Archive for the 'Academia' Category

Political comic strips around the Mississippi Bubble of the 1710s

Published on 18 February 2010 in Academia, Article Summary, Economics, Epistemology, Finance and Politics. Tags: , , , , . 0 Comments

I wish that I had time to read this paper by David Levy and Sandra Peart.

It’s about political comics (cartoons) drawn to depict John Law and the Mississippi Bubble of the early 1700s.  It also speaks to subtlely different meanings of the words “alchemy” and “occult” than we are used to today. Here is an early paragraph in the paper:

Non-transparency induces a hierarchy of knowledge. The most extreme form of that sort of hierarchy might be called the cult of expertise in which expertise is said to be accompanied by godlike powers, the ability to unbind scarcity of matter and time. The earliest debates over hierarchy focused on whether such claims are credible or not.

Here is the abstract:

Economists have occasionally noticed the appearance of economists in cartoons produced for public amusement during crises. Yet the message behind such images has been less than fully appreciated. This paper provides evidence of such inattention in the context of the eighteenth century speculation known as the Mississippi Bubble. A cartoon in The Great Mirror of Folly imagines John Law in a cart that flies through the air drawn by a pair of beasts, reportedly chickens. The cart is not drawn by chickens, however, but by a Biblical beast whose forefather spoke to Eve about the consequences of eating from the tree of the knowledge. The religious image signifies the danger associated with knowledge. The paper thus demonstrates how images of the Mississippi Bubble focused on the hierarchy of knowledge induced by non-transparency. Many of the images show madness caused by alchemy, the hidden or “occult.”

Hat tip: Tyler Cowen.

Epistemology in the social sciences (economics included)

Published on 2 December 2009 in Academia, Economics and Epistemology. Tags: , , , . 1 Comment

I’m not sure how I came across it, but Daniel Little has a post summarising a 2006 article by Gabriel Abend:  “Styles of Sociological Thought: Sociologies, Epistemologies, and the Mexican and U.S. Quests for Truth“.  Daniel writes:

Abend attempts to take the measure of a particularly profound form of difference that might be postulated within the domain of world sociology: the idea that different national traditions of sociology may embody different epistemological frameworks that make their results genuinely incommensurable.

[...]

Consider this tabulation of results on the question of the role of evidence and theory taken by the two sets of articles:

[...]

Here is a striking tabulation of epistemic differences between the two samples:

Abend believes that these basic epistemological differences between U.S. and Mexican sociology imply a fundamental incommensurability of results:

To consider the epistemological thesis, let us pose the following thought experiment. Suppose a Mexican sociologist claims p and a U.S. sociologist claims not-p.  Carnap’s or Popper’s epistemology would have the empirical world arbitrate between these two theoretical claims. But, as we have seen, sociologists in Mexico and the United States hold different stances regarding what a theory should be, what an explanation should look like, what rules of inference and standards of proof should be stipulated, what role evidence should play, and so on. The empirical world could only adjudicate the dispute if an agreement on these epistemological presuppositions could be reached (and there are good reasons to expect that in such a situation neither side would be willing to give up its epistemology). Furthermore, it seems to me that my thought experiment to some degree misses the point. For it imagines a situation in which a Mexican sociologist claims p and a U.S. sociologist claims not-p, failing to realize that that would only be possible if the problem were articulated in similar terms. However, we have seen that Mexican and U.S. sociologies also differ in how problems are articulated—rather than p and not-p, one should probably speak of p and q.  I believe that Mexican and U.S. sociologies are perceptually and semantically incommensurable as well. (27)

Though Abend’s analysis is comparative, I find his analysis of the epistemological assumptions underlying the U.S. cases to be highly insightful all by itself.  In just a few pages he captures what seem to me to be the core epistemological assumptions of the conduct of sociological research in the U.S.  These include:

  • the assumption of “general regular reality” (the assumption that social phenomena are “really” governed by underlying regularities)
  • deductivism
  • epistemic objectivity
  • a preference for quantification and abstract vocabulary
  • separation of fact and value; value neutrality

There is a clear (?) parallel dispute in the study of economics as well, made all the more complicated by the allegations leveled at economics as a discipline as a result of the global financial crisis.

Changing the typesetting margins in Scientific Workplace

Published on 18 November 2009 in Academia and Economics. Tags: , , , , . 1 Comment

At least half of the LSE economics department uses Scientific Workplace, but an absurdly large fraction of all PDFs they produce have two-inch margins so they end up wasting half the page.

I finally got sufficiently annoyed to discover how to change it:

  1. Open a SW tex file
  2. Under the ‘Typeset’ menu, choose ‘Options and Packages…’
  3. Under the ‘Packages’ tab, add the ‘geometry’ package
  4. Under the ‘Typeset’ menu, choose ‘Preamble…’
  5. Add a line at the end specifying the margins.

For example:

\geometry{left=1in,right=1in,top=1in,bottom=1in}

Units of measurement available are listed on the webpage where I got this:  http://www.mackichan.com/index.html?techtalk/370.htm

Approximating a demand function with shocks to the elasticity of demand

Published on 16 November 2009 in Academia and Economics. Tags: , , , , . 0 Comments

Entirely for my own reference …

A demand function commonly used in macroeconomics is the following, derived from a Dixit-Stiglitz aggregator and exhibiting a constant own-price elasticity of demand (\gamma):

Q_{it}=\left(\frac{P_{it}}{P_{t}}\right)^{-\gamma}Q_{t}

A demand-side shock can then be modelled as a change in the elasticity of demand:

Q_{it}=\left(\frac{P_{it}}{P_{t}}\right)^{-\gamma D_{t}}Q_{t}

Where \ln\left(D_{t}\right) is, say, Normally distributed and plausibly autocorrelated.  We can rewrite this as a function of (natural) log deviations from long-run trends:

Q_{it}=\overline{Q_{t}}e^{q_{t}-\gamma e^{d_{t}}\left(p_{it}-p_{t}\right)}

Where:

  • Variables with a bar above them are long-run trends:  \overline{X_{it}}
  • Lower-case variables are natural log deviations from their long run trends (so that for small deviations, they may be thought of as the percentage difference from trend):  x_{it}=\ln\left(X_{it}\right)-\ln\left(\overline{X_{it}}\right)
  • The long-run trend of all prices is to equal the aggregate price:  \overline{P_{it}}=\overline{P_{t}}
  • The long-run trend of D_{t} is unity

We’ll construct a quadratic approximation around q_{t}=p_{it}=p_{t}=d_{t}=0 but, first, a table of partial derivatives for a more general function:

Function Value at x=y=z=0
f\left(x,y,z\right)=ae^{x+bye^{z}} a
f_{x}\left(x,y,z\right)=ae^{x+bye^{z}} a
f_{y}\left(x,y,z\right)=abe^{x+bye^{z}+z} ab
f_{z}\left(x,y,z\right)=abye^{x+bye^{z}+z} 0
f_{xx}\left(x,y,z\right)=ae^{x+bye^{z}} a
f_{yy}\left(x,y,z\right)=ab^{2}e^{x+bye^{z}+2z} ab^{2}
f_{zz}\left(x,y,z\right)=abye^{x+bye^{z}+z}+ab^{2}y^{2}e^{x+bye^{z}+2z} 0
f_{xy}\left(x,y,z\right)=abe^{x+bye^{z}+z} ab
f_{xz}\left(x,y,z\right)=abye^{x+bye^{z}+z} 0
f_{yz}\left(x,y,z\right)=abe^{x+bye^{z}+z}+ab^{2}ye^{x+bye^{z}+2z} ab

So that in the vicinity of x=y=z=0, the function f\left(x,y,z\right) is approximated by:

f\left(x,y,z\right)\simeq a + a\left(x+by\right) + a\left[\frac{1}{2}\left(x+by\right)^{2}+byz\right]

From which we can infer that:

Q_{it}\simeq \overline{Q_{t}}\left[1+\left(q_{t}-\gamma\left(p_{it}-p_{t}\right)\right) + \frac{1}{2}\left(q_{t}-\gamma\left(p_{it}-p_{t}\right)\right)^{2}-\gamma\left(p_{it}-p_{t}\right)d_{t}\right]

If introduced to a profit function, the first-order components (q_{t}-\gamma\left(p_{it}-p_{t}\right)) would vanish as individual prices will be optimal in the long run.

Update (20 Jan 2010): Added the half in each of the last equations.

Not raising the minimum wage with inflation will make your country fat

Published on 10 November 2009 in Academia, Article Summary, Economics, Health Care, Thinking on the margin and USA. Tags: , , , , , , . 3 Comments

Via Greg Mankiw, here is a new working paper by David O. Meltzer and Zhuo Chen: “The Impact of Minimum Wage Rates on Body Weight in the United States“. The abstract:

Growing consumption of increasingly less expensive food, and especially “fast food”, has been cited as a potential cause of increasing rate of obesity in the United States over the past several decades. Because the real minimum wage in the United States has declined by as much as half over 1968-2007 and because minimum wage labor is a major contributor to the cost of food away from home we hypothesized that changes in the minimum wage would be associated with changes in bodyweight over this period. To examine this, we use data from the Behavioral Risk Factor Surveillance System from 1984-2006 to test whether variation in the real minimum wage was associated with changes in body mass index (BMI). We also examine whether this association varied by gender, education and income, and used quantile regression to test whether the association varied over the BMI distribution. We also estimate the fraction of the increase in BMI since 1970 attributable to minimum wage declines. We find that a $1 decrease in the real minimum wage was associated with a 0.06 increase in BMI. This relationship was significant across gender and income groups and largest among the highest percentiles of the BMI distribution. Real minimum wage decreases can explain 10% of the change in BMI since 1970. We conclude that the declining real minimum wage rates has contributed to the increasing rate of overweight and obesity in the United States. Studies to clarify the mechanism by which minimum wages may affect obesity might help determine appropriate policy responses.

Emphasis is mine.  There is an obvious candidate for the mechanism:

  1. Minimum wages, in real terms, have been falling in the USA over the last 40 years.
  2. Minimum-wage labour is a significant proportion of the cost of “food away from home” (often, but not just including, fast-food).
  3. Therefore the real cost of producing “food away from home” has fallen.
  4. Therefore the relative price of “food away from home” has fallen.
  5. Therefore people eat “food away from home” more frequently and “food at home” less frequently.
  6. Typical “food away from home” has, at the least, more calories than “food at home”.
  7. Therefore, holding the amount of exercise constant,  obesity rates increased.

Update: The magnitude of the effect for items 2) – 7) will probably be greater for fast-food versus regular restaurant food, because minimum-wage labour will almost certainly comprise a larger fraction of costs for a fast-food outlet than it will for a fancy restaurant.

The likelihood-ratio threshold is the shadow price of statistical power

Published on 9 November 2009 in Academia, Economics and Epistemology. Tags: , , , , . 0 Comments

Cosma Shalizi, an associate professor in statistics at Carnegie Mellon University, gives an interpretation of the likelihood-ratio threshold in an LR test: It’s the shadow price of statistical power:

[...]

Suppose we know the probability density of the noise p and that of the signal is q. The Neyman-Pearson lemma, as many though not all schoolchildren know, says that then, among all tests off a given size s, the one with the smallest miss probability, or highest power, has the form “say ’signal’ if q(x)/p(x) > t(s), otherwise say ‘noise’,” and that the threshold t varies inversely with s. The quantity q(x)/p(x) is the likelihood ratio; the Neyman-Pearson lemma says that to maximize power, we should say “signal” if its sufficiently more likely than noise.

The likelihood ratio indicates how different the two distributions — the two hypotheses — are at x, the data-point we observed. It makes sense that the outcome of the hypothesis test should depend on this sort of discrepancy between the hypotheses. But why the ratio, rather than, say, the difference q(x) – p(x), or a signed squared difference, etc.? Can we make this intuitive?

Start with the fact that we have an optimization problem under a constraint. Call the region where we proclaim “signal” R. We want to maximize its probability when we are seeing a signal, Q(R), while constraining the false-alarm probability, P(R) = s. Lagrange tells us that the way to do this is to minimize Q(R) – t[P(R) - s] over R and t jointly. So far the usual story; the next turn is usually “as you remember from the calculus of variations…”

Rather than actually doing math, let’s think like economists. Picking the set R gives us a certain benefit, in the form of the power Q(R), and a cost, tP(R). (The ts term is the same for all R.) Economists, of course, tell us to equate marginal costs and benefits. What is the marginal benefit of expanding R to include a small neighborhood around the point x? Just, by the definition of “probability density”, q(x). The marginal cost is likewise tp(x). We should include x in R if q(x) > tp(x), or q(x)/p(x) > t. The boundary of R is where marginal benefit equals marginal cost, and that is why we need the likelihood ratio and not the likelihood difference, or anything else. (Except for a monotone transformation of the ratio, e.g. the log ratio.) The likelihood ratio threshold t is, in fact, the shadow price of statistical power.

It seems sensible to me.

Who has more information, the Central Bank or the Private Sector?

Published on 5 November 2009 in Academia, Article Summary, Economics, Finance and Welfare. Tags: , , , , , . 0 Comments

A friend pointed me to this paper:

Svensson, Lars E. O. and Michael Woodford. “Indicator Variables For Optimal Policy,” Journal of Monetary Economics, 2003, v50(3,Apr), 691-720.

You can get the NBER working paper (w8255) here.  The abstract:

The optimal weights on indicators in models with partial information about the state of the economy and forward-looking variables are derived and interpreted, both for equilibria under discretion and under commitment. The private sector is assumed to have information about the state of the economy that the policymaker does not possess. Certainty-equivalence is shown to apply, in the sense that optimal policy reactions to optimally estimated states of the economy are independent of the degree of uncertainty. The usual separation principle does not hold, since the estimation of the state of the economy is not independent of optimization and is in general quite complex. We present a general characterization of optimal filtering and control in settings of this kind, and discuss an application of our methods to the problem of the optimal use of ‘real-time’ macroeconomic data in the conduct of monetary policy. [Emphasis added by John Barrdear]

The sentence I’ve highlighted is interesting.  As written in the abstract, it’s probably true.  Here’s a paragraph from page two that expands the thought:

One may or may not believe that central banks typically possess less information about the state of the economy than does the private sector. However, there is at least one important argument for the appeal of this assumption. This is that it is the only case in which it is intellectually coherent to assume a common information set for all members of the private sector, so that the model’s equations can be expressed in terms of aggregative equations that refer to only a single “private sector information set,” while at the same time these model equations are treated as structural, and hence invariant under the alternative policies that are considered in the central bank’s optimization problem. It does not make sense that any state variables should matter for the determination of economically relevant quantities (that is, relevant to the central bank’s objectives), if they are not known to anyone in the private sector. But if all private agents are to have a common information set, they must then have full information about the relevant state variables. It does not follow from this reasoning, of course, that it is more accurate to assume that all private agents have superior information to that of the central bank; it follows only that this case is one in which the complications resulting from partial information are especially tractable. The development of methods for characterizing optimal policy when di fferent private agents have di fferent information sets remains an important topic for further research.

Here’s my attempt as paraphrasing Svensson and Woodford in point form:

  1. The real economy is the sum of private agents (plus the government, but ignore that)
  2. Complete information is thus, by definition, knowledge of every individual agent
  3. If we assume that everybody knows about themselves (at least), then the union of all private information sets must equal complete information
  4. The Central Bank observes only a sample of private agents
  5. That is, the Central Bank information set is a subset of the union of all private information sets. The Central Bank’s information cannot be greater than the union of all private information sets.
  6. One strategy in simplifying the Central Bank’s problem is to assume that private agents are symmetric in information (i.e. they have a common information set).  In that case, we’d say that the Central Bank cannot have more information than the representative private sector agent. [See note 1 below]
  7. Important future research will involve relaxing the assumption in (f) and instead allowing asymmetric information across different private agents.  In that world, the Central Bank might have more information than any given private agent, but still less than the union of all private agents.

Svensson and Woodford then go on to consider a world where the Central Bank’s information set is smaller than (i.e. is a subset of) the Private Sector’s common information set.

But that doesn’t really make sense to me.

If private agents share a common information set, it seems silly to suppose that the Central Bank has less information than the Private Sector, for the simple reason that the mechanism of creating the common information set – commonly observable prices that are sufficient statistics of private signals – is also available to the Central Bank.

In that situation, it seems more plausible to me to argue that the CB has more information than the Private Sector, provided that their staff aren’t quietly acting on the information on the side.  It also would result in observed history:  the Private Sector pays ridiculous amounts of attention to every word uttered by the Central Bank (because the Central Bank has the one private signal that isn’t assimilated into the price).

Note 1: To arrive at all private agents sharing a common information set, you require something like the EMH (in fact, I can’t think how you could get there without the EMH).  A common information set emerges from a commonly observable sufficient statistic of all private information.  Prices are that statistic.

    Be careful interpreting Lagrangian multipliers

    Published on 15 October 2009 in Academia and Economics. Tags: , , , , , , . 0 Comments

    Last year I wrote up a derivation of the New Keynesian Phillips Curve using Calvo pricing.  At the start of it, I provided the standard pathway from the Dixit-Stiglitz aggregator for consumption to the constant own-price elasticity individual demand function.  Let me reproduce it here:

    There is a constant and common elasticity of substitution between each good: \varepsilon>1.  We aggregate across the different consumptions goods:

    C=\left(\int_{0}^{1}C\left(i\right)^{\frac{\varepsilon-1}{\varepsilon}}di\right)^{\frac{\varepsilon}{\varepsilon-1}}

    P\left(i\right) is the price of good i, so the total expenditure on consumption is \int_{0}^{1}P\left(i\right)C\left(i\right)di

    A representative consumer seeks to minimise their expenditure subject to achieving at least C units of aggregate consumption. Using the Lagrange multiplier method:

    L=\int_{0}^{1}P\left(i\right)C\left(i\right)di-\lambda\left(\left(\int_{0}^{1}C\left(i\right)^{\frac{\varepsilon-1}{\varepsilon}}di\right)^{\frac{\varepsilon}{\varepsilon-1}}-C\right)

    The first-order conditions are that, for every intermediate good, the first derivative of L with respect to C\left(i\right) must equal zero. This implies that:

    P\left(i\right)=\lambda C\left(i\right)^{\frac{-1}{\varepsilon}}\left(\int_{0}^{1}C\left(j\right)^{\frac{\varepsilon-1}{\varepsilon}}dj\right)^{\frac{1}{\varepsilon-1}}

    Substituting back in our definition of aggregate consumption, replacing \lambda with P (since \lambda represents the cost of buying an extra unit of the aggregate good C) and rearranging, we end up with the demand curve for each intermediate good:

    C\left(i\right)=\left(\frac{P\left(i\right)}{P}\right)^{-\varepsilon}C

    If that Lagrangian looks odd to you, or if you’re asking where the utility function’s gone, you’re not alone.  It’s obviously just the dual problems of consumer theory – the fact that it doesn’t matter if you maximise utility subject to a budget constraint or minimise expenditure subject to a minimum level of utility – but what I want to focus on is the resulting interpretation of the lagrangian multipliers.

    Let’s rephrase the problem as maximising utility, with utility a generic function of aggregate consumption, U\left(C\right).  The Lagrangian is then:

    L=U\left(\left(\int_{0}^{1}C\left(i\right)^{\frac{\varepsilon-1}{\varepsilon}}di\right)^{\frac{\varepsilon}{\varepsilon-1}}\right)+\mu\left(M-\int_{0}^{1}P\left(i\right)C\left(i\right)di\right)

    The first-order conditions are:

    U'\left(C\right)\left(\int_{0}^{1}C\left(j\right)^{\frac{\varepsilon-1}{\varepsilon}}dj\right)^{\frac{1}{\varepsilon-1}}C\left(i\right)^{\frac{-1}{\varepsilon}}=\mu P\left(i\right)

    Rearranging and substituting back in the definition for C then gives us:

    C\left(i\right)=\left(P\left(i\right)\frac{\mu}{U'\left(C\right)}\right)^{-\varepsilon}C

    In the first approach, \lambda represents the cost of buying an extra unit of the aggregate good C, which is the definition of the aggregate price level.  In the second approach, \mu represents the cost of buying an extra unit of income, which is not the same thing.  Comparing the two results, we can see that:

    \lambda=P=\frac{U'\left(C\right)}{\mu}

    Which should cause you to raise an eyebrow.  Why aren’t the two multipliers just the inverses of each other?  Aren’t they meant to be?  Yes, they are, but only when the two problems are equivalent.  These two problems are slightly different.

    In the first one, to be equivalent, the term in the lagrangian would need to be V - U\left(\left(\int_{0}^{1}C\left(i\right)^{\frac{\varepsilon-1}{\varepsilon}}di\right)^{\frac{\varepsilon}{\varepsilon-1}}\right), which would give us Hicksian demands as a function of utility level (V).  But since we assumed that utility is only a function of aggregate consumption, then in order to pin down a level of utility, it’s sufficient to pin down a level of aggregate consumption; and that is useful to us because a) a level of utility doesn’t mean much to us as macroeconomists but a level of aggregate consumption does and b) it means that we can recognise the lagrange multiplier as the aggregate price level.

    Which, when you think about it, makes perfect sense.  Extra income must be adjusted by the marginal value of the extra consumption it affords in order to arrive at the price that the (representative) consumer would be willing to pay for that consumption.

    In other words:  be careful when interpreting your Lagrangian multipliers.

    The Nobel committee can’t lose in their decision over Fama

    Published on 9 October 2009 in Academia, Betting markets, Economics, Finance and Humour. Tags: , , , . 0 Comments

    Alex Tabarrok points out the amusing truth:

    Ladbrokes gives Eugene Fama the best odds for winning the economics Nobel.  Thus, if Fama wins he will have deserved to have won and if Fama loses he will not have deserved to have won.  The Nobel committee cannot go wrong no matter what it does!  Think about it.

    In which I respectfully disagree with Paul Krugman

    Published on 25 August 2009 in Academia, Economics, Labour and USA. Tags: , , , , , , , . 0 Comments

    Paul Krugman [Ideas, Princeton, Unofficial archive] has recently started using the phrase “jobless recovery” to describe what appears to be the start of the economic recovery in the United States [10 Feb, 21 Aug, 22 Aug, 24 Aug].  The phrase is not new.  It was first used to describe the recovery following the 1990/1991 recession and then used extensively in describing the recovery from the 2001 recession.  In it’s simplest form, it is a description of an economic recovery that is not accompanied by strong jobs growth.  Following the 2001 recession, in particular, people kept losing jobs long after the economy as a whole had reached bottom and even when employment did bottom out, it was very slow to come back up again.  Professor Krugman (correctly) points out that this is a feature of both post-1990 recessions, while prior to that recessions and their subsequent recoveries were much more “V-shaped”.  He worries that it will also describe the recovery from the current recession.

    While Professor Krugman’s characterisations of recent recessions are broadly correct, I am still inclined to disagree with him in predicting what will occur in the current recovery.  This is despite Brad DeLong’s excellent advice:

    1. Remember that Paul Krugman is right.
    2. If your analysis leads you to conclude that Paul Krugman is wrong, refer to rule #1.

    This will be quite a long post, so settle in.  It’s quite graph-heavy, though, so it shouldn’t be too hard to read. :-)

    Professor Krugman used his 24 August post on his blog to illustrate his point.  I’m going to quote most of it in full, if for no other reason than because his diagrams are awesome:

    First, here’s the standard business cycle picture:

    DESCRIPTION

    Real GDP wobbles up and down, but has an overall upward trend. “Potential output” is what the economy would produce at “full employment”, which is the maximum level consistent with stable inflation. Potential output trends steadily up. The “output gap” — the difference between actual GDP and potential — is what mainly determines the unemployment rate.

    Basically, a recession is a period of falling GDP, an expansion a period of rising GDP (yes, there’s some flex in the rules, but that’s more or less what it amounts to.) But what does that say about jobs?

    Traditionally, recessions were V-shaped, like this:

    DESCRIPTION

    So the end of the recession was also the point at which the output gap started falling rapidly, and therefore the point at which the unemployment rate began declining. Here’s the 1981-2 recession and aftermath:

    DESCRIPTION

    Since 1990, however, growth coming out of a slump has tended to be slow at first, insufficient to prevent a widening output gap and rising unemployment. Here’s a schematic picture:

    DESCRIPTION

    And here’s the aftermath of the 2001 recession:

    DESCRIPTION

    Notice that this is NOT just saying that unemployment is a lagging indicator. In 2001-2003 the job market continued to get worse for a year and a half after GDP turned up. The bad times could easily last longer this time.

    Before I begin, I have a minor quibble about Prof. Krugman’s definition of “potential output.”  I think of potential output as what would occur with full employment and no structural frictions, while I would call full employment with structural frictions the “natural level of output.”  To me, potential output is a theoretical concept that will never be realised while natural output is the central bank’s target for actual GDP.  See this excellent post by Menzie Chinn.  This doesn’t really matter for my purposes, though.

    In everything that follows, I use total hours worked per capita as my variable since that most closely represents the employment situation witnessed by the average household.  I only have data for the last seven US recessions (going back to 1964).  You can get the spreadsheet with all of my data here: US_Employment [Excel].  For all images below, you can click on them to get a bigger version.

    The first real point I want to make is that it is entirely normal for employment to start falling before the official start and to continue falling after the official end of recessions.  Although Prof. Krugman is correct to point out that it continued for longer following the 1990/91 and 2001 recessions, in five of the last six recessions (not counting the current one) employment continued to fall after the NBER-determined trough.  As you can see in the following, it is also the case that six times out of seven, employment started falling before the NBER-determined peak, too.

    Hours per capita fell before and after recessions

    Prof. Krugman is also correct to point out that the recovery in employment following the 1990/91 and 2001 recessions was quite slow, but it is important to appreciate that this followed a remarkably slow decline during the downturn.  The following graph centres each recession around it’s actual trough in hours worked per capita and shows changes relative to those troughs:

    Hours per capita relative to and centred around trough

    The recoveries following the 1990/91 and 2001 recessions were indeed the slowest of the last six, but they were also the slowest coming down in the first place.  Notice that in comparison, the current downturn has been particularly rapid.

    We can go further:  the speed with which hours per capita fell during the downturn is an excellent predictor of how rapidly they rise during the recovery.  Here is a scatter plot that takes points in time chosen symmetrically about each trough (e.g. 3 months before and 3 months after) to compare how far hours per capita fell over that time coming down and how far it had climbed on the way back up:

    ComparingRecessions_20090605_Symmetry_Scatter_All

    Notice that for five of the last six recoveries, there is quite a tight line describing the speed of recovery as a direct linear function of the speed of the initial decline.  The recovery following the 1981/82 recession was unusually rapid relative to the speed of it’s initial decline.  Remember (go back up and look) that Prof. Krugman used the 1981/82 recession and subsequent recovery to illustrate the classic “V-shaped” recession.  It turns out to have been an unfortunate choice since that recovery was abnormally rapid even for pre-1990 downturns.

    Excluding the 1981/82 recession on the basis that it’s recovery seems to have been driven by a separate process, we get quite a good fit for a simple linear regression:

    ComparingRecessions_20090605_Symmetry_Scatter_Excl_81-82

    Now, I’m the first to admit that this is a very rough-and-ready analysis.  In particular, I’ve not allowed for any autoregressive component to employment growth during the recovery.  Nevertheless, it is quite strongly suggestive.

    Given the speed of the decline that we have seen in the current recession, this points us towards quite a rapid recovery in hours worked per capita (although note that the above suggests that all recoveries are slower than the preceding declines – if they were equal, the fitted line would be at 45% (the coefficient would be one)).