The Economics of the Grim Reaper

I am on a roll with wonkish posts. So here is another one.  I am going to explain the difference between two kinds of macroeconomic models, representative agent (RA) and overlapping generations (OG) models. And I will explain why OG models provide an explanation of why central banks should intervene in asset markets that is different, and in my view stronger, than any argument that might be leveled using the RA model as an organizing principle. Because the OG model assumes that people die and new people are born, I have called this post: The Economics of the Grim Reaper.

Macroeconomists have two "workhorse" models. In one, they assume that the world works "as if" there were a single representative family making all decisions. The head of that family has superhuman perceptions of all future possible outcomes and he/she makes plans accordingly. This is called the RA or "representative agent" model. In the second workhorse model, we assume that population consists of a sequence of overlapping generations of selfish individuals. This is called the "overlapping generations", or OG model. You can find a simple (as simple as any graduate text can get) introduction to these two kinds of models in my graduate textbook The Macroeconomics of Self-Fulfilling Prophecies.

The RA model may sound unrealistic, but it is more reasonable than it at first seems. For instance, many of the strong results that are known to hold in the RA model, also hold if there is a finite number of infinitely lived families all of whom trade with each other in the financial markets. The really strong assumption, which is added on top, is that people know the probabilities of all future events and they trade with each other, contingent on these events.

If we want to understand why government should intervene in financial markets, and I do, we must explain why government can do something that private markets cannot. Perhaps the reason is that the public really does not have superhuman perception of future events. Perhaps, that is, the rational expectations assumption is wrong. But that, in itself, is not a reason for governments to intervene in financial markets.

Hold your nose for a moment, and suppose that people can, and do, trade securities contingent on all future events. In order to argue that government should intervene in the financial markets, you must be able to show that treasury or central bank mandarins have superior knowledge. That seems a stretch. After all, we do not insist on shutting down gambling on horse races. But people only bet on horse races because they have different opinions as to the probabilities as to which horse will win. Rational expectations, in this context, is obviously false. If we assume the same is true of the financial markets, that people disagree about future probabilities, that in itself is not an argument for intervention. Government must be shown to have an advantage that allows them to intervene in a way that improves social welfare. And in my view, individual human beings are still the best judges of what is, and what is not, in their own best interests.

Absence of rational expectations, I will argue, is not a reason for government to intervene in financial markets. Death, on the other hand, is such an argument. To make that case, I need to say more about the OG model.

It is well known that the OG model behaves very differently from the RA model, For example, Paul Samuelson, in a seminal article that introduced this model to the English speaking world, showed that the overlapping generations model sometimes allows a role for governments to improve the arrangements that are made by private agents. That role relies on what economists call 'dynamic inefficiency' and it occurs when interest rates, in the model, are 'too low'.

If interest rates are too low, government can take resources from future generations, give them to current generations, and make everyone happier. Although the real world is looking more and more as if that might be a good assumption, it is not the reason I will emphasize in this post, for treasury and central bank intervention in financial markets. There is a second reason why death matters that was first pointed to by David Cass and Karl Shell in article that appeared in 1983 called "Do Sunspots Matter?"

The second reason why death matters is quite distinct from the property of dynamic inefficiency and it occurs, even when interest rates are high and all market exchange is dynamically efficient. This second reason occurs because, in OG models, economic activity can fluctuate as a consequence of self-fulfilling beliefs. Financial cycles arise in these models because people engage in self-fulfilling bouts of optimism and pessimism that cause fluctuations in output and employment. And the government DOES have an advantage over private agents (wonkish example here, and here). It can make trades on behalf of the unborn that can smooth out these cycles.

In my forthcoming book, Prosperity for All, I make the case that this second reason for inefficiency is important and is the main reason that financial cycles are so destructive for human welfare. By implementing the financial reform that I propose in my book, we can ensure that next time really will be different. 

Beliefs and the Monetary Transmission Mechanism

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In my last post, I urged the Fed to raise the interest rate at its next meeting. In response to that post, David Andolfatto asks, 

Suppose a CB was to raise its policy rate permanently in an attempt to raise the inflation rate (without the corresponding policies you favor [in your post]). You claim that this would ultimately raise the rate of inflation (possibly after a recession). Can you describe the economic mechanism that would work to produce this result? (I mean, an explanation that extends beyond simply stating that the Fisher equation must hold.)

Here is my necessary, (but Wonkish) response. 

If we write a 'Fisher like equation' of the form

EQ 1) i - rho = E[Pi_t+1] + E[y_t+1] - y_t

Here, i is the money interest rate, y_t is GDP, Pi_t is inflation between dates t-1 and t and rho is the real rate of interest. E[ ] is the subjective expectation formed at date t. An equation like this would arise in a representative agent model with logarithmic preferences.

Now we can agree, I think, that if the Fed sets i equal to some constant rate, if we impose rational expectations, and if we write down a process that determines {y_t}; then an increase in i will lead to an increase in inflation. You want to know the adjustment mechanism from one steady state rational expectations equilibrium to another.

Let's assume that the Fed operates an interest rate peg, and that at some date, it announces an increase in that peg. At date t, one of two things can happen. Either, the increase in i can lead to an increase in E[Pi_t+1] + E[y_t+1], OR it can lead to a fall in y_t. If expectations are slow to adjust, the increase in the peg will lead to a fall in current GDP.

In my view, the equations needed to close this model are equations that determine E[Pi_t+1] and E[y_t+1], as functions of Pi_t, y_t i_t, and, other observables. Those equations are fundamentals that behave like preferences. It is the fact that expectations are 'sticky' that leads to nominal shocks, such as an increase in a purely nominal variable, like i, to have real effects.

In a slightly more complicated model, where the coefficients on output growth and inflation in equation 1, are different, the following expectations rule works well at explaining data

EQ 2) E[Pi_t_1] + E[y_t+1] - y_t = Pi_t + y_t - y_t-1

in words, expected nominal income growth is a martingale. By closing a three-equation model with that specification of the belief function, and by writing down a slightly more sophisticated version of a Taylor rule (not just a simple interest rate peg) I showed here that a model closed with a belief function, outperforms the NK Phillips curve model.

The idea of making the belief function 'fundamental' is consistent with equilibrium and rational expectations because of my assumption that the labor market operates as what I call, in my forthcoming book, Prosperity for All,  a 'Keynesian search market'. Employment and GDP growth are not uniquely pinned down in the steady state: they depend on initial conditions and the entire history of shocks.

Why the Fed should raise interest rates at its next meeting

How to Raise Inflation

Conventional New-Keynesian macroeconomists assert that, to increase the inflation rate, the Fed must first lower the interest rate. A lower interest rate, so the argument goes, increases aggregate demand and raises wages and prices. As economic activity picks up, the Fed can raise the interest rate without fear of generating a recession. Some economists advocate that the Fed should raise the interest rate to meet the inflation target, a position that for reasons that escape me, has been labelled as neo-Fisherianism on the blogosphere (see my previous post, also  Stephen Williamson, David Andolfatto, and John Cochrane). My body of work, written over the past several years, (see my forthcoming book) explains how to raise the interest rate without simultaneously triggering a recession and, I suppose, that makes me a 'neo-Fisherian'.

There is also something new in this post that I discussed last week with Stephen Cecchetti while visiting the San Francisco Fed. This relates to the connection between the world we now live in, where the Fed pays interest on reserves, and the world we used to live in, where it did not. It goes without saying that Stephen does not bear responsibility for any perceived mistakes in the case I make.

I will argue that the Fed should raise the interest rate on reserves (IOR) and the federal funds rate (FFR) simultaneously, thereby keeping the opportunity cost of holding money at zero and enacting Milton Friedman's proscription for the optimal quantity of money.  In addition, the Fed should be given the authority to buy and sell an exchange traded fund (ETF) over a broad stock portfolio with the goal of achieving an unemployment target. This is an argument I have been making for some time but it is becoming more relevant as it becomes apparent that the world does not work in the way the New-Keynesians claim.

At the Jackson Hole conference this week, Janet Yellen argued for a broader range of Fed tools moving forwards. While I agree with that view, I would put a different emphasis on what those tools should be.  Maintaining a large stock of excess reserves is a good idea because money is costless for society to create. But, I argue, the Fed should actively trade the asset side of its balance sheet to promote real economic stability and a low unemployment rate. 

Two Interest Rates

Prior to 2008, commercial banks held reserves to meet a minimum required ratio of reserves to deposits. This ratio, the required reserve ratio, was mandated by the Fed and changed occasionally. In the period from the end of WWII up through 2008, banks held exactly this amount and excess reserves were equal to zero.

In October of 2008, the Fed began to pay interest on the  reserves of commercial banks held at the Fed. Figure 1, copied from the San Francisco Fed website, shows that, once that change in policy was enacted, the excess reserves of commercial banks increased from zero, before 2008, to approximately  $1.6 trillion in 2012. They are currently even higher at $2.2 trillion in 2016.

Prior to 2008, excess reserves were costly for commercial banks to hold because a commercial bank can make profits by lending reserves to private companies or to households or by purchasing interest bearing government securities. When three month T-bills pay positive interest, but reserves do not, a commercial bank will choose to hold zero excess reserves. After 2008, reserves held by commercial banks with the Fed are, to a first approximation, perfect substitutes for short term Treasury bills.

The post-2008 monetary environment is very different from the pre 2008 monetary environment. In the immortal words of Dorothy from the Wizard of Oz, “We’re not in Kansas anymore”.  In the brave new technicolor world, the Fed controls two money interest rates, not one; the interest rate on reserves held at the Fed (IOR), and the Federal Funds Rate (FFR). By raising the IOR and the FFR at the same time, the Fed can engineer an increase in nominal rates without altering the opportunity cost of holding base money. By keeping the difference between the IOR and the FFR at zero, the Fed is allowing the private sector to create what Milton Friedman called, the optimal quantity of money.

Because money is costless to create, from a social perspective, Friedman argued that society should set the opportunity cost of holding money equal to zero. That is precisely what happens when the IOR equals the FFR.  Because the demand and supply of money are identically equal, a simultaneous increase in the FFR and the IOR will not  lead to a contraction in the money supply.

The Real Effects of an Interest Rate Rise

Even if the opportunity cost of holding money is zero, a positive interest rate surprise may still reduce the money value of expenditures on goods and services as the values of existing dollar-denominated income flows are revalued downwards. This revaluation will not only affect fixed income dollar valued securities, it will also affect indexed bonds and corporate equities. The magnitude of that effect will depend on the public perceptions of future inflation.

In the past, we have observed a negative correlation between unanticipated increases in the money interest rate, and real GDP.  In 1979, the Volcker Fed engineered a big increase in the interest rate in order to bring inflation under control. It worked, and over the following decade, inflation fell.  But the interest rate increase triggered one of the largest post-war recessions in US history. The $64 trillion question is: can the Fed engineer a rate rise without triggering a recession? The answer to that question is yes.

New Keynesians believe that prices and wages were slow to adjust because of so called ‘menu costs’.  They incorporate that belief into their models with an equation that goes by the name of the ‘New-Keynesian Phillips Curve’. There is increasing evidence (Klenow and Malin) that menu costs are not large enough to explain the real effects of a monetary contraction and there is increasing evidence that there never was a Phillips curve in the sense in which the New-Keynesians need there to be one.

It is not prices that are sticky: it is expectations. The New-Keynesians are right to assert that the output gap and the unemployment rate are determined by ‘aggregate demand’. Aggregate demand depends on the beliefs of asset market participants about the future value of wealth and beliefs are self-fulfilling prophecies that depend on the ‘animal spirits’ of investors. We need a way for the Fed to intervene in the asset markets to stabilize asset prices and to prevent spillovers from volatile shifts in beliefs to the real economy.

One way to achieve that intervention would be to give the Fed the authority to trade in the stock market, as does the Bank of Japan. As I argued here, the Open Market Committee of the Fed should use that authority to actively trade an exchange traded fund in order to offset any potential drop in asset values that follows an interest rate increase. If unemployment is above target, the Fed would announce an increase in the growth path of the price of the ETF. If it were below target, they would announce a reduction in the growth path.

Why do I believe this would be effective? After all, conventional New-Keynesian wisdom holds that there is little or no connection between the value of the stock market and subsequent real economic activity. Conventional wisdom is wrong. Although there is little or no connections between short-run stock market fluctuations, I have shown in published empirical papers (2012,2015) that there is a strong and stable connection between persistent changes in the value of the stock market and changes in the unemployment rate. And I have shown in published theory papers, (2012,2013) why this chain is causal. When we feel wealthy, we are wealthy!

You can read more about these ideas in my book Prosperity for All, available for purchase on October 7th.

Thought for the Day: George Orwell and E.B. White

Animal Farm was published 0n this day in 1945. Maria Popova (@brainpicker) has written a piece inspired by George Orwell, on the freedom of the press, that every member of the chattering classes should read. She ends with this quote from E.B. White

"To exchange one orthodoxy for another is not necessarily an advance. The enemy is the gramophone mind, whether or not one agrees with the record that is being played at the moment. "E.B. White

Orwell's critique was of government control of ideas. White's point was that a 'free society' does not need the government to decide which ideas are fit to express and which are not. The intellectual establishment polices itself.

White's critique is as relevant as ever today as we ponder the political and economic challenges we face.

Has Labor Productivity Growth Fallen Permanently?

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                       Figure 1: Post-War Labor Productivity

J.W. Mason has an interesting series of posts over at slack-wire on the relationship between productivity growth, changes in the unemployment rate and changes in labor force participation. Productivity is a huge determinant of living standards and of GDP growth projections moving forwards. Mason's posts led me to ask the following question. Given the importance of labor productivity growth in determining the standard of living of the average American, how confident are we that it has actually fallen? And how confident are we that labor productivity growth has fallen permanently.

Figure 1 is a plot of US labor productivity from 1948Q1 through 2016Q2. The mean (plotted as the red line) is 1.42 and the standard deviation is 1.53.  The data, from FRED II, is quarterly GDP measured in 2009 dollars divided by total non-farm payrolls and expressed as an annual percentage four quarter rate of change. A few features stand out from Figure 1. First, productivity growth is highly volatile. Second, it is less volatile in the second half of the sample, and third, the mean appears lower after 1980. But I wouldn’t bet the farm on the fact that the mean of productivity has fallen permanently.

Figure 2: Data for Productivity Broken into Two Subsamples

One way to test this is to split the data into two subsamples and compare the means.  This is what I do in Figure 2.  The top sample is the data from 1948Q1 to 1982Q1. The second is from 1982Q2 to 2016Q2. The red line in each case is the common mean.

                                                  Mean               Std Dev.

Common Sample                    1.42                 1.53

First Subsample                      1.46                 1.82

Second Subsample                 1.38                 1.18

In each case, the mean of the second subsample lies well within one standard deviation of the mean of the second sample. Given reasonable assumptions about the distribution of these random variables, a formal hypothesis test would not reject the assumption that the means of the productivity distributions for the two subsamples are the same.

                    Figure 3: Smoothed Histograms for Both Subsamples

Figure 3 plots smoothed density estimates for the two subsamples from Figure 2. These estimates help gain a visual impression of the likelihood of observing a given value for productivity growth, before and after 1982Q1.

In each of these two graphs, the blue curve represents data from 1948Q1 through 1982Q1 and the red line represents data from 1982Q2 through 2016Q2. 

The graph in the top panel smooths the data using a smoothing window that is chosen on the assumption that each sample comes from a normal distribution. The graph in the lower panel uses a wider window to average adjacent points. This wider window takes account of the fact that the distributions may not be normal and may instead have fat tails. 

What do I learn from Figures 1 through 3? There is evidence for a reduction in the volatility of labor productivity growth after 1982. This is what is sometimes referred to as the 'Great Moderation'. There is weaker evidence for a reduction in the mean of labor productivity growth. Even during the 1950s and 1960s there were many years when labor productivity growth was negative, sometimes by as much as 2% per year. In the post 1980 period there are fewer years with large positive increases in labor productivity, but also fewer years with large drops.

Has productivity growth fallen permanently? The jury is still out.