by Filip Palda
The precise formulation of this view came in 1977 with the publication of a paper by Finn Kydland and Edward Prescott on rules versus discretion. A dynamic programming approach to economic policy epitomized the rational planner using some clever optimizing strategy as a means of fine-tuning the economy. Kydland and Prescott argued this hands-on or “discretionary” approach to policy could be a prescription for economic instability.
The problem that arises when applying a dynamic programming logic to the formulation of government policy is that dynamic programming was really invented to deal with entities guided by inertia, such as rocket ships. When the entities are sentient, as are humans, a government that sets policies using dynamic programming is acting as if policy at any future stage does not influence the function to be optimized at much earlier stages. Rocket ships satisfy this requirement but people seldom do. People might anticipate future government actions. If this is the case then the benefits the social planner imagines society receives at some future date through the optimal plan also influences the benefits from earlier policies. In such a case people’s expectations about future government policies wind the future and the present too tightly into each other for Bellman’s principle of optimality to hold. If government does not understand this and acts as a naive dynamic programmer it can see its policies blunted.
For example, suppose a federal government wants to guide economic development in one of its provinces. Government determines that at any given moment it will compensate for shortcomings in provincial investment, due perhaps to a limited access to capital markets for local investors by providing a subsidy. Here is a clear dynamic optimization problem if current investments determine future income growth in a cumulative manner and if utility is a declining function of consumption. The trade-off government must consider is between spending money now on social programs and investing it in regional development which will yield higher wealth in the future. The stated policy is that if firms are unable to invest the amount in machines that they wish government will make up the difference. Suppose government assumes that businesses will not react to its policy but passively allow it to bridge their investment gaps. Then the principle of optimality will hold. The government’s anticipated yield (the benefits to society) from its policy of subsidies at a future date does not influence its yield at an earlier date because future subsidies do not change private investment behavior today. If they did, then the total stock of capital today would go down.
Only without such forward looking subjects can the government act as a dynamic programmer who starts his or her plans at the end and works backward, not worrying about earlier steps in planning. Government cannot divide its planning problem into simple portions like this if what it is anticipated to do at the end influences the yields at the start of the planning horizon. For if government acts in this manner a surprise is in stock for it. If investors know the government strategy, they will hold back their investments in the expectation of obtaining future government largesse. Using simple dynamic programming to determine subsidies, the optimal strategy will require government to re-open its planning calculations at each period.
This is quite a conundrum. If you approach the problem purely as a dynamic programmer then the shortfall of investment provoked by your policy actually looks like a great opportunity to reopen the dynamic program and offer up more subsidy. But if investors also anticipate this intervention this will lead to a further retirement of private investment, calling for a further increase in subsidy, and so on. At each iteration in the response cycle of government, greater taxes have to be levied, and these present an exponential drag on the economy. So to achieve what was initially a simple and rational objective of economic growth now becomes a fool’s game of doubling down for linear gains versus exponential costs. Kydland and Prescott called this need to trim one’s policy sails at every turn the “inconsistency of optimal plans” or simply “time inconsistency”.
The problem government encounters when it acts as a clever dynamic programmer is that it must react to people’s reactions. If, instead, government could stick to a rule, then it would short-circuit these reactions. But then rather than being a dynamic programmer who acts with discretion according to circumstances it would be a passive enforcer of rules. If government declared it would send a fixed level of subsidy to a province regardless of what private businesses were investing there, then businesses would not reduce their investments in response to government aid.
What staggered economists and continues to bewilder students of the Kydland-Prescott article is that the “dumb” strategy of simply declaring an immutable policy dominates the “clever” dynamic programming strategy of adapting the equation of motion to feedback it is receiving from changes in the economic environment. How can this be so? There is a technical and then an intuitive explanation.
Technically, when people react to a government policy by anticipating it, they wind the future and the past into the government’s planning in such a way that makes it difficult if not impossible to chop up the maximizing problem into chunks manageable by dynamic programming. This just means that no consistent policy is initially possible, but it does not mean that dynamic programming is useless. As government adjusts its policy at any given moment to peoples’ reactions, eventually policies and reactions might converge to some stable point at which no further readjustments are necessary. At this point, the repeated application of the dynamic programming technique would have converged to the optimal policies. By then it would have achieved consistency but at a cost. The problem with adopting dynamic programming methods that need to be continually reopened to converge is that government accepts more general restrictions on its ability to maximize society’s well-being than had it simply opted for rigid rules. It immediately restricts the “space” of available optimal policies.
More intuitively, comparing the sub-optimality of discretionary government policy to following a fixed dumb policy is not an indictment of dynamic programming theory, or more general methods of dynamic optimization. Given its decision to intervene according to an optimal program, the best government can do at any given moment is to react to people’s reactions. This is actually the optimal thing to do in the environment government has itself created by deciding to follow a discretionary plan based on the repeated application of an inconsistent dynamic optimization approach to policy. The problem is that the optimum attainable in this government-created environment is inferior to the optimum possible in a different environment where government decides to act mulishly and never deviate from a fixed rule. Therein lies the answer to the paradox of the time-inconsistency of optimal plans.
The failure that Kydland and Prescott identified is not uniquely one of dynamic programming, but rather is a failure of government to integrate the reactions of private individuals into its plans. Once that is done, the problem of optimal government intervention becomes one of political will. Ultimately what Kydland and Prescott were saying is similar to what Lucas and Friedman had warned of earlier. The expectations of private individuals are a constraint on the effectiveness of government intervention. Governments break this constraint by submitting to rules that effectively cut the cycle of reaction. If government does not commit to rules it activates these constraints and thereby limits the range of best possible outcomes. That was really all the debate was about. Simple, no?
Quite apart from yielding unexpected insights into the challenges to the efficacy of government intervention, dynamic programming gave birth to the field of business cycle simulation based on intertemporal models of optimization by consumers and firms. Simulation had long existed in macroeconomics. Keynesian econometric models were all about simulation. But what had earlier been lacking, as strange as it may sound, was a model explicitly based on the assumption that people maximized profits and wellbeing.
Other applications of inter-temporal analysis
EARLIER KEYNESIAN MODELS were so-called ad hoc creations built up from loosely connected
assumptions. Real business cycle models were built up from a mathematically coherent view of interactions between firms and consumers explicitly seeking the best for themselves over the long-term. Dynamic programming allowed such models to be solved, or very closely approximated and thus allowed economists to explore the consequences of random shocks to the economy and also of diverse forms of government intervention.
Among the first to build such a model were, you guessed it, Finn Kydland and Edward Prescott in their 1982 article “Time to Build”. This bravura display of technical economics explained how to exploit the happy union of intertemporal optimizing techniques with the modern computer and economic reasoning. Their work allowed economists to see in clear pictures how an economy in which individuals maximizing their well-being by the choice of an optimal investment plan would evolve. Using dynamic programming techniques they built a dynamic model of the economy that was consistent with the past real evolution of consumption, investment, employment, and other variables. They achieved consistency by fiddling with, or “calibrating” the model’s fundamental constants or “parameters” until the model could reproduce the past. They also showed how to make chance variations in the productivity of industry, due to technological change, a factor that people took rational account of in at first making, and then updating their plans. Friedman had given this a shot by developing the concept of “transitory income” but his attempts had the tacked-on feel of an afterthought. The Kydland-Prescott model left nothing to surmise. It was a fully-cranked view of an economy evolving under the rational actions of optimizing agents.
The model that resulted could simulate what would happen to economic growth under different types of government policy such as permanent decreases in taxation versus temporary decreases. Kydland and Prescott’s conclusions about government policy mirrored those of the simpler permanent income, life-cycle model of consumption. Government’s attempts to stimulate the economy could be thwarted by forward-looking people who understood that any act of government generosity today had to be paid for later.
The Kydland-Prescott model went much further, though, than the Friedman-Modigliani model because it tied the productive side of the economy to the consumption side in a forward-looking manner. This enhancement allowed Kydland and Prescott to show how people’s decisions today could reverberate through time. The Friedman-Modigliani permanent income model has no arrow of time because it compresses time into the single datum of permanent income. The Kydland-Prescott model, moreover, allowed one to address the question of how random shocks to the economy, due perhaps to storms, or wars, or unexpected inventions, could also create cycles of ups and downs in national income. These cycles were not the product of irrational investors, as Keynes had bruited, but were the consequences of rational plans built in an uncertain environment. Thus was born real business cycle simulation.
There was a downside. Even if you were confident the numbers backed up your equations of motion you could not be certain whether it was your view of the world, your model, that was responsible for this time-path, or some other model. All you could say is that the numbers were consistent with your model. This is the enduring Achilles heel of the Kydland-Prescott approach to dynamic economic simulation. What calibration means more simply is what Sherlock Holmes does when he deduces from a man’s hat that he is married but in bad standing with his wife, that he cannot pay the gas bill, that he is of genteel but impoverished background, and that he has recently bought a Christmas goose. Those are facts that “fit” with or are in effect “calibrated” to the image of the world implicit in the hat. The problem of course is that there are many other interpretations consistent with the state of the hat. The interpretations you make now will then influence deductions you make about changes that may befall the owner of the hat.
Time in the general economic view
THE APPLICATIONS OF time in economics go beyond macroeconomics. I chose life-cycle income and some aspects growth theory because developments in this field make a nice story for illustrating the salient issues that arise when people try to best adjust their affairs over time. The presence of cumulative effects of past consumption behavior on investments clearly illustrates how an arrow of time can be established in economics.
This arrow of time can be seen in other fields as well. For example, there is branch of economic dynamics that does not focus on the consumer’s effect on his or her budget constraint, as growth theory does. Instead it focuses on the effect our choices have on the formation of our tastes. This is a much more intimate topic. Gary Becker and Kevin Murphy were among the first to apply the tools of dynamic growth theory to a question that touches deeply on the values that make us who we are. They believed that the consumption of certain products led to the formation of habits in consumption. These habits grow because past consumption may have a cumulative effect on our preferences for present and future consumption. One can imagine a person accumulating a stock of “consumption capital” that influences the ability to enjoy certain goods or activities. The consumption capital cannot be expressed in a constraint, as physical capital was in the problem of optimal investment over the lifetime, but rather appears directly in the individual’s utility. Nonetheless this raises the same issues as in optimal investment because the consumption decision now determines a path of pleasure in the future, just as consumption decisions in the investment model determined a path of future income. The past sets you on a firm course to the future and in this sense considerations of before and after are of prime importance in understanding how people behave.
A brief time of history
QUITE APART FROM training us to appreciate the subtleties of economic modeling, studying the economic approach to time heightens our perceptions of the past in a manner historians might not be able at first to appreciate. For what is a theory but a prescription for recognizing patterns in real life which we might have missed but for a bit of inspired and systematic guesswork?
A case in point is that until recently there was little we could do but live by the vagaries of the seasons. The Bible speaks of the difficulties of living through seven years of famine and the dubious pleasure of an ensuing seven years of feast. Famine and feast cycled through human lives for two reasons. Until about 200 years ago there was really no reliable means for storing food except the short-term expedients of curing meat and preserving vegetables in root cellars. Grain silos and refrigeration technology for meat did not exist in viable forms until the mid-19th century. Subsequently canned products were invented, but their reliability was poor until the 20th century. Until recent times, food was difficult to store, with the exception of alcohol.
Alcoholic beverages are a high-yield method of preserving a potable liquid with large caloric content against contamination by microorganisms. The long-term storage potential of alcohol is an example of the quest by humans to displace current consumption towards the future. The invention and refinement of spirits was the greatest advance in this quest. Spirits really only became widely consumed in Europe during the early 18th century. To produce the high alcoholic content of hard liquor, a great deal of heat is needed. Access to heat was not widely available until the industrial revolution of the late 1700s. This revolution produced the steam engine and iron rolling-techniques that allowed railed vehicles to transport coal in bulk to far-off places. The price of producing heat plummeted. The low price of heat allowed people to distill spirits and transmute the caloric content of coal into the caloric content of drinkable, storable alcoholic beverages. Today, alcohol is not seen as an essential nutrient and is even frowned upon by growing segments of society. Two hundred years ago, distilled alcohol was a caloric godsend that lowered the cost of contamination-free nutrition. To borrow a passage from Sophocles’ Oedipus, written during the caloric boom made possible by the exploitation of the olive 2,500 years ago, “There grows the grey-leaved olive whose rich oil breeds up our sturdy youth, so that no brash young general or arrogant commander can ever uproot, pillage, or plun
der the quiet of these silvery grey groves.”
Technological improvement in storage increasingly protected individuals from cycles of boom and bust, but just as important in creating stability were advances in the ways of commerce and the law. Before the 1800s, people thought hard about whether to put their money in the bank or leave it under a mattress at home. Thieves could rob your home, but banks might equally go bust or embezzle your funds. Out of the industrial revolution arose a reserve of wealth that allowed banks to insure each other against failure. This was the start of a banking “system” in which each member conformed to norms of probity and sound management and in return benefitted from help given by other members should a crisis beset it. This newfound stability encouraged people to deposit their savings in banks rather than stuff the funds in their mattresses. By investing the money, banks became an institutional “storage technology” that not only gave their depositors a degree of assurance that their funds would be available to them in the future, but also that a sum of interest would be earned on the deposit.
The key in applying economic concepts to history is to understand the cumulative link which the past has to the present. Storage technology enables the creation of stocks that connect past and present in complex ways never imagined possible by the ancients. They lived season-to-season, and even day to day. Such bucolic simplicity is no longer a realistic component of our lives. We have left Walden Pond so that we might gain the power to shape our futures. This quest has forced us to think in a new manner about what happiness means in a world of change. The economic analysis of this quest for happiness in new and turbulent settings is mundanely labelled as “intertemporal optimization”. As we have seen, the challenges this analysis poses are anything but mundane.