Tuesday, February 28, 2012

Population Dynamics and Nonlinearities in Economic Systems

Population Dynamics and Nonlinearities in Economic Systems Edward Hugh Florence : February 2012


• What follows is highly eclectic
• What Jean Francois Lyotard called grand narratives can seriously damage your health (together with that of those around you).

What Is Neoclassical Economics? According to a widely accepted view the neoclassical approach to economics rests on three basic assumptions, which may be elaborated in a variety of ways according to the nuances the exponent seeks to emphasise: • People have rational preferences among outcomes that can be identified and associated with a value. • Individuals maximize utility and firms maximize profits. • People act independently on the basis of full and relevant information.

And Macroeconomics?

"God put macroeconomists on earth not to propose and test elegant theories but to solve practical problems." Gregory Mankiw.

Macroeconomics is the modern descendent of two earlier lines of economic research: business cycle theory and monetary theory. Its best known early exponent was John Maynard Keynes, who attempted to derive a general theory of the economy that described the whole in terms of aggregates and their movements rather than building an overall picture starting from individual microeconomic components and then working up on an additive basis. In fact Keynes himself did not develop a workable and testable model from his General Theory, and it was left to one of his early followers, John Hicks, to develop a simplified, but more concrete “toy” model, the IS-LM framework. Life then went quietly along its course until, in 1976, Robert Lucas published a paper which effectively blew a hole straight through the midships of the Keynesian economic consensus which had dominated macroeconomic thinking since the days of the late 1940s when Paul Samuelson wrote his famed textbook.

And Macroeconomics II

Lucas’s highly influential paper effectively revolutionised modern economic thinking. He criticised the earlier large-scale Keynesian models widely used in forecasting and policy evaluation by arguing that economic models based on observed empirical relationships between variables tend to be of limited value given that the government policies which underpin them constantly change and a relationship which holds under one policy regime may no longer do so under another. In fact, Lucas’s argument could be turned against virtually any model based on the evaluation of historical time series. But this was not his objective. Lucas was focused on the role played by expectations in the movement of large economic aggregates, and he argued that generalisation about policy is difficult, since the impact of any given policy is critically determined by how that policy alters the expectations of the various economic agents involved.

Lucas formed part of what came to be known as the freshwater (sometimes sweetwater) school of economists, composed primarily of macroeconomists who, starting in the early 1970s, began to challenged the prevailing Keynesian consensus in macroeconomic research. The key element in their approach was the idea that macroeconomics had to be dynamic, quantitative, and based on how individuals and institutions make decisions under conditions of uncertainty. In other words, economic systems needed to be modelled from the bottom up, and not from the top down as the earlier Keynesian tradition had done.

There is no doubt that as a result of the work done by new neoclassical theorists like Lucas the field of macroeconomics had all the appearance of becoming increasingly rigorous, using ever more sophistocated mathematical techniques, and was wedded ever more closely to the basic tools of microeconomics. What was left in doubt from the start, and remains without an answer today, was whether the all that extra rigour and all the mathematical sophistication did not come at a price – a steady loss of realism, and distanciation from day to day economic reality. We have still yet to see testable models that enable us to predict, or foresee anything interesting about real world economies, and this surely is where the dividing line between science and “doxa” (or mere opinion) has to lie.

So while it was comparatively easy for proponents of the New Classicism like Lucas and Thomas Sargent to ridicule early Keynesian work - “For policy, the central fact is that Keynesian policy recommendations have no sounder basis, in a scientific sense, than recommendations of non-Keynesian economists or, for that matter, non- economists,” they said in one paper (1979) - they also had to recognise that their own approach was not able to generate a model that would be worth taking to Washington: “We consider the best currently existing equilibrium models as prototypes of better, future models which will, we hope, prove of practical use in the formulation of policy.” At the time they thought about a decade might be needed, but as it happens the world is still waiting. Keynesian economists responded to this critique by building more elaborate models of their own based on the incorporation of microeconomic foundations. Such approaches have often been termed the “New Neoclassical Synthesis”. Like the neoclassical-Keynesian synthesis of an earlier generation, the new synthesis attempts to merge the strengths of the competing approaches that preceded it. From the new classical models they took the tools of dynamic stochastic general equilibrium theory. Preferences, constraints, and optimization formed the starting point, with the analysis being steadily built up from such microeconomic foundations.

Yet it still remains unclear just how useful all this has been.

Gregory Mankiw has summed the situation up as follows:

“As a matter of science, there was much success in this research (although, as a participant, I cannot claim to be entirely objective).... but..... was this work also successful as a matter of engineering? Did it help policymakers devise better policies to cope with the business cycle? The judgment here must be less positive”. Hence he concludes: “There is also a less sanguine way to view the current the current state of play. Perhaps what has occurred is not so much a synthesis as a truce between intellectual combatants, followed by a face-saving retreat on both sides. Both new classicals and new Keynesians can look to this new synthesis and claim a degree of victory, while ignoring the more profound defeat that lies beneath the surface”.

Is This Obsession With Establishing Micro Foundations Really Helping Us Get Empirically Useful Results? 

“The Wheels Of Metaphysics Turn And Turn, But There Appears To Be No Motion In The Drive Shaft” – Gilbert Ryle (British Philosopher).

So we come to the real question I am trying to ask in this presentation. At the end of the day I am not convinced of the usefulness of the kind of micro foundations modern macroeconomists have been working with in the context of the general objectives Keynes set himself for macroeconomics, which was to improve our understanding of the factors that drive movements in broad economic aggregates, with a lick and a promise about being able to do something useful to counter the impact of deep recessions and depressions. I am also not clear what relationship the day to day grind of applied macro analysis has with the models built by theoretical macroeconomists using these aforementioned foundations.

From the standpoint of science, the greater rigor that the new classicals offered has much appeal. But from the standpoint of engineering, the cost of this added rigor seems too much to bear.

Gregory Mankiw “If economists could manage to get themselves thought of as humble, competent people on a level with dentists, that would be splendid.” John Maynard Keynes Following a division Keynes himself sought to identify with his dentist analogy, Greg Mankiw talks of economists as being either scientists or engineers.

I think at the end of the day this dichotomy fails to satisfy our needs, as it seems to be based on a very restrictive and even problematic conception of what science actually is. In addition the idea that what neoclassical economists are doing constitutes science simply due to the logical and mathematical rigour of the reasoning process used seems questionable, since surely good science is characterised by its parsimony and realism when it comes to the kind of assumptions it makes (Occam’s razor) and the empirical validity of the sort of rational expectations assumptions which form the cornerstone of modern neoclassical theory has never really been adequately established.

Meanwhile, many of those who belong to what Mankiw would call the engineering branch of the macroeconomics, seem to find themselves more than able to do reasonably useful macroeconomic analysis, analysis which often gives results which have a more than a random degree of predictive efficacy, and normally they achieve this outcome without reference to any of those supposedly key “micro foundations”. On the other hand those who build and work with such cumbersome apparatus do not appear to be able to demonstrate a comparable track record. As is evident, science is not only defined by analytical rigour, it is also defined by the reproducibility of its experimental results (something which is impossible for economics, since the world itself is the laboratory), and the falsifyability of daring predictions advanced on the basis of hypotheses formulated following the adoption of a set of plausible initial assumptions. Actually the philosopher of science Karl Popper never questioned the rigour of psychoanalytic or Marxian methodologies, although he did consider them to be prototypical examples of what he termed “pseudo science”. Interestingly, his colleague Imre Lakatos considered neoclassical economics also to belong to this latter group mainly due to the failure of realism in initial assumptions and the absence of falsifiablity for its predictions.

The procedure of induction consists in accepting as true the simplest law that can be reconciled with our experiences – Ludwig Wittgenstein Put another way, if I am not doing “scientific” macroeconomics, I have at least a certain degree of curiosity to find out exactly what it is I am doing. One leading theoretical economist – Columbia’s Xavier Sala i Martin – recently suggested that it was me – and not the neoclassics - who was practicing astrology in claiming predictive power for simple models. Yet I could reply that I save myself a lot time and effort by simply cutting out what seems to me to be a lot of useless rigmarole. In particular, my simplified approach enables me to get very close to the actual data, and make easily testable empirical hypotheses, hypotheses which are often associated with straightforwardly falsifiable predictions. Naturally, this is not to say that the task of building up useful models which can adequately describe long term movements in macroeconomic aggregates is in principle impossible, but merely to argue doing so with the current generation of simplifying assumptions, and the mathematics available does not appear to be possible. One comparison which could be made would be between machine and human translation.

Exact reproduction of meaning seems not to be possible using the existing technology, but this does not mean it never will be. In the meantime interpreters are not in any danger of losing their jobs.

Macroeconomics is all about identifying patterns which are to be found in the economic system as a whole and studying the system properties which are revealed by those patterns, which are often discrete and distinushable from the properties and relationships of elements observed at the micro level. To give an example, the above chart, which was generated by my friend and colleague Claus Vistesen , describes a simple model built to illustrates relationships between external balances, export dependency and population age. The model incorporates predictions which are perfectly testable. We will return to relationships postulated here later in the presentation.

Robert Solow In His Nobel Speech “How to reconcile these two visions of the economy—one founded on Adam Smith’s invisible hand and Alfred Marshall’s supply and demand curves, the other founded on Keynes’s analysis of an economy suffering from insufficient aggregate demand—has been a profound, nagging question since macroeconomics began as a separate field of study”. – Gregory Mankiw One of the areas of economic research which interests me most is growth theory. Why do economies grow at a certain rate at one point in time, and another rate later? Is there any underlying process here to be grasped, or is everything simply the result of random stochastic shocks? Robert Solow, the founder of modern neoclassical growth theory, produced his seminal work on the subject as a result of similar preoccupations. As he tells us in his Nobel acceptance speech, he really started to think seriously about the issue by asking himself one simple question: Under what conditions is an economy capable of steady growth at a constant rate? He was worried by the conclusion he drew from the assumptions made by his predecessors, assumptions that seemed to lead to the discomforting conclusion that instability was so inherent that “the possibility of steady growth would be a miraculous stroke of luck”.

This worry was what eventually lead him to formulate his now famous theory which links growth in labour and capital with the impacts of technological change. Solow tells us he was concerned about the inherent instability which was associated with the earlier Harrod Domar model, and in particular with the kind of instability associated with disequilibrium behavior, implying that there was no guarantee that an economy which once strays from an equilibrium growth trajectory would ever automatically find its way back to any equilibrium growth path. As he tells us, solving this problem really meant finding a way of integrating short-run and long-run macroeconomics, of bringing together growth theory and business-cycle theory. This very much takes us back to the kind of foundational issues which so concerned Keynes, and lead him to lay the foundations for the distinct discipline of macro economics. Early Keynesians, such as Samuelson, Modigliani, and Tobin, thought they had reconciled these visions in what is sometimes called the “neoclassical-Keynesian synthesis.” These economists believed that the classical theory of Smith and Marshall was right in the long run, but the invisible hand could become paralyzed in the kind of short run described by Keynes.

This kind of solution did not satisfy Solow, and, as he informs us in his Nobel speech, the problem of combining long-run and short-run macroeconomics , despite all best efforts, has still not been adequately solved. Not that, as he notes, there have not been some ingenious attempts. “One important tendency in contemporary macroeconomic theory evades this problem in an elegant but (to me) ultimately implausible way. The idea is to imagine that the economy is populated by a single immortal consumer, or a number of identical immortal consumers. The immortality itself is not a problem: each consumer could be replaced by a dynasty, each member of which treats her successors as extensions of herself. But no short- sightedness can be allowed. This consumer does not obey any simple short- run saving function, nor even a stylized Modigliani life-cycle rule of thumb. Instead she, or the dynasty, is supposed to solve an infinite-time utility- maximization problem. That strikes me as far-fetched, but not so awful that one would not want to know where the assumption leads”.

“The next step is harder to swallow in conjunction with the first. For this consumer every firm is just a transparent instrumentality, an intermediary, a device for carrying out intertemporal optimization subject only to technological constraints and initial endowments. Thus any kind of market failure is ruled out from the beginning, by assumption. There are no strategic complementarities, no coordination failures, no prisoners' dilemmas”. The tendency Solow is referring to is that best represented by the work of Nobel Laureate Edward Prescott, as exemplified most notably in his 1982 paper with Finn Kydland “Time to Build And Aggregate Fluctuations”. Solow was not convinced, and draws the conclusion that “historical time series do not provide a critical experiment”. We will return to this point.

No one could be against time-series econometrics. When we need estimates of parameters, for prediction or policy analysis, there is no good alternative to the specification and estimation of a model. To leave it at that, however, to believe as many American economists do that empirical economics begins and ends with time series analysis, is to ignore a lot of valuable information that can not be put into so convenient a form. Skepticism is always in order, of course. Insiders are sometimes the slaves of silly ideas. But we are not so well off for evidence that we can afford to ignore everything but time series of prices and quantities. Growth theory was invented to provide a systematic way to talk about and to compare equilibrium paths for the economy. Robert Solow

It will not do simply to superimpose your favorite model of the business cycle on an equilibrium growth path. That might do for very small deviations, more in the nature of minor slightly autocorrelated "errors." But if one looks at substantial more-than-quarterly departures from equilibrium growth, as suggested for instance by the history of the large European economies since 1979, it is impossible to believe that the equilibrium growth path itself is unaffected by the short- to medium-run experience. So a simultaneous analysis of trend and fluctuations really does involve an integration of long-run and short-run, or equilibrium and disequilibrium. Robert Solow

The most interesting case to consider is one where real wage and rate of interest are stuck at levels that lead to excess supply of labor and goods (saving greater than investment ex ante). The economy may eventually return to an equilibrium path, perhaps because "prices are flexible in the long run" as we keep telling ourselves. If and when it does, it will not return to the continuation of the equilibrium path it was on before it slipped off. The new equilibrium path will depend on the amount of capital accumulation that has taken place during the period of disequilibrium, and probably also on the amount of unemployment, especially long-term unemployment, that has been experienced. Even the level of technology may be different, if technological change is endogenous rather than arbitrary. Robert Solow

The main result of Malinvaud's analysis is a clarification of the condition under which a "Keynesian" steady state is possible, and when it is locally stable, i. e. when it will be approached by an economy disturbed from a nearby equilibrium path. The unstable case is just as interesting, because it suggests the possibility of small causes having big results. All these stability arguments have to be tentative because the interest rate and real wage are assumed to be fixed while quantities move. That is not an adequate reason to dismiss the results in a purist spirit; but obviously the research program is not complete. My own inclination - it is just an inclination - is to try a slightly different slant…. The obvious alternative to a model with sticky prices is a model with imperfectly competitive price-setting firms. Then, of course, one can no longer speak in any simple way of excess supply of goods. But we can find something just as interesting; the possibility of many coexisting equilibrium paths, some of which are unambiguously better than others. Robert Solow

In my 1956 paper there was already a brief indication of the way neutral technological progress could be incorporated into a model of equilibrium growth. It was a necessary addition because otherwise the only steady states of the model would have constant income per person and that could hardly be a valid picture of industrial capitalism. Technological progress, very broadly defined to include improvements in the human factor, was necessary to allow long-run growth in real wages and the standard of living. Since an aggregate production function was already part of the model, it was natural to think of estimating it from long-run time series for a real economy. That plus a few standard parameters - like saving rate and population growth - would make the model operational. Robert Solow

At one point in his paper Solow does examine whether the model could be applied to a case where population movement was endogenous rather than exogenous. His conclusion was that it could, but the explanation he offers is indeed interesting: “Instead of treating the relative rate of population increase as a constant, we can more classically make it an endogenous variable of the system. Suppose, for example, that for very low levels of income per head or the real wage population tends to decrease; for higher levels of income it begins to increase; and that for still higher levels of income the rate of population growth levels off and starts to decline”. What Solow postulates here is a kind of U shaped function, part of which roughly corresponds to what we could call the "Malthusian era" when population levels fluctuated as real wages (or income per head fluctuated), and part of which offers a first approximation to the modern growth era, in the sense that fertility (and hence population levels) tends to decline as income rises. But between these two fertility "regimes" there would seem to be a clear break, since what has not been observed (anywhere) is that as incomes fall back subsequent to the transition from one regime to another then fertility rises. Normally we find (in post Malthusian population environments) that as living standards fall, even in the longer run fertility also itself tends to fall.

Looking At The Limitations? To try to illustrate some of the difficulties which arise when researchers employ a theory of economic decision making and optimization based on the rational expectations hypothesis when attempting to account for long term movements in aggregate macroeconomic phenomena I will offer three examples derived from: • Currency Theory • Current Account Imbalances • Growth Theory “If It Doesn’t Work, Throw It Away” - American Pragmatist.

Equilibrium Currency Theory Perhaps one of the first people to think seriously about the problem of how monetary and fiscal policy would work in an economy in which capital flowed freely in and out in response to differences in interest rates was Robert Mundell, back in the 1960s. Mundell came to the conclusion that everything depended on what that country did about its exchange rate. If, for example, a country insisted on maintaining the value of its currency in terms of other nations' monies constant, monetary policy would become entirely impotent. Only by letting the exchange rate float would monetary policy regain its effectiveness.

This lead him later to broaden this initial insight by proposing what has become widely known as the concept of the "impossible trinity" – free capital movement, a managed exchange rate, and an effective monetary policy (Mundell, 1968). The trinity is impossible because a country can pick two (and only two) of the three. A country can fix its exchange rate without emasculating its central bank, but only by maintaining controls on capital flows; or it can leave capital movement free but retain monetary autonomy, but only by letting the exchange rate fluctuate; or it can choose to leave capital free and stabilize the currency, but only by abandoning its ability to control the movement of interest rates to fight inflation or recession. Key to the impossible trinity idea was the assumption that if there was free capital movement, and a floating exchange rate, macroeconomic stability in a small open economy could be ensured by the application of an adequate monetary policy. Many of the contemporary critics of the common Euro currency tend to work on this assumption – namely if the economies on Europe’s periphery had their own (floating) currency, and an appropriate monetary policy, then all would be for the best in the best of all possible worlds. Would that life were so simple!

Let’s Take A Look At Some Examples Columbian Peso New Zealand Dollar Swiss Franc Japanese Yen

The four examples in the last slide are not chosen at random. They provide clear, but not isolated examples of countries whose currencies, although floating, have fluctuated in what might be termed a counter intuitive fashion. The first pair, Columbia and New Zealand, provide examples of the case where, in a world which is awash in liquidity and permanently being swept by what Nouriel Roubini evocatively terms a “wall of money”, the application of conventional monetary policy (raising interest rates to curb overheating domestic demand) proves counterproductive, since it produces a “perverse” outcome – namely that a self reinforcing process is induced whereby inbound capital flows overheat domestic demand, and then the rising interest rates which are applied as a “cooling mechanism” only serve to attract an even stronger inward capital flow (due to the interest rate differential and the continually rising currency) which causes the central bank to raise interest rates even further, etc, etc, etc. Naturally such processes only go on for as long as they do, and then end in tears.

The second pair offer examples of what are often termed “safe haven” or “funding” currencies. This phenomenon arises in the context of mature economies which suffer from congenitally weak (see below) domestic demand which leads to either very low domestic inflation, or even deflation. Under these circumstances the respective central banks are constrained to maintain interest rates very near to what is termed the “zero bound” – again the perpetuation of this situation as a lasting one is certainly not contemplated under the standard neoclassical models. The assurance of very low interest rates over extended periods of time turns the currencies in question into funding currencies for what has become known as the “carry trade”. This trade operates on the basis of the anticipated interest rate differential between the funding country and the destination one (Columbia, or New Zealand, for example). As long as the global economy is in what is known as “risk on” mode, that is to say the risk sentiment level is high, then the funding currencies trade at values which are significantly below “economic fundamentals fair value” due to the fact that investors borrow in the currency and then sell to invest elsewhere. This mechanism drives the currency down.

However, when the global economy goes into “risk off” mode, and risk sentiment falls to very low levels, as happened during the Global Financial Crisis, this carry trade unwinds, and as investors buy the funding currency in order to close their positions that currency gets driven up to very high levels. This is precisely what has happened to both the Japanese Yen and the Swiss Franc during the first decade of this century. The consequences of this phenomenon for the domestic economies of both countries have been important. While the Yen was at a low value, Japanese exports drove the economy, and indeed such were the cost advantages that Japanese companies even relocated back home. Now, the situation is very different, since as the “Japanese disease” has spread, zero bound interest rates have become the norm rather than the exception in the developed world, with the consequence that both the Yen and the Swiss Franc have lost their pride of place as funding currencies of reference, while at the same time the “safe haven” status of the respective currencies in times of financial turbulence such as that associated with the current European Debt Crisis means that the currency is driven up rather than down.

In fact, the ideal carry trade needs to be symmetric (to optimise earnings), in the sense that as the destination currency gets driven up, the funding one should ideally be forced down. This means that the Euro is a much more desirable funding currency in the current environment than the Swiss Franc is, while the USD is obviously preferable to the Japanese Yen. Naturally, the consequences of this situation have been little short of disastrous for the Japanese economy, and the country has, for example, totally lost out to Germany in the key Chinese market. Exports have not returned to anything like their pre crisis levels, and the economy constantly flirts with recession.

On the other hand the Swiss Franc has been under constant pressure throughout the eurozone crisis, as the currencies safe haven status has attracted EU citizens anxious to seek protection from any possible knock on effects were Greece to exit the common currency. The Swiss National Bank has pegged the currency to the Euro and been directly and indirectly intervening in the market to maintain the peg. However, such was the fear aroused by electoral stalemate in Greece that the Swiss authorities admitted they were contemplating inbound capital controls if the situation deteriorated. Of course the hypothetical fragmentation of a large currency bloc is hardly a normal situation, but it is interesting to note the way in which the issue of capital controls has gradually shifted from one of avoiding capital flight to one of avoiding “over abundance”.

Far From Finding A Stable Equilibrium Path,In General Most Contemporary Currencies Are Either Systematically “Undervalued”” or “Overvalued”. Very Few Currencies Today Find What Used To Be Termed A “Fair Value”. Basically if you want to understand currency movements you need to understand the operation of the economic system at a global level. Simple knowledge of local conditions doesn’t necessarily help. You need to start at the top and work down, not from the bottom and work up. Or maybe you need to work from both ends and find out where they meet and interact. Global economics is “holistic”, and treats the global economy as a system. Studying the properties of “small open economies” in the abstract and building up from the bottom offers a poor guide.

Global Financial Accelerator – Carsten Valgreen. Latvia Iceland

Perhaps the first to note this “perverse” raising interest rates, revaluing currency stimulating credit growth circularity phenomenon was the Danish economist Carsten Valgreen – and he termed the phenomenon the “Global Financial Accelerator”. The thought involved is the following: real economic decision makers are increasingly isolated from local monetary conditions and more exposed to global monetary conditions and credit extension willingness (or, if you prefer, global risk sentiment).

As Valgreen says: “Take an arbitrary example: A Polish household wants to buy a second home in France. To do this they contact their local bank (which happens to be the subsidiary of a Swedish based banking corporation) in order to obtain mortgage finance. They then chose to borrow the money in Swiss Francs and Yen. This action is likely to have a large impact on the future income streams and net asset value of this Polish household, and – hence – its future behaviour in the real economy. However, as long as free capital flows are maintained the Polish central bank has limited influence on the transaction. None of it is in PolishZloty. And the credit decision of the private banking corporation extending the credit is taken based on a credit model maintained in Stockholm in Sweden”. “What will matter for the family is the future currency and rate moves in Swiss Francs and Yen. And the price developments for second homes in France. Andperhaps also the future credit attitude of a Swedish based credit institution”

The point of Valgreen’s example is to show just how powerless national monetary policy can actually become in small open economies in a world of fluid cross border financial flows. He goes on to illustrate his point by referring (in mid 2007, before the global financial crisis broke out) to two countries which were later to gain a certain notoriety. As he points out, neither the Icelandic nor the Latvian central bank would have been able, using simple recourse to conventional monetary policy tools to control the rate of credit extension in their countries, despite the fact that one country had floating exchange rates while the other had a currency peg. The Icelandic central bank could control the interest rate on Icelandic kronur. But that did not matter much for households, non-financial companies or banks borrowing funds in foreign currency. Neither does it seem to matter too much today that the official currency of Croatia is the Kuna, since the country has one of the most Euro-ised economies outside the actual Euro Area. As Valgreen argues in the Icelandic case, as long as the banks have a high credit rating and are perceived as sound by the international markets, credit flows easily to them in a liquid global environment. “Perversely”, he noted, “it even seems as if a stronger currency stimulates the Icelandic economy in the short run, as consumer spending reacts to increasing external buying power and as exports are concentrated in price insensitive commodity sectors.

“In the world of economics and finance, revolutions occur rarely and are often detected only in hindsight. But what happened on February 19 2010 can safely be called the end of an era in global finance. On that day, the International Monetary Fund published a policy note that reversed its long-held position on capital controls. Taxes and other restrictions on capital inflows, the IMF’s economists wrote, can be helpful, and they constitute a “legitimate part” of policymakers’ toolkit”. Dani Rodrik Capital Controls To Stop Inflows?

Another Theoretical Puzzle, Just Why Did Those Famous “Global Economic Imbalances” Build Up? As is well known, one group of countries - Japan, Germany and China – were running substantial current account surpluses in the years prior to the Global Financial Crisis. Another group – who we may call the debtor countries, in particular the UK, the US and Spain – ran substantial external deficits.

One Hypothesis - Could Something As Simple As Median Population Age Help Us To Understand? . Ours is an age of rapidly ageing societies. What is so modern about our current situation is not the ageing itself, but its velocity, its global extension, and the differing rates even between countries in the same group (developed economies, emerging markets, less developed economies etc.) Leaving aside the cases of China and Italy, many of the advanced countries running surpluses had notably higher median ages than those running deficits. The former group had median ages well over 40, while the latter group were typically in the range 35 to 40. Is there an association here?

.Median Age And The Imbalances As mentioned previously, the current account appears to show a non linear relationship with median population age, with the later also being reflected in the level of export dependency versus credit expansion involved in the attainment of economic growth. This hypothesis has been explored by the young Danish economist Claus Vistesen.

Steady State Growth?.

All theory depends on assumptions which are not quite true. That is what makes it theory. The art of successful theorizing is to make the inevitable simplifying assumptions in such a way that the final results are not very sensitive.' A "crucial" assumption is one on which the conclusions do depend sensitively, and it is important that crucial assumptions be reasonably realistic. When the results of a theory seem to flow specifically from a special crucial assumption, then if the assumption is dubious, the results are suspect. Robert Solow, A Contribution To the Theory of Economic Growth, 1956 Economic growth is an issue that has attracted economists’ attention ever since the phenomenon became really evident following the onset of the industrial revolution, but it was not until the middle of the last century, under the impact of the great depression in the US that theoretical economists really started to ask the question why continuous economic growth could be expected.

Steady State Growth II.

Today we take it for granted that this is just the way things are, and after each recession we expect a recovery almost automatically. But things weren’t always this way, and for thousands of years before the industrial revolution economies barely grew. So the idea that there should be growth is not an entirely self evident one, and, indeed, growth theory itself grew out of a historical episode where for more than a decade it seemed hard to believe that growth would eventually come, just like manna from heaven. The early attempts to systematise growth theory were born from an environment where it seemed more plausible to speculate that capitalist economies were doomed to permanent breakdown, or at least to the possibility of one serious breakdown after another. Few were willing to believe that financial and product markets provided a near permanent correction mechanism, and theorists rather than wondering why there was stability were more concerned with why there was so much instability.

Steady State Growth III. As Solow himself says about the early growth models, “An expedition from Mars arriving on Earth having read this literature would have expected to find only the wreckage of a capitalism that had shaken itself to pieces long ago”. However, despite the irregularities and evident vicissitudes of the business cycle. Solow was convinced that sufficient evidence was available to support the idea that some sort of stable long term growth path did in fact exist for developed economies, and thus he sought to produce a model which could illustrate how this might be. At this point it is worth emphasising that while there is at times ambiguity in Solow’s own writing – he often talks about an equilibrium growth path, while allowing that there may be more than one of these – he never in fact makes the assumption made by many modern representatives of the neoclassical growth tradition that the steady state growth path towards which a given economy will tend to converge involves a relatively constant rate of growth. That is to say, he leaves open the option that along the steady state, or balanced growth path the rate of growth may vary, and may even do so in a systematic fashion. That is the possibility I wish to explore here.

Steady State Growth IV. As he tells us, his attention was attracted to the various kinds of growth instability which seemed inherent in the earlier models. Naturally, as a good neoclassic Solow needs to use the term equilibrium (rather than balanced, or sustainable, or simply trend) growth path, “Growth theory,” he says, “was invented to provide a systematic way to talk about and to compare equilibrium paths for the economy”. However once we strip out such standard neoclassical vocabulary, it is easy to see that what really interested him was modelling why an economy which deviated from its balanced path should generally correct back to either that path or another similar one. Why, for example, once a given economy had strayed from what had been its trend path should it not head for catastrophe, or simply enter a period of terminal decline, or decadence. Argentina in the 20th century (not the 21st) has often been thought of as the archetypal case for such decline, since it moved from being a comparatively wealthy country to being a relatively poor one, although it should be noted that the position is only relative: Argentina’s economy still grew over the century. But why should this be an atypical, and not a typical phenomenon? Why should economies grow over time, and do so in a regular fashion?

Homeostasis This then was Solow’s starting question, and as becomes evident once we start to think about what is happening to developed economies post the Global Financial Crisis, it was a good one. According to standard growth theory, once the steady state growth rate is achieved any external perturbation which sends the economy off its growth path will only have a temporary (or transitional) impact before assumed homeostatic mechanisms send it back on course. In more conventional language, once the equilibrium growth rate is achieved, it should be stable, absent external shocks, since regardless of the initial value of key parameters like the capital-labour ratio, the system will exhibit a tendency to develop toward a state of balanced growth. Naturally the key here is the idea of homeostasis, better known in an economic context by its euphemism “the hidden hand”. If there is not some sort of automatic regulatory mechanism then there is no good reason why the system should not randomly veer off its path, never to return. However, as we will see when we come to think about population dynamics, it is not clear that any such overarching homeostatic mechanism actually exists in the longer run. It could thus be the case that the modern economic system is only locally stable since it incorporates components which are inherently unstable in the longer run.

Exogenous Variables The fundamental distinctive feature of Solow’s model is his assumption is that growth is exogenously determined – in other words, it is determined outside of the model – in this case by rates of saving and rates of population growth which take place in an environment characterised by a series of more or less random technological shocks. This is the leading “plausible” assumption Solow made when setting up his model. The basic idea is that the rate of growth of any economy in the longer run is effectively determined by the rates of growth of the labour and capital inputs which are themselves assumed to grow at a given relatively constant rate. Solow considered both population growth rates and savings rates to be behavioural variables which in mature economies vary from one country to another according to national characteristics. Thus along balanced paths growth rates vary from one country to another according to the values associated with these behavioural parameters, but in the case of a given country, once attained the steady state growth rate doesn’t fluctuate significantly.

Of course, it is important to understand that we are talking about models here, and simplifying assumptions which are made in building them. At the end of his path breaking paper Solow did consider other cases where rates of both population growth and saving might vary, and we will return to this possibility.

Steady State Growth VI. Solow’s basic workhorse model can be formalised in the following way: Y = f(K,L) Where Y is national output (or GDP), K is capital, and L is the labour force. Really the idea conforms to our most basic intuitions, in the sense that economies grow as the capital base expands and employment grows. Naturally, these intuitions also tell us that something is missing, otherwise, for example, the old soviet-style economies where emphasis was placed on increasing capital investment and putting growing numbers of people to work (including for example the female labour force) would have had the best growth performance of all, which manifestly they didn’t. The missing ingredient was evidently productivity, which is simply a relational variable which describes how the two basic ingredients are combined. Rather like a good cocktail, the outcome depends not only on the raw materials applied, but the shaker used, and who does the shaking.

“A balanced growth path in the neoclassical growth model is defined as a situation in which all quantities grow at constant exponential rates (possibly zero) forever”. Charles Jones For the sake of modelling simplicity an additional assumption is often made that the function has a specific form, namely that the parameter coefficiants add up to 1. This function is known to economists as a Cobb– Douglas one. In the above version of the function Y represents total economic output, A represents multifactor productivity (often generalized as technology), K is capital and L is labour. The Cobb Douglas assumption is a kind of stability ensuring one. As Solow says: “The basic conclusion of this analysis is that, when production takes place under the usual neoclassical conditions of variable proportions and constant returns to scale, no simple opposition between natural and warranted rates of growth is possible. There may not be- in fact in the case of the Cobb-Douglas function there never can be – any knife edge. The system can adjust to any given rate of growth of the labour force, and eventually approach a state of steady proportional expansion.

If, to take a different case production functions exhibit non-constant returns to scale in all factors, then the very existence of a balanced growth equilibrium path requires the production function to be a Cobb- Douglas one. Or as Charles Jones says: “The use of the word “balance” is suggestive in another way. In particular, consider the familiar phrase “balanced growth path” and ask what it is that is balanced along such a path. What must be ‘balanced’ to get a steady state with positive and constant factor shares? The answer is the growth rates of the two effective inputs, BtKt and AtLt. If one effective input grows faster, a trend is induced in the factor shares unless the production function is Cobb-Douglas.” Charles Jones Essentially it is this coefficient summing-to-one condition which guarantees the balance, otherwise growth in the model would either shoot down to zero or up exponentially towards infinity following an increase or decrease in one of the effective inputs.

Steady State Growth VII Now while the question of having the long run growth rate determined outside the model by national saving and population growth rates leaves us with a feeling of frustration over the scope of the Solow model, the external shock role given to technology seems to confound even our most basic intuitions about growth, since it is evidently the case that the function of a part of the labour and capital put to work inside the model is to generate just this techological change. In just the same way as more resources devoted to investment could be thought to generate employment and growth in the longer term, so more resources devoted to R&D would seem to do likewise. Always assuming of course the proviso – and this is a big proviso – that such investment and such research is “warranted” and profitable. This issue of the role of human capital in generating productivity/technology did in fact give rise in the first place to a whole generation of neoclassical growth models, and later to a wave of “new growth theory”.

The intent of this new wave of theory is perhaps best expressed in a recent paper by two of the movements best known exponents, Paul Romer and Charles Jones. “The very narrow focus of the neoclassical growth model sets the baseline against which progress in growth theory can be judged. Writing in 1961, Kaldor was already intent on making technological progress an endogenous part of a more complete model of growth.......Growth theorists working today have not only completed this extension but also brought into their models the other endogenous state variables excluded from consideration by the initial neoclassical setup. Ideas, institutions, population, and human capital are now at the center of growth theory. Physical capital has been pushed to the periphery”.

For thousands of years, growth in both population and per capita GDP has accelerated, rising fromvirtually zero to the relatively rapid rates observed in the last century. Jones & Romer document this argument with the above chart, which shows population and per capita GDP for “the West”—an amalgam of the United States and twelve western European countries for which Maddison (2008) reports data going back 2,000 years. Plotted on a linear scale, the by-now-familiar “hockey stick” pattern would be highlighted, where both population and per capita GDP appear essentially flat for nearly two thousand years and then rise very sharply in the last two centuries. We’ve chosen to plot these two series on a logarithmic scale instead to emphasize the point that the rates of growth — the slopes of the two series—have themselves been rising over time. More people lead to more ideas. For most of human history,more ideasmade it possible for the world to supportmore people. In a dynamic version of themodel used to explain Fact 1, this simple feedback loop generates growth rates that increase over time. Of course, it is biologically impossible for the population growth rate to become infinitein finite time. At some point, human fertility can’t keep up. This leads to a second way to close the model. One can relax the assumption that population adjusts instantaneously to drive income down to subsistence and replace it with an economic model of fertility. At low rates of growth and low levels of income, desired fertility may be able to keep up with new ideas, so per capita income remains close to the subsistence level and population growth accelerates. Eventually, though, fertility and population growth level out. Growth in per capita income then accelerates until it reaches modern rates.

The acceleration of population growth and per capita growth are striking bits of time series evidence that support the feedback between population and ideas. There is no comparable cross sectional evidence at the level of individual nations because economic integration lets countries of widely varying sizes draw from a shared pool of ideas. Until India reformed its trade and investment laws, workers in tiny Hong Kong may have had access to more ideas than workers in much of India. Looking forward, virtually all demographic projections call for the number of humans on earth to reach a maximum in this century, which may lead to a slowing of growth in technology. Many forces could offset this change. The effective number of people with whom each individual can share ideas could grow through more intense integration. The total number of people living in cities will continue to grow long after total population has begun its decline. Barring some drastic political setback, the trade and communication links between all these cities will also grow tighter still. Rising levels of human capital per capita could make the average individual better at discovering and sharing ideas. If new institutions change incentives, the fraction of the available human capital that is devoted to producing and sharing ideas could go up fast enough to offset the decline in the total.

These forces have been operating in much of the OECD during the last half century and there is much room for each to have big effects as policies and levels of human capital in places like China and India come to resemble those in the OECD. For all these reasons, it is quite possible that growth at the technological frontier could continue for the foreseeable future and who knows, might even increase yet again in this century compared to the last. Nevertheless, this century will mark a fundamental phase shift in the growth process. Growth in the stock of ideas will likely no longer be supported by growth in the total number of humans. The textbook explanation for the rapid catch-up growth that we see in Japan, South Korea, and China is transition dynamics in a neoclassical growth model. A significant problem with this explanation, of course, is that it is based on a closed-economy setting where capital cannot flow across countries to equate marginal products. But international capital flows seem important in practice;................ The fact that rates of catch-up growth have been rising over time is difficult to understand in a pure neoclassical framework but is a natural occurrence in a world of ideas, where the technology frontier is relevant to what can be achieved.

Steady State Growth VIII Now this presentation is about growth, and how to think about it, not how to model it, so essentially I am going to skirt all these issues, and come to a piece of work by Gregory Mankiw, David Romer and David Weil, “Taking Solow Seriously” (1992), which has the merit of being perhaps the most influential paper on neoclassical growth theory after Solow’s own work. As they point out, growth in the Solow model is exogenous, because rates of growth of capital and rates of growth of labour depend on national savings habits and population movements, respectively. Since both of these are determined outside the model, and vary between countries, then different countries will exhibit differing growth paths. These are then Solow’s “plausible” assumptions.

Steady State Growth VI But, as they say, this very simplicity of set-up enables us to derive a couple of very basic predictions which flow from it, and test them. These are, the higher the rate of saving the richer the country, and the higher the rate of population growth the poorer.

Steady State = Constant? Now maybe this is a good point to address one of the possible confusions which arises from Solow’s work, and that is whether or not the concept “steady state growth” necessarily implies constant trend growth. Despite the fact that Solow himself uses the term “relatively constant” from time to time, it is quite clear that it doesn’t, and that Solow himself didn’t think that it did. To go no further, if economic growth rates are associated to some extent with population growth rates and these latter are by no means constant for any given country, then clearly the so called steady growth rate is something of a moveable feast. And if in addition, these movements in population growth rates are associated with shifting population age group proportions then, assuming Modigliani’s life cycle model of saving and borrowing, then save rates will be similarly affected. Nonetheless, this has not stopped many working economists assuming that steady state means something like constant.

One reason why people have fallen into this apparent trap has been the recent history of the US economy. Using data taken from Angus Maddison , the US economist Charles Jones estimated that the growth rate of the US economy between 1950 to 1994 was an annual 1.95 percent, which was slightly higher than the rate he derived for 1870 to 1929, which was 1.75 percent. However even these highly aggregated numbers conceal a considerable degree of variance, since the growth rate registered in the 1950’s and 1960’s - 2.20 percent - was considerably higher than that found during the Solow productivity slowdown of the 1970s and 80s, which was a "mere" 1.74 percent. Nonetheless, if we look at a chart for the 10 year moving average for US growth from the mid 1950s, well, the result does show relative stability and constancy.

Thus the the existence of such apparent stability in U.S. growth rates over such long periods of time has given considerable support to the "common sense" and conventionally accepted view that the U.S. economy is, and has been, running at close to what is considered to be some sort of long-run steady-state (or balanced growth) path. GDP growth is, of course, always volatile, but when you strip out some of the volatility the smoothness of the US path really is quite remarkable – especially when compared, as we will see, with that of many other countries - making it hardly surprising that many US economists have found the idea of relatively constant steady state growth a fairly plausible one.

Transitional Dynamics? One distinction which may help get address the problem is the one Jones himself makes between a constant and a balanced growth path. Along both such paths, growth rates remain constant over an extended period of time, but in the former case constant growth is simply the (coincidental) by-product of a process which is effectively driven by series of transition dynamics while in the latter what is involved is stable and self correcting since what we have is a steady state. A balanced growth path is normally defined as a situation in which all variables grow at constant geometric rates (possibly zero). (Jones, 2002 ) So we might like to consider one further possibility at this point. Could it be that the "as a matter of empirical fact" transition dynamics associated with the various factors of production in the United States have worked in some strange way to precisely offset one another, and in so doing leave the growth rate of output per worker fairly constant?

A One Off Demographic Transition? Now, as we have already noted, it is a key postulate of neo-classical growth theory that each economy has its own long run steady state growth rate. One of the consequences of making this sort of initial assumption (albeit as a purely hypothetical and theoretical one) is not in fact that hard to see, since the steady state assumption would seem to imply that as the demographic transition which produced those earlier "transitional dynamics" is left steadily behind (the demographic transition remember is associated with large fluctuations in levels and growth rates of population) then a steady growth rate in the labour force (achieved in part via institutional efficiencies in the labour market) and a supply of savings regulated by effective monetary and interest rate policy, should mean that any given economy would have its own given balanced growth rate, irrespective of key population variables like fertility rates and life expectancy.

. This neo-classical long run steady state growth rate needs, of course, to be understood as a theoretical postulate, a sort of ideal limit case, but nevertheless the concept continues to orient and inform a good deal of conventional economic thinking about economic growth. It also informs the way most people conceptualise and approach the present global economic crisis, since underlying one rescue and stimulus package after another is the idea that there is a long term trend growth rate out there somewhere, just waiting to be "recovered".

Just A Heuristic?

So Let’s Take Solow At His Word It was in some sense with this kind of issue in mind that Mankiw, Romer and Weil wrote what has since become a highly influential paper - A Contribution To the Empirics of Economic Growth - since they clearly felt the need to try to put neo classical theory onto a somewhat more stable footing. In their paper the authors outline what they see as the core of the Solow thesis using following words: This paper takes Robert Solow seriously. In his classic 1956 article Solow proposed that we begin the study of economic growth by assuming a standard neoclassical production function with decreasing returns to capital. Taking the rates of saving and population growth as exogenous, he showed that these two variables determine the steady-state level of income per capita. Because saving and population growth rates vary across countries, different countries reach different steady states. Solow's model gives simple testable predictions about how these variables influence the steady-state level of income. The higher the rate of saving, the richer the country. The higher the rate of population growth, the poorer the country.

Are The Assumptions Plausible?

The first thing to notice about the argument is that the Solow model clearly predicts two pretty straightforward and neatly linear relations: more population-less growth, and more saving-more growth. Now, we are immediately presented with an important difficulty here since, as we will see below, there is now a considerable and accumulating body of empirical evidence which seems to suggest that among "mature" developed economies, those who have the fastest rates of population growth are also those who experience the highest rates of per capita income growth (the United States is the most obvious example) but as we will see this is also the case of France and the United Kingdom.

Growth Function That Looks Like An Inverted “U” In those countries where population momentum has slowed, even to the point where their populations may now decline (Italy, Japan, Germany, for example) do not seem able to achieve their former high rates of economic growth, and, even worse, seem to be losing ground in per capita income terms with those economies whose populations continue to grow reasonably rapidly. Now I do not seek here to explore this question in all its intricate detail, I simply wish to make one clear and central point, and that is that the relations involved between population growth and per capita income growth do not seem to be simple linear ones, and arguably it is this property which has thrown many previous researchers off track since in running growth correlations they have normally tended to treat them as if they were.

.Running Out Of Energy?

Pre Capita Income In Higher Population Growth Economies .

.Versus Per Capita Income Growth In The Slow Population Growth Group

. High Median Age And Lower Median Age.

. Whoops, More Steady State Growth?

Either Steady State Growth Exists, Or It Doesn’t!

As Bernanke and Gurkaynak say in their paper on neoclassical growth, there are two and only two possibilities here: either the long- run growth rate is the same for all countries (that is, g(i) = g for all i), as maintained (following Solow) by MRW, or it isn't. Even more to the point, "explaining" growth by assuming that growth rates differ exogenously (or for factors which lie outside the model) across countries is not particularly helpful, especially since such changes in the growth rate seem to be systematic and not incidental. Once it is allowed that long-run growth rates not only differ across countries, but that growth processes in individual countries often do not exhibit properties which are normally associated with a balanced growth path ( that all variables do not grow at constant geometric rates, for example) then we are naturally pushed to consider explanations for these differences, and towards a fresh approach in our models.

What Might Population Ageing Have to Do With All This? As far as we are able to understand the issue at this point, population ageing will have major economic impacts and these can be categorised under four main headings: i) ageing will affect the size of the working age population, and with this the level of trend economic growth in one country after another ii) ageing will affect patterns of national saving and borrowing, and with these the directions and magnitudes of global capital flows iii) through the saving and borrowing path the process can influence values of key assets like housing and equities iv) through changes in the dependency ratio, ageing will influence pressure on global sovereign debt, producing significant changes in ranking as between developed and emerging economies.

Life Cycle Hypothesis There is a generally accepted wisdom in academic work known as the “life cycle hypothesis” (Modigliani). This suggests that the population’s financial behaviour changes depending on age. In terms of adult life, those in their twenties and early thirties tend to be net borrowers as they are relatively low earners at the same time as they look to buy housing, expensive durables and fund their burgeoning families. At some point around middle-age this group then tends to move from being net borrowers to net investors as they move into their economic prime and accumulate financial assets to hopefully fund their retirement. As they approach retirement this group then start to shed the financial assets they’ve been accumulating to fund their nonworking days.

Different Rates Of Ageing • The pace of aging varies greatly across countries and regions, • Most pronounced and rapid in those countries that for decades have had fertility rates below replacement levels - Japan, German speaking countries, Southern and Eastern Europe. • The median age of populations in Europe as a whole will most likely increase from around 38 today to 49 in 2050 (with significant differences between countries), and at this point it will be over 20 years above the estimated median age in Africa (which will be the youngest continent). • Spain - with half its population older than 55 by 2050 – is expected to become the oldest country in the world, followed closely by Italy and Austria, where the median age is projected to be 54. Causes Of Population Ageing - Second Demographic Transition This process of rapid ageing is due to the combined impact of two factors

1) Declining fertility Spain Total Fertility Rate

2) Steadily Rising Life Expectancy Many Societies – Like The Italian One Have Had Stationary Populations Ex-immigration

But The Population Pyramid Has Been Shifting, And Will Continue To Do So

Before The Crisis Immigration Drove The Italian Population And The Workforce Upwards

The Same Thing Happened In Spain But Then The Housing Bust Sent Everything Into Reverse Gear

Latvia Has Similar Problems Population has been falling, due to low birth rates and outward migration. But now the economic crash, and the absence of strong recovery, is accelerating the process as young people leave in search of work.

Tentative Conclusions 

1/. You can do meaningful applied, predictive and testable macroeconomics without reference to the theoretical rigmarole associated with mainstream neoclassical economics.
2/. Economies are complex systems, characterised by the presence of widespread feedback mechanisms and should be treated as such.
3/ Far from the ideal type entities generated by applying the model of classical physics to economics, economies are path dependent entities where the outcome depends very sensitively on initial conditions
4/ For this very reason forecasting future conditions is extraordinarily difficult, since they very often depend on what happens tomorrow, and the day after.
5/ Population projections are fairly easy to offer based on plausible assumptions about future trajectories for fertility and life expectancy, but in a world where the main mover of population numbers in the developed countries is international migration it becomes a very difficult and sensitive process.

I defy anyone to tell me what Spain’s population will be in 2020!

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