability of changes in investment spending have not been realized. However discouraging this may be, it should not be surprising. The optimal capital stock and optimal rate of investment are inherently intertemporal decisions -- they involve current actions in anticipation of future consequences. Literally all of the variables involved in the investment decision require our best guess at expected future events. This is as true for the marginal productivity of capital and the interest rate as it is for taxes and even depreciation rates. Current events and policies can suddenly make our most careful calculations and past decisions look very foolish. Construction booms brushed by hints of recession, can quickly turn into the "over-building" that precedes a construction "bust". Because capital expenditures inevitably involve sticking our necks out with respect to future economic events, there will always be surprises (both pleasant and unpleasant) that can encourage us to pull back or extend even further.

This unpredictability as we move further into an intertemporal setting is frustrating, but should not necessarily be regarded as a failure of economic analysis. Much has been done in recent decades to systematize our understanding of the role and nature of expectations in macroeconomics. The development of theories of expectations, like the rational expectations hypothesis, has improved our predictive ability in some important ways. But it has also given us a clearer view of some limits to our predictive powers and, thereby, revealed important limitations to some old-fashioned kinds of stabilization policies.

12.6 Overview 1. Private consumption spending makes up over 60% of total demand in the U.S. and private investment spending another 15%. An understanding of the determinants of consumption and investment is central to any useful theory of overall economic activity -- both its long term trend (±∆y*) and its short run ups and downs around this trend (±∆(y-y*)). 2. Starting from the basic consumption and investment functions of the AD/AS framework (c=c0+c1(y-t) and i=i0-i2r), we developed an intertemporal framework based on Irving Fisher's two-period model. This chapter starts construction on a bridge from the no-growth AD/ASe model of previous chapters to a more complete framework incorporating economic growth. The first span of the bridge links consumption to saving, the second moves on to investment. The next two chapters will add capital markets and then combine investment with other sources of input growth to finally bring economic growth within our analysis. 3. The appeal of the two-period model is the relatively simple way in which it forces us to recognize that today's saving becomes tomorrow's consumption. It provides a framework, missing in the AD/AS approach, that links current decisions to a more meaningful concept of long run -- one in which markets are cleared and expectations realized, as before, but also in

Chapter 12 Consumption, Saving, and Investment 25 which the process of saving, investment, and capital formation is considered. Hence the consumption-saving choice is usefully seen as one between consumption now and consumption later, a choice of consumption path. It now becomes apparent that each decision we make involves both "this or that?" and "now or later?". 4. In dealing with intertemporal issues, the process of compounding/discounting is needed to compare values across periods in a meaningful way. A dollar now translates into $1(1+r) in next year's real dollars and $1(1+r)n in n years. A dollar one year from now has a present value of $1/(1+r) while a dollar that is n years away is worth $1/(1+r)n right now. 5. The real rate of interest can now be seen in its most basic and important role -- as an intertemporal price or, intuitively, the "price of time". It is the rate at which we can move goods and services back and forth across present and future through the "borrowing and lending" and "saving and investing" activities that underlie capital markets. 6. The wealth constraint defines feasible consumption paths for a given expected income path (endowment) and given interest rate. Different individuals with the same wealth constraint typically choose a different "now/later" balance, reflecting their subjective marginal rates of time preference. Those eager to consume right away (high time preference) will choose a consumption path along their wealth constraint with relatively high current consumption but low future consumption. The more patient consumer (low time preference) will choose a consumption path that emphasizes current sacrifice in favor of more consumption later. Capital markets provide the borrowing and lending opportunities that allow us to move toward what we consider the "best" consumption path along our wealth constraint. 7. Do consumers really think in an intertemporal context, considering not only "this or that?" but its implications for "now or later?"? One way to portray our degree of far-sightedness is to ask whether a movement along a given wealth constraint (a change in the timing of income but not its present value) will lead us to alter our consumption/saving choice. If, for example, our current income drops but future income rises (by the same amount plus interest), the response of a forward-looking consumer would be to leave her consumption path unchanged. A myopic consumer, on the other hand, would reduce current consumption, unaware or uninterested in the fact that his increased future income offsets his lower income today. Even though his wealth (or "permanent income") hasn't changed, he feels poorer and cuts back current consumption. 8. How forward-looking are we? This is a difficult question to answer at the macroeconomic level, but both common sense and statistical results confirm that we do look ahead to expected future income and other events in making today's consumption-saving decision. But it also appears that current income has a larger influence than predicted by the forward-looking hypotheses proposed by Franco Modigliani, Milton Friedman, and others. This could reflect many things and it is probably asking too much to expect aggregate, economy-wide data to give a very precise answer. One possibility is that fiscal policy doesn't have as much influence as we think but that errors of measurement have clouded our vision. Another is that the aggregate statistics contain a blend of different perceptions (ranging from eagles to ostriches) and there are enough myopic consumers (most families seem to have at least one) to give fiscal policy some traction. But even without myopic consumers, the presence of liquidity constraints in the capital market can result in current consumption responding "excessively" to current income even with very forward-looking consumers.

Part IV Long-Run Dynamics: Saving, Investment, and Growth 26 9. One important consequence of viewing consumption in an intertemporal setting is that to the extent that consumption responds to wealth as opposed to just current income, its time path will be much more stable because the ups and downs of transitory income changes have little impact. Events and policies will therefore exercise less influence on consumption, an important correction to the impression in the AD/ASe model that "fine tuning" can be done with some precision. 10. The tax discounting hypothesis simply extends the forward-looking consumer's domain to include taxes as well as earnings. It implies that forward-looking individuals, making their consumption-saving choice with after-tax dollars, will not be fooled by public deficits. They'll see that part of their current taxes have been postponed and they'll save accordingly. Therefore, a tax cut without a spending cut will not cause them to increase consumption spending, a conclusion quite at odds with what we used in the AD/ASe model and also at odds with most researchers' interpretations of the statistical evidence. While it seems apparent that we exhibit some forward-looking behavior with respect to future taxes, it may well be considerably less than for our before-tax earnings. In other words, while expected future earnings influence our current consumption-saving choice, it appears that we are somewhat less responsive to the expected future taxes from current deficits. However, statistical tests with aggregate data are often not very powerful and there is much disagreement over this. Aggregate data hide many clues and the relatively few clues we have could be consistent with a number of hypotheses. 11. The question is not whether we're pure tax discounters or pure tax myopics. Obviously we're somewhere in between, in the aggregate and probably for most individuals as well. A related issue is the extent to which we're liquidity-constrained. Individuals who are unable to borrow on their future earnings will exhibit behavior that looks tax myopic -- a tax postponement will lead them to increase their current consumption. But this actually reflects their economic relief at the government providing them with a low-interest loan (the deficit financing that allows them to postpone their taxes) that they couldn't get through the private sector. 12. Whatever unknown blend of myopia and tax constraint may exist, the result is that tax changes have a larger impact on spending and hence aggregate demand than is implied by the standard two-period model with forward-looking consumers. But this effect is still much smaller than predicted in our earlier, completely myopic, AD/ASe framework. Even though much of our understanding of policy impacts remains imprecise, on many topics we have continued to reduce the range of disagreement over what the government can do. 13. The consumption-saving decision determines the maximum amount of resources that are being released from current consumption and are available for capital formation. But how or whether these available resources will actually be used requires an understanding of the determinants of aggregate investment spending. Using a cost/benefit framework we can spell out the conditions under which an additional unit of capital will add more to a firm's revenues than to its costs. From this we can define the optimal capital stock (k*) as the level at which the marginal product of capital equals its user cost. In symbols, it requires that we pick that level of capital at which mpk=pk(r+δ)/(1-tk). 14. Investment occurs when the optimal capital stock diverges from the current one (k*-k>0). But because the cost of closing this gap rises as we try to do it more quickly, the optimal rate of investment will generally be such as to close the gap gradually. Statistical analyses

Chapter 12 Consumption, Saving, and Investment 27 generally confirm that real investment spending varies inversely with the real rate of interest (r), the real price of capital goods (pk), the rate of depreciation (δ), and the applicable tax rate (tk). This gives us a considerably richer understanding of the investment process than the simple investment function (i=i0-i2r) of the AD/AS model. 15. Investment spending remains the most volatile category of aggregate demand and we still have little ability to predict these sudden changes that are crucial determinants of the business cycle. This volatility appears to be a reflection of the intertemporal nature of investment -- it involves current actions in anticipation of distant outcomes. Any change in our expectations about future events can lead to quick and sizable alterations in our investment decisions. Theories of expectation formation can give some important insights, but ultimately it's the uncertainty of future events that creates the volatility in investment spending. 16. Where does this venture into the dynamics of intertemporal decision-making leave us? A very important result for stabilization policy is the reduced leverage of fiscal policy as we acknowledge forward-looking, tax-discounting behavior by consumers. But the possibility of an important role for liquidity constraints and a degree of myopia that seems to characterize our aggregate behavior still gives fiscal actions an influence on aggregate demand and, in the short run, real output and employment. Though the myopic AD/ASe model tends to overstate this influence, its short run analytics still provide a relatively complete and generally reliable analytical framework. The results of this chapter are intended to supplement and qualify the AD/ASe analysis, not replace it. They also begin the analytical bridge that will take us to an analysis of economic growth. 12.7 Review Questions 1. Explain the following terms and concepts: Consumption Path Initial Endowment Income Stream Intertemporal Budget

Constraint Wealth Constraint Intertemporal "Price"

Compounding Discounting Present Value Rate of Time Preference Two-Period Model Myopic Behavior Forward-looking Response

Liquidity Constraint Tax Discounting Optimal Capital Stock Marginal Product of

Capital User Cost of Capital Optimal Rate of Investment

2. Two nearly identical economies differ in one respect -- in Economy A households decide on their current consumption spending by looking only at their current after-tax income, whereas households in Economy B have a longer horizon and look at their expected lifetime after-tax income in choosing a consumption path. Both economies are currently in recession and policy-makers in both nations decide on a substantial one-time tax rebate (a 20% across-the-board tax reduction for one year) to give a quick stimulus and speed economic recovery. Predict the impact of this policy in each economy on:

a. the IS and AD curves. Explain. b. the optimal consumption path. (Use the two-period model.) Explain. c. Short run impact on y, P, r, i, x, b, and e using the AD/ASe model. Explain.

3. How would adding "market frictions", "policy lags" and "liquidity-constraints" to the analysis alter your answers to Question 2? Explain.

Part IV Long-Run Dynamics: Saving, Investment, and Growth 28 4. Suppose these two economies (in Question 2) decide to use a one-time monetary stimulus rather than a tax cut. Predict the impact of this policy in each economy on:

a. the LM and AD curves. Explain. b. Short run impact on y, P, r, i, x, b, and e using the AD/ASe model. Explain.

5. How would adding "market frictions", "policy lags" and "liquidity-constraints" to the analysis alter your answers to Question 4? Explain. 6. "It's ridiculous to think that a temporary tax cut will increase consumption spending. In fact it will probably reduce it because the tax cut means an increased deficit and this means we'll have to pay the taxes plus interest back later, leaving us worse off." Carefully evaluate the logic of this statement using the analytical framework of the AD/ASe model. 7. Use the AD/ASe model to analyze the relationship between saving and investment in both the short and long run. Specifically, suppose there's an autonomous increase in saving (from an equivalent decrease in autonomous consumption). Will this result in an equal increase in investment spending? Explain carefully. 8. Suggest some ways in which we might get evidence on whether taxpayers in the U.S. behave as if they are tax discounters or not. Remember that we can't do controlled experiments and that there is much evidence to support the conclusion that sample surveys are a very unreliable way to find out how people actually behave. So you've got to dig for clues in the uncontrolled experiment of history. What sorts of things would you look for? Be specific and also cite reasons why your particular test might not be absolutely definitive. 9. "The longer the time horizon used by consumers the larger the impact that expectations can have on current spending and the more volatile consumption spending is likely to be. Therefore we should expect cyclical unemployment to be less prevalent when decision-makers have a relatively short horizon." Evaluate. 10. Thinking of investment spending as a process by which the economy adjusts its actual capital stock to its optimal stock, explain the impact of each of the following events on investment spending:

a. a sudden drop in the marginal product of capital due to governmental limitations on its use.

b. an "investment tax credit" that allows companies to decrease their taxes by a fraction of the amount spent on new capital equipment each year.

c. replacement of the income tax with a national sales tax on consumption spending but not on saving.

12.8 Further Reading Alan Blinder, "Temporary Income Taxes and Consumer Spending," Journal of Political

Chapter 12 Consumption, Saving, and Investment 29 Economy, Vol. 89 (February 1981), pp. 26-53. Robert E. Hall, "Intertemporal Substitution in Consumption," Journal of Political Economy, Vol. 96, (April 1988), pp. 971-987. Robert E. Hall and Fredric Mishkin, "The Sensitivity of Consumption to Transitory Income: Estimates from Panel Data on Households," Econometrica, Vol 50 (March 1982), pp. 461-481. J. Hirshleifer, Investment, Interest and Capital (Englewood Cliffs, N.J.: Prentice Hall, 1970). Franco Modigliani, "Life Cycle, Individual Thrift, and the Wealth of Nations," American Economic Review, June 1986.