...Archive for April 2013

The mother of invention

I thought I’d quickly highlight a point made recently by two great posts. First, here’s J.W. Mason:

There is increasing recognition in the mainstream of the importance of hysteresis — the negative effects on economic potential of prolonged unemployment. There’s little or no discussion of anti-hysteresis — the possibility that inflationary booms have long-term positive effects on aggregate supply. But I think it would be easy to defend the argument that a disproportionate share of innovation, new investment and laborforce broadening happens in periods when demand is persistently pushing against potential. In either case, the conventional relationship between demand and supply is reversed — in a world where (anti-)hysteresis is important, “excessive” demand may lead to only temporarily higher inflation but permanently higher employment and output, and conversely.

Now, from the blog direct economic democracy:

Of course we COULD choose to have just a few in the owning class and have everyone else rioting. BUT the owning class would get no benefit at all by keeping itself select. In fact that would make each member of the owning class less rich because the market would be smaller. Technological innovations have very high development costs relative to the unit cost of the product. A product such as a new medicine or an innovative electronic gadget becomes dramatically cheaper to produce per unit item if the development costs are spread across many more units sold. Imagine if we lived in a world with greater disparities of wealth than we do now. Imagine if the market for the latest medicine or electronic gadget was 1/10000th the current size. Those few who could still afford such items would have to pay massively more to cover the development costs. That dynamic works in the opposite direction too. Imagine if the potential market for the latest product was all seven billion people on earth. Then development costs would be spread so thinly they would hardly be noticed. Capital goods such as the robotic workers themselves also have the same economy of scale. It starts to make financial sense if many factories staffed with robots are to be built but not if just a few… [H]aving an economy directed towards technological development is critically dependent on having lots of potential customers.

It’s something of a cliché, starting with Marx and moving through Schumpeter, to gush over capitalist economies’ capacity to innovate, reinvent, and overthrow themselves. Profit-seeking entrepreneurs constantly strive to find new and/or cheaper ways to “serve customer needs”. In a capitalist economy, necessity surely is the mother of invention.

But with a very large asterisk. Capitalist entrepreneurs are motivated by the accumulation of money claims. In a capitalist economy, it is not mere necessity, but purchasing-power-weighted necessity that is the mother of invention. American entrepreneurs don’t compete to meet the needs of money-poor Africans or Chinese. Instead, Chinese entrepreneurs compete to meet the needs of citizens of the country money comes from. Within the US, entrepreneurs don’t much innovate to discover and address unmet needs of the poor. That’s a rough business. The poor have more needs than they can pay for already, and entrepreneurs hope to be paid. There is, of course, plenty of business activity on behalf of the poor, but the preponderance of it is in sectors that are in one form or another subsidized, e.g. health-care, education, and finance. The customer businesspeople work to please is the state, or quasi-state financial firms, who may or may not need to solicit the collaboration of or delegate some decision-making to actually poor “end-users”. Entrepreneurial energy always goes where the money is.

It is in this light that I think we should interpret, for example, problems of “general glut” or “abundance”, as Izabella Kaminska puts it. Actual scarcity has not, in fact, been overcome. We have not achieved overcapacity in aggregate. In a depression, businessmen perceive overcapacity all over the place. But that is a distributional phenomenon. There is an abundance of goods and services relative to the needs and desires of people with purchasing power to consume. There is no such abundance in an absolute sense.

Abundance, ultimately, is a choice variable for the political class. “We” are presented with a devious choice, a Faustian seduction. We can choose abundance, for ourselves, by maintaining a distribution under which a relatively small fraction of humanity claims a sufficiently large share of world purchasing power that the economy’s capacity to produce will remain safely in excess of that group’s needs. Or we can choose scarcity, by distributing purchasing power widely enough to put our productive capacity under pressure, leaving all of us, even the affluent, at risk of actual shortage.

If we choose the abundance, we can expect Tyler Cowen’s “Great Stagnation” to continue. Technology will stagnate, because purchasing-power weighted necessity is the mother of invention, but people with needs have little purchasing power while people with purchasing power have trivial needs. If we choose scarcity, we take a risk. We may fail, and end up impoverished relative to where we (some of us) might have been, had we chosen the more conservative path. But purchasing-power-weighted necessity is the mother of invention, and in the past, mass affluence has inspired extraordinary innovation in pursuit of the mass dollar. If you believe in the power of capitalism and technology, then you should favor choosing scarcity, both for your own benefit (robots, yay!) and to expand the “we” by whom some level of abundance might plausibly be claimed.

Political conversation often obsesses over a pathological and ahistorical fear of idleness among the non-affluent. Given the choice, if not absolutely compelled by necessity, wouldn’t “they” become lazy slackers, eating diabetes chips and watching monster trucks on teevee all day? Or would they lift themselves up, spend a few hours at the gym, and take advantage of their leisure to find creative and productive use of their capacities?

Human fears project outward, and so it is for the political class. For as a group, it is “we”, not “they” who are choosing comfortable idleness. They are desperate for jobs. But we are collectively slouched on easy chairs in the sky, enjoying decent stock returns, low inflation, and remunerative careers. The question is whether “we”, the relatively well-to-do who call the political shots, have the moxie to shed our pantsuit pajamas and take a chance on capitalism’s capacity to transform the world. So far we have chosen a comfortable depression, which makes for grand debates and entertainments. Would you pass the remote? Shall we watch Maddow or O’Reilly or Colbert, or read yet another self-righteous blog post?

Update History:

  • 30-Apr-2013, 4:30 p.m. PST: Fixed too-general google books link to Mating by Norman Rush; fixed spelling of “asterisk”, was “asterix” like the comic character, thank you William Pietri!
  • 1-May-2013, 8:35 a.m. PST: Avoiding duplication of “constantly”: “economies’ capacity to constantly innovate”
  • 24-Mar-2013, 9:25 p.m. PDT: “enjoying a decent stock returns”

The generalized resource curse

A useful way to understand the pickle we’re in, I think, is that we are suffering from the so-called “resource curse”. If you are unfamiliar with the phrase, “resource curse” refers to the regularity with which countries “blessed” with abundant natural resources end up as dystopian polities with dysfunctional economies. Nigeria has a lot of oil but no one wants to live there.

The resource curse is pretty easy to understand. It’s not associated with just any sort of natural resource. Switzerland has beautiful mountains and stuff that people would pay a lot of money for, but it is still well-governed. Accursed resources are of a very particular type. They are valuable tradable goods the extraction of which requires a small numbers of workers relative to the size of the economy as a whole. [*] Goods like this create a very strong tension between private property and social welfare. In the mythology of capitalist economics, “as if by an invisible hand”, the self-interested pursuit of private wealth promotes the general welfare precisely because we all require one another’s help. The butcher slaughters her beasts and the baker sugars his cakes, each with an eye to their own profit. But the butcher needs her carbs and the baker likes his meat, so the end result of their self-interested selling is mutual aid rather than mere accumulation.

This logic breaks down in an economy dominated by a valuable natural resource. Yes, the miners require meat and mead, but if they are small in number relative to the rest of the population, that won’t cost them very much. They are few mouths to feed, and the not-miners are many and lack bargaining power. What makes happy capitalism work, the silent tendon of the mythologized hand, is a kind of balance between individuals’ desire to accumulate and their need for the assistance of others. If there exists a very valuable natural resource, and if that resource can be privately controlled, there is no balance. Self-interested agents drop their butchering and bakering, and try to gain control of the resource. No magic force turns that into a positive sum game. Unless there are “very strong institutions” — whatever that might mean — the pursuit of wealth becomes a game with winners and losers. The invisible hand can manage no more than to lift a middle finger.

So far this is all very comfortable. Clucking about places like Nigeria is almost a reflex, a familiar tic among Western economists. But meanwhile, we’ve hardly noticed that technological and international supply-chain developments have snuck the resource curse in through our own back doors. In aggregate, the goods and services we require have grown ever more tradable, and production has grown ever more amenable to control by relatively small groups of people. There’s a sense in which we are all Nigerians now.

The result of a resource curse, even in Nigeria, is not a triumphant über-class gleefully enslaving those outside the circle of winners in the resource-control game. In human affairs, “legitimacy” matters, and the sources of legitimacy are time- and context-dependent. Nigeria has all the forms of modern government, a civil service many of whose members are no doubt idealistic and hard-working. What evolves is the situation we refer to as corruption, under which those who control the valuable resource create incentives within the institutions that confer legitimacy — government and finance, media and academia — in order to ensure continuation of their control. In doing so, lines are genuinely blurred and resources are genuinely shared. The work of mining and the work of governing cease to be distinct enterprises, they become a partnership in the common project of maintaining control over the special resources. And words with moral valence like “common” and “shared” are appropriate, because within the circle of insiders, that’s what it feels like. There is a “we” that includes all of those fortunate enough to be civilized, that includes “me” and “my family”, “my friends and my family and my coworkers”, “my school and my teachers”, everyone that most people in the civilized circle ever interact with. There are, at the edge of the circle, people who are genuinely brutal, the people who put down insurrections or directly manage low-bargaining-power chattel labor. But those are a small minority. Most people who work to perpetuate “corrupt, extractive” regimes are, in their own eyes, serving their communities. The more resource-curse logic binds, the more likely as a technological matter that control over economic value will be concentrated among a relatively small fraction of the society. This leads to a greater separation of circumstance, between winners who perceive themselves and their communities as “civilized”, and losers exhibiting social pathologies that may be more effect than cause of disadvantage, but are nevertheless real, and usefully assist in reinforcing the arrangement’s legitimacy. Corruption and idealism become impossibly fused. Did Timothy Geithner “save the world”, or did he perpetuate the stranglehold of a particular extractive elite? He did both. He saved his world.

There is a regularity here, an order. We find ourselves on the inside of social phenomena that we have seen before, that we can understand. The global economy is succumbing to a technologically-driven resource curse, coalescing into groups of insiders and outsiders and people fighting at the margins not to be left behind. Our governments are transforming themselves from mediators among widely dispersed and interdependent interests to organizations that maintain and police the boundaries between the civilized and the marginal, who put down the insurgencies and manage the pathologies of the latter so that they do not very much impinge upon the lives of the former. Our financial systems are mechanisms by which legitimacy is conferred upon facially absurd distributions of aggregate wealth, by virtue of processes that claim to be “voluntary”, “private-sector” and “market-disciplined”, but which are none of those things in any meaningful way.

There are lots of places to go with this analogy. “Resource curse” countries are traditionally small, open economies whose elites are less fettered in their neglect of domestic populations because they can trade resource wealth for most of what they want from foreigners. One might argue that the analogy is incoherent for large, mostly self-sufficient economies like the United States or the world as a whole, whose elites must rely on “domestic” production. But here the analogy between technology and trade, usually used to support the latter, comes in to condemn the former. The amenities for which Nigerian elites rely upon Europe, American elites may rely upon robots to produce, once the Chinese labor cycle runs its course. American, like Nigerian, elites will have their tailors and masseuses. But in a resource-curse economy, service providers at the boundary between inside and outside remain small in number relative to pathologized mass publics.

This analogy is not entirely hopeless. Alaska and Norway blunt the resource curse by proactively distributing the proceeds of resource extraction, limiting concentrated control and ensuing disorders. “Technology” is not a tangible thing that can be publicly owned and sold for proceeds. But like oil in the ground, it is a resource the scale of whose product far exceeds the reward required to incentivize its production. If we imagine technology as a source of value embedded in most goods and services, we can distribute claims upon it simply by distributing new purchasing power. A money-financed basic income would amount to a partial dispersion of technological bounty from those involved in concentrated production to “outsiders”. Like Norway’s Oil Fund, this might help preserve balance, economically and politically, in the face of our creeping resource curse.

[*] It’s probably more accurate, although depressing, to qualify this, and rewrite it as “a small numbers of workers capable of achieving bargaining power relative to the size of the economy as a whole.” Feudal economies, in which the majority of people work to produce agricultural goods, look a lot like resource-curse economies, even though numerical involvement in production is not concentrated. Bargaining power, defined as the ability to assert control over production, remains very unequal. If you define the resource curse this way, you end up with “cursedness” as the normal state of human affairs, and it becomes more sensible to talk about the “industrial age blessing”, a fleeting mix of social and technological conditions under which large numbers of workers contributed to production through processes that required scale and coordination. These circumstances allowed unusually broad segments of the population to organize and achieve bargaining power, increasing the scope of economic prosperity and the impetus to mass production that economists eventually label “growth”.

Update History:

  • 29-Apr-2013, 7:30 p.m. PST: “broadening increasing the scope of economic prosperity along with and the impetus to the mass production that economists eventually label as ‘growth'”

A bit more on savings and investment

Steve Roth (1, 2), Scott Sumner (1, 2, 3), Bill Woolsey, and Matt Yglesias have been debating questions of saving versus investment and paradoxen of thrift. See also JW Mason in the comments here, and Simon Wren-Lewis a while back. Cullen Roche reminds us that, even under conventional definitions, the accounting identity S≡I only holds for a closed economy without government spending, and of JKH’s useful tautology S=I+(S-I). [See Update below.] I think the recent recrudation of these issues owes something to Garett Jones’ and my conversation on capital taxation, which Jones has continued and on which Matt Bruenig has weighed in.

As is often the case, I think that the protagonists agree more than we think we do. Our various allegiances — to schools or tribes or policy ideas — exploit the ambiguity of language to manufacture conflicts, through which we reassure ourselves that we are right and they are wrong. (And no, math doesn’t help much, because we must map it arbitrarily to the same ambiguous language for it to be of any use.) Now I will reassure myself that I am right and they are wrong.

I think we have all agreed, one way or another, that the K in a Ramsey model does not map easily to the financial investment whose (non)taxation we debate in the real world. If new cash or government debt can be understood as a kind of capital good, it’s not obvious that it behaves similarly to the physical capital in an aggregate production function. It might, but you’d have to do some work to persuade us. If the conjunction savings supplied, investment demanded, and “at potential” total expenditure depends upon interest rates or other financial variables that may vary independently, there is no reason to believe that privileging saving will unconditionally promote investment, qua Chamley-Judd logic. Savings supplied may not be the bottleneck.

Update: Ramanan (1, 2) and Hellestal say I’m wrong to write that “even under conventional definitions, the accounting identity S≡I only holds for a closed economy without government spending”. They make a very good case! But in doing so, they remind us of the ambiguities and limitations of this “conventional” framework. In the current conversation, we are most immediately confronted by an ambiguity surrounding the letter S. When people say that S ≡ I, they mean total savings equals total investment. But in many of the conventional equations used to discuss this stuff, S is refers only to private savings. That leaves tiny fragile minds like mine liable to confusion. Stealing a lot from Ramanan and Hellestal, in conventional accounting, savings are defined simply as the residual between what is produced and what is consumed (both by private partes and by government). Let’s consider a closed economy:

Y ≡ C + G + I //by definition [eq 1]
Y - C - G = I ≡ TOTAL_SAVINGS ≡ TOTAL_INVESTMENT //by definition [eq 2]
Y ≡ C + S + T //also by definition, but S here means private savings [eq 3]
C + S + T = C + G + I //combining equations 1 and 3 [eq 4]
S = I + (G - T) //remember S here is private rather than total saving [eq 5]

Equation 1 says production is comprised of the resources that we consume (C by definition), that the government consumes (G by definition), and whatever is left over, which is evocatively but perhaps misleadingly designated I for investment. But, as commenter Eric L emphasizes, in these accounts I is just a residual. It refers to whatever resources are not consumed (either by private parties or by government).

Equation 3 is most easily understood as a decomposition of claims on the resources produced. We choose to decompose these into the claims made by government (T), the claims of private consumers to precisely the resources they consume (C), and the claims of private parties on production extinguished by neither taxation nor private use (S). We reconcile the disposition of claims with the disposition of resources in equation 4. This tells us that private savers’ claims to production (at the moment of production, before any real investment outcomes have a chance to muddy things up) include the resources no one used (I by definition) and the resources the government used in excess of the taxes the government claimed.

To keep things clean, let’s adopt, um, a convention. When we use the word “savings” we should refer to claims. When we use the word “investment” we should refer to real resources. Let’s then separate “savings” from “investment”, claims from resources, in Equation 5:

S - (G - T) = I //subtract (G - T) from both sides of Equation 5
S + (T - G) = I //simplify [eq 6]

Equation 6 is what we should really mean when we say S ≡ I (even though algebraically it doesn’t because we mean different things by S). That is to say that total claims on unconsumed resources must equal the quantity of unconsumed resources. I, by definition, for a closed economy, represents unconsumed resources. (T - G) represents the claims government has made on resources by taxation in excess of the resources the government has actually consumed. S represents the claims on resources left to private parties after consumption and taxation. If we call the claims of the state “government savings”, the claims of private parties “private savings” and unconsumed resources “investment”, then we can write:


So, yay! This is true by definition. It is just a way of saying that balance sheets must balance. It says that total claims on resources must always be equal to the total quantity of resources to be claimed.

But before we get all triumphalist, let’s emphasize how unhelpful this mostly is. First, it is simultaneously conventional to claim that S ≡ I and to write equations in which S refers to private savings, which is not equal to I. It is conventional to claim that the letter I represents “investment”, when in fact it represents any resources that are unconsumed. In a hypothetical, instantaneous sense, unconsumed resources mean resources available for consumption. In an actual sense, much unconsumed production (as vlade emphasizes) goes to waste. I is not “investment”, in the ordinary meaning of the word. It is simply resources that are not consumed in a certain period, regardless of what befalls them. Cars produced and not consumed become “inventory investment”. That’s fine. But electricity produced and not consumed? It dissipates as heat. Bread produced and not consumed grows moldy. The product of a university, when left unemployed, becomes less employable. Trees cut and “invested” in unsellable desert homes get accounted as investment, but fail to contribute to future production.

So we can argue. Maybe stuff that’s wasted should get embedded in C, which keeps “investment” more accurate by doing violence to the commonsense meaning of consumption. But we can’t really embed “bad investment” in consumption, because we can’t know which investment is bad. The letter Y usually gets mapped to “gross domestic product”, but if we want to sum across periods and keep our stocks and flows consistent, when we do our Period 2 accounts, we must define Y as a net product, and include any losses and misadventures that befell our old “investment” in the new period’s I. (We refer to this as a “valuation adjustment”.) Again, the use of conventional mappings between letters in the equations (“Y”) and real-world referents (“GDP”) will mislead us. Alternatively, we can keep the periods separate and let Y ≡ GDP, but then we will need to impose valuation adjustments when summing savings and investment across periods to account for actual investment outcomes.

The framework grows shabbier still when we consider an open economy. Equations 1 and 2 become

Y ≡ C + G + I + NX //by definition [eq 8]
Y - C - G = I + NX ≡ TOTAL_SAVINGS //by definition [eq 9]

But now we’ve really mixed up our treatment of resources and claims. Equation 2 defined resources unconsumed as total savings, but equation 9 redefines it as the resources we have failed to consume, but that may have been consumed by others. Hmm.

S = I + (G - T) + NX // [eq 10]

Equation 10, the open-economy analog of equation 5, is a very useful decomposition of private savings. It stands at the core of MMT-ish intuitions about how a putatively savings-hungry private sector might be accommodated, and inspires JKH’s very clean reminder that private savings represent claims on domestic investment plus some other claims that can’t be mapped to domestic investment. But it might suggest to the incautious that all exported goods are matched by domestic claims, and that those claims against foreigners are good and stable and should be valued at par. In real terms, that is almost never true. The NX component of “investment”, like the I component, is unstable, and if we carry these accounts forward in time, we’ll have to include valuation adjustments there as well.

None of this is to say that this is a “bad” accounting framework. The only thing that’s really terrible is the inconsistent conventions, under which S sometimes means total saving and sometimes private saving. The deeper difficulties would be shared by nearly any accounting framework. In the accounting of private firms, it is not easy to classify “expenses” vs “capital investment”, just like it’s hard to distinguish consumption and investment in national accounts. In corporate accounting, there are valuation adjustments and statements of “other consolidated income” to reconcile differences between values between period t and period (t+1) that cannot be accounted for by current period undistributed profits. The real world is unruly, yet accounts must be defined. The accounts must find ways to track the unruliness of reality rather than expect the world to conform to simple definitions.

However, whenever anybody tries to make a substantive point by quoting S ≡ I, they are offering no insight at all into any nontrivial question. They are saying nothing more or less than balance sheets must balance. They reveal nothing whatsoever about how. It certainly doesn’t mean that the production of new claims (“savings”) is necessarily matched by the production of new resources (“investment”). It just reminds us that, if the new claims are not matched by real resources, we shall have to devalue the claims of others if we wish to keep our accounts straight.

This whole conversation started with questions about whether the S ≡ I identity somehow implies that real-world savings vehicles are necessarily matched by investment in the Ramsey/Chamley/Judd sense. The answer to that question is unequivocally and irrefutably “no”. Real-world savings vehicles need not be matched by any investment whatsoever. Suppose I purchase shares in a mutual fund which then lends it on as consumer loans that finance vacations. In a macroeconomic sense, there is neither savings nor investment, my saving is matched by vacationers’ dissaving, resources are consumed and none are invested. S ≡ I = 0 Nevertheless, my shares in the fund would yield returns in forms like dividends, interest, and capital gains. No matter how hard you squint at accounting identities, nothing in the logic of Chamley and Judd suggests that these “investment returns” should remain untaxed. Lending to finance private and government consumption represents a significant fraction of gross financial savings, even though it contributes nothing to net savings or the aggregate investment Chamley and Judd presume.

Update History:

  • 14-Apr-2013, 10:50 p.m. PST: Very long bold update, responding to Ramanan and Hellestal re S ≡ I
  • 19-Apr-2013, 6:45 p.m. PST: “insight at all to into

Some followups on capital taxation

I’m going to move on to other things, but before I do, I thought I’d point to some very good commentary inspired by the previous post on capital taxation.

You already know that interfluidity is like a really drab version of Playboy, no one reads it for the articles, the really good stuff happens in the centerfold under the fold, in the comments.

The piece provoked smart responses on other blogs, Increasing Marginal Utility, Separating Hyperplanes, and Asymptosis. [1]

Robert Waldmann points out that glib euphemisms like “the long run” lead one to overstate the case against capital taxation even on the most sympathetic understandng of the models, that under human relevant distributions and time parameters the models can favor capital taxation. Here is his case (in a PDF he describes as “heroically constructed by Sigve Indregard”).

Here are a very few substantive comments, in response to responses:

  • Beware fallacies of composition is justifying a constant-returns-to-scale production function at a macroeconomic level. It’s an assumption that is only remotely justifiable if you are sure that your production function includes all factors of production. At a macro level, it’s obvious that you can’t scale all factors of production — see e.g. the smart discussion in comments by Merijn Knibbe, JW Mason, and Douglas Edwards regarding land. Omitting factors of production in a model may be innocuous in microeconomic contexts where their quantities are unconstrained functions of the factors that you do model. We needn’t concern ourselves about oxygen as an input to our beauty salon. But in macro production functions, it is hard to know which factors are bottlenecks to increased production, and failing to include the inputs and their constraints can render the exercises useless. It is conventional in macroeconomics to model the most significant determinant of overall production as “technology”, measured as a residual between what the factors we model predict and the growth we actually observe. That’s an elegant way of ducking the fact that we are omitting important inputs. If we are omitting important inputs, scaling up the factors we do include may be no more effective than multiplying shovels without hiring more humans to wield them.

  • There are lots of ways to get confused about the idea that savings equals investment. It’s an accounting identity, and, as always with accounting identities, there are tensions between the definitions under which the identity is true (by definition) and “common-sense” notions of the phenomena described. There are two approaches to dealing with those tensions:

    1. You can accept the formal definitions that make the accounting identity true, but be very careful to avoid “slips of the tongue” in mapping those definitions to other contexts; or
    2. You can treat those definitions as very narrowly applicable formalisms, and urge caution in the opposite direction, when reconciling the common-sense idea with the formalism.

    Steve Roth takes the second approach. I’ll take the first.

    Let’s assume that S ≡ I, and define investment to mean whatever it must mean for that identity to hold true. The S will always be equal to I. However, that does not imply that investment can be modeled as a cumulation of savings! We add to savings over time, but investment returns are complicated and sometimes negative. So we might describe ΔS ≡ ΔI as a two-term sum of new saving plus return on total investment.

    ΔS ≡ ΔI = new_savings + valuation_adjustment

    Ramsey-inspired models take the second term always to be the marginal product of capital in a production function, less a constant depreciation rate. But that is not likely to be realistic, especially if we let S ≡ I include financial savings, rather than what the models imagine, the direct deployment of an unconsumed real resource. When consumers stuff dollar bills into a mattress, it may or may not be true that the resources they thereby fail to consume get usefully deployed into production. If it is true, it must depend on the complex ability of the monetary and financial system to allocate the slack made available by nonconsumption in ways that contribute to future production. By definition, putting dollar bills in a mattress rather than spending the income may count as investment (if not offset by consumption elsewhere). But there is no guarantee that it is good investment, directly or indirectly. So, in addition to cumulation of savings, we have to think much harder than the Ramsey model does about that second term, about the dynamics of valuation changes. (For a great example, consider how the United States’ chronic current account deficits have failed to cumulate into a large negative NIIP, as pointed out today by Paul Krugman.)

    Ramsey model intuitions do fine if “bad investments” are a relatively constant fraction of total savings. Failed projects just fall into the constant depreciation rate. The key is to assume that investment returns are independent of the qunatity new savings. Unfortunately, if we allow the second, valuation term of ΔS ≡ ΔI to vary as a function of the first term, if, for example, an increased rate of savings tends to be matched by poorer aggregate investment returns, then Ramsey model logic falls out the window.

    In practice, we observe that increased rates of gross saving do correlate with poor investment returns. When the financial system is asked to allocate giant pools of money, it fucks up (and steals a lot). We have to be careful in mapping these real-world observations to modeled constructs — net investment rather than gross savings is the closest Ramsey-model referent. Net domestic saving was actually low during the housing-boom-era of malinvestment, but net investment was not so low thanks to a very large capital account surplus (those scary trade deficits). Total US S ≡ I was robust when foreign saving was included. But returns on that S ≡ I were unusally poor. If you accept the accounting definitions under which S ≡ I, you must be especially attentive to the complex dynamics of financial investment returns. You cannot just map that kind of S ≡ I to the capital term in a Ramsey model.

  • That last point was already over-mathy, but for those of you who like this sort of thing, a concise way to make much of the anti-anti-capital tax case is to observe that conventionally we often write production functions like:

    Y = F(K, AL)

    where A is a stand-in for labor-augmenting technology and is presumed to be either independent of the production process or, in the most common “endogenous growth” models, a function of cumulative capital investment. To break the Chamley-Judd result, all we have to do is write

    Y = F(K, A(w)L)

    that is, let labor-augmenting technology be in part a function of (after-tax) wages, defined either as current wages or especially as a cumulation of past wages. The choice to model A as independent of wages is rarely justified, and is not remotely obvious. It is merely conventional. Funny, the direction conventions in economics seem so frequently to tilt.

[1] If I’ve left you out, it’s because I am an idiot, not because I have judged you to be. Let me know and I’ll add you.