When most people worry about recessions, they’re worried about involuntary unemployment. If we want to think about the role of monetary policy in recessions, then, it feels natural to worry about sticky wages.
In their heart of hearts, I think a lot of macroeconomists – and casual observers of macro – think sticky wages are in fact the most important reason for thinking about the role of monetary policy in recessions.
But in our baseline New Keynesian macroeconomic models, we think about price stickiness and not wage stickiness. In the baseline textbook monetary model, as in e.g. Gali/Woodford/Walsh, we work with a model of sticky prices as our base case; and only teach sticky wages as supplementary material.
Tracing the history of thought on this, going back to the advent of “new Keynesianism” in the 1980s, my takeaway is that:
The preference for sticky price models over sticky wage models is somewhat of a historical accident; in that the original critiques of sticky wage models are now broadly accepted to be incorrect.
One of the first papers to use the term “new Keynesian” (with a lowercase ‘n’, rather than the uppercase that is now used) was the Rotemberg (1987) Macro Annual paper on “The New Keynesian Microfoundations”. Here’s how he described what made this “new”:
“One might ask in all seriousness what is new about the current generation of Keynesian models. The major difference between the current and previous generations (Fischer 1977, Taylor 1980) is an emphasis on the behavior of product markets.”
As highlighted here by Rotemberg, in the mid-1980s there was a switch from the Fischer and Taylor sticky wage models (focusing on the labor market) to sticky price models (focusing on the product market).
If you think of high involuntary unemployment as being the defining feature of recessions, how do such sticky price models explain unemployment? As Mankiw explains in a comment on Rotemberg’s paper,
“Firms lay off workers in recessions not because labor costs are too high [due to nominal wage stickiness], but because sales are too low [due to goods price stickiness].”
That is: you weren’t fired from your job because you were “too stupid and too stubborn” to lower your wage demand. You were fired because your firm’s sales fell, and so they no longer needed to produce as much, and so didn’t need you. (See also: Barro and Grossman 1971 or the first half of Michaillat and Saez 2015.)
Unemployment, here, is the same phenomenon as a classical model: you chose to be unemployed because you preferred the leisure of Netflix compared to working for a lower real wage. More complicated models can and do add frictions that change this story – labor search frictions; sticky wages on top of sticky prices – but as a baseline, this is the logic and mechanism of these models.
Why was this switch to sticky price models made? With sticky wage models, by contrast, people are genuinely involuntarily unemployed – which again is plausibly the defining characteristic of recessions. Why switch away towards this muddier logic of sticky prices?
Two critiques of sticky wage models led to the adoption of sticky price models:
As we’ll get to in a bit, today no one (?) agrees with the empirical critique, and the theoretical critique both does not have real bite and is anyway typically ignored. First, a summary of each critique:
1. Arguably the strongest critique against sticky wage models at the time was the evidence that real wages don’t go up during recessions. After all, if unemployment is caused by real wages being too high – the price level has fallen but nominal wages cannot – then we should see real wages going up during recessions.
In the aggregate US data, this simply did not hold: depending on the time period and the deflator used, real wages could appear countercyclical as predicted, basically acyclical, or even procyclical. To get the general idea (we’ll quibble over measurement later) here’s a graph of a measure of real average hourly earnings I grabbed from the WSJ:
Average real wages are not strikingly obviously “too high” during recessions here – earnings don’t spike upward in the shaded areas – particularly when you look at the 1970s and 1980s.
2. The second, theoretical critique was advanced by Barro (1977) and described by Hall (1980). This argument is usually summarized as: employer-employee relationships could be implicitly long-term contracts, and so observed nominal wage stickiness in the short run need not imply allocative inefficiency.
For example, if I expect to produce $3 of (marginal) value this year and $1 next year, I don’t really care if my boss promises to pay me $2 in each year – even though this year I’m being paid less than my value.
Similarly, even if my nominal wages don’t fall during a recession, perhaps over my entire lifetime my total compensation falls appropriately; or, other margins adjust.
Arguably, price stickiness is not vulnerable to either of the above critiques of wage stickiness, and hence the appeal over wage stickiness:
Hence, the transition from sticky wage models to the dominance of sticky price models starting in the 1980s. Yun (1996) builds the full dynamic model with Calvo sticky pricing at the heart of the New Keynesian framework; Woodford, Gali, and Walsh organize NK thought into textbook format.
But – these critiques are at best incomplete and at worst conceptually incorrect. Here’s why:
“Observed real wages are not constant over the cycle, but neither do they exhibit consistent pro- or countercyclical tendencies. This suggests that any attempt to assign systematic real wage movements a central role in an explanation of business cycles is doomed to failure.”Mankiw (1991) – another comment on a later Rotemberg Macro Annual paper coauthored with Woodford – writes: “As far as I know, there are six ways to explain the failure of real wages to move countercyclically over the business cycle... None of these explanations commands a consensus among macroeconomists, and none leaves me completely satisfied.” He offered this list of possible explanations:
I don’t want to go through each of these in detail – see Mankiw’s comment; and note some of these suggestions are pretty esoteric. Most of these are immediately unsatisfactory; on #2, implicit contracts, we’ll come back to.
The problem I want to highlight is that: the late-80s/early-90s understanding summarized in this table leaves out the three most compelling – and now widely-recognized – reasons that the cyclicality of the aggregate real wage is not diagnostic of the sticky wage model.
1. Identification: the source of the shock matters!
Recessions caused by tight monetary policy should cause real wages to increase and be too high, leading to involuntary unemployment. Recessions caused by real supply-side shocks should cause real wages to fall and nonemployment to rise.
If the economy experiences a mix of both, then on average the correlation of real wages and recessions could be anything.
Maybe in 1973 there’s an oil shock, which is a real supply-side shock: real wages fall and nonemployment rises (as in the data). Maybe in 2008 monetary policy is too tight: real wages spike and unemployment rises (as in the data). Averaging over the two, the relationship between real wages and unemployment is maybe approximately zero.
This view was around as early as Sumner and Silver (1989) JPE, where they take a proto-“sign restrictions” approach with US data and find procyclical real wages during the real shocks of the 1970s and countercyclical real wages during other recessions.
But: while Sumner-Silver was published in the JPE and racked up some citations, it seems clear that, for too long a time, this view did not penetrate enough skulls. Macroeconomists, I think it’s fair to say, were too careless for too long regarding the challenge of identification.
My sense is that this view is taken seriously now: e.g. in my second-year grad macro course, this was one of the main explanations given. At the risk of overclaiming, I would say that for anyone who has been trained post-credibility revolution, this view is simply obviously correct.
2. Composition bias: the measured real wage can be deceptive
Solon, Barsky, and Parker (1994) QJE make another vitally important point.
Thus adjusting for this composition bias – as long as (2) continues to hold – causes you to realize that the more conceptually correct “shadow aggregate average real wage” is even lower, not higher, during recessions. It does point out, however, that the measured aggregate real wage is simply not the right object to look at!
(For the most comprehensive analysis of this general topic and evidence that the importance of this composition bias has grown over time, see John Grigsby’s job market paper.)
3. New hire wages, not aggregate wages, is what matters anyway
The third important point is that: conceptually, the average real wage of the incumbent employed – which is what we usually have data on – is not what matters anyway!
As Pissarides (2009) ECMA pointed out, it doesn’t really matter if the wages of incumbent employed workers are sticky. What matters is that the wages of new hires are sticky.
Why is this? Suppose that the wages of everyone working at your firm are completely fixed, but that when you hire new people, their wages can be whatever you and they want. Then there’s simply no reason for involuntary unemployment: unemployed workers will always be able to be hired by you at a sufficiently low real wage (or to drop out of the labor force voluntarily and efficiently). If new hire wages were sticky on the other hand, that’s when the unemployed can’t find such a job.
That is: it is potential new-hire wages that are the relevant marginal cost for the firm.
Putting it all together, we have three reasons to think that the data which informed the move from sticky wage to sticky price models were misleading:
Now, maybe correcting for these, we would still find that (new-hire) real wages are not “too high” after a contractionary monetary policy shock. But this is an open question. And the best evidence from Hazell and Taska does argue for sticky wages for new hires from 2010-2016 – in particular, sticky downwards.
With that discussion of the empirical critique of sticky wage models, on to the theoretical critique.
Brief reminder: the Barro (1977) critique says that merely observing sticky nominal wages in the data does not necessarily imply that sticky wages are distortionary, because it’s possible that wages are determined as part of long-term implicit contracts.
1. So what?
But! This also does not rule out the possibility that observed nominal wage stickiness is distortionary!
We observe unresponsive nominal wages in the data. This is consistent either with the model of implicit contracts or with the distortionary sticky wage hypothesis. Based on this alone there is an observational equivalence, and thus of course this cannot be used to reject the hypothesis that sticky wages are distortionary.
Moreover, it’s unclear that we observe contracts of the type described in Barro (1977) – where the quantity of labor is highly state-dependent – in the real world, at all.
2. Circa 2021, this critique is most typically ignored anyway
The other thing to note here is: despite the concern in the 1980s about this critique of sticky wage models... we’ve ended up using these models anyway!
Erceg, Henderson, and Levin (2000) applied the Calvo assumption that a (completely random) fraction of wage-setters are (randomly) unable to adjust their wages each period. This modeling device is now completely standard – though as emphasized above only as an appendage to the baseline New Keynesian framework.
Moreover, the ascendant heterogeneous agent New Keynesian (HANK) literature often does, in fact, takes sticky wages as the baseline rather than sticky prices. See the sequence of Auclert-Rognlie-Straub papers; as well as Broer, Hansen, Krusell, and Oberg (2020) for an argument that sticky wage HANK models have a more realistic transmission mechanism than sticky price ones (cf Werning 2015).
Now maybe you think that large swathes of the macroeconomic literature are garbage (this is not, in general, unreasonable).
But this certainly does reveal that most macroeconomists today reject, at least for some purposes, the critique. Hall (2005) for example writes of, “Barro’s critique, which I have long found utterly unpersuasive.”
The history of thought here and how it has changed over time is interesting on its own, but it also suggests a natural conclusion: if you think of involuntary unemployment as being at the heart of recessions, you should start from a sticky wage framework, not a sticky price framework. The original empirical and conceptual critiques of such a framework were misguided.
More importantly, this should affect your view on normative policy recommendations:
We don’t want to stabilize P; we want to stabilize W!
These can be quite different. Let’s cheat and note that in a model without labor force fluctuations, stabilizing nominal wages W is the same as stabilizing nominal labor income WN. Then, for example, observe in the critical period of 2007 through late 2008 – before the Fed hit the zero lower bound – nominal labor income growth (blue) was steadily declining even though inflation (red) was rising due to spiking oil and food prices.
The accelerating inflation is why we had the FOMC meeting on September 16, 2008 – the day after Lehman Brothers declared bankruptcy (!!) – and stating, “The downside risks to growth and the upside risks to inflation are both of significant concern to the Committee” and unanimously refusing (!!) to cut its policy rate from 2%.
If the Fed had been targeting nominal wages or nominal income, instead of inflation, it would have acted sooner and the Great Recession would have been, at the least, less great.
Finally, while I just wrote that sticky prices prescribe inflation targeting as optimal monetary policy, in fact this is not generically true. It is true in the textbook New Keynesian model, where price stickiness is due to exogenously-specified Calvo pricing: a perfectly random fraction of firms is allowed to adjust price each period while all others remain stuck.
Daniele Caratelli and I have a new paper (almost ready to post!), though, showing that if price stickiness instead arises endogenously due to menu costs, then optimal policy is to stabilize nominal wages. Under menu costs, even if wages are completely flexible, then ensuring stable nominal wage growth – not stable inflation – is optimal, just as in the basic sticky wage model.
Thanks to Marc de la Barrera, Daniele Caratelli, Trevor Chow, and Laura Nicolae for useful discussions around this topic.
TLDR: “GDP percentage growth is slowing down” emphatically does not mean that “the rate at which human lives are improving” is slowing down, even under the assumption that GDP is all that matters for human wellbeing. Percentage growth slowdowns are even consistent with wellbeing growth accelerating.
1. Here’s one perspective. The average percentage growth rate of GDP per capita in the US has fallen nearly monotonically by decade: From 2.8% in the 1960s to 0.8% in the 2000s, before rebounding to 2.5% in the recovery years of the 2010s. Pretty depressing! The growth rate is mostly slowing down.
2. Here’s another perspective. The average dollar growth rate of GDP per capita in the US has risen nearly monotonically by decade, excepting the depression years of the 2000s: From $592 in growth per year in the 1960s to $852 in the 2010s. Pretty good! The growth rate is speeding up.
3. Why should we privilege the percentage growth rate metric over the dollar metric? In contemporary discussions of our “productivity slowdown” and “great stagnation”, or debates on “how to speed up growth”, inevitably the first chart with percentage growth is shown.
I can’t eat 3 percent GDP growth; but 850 dollars in cash, I certainly know what to do with that. Does that mean that we should say “growth”, quote unquote, is not slowing down?
This isn’t a trick question: we should not in fact attach so much importance and status to percentage growth rates. But dollar terms isn’t the right metric either.
Ultimately, what we care about is welfare: how happy are people. And in that case, the relevant comparison has to use a cardinal measure of utility: how fast is utility growing?
We’re going to need to do a bit of math to go further.
Say that – just to make the point as clear as possible – utility is only a function of GDP: higher GDP means more happiness. (Thinking of utility as depending on other factors – which it definitely does! – only strengthens the point.)
Also suppose that GDP is growing at a constant rate g:
y(t+1) = y(t) * exp(g)
If utility is log of GDP, U(t)=ln[y(t)], then percentage change in GDP exactly equals growth in welfare:
U(t+1) - U(t)
= ln[y(t+1)] - ln[y(t)] = ln[y(t+1)/y(t)] = ln[exp(g)]
Thus, under log utility, we have a direct justification for caring about percentage growth: it is exactly informative of how fast welfare is growing.
Log utility is a very specific, knife-edge functional form, though!
More generally, think of the graph of ln(y): it’s upward sloping, at a diminishing rate – it’s curved. That is: there is diminishing marginal utility from higher GDP. (Diminishing marginal utility rules everything.)
Here’s the key question for any non-log utility function: How quickly does marginal utility diminish? Or graphically, how curved is the function (in GDP space)? More curved than log, or less curved than log?
For example, consider the frequently-used CRRA utility function. If the CRRA coefficient is less than 1, then the utility function is less curved than log – marginal utility diminishes slowly. Vice versa for a coefficient greater than 1. (With a coefficient equal to 1 the function becomes log).
You can see visually what I mean by more-or-less curved here: where “more curved” is CRRA with coefficient of 2, and “less curved” with a coefficient of 0.5.
The gray line – a “less curved” utility function – is closer to being linear than the other two “more curved” lines.
Here’s the resulting kernel of insight from thinking about more vs. less curved:
1. If the utility function is “more curved” than log – and marginal utility thus diminishes faster – then welfare grows slower than g. That is: if utility is more curved than log, then we need accelerating percentage growth in GDP just to maintain the same growth rate in well-being.
2. If the utility function is “less curved” than log – and marginal utility thus diminishes slower – then welfare grows faster than g. That is: if utility is less curved than log, then decelerating percentage growth in GDP can even be consistent with accelerating levels of welfare.
(In the extreme case when utility is not curved at all – when utility is linear – that is precisely when the dollar metric for growth is the right metric.)
The intuition for these points comes exactly from diminishing marginal utility: with log utility and constant percentage GDP growth, we saw that welfare growth is constant. If marginal utility diminishes faster than log, then the level of utility is of course growing slower; and vice versa.
The next figure shows this. Constant GDP growth leads to constant welfare gains under log, as time passes; accelerating welfare gains under “less curved”; and decelerating gains under “more curved”.
TLDR: “GDP percentage growth is slowing down” emphatically does not mean that “the rate at which human lives are improving” is slowing down, even under the assumption that GDP is all that matters for human wellbeing. Percentage growth slowdowns are even consistent with wellbeing growth accelerating.
Finally, to translate all this to academic-ese: even a balanced growth path model, like the semi-endogenous growth model, can have ever-accelerating welfare growth; it just depends on the utility function.
(PS: The vast majority of models of economic growth are built around functional forms that result in constant percentage growth in key variables in the long run. Thus from a modeling perspective, you may also be interested in GDP percentage growth as a test of how well these assumptions fit the data: is it constant in the long run, or not.)
(Ex post update: After this post was published, the FOMC met for an emergency meeting, in which it cut the policy interest rate to zero and began a new round of quantitative easing, among other measures!)
If I closed my eyes and completely wiped from my mind the fact of the coronavirus pandemic, here's what I would see in the last week:
1. Real interest rates are rising: 5 year TIPS rates are up 80bps (!!) in the last 1.5 weeks
2. Inflation expectations are collapsing: 5-year breakeven inflation is down to 0.50%
3. In the last week, even nominal interest rates are rising: 2-year treasuries rose in the past few days, including even on Thursday when equity markets were down 10%
4. Equity prices, of course, cratering
The data are not 100% clear, but this looks like a massive contractionary monetary policy shock. Interpreting these data:
1. Real rates are rising: this could be due to
(1) rising growth expectations (...unlikely);
(2) risk premia movements (maybe? Would have to be large);
(3) higher TIPS illiquidity premium (probable – cf Fed action on Thursday); or
(4) changing subjective discount factor (seems unlikely for a five-year horizon?)
(5) tighter monetary policy expectations (seems very possible!)
This reads to me like monetary policy is tightening. Even if much of the movement is due to liquidity issues rather than a change in the expected path of real rates, that illiquidity would also suggest monetary policy is too tight!
2. Inflation expectations are falling: this could be in part due to the positive oil supply shock; but expectations were falling before Saudi Arabia and Russia made their moves on March 9. Moreover, we would ceterus paribus think that the negative supply-side effects of the coronavirus would increase inflation.
3. Nominal rates: It is truly bizarre, in my mind, to see nominal Treasury yields rising in the past few days – and not just on days when the stock market was up, like Friday. That seems suggestive of expectations for tighter-than-previously-expected monetary policy.
It's also possible that liquidity issues in both the nominal and real government bond markets are distorting all of these measures. I don't know, these are some of the most liquid markets in the world.
The data above are for the US, but looking at French government bonds, I also see real rates rising (!!) and inflation expectations falling:
Meanwhile, the ECB on Thursday chose not to cut interest rates, despite widespread expectation for them to cut, which seems frankly insane (and equity markets were subsequently down 10-15%!).
Watching these various indicators – particularly real interest rates rising almost a full percentage point (!) – frankly I feel a little like I'm going crazy. Everyone is talking about the pandemic – rightly – but it seems to me that we have a dual crisis at the moment. The virus, and monetary policy is way too tight.
In the US, we are not at the zero lower bound, so the Fed has no excuse for not acting. And before the FOMC uses the ZLB as an excuse anyway, they could at least attempt forward guidance or actual QE (not the repo liquidity measures that occurred on Thursday).
Obviously, the pandemic is a big crisis with its own set of complicating issues. But central banks shouldn't be making the problem worse than it need be. I.e., even if potential real GDP falls due to the pandemic and associated shutdowns, central banks should still be (approximately) trying to keep GDP on track with potential GDP (modulo perhaps some tradeoff with price dispersion), not implicitly tightening policy and making things even worse.
The supply side, as almost always, is more important; but at the moment central banks seem like they're actively or passively making things worse.
It will be very informative, I think, to watch the market open tonight.
The efficient market hypothesis says that you can't pick out which stocks are undervalued versus which are overvalued. Likewise, I claim that you can't pick out which restaurants are underpriced versus which restaurants are overpriced.
Think you've found a great company, so that their stock will outperform on a risk-adjusted basis? Nope, someone else has already incorporated that information into the stock price and pushed the price up.
Think you've found a great restaurant which offers meals at a decent price? Nope, they've already raised their prices to the point where the extra cost just equals the extra utility you get from their extra delicious cuisine.
A. But, first of all, we need to emphasize that this is on a risk-adjusted basis. A portfolio of stocks might have higher expected returns – but only if it's riskier.
This applies to restaurants as well to stocks – trying a new exotic cuisine could be eye-opening and awesome, or awful. Admittedly, this is quantitatively much less important for restaurants.
(This is the essence of modern asset pricing theory.)
B. Similarly to stocks, fund managers will not consistently deliver alpha to their investors: if any manager can consistently deliver alpha, that manager will simply raise their fees to capture it for themselves. (This is the essence of the "rational model of active management" model of Berk and Green 2004.)
Moreover, second of all, cheap restaurants and cheap managers might exist, but they can have very high search costs.
Truly great cheap restaurants might exist, but you have to pay a lot in time, money, and energy spent searching and reading reviews to pinpoint them. These search costs, this time wasted digging around on Yelp, are real costs: they take time and money that you could otherwise have spent on better food or anything else which gives you utility.
This is likewise true of asset managers. Cheap asset managers that provide alpha might truly exist, but you have to spend so much time and money searching and evaluating potential such managers that these search costs will eat up that alpha. Otherwise, other investors would have already found the manager and grabbed that alpha.
(This is the essence of Garleanu and Pedersen's "Efficiently Inefficient" model.)
Third and finally: the utility of eating out at a restaurant is not just a result of tastiness and search costs. It incorporates every stream of services provided by the restaurant: convenience of location most of all, but also quality of service, ambience, and the social aspect of the other patrons. If a given restaurant achieves higher on these marks – e.g. a restaurant full of beautiful fashion models – then it should be expected that the quality of the food is less.
Similarly, to a lesser extent, with assets or with asset managers. Assets provide more than just a stream of returns: they provide the service of liquidity, or a "convenience yield". We can think of people enjoying the comfort provided by liquid assets, much like they enjoy the ambience of a nice restaurant. And just as a restaurant full of fashion models will – all else equal – have lower quality food, an asset or manager that offers higher liquidity should be expected to provide a lower pecuniary return.
[Personal aside: This area is a core component of my own research agenda, as I currently envision it.]
Conclusion: in equilibrium, assets or asset managers should not be undervalued or overvalued, on a risk-adjusted, fee-adjusted, search cost-adjusted, liquidity-adjusted basis. Likewise, in equilibrium, restaurants should not be underpriced or overpriced, once one takes into account their riskiness; the time spent searching for them on Yelp and reading reviews; and the ambience and other "convenience yield" services provided by the restaurant.
Most people are probably somewhat overconfident. Most people – myself surely included – probably typically overestimate their own talents, and they (we) are overly confident in the precision of their estimates, underestimating uncertainty.
This bias has viscerally real, important consequences. Governments are overconfident that they can win wars quickly and easily; overconfident CEOs have a higher tendency to undertake mergers and issue more debt than their peers.
I claim, however, that this bias does not matter for asset pricing in particular. That is, stock prices (and other asset prices) are not affected by overconfident investors.
In fact, I claim that any kind of behavioral bias cannot in and of itself affect stock prices.
The idea that behavioral biases, on their own, can affect asset prices is one of if not the most widely held misconceptions about financial markets. Just because most people (myself included!) are blinded by cognitive biases – overconfidence, status quo bias, confirmation bias, etc. – does not mean that stock prices are at all affected or distorted.
If this seems crazy, let me try putting it another way: just because behavioral biases exist does not mean that you can get rich by playing the stock market and exploiting the existence of these biases.
The trick is that it only takes the existence of one rational unconstrained arbitrageur to keep prices from deviating away from their rational level.
To see this, consider two extremes.
All it takes is one
First, suppose everyone in the world is perfectly rational and unbiased, except for one poor fellow, Joe Smith. Joe is horribly overconfident, and thinks he's smarter than everyone else. He invests all of his money in Apple stock, insisting that everyone else is undervaluing the company, and pushing the Apple share price up.
Of course, since every other investor is perfectly rational and informed, they will notice this and immediately race to go short Apple, betting against it until the price of the Apple stock is pushed back to the rational level.
Now, consider the inverse situation. Everyone in the world is systematically biased and cognitively limited, except for one rational informed Jane Smith. Perhaps more realistically, instead of Jane Smith, the one rational agent is some secretive hedge fund.
Now, billions of irrational investors are pushing prices away from their rational value. However, as long as Rational Hedge Fund LLC has access to enough capital, this one rational agent can always buy an undervalued stock until the price gets pushed up to its rational level, or short an overvalued stock until the price gets pushed down to the rational level. Rational Hedge Fund LLC profits, and prices are kept at their rational levels.
Even more realistically, instead of a single hypervigilant rational hedge fund keeping all stocks at their respective rational levels, there could be many widely dispersed investors each with specialized knowledge in one stock or one industry, collectively working to keep prices in line.
The marginal investor
The real world, of course, is somewhere between these two extremes. Most people have a host of cognitive biases, which leads to "noise traders" randomly buying and selling stocks. However, there is also a small universe of highly active, often lightning fast rational investors who quickly arbitrage away any price distortions for profit.
It is these marginal investors who determine the price of stocks, not the biased investors. This is why I say that "cognitive biases don't matter for stock prices" – the existence of any unconstrained rational investors ensures that biases will not flow through to asset pricing.
The important caveat: the "limits to arbitrage"
There is an extremely important caveat to this story.
Note that I quietly slipped in the requirement that Rational Hedge Fund LLC must have "access to enough capital." If the rational investors cannot raise enough money to bet against the noisy irrational traders, then prices cannot be pushed to their rational equilibrium level.
(The importance of access to capital is more than just the ability to apply price pressure. It's also important for the marginal investor to be able to withstand the riskiness of arbitrage.)
This assumption of frictionless access to leverage clearly does not hold perfectly in the real world: lending markets are troubled by principal-agent problems, moral hazard, and other imperfections.
This (very important) friction is known as the "limits to arbitrage."
It is irrationality in conjunction with limits to arbitrage which allow for market prices to diverge from their rational levels. It is important to acknowledge that cognitive biases alone are not a sufficient condition for market inefficiency. Irrationality and limits to arbitrage are both necessary.
More pithily: Peanut butter alone is not enough to make a PB&J sandwich, and behavioral biases alone are not enough to make the stock market inefficient.
The Efficient Market Hypothesis (EMH) was famously defined by Fama (1991) as "the simple statement that security prices fully reflect all available information."
That is, you can't open the Wall Street Journal, read a news article from this morning about Google's great earnings numbers that were just released, and make money by buying Google stock. The positive information contained in the earnings numbers would already have been incorporated into Google's share price.
To put it another way, the EMH simply says that there is no such thing as a free lunch for investors.
Does this imply that stock prices (or other asset prices) are unpredictable? No! The EMH unequivocally does not mean that prices or returns are unpredictable.
This fallacy arises all the time. Some author claims to have found a way to predict returns and so declares, "The EMH is dead." Return predictability does not invalidate the EMH. This is important – the empirical evidence shows that returns are indeed eminently predictable.
The key lies with risk premia.
I. What are risk premia?
The price of a stock (or any other asset) can be decomposed into two parts:
The first part is the standard discounted present-value that you might read about in an accounting textbook. The second is the compensation required by the stock investor in order to bear the risk that the stock might drop in value, known as a risk premium.
To understand risk premia, suppose that I offer you the following deal. You can pay me $x, and then get to flip a coin: heads I give you $100, tails you get nothing. How much would you be willing to pay to have this opportunity?
Although the expected value of this bet is $50, you're probably only going to be willing to pay something like $45 for the chance to flip the coin, if that. The five dollars difference is the compensation you demand in order to bear the risk that you could lose all your money – the risk premium.
II. Return predictability is compensation for risk
The above decomposition suggests that return predictability can either be the result of
If the first type of predictability were possible, this would in fact invalidate the EMH. However, the second sort of predictability – predictability of risk premia – allows for stock returns to be predictable, even under the EMH.
This is because, if only risk premia are predictable, then there is still no free lunch.
Sure, you can predict that a stock portfolio will outperform the market over the next year. However, this excess return is simply compensation for the fact that this set of stocks is extra risky – i.e., the portfolio has a high risk premium.
As an extreme example, consider the well-known fact that buying and holding a diverse basket of stocks predictably has higher expected returns than buying and holding short-term Treasury bills.
Is this a free lunch? Does the existence of the stock market invalidate the EMH? No. This return predictability exists only because equities are fundamentally riskier than T-bills.
III. Summing up
This is all to say that while returns may be predictable, it is likely that any profits earned from such predictable strategies are merely compensation for extra risk.
The EMH says that there is no free lunch from investing. Just because returns are predictable does not mean you can eat for free.
Postscript. There is another (outdated) theory, the "random walk hypothesis", defined as the claim that returns are not predictable. This is different from the EMH, which says that asset prices reflect all available information. The random walk hypothesis has been shown to be clearly empirically false, per links above.
Update: Selgin points out in correspondence and Sumner points out in comments below that, the below discussion is implicitly using variables in per capita terms.
I. The benefit of NGDP targeting is that inflation can fluctuate in the short run. But can NGDP targeting achieve a long-run optimal inflation rate?
Targeting NGDP rather than targeting inflation allows inflation to fluctuate in the short run. This is the major benefit of NGDP targeting, since it makes sense to have higher inflation in the short run when there is a cyclical growth slowdown and lower inflation when there is a growth boom, (see Selgin, Sumner, Sheedy, myself).
This is an argument about the short or medium run, at the frequency of business cycles (say 2-5 years).
Separately, you could imagine – whether or not inflation is allowed to vary in the short run, as it would be under NGDP targeting – that there is a long-run rate of inflation which is optimal. That is, is there a "best" inflation rate at which the economy should ideally settle, at a 10+ year horizon?
If there is an optimal long-run inflation rate, you would hope that this could be achieved under NGDP targeting in the long-run, even while inflation is allowed to fluctuate in the short run.
II. The optimal long-run inflation rate
Economists have thought a lot about the question of what the long-run optimal inflation rate is. There are two competing answers :
1. No inflation: One strand of literature argues that the optimal long-run inflation rate is precisely zero, based on price stickiness. The argument goes: by keeping the price level stable, sticky prices cannot distort relative prices.
2. Friedman rule: Alternatively, another strand of the literature going back to Milton Friedman argues that the optimal inflation rate is the negative of the short-term risk-free real interest rate (i.e. slight deflation). The argument here is that this would set the nominal risk-free interest rate to zero. In this world, there would be no opportunity cost to holding money, since both cash and risk-free bonds would pay zero interest, and the economy could be flush with liquidity and the optimum quantity of money achieved.
These two schools of thought clearly contradict each other. We will consider each separately.
What we want to know is this: could NGDP targeting achieve the optimal inflation rate in the long run (even while allowing beneficial short-run fluctuations in inflation)?
III. NGDP targeting and zero long-run inflation
In a previous essays post, I critiqued NGDP targeting by pointing out that NGDP targeting could not achieve zero inflation in long-run, unless the central bank could discretionarily change the NGDP target. In other words, I was arguing based on the first strand of literature that NGDP targeting was deficient in this respect.
The accounting is simple: NGDP growth = real growth + inflation. Under NGDP targeting without discretion, the growth rate of NGDP is fixed. But, real growth varies in the long run due to changing productivity growth – for example, real growth was higher in the 1960s than it has been in recent decades. As a result, the long-run inflation rate must vary and thus is unanchored.
Zero inflation can be achieved in the long run, but only at the cost of trusting the central bank to act discretionarily and appropriately modify the long-run NGDP target.
I think that such discretion would be problematic, for reasons I outline in the original post. I'll note, however, that I (now) assess that the benefits of NGDP targeting in preventing short-run recessions outweigh this smaller long-run cost.
IV. NGDP targeting and the Friedman rule
On the other hand – and I haven't seen this result discussed elsewhere before – NGDP targeting can achieve the Friedman rule for the optimal inflation rate in the long run without discretion. That is, under the logic of the second strand of literature, NGDP targeting can achieve the optimum. Here's the accounting logic:
The Friedman rule prescribes that the optimal inflation rate, pi*, be set equal to the negative of the real interest rate r so that the nominal interest rate is zero:
pi* = -r
Here's the kicker: Under a wide class of models (with log utility), the long-run real interest rate equals the rate of technological progress g plus the rate of time preference b. See Baker, DeLong, and Krugman (2005) for a nice overview. As a result, the optimal inflation rate under the Friedman rule can be written:
pi* = -r = -(b+g)
This can be achieved under NGDP targeting without discretion! Here's how.
Suppose that the central bank targets a nominal GDP growth rate of -b, that is, an NGDP path that declines at the rate of time preference. Recall again, under NGDP targeting, NGDP growth = g + pi. Since the central bank is targeting an NGDP growth rate of -b, if we rearrange to solve for inflation, we get that
pi = NGDP growth - g = -b - g
That's the optimal inflation rate implied by the Friedman rule shown above. This result holds even if the long-run rate of productivity growth (g) changes.
Thus, we have shown that if the central bank targets an NGDP path that declines at the rate of time preference, then in the long run the Friedman rule will be achieved.
To summarize, under such a regime, the economy would get the short-run benefits of flexible inflation for which NGDP targeting is rightfully acclaimed; while still achieving the optimal long-run inflation rate.
This is a novel point in support of NGDP targeting, albeit a very specific version of NGDP targeting: an NGDP target of negative the rate of time preference.
V. Summing up
There's still the tricky problem that economists can't even agree on whether the Friedman rule or no-inflation is superior.
So, to sum up once more:
To close this out, I'll note that an alternative middle ground exists... an NGDP target of 0%. This would see a long-run inflation rate of -g: not as low as -g-b as prescribed by the Friedman rule; but not as high as 0% as prescribed by no-inflationistas.
Such a policy is also known as a "productivity norm," (since long-run inflation is negative of productivity growth), advocated prominently by George Selgin (1997).
 I ignore ZLB considerations, which typically imply a higher optimal inflation rate, since many advocates of NGDP targeting do not see the ZLB as a true policy constraint (myself included).
I. Marx vs. Smith and food banks
When Heinz produces too many Bagel Bites, or Kellogg produces too many Pop-Tarts, or whatever, these mammoth food-processing companies can donate their surplus food to Feeding America, a national food bank. Feeding America then distributes these corporate donations to local food banks throughout the country.
What's the economically optimal way to allocate the donations across the country?
Option one is what you might call "full communism." Under full communism, Feeding America collects the food donations and then top-down tells individual food banks what endowments they will be receiving, based on Feeding America's own calculation of which food banks need what.
Prior to 2005, this was indeed what occurred: food was distributed by centralized assignment. Full communism!
The problem was one of distributed versus centralized knowledge. While Feeding America had very good knowledge of poverty rates around the country, and thus could measure need in different areas, it was not as good at dealing with idiosyncratic local issues.
Food banks in Idaho don't need a truckload of potatoes, for example, and Feeding America might fail to take this into account. Or maybe the Chicago regional food bank just this week received a large direct donation of peanut butter from a local food drive, and then Feeding America comes along and says that it has two tons of peanut butter that it is sending to Chicago.
To an economist, this problem screams of the Hayekian knowledge problem. Even a benevolent central planner will be hard-pressed to efficiently allocate resources in a society since it is simply too difficult for a centralized system to collect information on all local variation in needs, preferences, and abilities.
This knowledge problem leads to option two: market capitalism. Unlike poorly informed central planners, the decentralized price system – i.e., the free market – can (often but not always) do an extremely good job of aggregating local information to efficiently allocate scarce resources. This result is known as the First Welfare Theorem.
Such a system was created for Feeding America with the help of four Chicago Booth economists in 2005. Instead of centralized allocation, food banks were given fake money – with needier food banks being given more – and allowed to bid for different types of food in online auctions. Prices are thus determined by supply and demand.
At midnight each day all of the (fake) money spent that day is redistributed, according to the same formula as the initial allocation. Accordingly, any food bank which does not bid today will have more money to bid with tomorrow.
Under this system, the Chicago food bank does not have to bid on peanut butter if it has just received a large peanut butter donation from another source. The Idaho food bank, in turn, can skip on bidding for potatoes and bid for extra peanut butter at a lower price. It's win-win-win.
By all accounts, the system has worked brilliantly. Food banks are happier with their allocations; donations have gone up as donors have more confidence that their donations will actually be used. Chalk one up for economic theory.
II. MV=PY, information frictions, and food banks
This is all pretty neat, but here's the really interesting question: what is optimal monetary policy for the food bank economy?
Remember that food banks are bidding for peanut butter or cereal or mini pizzas with units of fake money. Feeding America has to decide if and how the fake money supply should grow over time, and how to allocate new units of fake money. That's monetary policy!
Here's the problem for Feeding America when thinking about optimal monetary policy. Feeding America wants to ensure that changes in prices are informative for food banks when they bid. In the words of one of the Booth economists who helped design the system:
"Suppose I am a small food bank; I really want a truckload of cereal. I haven't bid on cereal for, like, a year and a half, so I'm not really sure I should be paying for it. But what you can do on the website, you basically click a link and when you click that link it says: This is what the history of prices is for cereal over the last 5 years. And what we wanted to do is set up a system whereby by observing that history of prices, it gave you a reasonable instinct for what you should be bidding."
That is, food banks face information frictions: individual food banks are not completely aware of economic conditions and only occasionally update their knowledge of the state of the world. This is because obtaining such information is time-consuming and costly.
Relating this to our question of optimal monetary policy for the food bank economy: How should the fake money supply be set, taking into consideration this friction?
Obviously, if Feeding America were to randomly double the supply of (fake) money, then all prices would double, and this would be confusing for food banks. A food bank might go online to bid for peanut butter, see that the price has doubled, and mistakenly think that demand specifically for peanut butter has surged.
This "monetary misperception" would distort decision making: the food bank wants peanut butter, but might bid for a cheaper good like chicken noodle soup, thinking that peanut butter is really scarce at the moment.
Clearly, random variation in the money supply is not a good idea. More generally, how should Feeding America set the money supply?
One natural idea is to copy what real-world central banks do: target inflation.
The Fed targets something like 2% inflation. But, if the price of a box of pasta and other foods were to rise 2% per year, that might be confusing for food banks, so let's suppose a 0% inflation target instead.
It turns out inflation targeting is not a good idea! In the presence of the information frictions described above, inflation targeting will only sow confusion. Here's why.
As I go through this, keep in the back of your mind: if households and firms in the real-world macroeconomy face similar information frictions, then – and this is the punchline of this entire post – perhaps inflation targeting is a bad idea in the real world as well.
III. Monetary misperceptions
I demonstrate the following argument rigorously in a formal mathematical model in a paper, "Monetary Misperceptions: Optimal Monetary Policy under Incomplete Information," using a microfounded Lucas Islands model. The intuition for why inflation targeting is problematic is as follows.
Suppose the total quantity of all donations doubles.
You're a food bank and go to bid on cheerios, and find that there are twice as many boxes of cheerios available today as yesterday. You're going to want to bid at a price something like half as much as yesterday.
Every other food bank looking at every other item will have the same thought. Aggregate inflation thus would be something like -50%, as all prices would drop by half.
As a result, under inflation targeting, the money supply would simultaneously have to double to keep inflation at zero. But this would be confusing: Seeing the quantity of cheerios double but the price remain the same, you won't be able to tell if the price has remained the same because
(a) The central bank has doubled the money supply
(b) Demand specifically for cheerios has jumped up quite a bit
It's a signal extraction problem, and rationally you're going to put some weight on both of these possibilities. However, only the first possibility actually occurred.
This problem leads to all sorts of monetary misperceptions, as money supply growth creates confusions, hence the title of my paper.
Inflation targeting, in this case, is very suboptimal. Price level variation provides useful information to agents.
IV. Optimal monetary policy
As I work out formally in the paper, optimal policy is instead something close to a nominal income (NGDP) target. Under log utility, it is exactly a nominal income target. (I've written about nominal income targeting before more critically here.)
Nominal income targeting in this case means that the money supply should not respond to aggregate supply shocks. In the context of our food banks, this result means that the money supply should not be altered in response to an increase or decrease in aggregate donations.
Instead, if the total quantity of all donations doubles, then the price level should be allowed to fall by (roughly) half. This policy prevents the confusion described above.
Restating, the intuition is this. Under optimal policy, the aggregate price level acts as a coordination mechanism, analogous to the way that relative prices convey useful information to agents about the relative scarcity of different goods. When total donations double, the aggregate price level signals that aggregate output is less scarce by halving.
It turns out that nominal income targeting is only exactly optimal (as opposed to approximately optimal) under some special conditions. I'll save that discussion for another post though.
Feeding America, by the way, does not target constant inflation. They instead target "zero inflation for a given good if demand and supply conditions are unchanged." This alternative is a move in the direction of a nominal income target.
V. Real-world macroeconomic implications
I want to claim that the information frictions facing food banks also apply to the real economy, and as a result, the Federal Reserve and other central banks should consider adopting a nominal income target. Let me tell a story to illustrate the point.
Consider the owner of an isolated bakery. Suppose one day, all of the customers seen by the baker spend twice as much money as the customers from the day before.
The baker has two options. She can interpret this increased demand as customers having come to appreciate the superior quality of her baked goods, and thus increase her production to match the new demand. Alternatively, she could interpret this increased spending as evidence that there is simply more money in the economy as a whole, and that she should merely increase her prices proportionally to account for inflation.
Economic agents confounding these two effects is the source of economic booms and busts, according to this model. This is exactly analogous to the problem faced by food banks trying to decide how much to bid at auction.
To the extent that these frictions are quantitatively important in the real world, central banks like the Fed and ECB should consider moving away from their inflation targeting regimes and toward something like a nominal income target, as Feeding America has.
To sum up, I'll use a metaphor from Selgin (1997).
Consider listening to a symphony on the radio. Randomly turning the volume knob up and down merely detracts from the musical performance (random variation in the price level is not useful). But, the changing volume of the orchestra players themselves, from quieter to louder and back down again, is an integral part of the performance (the price level should adjust with natural variations in the supply of food donations). The changing volume of the orchestra should not be smoothed out to maintain a constant volume (constant inflation is not optimal).
Central banks may want to consider allowing the orchestra to do its job, and reconsider inflation targeting as a strategy.
Behavioral economists have a concept called loss aversion. It's almost always described something like this:
"Loss aversion implies that one who loses $100 will lose more satisfaction than another person will gain satisfaction from a $100 windfall."
– Wikipedia, as of December 2015
Sounds eminently reasonable, right? Some might say so reasonable, in fact, that it's crazy that those darn neoclassical economists don't incorporate such an obvious, fundamental fact about human nature in their models.
It is crazy – because it's not true! The pop definition of loss aversion given above – that 'losses hurt more than equivalently sized gains' – is precisely the concept of diminishing marginal utility (DMU) that is boringly standard in standard price theory.
Loss aversion is, in fact, a distinct and (perhaps) useful concept. But somewhat obnoxiously, many behavioral economists, particularly in their popular writings, have a tendency to conflate it with DMU in a way that makes the concept seem far more intuitive than it is, and in the process wrongly makes standard price theory look bad.
I'm not just cherry-picking a bad Wikipedia edit. I name names at the bottom of this post, listing where behavioral economists have (often!) given the same misleading definition. It's wrong! Loss aversion is about reference dependence.
To restate, what I'm claiming is this:
Let me walk through the difference between DMU and loss aversion painstakingly slowly:
Diminishing marginal utility
"Diminishing marginal utility" is the idea that the more you have of something, the less you get out of having a little bit more of it. For example:
If you own nothing but $1,000 and the clothes on your back, and I then give you $100,000, that is going to give you a heck of a lot more extra happiness then if you had $100 million and I gave you $100,000.
An important corollary follows immediately from this: losses hurt more than gains!
I made a super high quality illustration to depict this:
What we have here is a graph of your utility as a function of your wealth under extremely standard (i.e., non-behavioral) assumptions. The fact that the line flattens out as you get to higher wealth levels is the property of DMU.
We can also see that equivalently sized losses hurt more than gains. As you go from 10k wealth to 2k wealth (middle green line to bottom green line), your utility falls by more than the amount your utility rises if you go from 10k wealth to 18k wealth (middle green to top green lines), despite the change in wealth being the same 8k in both directions.
Standard economics will always assume DMU, thus capturing exactly the intuition of the idea described in the above Wikipedia definition of loss aversion.
More mathematically – and I'm going to breeze through this – if your utility is purely a function of your wealth, Utility=U(W), then we assume that U'(W)>0 but U''(W)<0, i.e. your utility function is concave. With these assumptions, the result that U(W+ε)-U(W) < U(W)-U(W-ε) follows from taking a Taylor expansion. See proof attached below.
Loss aversion is a consequence of reference dependence and is an entirely different beast. The mathematical formulation was first made in Tversky and Kahneman (1991).
In words, loss aversion says this: Suppose you have nothing but the clothes you're wearing and $10,000 in your pocket, and then another $10,000 appears in your pocket out of nowhere. Your level of utility/happiness will now be some quantity given your wealth of $20,000.
Now consider a situation where you only own your clothes and the $30,000 in your pocket. Suppose suddenly $10,000 in your pocket disappears. Your total wealth is $20,000 – that is, exactly the same as the prior situation. Loss aversion predicts that in this situation, your level of utility will be lower than in the first situation, despite the fact that in both situations your wealth is exactly $20,000, because you lost money to get there.
Perhaps this concept of loss aversion is reasonable in some situations. It doesn't seem crazy to think that people don't like to lose things they had before.
But this concept is entirely different from the idea that 'people dislike losses more than they like gains' which some sloppy behavioral economists go around blathering about. It's about reference dependence! Your utility depends on your reference point: did you start with higher or lower wealth than you currently have?
In their academic papers, behavioral economists are very clear on the distinction. The use of math in formal economic models imposes precision. But when writing for a popular audience in the less-precise language of English – see below for examples – the same economists slip into using an incorrect definition of loss aversion.
Behavioral economics has not developed a brilliant newfound qualitative insight that people hate losses more than they like gains. This has been standard in price theory since Alfred Marshall's 1890 Principles of Economics.
Until very recently – see last month's WSJ survey of economists – the FOMC was widely expected to raise the target federal funds rate this week at their September meeting. Whether or not the Fed should be raising rates is a question that has received much attention from a variety of angles. What I want to do in this post is answer that question from a very specific angle: the perspective of a New Keynesian economist.
Why the New Keynesian perspective? There is certainly a lot to fault in the New Keynesian model (see e.g. Josh Hendrickson). However, the New Keynesian framework dominates the Fed and other central banks across the world. If we take the New Keynesian approach seriously, we can see what policymakers should be doing according to their own preferred framework.
The punch line is that the Fed raising rates now is the exact opposite of what the New Keynesian model of a liquidity trap recommends.
If you're a New Keynesian, this is the critical moment in monetary policy. For New Keynesians, the zero lower bound can cause a recession, but need not result in a deep depression, as long as the central bank credibly promises to create an economic boom after the zero lower bound (ZLB) ceases to be binding.
That promise of future growth is sufficient to prevent a depression. If the central bank instead promises to return to business as normal as soon as the ZLB stops binding, the result is a deep depression while the economy is trapped at the ZLB, like we saw in 2008 and continue to see in Europe today. The Fed appears poised to validate earlier expectations that it would indeed return to business as normal.
If the New Keynesian model is accurate, this is extremely important. By not creating a boom today, the Fed is destroying any credibility it has for the next time we hit the ZLB (which will almost certainly occur during the next recession). It won't credibly be able to promise to create a boom after the recession ends, since everyone will remember that it did not do so after the 2008 recession.
The result, according to New Keynesian theory, will be another depression.
I. The theory: an overview of the New Keynesian liquidity trap
I have attached at the bottom of this post a reference sheet going into more detail on Eggertsson and Woodford (2003), the definitive paper on the New Keynesian liquidity trap. Here, I summarize at a high level –skip to section II if you are familiar with the model.
A. The NK model without a ZLB
Let's start by sketching the standard NK model without a zero lower bound, and then see how including the ZLB changes optimal monetary policy.
The basic canonical New Keynesian model of the economy has no zero lower bound on interest rates and thus no liquidity traps (in the NK context, a liquidity trap is defined as a period when the nominal interest rate is constrained at zero). Households earn income through labor and use that income to buy a variety of consumption goods and consume them to receive utility. Firms, which have some monopoly power, hire labor and sell goods to maximize their profits. Each period, a random selection of firms are not allowed to change their prices (Calvo price stickiness).
With this setup, the optimal monetary policy is to have the central bank manipulate the nominal interest rate such that the real interest rate matches the "natural interest rate," which is the interest rate which would prevail in the absence of economic frictions. The intuition is that by matching the actual interest rate to the "natural" one, the central bank causes the economy to behave as if there are no frictions, which is desirable.
In our basic environment without a ZLB, a policy of targeting zero percent inflation via a Taylor rule for the interest rate exactly achieves the goal of matching the real rate to the natural rate. Thus optimal monetary policy results in no inflation, no recessions, and everyone's the happiest that they could possibly be.
B. The NK liquidity trap
The New Keynesian model of a liquidity trap is exactly the same as the model described above, with one single additional equation: the nominal interest rate must always be greater than or equal to zero.
This small change has significant consequences. Whereas before zero inflation targeting made everyone happy, now such a policy can cause a severe depression.
The problem is that sometimes the interest rate should be less than zero, and the ZLB can prevent it from getting there. As in the canonical model without a ZLB, optimal monetary policy would still have the central bank match the real interest rate to the natural interest rate.
Now that we have a zero lower bound, however, if the central bank targets zero inflation, then the real interest rate won't be able to match the natural interest rate if the natural interest rate ever falls below zero!
And that, in one run-on sentence, is the New Keynesian liquidity trap.
Optimal policy is no longer zero inflation. The new optimal policy rule is considerably more complex and I refer you to the attached reference sheet for full details. But the essence of the idea is quite intuitive:
If the economy ever gets stuck at the ZLB, the central bank must promise that as soon as the ZLB is no longer binding it will create inflation and an economic boom.
The intuition behind this idea is that the promise of a future boom increases the inflation expectations of forward-looking households and firms. These increased inflation expectations reduce the real interest rate today. This in turn encourages consumption today, diminishing the depth of the recession today.
All this effect today despite the fact that the boom won't occur until perhaps far into the future! Expectations are important, indeed they are the essence of monetary policy.
C. An illustration of optimal policy
Eggertsson (2008) illustrates this principle nicely in the following simulation. Suppose the natural rate is below the ZLB for 15 quarters. The dashed line shows the response of the economy to a zero-inflation target, and the solid line the response to the optimal policy described above.
Under optimal policy (solid line), we see in the first panel that the interest rate is kept at zero even after period 15 when the ZLB ceases to bind. As a result, we see in panels two and three that the depth of the recession is reduced to almost zero under policy; there is no massive deflation; and there's a nice juicy boom after the liquidity trap ends.
In contrast, under the dashed line – which you can sort of think of as closer to the Fed's current history independent policy – there is deflation and economic disaster.
II. We're leaving the liquidity trap; where's our boom?
To be completely fair, we cannot yet say that the Fed has failed to follow its own model. We first must show that the ZLB only recently has ceased or will cease to be binding. Otherwise, a defender of the Fed could argue that the lower bound could have ceased to bind years ago, and the Fed has already held rates low for an extended period.
The problem for showing this is that estimating the natural interest rate is extremely challenging, as famously argued by Milton Friedman (1968). That said, several different models using varied estimation methodologies all point to the economy still being on the cusp of the ZLB, and thus the thesis of this post: the Fed is acting in serious error.
Consider, most tellingly, the New York Fed's own model! The NY Fed's medium-scale DSGE model is at its core the exact same as the basic canonical NK model described above, with a lot of bells and whistles grafted on. The calibrated model takes in a whole jumble of data – real GDP, financial market prices, consumption, the kitchen sink, forecast inflation, etc. – and spits outs economic forecasts.
It can also tell us what it thinks the natural interest rate is. From the perspective of the New York Fed DSGE team, the economy is only just exiting the ZLB:
Barsky et al (2014) of the Chicago Fed perform a similar exercise with their own DSGE model and come to the same conclusion:
Instead of using a microfounded DSGE model, John Williams and Thomas Laubach, president of the Federal Reserve Bank of San Francisco and director of monetary affairs of the Board of Governors respectively, use a reduced form model estimated using a Kalman filter. Their model has that the natural rate in fact still below its lower bound (in green):
David Beckworth has a cruder but more transparent regression model here and also finds that the economy remains on the cusp of the ZLB (in blue):
If anyone knows of any alternative estimates, I'd love to hear in the comments.
With this fact established, we have worked through the entire argument. To summarize:
III. What's the strongest possible counterargument?
I intend to conclude all future essays by considering the strongest possible counterarguments to my own. In this case, I see only two interesting critiques:
A. The NK model is junk
This argument is something I have a lot of sympathy for. Nonetheless, it is not a very useful point, for two reasons.
First, the NK model is the preferred model of Fed economists. As mentioned in the introduction, this is a useful exercise as the Fed's actions should be consistent with its method of thought. Or, its method of thought must change.
Second, other models give fairly similar results. Consider the more monetarist model of Auerbach and Obstfeld (2005) where the central bank's instrument is the money supply instead of the interest rate (I again attach my notes on the paper below).
Instead of prescribing that the Fed hold interest rates lower for longer as in Eggertsson and Woodford, Auerbach and Obstfeld's cash-in-advance model shows that to defeat a liquidity trap the Fed should promise a one-time permanent level expansion of the money supply. That is, the expansion must not be temporary: the Fed must continue to be "expansionary" even after the ZLB has ceased to be binding by keeping the money supply expanded.
This is not dissimilar in spirit to Eggertsson and Woodford's recommendation that the Fed continue to be "expansionary" even after the ZLB ceases to bind by keeping the nominal rate at zero.
B. The ZLB ceased to bind a long time ago
The second possible argument against my above indictment of the Fed is the argument that the natural rate has long since crossed the ZLB threshold and therefore the FOMC has targeted a zero interest rate for a sufficiently long time.
This is no doubt the strongest argument a New Keynesian Fed economist could make for raising rates now. That said, I am not convinced, partly because of the model estimations shown above. More convincing to me is the fact that we have not seen the boom that would accompany interest rates being below their natural rate. Inflation has been quite low and growth has certainly not boomed.
Ideally we'd have some sort of market measure of the natural rate (e.g. a prediction market). As a bit of an aside, as David Beckworth forcefully argues, it's a scandal that the Fed Board does not publish its own estimates of the natural rate. Such data would help settle this point.
I'll end things there. The New Keynesian model currently dominates macroeconomics, and its implications for whether or not the Fed should be raising rates in September are a resounding no. If you're an economist who finds value in the New Keynesian perspective, I'd be extremely curious to hear why you support raising rates in September if you do – or, if not, why you're not speaking up more loudly.
Edit: The critique in this post – that NGDP targeting cannot achieve zero inflation in the long run without discretion – is somewhat tempered by my 2017 follow-up here: perhaps zero long-run inflation would be inferior to a long-run Friedman rule; which in fact can be naturally implemented with NGDP targeting.
I want to discuss a problem that I see with nominal GDP targeting: structural growth slowdowns. This problem isn't exactly a novel insight, but it is an issue with which I think the market monetarist community has not grappled enough.
I. A hypothetical example
Remember that nominal GDP growth (in the limit) is equal to inflation plus real GDP growth. Consider a hypothetical economy where market monetarism has triumphed, and the Fed maintains a target path for NGDP growing annually at 5% (perhaps even with the help of a NGDP futures market). The economy has been humming along at 3% RGDP growth, which is the potential growth rate, and 2% inflation for (say) a decade or two. Everything is hunky dory.
But then – the potential growth rate of the economy drops to 2% due to structural (i.e., supply side) factors, and potential growth will be at this rate for the foreseeable future.
Perhaps there has been a large drop in the birth rate, shrinking the labor force. Perhaps a newly elected government has just pushed through a smorgasbord of measures that reduce the incentive to work and to invest in capital. Perhaps, most plausibly (and worrisomely!) of all, the rate of innovation has simply dropped significantly.
In this market monetarist fantasy world, the Fed maintains the 5% NGDP path. But maintaining 5% NGDP growth with potential real GDP growth at 2% means 3% steady state inflation! Not good. And we can imagine even more dramatic cases.
II. Historical examples
Skip this section if you're convinced that the above scenario is plausible
Say a time machine transports Scott Sumner back to 1980 Tokyo: a chance to prevent Japan's Lost Decade! Bank of Japan officials are quickly convinced to adopt an NGDP target of 9.5%, the rationale behind this specific number being that the average real growth in the 1960s and 70s was 7.5%, plus a 2% implicit inflation target.
Thirty years later, trend real GDP in Japan is around 0.0%, by Sumner's (offhand) estimation and I don't doubt it. Had the BOJ maintained the 9.5% NGDP target in this alternate timeline, Japan would be seeing something like 9.5% inflation today.
Counterfactuals are hard: of course much else would have changed had the BOJ been implementing NGDPLT for over 30 years, perhaps including the trend rate of growth. But to a first approximation, the inflation rate would certainly be approaching 10%.
Or, take China today. China saw five years of double digit real growth in the mid-2000s, and not because the economy was overheating. I.e., the 12.5% and 14% growth in real incomes in China in 2006 and 2007 were representative of the true structural growth rate of the Chinese economy at the time. To be conservative, consider the 9.4% growth rate average over the decade, which includes the meltdown in 2008-9 and a slowdown in the earlier part of the decade.
Today, growth is close to 7%, and before the decade is up it very well could have a 5 handle. If the People's Bank had adopted NGDP targeting at the start of the millennium with a 9.4% real growth rate in mind, inflation in China today would be more than 2 percentage points higher than what the PBOC desired when it first set the NGDP target! That's not at all trivial, and would only become a more severe issue as the Chinese economy finishes converging with the developed world and growth slows still further.
This isn't only a problem for countries playing catch-up to the technological frontier. France has had a declining structural growth rate for the past 30 years, at first principally because of declining labor hours/poor labor market policies and then compounded by slowing productivity and population growth. The mess that is Russia has surely had a highly variable structural growth rate since the end of the Cold War. The United States today, very debatably, seems to be undergoing at least some kind of significant structural change in economic growth as well, though perhaps not as drastic.
Source: Margaret Jacobson, "Behind the Slowdown of Potential GDP"
III. Possible solutions to the problem of changing structural growth
There are really only two possible solutions to this problem for a central bank to adopt.
First, you can accept the higher inflation, and pray to the Solow residual gods that the technological growth rate doesn't drop further and push steady state inflation even higher. I find this solution completely unacceptable. Higher long term inflation is simply never a good thing; but even if you don't feel that strongly, you at least should feel extremely nervous about risking the possibility of extremely high steady state inflation.
Second, you can allow the central bank to periodically adjust the NGDP target rate (or target path) to adjust for perceived changes to the structural growth rate. For example, in the original hypothetical, the Fed would simply change its NGDP target path to grow at 4% instead of 5% as previously so that real income grows at 2% and inflation continues at 2%.
IV. This is bad – and particularly bad for market monetarists
This second solution, I think, is probably what Michael Woodford, Brad DeLong, Paul Krugman, and other non-monetarist backers of NGDP targeting would support. Indeed, Woodford writes in his Jackson Hole paper, "It is surely true – and not just in the special model of Eggertsson and Woodford – that if consensus could be reached about the path of potential output, it would be desirable in principle to adjust the target path for nominal GDP to account for variations over time in the growth of potential." (p. 46-7) Miles Kimball notes the same argument: in the New Keynesian framework, an NGDP target rate should be adjusted for changes in potential.
However – here's the kicker – allowing the Fed to change its NGDP target is extremely problematic for some of the core beliefs held by market monetarists. (Market monetarism as a school of thought is about more than merely just NGDP targeting – see Christensen (2011) – contra some.) Let me walk through a list of these issues now; by the end, I hope it will be clear why I think that Scott Sumner and others have not discussed this issue enough.
IVa. The Fed shouldn't need a structural model
For the Fed to be able to change its NGDP target to match the changing structural growth rate of the economy, it needs a structural model that describes how the economy behaves. This is the practical issue facing NGDP targeting (level or rate). However, the quest for an accurate structural model of the macroeconomy is an impossible pipe dream: the economy is simply too complex. There is no reason to think that the Fed's structural model could do a good job predicting technological progress. And under NGDP targeting, the Fed would be entirely dependent on that structural model.
Ironically, two of Scott Sumner's big papers on futures market targeting are titled, "Velocity Futures Markets: Does the Fed Need a Structural Model?" with Aaron Jackson (their answer: no), and "Let a Thousand Models Bloom: The Advantages of Making the FOMC a Truly 'Open Market'".
In these, Sumner makes the case for tying monetary policy to a prediction market, and in this way having the Fed adopt the market consensus model of the economy as its model of the economy, instead of using an internal structural model. Since the price mechanism is, in general, extremely good at aggregating disperse information, this model would outperform anything internally developed by our friends at the Federal Reserve Board.
If the Fed had to rely on an internal structural model adjust the NGDP target to match structural shifts in potential growth, this elegance would be completely lost! But it's more than just a loss in elegance: it's a huge roadblock to effective monetary policymaking, since the accuracy of said model would be highly questionable.
IVb. Rules are better than discretion
Old Monetarists always strongly preferred a monetary policy based on well-defined rules rather than discretion. This is for all the now-familiar reasons: the time-inconsistency problem; preventing political interference; creating accountability for the Fed; etc. Market monetarists are no different in championing rule-based monetary policy.
Giving the Fed the ability to modify its NGDP target is simply an absurd amount of discretionary power. It's one thing to give the FOMC the ability to decide how to best achieve its target, whether than be 2% inflation or 5% NGDP. It's another matter entirely to allow it to change that NGDP target at will. It removes all semblance of accountability, as the Fed could simply move the goalessays whenever it misses; and of course it entirely recreates the time inconsistency problem.
IVc. Expectations need to be anchored
Closely related to the above is the idea that monetary policy needs to anchor nominal expectations, perhaps especially at the zero lower bound. Monetary policy in the current period can never be separated from expectations about future policy. For example, if Janet Yellen is going to mail trillion dollar coins to every American a year from now, I am – and hopefully you are too – going to spend all of my or your dollars ASAP.
Because of this, one of the key necessary conditions for stable monetary policy is the anchoring of expectations for future policy. Giving the Fed the power to discretionarily change its NGDP target wrecks this anchor completely!
Say the Fed tells me today that it's targeting a 5% NGDP level path, and I go take out a 30-year mortgage under the expectation that my nominal income (which remember is equal to NGDP in aggregate) will be 5% higher year after year after year. This is important as my ability to pay my mortgage, which is fixed in nominal terms, is dependent on my nominal income.
But then Janet Yellen turns around and tells me tomorrow, "Joke's on you pal! We're switching to a 4% level target." It's simply harder for risk-averse consumers and firms to plan for the future when there's so much possible variation in future monetary policy.
IVd. Level targeting exacerbates this issue
Further, level targeting exacerbates this entire issue. The push for level targeting over growth rate targeting is at least as important to market monetarism as the push for NGDP targeting over inflation targeting, for precisely the reasoning described above. To keep expectations on track, and thus not hinder firms and households trying to make decisions about the future, the central bank needs to make up for past mistakes, i.e. level target.
However, level targeting has issues even beyond those that rate targeting has, when the central bank has the ability to change the growth rate. In particular: what happens if the Fed misses the level target one year, and decides at the start of the next to change its target growth rate for the level path?
For instance, say the Fed had adopted a 5% NGDP level target in 2005, which it maintained successfully in 2006 and 2007. Then, say, a massive crisis hits in 2008, and the Fed misses its target for say three years running. By 2011, it looks like the structural growth rate of the economy has also slowed. Now, agents in the economy have to wonder: is the Fed going to try to return to its 5% NGDP path? Or is it going to shift down to a 4.5% path and not go back all the way? And will that new path have as a base year 2011? Or will it be 2008?
(Note: I am aware that had the Fed been implementing NGDPLT in 2008 the crisis would have been much less severe, perhaps not even a recession! The above is for illustration.)
(Also, I thank Joe Mihm for this point.)
IVe. This problem for NGDP targeting is analogous to the velocity instability problem for Friedman's k-percent rule
Finally, I want to make an analogy that hopefully emphasizes why I think this issue is so serious. Milton Friedman long advocated that the Fed adopt a rule whereby it would have promised to keep the money supply (M2, for Friedman) growing at a steady rate of perhaps 3%. Recalling the equation of exchange, MV = PY, we can see that when velocity is constant, the k-percent rule is equivalent to NGDP targeting!
In fact, velocity used to be quite stable:
For the decade and a half or two after 1963 when Friedman and Schwartz published A Monetary History, the rule probably would have worked brilliantly. But between high inflation and financial innovation in the late 70s and 80s, the stable relationship between velocity, income, and interest rates began to break down, and the k-percent rule would have been a disaster. This is because velocity – sort of the inverse of real, income-adjusted money demand – is a structural, real variable that depends on the technology of the economy and household preferences.
The journals of the 1980s are somewhat famously a graveyard of structural velocity models attempting to find a universal model that could accurately explain past movements in velocity and accurately predict future movements. It was a hopeless task: the economy is simply too complex. (I link twice to the same Hayek essay for a reason.) Hence the title of the Sumner and Jackson paper already referenced above.
Today, instead of hopelessly modeling money demand, we have economists engaged in the even more hopeless task of attempting to develop a structural model for the entire economy. Even today, when the supply side of the economy really changes very little year-to-year, we don't do that good of a job at it.
And (this is the kicker) what happens if the predictability of the structural growth rate breaks down to the same extent that the predictability of velocity broke down in the 1980s? What if, instead of the structural growth rate only changing a handful of basis points each year, we have year-to-year swings in the potential growth rate on the order of whole percentage points? I.e., one year the structural growth is 3%, but the next year it's 5%, and the year after that it's 2.5%?
I know that at this point I'm probably losing anybody that has bothered to read this far, but I think this scenario is entirely more likely than most people might expect. Rapidly accelerating technological progress in the next couple of decades as we reach the "back half of the chessboard", or even an intelligence explosion, could very well result in an extremely high structural growth rate that swings violently year to year.
However, it is hard to argue either for or against the techno-utopian vision I describe and link to above, since trying to estimate the future of productivity growth is really not much more than speculation. That said, it does seem to me that there are very persuasive arguments that growth will rapidly accelerate in the next couple of decades. I would point those interested in a more full-throated defense of this position to the work of Robin Hanson, Erik Brynjolfsson and Andrew McAfee, Nick Bostrom, and Eliezer Yudkowsky.
If you accept the possibility that we could indeed see rapidly accelerating technological change, an "adaptable NGDP target" would essentially force the future Janet Yellen to engage in an ultimately hopeless attempt to predict the path of the structural growth rate and to chase after it. I think it's clear why this would be a disaster.
V. An anticipation of some responses
Before I close this out, let me anticipate four possible responses.
1. NGDP variability is more important than inflation variability
Nick Rowe makes this argument here and Sumner also does sort of here. Ultimately, I think this is a good point, because of the problem of incomplete financial markets described by Koenig (2013) and Sheedy (2014): debt is priced in fixed nominal terms, and thus ability to repay is dependent on nominal incomes.
Nevertheless, just because NGDP targeting has other good things going for it does not resolve the fact that if the potential growth rate changes, the long run inflation rate would be higher. This is welfare-reducing for all the standard reasons. Because of this, it seems to me that there's not really a good way of determining whether NGDP level targeting or price level targeting is more optimal, and it's certainly not the case that NGDPLT is the monetary policy regime to end all other monetary policy regimes.
2. Target NGDP per capita instead!
You might argue that if the most significant reason that the structural growth rate could fluctuate is changing population growth, then the Fed should just target NGDP per capita. Indeed, Scott Sumner has often mentioned that he actually would prefer an NGDP per capita target. To be frank, I think this is an even worse idea! This would require the Fed to have a long term structural model of demographics, which is just a terrible prospect to imagine.
3. Target nominal wages/nominal labor compensation/etc. instead!
Sumner has also often suggested that perhaps nominal aggregate wage targeting would be superior to targeting NGDP, but that it would be too politically controversial. Funnily enough, the basic New Keynesian model with wage stickiness instead of price stickiness (and no zero lower bound) would recommend the same thing.
I don't think this solves the issue. Take the neoclassical growth or Solow model with Cobb-Douglas technology and preferences and no population growth. On the balanced growth path, the growth rate of wages = the potential growth rate of the economy = the growth rate of technology. For a more generalized production function and preferences, wages and output still grow at the same rate.
In other words, the growth rate of real wages parallels that of the potential growth rate of the economy. So this doesn't appear to solve anything, as it would still require a structural model.
4. Set up a prediction market for the structural growth rate!
I don't even know if this would work well with Sumner's proposal. But perhaps it would. In that case, my response is... stay tuned for my critique of market monetarism, part two: why handing policymaking over to prediction markets is a terrible idea.
VI. In conclusion
The concerns I outline above have driven me from an evangelist for NGDP level targeting to someone extremely skeptical that any central banking policy can maintain monetary equilibrium. The idea of optimal policy under NGDP targeting necessitating a structural model of the economy disturbs me, for a successful such model – as Sumner persuasively argues – will never be built. The prospect that NGDP targeting might collapse in the face of rapidly accelerating technological growth worries me, since it does seem to me that this very well could occur. And even setting aside the techno-utopianism, the historical examples described above, such as Japan in the 1980s, demonstrate that we have seen very large shifts in the structural growth rate in actual real-world economies.
I want to support NGDPLT: it is probably superior to price level or inflation targeting anyway, because of the incomplete markets issue. But unless there is a solution to this critique that I am missing, I am not sure that NGDP targeting is a sustainable policy for the long term, let alone the end of monetary history.
In 2008, Christina and David Romer published an interesting paper demonstrating that FOMC members are useless at forecasting economic conditions compared to the Board of Governors staff, and presented some evidence that mistaken FOMC economic forecasts were correlated with monetary policy shocks.
I've updated their work with another decade of data, and find that while the FOMC remained bad at forecasting over the extended period, the poor forecasting was not correlated with monetary policy shocks.
First, some background.
Before every FOMC meeting, the staff at the Board of Governors produces the Greenbook, an in-depth analysis of current domestic and international economic conditions and, importantly for us, forecasts of all kinds of economic indicators a year or two out. The Greenbook is only released to the public with a major lag, so the last data we have is from 2007.
The FOMC members – the governors and regional bank presidents – prepare consensus economic forecasts twice a year, usually February and July, as part of the Monetary Policy Report they must submit to Congress. (Since October 2007, FOMC members have prepared projections at four FOMC meetings per year. That data, from the end of 2007, is not included in my dataset here, but I'll probably put it in when I update it in the future as more recent Greenbooks are released.)
Summary of Romer and Romer (2008)
The Romers took around 20 years of data from these two sources, from 1979 to 2001, and compared FOMC forecasts to staff forecasts. They estimate a regression of the form
Where X is the realized value of the variable (e.g. actual GDP growth in year t+1), S is the staff's projection of the variable (e.g. the staff's projected GDP growth next year), and P is the FOMC's projection of the variable (e.g. the FOMC's projected GDP growth next year).
They find "not just that FOMC members fail to add information, but that their efforts to do so are counterproductive." Policymakers were no good at forecasting over this period.
They then ask if the mistaken forecasts cause the FOMC to make monetary policy errors that cause monetary policy shocks. The two use their own Romer and Romer (2004) measure, which I've updated here, as the measure of monetary policy shocks. They then estimate the regression
Where M is the measure of shocks, and P and S are as before. They only ran this regression from 1979 through 1996, as that was the latest the measure of shocks went up to in the 2004 paper.
They find that, "The estimates suggest that forecast differences may be one source of monetary shocks... An FOMC forecast of inflation one percentage point higher than the staff forecast is associated with an unusual rise in the federal funds rate of approximately 30 basis points."
That seemed like a very interesting result to me when I first read this paper. Could bad monetary policymaking be explained by the hubris of policymakers who thought they could forecast economic conditions better than the staff? It turns out, after I updated the data, this result does not hold.
Updating the data
I followed the same methodology as when I updated Romer and Romer (2004): first replicating the data to ensure I had the correct method before collecting the new data and updating. The data is from 1979 through 2007, and all my work is available here and here.
I find, first, that policymakers remained quite poor economic forecasters. Here is the updated version of Table 1 from the paper, with the old values for comparison:
The coefficient on the FOMC forecast for inflation and unemployment is still right around zero, indicating that FOMC forecasts for these two variables contain no useful information.
However, it appears that once we extend the monetary policy shock regression from 1996 to 2007, the second result – that forecast differences are a source of monetary policy shocks – does not hold. Here is the updated version of Table 2 from the paper, again with old values for comparison:
When the Romers published their paper, the R-squared on the regression of monetary shocks over all three variables was 0.17. This wasn't exactly the strongest correlation, but for the social sciences it's not bad, especially considering that monetary shock measure is fairly ad hoc.
As we can see in the updated regression, the R-squared is down to 0.05 with the extended data. This is just too small to be labeled significant. Thus, unfortunately, this result does not appear to hold.
I've updated the Romer and Romer (2004) series of monetary policy shocks. The main takeaway is this graph of monetary policy shocks by month, since 1969, where the gray bars indicate recession:
When the two published their paper, they only had access to date up through 1996, since Fed Greenbooks – upon which the series is based – are released with a large lag. I've updated it through 2007, the latest available, and will update it again next month when the 2008 Greenbooks are released.
The two interesting points in the new data are
Below I'll go into the more technical notes of how this measure is constructed and my methodology, but the graph and the two points above are the main takeaway.
How is the R&R measure constructed?
First, the Romers derive a series of intended changes in the federal funds rate. (This is easy starting in the 1990s, since the FOMC began announcing when it wanted to change the FFR; before that, the two had to trawl through meeting minutes to figure it out.) They then use the Fed's internal Greenbook forecasts of inflation and real growth to control the intended FFR series for monetary policy actions taken in response to information about future economic developments, specifically RGDP growth, inflation, and unemployment.
In other words, they regress the change in the intended FFR around forecast dates on RGDP growth, inflation and unemployment. Then, as they put it, "Residuals from this regression show changes in the intended funds rate not taken in response to information about future economic developments. The resulting series for monetary shocks should be relatively free of both endogenous and anticipatory actions."
The equation they estimate is:
The Romers show in their paper that, by this measure, negative monetary policy shocks have large and significant effects on output and the price level.
It is worth noting the limitations of this measure. It is based on the federal funds rate instrument, which is not a very good indicator of the stance of monetary policy. Additionally, if the FOMC changes its target FFR between meetings, any shock associated with that decision would not be captured by this measure.
First, I replicated the Romer and Romer (2004) results to confirm I had the correct method. Then I collected the new data in Excel and ran the regression specified above in MATLAB. The data is available here and here (though there might have been errors when uploading to Google Drive).
The residuals are shown above in graph form; it is an updated version of figure 1a in Romer and Romer (2004).
The coefficients and statistics on the regression are (this is an updated version of table 1 in the original paper):
Last, for clarity, I have the monetary policy shock measure below with the top five extremes removed. This makes some periods more clear, especially the 2007 shock. Again, I will update this next month when the 2008 Greenbooks are released. It should be very interesting to see how large a negative shock there was in 2008.
(Adapted from the system of Cameron Harwick.)