Random Shots

With course work coming up and with my internet connection just coming on-stream this weekend I hope that I can be forgiven for not posting in the past week. And now that I am I can only find the energy to move in with some random shots since a lot of things can and will happen in econ and finance land when you are away for a week or two. Yet, I still managed to pick up a couple of bits and pieces as I have settled in here across the (small) pond.

The Eurozone has its "does not compute" moment

First, it was there, then it left and then suddenly the Spanish prime minister Zapatero assured us that it was gone, but somehow the lingering European crisis of confidence in relation to the status of sovereign and private debt sustainability in key membership economies never seem to have gone away.

Now, please don't think that the headline above is in any way related to the flurry of whether Spain has been faking its GDP numbers. FT Alphaville ran the story, got cold feet and took it down (although I reckon you can easily find the report if you try). Now, the flurry was real and the questions asked by the report fair I think. Clearly, if it was such nonsense it should be easily refutable and while some of the explanations I have seen for the the sudden dis-correlation between the Market Services Gross Value Added (GVA) and the Indicator of Activity in the Service Sector (IASS/SSAI) make sense (especially the import component point) the Spanish statistical office is still mute and the ministry of finance is just playing the part of an insulted child. So, if those of us who are skeptic are so stupid then really, now is the chance for those much more clever than us to give us a lecture.

But I digress.

Moving on, Ireland has recently been at the center stage of things and the latest number from the finance ministry is that the butcher's bill for bailing out Anglo Irish amounts to more than 30% of GDP in the form of a running deficit in 2010. That is a almost unbelievable number by any standards and I would take very little comfort here in the fact that Ireland remains fully financed until mid 2011. What really matters here is that with this amount of debt overhang that needs to be transferred to the government's balance sheet and ultimately over to the private sector in the form of taxes Ireland is being played straight into the hands of the IMF and the European Stability Fund. But this is not only about Ireland since the all the fundamental questions are still left unanswered.

• How do you correct external competitiveness deficiency from within a currency union at the same time as implementing fiscal austerity without risking debt levels to spin out of control?
• How long should Southern Europe and Ireland endure deflation relative to the core to restore external competitiveness (will Germany accept a lower external surplus as result)?
• How might a sovereign restructuring in a Eurozone economy play out?

The last one is particularly important since no official inside the Eurozone has even begun to voice an opinion on this even if it is blatantly obvious that this is where we are headed. I mean, I am not talking about the entire stock of PIGS bonds being wiped out and marked to 0, but merely of a reasonable and fair estimate of the haircut we all know that is coming. Yet, so much water has gone under the bridge that it is difficult to see how such a memo would look. For starters, the stress tests carried out recently on Eurozone banks would have to be, uhm, redone with proper assumptions of haircuts and impairment in the context of real sovereign stress in the Eurozone.

However, what really clinched it for me and what leads me to note that we have now had one of (several to come) those does not compute moments was Wolfgang Munchau's basic bond arithmetic of the the European Stability Funds lending conditions and the means with which it allows access to its funds. From FT Alphaville ...

Münchau comes up with a rough estimate that borrowers could end up paying a total interest rate of about 8 per cent — far above and much more than the 5 per cent Greece paid when it tapped its €110bn European Union emergency loan back in May.

BarCap’s back-of-the-envelope calculations has the total borrowing cost above 8 per cent. That’s about 80bps (3m Euribor) + 300bps (EFSF mark-up) + 150bps (due to the fact that the interest has to be paid on the whole loan) + 300bps (service fees). As BarCap also note, requesting EFSF funds would also likely entail some strict policy conditions, similar to IMF conditionality.

Now, let me be quite clear here. 8% or even anything in that vicinity makes the whole exercise quite pointless since there is no way that any of the Eurozone economies would be able to pay off their debts at these conditions. So, if one or more Eurozone economies were to find themselves in a situation where they could no longer tap international bond markets due to the yield on offer, the alternative would be no better. I called this a catch 22 recently and even wrote a paper, in part, about it. However, Munchau's article makes it all so clear. Whatever funds that are paid out of the stability fund at these conditions would in itself be subject to a haircut in the context of an inevitable sovereign debt restructuring and thus it is really and ultimately a question of on whose balance sheet the final loss will be put. One would only hope that this soon will come to compute a little better with the agenda that will and has to emerge in the Eurozone at some point.

Some (academic) food for thought

As many of you might have noticed I am about to start my research degree here in the UK and I am looking forward to another round of neo-classical economics with all the lovely and unwordly math that such things entail. On that note and while the cracks have clearly not yet transcended to the way underlings such as myself are treated, I found the following paper (The Dahlem Report) interesting and important (thanks Scott for sending it over).

The economics profession appears to have been unaware of the long build-up to the current worldwide financial crisis and to have significantly underestimated its dimensions once it started to unfold. In our view, this lack of understanding is due to a misallocation of research efforts in economics. We trace the deeper roots of this failure to the profession’s insistence on constructing models that, by design, disregard the key elements driving outcomes in real-world markets. The economics profession has failed in communicating the limitations, weaknesses, and even dangers of its preferred models to the public. This state of affairs makes clear the need for a major reorientation of focus in the research economists undertake, as well as for the establishment of an ethical code that would ask economists to understand and communicate the limitations and potential misuses of their models.

Now, as an immediate testament to the importance of this paper and echoeing my points above I can say for certain that my generation of economists will be trained no differently on a PhD level than they were, I suspect, 30 years ago. Same old axioms, same old models, same booring (and often stupidly difficult) math problems. Two of the co-signers of the paper are David Colander and Alan Kirman and I recommend readers to have a look at their work if you want a good critique of the way we (still) do economics today (don't forget James E. Hartley too). I don't want to be a cry-baby, but surely; running through the proof of why a utility function should and might exist (in mathematical terms) is not only waste of good time, it is an insult to any serious economist eager to get on with some real work. But now, I really(!) digress.

To balance things a bit I did actually find much enjoyment in Oded Galor's recent synthesis of what really kicked off the demographic transition back in the days of the industrial revolution.

This paper develops the theoretical foundations and the testable implications of the various mechanisms that have been proposed as possible triggers for the demographic transition.Moreover, it examines the empirical validity of each of the theories and their signi…cance forthe understanding of the transition from stagnation to growth. The analysis suggests thatthe rise in the demand for human capital in the process of development was the main triggerfor the decline in fertility and the transition to modern growth.

Here in the 21st century such a paper essentially reads as a piece of economic history as the demographic transition never really ended and whereas some form of the quantity/quality tradeoff might have started the whole process, we are now dealing with a much more complicated process in which both a quantum and tempo effect acts as a driver of the fertility decline (and eventual or potential(?) catch-up as the tempo effect fades). However, Galor's recent paper provides an important finetuned representation of the way we think about the quantity/quality trade off and as such it is important.

I also take more than a passing interest here since it is after all my field and while I eventually opted for the original quantity/quality model by Becker and Lewis in my thesis I have almost been turned to Oded Galor's theory with this recent paper. Yet, the two theories are still ultimately very close to each other and for laymen the finer grained theoretic subtleties of the trade-off are not important.

Perhaps you should read Oded Galor first and then the Dahlem paper afterwards. Actually, yes you definitely should!

Macroeconomics, Representative Agents and Demographics (wonkish)

Upon first reading what I am pasting below, my thesis councillor opinioned that this particular piece of text was a malignant tumor that had to be surgically removed if the patient (in this case, my master's thesis) were to make it alive. I agreed with him back then and I still do, but I thought that the section was too interesting to be devoted entirely to the dustbin. Moreover, the debate on the state of macro has gotten new life on the back of the financial and economic crisis with a lot of interesting contributions in the past 2 years [1] and I wanted to add my own spin on, at least, part of the issues involved. 

The impetus for the the discussion below essentially came as I realized that the only way that I could meaningfully attempt to stand on the shoulders of giants in terms of mapping a relationship between ageing and capital flows was through the use of representative agent models and thus through the use of classic macroeconomic microfoundations. This is naturally logic for any trained macroeconomist, but I started out believing that my specific problem demanded a different theoretical approach and it lead to a discussion on the merits of the representative agent.

So without further ado ...

The Macroeconomics of Demographics, do we need micro foundations?

One key proposition for this thesis is that the demographic transition needs to be rethought or perhaps more aptly reformulated Edward Hugh (2006). Although this is certainly not a new proposition, it is important to emphasize in the context of the applying a model (idea) of the DT as a foundation for economic analysis. One particularly important feature is that while many of the outcomes of the demographic transition may be operationalized in the context of economic phenomena (and thus theory), economic theories cannot, alone, explain the underlying processes which give rise to these economic facts. In essence, this means that we need to venture beyond core economic theories to adequately account for the links between demographics and macroeconomics.

This presents us with a rather unique challenge. One the one hand economic convention demands that results and modeling be expressed in a sometimes rigid and arcane mathematical language, but this may not always be appropriate. Considerably complexity on the conceptual level may be lost in the transition from complex empirical regularities to formal economics. As a result, The idea that a proper understanding of the demographic transition demands an interdisciplinary approach in relation to economics is a key proposition for this thesis, but also one which is difficult to adhere to since the theoretical framework through which ideas on macroeconomics and demographics are usually expressed remains the classical one with utility maximizing representative agents whose behavior in optimum is aggregated to the macroeconomy. Specifically, this aggregation is crucial but also, as it turns out quite problematical in both a theoretical and methodological sense.

With this point stated as an initial qualifier, the main theoretical model chosen to motivate the empirical analyses in my thesis is the intertemporal current account [2] and in this context, the notion of intertemporal optimality and intertemporal optimization are key principles.

The idea of intertemporal choice comes from Fischer (1930) who laid the foundation for the idea that value has both a time and quantity perspective. This fundamental proposition which today forms the backbone of financial and economic theory was later treated by Roy Harrod (Harrod (1939, 1960 and 1963)) to formulate the dynamic theory which later has given rise to the notion that the utility of consumption in two periods be related via the market (as well as potentially subjective) discount rate. The main idea to recognize here is the fact that income (Y) can only be saved (s) or consumed (c) and that the decision to do so depends on the discounted value of foregoing consumption today relative to tomorrow. The imperative question to answer in the present context is thus how ageing might explain this intertemporal substitution between savings and consumption on an aggregate level.

This research program, as it were, has been given plenty of thought in the annals of economic theory as it is addressed by Modigliani’s life cycle hypothesis and thus complemented by Friedman’s famous permanent income hypothesis Friedman (1957), Modigliani and Brumberg (1954) and Modigliani and Ando (1963). These contributions have been the source of an almost dizzying amount of empirical tests and further theoretical elaborations and in order not to get bogged down in too much detail it is worthwhile to focus on the main faultlines. where the life cycle and permanent income hypothesis have widely used to differentiate Keynes' original idea that consumers spend out of current disposable income which again has led to a never ending discussion about time horizons. This discussion however is also somewhat of a false debate I think since the Keynesian idea of a marginal propensity to consume out of current income and consumption smoothing frameworks presented by Modigliani and Friedman are not mutually exclusive. In fact, knowing when to apply either one is a key task for macroeconomists since both ideas may teach us important things depending on the setting.

Further into the realms of Neo-Classical economics and what has become the leading paradigm in moder macroeconomics the Keynesian result has decisively been dragged through the mud. For example, Robert Lucas’ rational expectations hypothesis was specifically formulated in the context of showing the irrelevance of policies to affect output and inflation in short run (The Lucas Critique). Even as the pure supply side economics was surplanted by the New Keynesians up through the 1980s and 1990s the representative agent paradigm had already been locked in and relative to the core neo-classical models the New Keynesian models are very similar in methodological setup. 

This thesis shall neatly sidestep the grand old issue of the short run vs. the long run but rather home in on the principle of intertemporal substitution (or consumption smoothing in the lingo of the theory) and forward looking behavior of economic agents. Specifically the topics under consideration will be the presence of an aggregate economic life cycle of consumption and saving driven by this intertemporality, how this intertemporality manifests itself, and how the divergence in time horizons between consumers, governments, and companies may affect this life cycle. In a concrete context the idea of intertemporal preference between consumption and saving shall be cast in the context of an economy’s preference or tendency to run an external surplus or deficit.

A Benchmark Problem

In the present context, the use of the intertemporal consumption result can be motivated by the following expression of the agent’s maximization problem (1).

In this setup (a) is equal to assets, (r) is the interest rate which is assumed constant, (c) is consumption and finally (y) is income ( assumed exogenously given). The value of beta (β) is given by 0< β<1. This variable is a measure of our representative agent’s patience. If beta is equal to 1 consumption tomorrow is of equal value to consumption today and if it is zero our agent only cares about consumption today.  The budget constraint simply states that our assets in time (t+1) is equal to the accrued return on our assets in time (t=0) + income minus consumption.

The problem presents one of the simplest forms of the intertemporal decision by our representative consumer. Solving the problem we get the classic result that marginal utility in period (0) depends on the discounted marginal utility in period (t+1); where beta is the subjective discount rate (time preference). In fact, why don't we just go ahead and solve the thing so that you can see for yourself what is going on. Now, I am going to go through with brute force here and assume that any readers with no knowledge of calculus will know full well to skip this part [3]. Using the problem above, we can setup the following constrained optimization problem.

The important thing to understand in these kinds of problems is the distinction between state and choice variables. Here the agent chooses assets and consumption given income and the interest rate. This leads to three first order conditions.

Recognize that as always in such an optimization problem we would first of all like to solve out the Lagrange multipliers in order to get a closed form solution. Moreover, we would like to follow in the mental footsteps of Irvin Fischer and Euler and express this solution as a dynamic relationship between consumption in period 0 and period t+1. Fortunately this is quite easy in the present case (setting "s" to 1 in the third step);

This Euler equation shows exactly the relationship I explained above in words, namely that the consumer’s marginal utility in period (t+1) is equal to the marginal utility in period (t) discounted by the market discount rate as well as the subjective discount rate (beta)

The Origins of the Representative Agent

So, if you made it this far and before an actual discussion of whether the representation above is an adequate and useful macroeconomic construct it is worthwhile to trace its origins  because its story is a remarkable one. It first appeared in the context of Alfred Marshall’s Principles of Economics in the form of the representative firm Hartley (1996) and Marshall originally conjured this entity in the context of constructing a supply curve for the industry and essentially, as Hartley points out, the creation seemed rather innocent at first.

However, this was not the position taken by Marshall’s peers and after a devastating critique by, among others, John Maynard Keynes and Lionel Robbins the idea of the representative agent was put to rest in the first part of the 20^th century Hartley (1996). It would take some 40 years before the idea of the representative agent was resurrected and this time its endurance would prove pervasive.

According to Hartley (1996) the first use of representative agents in a post Marshall perspective has its origins in the period in which neo-classical economics was reaching its zenith. Concretely, Lucas and Rapping (1970) is cited as the first contribution using a representative agent detailing the theory of intertemporal labour supply which is a core assumption of most real business cycle models Romer (2006, ch. 4). Generally, representative agent models are often narrated in the form of an ideal type Walrasian model where the parameters in question are assumed to represent fixed entities which do not change with policy regimes. The model described above is an example of such a model. Apart from adhering to the ideal of constructing a Walrasian equilibrium model, the modern use of representative agents are also closely linked with the idea of rational expectations Sargent (1993), Lucas (1976) and the famous Lucas Critique attacking traditional Keynesian policy evaluation models Hartley (1997, ch. 4) and Lucas (1976). Finally and as David Colander points out in a review of Hartley (1997), the use of representative agents is also closely tied to the pedagogy of macroeconomics Colander (1997).

Ironically, the occasion for the return of the representative agent to macroeconomics was a widespread need and desire among scholars to provide microfoundations for macroeconomics and thus to differentiate the Keynesian idea of a pure macroeconomic theory. In addition, the modern reincarnation of representative agent models is primarily motivated by the desire to build Walrasian general equilibrium models as well as to imbue agents with rational expectations Lucas (1976). This desire can of course be debated on its own merit, but more interestingly would be to find out whether the use of representative agent models is useful in general. Kirman (1992) and, in particular, Hartley (1997) think that they are not and is devastating in his critique arguing that the impetus to construct microfoundations through Walrasian ideal type representative agents with rational expectations fail on a number of critical measures. Key issues here are the representative agent’s inability to model the obvious degree of heterogeneity on a macro level as well as the issue of aggregating the results derived in a microeconomic context. Hartley (1997) thus attempts the ultimate coup-de-grâce;

The idea that we can start with nothing other than individuals maximizing their own utility and build up a model that explains the macroeconomy is nothing but a myth

It is important to note that the discourse fielded in Hartley (1997) and Kirman (1992) is a fringe conversation, at best. Indeed, as economists attempt to build ever more complex models these always take their point of departure in the representative agent. Especially, it is important to note that modern dynamic general equilibrium models are also fundamentally rooted in representative agent models and as such, these continue to represent the main work horse models in macroeconomics. Moreover, and I am speaking out of personal experience here; no respectable econ department today will accept a paper from their PhD or graduate students as "eligible" without proper neo-classical microfoundations. In this sense, the mathematical expression of representative agents remain the core tool in almost all macroeconomic analysis today (although this may about to change).

Take it to the Dumps?

Two obvious questions impose themselves at this point. One is whether the use of representative agents in macroeconomics has something, in general, to do with the recent soul searching among macroeconomists and the critique against the profession. And the second is whether the study of macroeconomics and demographics in particular calls for the non-use of representative agent modelling.

On the first I don't necessarily think that it exists to the detriment of macroeconomics as a discipline, but I do think that a couple of points need mention. First of all I will echo the point made in Hartley (1997) that given the widespread use of representative agent modelling in almost all corners of macroeconomics and the almost religious devotion to it in graduate and PhD economics I think it is highly problematic that we have not had a more serious debate of its methodological merits. I would emphasize this in particular in the context of the fact that the use of representative agents leads to very inflexible (although rigorous) mathematical models and the blind faith in these models tend to steer macroeconomics onto a very narrow methodological path. During my research and initial ground work for the thesis I actually did write my own representative agent model to suit my specific agenda, but found in the end that I was paying more tribute to the laws of calculus than the connection between ageing and capital flows/open economy dynamics and as I set up the problem I ended up very close to the original benchmark problem.

On the second, I have not come to a decisive conclusion yet but I want to strongly emphasize  that this is a very important question. The key transmission mechanism from demographics to the macroeconomy lies exactly in the aggregation of individual behaviour on the basis of life cycle and life course theory and at the moment, the only way that we are able to make such a link is through the representative agent. It is a fair question to ask here whether this is methodologically viable. Another issue would be that at the current juncture life course and life cycle theory are built as bottom-up theories in the sense that they both invariably start on the micro level. But it does not need to be like this. The formulation of a pure macroeconomic theory on how demographics processes affect our economies is something worth thinking about and devoting resources to.

In the end I think that the use of representative agent modelling represent one of the core debates that macroeconomists must have in relation to the recent upheaval in the profession. It would be a mistake to consider me a one-sided opponent of representative agent modelling, but I am skeptical and more often than not I think that the representative agent represents more of a straitjacket than a rigorous economic tool. On the other hand, the rigorous treatment of economic problems that follows from the setup of representative agent models is also fundamentally appealing I think.

Ultimately, I am agnostic when it comes to the need for micro foundations. Clearly we need some form of micro oriented analysis when we study macro variables, but too much of a focus on the micro level may remove attention from complex processes whose main and only playing field is at the macro level. As such and while I would not advocate taking it to the dumps I think that the current macroeconomic debate should reflect a more nuanced view of the representative agent (and the use of Walrasian microfoundations) than is currently the case.

List of References

Colander, David (1996) – Beyond Microfoundations, Cambridge University Press; the book is a compilation of papers with David Colander as an editor of the entire volume.

Fisher, Irvin (1930) – The Theory of Interest

Friedman, Milton (1957) – A Theory of the Consumption Function, NBER

Harrod, Roy F (1939) – An Essay in Dynamic Theory, The Economic Journal, vol. 49, no. 193 (Mar,. 1939) pp. 14-33.

Harrod, Roy F (1960) – Second Essay in Dynamic Theory, The Economic Journal, vol. 70, no. 278 (Jun,. 1960) pp. 277-293.

Harrod, Roy F (1963) – Themes in Dynamic Theory, The Economic Journal, vol. 73, no. 291 (Sep,. 1963) pp. 401-421.

Hartley, James E (1996) – The Origins of the Representative Agent, The Journal of Economic Perspectives, Vol. 10, No. 2 Spring 1996 pp. 169-177

Hartley, James E (1997) – The Representative Agent in Macroeconomics, Routledge, Frontiers of Political Economy (1997)

Hugh, Edward (2006) – Rethinking the Demographic Transition, Working Paper

Kirman, Alan P (1992) – Whom or What Does the Representative Individual Represent? Journal of Economic Perspectives volume 6 no. 2 Spring 1992 pp. 117-136 

Lucas, Robert E. Jr (1976) – Econometric Policy Evaluation: A Critique, Carnegie-Rochester Conference Series on Public Policy, issue 1 (Jan), pp. 19-46

Lucas, Robert E. & Rapping, Leonard (1970) – Real Wages, Employment and Inflation, In E. S. Phelps. ed. Microeconomic Foundations of Employment and Inflation Theory. New York: Norton, 1970.

Modigliani, Franco & Ando, Albert (1963) – The “Life Cycle” Hypothesis of Saving: Aggregate Implications and Tests, The American Economic Review, vol. 53, no. 1, part 1 (Mar., 1963) pp. 55-84

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[1] - See links in this one for an overview of the initial flurry.

[2] - The main topic being international capital flows and ageing.

[3] - The point here is simply that for graduate economists, this problem is almost too simple but for many others it is unworldly. Here of course lies a great part of the problem!

Demographics and Macroeconomics - Part 1 (Wonkish)

Blog post series, like the vuvuzela, is the new bacon; it works with everything and with John Hempton’s recent excellent series on the economics of default in the Eurozone and Edward’s recent postings on AFOE in which he pulls out some of our old paper abstracts has inspired me to a series in which I try to pin point exactly how demographics and macroeconomics interact and where I believe we need more focus and work.

When it comes to the overall link between demographics and macroeconomics we already have a number of core workhorse models in the form of the life cycle and life course framework where the former deals with consumption and savings decisions as a function of age and the latter deals, broadly, with life time events and their individual and aggregate importance on economic dynamics. The adequate impact on the macro economy from the dynamics of demographics must then be developed as a function of the attempt to do two things; firstly, to continuously develop the life cycle and life course theories themselves and secondly to seek out new ways to apply life cycle and life course theory to existing macroeconomic problems and themes.

In the first series, I will begin with the latter.  Overall, I will highlight 6 areas where demographics enter  macroeconomic theory  and research as an important variable and I will try to offer my view on where to progress further. I will begin with two classics in the form of growth theory and open economy dynamics.

Growth Theory

Firstly, I need to say that I am not an expert on growth theory and this represents somewhat of a problem since growth theory although somewhat out of vogue at the moment has grown to become an extremely diverse field with a wide number of different schools and discourses. For the purpose here it will suffice to note that most economists today still use some form of the classic production function framework which has its roots in the work by Charles Cobb and Paul Douglas in 1928 and was popularized in 1958 by Solow’s famous article. This is what it looks like;

Where Y is output, K is physical capital, A is the illusive residual or more specifically technology/production function, L is the size of the labour force and H is a measure of human capital. Now, I certainly won’t do any math at this point and it is important to note that the functional form may take many exotic forms (which are not necessarily Cobb-Douglas), but just to give you one example the following is a Cobb-Douglas production function which incorporates human capital as above (here with constant returns to scale);

The key point I want to emphasize here is simply that we have output as a function of some input and that we would like to account for and explain the dynamics and behaviour of this input. How might we imbue this model with reasonable characteristics that reflect demographic dynamics?  As it turns out, we already have some pretty solid frameworks to deal with this questions and we can see this by looking at the inputs one at a time.

The evolution of capital (K) – In most traditional models the evolution of capital is simply expressed as the fraction of income save minus any depreciation of the capital stock in the last period and here of course we have several workhorse models to show demographic dynamics that are all wrapped up in the form of the life cycle hypothesis of savings and consumption. Usually and since most of these models are constructed on the basis of Walrasian microfoundations, we have some form of intertemporal optimization problem ticking away in the background which assumes an OLG (overlapping generations) form. The classic model here is the Diamond model who is based on Diamond (1965) which is the father of all OLG models, but over time a plethora of different OLG models have been developed with differing degree of analytical complexity.

The basic problem here though remains the concept of the steady state which means that we must construct model such as to allow the change of capital through time (or its derivative with time) to be 0 in the long run. Please note here that this condition is not imposed on the basis of empirical behaviour but on the basis of (mathematical) analytical tractability. So, apart from the uncertainty surrounding exactly what this ”long run” is it also locks in the analysis and assumes away a large part of the important aspects of even basic life cycle behavior. Specifically, the idea that once reaching a steady state any change in the savings/consumption rate will one have transitory effect and that the economy will automatically (and always) converge to the same growth rate/state as before is a problem. Essentially, the whole idea of a steady state whether be it in the form of an exogenous or endogenous growth theory framework is a huge problem since it is evident that such a thing does not exist. And even if we could establish over a very long run horizon that such an average/constant path is a good approximation we would be ironing out all the interesting and important questions in the process.

The evolution of human capital (H)  – The adoption of human capital into the growth theory framework is famously due to a paper by Mankiw, Romer and Weil in 1992 in which human capital is proxied by rates of schooling and thus the perspective becomes one of the quality of human capital and to the extent that the formation of human capital also includes the evolution of the population (or perhaps working age population) we can say that this is a direct way in which demographics enter the framework. Again, we might simply ask here; to what extent does the aggregate quality of human capital in an economy depend on the age structure of its population and here I am not only talking about the level of education but much more broadly about the idea of innovative capacity as a function of population structure.

The evolution of technology (A) – Technology and productivity are famously assumed exogenous in the Neo-Classical tradition while New Growth theory as it was developed in the 1980s and 1990s emphasised the need to specifically account for the evolution of technology. Today, I would venture the claim that there is a consensus that productivity and technology is a function of what we could call, broadly, institutional quality which encompass almost anything imaginable from basic property rights to the level of entrepreneurship. Indeed, a large part of research is still devoted to pinning down exactly which determinants that are most important here both across countries and through time. Now, I would argue that, in the context of standard growth theory, this is where the scope for the study of the effect of population dynamics is largest. Thus I don’t think it is unreasonable to expect the level and evolution of productivity growth and technological development to be a function of the current population structure but also its velocity which is a function of e.g. migration (new inputs?), future working age size etc. Also, this is also where human capital and the evolution of technology is joined at the hip through the idea of innovative capacity and readiness.

As you might have inferred from the exposition above, I have some difficulties with growth theory. I can admire the framework for its internal logic and I can see why it is an important part of a macroeconomist’s toolkit, but I also think that growth theory (as I describe it above) has outlived itself. In this sense, most of the questions that we have as economists when it comes to the evolution of growth and welfare of our economies both individually and through their interaction is not addressed by growth theory. Especially the effect of an ongoing and ruthless process of ageing is completely impossible to analyse in the standard framework. Naturally, I am also being a bit unfair here since the kind of growth theory I am describing above is also too simple to give adequate credit to where the field is today. For example in relation to demographics, I am grossly overlooking important strides in the development of OLG models which have been perfected continuously so that we today have a very large battery of very complex models. But also more generally, growth theory is being used today to produce a lot of useful research. As I say, it remains a key tool in our toolbox.

Yet, the basic growth theoretical setup remains flawed in key a number of un-salvagable ways. Concretely, specifying a production function and specifying the underlying inputs as differential equations through whose solution we reach a steady state equilibrium is not, in my opinion, the way to go. Thus and in an intuitive sense I feel much more at home, for example, in the company of evolutionary growth theorists [2] whose argument and methodology is more agile. In summary then and as I try my utmost not to become a hostage of the notion of a steady state I will simply make the following observations in the context of what we macroeconomists consider the main inputs to growth where the ”age” is simply an unspecified collection/function of variables that pertains to fertility, age structure, mortality etc (and of course a whole slew of other factors, but for the sake of argument let us keep it monocausal here).

Where age in the context of the capital stock relates to the size and evolution of the capital stock as well as savings and investment dynamics, in the context of human capital it may be argued to enter directly, but may also affect the quality of human capital. Finally, I think that the impact of demographics on innovation and especially the idea of velocity of innovation and innovative capacity represents an area which is not well understood. In general though and short of letting some variant of demographics enter directly, I think an important research program would be to examine the effect from demographics on the inputs to growth which we traditionally operate with. Especially, the process unprecedented process of ageing is a completely new phenomenon here in the context of traditional growth theoretical analysis.

Open Economy Dynamics

An enduring feature of macroeconomics is that the entities we study are not black boxes but interdependent entities who interact in very complex ways in the global economy. This statement was true 40-50 years ago and today it is almost a cliché. In fact, for non-macroeconomists it must seem very strange that we still distinguish so strongly between closed and open economy analysis as the use of studying the former must surely be almost nill. I would agree with this statement but simply note that important things do actually happen when we go from a closed to an open economy and the way this transition is operationalised is important in itself.

Now, I could write a lot about this (in fact, I have penned a whole thesis about it), but I will only cover the essentials. What you need to know upfront are two things. The first is that the economic theory used to handle the effect of age structure/demographics on open economy dynamics is again the life cycle framework and, in most cases, we still have a OLG representative agent model taking care of the microfoundations. Secondly, it is important to be aware of the concrete specifics of the transition from a closed to an open economy. Luckily, this can be handled by some very simple algebra from macroeconomics 1-0-1.

The whole point is to find an expression for savings, so for the closed economy we have;

By definition every unit of output has to equal a unit of income, and national income in any given period can either be saved or consumed. This means that national income can either be put aside for saving or consumed through government (G) or private consumption (C). In this way, we define national saving in any given period as;

This is a fundamental result in basic macroeconomics and what is equally fundamental is why this changes in one key aspect when we move into an open economy setting. We then have;

 With (x-m) equal to the trade balance and by doing the same exercise above we get;

In this context and remembering that the life cycle hypothesis tries to map consumption and saving as a function of age, the transition from a closed to an open economy becomes crucial in order to see how demographics may affect open economy dynamics. As such, allow me to quote the following passage of my thesis which I find myself coming back to when thinking about this topic;

The best way to think about this [3] is to imagine that savings and investment are in a race governed and controlled, as it were, by the transition in age structure that occurs as a result of the demographic transition. Initially, as the transition sets in with a decline in mortality and where fertility only follows with a lag, investment demand outruns the supply of savings and the economy is running an external deficit. Steadily however, the supply of saving catches up with investment demand which itself begins to decline and thus the external balance moves into a surplus. Finally, the pace of savings accumulation is replaced by outright decumulation (dissaving) and the external balance moves into deficit as savings decline faster than domestic investment demand

This is stylized of course, but especially the idea of the race between savings and investment is a very helpful metaphor. Consider then a closed economy; in such a setting there can be no race as described above since savings and investment will be tied together at all points in time, but in an open economy savings and investment dynamics are exactly what provokes relations between economies and more specifically, the fact that the economies have different preferences for savings and investment at different points in time. This gives a very strong foundation for thinking about how demographics affect open economy dynamics.

Concretely, and in order to tie the argument up on the underlying theory capital flows occur precisely because economies have different intertemporal preferences for consumption and saving and since this intertemporal preference itself is a function of age (through the life cycle/OLG framework) demographics become a driving force for international capital flows.

This as it were is also where the fun begins since exactly how this process should be understood both from the point of view of the individual economy, but also in a global context remains, for all intent and purposes, an unresolved question. Surely, we have studies that use basic life cycle frameworks to simulate capital flows between economies and they do have some intuitive appeal and explanatory power, but they are hampered by, in my opinion, by an inadequate understanding of the life cycle thesis and how exactly it manifests itself. As I noted in the beginning, part of all this also requires a continuous development of the life cycle hypothesis itself and here this becomes important. Personally, I have cast my eyes on two areas of research where I believe that the influence of demographics on open economy dynamics is important.

1 – Global Imbalances

This represents an enduring feature of the global economic system and while everyone can agree that they need to be resolved some way or the other I think that the proper understanding of demographics shows us that they are essentially structural. Especially on the side of surplus economies I have argued (both in my thesis and in genera) why we cannot suddenly expect economies such as Germany and Japan to do their part and crucially, why we should expect more economies to venture down the same path as they are also ageing rapidly. Importantly, this provides a concrete theoretical spin to the question everyone seems to be asking at the moment of who exactly is going to run the deficits? The pessimistic answer here is no-one and herein lies the rub.

2 – Export dependency

This one is essentially the concrete theoretical proposition used to make the argument above on global imbalances. Ageing leads to a decline in domestic demand and in a closed economy there is really not a lot you can do; savings/investment will fall and consumption will be lacklustre since there is no underlying dynamic to feed it other than dissaving. However, in an open economy you can fight this through claims on other economies or put in another way, you can save more than merited by domestic demand and thus you can invest your savings abroad. Note here that technically this is exactly what e.g. Germany and Japan are doing in the sense that their excess savings have to be matched by excess borrowing/investment demand elsewhere.

I am still developing these two areas, but there are plenty of meat on this topic I think. One crucial task is to develop the life cycle hypothesis on the basis of observed behavior of economies as they age and another is to.

Stay tuned for the next post in this series which looks at the influence from demographics on asset prices, demand, and return and composition of consumption. Suggestions and comments on potential omissions on my part are welcome.

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[1] -  Most often operationalized through an OLG framework.

[2] - Evolutionary Growth goes back to this one "Nelson, R.R., Winter, S.G., 1982. An Evolutionary Theory of Economic Change. Harvard University Press, Cambridge, MA" and is a must read I think. The work by Jan Fagerberg is a good place to begin as well as for a more modern exposition.

[3] - I.e. demographics and savings and investment behavior in an open vs closed economy