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:

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.

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)?

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).

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).

A Simple Model With Consumer Durables

Nick Rowe on twitter:

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).

Fiscal Policy Does Not Affect Aggregate Demand

This is a follow up to my last post; here I am going to go more in depth into why fiscal stimulus never really impacts aggregate demand in any DSGE.

Start with the simple consumption euler equation that everyone should be familiar with:

$$(1)\:c_t^{-\sigma} = \beta E_t c_{t+1}^{-\sigma} \left(\frac{1 + i_t}{1 + E_t \pi_{t+1}}\right)$$

where $c_t$ is consumption, $\beta$ is the representative agent's discount factor, $i_t$ is the nominal interest rate, and $\pi_t$ is the rate of inflation. Assuming there is no capital accumulation, this equation can be simply edited to include real GDP and government spending:

$$(2)\:(y_t - g_t)^{-\sigma} = \beta E_t (y_{t+1} - g_{t+1})^{-\sigma} \left(\frac{1 + i_t}{1 + E_t \pi_{t+1}}\right)$$

This can now be written in log-linear form, so that all variables are expressed as a percentage deviation from their steady states (except for the various interest rates):

$$(3)\:\hat{y}_t = E_t \hat{y}_{t+1} + \hat{g}_t - E_t\hat{g}_{t+1} - \frac{1}{\sigma}(i_t - E_t \pi_{t+1} - \rho)$$

where $\rho$ is the discount rate, which is equal to $\frac{1-\beta}{\beta}$. Keep in mind that $\hat{g}_t$ is actually the deviation of government spending as a percentage of GDP from trend, but this shouldn't have much of an impact on the analysis.

If we define the 'natural rate of interest' as the real rate of interest at which the output gap remains constant, only a small amount of algebra is required to solve for it:

$$(4)\:r^n_t = \rho - \sigma(E_t\hat{g}_{t+1} - \hat{g}_t)$$

It is clear from this that fiscal stimulus, that is increases in $\hat{g}_t$ absent changes in $E_t\hat{g}_{t+1}$, causes the natural rate of interest to increase. Why is this important? In most cases, it isn't; fiscal stimulus will just have the effect it normally does in a frictionless model (that is, generally speaking, have a multiplier on output somewhere between zero and one depending on the calibration of that model) and the central bank will simply raise the real interest rate so that the output gap remains equal to zero.

This is exactly what all the market monetarists are talking about when they mention monetary offset; any demand-side effect that fiscal stimulus might have is simply the result of central bank inaction in the face of a higher natural rate. Say, for instance, that the central bank set the nominal interest rate according to the following rule:

$$(5)\:i_t = max(0,r^n_t + E_t \pi_{t+1})$$

Now, suppose the fiscal authority does a fiscal stimulus, which raises $r^n_t$. Assuming the zero lower bound is not binding, the central bank will simply raise the nominal interest rate one for one with the increase in the natural rate caused by the fiscal stimulus.

The only reason a New Keynesian model ever exhibits a fiscal multiplier greater than one is that the zero lower bound is at some point binding. In this case, the fiscal authority can lower the value of $r_t - r^n_t$ without central bank intervention ($r_t$ is the real rate of interest). Basically, fiscal stimulus appears effective because of central bank inaction.

In this sense, the actual act of fiscal stimulus never has demand-side effects; it can only influence the natural rate of interest, which is only helpful to the extend that the zero lower bound is binding. Because of this, we should really stop thinking of fiscal stimulus as a way of manipulating aggregate demand; it's really only helpful to the extent that is has real effects -- if anyone says otherwise, then they are unduly influenced by IS-LM.

How Easy is it to Raise LRAS?

There's recently been quite a bit of talk about greatly increasing the growth rate of GDP in the US over the next decade or so. The only way big aggregate demand stimuli could achieve this goal is if 1) output is currently far below potential in the US or 2) demand side stimulus can raise the long run level of output.

The first option is evidently not the case, given the fact that the labor market is reasonably tight -- the employment rate for Americans between the age of 15 and 64 has recovered most of what it lost in 2008, so output is clearly close to where it would be at full employment. By basically any reasonable account, output is pretty close to potential, so not much in the way of aggregate demand stimulus would have any effect other than increasing inflation. There are no credible models that I have ever seen that suggest that aggregate demand has any effect over the long run level of output, so it's almost fair to simply reject the hysteresis hypothesis simply based on its lack of theoretical reasoning. If this isn't enough, simply taking it to its logical conclusion should reveal some of the absurdity. If central banks, by increasing aggregate demand, could increase potential GDP, then they essentially have the power to decide the equilibrium level of employment, irrespective of demographics. Alternatively, they could be fueling innovation by printing loads of money and causing TFP growth to increase. Both options strike me as completely absurd; personally I see LRAS as completely deterministic to the Federal Reserve.

I will not, however, completely discount the role of fiscal policy. Certainly the Federal Government has the capability to engage in policies that have real effects. For instance, the government could permanently increase government spending as a percentage of GDP and induce everyone to work more by making them feel poorer. Also, the government could invest in a bunch of infrastructure, which could be treated as 'government capital' in all our Cobb-Douglas production functions and would, as such, be stimulative. Basically, the government could very well be boosting potential output, just not with anything that should be labeled 'demand' stimulus. In fact, this is probably true about any fiscal expansion that is ever undertaken -- we should only ever talk about the real effects of fiscal stimulus because everything else is the product of monetary-fiscal interaction. For example, any fiscal expansion will raise the 'natural rate of interest' in a New Keynesian model and the only reason the 'fiscal multiplier' will be any higher than that of a similarly calibrated RBC model is that the central bank refuses to raise the nominal interest rate one for one with the increase in the natural rate. In this sense, fiscal stimulus can almost have demand-side effects at the zero lower bound, but what is really happening is that the central bank fails to tighten monetary policy in the event of stimulus.

Basically, the only way for the government to increase potential output is by taking advantage of the real effects of fiscal policy -- people should stop preoccupying themselves with aggregate demand.

Assessing the Effect of Austerity in the UK

Whether or not austerity has been successful in the UK is perhaps the most natural test of Market Monetarism. The UK, after all, has an independent central bank and there is no question as to whether or not it actually engaged in austerity (the same case can not be made for the United States, in my opinion). 

It has previously been noted that, even though austerity evidently had a negative effect on real GDP in the UK, what really happened is that productivity growth just happened to be zero while Chancellor Osborne was having a fit with the exchequer. I think that the data clearly disagree with the position; as you can see both the employment rate and real GDP lagged during the period of austerity, which I will argue was only pursued fervently in 2010 and 2011, before it was significantly weakened and the economy proceeded to improve.

First, look at employment and real GDP between Q2 2010 (when the first austerity budget was suggested by the new coalition) and 2011 (the last year that the government actually maintained its commitment to austerity). It's clear that both real GDP and employment suffered during this period -- basically disproving the hypothesis that slow productivity growth and austerity were coincidental. 

Of course, the government never vocally backed down on austerity, so why am I limiting my analysis to 2010 and 2011? Well, for that you need to look at the actual and the projected deficits over the course of the Cameron government:

As you can see, the actual deficit was only less than was predicted by the government during 2010 and 2011. After this, the deficit clearly begins exceeding the 2011 vintage projection; that is the government raised the deficit above what they were initially intending. It was only after this point that the economy and employment began to recover, so evidently fiscal policy was loosened in 2012 and this explains the apparent recovery that happened afterward.

The data seem to corroborate the Keynesian view a lot more than the Market Monetarist one; fiscal tightening did cause both output and employment to fall relative to trend, and the economy only began to recover with fiscal easing.

Don't Be Fooled By Annual Inflation

If you look at Fred right now, you'll see that the CPI is currently 1.3% higher than it was a year ago. This figure can mislead people into think that inflation is a lot closer to target than it really is. To understand this, you need to look at the actual graph for the CPI over the last 12 months or so.

As you can see, the current CPI is really barely any higher than it was last month and is a long way away from the level of CPI inflation consistent with the Fed's 2% annual PCE inflation target. In fact, the CPI is just under 0.03% higher than it was a month ago.

If CPI were to grow at 2% each year, this would require 0.16% inflation each month, which is a whole lot higher than the current 0.03%. Basically, even though the current price level is 1.3% higher than it was a year ago, the price level has not been growing even that fast for quite a while. If you want to see whether or not inflation will be on target, you should look at the compounded annual rate of change, and not percentage change from a year ago.

Update:

The new PCE numbers are in and, guess what, inflation is indeed chronically below target; at least the y/y rate is closer to the compounded annual rate of change, though.

Potential GDP is Not Linear

Recently I've seen a few people defending the Friedman analysis of Sanders' economic plan on the grounds that 5.3% growth over a decade would be consistent with closing the output gap. They typically estimate the 'output gap' by comparing GDP to the linear trend implied by the post-WWII time series (excluding data after 2008).

This is ridiculous. I'm tempted to just stop writing here because of how obvious I think this should be, but evidently a lot of people think that potential GDP is linear. The primary problem with this  approach is that it completely ignores demographic factors. If, for instance, you decided that real potential GDP (not per capita) followed a linear trend, then you'd be suggesting that TFP automatically grows faster whenever population growth is low. Naturally, this doesn't make any sense whatsoever, so most people who want to estimate linear trends for RGDP usually go for real GDP per capita.

This has its own problems, however. If real potential GDP per capita grows at a constant linear rate, then TFP growth increases when the working age population shrinks relative to the total population (when the dependency ratio goes up) and vice versa. This also makes no sense whatsoever; to suggest that TFP grows more quickly when people have lots of children or when a bunch of people are reaching retirement age is ridiculous. It's obvious that real GDP per capita should be a negative function of the dependency ratio.

This leaves one option for a demographic-adjusted estimate of potential output: real GDP per working age person.

The output gap that can be extrapolated from this is a lot more sane than the predictions of some of Sanders' defenders -- it's about 9%, but I still have a problem with inferring linear trends from demographically adjusted potential output.

See, my approach so far basically assumes constant TFP growth (which is a whole lot less stupid than TFP growth that changes with population growth), but I don't even think this is really that fair of an assumption. To argue that technological progress always occurs at the same rate and with the same fervor doesn't make any sense.

That being said, I think the best (only) way to measure the output gap is to use some labor market indicator. For some reason, a lot of people seem to hate the unemployment rate for this, so I'll use the employment to working age population ratio:

This suggests that we are pretty close to full employment, but not quite there yet. That's a completely different story from what Sanders supporters (and most people in the GOP) are saying. Granted, I think this approach has its own flaws -- I think it drastically overestimates the output gap in 2000, but it seems to give a pretty good estimate of where the output gap is right now; i.e., somewhat understated in absolute value terms by the unemployment rate, but overstated by the employment to population ratio.

Needless to say, no one should listen to anyone who thinks real potential GDP per capita follows a linear trend.

Update:

Nick Rowe suggested in the comments that I come up with a projection for potential GDP given estimates for the working age population over the next few years. I used the US Census Bureau's estimates for population between 14 and 64 years old and assumed the 14-year-old population will be constant over the next few decades (it's a shortcut, I know, but I can't be bothered to find a better estimate of the future working age population) to get my projections for the working age population. I then took the real GDP to working age population ratio, got the trend growth rate between 1989 and 2007, and extrapolated that to 2026 to get my potential GDP per working age person value.

Then I multiplied the whole thing by the time series for the working age population (including the projected values until 2026) to get potential GDP. Here is my estimate of potential GDP to 2026 compared with the CBO estimate and actual GDP (going up until 2015):

Update #2:

I thought I'd add this comparison between my estimate of potential GDP and what potential GDP would be if it followed the 1990-2007 trend here:

Also I realized I made a couple mistakes when removing the 14-year-olds from the Census Bureau projection. All the graphs on the blog are updated, but not the ones on Twitter, so don't take them from there if you want to use them.

In Which I Do Some Bad Econometrics

I decided I would do a linear regression on the growth rate of real GDP per capita (RGDPPC) with respect to the change in the Civilian Employment to Population ratio (EPOP). I used the period between 1950 Q1 and 2015 Q3 and came up with this result:

Vertical Axis: RGDPPC growth, Horizontal Axis: Change in EPOP

So, a linear regression suggests that the relationship between RGDPPC and EPOP is

$$(1)\:100\Delta\ln{y_t} = 2.458 \Delta e_t + 1.9333$$
where $y_t$ is real GDP per capita and $e_t$ is the Employment to Population ratio.

With this relationship, we can make some interesting predictions. It has recently been popular to argue that the employment to population ratio can and should be raised to its April 2000 high (coincidentally, I was born in April 2000). If this were to occur, it would mean that the Employment to Population ratio would go up by 5.1%, which corresponds to an increase in real GDP per capita of about 14.5%. Or, if the change were to take place over ten years, then real GDP per capita would grow at about 3.2% per year.

Given ~1% annual population growth, this could make the extravagant economic promises by the likes of Bernie Sanders and Jeb Bush seem in reach. After all, all we need do is employ as many people as we were in 2000. Unfortunately, it is not that simple. First of all, there are reasons to believe that some, if not most, of the decline in EPOP over the last 16 years is secular. Namely, the working age population (i.e., population between 15 and 65 years of age) has increased a lot less than total population in the last few years. In fact, the Employment to Working Age Population ratio has recovered pretty well since the Great Recession:

Now, there's definitely still a gap; employment still has room to grow, but now at least, it should be clear that there was a lot of over-employment by the end of the Clinton administration. It appears as if the equilibrium Employment to Working Age Population ratio is closer to 74% than 77%, which means that there are a lot less employment gains to be had than a simple look at the EPOP would suggest.

The other issue with both Senator Sanders' and Governor Bush's plans is that it's unclear how they would actually raise the employment to population ratio. In the case of Sanders, programs like expanded Social Security and free college tuition would probably lower the Employment to Population ratio (since we'll be paying people more to retire and getting an education will be so cheap that students won't need to work, or can leave a job to get a degree). With Governor Bush, there is at least a case to be made that significantly lower taxes might incentivize millions of Americans who were otherwise not going to work to now go out and get a job, but I don't really see it.

Yes, a government can increase employment by reducing the labor tax in a simple neoclassical model, but how much does that really map to determining whether or not someone is even in the labor force. Honestly, the tax rate that someone has to pay may lead to changes in hours worked, but says little as to whether or not they work in the first place; to argue that because the tax rate goes down, all of a sudden people who refused to work at the previous after tax wage will now start searching for jobs seems nonsensical. I can see people increasing their hours if they are all of a sudden paid more for work, but not leaving the labor force altogether because taxes are too high or joining it because they are now low.

On top of that, key to the success of any supply side reform is whether or not the lack of employment is voluntary; if people who are unemployed actually want to be employed, then a tax cut won't change anything relating to their job search, whereas, if the people who are not employed are in that state by choice, then a tax cut might make them reassess (personally, I think the case for this is really weak, but I'm open to it). The key question is, then, was the non-secular part of the decline in the EPOP in 2008 caused voluntary or involuntary. There are those that disagree, but personally I think that the obvious answer is that the decline was involuntary. If this is the case, the degree to which supply side reforms would be beneficial is probably low.

So, by now I've spent most of this post complaining about Governor Bush's promise of 4% growth even though I find the crimes of the Sanders campaign more egregious. For this apparent injustice, I offer the following explanation: the reason Bernie Sanders' proposals would fail to create an employment boom is extremely easy to understand, whereas Bush's plan requires a much more in depth criticism to be understood. Regardless, both 4% growth and 5.3% growth are almost equally absurd and no one wishing to be on the side of sane economic analysis should support either claim.

What 'Off-the-Shelf' Monetary Models Actually Say about Neo-Fisherism

Stephen Williamson wrote this in a blog post today:

Standard off-the-shelf monetary models essentially all exhibit a neo-Fisherian effect. That's nothing special. The Fisher effect is important. Typically increases in nominal interest rates lead to increases in inflation.

Testing this claim should be pretty simple, all we need is to get some "off-the-shelf" monetary models and see what happens when a central bank switches from one interest rate peg to another. I guess the only difficulty here would be that most standard monetary models exhibit indeterminacy when there's an interest rate peg, but I guess that doesn't seem to phase Williamson.

Let's start with the most basic monetary model I can think of: Cash-In-Advance. I won't bother with much derivation here since I've already talked in detail about CIA models in previous posts, so here is a simple CIA monetary model (assuming that the nominal interest rate is always greater than the interest rate that money pays):
$$(1)\: M_t = P_t y $$
$$(2)\: R_t = \frac{1}{\beta}\frac{P_{t+1}}{P_t} $$
where $M_t$ is the money supply, $P_t$ is the current price level, $y$ is the constant level of output, $R_t$ is the gross nominal interest rate, and $\beta$ is the representative agent's discount rate.

It's clear from this that, by pegging the nominal interest rate, the central bank can peg the ratio of the future price level to the current price level to whatever it wants, but here's where the indeterminacy comes in. The actual current price level is not determined under a pure interest rate peg; only the expected rate of inflation. If the central bank raises the nominal interest rate, then the future price level will be higher than the current one, but what happens to the current price level is unclear.

If, instead of pegging the interest rate, the central bank decides to set the money supply to the desired level each period, the current price level is actually determined, but the relationship between the current price level and the nominal interest rate is still unclear. If, for instance, the central bank temporarily lowers the money supply in the current period then returns it back to it's previous level in the following period, the nominal interest rate will go up, but the current price level will fall. Any permanent changes in the money supply impact the price level without changing the nominal interest rate at all and any temporary increases in the money supply result in a higher price level and a lower nominal interest rate.

Of course, if the nominal interest rate is at the zero lower bound, the basic CIA model predicts that the money supply no longer determines the price level, so the effect of a change in the nominal interest rate on the price level is even more unclear. The only reliable way to exit the zero lower bound (without using fiscal policy) in a CIA model is to shrink the current money supply until the cash in advance constraint once again binds, which at the very least means that the current price level doesn't increase. Effectively, even when escaping the zero lower bound, increases in the nominal interest rate mean a lower current price level.

It's interesting that even this exceedingly simple monetary model fails to fully support the neo-Fisherian hypothesis. Granted, it comes closer than most models: a higher nominal interest rate given the current price level does mean a higher future price level, but this can be easily dealt with if we add some kind of nominal rigidity to the model. Furthermore, CIA models don't exhibit interest elasticity in money demand, which, if present, would mean that permanent increases in the money supply would result in a lower nominal interest rate and a higher price level. Perhaps Stephen spoke too soon.

Extended Response to Nick Rowe

Nick Rowe on Twitter earlier today:

If [a] central bank targeted the price of peanuts, would we blame recessions on bad peanut harvests? Or blame [the] central bank for not raising [the] target price?

It depends. It depends on how quickly the central bank finds out about the bad peanut harvest, how quickly the new policy can be enacted, and how effectively the central bank can control the price of peanuts.

Suppose no one know about the size of the peanut harvest until the following period. In this case, the central bank, which we will assume can completely control the price of peanuts for the time being, is not culpable for the recession that occurs because the price of peanuts is too low. The central bank could not have known that the price level (of peanuts) at which output remained at potential was higher than they otherwise thought, so they cannot be blamed for the recession that ensues.

If, on a slightly different note, the central bank faces a delay in policy implementation, it may not be able to act quickly enough to prevent a recession; they can raise the target price with a delay, but there will still be a recession in the meantime and the central bank is not culpable.

Alternatively, assume that the central bank knows about the bad harvest in real time and doesn't face a policy lag, but, for some reason, is unable to set the price of peanuts any higher. In this case, the central bank can't be blamed either -- there is nothing it can do to prevent it from happening, so the correct culprit for the recession is the bad peanut harvest.

Generally, assuming there are no significant lags in information or implementation, the central bank would be to blame for not preventing the recession. The only time that the blame really shouldn't fall on a central bank is when it can't control the price (of peanuts) -- in this case, central bank impotence is to blame for the recession, not actions taken by the central bank.

With that aside, now we can go about determining when central banks are impotent.

Objectives vs. Tools of Monetary Policy

In the comments of one of Nick Rowe's recent posts, Scott Sumner has accused me of confusing objectives and tools of monetary policy:

You are looking at the causal effects of QE, whereas it makes more sense to view QE as the effect of a tight monetary policy that drives rates to zero. If you do a more expansionary monetary policy, such as currency depreciation, then you do not need as much QE. QE is a defensive mechanism, monetary policy needs to be viewed in terms of the policy goals of the central bank, and in terms of whether it will do whatever it takes to reach those goals.

Basically, Scott is suggesting that quantitative easing isn't actually a monetary policy, and is instead the natural conclusion to what he does view as monetary policy -- currency depreciation. Here, Sumner provides an interesting set of definition for what constitutes monetary policy and, more generally, what can reasonably be considered exogenous to a central bank.

In his mind, exchange rates are basically exogenous to the extent that central banks try to influence them. This is evident from his implicit assertion that, if central banks are "doing whatever it takes to reach [their] goals," they will invariably reach those goals. Of course, this isn't necessarily news, everyone has know Sumner's opinion that central banks are nearly omnipotent for quite some time, but this time he has laid it out more directly.

According to Sumner, the evolution of any nominal variable over time can be completely controlled by a central bank and, as such, can be used as a point of criticism for that central bank: "monetary policy needs to be viewed in terms of the policy goals of the central bank." As such, the actual polices that central banks follow are completely irrelevant; it doesn't matter what the path of interest rates is, the correct judge of current Federal Reserve policy (for example) is whether or not inflation is on target.

Of course, I, along with I hope the majority of people, don't see monetary policy in this light. Sumner seems to have made a point of confusing monetary policy -- e.g., QE, interest rate setting, open market operations -- with whatever nominal variable he happens to care about at the moment -- in this case exchange rates. This separation is important; it allows us to understand more directly a central bank's goals and how it intends to achieve those goals.

Evidently, Scott could care less about the how and only wants us to focus on the goals. He basically has reduced his thinking about monetary policy to the point that he views NGDP as an instrument of the central bank -- effectively an exogenous variable -- rather than a variable that a central bank may act to control. This level of abstraction from the operation of monetary policy, in my opinion even more grievous than the New Keynesian obsession with the nominal interest rate, is what allows Market Monetarists to callously ignore every model that doesn't allow exogenous NGDP that says the zero lower bound actually represents a constraint on monetary policy.

If central banks could make NGDP exogenous, would they be able to make NGDP exogenous? Naturally, but no one should care about the answer to such a redundant question, yet this is effectively the answer that you get from Sumner; he'll simply assert that "the BOC can always depreciate the Canadian dollar. The zero bound is not an issue in Canada" (from an earlier comment on the same post). Naturally, we should all trust Sumner's clairvoyance on this issue, clearly no argument about monetary policy effectiveness is necessary (see my first comment on Nick Rowe's post, if you want one anyway) and we can rest assured that fiscal policy is never necessary.

Ideally, considering the ability of monetary policy to effectively deal with challenges should be at least of some consideration and, since monetary policy has proved theoretically capable of offsetting the demand-side effects of fiscal stimulus among other shocks, the only point at which this can be of much concern is the zero lower bound. Both Sumner's and Rowe's refusal to give theoretical arguments against me in this area is rather troubling, evidently just assuming monetary policy is effective in every circumstance is completely acceptable.

Timing and Composition

Family members are often confused by my simultaneous support for looser fiscal policy in the United States and disdain for Republican tax proposals during this election cycle on the ground that they would result in too much deficit spending. On the surface, my policy preferences seem contradictory; I neither support efforts to rein in the deficit nor the large tax cut proposals of the majority of Republicans. There are two primary reasons for this seemingly strange predilection: timing and composition.

The length of time each policy lasts is crucial to my support. As per the 'New Keynesian consensus,' loose fiscal policy should only be used until monetary policy can be reasonably declared unconstrained by the zero lower bound. This is why deliberate deficit cutting policies should not have been undertaken, and arguably should not be pursued further, until two criteria have been met: the federal funds rate must be above the zero lower bound and there must be little to no risk that the zero lower bound will be made to bind by either a tightening of fiscal policy or some other shock to the economy. At the time of writing this post, only the first criterion is fulfilled -- the Federal Reserve has decided to raise the target fed funds rate, but, since it stands somewhere between 0.25% and 0.5% (the Fed has adopted a target range instead of a strict target), it would be reasonable to suggest that a large negative fiscal shock could be more than the Fed can handle without being thrown back into a liquidity trap (in this sense, the US could still be considered to be in a liquidity trap, even though the zero lower bound no longer binds).

GOP tax cut proposals would undoubtedly achieve the temporary goal of looser fiscal policy, but they would be on a completely wrong timescale. Conventional analysis only suggests loose fiscal policy for the duration of the liquidity trap, and, since the tax cuts are permanent to the extent that they are not repealed by future administrations, they fail miserably in this regard. In other words, fiscal policy would be too loose for too long under large tax cuts -- especially if they are not accompanied by corresponding reductions in government spending. Additionally, spending cuts are arguably more damaging than tax cuts are stimulative in liquidity traps, so a fiscal adjustment fully in line with, e.g., Rand Paul's or Ted Cruz' preferences could completely fail to comply with the recommendations of mainstream economics, which scares me enough in its own right to warrant a revocation of support.

My second criticism of the GOP tax plans is more personal; I think that government spending and taxes in the United States should be higher, not lower. There are certainly arguments to be made that government spending in the United States does nothing to raise aggregate utility and should thus be cut, but I believe, and I think most other economists agree with me, that this is definitely not the case. This is especially true in infrastructure, or more generally government investment -- currently at its lowest level as a percentage of GDP since 1948 -- which sorely needs to be increased. Further, spending on Social Security and Medicare should increase over the next decade or two because of the changing demographics of the country. If we adopt the tax proposals of many if not all of the GOP candidates, spending cuts will have to come from somewhere and, given the Republican obsession with massive military spending, they will probably not be defense cuts. This pretty much leaves entitlements and investment -- both of which would cause significant pain going forward if they were cut significantly.

Ideally, fiscal policy makers would focus in the short term on simply not cutting spending too ferociously and in the long run on figuring out how to raise the revenue required for higher levels of government investment and entitlement spending. The GOP seems prepared to do neither of these and, as such, I am not prepared to endorse them for their fiscal policy.

Choosing the Best Model For Each Context

In spite of perhaps attracting the wrath of Jason Smith, I think it is safe to say that economics is too complicated for there to be one generally applicable model of everything. Because of this, there is a veritable plethora of economic models available to the economic theorist. This simply leaves the question of which one to use in which circumstance.

Simon Wren-Lewis seems to think that economists should select between models in an ex-post manner -- that is, we should seen which model better represents the data and use that model from then on:

How do we know if most economic cycles are described by Real Business Cycles (RBC) or Keynesian dynamics. One big clue is layoffs: if employment is fall because workers are choosing not to work, we could have an RBC mechanism, but if workers are being laid off (and are deeply unhappy about is) this is more characteristic of a Keynesian downturn.

 The issue here is that we can only diagnose events after the fact, we cannot reasonably make predictions because of the impossibility of ex ante empirical validation: it is impossible to determine whether or not a recession is New Keynesian or if it is a Real Business Cycle before data are released.

This is why context-based validation of theory is superior to empirical validation in the case of economics. The context -- i.e. the sub-field of economics that is being studied -- should inform model choice almost entirely. If the field is business cycles, then the relevant model is a New Keynesian DSGE model and if the field is growth theory, then New Keynesian models are superfluous and should be tabled in favor of neoclassical models -- whose only difference from their New Keynesian counterparts is nominal rigidity, which is irrelevant over a time scale longer than a decade.

Predictions about the economy can now be made based on currently available information: it is possible to determine whether or not, e.g. financial frictions should be present in our business cycle model based on the current state of the economy: we knew by Q3 2008 that financial frictions were relevant, so we should have put them in a model if we were trying to predict the next few years.

Alternatively, the model I should choose to use depends on the kind of thought experiment I choose to embark on. Am I trying to compare PAYGO pensions with Social Security? If so, the obvious model to use is a simple OLG model without a labor-leisure trade-off or sticky prices. Choice of models is equivalent to choice of assumptions, at least when it comes to the DGE approach currently dominant in economics, and assumption choice depends entirely on the question being asked. Nominal rigidity is obviously relevant for business cycle theory, but completely useless when it comes to determining the level effect of a tax increase.

Hopefully this selection mechanism is specific enough to not be "basically feelings," as Jason Smith would suggest is the case for most of economics.

People Should Be More Honest With Charts

Recently, Scott Sumner wrote a blog post with this chart in it:

 I thought it would be interesting to see how well this relationship held over the period that Sumner didn't include in his chart. Here it is:

It's interesting to note that the relationship doesn't look so good when you look at the entire sample in which all of the data is available. This is aside from that fact that the idea that the NGDP/Wage ratio would track unemployment is part of basic neoclassical theory and has nothing to do with wage stickiness.

Start with a simple Cobb-Douglas production function with employment and capital:

$$(1)\: Y_t = F(K_{t-1},L_t) = K_{t-1}^\alpha L_t^{1-\alpha} $$

Assume that the firm maximizes profits, $Y_t - w_t L_t - r_{t-1} K_{t-1}$ and you get the following first order condition for labor:

$$(2)\: w_t = (1-\alpha)\left(\frac{Y_t}{L_t}\right) $$

Dividing by $Y_t$ will give the nominal wage to NGDP ratio (since the nominal wage to NGDP ratio is the same as the real wage to RGDP ratio), which is

$$(3)\: \frac{w_t}{Y_t} = \frac{1-\alpha}{L_t} $$

It's clear from this that, in a simple neoclassical model, the nominal wage to NGDP ratio is expected to be negatively correlated with employment and, therefore, positively correlated with unemployment -- which is coincidentally the exact thing that Scott's chart shows. Variations in the nominal wage to NGDP ratio are not, in fact, vindications of the musical chairs model.

What's the Significance of Low Real Interest Rates?

  

[Note: I started writing this post a while ago, so it ostensibly has no connection with these two posts that Nick Rowe and Scott Sumner wrote recently. I just realized that this is somewhat relevant, so I decided to finish it] 

For the last twenty years or so, real interest rates on government bonds have continued to fall from their high of about 9%. Determining the cause of such a fall is by no means an easy task; after all economic theory generally suggests that real interest rates on safe assets -- like government bonds -- should be relatively constant in the long run and reflect the rate at which consumers discount future spending relative to current spending. Economic theory tells us that low real interest rates mean that current consumption is high and future consumption is low relative to what it otherwise would have been. This certainly is a possibility; perhaps falling real interest rates are indicative of a shift in consumer spending patterns away from saving and into borrowing, although the causality seems to be backwards if that is truly the case, which leaves the question of what has caused this decline in real interest rates open once again. 

Perhaps the basic models in which the government has no power over the real interest rate in the long run are incorrect; given the sharp increase in the real interest rate on government bonds during the 1980s, this certainly seems plausible. In this case, it may be useful to switch to looking at this problem through the lens of an OLG model instead of a basic representative agent RBC/Neo Classical one. Every period, a new young agent is born with the endowment $y$ which can be used to buy either consumption ($c^y_t$) or government bonds ($b_t$), or to invest in capital ($k_t$). The young agent faces the budget constraint

$$(1)\: y = c^y_t + b_t + k_t$$

In the next period, the young become old and use income from interest on government bonds, $R_t b_t$, and from income generated from capital, $f(k_t)$ to finance their consumption and the taxes levied by the government. Old agents face the budget constraint

$$(2)\: c^o_{t+1} = R_t b_t + f(k_t) - \tau_t$$

Agents are born wanting to maximize their consumption in both periods of their life, with consumption when old discounted at rate $\rho$. The agents' discount factor is $\beta = \frac{1}{1 + \rho}$. Utility it derived from the log of current young consumption and the log of future old consumption:

$$ U = \log c^y_t + \beta \log c^o_{t+1} $$

Agents maximize their utility function subject to both of their budget constraints. Young agents choose their consumption so that

$$ (3)\: \frac{1}{c^y_t} = \beta \frac{1}{c^o_{t+1}} R_t $$

That is, young agents take as given the interest rate the they can receive by saving now and consuming later or that they would pay if they consumed now and saved later and decide to save more if the interest rate is high -- since their lifetime income can be increased by their saving -- and save less if the interest rate is low. The government sets the number of bonds that it issues by discretion each period which, given the young agent's consumption decision, determines the level of capital investment. 

Another first order condition of the model is the the real interest rate on government bonds is equal to the marginal productivity of capital. That is, 

$$ (4)\: R_t = f'(k_t)$$

Since the level of government bonds determines capital investment, it also determines the real interest rate on government bonds. More government debt means less capital which, per $4$, means a higher real interest rate (assuming that $f(k)=k^\alpha$ where $\alpha < 1$). This works because agents must be indifferent between holding more government bonds or more capital in equilibrium; otherwise they would end up demanding more or less capital than they wanted. 

In this model, low real interest rates are a result of high capital expenditure and low government debt. The prescription for low interest rates, then, is to engage in a large fiscal expansion that would increase the amount of government bonds in the economy. Less capital demand would have to be justified by a higher real interest rate. Of course, this seems empirically slightly dubious. After all, the amount of government debt skyrocketed in 2008 and interest rates failed to rise. To understand why this wouldn't necessarily be consistent with higher real interest rates, it's important to think along the lines of a demand for government bonds. 

Agents in this model are willing to demand more government bonds at higher interest rates, so if the government sets the supply of government bonds higher, then the demand must correspondingly rise through an increase in the real interest rate. The reason that massive increases in government debt in 2008 and 2009 are not consistent with higher real interest rates is that demand for government debt increased; perhaps even by more than the increase in supply. This was likely caused by the sudden illiquidity associated with other assets that were previously considered safe - e.g. mortgage backed securities or Greek government bonds. The resulting surge in demand for government bonds is known almost colloquially as a 'flight to quality.' 

The ideal fiscal response to this is to satiate demand for government debt by running large deficits (note that this is the exact opposite of the policy actions taken by the majority of governments since 2008). In a way, this is a non-Keynesian reason for pursuing fiscal stimulus; more government debt would be useful for raising the real interest rate. Not only would this make the economy closer to a competitive equilibrium (one without government intervention), it would likely make monetary policy more effective. Narayana Kocherlakota, president of the Minneapolis Fed, made this point in a speech in July. The basic argument he presents is that the government can raise the long-run neutral real interest rate by increasing the amount of government debt. The higher neutral rate of interest (i.e. the real interest rate in this model, since there is no money) will make it so that the Fed will be less likely to hit the zero lower bound when trying to ensure that target is hit. 

Effectively, fiscal policy should be used to remedy situations in which the demand for money is indeterminate and the central bank cannot adequately influence the real interest rate (see, e.g., here).