Japan in NOT a Market Monetarist Success Story

Annoyingly (starting a post with that word is strangely entertaining), Scott Sumner has once again claimed that the increase in Japanese inflation that we have seen over the last few years provides vindication for Market Monetarism. Perhaps most infuriating was his magical ability to know that the thing that has caused the increase in inflation (which is really very modest, which I will address shortly) is the Bank of Japan's monetary stimulus program: "and monetary stimulus did get [Japan] out of deflation."

The real question here is what would actually enable Sumner to reasonably make this claim (news flash, it is not the evidence, which in this case agrees with both the Keynesian and Market Monetarist view). This is where I once again delve into philosophy of science, but don't worry, this is very general. As economics is quasi-experimental in that policy experiments can be conducted, but the system can never be closed, a good method for testing a hypothesis is something along the lines of what Jason Smith has suggested: "any system can become an effective closed system if your instrumental variables move faster (move a greater magnitude in a shorter period of time) than your unobserved variables."

That is, all we need to do is have Japan engage in a massive monetary stimulus in order to see if monetary stimulus works in liquidity trap conditions. Oh, wait... Yes, as it turns out, Japan has been doing massive monetary stimulus, so I guess we have our ideal (if not perfect) experiment. Evidently the massive expansion of the monetary base in Japan has led to inflation. Market Monetarists win!

No. It's extremely important to note that the lukewarm response of inflation to the monetary stimulus is completely consistent with a Keynesian analysis in which the improved labor market has increased inflation via the Phillips curve and that the inflation has little or nothing to do with the monetary stimulus. How do we know which one of these models is more accurate in this case? We can easily use one of Scott Sumner's pet models and see if it squares with his predictions -- then we could have a slightly more testable prediction than 'increasing monetary base growth leads to increased inflation' which doesn't actually specify how structural the supposed relationship is (and allows Scott to get away with his terrible declaration of victory).

It must first be understood that Scott can claim his prediction is correct even though the increase in the Japanese monetary base has been much quicker than the increase in nominal GDP, which is evidence in and of itself against monetary policy effectiveness. However, because Sumner's prediction was simply that the monetary stimulus would cause an increase in inflation (never mind the magnitude), the apparent failure of Market Monetarism to explain Japan can be ignored.

Fortunately for those of us who aren't trying to be dishonest (I'm growing tired of giving people the benefit of the doubt), Sumner has given us a model. Namely, he has frequently argued that velocity is a positive function of the nominal interest rate. With this, we can look at the nominal interest rate in Japan (noting that it has been relatively constant since the Bank of Japan began monetary easing) and the velocity of the monetary base in Japan (noting that it has fallen precipitously since Abenomics began) and see if Sumner's model, which predicts relatively constant velocity at constant interest rates, fits with reality.

Evidently it doesn't. Now, Scott will likely defend himself by saying he doesn't pretend to have an explanation for why real money demand would have risen so sharply in Japan since the nominal money supply began increasing sharply, but the fact remains that the nominal and real monetary base should not track each other so closely if market monetarism were indeed correct. In fact, Sumner has repeatedly said that expectations of more NGDP growth (in this case equivalent to more inflation) would make demand for the monetary base fall. I agree with this theory, but this is evidently not what has happened in Japan -- the Japanese situation is simply incongruous with his position.

Of course, Scott only predicted that inflation and monetary base growth would be positively correlated, not that the degree of correlation would be somewhat constant. Any positive inflation response is thus a positive result for Market Monetarism!

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.

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:

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.

Using Demographics to Estimate Potential Output in Japan

I don't stray into empirical matters very frequently because I'm really not all that adept at them, but I thought it would be interesting to feed Japan's working age population growth into a basic Solow growth model.

Skip the following if you already understand the Solow model:
In the Solow model, it is assumed that output is produced using three inputs: capital, labor, and productivity. The production function is Cobb-Douglas for capital and labor (with constant returns to scale), but is multiplied by what's called the Total Factor of Productivity, or TFP, which represents technological progress. Defining output as $Y_t$, capital as $K_t$, labor as $N_t$, and TFP as $A_t$, the production function can be written as
$$ (1)\: Y_t = A_t K_t^\alpha N_t^{1-\alpha}$$
where $\alpha$ is capital's share in production and $1-\alpha$ is labor's share in production. Workers devote a constant share $c$ of production to consumption ($C_t$), so $ C_t = c Y_t $. Non-consumed income is used to increase the capital stock, which exogenously depreciates at $\delta$. Defining $s$, the share of income put toward investment in each period as $1-c$ allows us to write the capital accumulation equation as such:
$$ (2)\: K_{t+1} = (1 - \delta) K_t + s Y_t $$
The labor force is assumed to grow at constant rate $n$, so next period's labor forced is defined as
$$ (3)\: L_{t+1} = L_t (1 + n) $$
TFP is assumed to grow at constant rate $g$, so TFP evolves according to
$$ (4)\: A_{t+1} = A_t (1 + g) $$
Given $L_0$, $A_0$, and $K_0$, the economy will eventually converge to a balanced growth path in which all variables grow at the same rate as productivity: $g$. If one of the parameters ($\alpha$, $\delta$, $s$, $n$, or $g$) changes, then the economy will take time to adjust to new equilibrium levels.

Figure 1

As you can see in figure one, Japan began to see a secular decline in it's working age population growth rate in about 1990. This decline coincides roughly with Japan's lost decade -- the period between the mid 90s and the early 2000s characterized by low growth and high unemployment. Given the low working age population growth, it may be possible to explain some of this lack of economic activity with the Solow model. Assuming constant technological growth of 1%, a capital depreciation rate of 2.5%, a capital share of 33%, and a savings rate of 10% (I have no clue how close to accurate this calibration is, if someone wanted to find the average values of each variable over the last 20 years or so in Japan, I'll update them, but right now I can't be bothered to find the information myself), I was able to come up with an estimate of 'potential' output in Japan -- i.e. what Japanese output would be absent any shocks to productivity, government spending, or monetary policy (or natural disasters, which explain the 2011 output contraction).

Here are a couple of graphs relating actual output to demographically-adjusted potential output:

Figure 2

 

 

Figure 3

Figure 2 plots my estimate of potential output against actual output, assuming potential output was 2% above actual output in 1995 and figure 1 plots the output gap, or the percentage gap between actual and potential output. An interesting note here is that potential output, absent any demographic or technological changes, is predicted converge to a decay rate of roughly 0.5% per year and potential output is currently growth at about zero percent per year, meaning that, not only is potential growth for the next couple of years zero, the economy should be expected to shrink without being in a recession in the future. That is, unless the workforce stops decaying so quickly.

Another interesting observation is that Japan's lost decade seems to closely resemble the experience that the United States has had since the Great Recession. This is entirely unsurprising given that both periods are characterized by monetary policy ineffectiveness (the zero lower bound), but the post 2007 experience in Japan could possibly be used to predict the outcome of another large recession in the US absent monetary policy normalization. Perhaps more on this later.