## 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.