## 25 March 2016

### How Would You Know?

How would you know if central banks were impotent at the zero lower bound?

You would have them target some nominal variable and then see if they can achieve that target. Wait, every central bank that I can think of off the top of my head does this: the Federal Reserve, BOJ, BOC, BOE, and the ECB. So, given that all of these central banks have had limited success at keeping inflation on target, monetary policy seems to have been pretty impotent.

Even if we restrict the analysis to countries that adopted the inflation target during the zero lower bound period (i.e. the BOJ and the Federal Reserve), we would find the same result: since the new target was adopted, in both cases 2% inflation, the target variable has been consistently below target.

Of course, all the market monetarists will respond by basically saying that inflation is always on target, so the recent experience only means that central banks are liars. This proposition is so ridiculous that I refuse to comment further on it.

For the remaining sane people in the room, the failure of inflation targeting central banks to have inflation on target is an indication of the ineffectiveness of monetary policy at the zero lower bound. Specifically, chronically low inflation means that the ability of central banks to loosen monetary policy (whatever the heck that means, everyone please stop referring to undefined terms like the 'stance' of monetary policy) has been severely limited over the last 8 years.

Actually, I do want to comment a little bit on the aforementioned ridiculousness. If your view is consistent with any empirical outcome, then it is unfalsifiable and should probably be ignored. Then again, this is probably true for the majority of economics, which is why your opinions, along with those of Post Keynesians, Austrians, and probably yet other heterodox school that I have never heard of, still exist.

Why can't we (unfortunately, I might add) reject market monetarism based on the last 8 years? Because if we did that, we'd also have to reject all the good theories like the Phillips curve, sticky prices at the individual firm level, Marshallian labor markets, etc.

## 23 March 2016

### 'Low Interest Rates Are Contractionary'

I wanted to delve a little bit deeper into Scott Sumner's claim that low interest rates are contractionary. Unfortunately, the model he uses to prove this is complete nonsense, since it requires the central bank to control the money supply and the nominal interest rate at the same time to achieve the result. Because of this, I think a dynamic analysis is pertinent.

Consider a dynamic and slightly altered version of Scott's money demand model:
$$(1)\: m_t - p_t = y_t - \alpha i_t$$
where $m_t$ is the (log) money supply, $p_t$ is the (log) price level, $y_t$ is the (log) of output, and $i_t$ is the nominal interest rate. Since the model is dynamic, I will also add the Fisher relation and the Euler equation:
$$(2)\: i_t = r_t + E_t\pi_{t+1}$$
$$(3)\: y_t = E_t y_{t+1} - \sigma r_t$$
where $r_t$ is the real interest rate and $\pi_t$ is the inflation rate ($\pi_t = p_t - p_{t-1}$).

Currently this model lacks an aggregate supply curve, so, for the time being, I'll go with a vertical AS curve for simplicity: $y_t = 0$. The central bank also sets the money supply in period $t+1$ such that $p_{t+1} = \bar p$. In this case, what happens when the central bank increases the money supply?

Well, if we simplify the model slightly, we can reduce it to
$$(4)\: p_t = \frac{m_t + \alpha\bar p}{1 + \alpha}$$
That is, an increase in the money supply causes the price level to rise and the nominal interest rate to fall ($\frac{\partial p_t}{\partial m_t} = \frac{1}{1 + \alpha} < 1$) -- interestingly the conventional result.

Of course Scott is now screaming at me for committing the same sin as Krugman by fixing the future price level. Don't worry, I'll get to a more complex model, I just wanted to show that Sumner's result doesn't make sense in this pseudo-dynamic context (that, I might add, is already much better than his lazy static model. The same goes for Krugman's 1998 model, which was also dynamic).

If we relax the assumption that the price level is fixed in the next period, the model instead simplifies to
$$(5)\: p_t = E_t\frac{1}{1 + \alpha}\sum^\infty_{j=t}\left(\frac{\alpha}{1+\alpha}\right)^{j-t}m_j$$
From this we know that the current price level is a function of the discounted sum of expected money supplies. This is basic market monetarist stuff: if an increase in the money supply is expected to be immediately reversed, the price level will not rise. Keep note of the fact that, in contrast with most market monetarist assertions, an expected reversal far in the future has a highly diminished effect on the price level. Expected monetary tightening ten years from now is as good as useless.

The point here, though is that a central bank can effect a reduction in the nominal interest rate without increasing the current money supply -- it simply has to reduce expected money supply growth. My point here is that Sumner never brought this up, and, since his reasoning is based entirely on the static version of the model, he has no right to say that his model implies contractionary low interest rates.

Changing aggregate supply only makes the model more difficult to understand, but, if the aggregate supply curve became
$$(6)\: y_t = f(p_t)$$
it would then be possible to argue that expected monetary tightening has an adverse effect on the economy. At this point, though, I don't think anyone should care. Sumner may have been claiming this, but his model certainly didn't justify the claim, so he should have been ignored.

## 21 March 2016

### More On Japan's Phillips Curve

When I saw these two graphs from Jason Smith, I was immediately a little wary:

It seems that the slope of the Phillips curve in Japan has decline significantly over the last few decades.

But I thought I would do some of my own calculations, so I took the same data I was using before, except now expressed as a change from twelve months ago, and found the slope and p-values over the prior five years for each year between 1992 and 2015. The results were a little different than Jason's (which is understandable given the shorter time horizon):

Interestingly, if you ignore the periods with really high p-values (1992-1997, 2003-2007, and 2015), the Phillips curve seems to have a pretty consistent slope over the previous five years.

I'm not sure what to make of the previously mentioned periods with really high p-values except that the slope of the Phillips curve was effectively zero at those times. Basically the 2003-2007 period saw little change in inflation corresponding with consistent, high employment growth. Theoretically, I'd say this probably reflects non-cyclical changes in employment, which would mean that the Phillips curve wouldn't be seen in the data, but this explanation may not be satisfactory.

I don't know how to explain '92-'97 (which also includes the prior five years: 1987-1991), although I would note that Jason seems to have gotten a relatively high slope for this period and that the period I was most concerned with was the period directly following the great recession, in which the Phillips curve seems to have reasserted itself -- which does indeed make sense, considering the recession of 2008 was almost definitely cyclical.

My hypothesis is that Jason's slopes for the 2008-2015 period are held down by his inclusion of the Koizumi boom.

## 20 March 2016

### Some Proper Philosophy of Science

Noah Smith and Jason Smith have been writing a series of blog posts focusing on three main ideas: Empiricism, paradigm shifts, and 'negative empiricism' (which is, as far as I'm concerned, equivalent to Postpositivism, which would basically be synonymous with 'whatever Karl Popper said,' but whatever).

Regarding empiricism, I'm not sure why this is getting any attention from people discussing philosophy of science in the 21st century. Empiricism is most closely associated with David Hume -- i.e. an enlightenment philosopher -- and, while it serves as the backdrop for newer philosophy of science, is neither new nor worthy of attention when considering a new philosophy of economics. It seems that people have confused empiricism with caring about empirical evidence when in reality empiricism is an epistemology that elevates experience over a priori deductions (which are characteristic of rationalism). For a more in-depth look into this, see "Rationalism vs. Empiricism" in the Stanford Encyclopedia of Philosophy. Needless to say empiricism alone does not qualify as a philosophy of science.

Jason somewhat repairs this by arguing for "negative empiricism" which he defines as "theory rejection." Here my only issue is that Jason has almost literally argued for Postpositivism, which is exactly that: hypothesis rejection. Basically think Popper; what really matters for a theory is falsifiability. Interestingly, Popper essentially solves the empiricist (Humean) problem of induction by arguing that empirical evidence in favor of a hypothesis is irrelevant and falsification is all that matters. In this sense, Jason is basically a Postpositivist by arguing for "theory rejection" based on empirical evidence. Noah Smith also weighs in, suggesting that economics was in "an age of great theoryderp" before the IT revolution which (according to him, not me) allowed for theories to be invalidated. To his credit, Noah acknowledges that "you can be a pure theorist and still subscribe to empiricism - you just don't believe in theories until they've been successfully tested against data," which is, in my opinion, the way most of economics currently is and will remain forever.

Both Smith's talk about paradigm shifts (further solidifying my suspicion that neither of them are empiricists and that they did not just come forward in time from 1748), which are attributed to Thomas Kuhn (another 20th century philosopher of science). In Kuhn's view, science operates in a single paradigm until the usefulness of said paradigm is exhausted at which point there will be a revolution. Both of the Smith's seem to be arguing for such a regime change, whether it is Jason's Information Transfer Framework or Noah suggesting that economics is experiencing a wave of "new empiricism" (OK, every time I read the word empiricism in this topic I shudder, please stop calling it that). Either way, each of them sees economics as being on the verge of or currently undergoing a revolution which begs the question of whether or not the current paradigm is really exhausted. I'll leave this to others to determine, but I personally don't see the field as being in a dead-end right now.

So, really, this post all comes down to two requests: please stop calling Postpositivism Empiricism and please stop trying to get economists to accept an 18th century epistemology instead of actually arguing for a new philosophy of economics (or, at least, coming clean and saying you are a Postpositivist).

## 19 March 2016

### 生きています！

あの$R^2$の値を見られますか？見られますか？そうです、日本でフィリップス曲線は健在なので、日本は「信用の理論が顕著に強い戻ってくる経済研究所」になりました。

もし散布図は好きではないと、このすごいインフレーションの予言に見て下さい。
この予言は一値だけ使うことに留意して下さい。つまり、１５と７４の間に高齢者のための雇用率を使い、うまく動作するようです。特に期待インフレーションが使用されていないのです。生きています！

## 18 March 2016

### It's Alive!

Noah Smith seems to think that Japan is "an economics lab where theories go to die," notably asserting that "a tight labor market hasn't caused increasing prices. New Keynesian theory ... has failed to explain Japan's lack of inflation."

Au contraire! You see, Noah and other Phillips Curve doubters, Japan actually has an exceptionally good Phillips Curve, so unfortunately Noah Smith's eyeballing led him astray:
See that $R^2$ value? Do you see it? That's right, the Phillips Curve is alive and well in Japan, seemingly making it, at least in this case, an economics lab where theories that some people thought were discredited conspicuously come back strong.

If you don't like the scatter plot, look at the pretty awesome prediction for inflation that the linear fit gives:
Keep in mind that this prediction uses only one variable, the employment rate for people aged between 15 and 74, and it seems to work incredibly well, especially because expected inflation is nowhere to be seen (pun intended). It lives!

Update:

Same graph with core CPI instead:

## 17 March 2016

### The (Lack of) Usefulness of Empirical Evidence in Economics

My argument with Jason Smith about the philosophy of economics has become rather spread out and hard to follow, so I thought I would compile my argument into one blog post.

First, let's start where I did with my previous post. Suppose there is some effect $y$ that is caused by $x,z,...$. This can be written as
$$y = f(x,z,...)$$
I hypothesize that $y = g(x,u)$. How do I test this hypothesis? I must isolate all other variables but $x$ or $u$ at one time and then change one of the independent variables ($x$ or $u$). If I do this, then I will be able to determine if $g(\bullet) = f(\bullet)$ and whether or not $x$ or $u$ causes $y$.

This can't [easily] be done in economics; it is simply not possible [probable that it would be possible] to conduct a generalizable experiment in a closed system -- i.e., only one independent variable can change at once. Take my previous example of the minimum wage. There are two issues with concluding that the econ 101 partial equilibrium model is wrong in the face of apparently conflicting empirical evidence: there is no way to determine whether or not the minimum wage increase caused employment to be lower than it otherwise would have been, since there can be no control experiment, and, if employment is $y$ and the minimum wage is $x$ from the example above, empirical evidence can only prove that the theory is incomplete; i.e. that it doesn't capture all of the possible causes of $y$.

So, in this sense, it is possible to invalidate an economic model with data, but it doesn't help with anything; it doesn't even say whether the model is actually wrong, or simply lacking the full number of causes that effect $y$. The econ 101 model may be completely right about what happens to employment given a minimum wage increase in a closed system, but we can never know. It is for this reason that empirical evidence is not very valuable in economics, not because people have too strong of priors (even though this is frequently the case).

This also means, as Jason rightly acknowledges, that empirical accuracy is not something worth praising very highly in economics:
[*] You'll never nail down correlation vs causation
Due to external factors (and lack of controlled experiments), this may be true. However, this is a reason not to praise an empirically successful model.
The problem is that the flip-side of this is that you can never actually determine whether or not the supposed cause and effect relationships in models are correct. This is why Popperian rejection of hypotheses is not [rarely] possible in economics; why empirical evidence cannot "falsify economic models."

Jason also challenges my claim that DSGE models are [should be] qualitative models:
John makes the case that it is the latter: DSGE models are qualitative models. I don't buy this. For one, they are way too complex to be a qualitative model.
I agree with this when it comes to, e.g., the NY Fed DSGE, but not for DSGE in general. Basic DSGE models, without all the bells and whistles that try to make them empirical, are indeed, in my opinion qualitative. They are simply internally consistent ways of diagnosing a single problem in economics. If I want to come up with a theory about whether it is better to have PAYGO pensions or American-style social security, I don't bother modeling monopolistic competition or sticky prices because all I want is a qualitative analysis.

I disapprove of even using the supposedly structural DSGE models of the economy such as Smets-Wouters or the NY Fed DSGE on the grounds that it should be apparent that the assumptions of these models deviate far from reality; they are in no way structural, so expecting them to be accurate models is almost ridiculous. Because of this, they should just be thrown out for their complexity.

When it comes down to it, Jason seems to immediately associate DSGE with big, clunky models with tons of dubious assumptions that somehow approximate reality whereas I associate DSGE with utility maximization, budget constraints, and rational expectations. Every DSGE model I bother using is, in my opinion, qualitative and that's how it should be.

So, to make one of my previously misunderstood arguments slightly more clear, does the great recession invalidate the basic 3-equation reduced form New Keynesian model? No, it only shows that the model is incomplete, since there is no way to disprove any of the supposed causal relationships in the model, especially since rational expectations are unobservable. The lack of empirical support for New Keynesian DSGE (as I define it) does not inherently mean that any of the hypothesized cause and effect relationships in the model are wrong. It could be this, or that the model lacks enough complexity to explain the data.

## 16 March 2016

### It's Not Over Yet

Jason Smith today in a blog post:
New Keynesian economics = Ignore empirical data
...
Information transfer economics = Use empirical data
I'd like to venture to explain why exactly this might be true. Start with basic Humean epistemology in which knowledge is the relationship between cause and effect and, for a given effect, there might be multiple causes. This can be expressed as
$$y = f(x,z,...)$$
where $y$ is the effect, and $x,z,...$ are the causes. How do you go about determining whether or not $x$ causes $y$? You create a closed system in which only $x$ and $y$ can change and then change $x$. If you then observe $y$, you may then (and only then) conclude that $x$ causes $y$. If, however, you cannot create a closed system, you cannot conclude whether or not your hypothesis that $x$ causes $y$ is true.

Of course, this is all really basic, but what does it have to do with New Keynesian economics (or, more generally, mainstream economics). I'll start with a general example. Consider the minimum wage. Basic partial equilibrium analysis suggests that increasing minimum wage will cause an increase in unemployment, but empirical research seems to not confirm this prediction. Case closed, Econ 101 is wrong and Info Econ 101 is right!

No. The only way for any empirical research to invalidate the partial equilibrium analysis with the minimum wage is if it were done in a closed system; i.e., the only two variables were employment and the minimum wage, which has not been the case in any study that I have seen referenced. In this sense, the causal relationship between the minimum wage and employment has not been falsified -- the data have only proven that the partial equilibrium model of labor markets is incomplete (i.e., it doesn't capture all of the causes of changes in unemployment), which we all already knew.

This same problem is captured by the failure of NK DSGE models to explain the Great Recession; the only conclusion that can be drawn from the empirical evidence is that the model is incomplete, which everyone already knew anyway, and therefore failed to capture all the possible causes of the Great Recession -- this has no bearing on the correctness of the rest of the model.

Since it is obvious that closed systems can't be dealt with very often in social science, especially if the hypothesis being tested (e.g., NK DSGE) is rather complex, it should be obvious that empirical evidence is not very useful for social science. That said, the appropriate conclusion is probably that all economic models are doomed to be quantitatively unsuccessful (and even if they are, that is not necessarily an indication that the model in question is correct in the sense that it correctly matches causes with effects), even if they do capture some of the correct cause and effect relationships, and we should only judge models based on their qualitative predictions, not their quantitative ones.

## 15 March 2016

### Central Banks Can't Control Money Demand!!!!!!!

After posting too many lengthy comments on Scott Sumner's blog a while back, I decided I was going to ignore his claims that high interest rates are "expansionary" because they increase velocity. I tried, but he has crossed the line. He has elevated his already excessive list of central bank abilities to also include the ability to control money demand as well as the money supply.
NGDP = MB*(Base Velocity), where V is positively related to nominal interest rates.
Thus if you cut interest rates without increasing the money supply, then V falls and policy becomes more contractionary.
Read that a few times to get the full point that Sumner is making. His money demand equation is, of course, perfectly fine; you'd have to be ignorant to not understand that velocity is a positive function of nominal interest rates (or, in my preferred terminology, money demand is decreasing in nominal interest rates). The problem comes in when Scott says "if you cut interest rates without increasing the money supply." When you read this, sirens should have begun screeching in your head; Scott's weird partial equilibrium analysis in which there are three things that determine the nominal interest rate (money demand curve, interest rate chosen by central bank, and money supply) may be "monetary economics 101" in his mind, but it's certainly not economics 101, in which a monopoly supplier of something can't control its price and its quantity.

I mean, come on, this should be obvious, but apparently someone with a PhD in economics can make such a mistake without being universally discredited. In Scott's world, all a central bank must do is apparently announce higher nominal interest rates as well as monetary expansion, and NGDP will go up by the desired amount. Well, duh, but the real world doesn't work that way; just because you can force the money demand curve to shift so that a higher money supply means a higher nominal interest rate by making the nominal interest rate and the money supply exogenous in a model doesn't mean that this is actually possible. Seriously, the effective argument that Scott is making here is "thus if you reduce NGDP, then NGDP falls which means that monetary policy has become more contractionary." I'm sorry, but there's seriously no excuse for this; Sumner really needs to start working with general equilibrium sometime before he just skips this misleading line of reasoning and goes straight to "NGDP should have been higher in 2009, if that Fed had simply done this, then a recession wouldn't have happened" (bear with me and pretend Scott hasn't said almost exactly this before).

Of course, a central bank can go about raising the nominal interest rate without changing the current nominal interest rate, but this requires expected increases in the money supply, which Scott never mentions (probably because of previously mentioned attachment to partial equilibrium). That is, if expected money supply growth increases, then so will expected inflation, but this is not the argument that Scott is making, he only talks about the current money supply and the nominal interest rate in his post, and I'm not willing to give him the benefit of the doubt. Beyond that, Sumner was using a one period model to do dynamic analysis (someone explain to me why he's so dedicated to partial equilibrium), which is a sin in and of itself and he would still be guilty of even if he secretly meant to say "thus if you reduce expectations of future money supply growth without increasing the current money supply, then velocity falls [money demand goes up] and policy becomes more contractionary."

The worst part is that I haven't seen anyone complain about this apparent lapse of understanding of basic economics, everyone seems to be obsessed with Sumner's alleged Neo-Fisherism. Everyone, that's not the issue, you don't need to be bothered about Sumner appealing to an extremely basic one period model that you all should agree with, you should be screaming that "central banks can't control money demand!!!!!!!!!!"

## 12 March 2016

### The Three Pronged Republican Economic Platform

The Republican economic platform can basically by summed up by three defining characteristics: 1) increase military spending, 2) cut taxes, primarily for high-income individuals, and 3) balance the budget. If you look at each of the Republican candidates' websites, you'll see pretty much all of the same policies (with the exception of Trump, who, instead of a balanced budget amendment, proposes what he calls 'revenue neutral' and everyone else calls 'budget busting' policies), with everything else pretty much secondary.

Perhaps the most interesting part of this nearly ubiquitous threefold policy is that each of these objectives are pretty much mutually inconsistent. Each candidate is effectively proposing massive spending increases (military buildup) as well as massive tax cuts (ranging in severity from 'insane' -- Cruz -- to 'I can't judge because there are no specifics' -- Kasich). Unless you buy into the idea that cutting income taxes incentivizes people to work so much more that the net effect on revenue is positive (relative to the higher-tax counterfactual, shut up Reaganites), you should realize that the three effects of each Republican's plan will be 1) massive deficits, 2) whatever supply-side effects (if any) the tax cuts have. and 3) no effect on the output gap, because the Fed, which reasonably thinks that the economy is already near potential, will offset the effects of any expansionary fiscal policy (the same can't be said for contractionary fiscal policy, shut up Market Monetarists).

So, when Rubio accuses Trump of having numbers that don't add up, he should really include himself in the same boat; balanced budgets do not go together with tax cuts and military buildups. Even George W. Bush knew this, at least he admitted that his plan would erase the surplus, even if Mr. NCLB accused Gore of "fuzzy math." Of course, everyone is now going to argue that the spending cuts that each administration will undertake will outweigh the military spending increases. My response: maybe, but have any recent Republican administrations done that? No? I thought so. Keep in mind that government spending has been more restrained as a percentage of GDP under Obama (and under Clinton) that it was under either Reagan or W.
What about the supply-side effects of tax cuts? Well, we do have one pretty good experiment of this from 2003, when Bush passed his tax cuts and, well, I'll let the subsequent lack of employment growth speak for itself:
Now, before everyone freaks out, I know I didn't adjust for demographics here, but I think it's fair to say (based on my own analysis linked above) that the demographic adjustment for Obama would be larger than for Bush, so I'm really being kinder to the Bush tax cuts that I should be. With that aside, it seems pretty clear that the 2003 tax cut did pretty much nothing in the way of speeding up the recovery, so what should make anyone think that more of the same thing will be all that different?

When it comes to monetary offset, as I wrote here, fiscal policy only has demand-side effects to the extend that the central bank doesn't act in the face of fiscal shocks. So, in the event of a massive fiscal expansion (assuming the candidates can't achieve the desired balanced budgets by gutting the government), we should simply expect the Fed to raise interest rates faster, which will mean that the only effect that fiscal policy will have is the supply-side one, which is probably minimal.

TL;DR: Republican fiscal plans = deficits + not much else

### Demographically Adjusting Working Age Employment

I've mentioned in the past that my preferred indicator of economic slack is the employment to working age population rate (or, equivalently, the employment rate of people between the age of 15 and 64). This measure is a lot better than the employment to population ratio for obvious reasons: it takes aging into account, which serves to explain the lack of employment growth since 2008; most of the decline in the employment to population ratio since the Great Recession is secular and solely happened because of older people retiring.

The employment to working age population ratio is not without its own problems though. Perhaps the biggest of these is the fact that it fails to take into account women entering the labor force during most of the twentieth century. Because of this, the employment to working age population ratio is skewed downward between 1970 and 1990 and skewed upward in the 1990's (because women entering the labor force enables some men to leave it).

In order to solve the gender problem, I decided to try to remove the skew created by women entering and men leaving the labor force. First, I took the male employment to working age population ratio and postulated a linear downward trend. I then determined the cyclical gap in male employment and assumed that women would experience the same cyclical underemployment as men. From this, I could determine 'equilibrium' female employment and determine a trend.

I postulated that the trend for female employment would be quadratic -- it would increase quickly at the beginning of the time series and then level out (this is technically more logarithmic, but the logarithmic function had a terrible fit). This matched pretty well with the data, so I now had a trend value for female employment.

It was now possible to determine demographically adjusted female employment by taking the actual employment rate and adding the gap between the 'full employment' rate (which I assumed to be about 80%, the male employment rate in 1990) and the trend employment rate. The same process could be done to the male employment rate and the linear downward trend.

Now, with the demographically adjusted female and male employment rates, I could determine the full demographically adjusted rate. Given that
$$\frac{E_m}{WAP_m}\frac{WAP_m}{WAP} + \frac{E_f}{WAP_f}\frac{WAP_f}{WAP} = \frac{E_t}{WAP}$$
where $E_{gender}$ is [gender] employment and $WAP_{gender}$ is [gender] working age population, I could simply multiply each gender's adjusted employment rate by their percentage of the total working age population.

Here is the demographically adjusted employment rate:
And here is the non-demographically adjusted measure:

## 10 March 2016

### Japan is Not THAT Enigmatic

Today Noah Smith wrote a piece in Bloomberg View that discussed the apparent failure of mainstream economics to explain the Japanese experience of the last twenty years. Naturally, as a firm proponent of mainstream macro, I am skeptical of Noah's skepticism, so I thought I would try to see if mainstream macro does indeed fail to explain Japan.

I don't have any problems with Noah's first criticism; falling bond yields despite large deficits is confusing, but is not my forte, so I'll move on.

Noah moves on to criticize the New Keynesian Phillips Curve. This is where the issues start. First, here is what Noah has to say on the subject:
Another theory that runs into big trouble in Japan is the New Keynesian Phillips Curve. This curve postulates a relationship between inflation and the output gap -- when everyone has a job, competition for workers is supposed to push up wages and prices, this increasing inflation.
While, on the surface, there isn't much wrong here, the problem becomes apparent when you actually look at the New Keynesian Phillips Curve:
$$\pi_t = \beta E_t \pi_{t+1} + \kappa x_t$$
where $\pi_t$ is inflation and $x_t$ is the output gap. As you can see, and Noah fails to mention, expected inflation joins the output gap on the right hand side of the equation. So, when Noah cites the lack of inflation since Abenomics, I worry that he is ignoring what a proper New Keynesian analysis would suggest: the modest rise in inflation is consistent with a much tighter labor market because inflation expectations remain anemic.
If you solve the NKPC forward, you'll notice that current inflation depends on the discounted sum of expected output gaps. In this sense, a really pure New Keynesian analysis would suggest that output isn't expected to remain above full employment for all that long in Japan, hence the lack of inflation.

Noah then goes on to argue that, despite the large increase in the money supply since 2010, inflation has remained low; seemingly damning for mainstream theory:
[T]he theory of money demand ... also runs into big problems in the Land of the Rising Sun. According to this idea, increases in the money supply are supposed to push up inflation. But Japan's M2 money supply has risen steadily, despite falling population, and inflation hasn't kept up.
There are two possible criticisms that I think mainstream macro would offer against Noah in this case. The most obvious is that Japan has been in a liquidity trap since the late 1990's, so changes in the money supply should have no apparent effect. Or, more specifically, if you happen to like Cash In Advance models, the CIA constraint is not binding because the nominal interest rate is at or near zero, so money demand is indeterminate. If you are more of a Money in the Utility Function/Transactions Costs/Shopping Time kind of person, you would argue that low nominal interest rates imply extremely high money demand and even modest reductions in the nominal interest rate (when it is at or near zero) require massive increases in real money demand, thus pretty much negating the effect of large increases in the nominal money supply at the zero lower bound.

The second criticism I have is what I would call pseudo-Neo-Fisherian. Since Japan is in a liquidity trap, looking at the money supply is irrelevant, and the only way to get sustainably higher inflation is to increase the nominal interest rate. If we, for a moment ignore the liquidity trap, I will attempt to offer a bit of an explanation:

Suppose money demand in Japan follows the following equation:
$$(1)\:m_t - p_t = y - \sigma i_t$$
where $m_t$ is the log money supply, $p_t$ is the log of the price level, $y$ is real GDP (assumed constant for simplicity) , and $i_t = p_{t+1}-p_t$ is the nominal interest rate.

It is useful to think of this model as if the level of real balances determines the nominal interest rate, which in turn determines the future inflation rate. Or, if we switch to growth rates, $1$ can be rewritten as
$$(2)\:\Delta m_t - \pi_t = -\sigma\Delta i_t$$
or
$$(2a)\:\Delta m_t - \pi_t = -\sigma (\pi_{t+1} - \pi_t)$$

Notice that the steady state inflation rate, and consequently steady state nominal interest rate, is equal to the steady state money supply growth rate. So, if Japan weren't in a liquidity trap, a permanent increase in the growth rate of the money supply would result in a permanent increase in the inflation rate.

The liquidity trap complicates this, because (if we continue with the CIA description) the money supply does not determine price level. This is where my model, which, up to this point, has basically been Neo-Fisherian, becomes 'pseudo-Neo-Fisherian.' I will argue that, at the zero lower bound, the total stock of government liabilities (i.e., including government bonds) determines inflation, which is in line with David Andolfatto's analysis from a few years back. I won't bother explaining the model since this post is already too long, but basically, at the zero lower bound, open market operations don't work, so the inflation rate is determined by the growth rate of the total stock of government liabilities. In this model, the way to painlessly escape a liquidity trap (i.e., escape the liquidity trap without reducing the money supply) is to engage in a massive fiscal expansion that is not expected to be reversed, basically credibly plan to be fiscally, rather than monetarily, irresponsible.

I have no problem with Noah's criticism of Verdoorn's law or secular stagnation, neither of which I am convinced by and neither of which I think genuinely represent mainstream macro, even if some mainstream macroeconomists have proposed/supported them.

### A Defense of Neo-Wicksellian Analysis

Typical Neo-Wicksellian analysis takes the natural interest rate as given and suggests that setting the nominal interest rate below the given natural rate will result in a boom while doing the opposite will result in a recession. There is nothing fundamentally wrong with the analysis, except that it seems to suggest that lower nominal interest rates always imply looser monetary policy.

This is not a flaw of the Neo-Wicksellian framework, but rather the assumption of a natural rate that is exogenous to central banks. There are, in reality, two ways that a central bank can ease monetary policy in a Neo-Wicksellian model: it lower the nominal interest rate and it can raise the natural rate. Monetary expansions that result in higher interest rates do not confound Neo-Wicksellian analysis, they simply confound the notion of an exogenous natural rate.

If, for instance, a central bank credibly adopts a higher inflation target, it is only natural that output, inflation, and the nominal interest rate should rise almost immediately. This is because the credible increase in the inflation target resulted in a corresponding increase in inflation expectations, which raises the natural rate. So long at the central bank fails to fully offset the increase in the natural rate that it caused, there will be a boom in output as well as an increase in inflation.

Neo-Fisherism is also Neo-Wicksellian, it simply abstracts from the credible increase in inflation expectations and assumes that they occur whenever the nominal interest rate is increased. In a Neo-Fisherian world, the natural rate moves with the nominal interest rate instead of being given exogenously.

In sum, a proper Neo-Wicksellian framework suggests two policy tools are available a central bank; the nominal interest rate and the Wicksellian natural rate. A central bank may very well increase the natural rate in normal times (i.e., times when there is not a liqudity trap) instead of reducing the nominal interest rate, which explains how a rising nominal interest rate might be consistent with loose monetary policy and how a low rate might mean tight policy.

## 09 March 2016

### Market Monetarism

My list of questions and/or criticisms that I don't think have been properly addressed for/of Market Monetarists has increased to such a degree that I think the best way to deal with everything is just to write one blog post and send it to a Market Monetarist (probably Nick Rowe, who seems to be the most reasonable one, from my experience, and probably the only one who will bother to respond).

Natural Rate Hysteresis:

The Wicksellian natural rate is completely forward looking in sticky price NK models (with either Calvo or Rotemberg pricing). Does switching to something like Taylor Contracts for the price level or nominal wage result in a backward looking natural rate? If not, why do you think that there is natural rate hysteresis (theoretical explanation, please. I don't care if you think you see it in the data, because the natural rate is unobservable).

Falsification:

What, if anything, would you have to observe in the data to determine that liquidity traps genuinely exist? Apparently low inflation despite high monetary base growth (i.e., money demand at unprecedented levels) since 2009 doesn't convince you, so what would?

Concrete Steppes:

Since central banks don't commit to monetary policy in the very long run (or, if they do, the commitment doesn't suggest anything quantitative), is it not reasonable to conclude that deliberately communicated actions by a central bank (forward guidance can be included here) are necessary for actual changes in monetary policy?

NGDP Targeting:

In sticky price models, NGDPLT does not prevent the zero lower bound from binding when there are large persistent negative shocks to the real natural rate. Does wage stickiness remove this problem? If so, what evidence is there for wage stickiness (I mean, there has to be a reason why the profession switched to sticky prices and I'm fairly certain that reason is usually stated as 'there's no evidence for a high degree of wage stickiness').

Liquidity Traps:

Imagine we're in a multi-period version of Krugman (1998) in which the CIA constraint is not binding and will not bind for the next five periods. Do you agree that any current OMO will be completely useless? Of course, the central bank can simply increase the money supply five periods in the future (when it once again has control over the price level) and recursively set the nominal interest rate to be greater than zero, so there is a way out when the liquidity trap is finite. But, in the real world, the length of the liquidity trap is not set in stone. What if this is the case, so the central bank has no idea how far in the future it must induce expectations of the money supply to be higher in order to escape the liquidity trap. In this case, would you agree that the only reliable way to escape the liquidity trap is to decrease the current money supply until the CIA constraint binds?

Fiscal Policy:

I'm assuming you would agree that, ceterus paribus, fiscal stimulus raises the real natural rate. Given this, what reason do you have to oppose fiscal stimulus at the zero lower bound -- I know you don't think monetary policy is impotent in this case, but, given the possibility that us Keynesian's are right, what's wrong with a higher natural rate (and, correspondingly, a higher nominal interest rate), especially since we all agree that monetary policy is effective off of the zero lower bound. Similarly, why support austerity if it lowers the natural real rate; what's wrong with making the job of a central bank easier?

Money Demand:

Does your preferred money demand function more closely resemble MIUF (in which the nominal interest rate can never actually hit zero, lest money demand be infinite) or CIA (in which a zero nominal interest rate implies indeterminate money demand, which means that OMO's are completely useless as long at the nominal interest rate equals zero)?

## 07 March 2016

### News Media

Both Paul Krugman and Simon Wren-Lewis have a bit of a penchant for criticizing the media. In Wren-Lewis' case, 'mediamacro' -- decidedly non-mainstream economic 'theory' that seems to favor the Conservative Party -- is perpetuated by the British media and, according to Krugman, the American media is willing to give completely nonsense ideas (specifically nonsense ideas about economics and global warming) equally gratifying coverage to the correct (in the case of global warming) or the mainstream (in the case of economics) position for the sake of avoiding 'bias.'

These criticisms really call into question what the point of the media is -- it is the job of the media to be an advocate of 'facts' an/or mainstream academic positions, or should the media continue as it allegedly has been; acting as if every political debate has equally valid positions from each corner of the political spectrum? Of course, I think the world would certainly be a much better place if the media decided, e.g., to take a hard stance on global warming and to debunk any dissidents, or if the media decided that they wouldn't try to shout over Ph. D. economists, but I'm not sure if this is really the proper role of news organizations.

The media surely has an obligation to the truth, but this seems to be in conflict in the case of politics. It would be an error of omission to simply refuse to report on statements that people make, even if they are completely inconsistent with facts or consensus academic opinions. Conversely, simply allowing Donald Trump to talk on television unfettered would result in an inordinately large amount of people hearing various lies, generalizations, and complete failures to understand economics. Of course, it would perhaps be ideal for the media to show Donald Trump on television, but then promptly explain that he is wrong, and exactly why this is the case.

The question now becomes whether or not such a policy is even possible. If, as Krugman suggests (and, from recent experience, I am inclined to agree), the parties in the US are not symmetric -- with the GOP consistently peddling falsehood and bunk economics (although Bernie Sanders seems to be trying really hard to add the latter to the Democratic party as well) -- then the portion of the population on the side of the worse offenders would certainly find the fact that the media consistently points out their wrongness deeply disturbing and, considering these people are already convinced that the only non-biased media source is Fox News (the irony is hard to overcome, I know).

Alternatively, it may simply not be the role of the media to promote facts and consensus views. If this is truly not the case, then no one has any obligation to dismantle 'mediamacro' and, in the interest of representing every opinion, the media should provide coverage to climate change deniers -- no matter how crazy their views are. Honestly, I can see no reason why this should be the case, but it does seem more broadly consistent with what would be popular and what the media actually does (come to think of it, this is probably not a coincidence at all).

## 06 March 2016

### History Dependence in the Natural Rate

One of the pet claims of Market Monetarists is that the Federal Reserve's failure to cut the nominal interest rate quickly enough in 2008 caused the natural interest rate to become negative in 2009 -- basically that the natural rate is history dependent. This claim does not immediately seem suspect; after all, if you cause a recession in the current period by setting the nominal interest rate above the natural rate, then it only makes sense that simply reversing that decision in the next period will not close the output gap.

The problem with this is that it is ignorant of what the Wicksellian natural rate actually is: expected inflation plus the real natural rate (which is completely independent of monetary policy, unless you believe in hysteresis, which, as far as I know, no Market Monetarists do). To argue that setting the interest rate above the natural rate in the current period results in a reduction in the natural rate in the next period is to argue that the current nominal interest rate affects the inflation rate expected to prevail two periods from now.

So, either agents are backward looking (which no market monetarists, who generally like the EMH, believe to my knowledge) or monetary policy affects potential output. Also take note that a lower natural real rate is either consistent with higher current potential output (which would mean that current tight money raises potential output in the next period) or lower future output (which would mean that current tight money causes potential output two periods in the future to fall).

Given the forward looking nature of the natural rate, it should be clear that the only way that a central bank can influence the natural rate is by changing the expected path of future interest rates relative to the expected path of future real natural interest rates (I guess Woodford is smarter than some Market Monetarists might like to admit).

Then what actually happened in 2008? Evidently the Fed allowed expectations of future interest rates to exceed expectations of future natural rates, something that they could not have prevented by cutting the nominal interest rate further in 2008 and something that could not have been prevented without a large increase in inflation expectations -- which could not have happened under a 2% inflation targeting regime or an NGDPLT regime that would be broadly consistent with 2% inflation.

Note: before you take issue with my last statement, I simulated a simple New Keynesian model in which the real natural rate goes negative for five periods under two different regimes. In one, NGDP is banned from being off-target and, in the other, the central bank sets the nominal interest rate equal to the (nominal) natural rate. In both cases, the only thing that prevented the zero lower bound from binding was an increase in the inflation target and/or the equilibrium growth rate of NGDP; NGDPLT on its own can't circumvent the zero lower bound problem.

If you want proof, I have all the pictures here (it may not be immediately clear what each one means, be careful not to misinterpret).

## 01 March 2016

### A Simple Model With Consumer Durables

How negative do real interest rates have to go before storing consumer goods (e.g. food) becomes profitable?
This question inspired me to try to come up with a model with durable consumer goods (i.e., goods that aren't immediately consumed when purchased, but instead last multiple periods) and sticky prices. I won't bother with adding sticky prices (or monopolistic firms) until I have a basic model sketched out, so here goes:

There is a representative agent which derives utility from their consumption of non-durable goods, their stock of durable goods, and leisure. The utility function is
$$(1)\: U = \sum^\infty_{t=0}\beta^t u(c^d_t,c^p_t,l_t)$$
where $\beta$ is the discount factor, $c^d_t$ is the current stock of durable goods, $c^p_t$ is the agent's current consumption of non-durable (perishable) goods, and $l_t$ is leisure. The agent uses income from working, holding government bonds, and profit from the representative firm to pay for perishable consumption, the increase in durable goods that it owns (which depreciates at rate $\delta$), new government bonds, and lump sum taxes. The budget constraint is:
$$(2)\: c^p_t + c^d_t - (1-\delta)c^d_{t-1} + B_t + T_t = R_{t-1}B_{t-1} + w_t (1-l_t) + \pi_t$$
The agent maximizes $1$ w.r.t. $2$, which yields the following first order conditions:
$$(3)\: \beta^t u_2(c^d_t,c^p_t,l_t) - \lambda_t = 0$$
$$(4)\: \beta^t u_3(c^d_t,c^p_t,l_t) + \lambda_t w_t = 0$$
$$(5)\: \beta^t u_1(c^d_t,c^p_t,l_t) -\lambda_t + E_t \lambda_{t+1} (1-\delta) = 0$$
$$(6)\: -\lambda_t + R_t E_t \lambda_{t+1} = 0$$
where $\lambda_t$ is the Lagrange multiplier on the maximization problem.

These can all be simplified to:
$$(7)\: u_2(c^d_t,c^p_t,l_t) = \beta E_t u_2(c^d_{t+1},c^p_{t+1},l_{t+1})R_t$$
$$(8)\: w_t = -\frac{u_3(c^d_t,c^p_t,l_t)}{u_2(c^d_t,c^p_t,l_t)}$$
$$(9)\: u_1(c^d_t,c^p_t,l_t) = u_2(c^d_t,c^p_t,l_t)\left(1 - \frac{1-\delta}{R_t}\right)$$

Given that the government budget constraint is
$$(10)\: B_t + T_t = R_{t-1} + B_{t-1}$$
it is possible to rewrite the agent's budget constraint as:
$$(11)\: c^p_t + c^d_t - (1-\delta)c^d_{t-1} = w_t (1 - l_t) + \pi_t$$

There is a representative firm that maximizes profit, $\pi_t = y_t - w_t(1-l_t)$, where $y_t$ is production and $w_t$ is the real wage, subject to the production function
$$(12)\: y_t = f(1-l_t)$$
which gives the following first order condition:
$$(13)\: w_t = f'(1-l_t)$$
Given that $\pi_t + w_t(1-l_t) = y_t$, it is possible to rewrite $11$ as
$$(14)\: y_t = c^p_t + c^d_t - (1-\delta)c^d_{t-1}$$

Now, we have the full equilibrium of the model:
$$(1)\: u_2(c^d_t,c^p_t,l_t) = \beta E_t u_2(c^d_{t+1},c^p_{t+1},l_{t+1})R_t$$
$$(2)\: w_t = -\frac{u_3(c^d_t,c^p_t,l_t)}{u_2(c^d_t,c^p_t,l_t)}$$
$$(3)\: u_1(c^d_t,c^p_t,l_t) = u_2(c^d_t,c^p_t,l_t)\left(1 - \frac{1-\delta}{R_t}\right)$$
$$(4)\: y_t = f(1-l_t)$$
$$(5)\: w_t = f'(1-l_t)$$
$$(6)\: y_t = c^p_t + c^d_t - (1-\delta)c^d_{t-1}$$

I'll probably do more analysis tomorrow, but what immediately strikes me as interesting (and relevant to Nick's question) is that consumer durables are basically the same as money in MIUF models, if the real return on government bonds falls below $-\delta$, then the demand for consumer durables will skyrocket -- basically representing a lower bound on the real interest rate in addition to the nominal one.

The only question should then be what the average depreciation rate of durable consumer goods is; if it's not too high, I may have just found an undeniable (real) constraint on monetary policy -- if the natural rate of interest should ever fall below $-\delta$, then the central bank genuinely can't do anything about it; only fiscal policy can (by raising the natural rate).