Friday, July 19, 2013

A Market Monetarist Approach to the Interest Rate Puzzle

What’s going on with real rates, inflation breakevens, and the stock market? From the beginning of 2010 to the end of 2012, these three variables have affected each other in a predictable way. Higher inflation breakevens pushed up the stock market as they served as a sign that aggregate demand was rising. Growth in real rates was associated with increases in the stock market as the real rates served as a predictor of future growth. However, these relationships have broken down in this first half of 2013. In this post, I aim to explain why. By combining movements in market data with traditional economic theory, there is convincing evidence that the recent change is due to a positive aggregate supply shock, and therefore bodes well for economic growth looking forward.

This post will proceed in three acts. In Act One, I introduce some work that has already been done on this question. In Act Two, I present a new approach to process the market data and the theory that justifies the observations. And in Act Three, I address any residual concerns. Let us now begin.

Act One -- The Work that Has Been Done

Recent trends in financial markets since 2010 are summarized below. In it we have the movement in the 10 year real interest rate, the 10 year inflation breakeven, and the SP500. During the 2010-2012 time period, the 10 year inflation breakeven was very tightly correlated with the SP500, and if you squint you will notice that increases in the 10 year treasury yield also were correlated with increases in the SP500. However, this seemed to reverse itself starting in 2013. Even as inflation expectations were falling, the SP500 still gained steady ground. Also, when the 10 year real interest rate spiked in recent weeks, we saw a temporary fall in the SP500.

Evan Soltas has documented the breakdown of the interest rate relationship. There are two signals communicated by a rising rate. First, it could be a signal of stronger future growth -- which should send the SP500 up. On the other hand, it could be a sign that monetary policy will be too tight -- which should send the SP500 down. By looking at 90 day rolling correlations between the daily percent change in the 10 year treasury yield and the SP500 stock index, we can tell the difference. Evan has observed that the correlation coefficient between the two changes is quickly approaching zero. According to him, this signals that “over the past 90 days, monetary tightening has been as important to rates as has been macroeconomic strengthening”. The June survey of primary dealers further confirms this hypothesis.

Brad Delong and Matt Yglesias have both come into this debate on Evan’s side, arguing that the Fed has been engaging in a stealth monetary policy tightening. To them, these trends are signs that growth could suffer again in the upcoming months as the Fed decides to tighten too early.

On the other hand, I have looked at the relationship between inflation breakevens and the SP500 and believe what we’re really looking at is a positive supply shock. I find that even though 2013 has been characterized by falling inflation breakevens alongside a rising SP500, marginal increases in the TIPS spread still have a positive effect on equity prices. The only difference is that the SP500 seems to have a higher trend growth level -- an alpha with respect to inflation, if you will. I interpret this as an expectation of higher output at every level of inflation. I identify this with a textbook increase in aggregate supply, and thus argue against the monetary tightening hypothesis.

Act II - Another Look at the Data

One unfortunate oversight of the analysis Evan and I have each done is that we don’t fit our stories together. He says tightening, I say aggregate supply, and we each point to our individual data. But an open question remains: how do our theories explain the other person’s data?

To try and estimate this, I roll with Evan’s calculations, but with slight modification. Instead of calculating correlation coefficients, I instead compute rolling regression coefficients. I look at week to week changes in inflation breakevens, the 10 year TIPS yield, and the SP500. For each week I compute regressions of percent changes in the SP500 against percentage point changes in the TIPS yield and inflation breakevens for the past 26 week window. The regression slopes measure the response of the SP500 to either interest rate changes or expected inflation. It corresponds loosely to the correlation coefficient Evan calculates. The regression intercept measures the “intrinsic” trend growth of the SP500, independent of interest rates or inflation. By looking at these coefficients in context, I will try and construct a more holistic vision of what the financial markets are trying to say.

First, let us take a look at the right side panels which describe the responsiveness of the SP500 to expected inflation. In some sense, changes in the SP500 represent changes in expected future nominal GDP. Therefore, when we look at the relationship between inflation expectations and the SP500, this serves as a proxy for the relationship between inflation and nominal GDP.

In my view, the spike in the TIPS breakeven intercept is a smoking gun for a positive aggregate supply shock. Think about what the higher intercept means. The regression is of changes in the SP500 against changes in the TIPS breakeven. Therefore an increase in the intercept means that the SP500 grows faster for every level of expected inflation. This effect is quantitatively important as well. In comparison to the 6 months ending 2012, the intercept for the past 6 months suggests that the SP500 has kicked it up from about 0% weekly trend growth that is independent of inflation expectations to about 0.8%. Meanwhile, the slope for the breakeven-SP500 relationship is still positive. This all suggests a more permanent aggregate supply shock is driving the intercept up, whereas day to day aggregate demand shocks keep the slope positive. A diagram of this is shown below.

However, careful readers will note that you can get “more output at every price” from a story with a structural shift in aggregate demand with marginal shocks coming from aggregate supply. However, this hypothesis fails on two counts. First, if marginal changes in inflation reflected changes in aggregate supply, not demand, then because aggregate supply shocks send prices in the opposite direction of output, we should expect the TIPS breakeven slope to be negative. Second, the AD story does not match up with the changes in levels. As I showed above, inflation expectations have fallen while the SP500 has risen. If there were a large aggregate demand shock, then we should have seen both the SP500 and TIPS breakeven rise in levels. Therefore, a positive aggregate supply shock provides the most natural interpretation for the right hand panels.

Now comes the out of sample test. Can an aggregate supply shock explain the low slope and moderately higher intercept in the SP500-real rate relation? Absolutely.

To see how, I appeal to a version of the IS-MP (Investment Savings, Monetary Policy) model, pictured below. In the diagram, nominal GDP growth is on the x-axis and the real interest rate is on the y-axis. The IS curve is the standard IS curve from intro macro. It describes various combinations of interest rates and nominal GDP levels that give equilibrium in the goods market. At lower levels of the real interest rate, people want to hold onto less money and consume more goods. This results in higher levels of nominal GDP and a downward sloping curve. The MP curve is slightly different because it describes not equilibria but a central bank reaction function. At higher levels of nominal GDP, the Fed sets higher a higher interest rate in order to prevent rapid inflation. These two curves now give a unique equilibrium characterized by an interest rate and a level of nominal GDP.

Now what happens if there is a supply shock? The increased productive capacity, on first approximation, has no effect on the IS curve. To see why, suppose the monetary authority does not react. Then because a supply shock leaves nominal GDP relatively unchanged, then the IS curve should not move. However, because the Federal Reserve is an inflation targeting central bank, the MP curve shifts down. Now that every unit of nominal GDP consists of more real growth and less inflation, monetary policy becomes easier. Therefore, the new monetary policy curve will look something like MP(2) in the picture above.

This matches two more details from the regression.

First, the downward shift of the MP curve means that at every interest rate you observe more output. This matches the somewhat higher regression intercept on the interest rate graph.

Second, since the MP curve is moving, we should expect a weaker correlation between interest rates and output. This is illustrated above. If the MP curve is held constant while the IS curve shifts back and forth, then we will observe a strong correlation between interest rates and output, as shown by the blue line. On the other hand, if the MP curve is moving to MP(2) at the same time, we may end up observing the red dots and finding that the correlation drops. We also should expect this correlation confusion to be a bigger deal for the monetary policy shift than for the aggregate supply shift. As Bernanke is finding out, shifts in MP are linked to relatively unstable market expectations whereas a positive AS shock from something like oil discoveries is much more predictable. The theory behind this explanation of the fall in the correlation is illustrated in the sketch below, and it is actually exactly what we observe in the markets during the first half of this year.

The final step is to get the higher interest rate from the taper, and this can be seen as just the effect of a slight Fed tightening along with a slight rightward shift of the IS curve as business confidence requires. In the end, you have higher growth, higher rates, even though the Fed has tightened (as per the Dealer survey) relative to where it was before.

Act 3 -- Addressing Additional Concerns

While I believe the above story is the one most consistent with the regression data, there are always additional concerns.

Most importantly: what is the positive supply shock? I believe the most plausible supply shock could be the further discovery and development of unconventional oil and gas reserves. Therefore when compared to the counterfactual of perpetually rising oil prices, the new discoveries makes it easier for policy makers to respond to energy shocks and improve the economy’s productive capacity.

An important note is that a rise in oil prices, when it occurs alongside a rising SP500, does not contradict the aggregate supply hypothesis. An aggregate supply shock is characterized by a general fall in inflation as output rises. But if aggregate demand is moving at the same time, we could end up observing higher prices with even higher output. Therefore we identify an aggregate supply shock by seeing higher output *for any given level of inflation*. And this is precisely what we see from the rolling regressions.

Also, I have somewhat of a harder time explaining the past movements in the intercepts and slopes. Fortunately, the intercepts seem to move up and down together, whereas the slopes do the same. Moreover, the intercepts often go in opposite directions when compared to the slopes. This suggests that supply shocks may be more recurrent than we are led to believe.

Others may criticize the above approach as too ad-hoc. While to some extent, it certainly is, I believe I have done justice to the spirit of the AS/AD and IS/MP models. Furthermore, if you break down all the layers of abstraction and ad-hoc econometrics, the story is quite simple:

The massive increase in U.S. petroleum resources has expanded aggregate supply, allowing the economy to attain higher levels of output at every level of inflation. This serves as a massive tailwind for equity markets that no longer depend on aggregate demand inflation to grow. This requires a muddled monetary policy adjustment -- reducing the previously observed correlation between interest rates and growth. Nonetheless, the aggregate supply shock has increased trend growth, making the fluctuations in interest rates matter less.



  1. Incredibly well thought out and put together. what amazes me is the amount of thought that goes into the TIPS market, considering there are only 2 maybe 3 major market participants that trade in that market and set the price. It might be the most easily known manipulated market out there. Look at the float and look at the players and explain to me how any valuable information comes from that market. Maybe you could argue there isn't better inflation px'ing information to hang your hat on, which i may agree with. TIPS however not only are poor indicators, but i would also argue contain large misinformation based on the lack of participants and liquidity.

  2. If the supply shock story is "true", that´s even more reason for the Fed to increase NGDP (AD) growth, i.e. adopt a more expansionary MP given that the economy is below the trend growth level of AD