QE2 in Five Easy Pieces

A lot of people appear confused about QE2 and the Fed has recently come under a lot of attack following its recent announcement. Well, maybe the following will help a bit.  James Bullard, president of the St. Louis Fed, recently delivered a speech on QE2 entitled QE2 in Five Easy Pieces. For those that are interested, you can view his presentation slides here.

Ron Paul on the Fed Again

I have to admit that I like listening to the little guy speak. My view of Ron Paul (and yes, I have read End the Fed, though I haven't had time to comment on it yet) is that he is a smart guy with good instincts and a good understanding of the events that have shaped monetary history in the U.S. and elsewhere. (This is unlike PK who, while also very smart, appears to have shaped his macroeconomic theory entirely on the apparent failure of a local babysitting cooperative).

Here is Ron Paul's attack on the Fed today: Fed Will Self-Destruct. I don't necessarily disagree with any of the points made in the written article (apart from the fact that Bernanke has never advocated 4% inflation). Some of the things he says in the video interview, however, seem rather strange.

With respect to our "deeply flawed monetary system" he appears to be concerned that one person (Bernanke) has the power to create $600B with the stroke of pen (out of thin air) and then spend it (foolishly).

Note: while the Fed is indeed able to create cash (or reserve balances) "out of thin air," under normal circumstances, the Fed is effectively prevented from spending this cash on anything other than U.S. government bonds. These bonds are also created "out of thin air" (they exist almost exclusively in book entry form). When the Fed purchases government bonds, it is really just swapping one form of air for another.

When phrased in this way, it becomes a little harder to see why a swap of Fed air for Treasury air should be inflationary (though note, his definition of inflation is money creation -- so of course he sees inflation everywhere, even though price-level inflation remains anemic).

Paul "Malibu Barbie" Krugman?

Did you see this recent post by Brad DeLong? 

In terms reminiscent of Malibu Barbie's "math is hard," now comes Paul Krugman from the New York Times to say that "Macroeconomics is Hard."

What, you didn't see it? That's because it didn't happen. DeLong evidently doesn't have the balls to mock Krugman the way he does junior members of the profession (who stress essentially the same thing); see here.

Here is what Krugman has to say:

The thing is, no amount of experience meeting a payroll helps you understand issues that are critically affected by the way things add up at a macro level. Businesses are open systems; the world economy is a closed system, with feedback effects that are crucial but play no role in ordinary business experience. In particular, an individual businessman, no matter how brilliant, never has to worry about the fact that total income equals total spending, so that if some people spend less, either someone else must spend more, or aggregate income must fall.

Every macroeconomic theorist is going to agree with Krugman that identifying, accounting for, and anticipating "feedback effects" is what makes macro hard. These feedback effects are sometimes called "general equilibrium effects" in the literature. Coming to grips with these feedback effects is the whole point behind dynamic general equilibrium modeling.

My only quibble with Krugman's statement above is that he implicitly suggests that these feedback effects work solely, or predominantly, via spending decisions. One could have alternatively written:

In particular, an individual businessman, no matter how brilliant, never has to worry about the fact that total production equals total spending equals total income, so that if some people produce less, either someone else must produce more, or aggregate income must fall.

Don't say something like this in public though (you'll get accused of worshipping at the idol of JB Say). But on a more serious note, one might also expect feedback effects to operate via prices, credit limits, participation decisions, etc., etc.
 
I must confess though...I do find something odd about Krugman's position here. That is, he feels compelled here to discount the views of individual businessmen; such views, while informed, are necessarily "local" in nature--they are not necessarily useful for understanding or interpreting what is happening at the macro level. 

Unless, that is, their views happen to support your own pet hypothesis (er, knowledge of truth, excuse me); see here: It's Demand, Stupid. To quote:

I’ve said this before, but Catherine Rampell has a very nice chart making the point: if you ask businesses — as opposed to their lobbyists — what their problem is, you find no hint of the stories the usual suspects are telling you about government interference, political uncertainty, etc.. Businesses aren’t hiring because of poor sales, period, end of story.

Yes...end of story. The science is settled. Well done, Paulo.

But I guess this is why Krugman labels his column "The Conscience of a Liberal," instead of "The Thoughts of a Scientist."

What is Clear and Not so Clear About Fed Policy (Part 2)

Today's FOMC statement is available here: FOMC November 03, 2010. Thought it might be a good time to follow up on my earlier (September 23) post: What is Clear and Not so Clear About Fed Policy.

On September 23, I said the following (let me summarize):

What was clear: The Fed will stand ready to do "whatever it takes" to make sure inflation expectations remain anchored at around 2% per annum. With inflation still on the low side of this target and the labor market still weak, it is not surprising that the Fed today a program to expand the size of its balance sheet.

What was not so clear: The Fed was not clear on the tactics it meant to employ to anchor long-term inflation expectations. I suggested that a good bet would be a program designed to purchase longer-dated treasuries, with purchases following a state-contingent rule (depending on how economic events turned out). This is what we got:

To promote a stronger pace of economic recovery and to help ensure that inflation, over time, is at levels consistent with its mandate, the Committee decided today to expand its holdings of securities. The Committee will maintain its existing policy of reinvesting principal payments from its securities holdings. In addition, the Committee intends to purchase a further $600 billion of longer-term Treasury securities by the end of the second quarter of 2011, a pace of about $75 billion per month. The Committee will regularly review the pace of its securities purchases and the overall size of the asset-purchase program in light of incoming information and will adjust the program as needed to best foster maximum employment and price stability.

Well, looks like I was half right. What surprised me here were the stipulated size and time limits; i.e., $600B figure by 2011:Q2. Why $600B and not $500B or $700B? No idea. Why 2011:Q2 and not 2011:Q1 or 2011:Q3? No idea.

The coexistence of the "state-contingent" and "size/time limit" language in the statement above may reflect a possible compromise between groups arguing for one or the other. But the "size/time limit" language seems somewhat redundant in my view; at least, given that we believe that the Fed is commited to 2% inflation. For example, what happens at the end of 2011:Q2 if inflation is still running at 1% with unemployment near double digits? Answer: a likely repeat, going further out along the yield curve, if necessary. But this is likely to happen (under the hypothesized contingency) whether or not these size/time limits were in place to begin with.

Finally, what was downright blurry in my previous post continues to remain hazy, in my view.

Bumper Stickers: Election 2010

Pretty much sums up the mood of the country, I'd say... (I saved the best one for last).

The Cyclical/Structural Unemployment Debate

There's been a lot of talk these days about whether unemployment in the U.S. today is the product of "cyclical" or "structural" factors. For example, see: And he huffed...and he puffed...and he blew the structural unemployment house down!

This blustering (by the big bad blog wolf) brings back a fond memory. In the fall of 1988, I had the good fortune of being enrolled in a PhD macro class taught by  Peter Howitt. Peter had just returned from sabbatical leave (at MIT, if memory serves) and perhaps it was there that he picked up on the labor market search literature. (I should like to point out that he has a very nice paper on the subject, coauthored with Preston McAfee, published in 1987: Costly Search and Recruiting).

Anyway, it was in that class that the first learned of the "cyclical vs structural" debate. Evidently, the modern version of this debate started out with Lilien's "Sectoral Shifts and Cyclical Unemployment" paper (JPE 1982). Abraham and Katz countered with "Cyclical Unemployment: Sectoral Shifts or Aggregate Disturbances?" (JPE 1986).

One part of the AK counterargument exploited Beveridge curve evidence. I understood their argument as saying that if structural shifts are the primary driving force, then one would expect to see a positively sloped Beveridge curve (much like what we are seeing right now in the U.S.).  In fact, the Beveridge curve is negatively sloped. Ergo, aggregate demand shocks yes; structural shifts no.

As I had just finished reading Pissarides' now-famous AER 1985 piece, I knew exactly what AK were on about. And so, why not formalize the AK hypothesis in a Pissarides-style search model? (We were all scheduled to present a short seminar in Peter's class on a research topic, and this sounded as good as any). Now, let me describe the model I wrote down and what I discovered.

The model

The model I used was a simplified version of Pissarides (AER 1985).

The economy consists of a fixed number of workers (mass normalized to unity) and a potentially "large" supply of jobs (or firms--I use the two terms interchangeably). Each job requires one worker. A firm-worker pair produce y units of output. (I assumed y to be common across matches, but allowed y to vary over time as an exogenous stochastic process).

Workers did not have any interesting decisions to make in the model. At any point in time, they were either matched with a firm or not. If they were matched, they produced output. If they were not matched, they used their fixed time endowment in search activity. Unmatched workers were "involuntarily" unemployed (because, by assumption, even menial jobs do not exist). Let u denote the unemployment rate at an arbitrary date (employment is given by n = 1 - u ).

Central to this literature is the notion of an aggregate matching function. The idea is that the aggregate recruiting intensity of firms (measured by vacancies v ) and the aggregate search intensity of workers (measured by unemployment u ) combine in some "black box" search market to produce an aggregate flow of new matches m. Formally, m = M(u,v), where M(.) was frequently specified as Cobb-Douglas (the rationale for CRS being that the ratio θ ≡ v/u displayed no secular trend in the data).

Now, Jeremy Greenwood had introduced me the year before to RBC theory. The idea there was that aggregate production possibilities, as measured by an aggregate production function y = zF(k,n) might bounce around owing to exogenous movements in aggregate productivity, z. It occurred to me that the AK hypothesis might be formalized by assuming that the efficiency of the aggregate matching function is subject to time variation owing to "structural" disturbances. That is, why could I not write m = xM(u,v), where x is analogous to the productivity shock in the RBC literature?

The idea is that a structural shock that (say) required sectoral or occupational reallocation is likely to reduce the efficiency with which matches are formed at the aggregate level (a lower x ). A lower x, in turn, would cause an "outward" (thanks, Nick) shift of the theoretical Beveridge curve, leading to the AK observation that structural shocks should induce unemployment and vacancies to move in the same direction. I was getting excited. But then, I was still young back then.

Alright then, back to the model. Following Pissarides, I denoted q ≡ m / v and p ≡ m / u as the match probabilities for vacant firms and unemployed workers, respectively. Utilizing the CRS matching technology about, we can write these match probabilities as functions of the "labor market tightness" variable θ (as well as the structural shock x, which I leave implicit). It turns out that q(θ) is a decreasing function of θ; more vacancies competing for the pool of unemployed reduces each firm's chances at making a match. Likewise, p(θ) is an increasing function of θ; more vacancies makes it easier for the unemployed to find work.

Firms and workers bargain over the output produced in a match. I assumed, for simplicity, that the wage is given by w = αy; where 0 < α < 1 is a parameter indexing the worker's bargaining power.

At the beginning of the period, the firm-worker match breaks up with probability 0 < σ < 1. Call this the separation rate. Let 0 < β < 1 denote the discount factor. If the value of a firm without a worker is normalized to zero, then the capitalized value of a firm with worker is simply the expected discounted stream of profits. If I let J denote the capital value today, and J⁺ the capital value tomorrow, then we have the following Bellman equation:

[1] J = (1 - α)y + (1 -σ)βE[J⁺ | ω]

The term E[J⁺ | ω] denotes the expected future value of firm operations, where the expectation is formed conditional on information ω.

Notice that I can embed the usual RBC assumption of persistent aggregate productivity shocks by assuming that ω = y. Or, we might model aggregate demand shocks as exogenous shifts in ω (my preferred interpretation is that these are news shocks). Absent any aggregate uncertainty, we can impose J = J⁺ and solve for the steady state capital value J^*; i.e.,

[1a] J^* = (1 - α)y / [1 - (1 - σ)β]

The next step is to figure out what determines aggregate recruiting intensity. Assume that posting a vacancy incurs the resource cost κ. Then, assuming free-entry in vacancy creation, the equilibrium labor-market tightness variable θ is determined by:

[2] q(θ)(1 -σ)βE[J⁺ | ω] = κ

The formulation above assumes that even newly created matches are subject to exogenous separation in the following period. In any case, note that since u is predetermined, condition [2] pins down equilibrium vacancies v. That is, v is a "jump variable" that responds instantaneously to any shock. If an increase in ω results in an increase in the value of a firm, for example, the effect will be to increase vacancy creation. As new vacancies come online, the probability of successfully finding a worker falls, until condition [2] is again satisfied.

Note that we can combine [1a] with [2] to determine the steady-state labor market tightness variable:

[2a] q(θ^*)(1 -σ)βJ^* = κ

Finally, we need an expression that describes the evolution of the equilibrium unemployment rate. This is given by u⁺ = u + σ(1-u) - (1-σ)p(θ)u; or

[3] u⁺ = σ + [ 1 - (1-σ)(1-p(θ)) ]u

The steady-state version of [3] is given by:

[3a] u^* = σ / [ 1 - (1-σ)(1 - p(θ^*) ]

That's it. What a beautiful little model. Note its lovely recursive structure: condition [1] determines J; given J, condition [2] determines θ; and given θ, condition [3] determines the unemployment rate.

Moreover, the model generates a nice downward sloping Beveridge curve. That is, an increase in aggregate demand (an increase in ω that increase J⁺) stimulates v, which reduces u. A structural shift that reduces matching efficiency (a reduction in x) shifts the Beveridge curve outward. Wonderful.

And so, following the RBC methodology I learned from Greenwood, I parameterized the model and calibrated the steady-state to some data. I specified the usual AR(1) process for the aggregate technology shock. And I added an AR(1) process for the match-efficiency (structural disturbance) shock. Then I simulated the model output for unemployment and vacancies under two scenarios. First, I shut down the structural disturbance, assuming only the TFP shock. And then I shut down the TFP shock, assuming only the structural disturbances.

To my surprise, both experiments generated downward sloping Beveridge curves (in the sense that unemployment and vacancies were negatively correlated). The correlation was a bit weaker under the structural shocks (something like -0.50 vs. -0.80, if I remember correctly). But the correlation was still negative! (I am going to assume that this was not the product of a coding error!)

In any case, during my class presentation, I explained the result as follows. Imagine hitting this model economy with a structural disturbance that manifests itself as a decrease in matching efficiency. In terms of condition [2], this is like a negative technology shock to the match probability q(θ). On impact, the unemployment rate remains fixed; hence, all the adjustment must be absorbed by the "jump" variable, vacancies. And if firms now find it harder to match, vacancies are going to jump down. The contraction in job availability then manifests itself as a higher (future) unemployment rate. Could the logic supplied by Abraham and Katz in refuting Lilien's hypothesis be wrong? Maybe.

Lessons

I don't want to make too much out of this simple model. One reason not to like it for the question at hand is that it is only a one-sector economy (though, my classmate, Paul Storer, eventually produced and estimated a very nice two-sector model here). 

The point here is not to say who is right and who is wrong. Maybe the Abraham and Katz hypothesis is correct...or maybe it is not. I don't know. The important thing, in my mind, is what I learned from this experience; namely, to be very careful in accepting too quickly (or too uncritically) predictive statements based on informal stories.

Beveridge Curves for 4 U.S. Regions (JOLTS)

Regarding my earlier post, a few people have pointed out that the measure of job vacancies I employed was based on newspaper advertisements. To the extent that there has been a shift in advertising away from print to online media, the Beveridge curves I plotted earlier may be distorted.

Evidently, the conference board has some measure of online job advertisements, available (I think) for only since 2005 or so. My RA reports that they want $20K for the data. Uh...sure. I'll see what I can do about this.

But in the meantime, I provide plots of regional Beveridge curves using JOLTS data which, unfortunately, is available only for the past decade. I do this first the conventional way, plotting vacancies against unemployment. But because I am no fan of unemployment measures (half of the flow into employment comes from out of the labor force), I also plot the BC my preferred way; that is, with vacancies plotted against the employment ratio.