by Filip Palda
Permanent income, life-cycle hypothesis
THE CONSTANCY OF discounted lifetime income also explains why people can uncouple the timing of income over the lifetime and the timing of their consumption. The sum of income in every year adds to a single number. That number and not the incidence of income in the series that makes up the sum is what the consumer bases his or her consumption decisions in any period upon. Grasp this and you have the essence of the permanent income hypothesis in your hands. Let us examine these concepts in a bit more detail.
The permanent income, life-cycle model seeks to understand how a person who can either save or borrow against future earnings will decide to allocate consumption between the present and the future. The question of why it even matters to a person how to allocate consumption over time arises for two reasons. First, people are impatient. They value a dollar of consumption today more than the same dollar a year from now. Despite their impatience they are also opportunistic. The reason they do not consume everything in one giant feast today is that the interest to be earned by putting some money in the bank could more than compensate the individual for delaying his or her consumption for a year. Then why not just put everything in the bank and commit to a complete delay of gratification?
The reason lies in the economist’s assumption that each increment to your consumption in a given period brings less happiness than did the previous increment. Consumption in any one period brings diminishing returns. To maximize the pleasure from consumption you would want as a first principle to spread your consumption out evenly over all periods. If you bunch consumption too tightly in one period each additional unit in that period is giving you less and less pleasure. It is better to transfer that unit of consumption to another time period where you can consume it with renewed enthusiasm. If you have a table set for a banquet but no guests show up you would prefer not to gorge yourself on all the food at one sitting but to divide your dining into small Tupperware containers, to be enjoyed in more pleasurably dispersed dining episodes. That is the crux of the life-cycle model. Because of diminishing returns to consuming in any given period, people have an innate urge to spread out their consumption evenly over time. This basic urge can be somewhat altered if interest rates are high, thereby suggesting an advantage to skewing consumption to the future. On the contrary, if impatience is high then there is a tendency to skew consumption to the present. If the effects of impatience and interest rates cancel each other out then the basic need to consume equally in all periods fully asserts itself and consumers choose to spend the same present-value amount of income in each period.
The sum of the present value of all future income streams is implicit in this discussion. In a world of perfect certainty, the consumer has access to all of his or her future income through a banking system that allows him or her to borrow against these anticipated revenues. In principle you could blow the present value of your entire lifetime income in the immediate present. This extreme example illustrates that to make the most of your possibilities you must take into account the fact that your ability to consume in any given period is not restricted to the income you earn in that period, but to the sum of income through your life. The decision to equalize spending in all periods arises from your consideration of how to allocate the sum of these revenues. This is why the theory refers to the life-cycle.
Economists refer to this methodical manner of deploying one’s resources rather neutrally as “consumption smoothing”, yet the consequences are anything but neutral. Suppose you win $10,000 in a quiz show. Friends might advise you to throw a party and go on a shopping spree, but you would first look at the returns from putting that sum in the bank and allowing it to grow for several years. The balance you need to strike is between how much it strains you to delay gratification and how much extra gratification you would get in the future from the interest gained on your delayed consumption, that is, your savings. Consumption smoothing means that you would consume your windfall in dribbles, spread out over time. This is what led Milton Friedman to distinguish between permanent and transitory components of income. If the consumer considered the $10,000 to represent a permanent rise in annual revenue then he or she would consider it “permanent income”, and spending in each year would rise by as much as $10,000. If the consumer considered it a one-shot event then it would be considered “transitory income” to be consumed in packets spread over the remaining years. Though he called it the “permanent income hypothesis”, Friedman could with equivalent logic have called it the “transitory income hypothesis”.
We must keep in mind that these are theories about how people following a rational plan should behave. Sometimes people do not stick to plan and blow a lottery windfall in a massive spending spree. These deviations can be worked into the theory, and while they are spectacular, theorists hope that they are rare enough to qualify as aberrations.
We must also keep in mind that I have pulled a slight pedagogical fast-one in explaining the logic behind consumption smoothing as being the diminishing utility from increased consumption in any period. While there is nothing wrong with this explanation, it gets up the dander of purist economists who quite rightly would point out that the assumption of diminishing absolute returns to utility is not strictly necessary. The tendency towards consumption smoothing over time can more generally be obtained from the assumption that the relative rate at which people are willing to trade off consumption between now and later falls as people consume more now and less later. To get such a relatively diminishing effect you do not need to assume diminishing marginal utility but simply diminishing relative marginal utilities. The point of this somewhat tedious exposition is to show that the permanent income, life-cycle hypothesis is consistent with a broad category of preferences. What these preferences have in common is that people tend to prefer averages to extremes. You don’t strictly need to assume diminishing extra, or “marginal” utility to get this result. You just need to assume that relative valuations diminish as more is consumed in a certain period. The advantage of keeping preferences structures general is that one can search more broadly in the data for patterns that confirm the theory.
Life-cycle theory and government
AN IMPORTANT IMPLICATION of the life-cycle model is that because people can shift consumption to the future, governments that borrow and spend today may have a limited ability to “stimulate” people into bouts of economy-boosting consumption. People realize that sooner or later government spending will have to be paid for by increased taxes. Looking at their inter-temporal budget constraint they realize that increased government largesse today will be largely cancelled in their lifetime incomes by increased taxes in the future. In reaction they reduce their consumption, thus thwarting the government’s attempt at stimulus.
Robert Barro called this “Ricardian equivalence” in his 1974 paper on the topic. He argued that if the life-cycle income theory of consumption is correct, then people should “internalize” government’s ability to borrow, spend, and later tax, the so-called government budget constraint, into their calculations, thereby rendering the timing of government taxes and spending irrelevant. More prosaically, a government that decides to boost spending today by borrowing is not going to have any different effect on the economy than a government that boosts spending today by increasing taxes. Most people understand quite easily that tax-and-spend is not a good way to stimulate the economy. On the one hand, government spending stimulates, and on the other hand, taxation depresses. Deficit-financed spending seems to get around this problem. Yet according to Barro and his followers, consumers view deficits with a jaundiced eye. Deficits are harbingers of taxes and as such are conceptually and operationally no different to a consumer than direct current taxation.
The Ricardian Equivalence theorem is an example of an application of the life-cycle, permanent income theory that provoked controversy among academics. If taken seriously, permanent income thinking meant that government had to reconsider its role as an engine
of economic growth. The idea that government could stimulate the economy did not really emerge until the depression of the 1930s when Keynes argued that government could “fine tune” and “jump start” economic growth by “stimulating” pent-up consumer demand. Before then economic growth had been thought to be the work of private entrepreneurs rising and sinking through the success of their ideas on how to please consumers. World War I trained government to regulate and control the economy in a way that was both modern and unprecedentedly broad. Keynes’ views on government’s role may or may not have helped government grow. We cannot be certain. Perhaps government did intervene simply because it could.
What we do know is that starting in the 1950s, the appearance of the life-cycle, permanent income model challenged Keynesian apologists for government intervention. The model postulated a forward-looking individual taking full advantage of modern borrowing and lending technology. This individual connected with the future in a way that could thwart government attempts at economic stimulation.
What do the numbers say? In a fascinating book published in 2000 on how economists can use theory to bolster their political views, Robert Leeson describes how neither Keynes, nor his nemesis Friedman, were very convinced that the proof for their theories would ever be found in the numbers. Both were polemicists who used economics as a language by which they communicated in a coherent manner accessible to large numbers of the economically literate their unshakable inner convictions about the proper role of government intervention in markets.
Later generations of researchers were not as pessimistic as Keynes and Friedman. They developed new ways of looking at the numbers to support or refute their theories. For example, Robert Hall (1978) suggested that economists stop trying to identify cause-and-effect relationships. Instead he suggested that the permanent-income, life-cycle hypothesis did not need to be tested by looking at the numbers to see if the level of consumption was related to permanent income in the strict sense dictated by the theory. Rather, you could, if not test, then get a feel for the validity of the theory by seeing if the change in consumption over time as dictated by the equations of motion of the model conformed to actual changes observed in the real world. Change is a far less exacting criterion by which to validate a theory than is some measure of absolutes.
Hall mixed uncertainty about future income into his model to suggest that consumers optimizing their happiness should smooth consumption in such a way that both consumption and wealth followed what statistician’s call a “random walk”. Namely, consumption should remain steady with year-by-year corrections for unanticipated changes to income and by so doing would also induce a random walk in wealth regardless of whether background changes in salary followed such a random walk or were “serially correlated”, meaning they followed an uncertain but nonetheless trending path. Hall’s work ushered in a new era into the analysis of time in economics, whereby “equations of motion” rather than cause-and-effect relations would become the dominant theme in the dynamic macroeconomist’s research agenda. We we now turn to this important idea.
The complex face of time
SO FAR WE have focused exclusively on how consumers behave in reaction to an anticipated stream of future income, but from where does income derive? The life-cycle hypothesis does not answer this question. It simply assumes that consumers can expect a stream of income in the future that can be discounted and summed into a single number. This data point is then all a person needs to know for him or her to decide how to divide consumption between present and future. Permanent, or life-time income, or whatever you choose to call it is a given. It is the fundamental constraint on life-time consumption patterns and it does not change, no matter what action the consumer takes.
In a way, the strength of this model is that it takes permanent income to be a given. Nothing that consumers do today can influence permanent income. Of course you can save and expect to earn more money in the future, but as shown earlier, in present value terms, those extra earnings from interest represent no accretion to the present discounted value of your lifetime wealth. Borrowing and lending merely serve to displace consumption through time, but not to increase its discounted value. This guarantees the constancy of the budget constraint and vastly simplifies the problem of how the consumer should adjust consumption over the life-time. If consumption decisions do not affect the budget constraint then the optimization problem boils down to a simple spreading of income evenly over time, moderated in part by interest rates, and in part by impatience.
The weakness of the model is that clearly the world does not work that way. People do not simply look to interest rates in order to accrue income. They seek ways of becoming more productive through education or by discovering natural resources or by coming up with some great technical invention, and of course, later they may multiply these enhanced earnings by saving them and earning interest. Lifetime income is not a given but rather a malleable quantity under our control. A decision on how much to consume today is also a decision on how much to invest, because what you do not consume today is saved and then invested. When you invest in some production technology such as machines, or more generally “capital”, you add to the stock of capital in every subsequent period. And this stock influences your ability to make money in any subsequent period in a manner that changes the present discounted value of your income.
More technically, by saving today, you influence the entire future path income will take in the future, and once set on this path, if that is the one you wish to commit to, then you must decide upon an optimal degree of consumption smoothing. But each future decision to consume further alters the path to follow which requires further considerations of optimal consumption smoothing “trajectories” and so on. As you might surmise, what we have here are the makings of a devilish problem. In this context any consumption decision you make now, changes the whole profile of future income, which calls for a calculation of future optimal consumptions which change the income profile, calling for a recalculation and so on. Each consumption decision in effect creates a new path of future income which itself has implications for the optimal stream of consumption along that path, with each point on the stream altering the remaining stream. Basically, with every consumption choice you make you are remaking your budget constraint, which in turn forces you to reconsider your consumption choices, which changes your budget constraint and lifetime discounted income, and so on.
This cumulative and reverberative effect of investment decisions would be of lesser importance to intertemporal choice if consumption always had a constant, or linear effect on wellbeing. In that case you really would not care how consumption is spaced, tradeoffs between periods would become irrelevant, and the best path would simply be the one that maximized lifetime present discounted income. The complexity arises when people don’t like to gorge themselves or go very short of consumption in any given period and when investment decisions have cumulative effects. Such a situation creates many paths from which to choose. One can see that the problem is in a league beyond that which the permanent income hypothesis could compete.
Friedman and Modigliani avoided assumptions about investment and its cumulative effect on future income and hence its ability to change the budget constraint perhaps out of fear that it might lead them into an appallingly difficult field of mathematics known as the “calculus of variations”. As Richard Bellman, one of the great mathematicians of the 20th century wrote of the field, “A course in the subject in college had given me simultaneously a rather low opinion of its intrinsic interest and a healthy respect for its intricacies. It appeared to be filled with complicated existence and uniqueness theorems with self-imposed restrictions, none pointing in any particular direction” (Dreyfuss, 2002, 50).
The calculus of variations of which Bellman voiced his misgivings is a tool for making a sequence of choices that will optimize some target quantity you care about when each preceding choice changes the constraint you are facing for the rest of the life
of the problem. As Bellman wrote “An interesting fact that emerged from this detailed scrutiny was that the way one utilized resources depended critically upon the level of these resources, and the time remaining in the process. Naturally this was surprising only to someone unversed in economics such as myself.”(Dreyfuss 2002, 49). It is called calculus of variations because its objective is not to find an optimal point that maximizes a function of a variable, as is the case in the simple differential calculus invented by Newton, but rather to find an optimal, and varying path that maximizes the value of a function of that path, or a “functional”. This functional associates each path with some value of interest (lifetime wellbeing from a certain path of consumption is an example), as opposed to a simple function which associates a point, such as permanent income, with a target value.
As you can imagine, finding an optimum path is usually a harder problem than finding an optimum point. A modern twist on the calculus of variations is called optimal control theory. We need not worry too much about these distinctions. The main thing we need to understand is that unlike in simple economic optimization problems where the budget constraint is fixed, optimal control allows you to vary the budget constraint. The tradeoff that makes the problem difficult is that enhancing the budget constraint in the future may impose unpleasant costs upon you now. Each moment is a balancing act between enhanced possibilities now and the benefit that brings, and enhanced possibilities later.