One of the more interesting developments this summer in my own set of intellectual tics is that I've become increasingly enthusiastic about using atheoretic time series models as smoothing functions. If I want the "smoothed" value for a function at a particular time, I use the atheoretic model to predict its value a few periods out, and I use that predicted value as the smoothed value; particularly if I'm using a model that will always predict a constant value for the series once it's taken more than a couple periods out — e.g. an ARIMA(0,1,n) model will give the same prediction for n periods from now as for n+1, n+2, etc. — then any change in the "long-run" value represents "innovation", i.e. a surprise; a large rise in unemployment claims that results in very little change in the prediction is mostly not new economic news, but simply an expression of the short-term dynamics that were anticipated from previous data points. A model that does a good job of capturing these short-term dynamics should therefore result in predictions that change much less than the series itself does, and so provides a smoother series than the input.
For longer-term periods of time, there's probably some philosophical value to separating the short-term smoothed data to a prediction of where the data will be later; in particular, a model that did a very good job of predicting the data five years out would not be suitable for "smoothing" if I'm hoping to use the smoothed data to observe the business cycle. Measurement errors aside, each time scale will have fluctuations that are to be viewed as material and shorter-term "noise"; the real purpose of smoothing functions is to eliminate the noise, preserving as much of the "signal" as possible. As long as my projections only go a few periods out, I imagine that's what I'm doing; again, changes in my projection represent changes in inferred "signal", while fully anticipated changes in the data series are identified as being due to noise.
I have, in the past, looked at smoothing functions that require future data points to construct today's value; for example, if I look at data from 2008 and I wish to smooth stock-market prices, my smoothed function might start decreasing substantially in August or September because of the lower values it needs to achieve to match the data in November. If the point is to look at data as it comes in and identify trends early, though, that doesn't work so well; hence my preference for looking at purely backward-looking measures, even when I have forward data sets available to me. There are good economic contexts in which it makes sense to use all available data to try to extract noise from signal and seek dynamics that may not have been ascertainable in real-time; in those situations, atheoretic ARIMA models are probably not your best choice.
Saturday, July 25, 2009
Wednesday, April 8, 2009
liquidity
In an economy with a single medium of exchange, "liquidity" of anything else represents the ability to convert that else into that medium. If I have two assets, one with a 5% bid-offer spread but very stable, the other more tightly bid but very likely to drop well over 5% before I'm looking to convert the asset to something else, it seems to me the former better serves any needs that tend to get lumped under the term "liquidity". This is how I model it mentally, is as a softish lower bound on the price for which I could sell it if the value of money to me (and its associated discount rate — i.e. where selling today might be better than selling at 1% more tomorrow) were to spike.
Stock price volatility tends to increase as stock prices drop, and this is usually couched in terms that suggest the latter causes the former, but it kind of makes more sense that it would run the other way: part of the value of stock is its "liquidity", i.e. one's ability to convert it, at little notice, into cash should that be necessary. When uncertainty increases, that, other things equal, is going to reduce the value of the stock.
Stock price volatility tends to increase as stock prices drop, and this is usually couched in terms that suggest the latter causes the former, but it kind of makes more sense that it would run the other way: part of the value of stock is its "liquidity", i.e. one's ability to convert it, at little notice, into cash should that be necessary. When uncertainty increases, that, other things equal, is going to reduce the value of the stock.
Wednesday, February 25, 2009
frames and prospects
When I think about "prospect theory" and behavioral economics in general, I tend mostly to think about loss-aversion and to be bemused by framing effects, but one of the other reliable findings is that agents who face losses become risk-seeking rather than risk-averse. Someone presented with a sure $25 or a coin-toss for $50 will usually take the bird in hand, but presented with losses of the same magnitude, people will frequently prefer the coin toss — any chance to maybe, possibly reduce the losses.
It occurs to me that this is something we observe on the macro level. Insurance companies do well for a while, rates start to come down, they start seeking out riskier insurees and refuse to give up share of unprofitable business, and eventually KABOOM! Financial institutions see risk premia or even just interest rates come down, they think they're entitled to higher returns, they go "yield-chasing" (buying up riskier assets) and increase leverage, and eventually KABOOM!
I wonder if there's a good institutional way to check this propensity for making a bad thing worse. Getting insolvent companies into bankruptcy before they can cause harm seems like a good start.
It occurs to me that this is something we observe on the macro level. Insurance companies do well for a while, rates start to come down, they start seeking out riskier insurees and refuse to give up share of unprofitable business, and eventually KABOOM! Financial institutions see risk premia or even just interest rates come down, they think they're entitled to higher returns, they go "yield-chasing" (buying up riskier assets) and increase leverage, and eventually KABOOM!
I wonder if there's a good institutional way to check this propensity for making a bad thing worse. Getting insolvent companies into bankruptcy before they can cause harm seems like a good start.
Wednesday, January 28, 2009
factors of production
Are slaves labor or capital?
I was just reading the introduction to Hayek's "The Pure Theory of Capital" — a book I fully expect not to finish — and he ultimately decides to use the term "capital" to mean "the total stock of the non-permanent factors of production". Presumably this includes some of "natural resources", insofar as those are depletable; I typically think of "capital" as something in which one can invest. (What "human capital" and "physical capital" have in common; each represents the devotion of some economic resources in the past to enhance production in the future. Natural resources I suppose represent a decision not to have depleted them faster in the past than we have. Perhaps Hayek's distinction makes sense.)
Of course, I can gear my slaves toward reproduction rather than production of something else, thereby enhancing my future stock of slaves. This isn't so different from human capital in general, though. In many ways, labor simply looks like a particular kind of capital. I wonder how fundamental the "factors of production" are, and how much they rely on ontology to be useful.
I was just reading the introduction to Hayek's "The Pure Theory of Capital" — a book I fully expect not to finish — and he ultimately decides to use the term "capital" to mean "the total stock of the non-permanent factors of production". Presumably this includes some of "natural resources", insofar as those are depletable; I typically think of "capital" as something in which one can invest. (What "human capital" and "physical capital" have in common; each represents the devotion of some economic resources in the past to enhance production in the future. Natural resources I suppose represent a decision not to have depleted them faster in the past than we have. Perhaps Hayek's distinction makes sense.)
Of course, I can gear my slaves toward reproduction rather than production of something else, thereby enhancing my future stock of slaves. This isn't so different from human capital in general, though. In many ways, labor simply looks like a particular kind of capital. I wonder how fundamental the "factors of production" are, and how much they rely on ontology to be useful.
Monday, January 26, 2009
The Wealth and Debt of Nations
Consider an international economic system in which there is relatively little trade, and then it opens up to trade in goods and to mobility in one and only one factor of production. Assume the different nations have different total factor productivities, due to technology or institutions, but that such differences are factor-neutral. What one would see is that the mobile factor would tend to move toward productive nations, increasing (even further) the marginal product of the other factors in those countries, while reducing the comparative attractiveness of the now abundant factor in those countries. If domestic "supply" of factors is at all elastic, the domestic supply of the mobile factor should decrease as its supply from foreigners surges.
I just read a snippet suggesting that it is inappropriate or confusing that the wealthiest nation on earth should have become (based on net foreign investment) a huge debtor nation. That doesn't strike me as a paradox; it just tells me that capital is more mobile than labor.
I just read a snippet suggesting that it is inappropriate or confusing that the wealthiest nation on earth should have become (based on net foreign investment) a huge debtor nation. That doesn't strike me as a paradox; it just tells me that capital is more mobile than labor.
Sunday, January 4, 2009
GDP as a welfare proxy
GDP growth is popularly spoken of as though it were the ne plus ultra of economic policy; if growth is high, policy is succeeding, and if it's low, it's failing. Exogenous effects aside, GDP is not a perfect proxy for what economists call "welfare", namely how well off everyone is. One illustration of the discrepancy was recently given by Mankiw; longer ago the misuse of GDP was decried by Bobby Kennedy*. The best defense of the use of GDP in these ways has been that, while it doesn't conceptually capture everything it should, it's likely to correlate with welfare, and that eras of high GDP growth tend to be better for welfare growth than other eras. (I've made this argument myself.)
As Robert Lucas noted, though, correlations can be true under certain policy regimes but not others; in particular, policy tailored to a historical correlation, by creating an incentive by policy-makers to optimize a single (imperfect) measure of welfare rather than (unmeasurable) welfare itself, is likely to reduce that measure's correlation with welfare. Just as a chandelier factory in the USSR, told it would be paid by weight for its product, produced the heaviest chandeliers in the world, the focus on a particular measure will optimize that measure, both in ways that optimize what it should be measuring, and in ways that do not. As Mankiw pointed out, it's possible to design stimulus that increases GDP but not welfare. If GDP is being optimized, those forms of stimulus will look like a good idea.
In every popular, simple, short-term policy model of the economy — I'm thinking in particular of a sticky-wages model for the effects of unexpected inflation, but I've also thought in the last couple days that this is likely true of a simple microeconomic analysis of Keynesian demand-pumping — a boost in GDP comes at the expense of welfare. Unexpected inflation reduces real wages, so that workers work more than they would prefer at that wage; a deficit reduces savings, boosting consumption at the expense of capital accumulation. Other sticky prices or other mechanisms that these models leave out might change things, and certainly a good argument for boosting GDP is the psychological effect it has — the recession-as-a-coordination-problem model — and I'm pretty sure that in both cases I give above, the GDP boost is first-order while the welfare loss is second-order, so that a small error of analysis is likely to change the qualitative outcome. Still, it seems worth remembering that there is a distinction, and worth occasionally asking whether something targeted at GDP as a proxy for welfare is actually welfare-enhancing or not. I'm not sure Keynesian stimulus usually or always is.
* I would quibble with some of what Kennedy says, e.g. that GDP counts "destruction of our redwoods and the loss of our natural wonder". A better welfare measure would subtract environmental losses; GDP does not include additions for them, but does include additions for products that entail those losses. In any case, his broad thesis is correct.
As Robert Lucas noted, though, correlations can be true under certain policy regimes but not others; in particular, policy tailored to a historical correlation, by creating an incentive by policy-makers to optimize a single (imperfect) measure of welfare rather than (unmeasurable) welfare itself, is likely to reduce that measure's correlation with welfare. Just as a chandelier factory in the USSR, told it would be paid by weight for its product, produced the heaviest chandeliers in the world, the focus on a particular measure will optimize that measure, both in ways that optimize what it should be measuring, and in ways that do not. As Mankiw pointed out, it's possible to design stimulus that increases GDP but not welfare. If GDP is being optimized, those forms of stimulus will look like a good idea.
In every popular, simple, short-term policy model of the economy — I'm thinking in particular of a sticky-wages model for the effects of unexpected inflation, but I've also thought in the last couple days that this is likely true of a simple microeconomic analysis of Keynesian demand-pumping — a boost in GDP comes at the expense of welfare. Unexpected inflation reduces real wages, so that workers work more than they would prefer at that wage; a deficit reduces savings, boosting consumption at the expense of capital accumulation. Other sticky prices or other mechanisms that these models leave out might change things, and certainly a good argument for boosting GDP is the psychological effect it has — the recession-as-a-coordination-problem model — and I'm pretty sure that in both cases I give above, the GDP boost is first-order while the welfare loss is second-order, so that a small error of analysis is likely to change the qualitative outcome. Still, it seems worth remembering that there is a distinction, and worth occasionally asking whether something targeted at GDP as a proxy for welfare is actually welfare-enhancing or not. I'm not sure Keynesian stimulus usually or always is.
* I would quibble with some of what Kennedy says, e.g. that GDP counts "destruction of our redwoods and the loss of our natural wonder". A better welfare measure would subtract environmental losses; GDP does not include additions for them, but does include additions for products that entail those losses. In any case, his broad thesis is correct.
Friday, January 2, 2009
time-ordering and information-ordering
There is a famous puzzle, which some googling suggests is known as Newcomb's paradox, involving an expert on human nature (or something) who presents each player of a game with two envelopes, one of which the player knows to contain $1000. The player is permitted to receive either just the other envelope, or both envelopes; if this expert believes both envelopes will be taken, the second envelope is empty, while if the expert believes that only that second envelope will be taken, then it contains $1,000,000. After observing several other players, for each of whom the expert's prediction was correct, do you choose to accept both envelopes, or do you decline the $1,000 to take just the second?
My answer is that I take only the second envelope. I don't know what's going on in precise detail, but it appears to me that, one way or another, my decision is available to the expert when the envelopes are sealed. I apparently take my action after the expert acts first, but, the way the game appears to me, the information I have available when I act is circumscribed — I don't know what's in the second envelope — but the expert's decision is made knowing what I will do. The game, in information order, is that I make my decision, and then the expert places the checks, even though that is not the time-ordering of events.
There are a lot of situation in which uncertainty is of importance in economics, and it is very rarely the case that it matters whether the uncertainty is due to a lack of knowledge about the present or a lack of knowledge about the future. If you and I are stuck together for six hours, and we know that a football game has taken place during that time but that neither of us knows how it has gone, it is just as reasonable for us to bet on it at the end of six hours as at the beginning; in the former case we are betting on an event that has, in a time sense, already happened, but for which we are just as uninformed as if it hadn't taken place yet. Similarly, if I am about to have a test done to determine whether I have a genetic predisposition to some disease, it seems reasonable to ask an insurance company to provide me insurance against an adverse result, provided I don't initially know any more than the insurance company does, even though the genes are already there and the information in some sense already exists.
Studying actions of policy-makers or financial markets is invariably complicated by causal relationships running both directions in time; the stock market may rise because the economy is likely to improve in six months, but the economy may improve because the stock market rose. In that case, the effects likely reintensify their own causes — a "positive feedback loop" — but there are negative (i.e. stabilizing) feedback loops as well. Monetary economists speak of a "price puzzle" when one does a naive analysis of the effect of monetary policy on the economy, where tighter monetary policy seems to be followed by an increase in inflation for a short period of time; this is what one would expect if monetary policy is being done competently — the monetary authority should tighten policy when an increase in inflation is coming. Because the earlier event is being taken on the basis of anticipation of the later event, the causal relationship runs backward in time (though, in these cases, it runs forward as well).
I think the real-world solutions to a lot of game theory conundrums — incidentally, I've done less reading on this than I should — involve effects of this nature. People will work out that a repeated Prisoners' dilemma can yield cooperation, at least for a while, so long as future results are discounted relative to current ones, or some such, but, while time-preferences can be screwy and extreme, it usually seems to require too big a discount to generate the results you see in experiments (or real life), and almost certainly isn't in accord with how the agents themselves would describe their rationales. They might talk in moral terms, but it seems likely to me that a certain amount of what is going on is that people know that other people are somewhat cooperative, and — especially in real life — they believe they can tell "what kind of person" some counterparty to some arrangement is. Insofar as one can be read ahead of time, one is at least partially precommitted before the game formally begins.
My answer is that I take only the second envelope. I don't know what's going on in precise detail, but it appears to me that, one way or another, my decision is available to the expert when the envelopes are sealed. I apparently take my action after the expert acts first, but, the way the game appears to me, the information I have available when I act is circumscribed — I don't know what's in the second envelope — but the expert's decision is made knowing what I will do. The game, in information order, is that I make my decision, and then the expert places the checks, even though that is not the time-ordering of events.
There are a lot of situation in which uncertainty is of importance in economics, and it is very rarely the case that it matters whether the uncertainty is due to a lack of knowledge about the present or a lack of knowledge about the future. If you and I are stuck together for six hours, and we know that a football game has taken place during that time but that neither of us knows how it has gone, it is just as reasonable for us to bet on it at the end of six hours as at the beginning; in the former case we are betting on an event that has, in a time sense, already happened, but for which we are just as uninformed as if it hadn't taken place yet. Similarly, if I am about to have a test done to determine whether I have a genetic predisposition to some disease, it seems reasonable to ask an insurance company to provide me insurance against an adverse result, provided I don't initially know any more than the insurance company does, even though the genes are already there and the information in some sense already exists.
Studying actions of policy-makers or financial markets is invariably complicated by causal relationships running both directions in time; the stock market may rise because the economy is likely to improve in six months, but the economy may improve because the stock market rose. In that case, the effects likely reintensify their own causes — a "positive feedback loop" — but there are negative (i.e. stabilizing) feedback loops as well. Monetary economists speak of a "price puzzle" when one does a naive analysis of the effect of monetary policy on the economy, where tighter monetary policy seems to be followed by an increase in inflation for a short period of time; this is what one would expect if monetary policy is being done competently — the monetary authority should tighten policy when an increase in inflation is coming. Because the earlier event is being taken on the basis of anticipation of the later event, the causal relationship runs backward in time (though, in these cases, it runs forward as well).
I think the real-world solutions to a lot of game theory conundrums — incidentally, I've done less reading on this than I should — involve effects of this nature. People will work out that a repeated Prisoners' dilemma can yield cooperation, at least for a while, so long as future results are discounted relative to current ones, or some such, but, while time-preferences can be screwy and extreme, it usually seems to require too big a discount to generate the results you see in experiments (or real life), and almost certainly isn't in accord with how the agents themselves would describe their rationales. They might talk in moral terms, but it seems likely to me that a certain amount of what is going on is that people know that other people are somewhat cooperative, and — especially in real life — they believe they can tell "what kind of person" some counterparty to some arrangement is. Insofar as one can be read ahead of time, one is at least partially precommitted before the game formally begins.
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