A Practitioner's Thoughts on Market Monetarism

This summer, I have been working at MKM partners with Michael Darda doing a wide range of macro research. Since Michael is one of the leading street economists who uses a lot of market monetarist concepts in his work (monetary offset, nominal GDP targeting, market signals), I have accordingly been doing a lot of work on monetary policy and nominal GDP during my time here. This blog post is meant to talk about some problems I have encountered as I have tried to write about these market monetarist concepts in my reports for Michael, and I hope this can be useful for fellow market monetarists -- especially fellow practitioners.

Before I delve into the specific problems, it might be useful to consider a summary of key propositions that recur in market monetarist discussions. In no particular order, they are summarized below:

1. Interest rates are an unreliable indicator of the stance of monetary policy. As Milton Friedman reminds us, low interest rates typically indicate that monetary policy has been too tight, and high interest rates typically indicate that monetary policy has been too easy. For example, monetary policy throughout Japan's lost decade was too tight as the central bank would raise interest rates at the first sign of inflation. But as a result, Japanese interest rates have held steady at very low levels. On the other hand, monetary policy in the United States during the 1970's was far too easy, and as a result interest rates were very high. This is because the level of the 10 year nominal rate is determined more by money velocity than anything else.

2. The only reliable indicator of the stance of monetary policy is a nominal aggregate, such as nominal GDP. Given that interest rates are an unreliable guide, we are left with judging a policy stance by its outcomes. Since the goal of monetary policy is to provide a nominal anchor, then the stance of monetary policy is determined by how the nominal aggregate performs relative to the target. So if nominal GDP is above trend, monetary policy is too tight, and if it is above trend, then policy is too easy. 

3. Market signals serve as the optimal forecast of future economic conditions. Since the price of securities typically reflect all available information, they can serve as a high frequency measure of market expectations. This is particularly attractive because it means a relatively small firm like MKM can abstract away from building a structural forecasting model and instead focus on interpreting the price signals in individual markets. 

4. Never reason from a price change. Clients struggle with this one, but it's really quite simple. In economics, whenever there's a change in conditions, it's because a curve -- supply or demand, liquidity preference, etc. -- has shifted. As a result, a quantity or price changes. But for any given increase in price, whether quantity goes up or down depends crucially on whether the change in price is caused by a supply or demand shock. This sounds like trivial microeconomics, but people often forget it when they start talking about finance. Clients tend to go straight to questions such as "how does this rate hike affect housing markets?" or "how will this increase in crude prices affect the economy?" without asking "why are rates rising?"
Looking back at some of the work I did this summer, I have two takeaways -- one positive, one negative -- from these four core ideas.

First, the positive. The notion of market signals and of reasoning from curve shifts (i.e. 3 + 4), and not price changes, led me down an interesting path of trying to identify curve shifts from financial market data. This led to my "Market Monetarist Approach to the Interest Rate Puzzle". The core idea here is that you can use three financial indicators -- the SP500, the TIPS spread, and the 10 year treasury -- as proxies for three "real" economy indicators -- nominal GDP, the inflation rate, and the risk free rate. Now, the stock market one is a bit difficult because equity values are not only a positive function of cash flows (~ nominal GDP), but also a negative function of the risk free rate (because of discounting). Nonetheless, it's one of the few real time metrics we have for growth expectations.

With these three changes, I interpreted the recent change in the relationship between the 10 year inflation breakeven and the SP500 as a sign of an aggregate supply shock. This was my conclusion from some time series analysis that showed the slope of the relationship between the SP500 and the TIPS spread has not changed, but the intercept has increased. Statistically, this translates to the statement "at all levels of expected inflation, the stock market has higher returns." If we accept the above dictionary into real economy terms, this translates to "at all levels of inflation, nominal GDP is higher" -- the smoking gun of a supply shock.

I did some follow up work on interpreting these structural shifts in the interest rate puzzle post.

But now, the negative. Identifying the stance of monetary policy by the outcome leads to circular statistics. If you attribute all fluctuations in nominal GDP to bad monetary policy, then of course monetary policy will seem like a big issue! Put another way, you can observe the positive relationship between nominal GDP and real growth without requiring that monetary policy drives nominal GDP. The tight correlation between nominal GDP and a whole host of other aggregates does not identify a market monetarist viewpoint of the world. And because of the Lucas critique, monetary policy may be unable to exploit this relationship to restore real growth. Perhaps if you use a good bit of economic history, you could identify certain scenarios of exogenous monetary contractions. But in the end, focusing on nominal GDP to determine the stance of monetary policy makes it hard to do any kind of systematic statistical analysis.

But that doesn't mean there isn't any statistical evidence.

In my view, one of the more robust pieces of evidence for the power of monetary policy comes from an analysis of fiscal multipliers in open and closed economies. To see why this matters, we need to think about Mundell's impossible trinity. The impossible trinity states that no economy can simultaneously have free flows of capital, a pegged exchange rate, and a sovereign monetary policy at the same time -- you have to give up at least one. Given that most countries have been dismantling their capital controls (especially since capital controls eventually become porous), you can identify whether a country has a sovereign monetary policy by seeing if it has a pegged exchange rate regime. Econometrically, the exchange rate regime serves as an instrument for effective monetary policy that avoids the problems inherent in using interest rates.

With a few more assumptions, we'll be going places. Suppose that central banks with sovereign monetary policies tend to maintain some kind of nominal stability -- whether inflation or nominal GDP. Then as a result, these central banks would tend to offset fiscal policies more, as those central banks under pegged exchange rates would have to subjugate their monetary policy to maintaining the exchange rate. As a result, if monetary policy matters for real growth, then countries with pegged exchange rates (and therefore no sovereign monetary policy) should exhibit higher fiscal multipliers. This is because these countries have no potential for fiscal offset. By this chain of logic through Mundell's policy trilemma, I have reduced the problem of "Does monetary policy matter for real growth?" to "Are fiscal policy multipliers higher in pegged exchange rate regimes?"

And are they? Most certainly. In an NBER working paper titled "How Big (Small?) are Fiscal Multipliers?", the authors find that the long run multiplier for countries under pegged exchange rates is around 1.4, whereas the multiplier for countries under floating exchange rates is statistically no different from 0. In fact, the authors themselves come to this conclusion about monetary policy. In particular, they show that the monetary offset if floating rate regimes doesn't come through the current account, but rather through private consumption. Their conclusion is that "consumption responds positively to government consumption shocks only when the central bank accommodates the fiscal shock" -- a sure sign that monetary policy is an important force governing the nominal (and real) economies in the short run.

This pegged/floating exchange rate example bears itself out through the natural experiment comparing austerity in the Eurozone and the United States. Because Eurozone monetary policy has been much more tepid, they can be identified as lacking a responsive monetary policy. So although both economic areas have undergone savage austerity, only the Eurozone has really suffered -- more evidence that monetary policy really does matter.

(Note, an older version of the plot with government spending was used, but data concerns were raised by Mark Sadowski and David Beckworth. In particular, Beckworth pointed out the correct measure of austerity is the change in the cyclically adjusted primary balance, as provided by the IMF Fiscal Monitor)

However, one consequence of this kind of analysis is that it's hard to quantify the effect of monetary policy on nominal GDP growth -- there's little guidance on how much QE translates into how much growth. Perhaps the expectations channel means that this effect is impossible (and maybe even meaningless) to quantify, but it is a limitation of this mode of analysis.

Once we accept this analysis and think of monetary policy as driving nominal growth, then the market monetarist mindset of using deviations of nominal GDP to track monetary policy starts to make sense. Once you establish the empirics through other means, the theory of market monetarism comes into play.

Overall, I find the core ideas espoused by Scott Sumner and fellow market monetarists very powerful. In some regards, they lend themselves easily to financial econometrics and help to organize a a coherent explanation of the macro environment. But some of these ideas need more formal empirical backing -- something that becomes very apparent when talking to clients.

The Taper and Growth -- A Reply to Brad DeLong

Intellectual honesty means disagreeing with even those who are “on my side”. So when the arguments I have made against Reaching for Yield are also arguments against doomsday predictions for the taper, I have to speak up.

In this case, I have Brad DeLong in mind. In a post today, Brad sees the recent rise in real interest rates as measured by the 10 Year TIPS yield and the fall in inflation expectations as measured by the 10 year breakeven as cause for alarm, claiming that “Not since 1991 have we had such a large and rapid contractionary shift in the market's belief about what the Federal Reserve's reaction function.”

Reading his post, it almost sounds like Fed policy is going to collapse growth. But I would argue that while Fed policy is failing to promote maximum employment, it hardly follows that growth will collapse. I come to this conclusion also by looking at financial data. Below I reproduce a plot of the real interest rate, inflation breakeven (both 10 year), and add a plot of the SP500. I focus in on 2013 to see the recent dramatic changes.



We can make some stylized observations. First, the real interest rate has been on a steady rise since May. Second, the inflation breakeven has been on secular decline since about March. Third, in spite of all of this, the SP500 has been steadily growing, rising more than 10% on a year to date basis.

How should we interpret this? If we accept the uncontroversial proposition that stock market movements reflect expectations of future growth, it should be clear that the fall in inflation expectations does not reflect a fall in expected future nominal GDP. This is a break from the trends from 2010 to 2012. But if inflation is not moving in the same direction in output, it must be that a positive supply shock is the driving factor behind the fall in inflation breakevens.

The natural candidate for the positive supply shock is the fall in oil prices. The recent slowdown in emerging markets and massive expansion in oil production has lowered energy costs for the United States. This is a textbook expansion in aggregate supply, and we should naturally expect output to rise, inflation to fall -- precisely what we observe above.



Nonetheless, I still agree that more monetary stimulus is desired. To see this, we should consider the first differences in inflation expectations and the SP500. In the plot below, I have plotted weekly percent changes in the inflation breakeven and the SP500. Blue denotes points in the 2010-2012 time period, and red denotes the points on a year to date basis. Note that in both samples there is a positive relationship between changes in inflation expectations and changes in the SP500. However, the year to date group has a higher intercept, reflecting that the SP500 has shifted to a higher trend growth path relative to the 2010-2012 period. Indeed, if you run the regressions on the first differences, you find that in the 2010-2012 period, the SP500 would gain only 0.23% in a week if inflation expectations were unchanged. However, in 2013, the value is 0.76% -- almost triple what the previous trend growth rate.

These facts show the simplest version of the aggregate supply/aggregate demand model in action. If inflation falls while nominal GDP rises, then it must be a positive supply shock. For every level of inflation we achieve a higher level of output. But even after the positive supply shock, aggregate demand policy still plays a role -- i.e. any marginal rise in inflation still translates to a rise in output.

What went wrong in DeLong’s original analysis was that he reasoned from a price change. He started by talking about inflation and interest rates and then translated that into a statement about monetary policy. On the other hand, I started with a quantity -- the SP500 -- and used that to interpret the price changes. This allows me to fit the data into the standard AS/AD model.

I can then break down potential data changes to events in the AS/AD model. DeLong writes out a list of four possibilities to interpret changes in the real interest rate and the inflation breakeven. II have produced a similar table below that translate the AS/AD arguments I made above. My version provides endogenous predictions for the real interest rate -- the market indicators are inflation expectations and the SP500.

In my view, the economy is in state (4). Inflation is weak, but growth will be strong. These growth prospects are also corroborated by the relative strength of cyclical stock sectors relative to safe ones. Investors are ramping up -- not buckling down -- as expectations of future nominal GDP rise. Bottom line? The taper isn't going to knock growth far off track.

This rate story shows how important markets are in market monetarism, TIPS spreads and movements in the SP500 make for an easy breakdown of aggregate supply aggregate demand. We should take them seriously, even if it’s politically inconvenient for those of us arguing for monetary easing. Interest rate movements signal changes in the reactions of the Fed. But since it's unlikely that the Fed will screw up so badly so as to have elevated interest rates for an extended period when the economy is suffering, rising long rates almost always indicate higher expected nominal GDP. These financial indicators provide policy makers with forward looking data on which to base policy -- a cornerstone of market monetarism.

I want to end on what the above means for monetary policy and advocates of monetary easing, such as myself.

First, the recent fall in inflation breakevens should not be interpreted as a monetary tightening -- the change is not being driven by demand, but rather by supply. Second, the Fed is severely failing its dual mandate. Now that inflation is falling, the Fed should have even more latitude to pursue its full employment objectives. In this light, the taper is madness. Third, advocacy for monetary easing should focus on the human costs, not financial costs, of tight money. Wall Street will move on, but Fed complacency in the face of half a decade of slow job growth will leave scars on Main Street for years to come.

For Sussing Out Whether Debt Affects Future Growth, the Key is Carefully Taking into Account Past Growth

On Miles' website we have a companion post to the previous post on an instrumental variables analysis of the RR dataset. In the companion post, we walk through more of the regressions and illustrate how controlling for past growth can erase almost any effect of debt on future growth. The core conclusion?

The two of us could not find even a shred of evidence in the Reinhart and Rogoff data for a negative effect of government debt on growth for either growth either in the short run (the next five years) or in the long run (as indicated by growth from five to ten years later).

Even though the estimated slopes are still small, we also discuss why this difference -- between small negative and small positive numbers -- matters for policy. For more, be sure to read the full post here.

Instrumental Tools for Debt and Growth

A Joint Post by Miles Kimball and Yichuan Wang

In a recent Quartz column, we found that high levels of debt do not appear to affect future rates of growth. In the Reinhart and Rogoff (henceforth RR) data set on debt and growth for a group of 20 advanced economies in the post WW-II period, high levels of debt to GDP did not predict lower levels of growth 5 to 10 years in the future. Notably, after controlling for various intervals of past growth, we found that there was a mild positive correlation between debt to GDP and future GDP growth.

In a companion post, we address some of the time window issues with some plots how adjusting for past growth can reverse any observed negative correlation between debt and future growth. In this post, we want to address the possibility that future growth can lead to high debt, and explain our use of instrumental variables to control for this possibility.

One major possibility for this relationship is that policy makers are forward looking, and base their decisions on whether to have high or low debt based on their expectations of future events. For example, if policy makers know that a recession is coming, they may increase deficit spending to mitigate the upcoming negative shock to growth. Even though debt may have increased growth, this would have been observed as lower growth following high debt.On the other hand, perhaps expectations of high future growth make policy makers believe that the government can afford to increase debt right now. Even if debt had a negative effect on growth, the data would show a rapid rise in GDP growth following the increase in debt.

Apart from government tax and spending decisions informed by forecasts of future growth, there are other mechanical relationships between debt and growth that are not what one should be looking for when asking whether debt has a negative effect on growth. For example a war can increase debt, but the ramp of the war makes growth high then and predictably lower after the ramp up is done and predictably lower still when the war winds down. So there is an increase in debt coupled with predictions for GDP growth different from non-war situations. None of this has to do with debt itself causing a different growth rate, so we would like to abstract from it. 

To do so, we need to extract the part of the debt to GDP statistic that is based on whether the country runs a long term high debt policy, and to ignore the high debt that arises because of changes in expected future outcomes or because of relatively mechanical short-run aggregate demand effects of government purchases as a component of GDP. Econometrically, this approach is called instrumental variables, and would involve using a set of variables, called instruments, that are uncorrelated with future outcomes to predict current debt.

Since we are considering future outcomes, a natural choice for instrument would be the lagged value of the debt to GDP ratio. As can be seen below, debt to GDP does not jump around very much. If debt is high today, it likely will also be high tomorrow. Thus lagged debt can predict future debt. Also, since economic growth is notoriously difficult to forecast, the lagged debt variable should no longer reflect expectations about future economic growth.   
By using lagged debt and growth as instruments, we isolate the part of current debt that reflects debt from a long term high debt policy, and not by short run forecasts or other mechanical pressures. We plot the resulting slopes on debt to GDP in the charts below, for both future growth in years 0-5 and for future years 5-10. For the raw data and computations, consult the public dropbox folder.


From these graphs, we can make some observations.

First, almost all the coefficients, across all the different lags and fixed effects, are positive. Since these results are small, we should not put too much weight on statistical significance. However, it should be noted that the plain results, OLS and IV, for both growth periods are all statistically significant at at least the 95% confidence level, and the IV estimates for the 5-10 year period in particular are significant at the 99% confidence level.

The one negative estimate, OLS estimate with country fixed effects, has a standard error with absolute size twice as large as the actual slope estimate.Moreover, country fixed effects are difficult to interpret because they pivot the analysis from looking at high debt versus low debt countries towards analyzing a country's indebtedness relative to its long run average.

These results are striking considering therobustness with which Reinhart and Rogoff present the argument thatdebt causes low growth in their 2012 JEP article.Yet instead of finding a weaker negative correlation, aftercontrolling for past growth, we find that the estimated relationship between current debt and future growth is weakly positive instead.

Second, when taking out year fixed effects, there is almost no effect of debt and future . Econometrically, year fixed effects takes out the average debt levelin every year, which leaves us analyzing whether being more heavilyindebted relative to a country's peers in that year has an additional effect on growth. Because this component isconsistently smaller than the regular IV coefficient, this suggests,for the advanced countries in the sample, it's absolute, not relative, debt that matters.

This should be no surprise. As most recently articulated in RR's open letter to Paul Krugman, much of the argument against high debt levels relies on a fear that a heavily indebted country becomes “suddenly unable to borrow from international capital markets because its public and/or private debts that are a contingent public liability are deemed unsustainable.” The credit crunch stifles growth and governments are forced to engage in self-destructive cutbacks just in order to pay the bills. At its core, this is a story about whether the government can pay back the liabilities. But whether or not liabilities are sustainable should depend on the absolute size of the liabilities, not just whether the liabilities are large relative to their peers.

Now,our conclusion is not without limitations. As Paul Andrew notes,the RR data set used focuses on “20 or so of the most healthy economies the world has ever seen,” thus potentially adding a high level of selection bias.

Additionally, we have restricted ourselves to the RR data set of advanced countries in the post WW-II period. The 2012 Reinhart and Rogoff paper considered episodes of debt overhangs from the 1800's, and thus the results are likely very different. However, it is likely that prewar government policies, such the gold standard and the lack of independent monetary authorities, contributed to the pain of debt crises. Thus our timescale does not detract from the implication that debt has a limited effect on future growth in modern advanced economies.

In their New York Times response to Herndon et. al., Reinhart and Rogoff “reiterate that the frontier question for research is the issue of causality”. And at this frontier, our Quartz column, Dube's work on varying regression time frames, and these companion posts all suggest that causality from debt to growth is much smaller than previously thought.

Innovations in Data in Economics

Imagine you are tasked with investigating the effect that household income changes have on a certain variable, such as the risk of war. But unfortunately, war can affect growth, so how can you disentangle the twoway causality? Check the weather.

In fact, the above approach is precisely the approach used in one of the most influential papers on the relationship between economic growth and civil violence. As Collier notes in The Bottom Billion, because many developing countries depend on agriculture, getting too little or too much rain can severely affect growth. But fortunately for us economists, "prospective rebels do not say, 'it's raining, let's call off the rebellion'". As such, rain functions as an instrumental variable that allows us to proxy for the effect of growth on war, but avoids the effect that war has on growth. Besides in the study of civil conflict, rainfall shocks have long been used to investigate a diverse range of issues, which can range from the role of remittances as insurance, human capital accumulation, and sex-selection. While rainfall shocks seem like quite an obvious tool after the fact, I cannot help but smile at the thought of using them as such a, pardon the pun, instrumental part of research on development.

It also makes me smile because it excites me about what other data sources economists will have to leverage in the future. For example, an important part of Mian and Sufi's work on the effects of subprime mortgages was Saiz' house price elasticity data. Saiz calculated house price elasticities in metropolitan areas based on very specific geographic properties such as the percentage of area covered by water or the presence of steep terrain. He was able to generate such a thorough dataset by using satellite and topological data. Such computations, while impossible a few decades ago, are now much simpler. From the comfort of my apartment, I can easily pull up a street level map of New Delhi* and customize it using open source R. And if even I can manipulate such powerful tools from the comfort of my laptop, just imagine the new opportunities that could open up as the result of concerted research.

Other writers have commented on this "new generation" of economic data, but I think the studies discussed above add a little color on what more data really provides us.

It's tempting to say that more data will give us more correlations to work with and better predictive power. This is not necessarily the case as the number of spurious and uninformative correlations necessarily increase as the amount of data analyzed rises. However, something Big Data does give us is a better way to organize all the "natural" data sitting out there in the world. When Watson was introduced, attention shifted to the possibilities that a "personal Watson" could have on tasks that involved large database searches, such as medical care or legal research. There is no reason for economists to not share in these benefits. Many clever studies pivot on a very clever design, whether rainfall shocks or regression discontinuities because of geography. Thus Big Data may become less of a tool for direct prediction, and instead become an indispensable tool for economists to identify and deploy increasingly clever instruments and natural experiment designs.

This kind of "data mining" would not be so much as for finding correlations but to enrich the datasets that we have available. As I found out this year working on a housing finance project working with the AHS, privacy is a big deal in surveys. But with the possiblity of estimating non-economic public variables such as weather or geography, we have ever more powerful tools for estimating parameters for large groups while preserving the privacy of individual people. And even if merging individual entries is always difficult when comparing multiple datasets, such common public variables would allow us to create a base set of variables to enrich any dataset and analysis.

This change in data capabilities also has implications for the intellectual tools needed by economists to understand the data. While rigorous econometrics, especially spatial econometrics, will stay very important, it may become more important than ever to have a solid foundation in economic history. In the wake of the financial crisis, it has been fashionable to talk about how economic history would have given us a better idea of how to respond to the crash. Yet even beyond these policy implications, a better understanding of economic history could motivate the mining of old data sources, such as newspapers.

A Google scholar search for "rainfall shocks" or "rainfall shock" yields about 1400 results. What will be the future analogous tool for other fields of economics?

*On google maps, go to New Delhi and start scrolling to the west. While you are amazed by the ability to discern individual streets and apartment buildings, observe the dramatic change to a checkerboard of individual farm plots. In fact, the first time I saw this I thought the graphics resolution on my computer messed up the rendering.

A Beginner's Observations with STATA

This year, I have been occupied with a real estate finance project through the Undergraduate Research Opportunities Program here at the University of Michigan. Below are some observations about STATA that may be of use for some people.


1. Macros are useful, but rather peculiar. As a first time user, I found it very difficult to differentiate between when I should use "`variable'" and `variable'. From what I see, any time that the variable is meant to denote a string, it should be enclosed as "`variable'", whereas if it supposed to be a variable call or something of that sort, it should be`variable'

2. STATA is programmable, but not necessarily a 'programming' language. When working in STATA, you don't really have the flexibility that you would have in R or Python. It's difficult to make arbitrary functions, and sometimes I just want to say "int x = 4;", but there's no natural way to implement that. Another STATA construct that I had to familiarize myself with was the "foreach" command. It does do a natural way of iterating over an array in other languages, but I often get caught typing "for" by mistake.

3. If only I understood if's, my life would be easier. In STATA, there's two kinds of if's, one is a qualifier, and one is the standard if in programming that changes the flow of the program. For example, if I were to say

count if smsa == 0320

It would count the number of observations whose smsa variable entry was 0320. On the other hand, if I had

if(`nat'){
di "Merging with smsa control"
merge 1:1 smsa control using "tmortg`y'_`d'"
}
else{
di "Merging with control"
merge 1:1 control using "tmortg`y'_`d'"
}

The program would merge the file by smsa control if `nat' is true, and it would merge by just control otherwise.

4. On the above note, it may be useful to put a few display statements in your code. It's helpful to see  in the log where the program went, especially when there's these flow control issues.

5. While writing functions may be hard, it is certainly not impossible. To this end, the guide by Roy Mill was invaluable for me. I was able to more effectively abstract my code and reconcile it with my programming instincts.

6. Careful with do files and local variables. After I declared local variables in my do files, I could not access them once I was back in interactive mode. However, I had no problem with those local variables when I was working within the do file.

And for those STATA veterans among you, is there any way to do error handling? In Java, C++, Python, and R, there are tryCatch constructs that can keep the program running even if a variable is missing. This would be useful because it would allow the program to try to do something, and then if that doesn't work I would like to make the program go down a different path.

Any additional advice on STATA would be appreciated. Hope my observations can help some others avoid (too much) frustration.

NBER Macrohistory: A Few Interesting Results

As I was browsing the FRED database for data, I noticed the front page posting of academic historical data that covers various time series that cover the time between the mid 1800's to the mid 1900's. It's quite amazing the wealth of data available, and I thought I would corroborate some conclusions that fellow bloggers and I have regarding the impact of certain economic policies and phenomena.

First exhibit: Openness to Trade

While the Bretton Woods period after the Gold Standard is typically characterized as a dark era for international trade, in reality trade grew at a steady clip. From 1870 to 1944, trade grew an average of 4.0% every year, whereas during the Bretton Woods period, from 1944 to 1971, trade grew at about 6.6% per year. However, after the breakup of Bretton Woods, trade boomed, with yearly growth in trade averaging 9.6%. This corroborates Evan's analysis that trade went parabolic in the 1970's as global trade barriers steadily went down. I've graphed the data below in terms of log of the index, so the distance between two vertical values is actually a measure of percent change, making historical comparisons much simpler.

Looking at the data, we can also see that, among the post war recessions, trade has fallen the most in percentage terms in the Great Recession than in any other recession. A close inspection indicates that it still has not caught up with the pre-recession trend, but an even closer inspection indicates that the lack of catch-up growth should not be too surprising, as in the last two recessions, trade never caught up to the pre-crisis trend.

Second exhibit: Price Stability

Prices were incredibly stable during the Gold Standard era, to the point of bordering on pathology. The prospect of decades of deflation is unthinkable now, but it was something that Americans had to deal with during the time period from 1880 to 1900. It's amazing to think that the price level was fundamentally controlled by gold discoveries, as the mid 1860's boom in the price level can be directly traced to the gold rush during that time period. Yet as production rose, the price level fell, the natural result of a commodity price regime in which the supply of the commodity is severely limited.

The behavior of prices during the interwar period is also interesting, as prices doubled with the beginning of World War I, and then collapsed 40% with the onset of the Great Depression. And during the Great Depression, although FDR's dollar debasement strategy did work to significantly raise the price level, it was not enough to return it to its pre-war trend before he cut it off with his policy reversals in 1937.

Third Exhibit: Turn of the Century Wage Levels

This provides an interesting complement to the price stability graph because it seems to show that the rise and fall in the price level were the ultimate drivers of the wage rate, and not so much other factors such as the extremely large flows of immigrants in the late 1800's and early 1900's. By looking at the graph, it would be impossible to try to pin down when immigration was at its highest or when restrictions on immigrants were put into place. This goes down as a historical point to explain in debates about unskilled immigration and wage rates, a some of the most prosperous periods of American history took place side by side with large immigration flows. On the other hand, hard money seems to be a serious issue holding back wage growth, so this graph should help in showing how problematic the Gold Standard truly was and how a similar commodity standard today would be seriously detrimental to necessary growth in nominal GDP.

Nominal and Real GDP: A Barrier to a Statistical Approach

Scott Sumner regularly talks about how almost all discussions of inflation become much clearer in terms of NGDP. This is because people have a hard time differentiating between inflation as a result of more aggregate demand (demand-push) and inflation as a result of less aggregate supply (cost-pull). The difference is summarized in the textbook aggregate demand/aggregate supply diagrams below:

Aggregate demand expansion = Inflation

Aggregate supply contraction = inflation

The first kind of inflation changes NGDP, while the second has minimal impact. This way, when we are in a recession and demand more inflation, what we really mean is that we need more of the first kind of inflation because we need more NGDP. If we were in the second situation, we wouldn't be demanding more or less NGDP because the supply shock would have had minimal impact.

Another example in which NGDP makes explanations easier is in discussions of whether deflation is bad in an economy. Often times, liberal economists will point to the recent recession and say deflation is bad, while libertarians might point to the late 19th century, early 20th century and say that deflation is good. The more correct answer is that stable NGDP is best. So because the first kind of deflation reduced NGDP, it was bad, while the second type of deflation kept NGDP steady, and therefore was good.

While NGDP is simple, it makes it hard to statistically show NGDP boosts RGDP. You can't look at a graph and point to any correlation; a skeptic could just say that it's the RGDP that's driving the movements in NGDP, and not the other way around. In the end, to explain the relationship between nominal and real output in AD shocks, I have to find specific channels, such as nominal debt. On the other hand, inflation and output make much more sense in terms of trying to find statistical relationships. These concepts are far enough in people's minds that a relationship doesn't seem like a tautology. However, when you start directly talking about NGDP and RGDP, it's too easy for people to think the observed relationship between NGDP and RGDP is just because the second is a component of the first.

NGDP Autoregressions and the Lucas Critique

Is NGDP growth sticky? In other words, does above NGDP growth in one period affect GDP growth in the next? Evan Soltas has previously shown that RGDP appears to be sticky. He constructed some impulse response functions and found that there is no instantaneous self-correction mechanism. On the nominal side, there is substantial evidence indicating that inflation is sticky. The correlation coefficient for the relationship between the current inflation rate and the inflation rate measured one quarter ago is 0.75. Another way of saying this is that about 50% of the variability in current inflation can be predicted by inflation one quarter ago.

Does NGDP, the sum of inflation and RGDP, suffer from the same stickiness? If it does, this could have serious implications for NGDP level targeting. If it takes a long time for past NGDP surges to slow down, this could affect the speed at which central banks can change expectations of NGDP. central banks may need to take even more drastic action to adjust NGDP at the necessary speed, causing monetary policy to be blunt and not credible.

To answer this, I looked at the NGDP time series from 1947 to today and constructed a multiple regression model to explain the current NGDP continuously compounded annual rate of growth as a function of the NGDP growth rate for the past six quarters. As only the coefficients for the past two quarters were statistically significant at the 95% confidence level, I settled with testing NGDP as an AR(2) model. The results of my regression are listed below:

Call:

lm(formula = n[, 1] ~ n[, 2] + n[, 3])

Residuals:

     Min       1Q   Median       3Q      Max 

-14.5968  -2.1681  -0.1866   2.0848  13.5262 

Coefficients:

                 Estimate  Std. Error t value   Pr(>|t|)    

(Intercept)  2.82257    0.47431   5.951     8.93e-09 ***

n[, 2]         0.43320    0.06257   6.923     3.67e-11 ***

n[, 3]         0.13255    0.06250   2.121     0.0349 *  

---

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 3.943 on 251 degrees of freedom

Multiple R-squared: 0.2631,     Adjusted R-squared: 0.2572 

F-statistic:  44.8 on 2 and 251 DF,  p-value: < 2.2e-16 

From this, we can say that about 26% of the variability in current NGDP growth is explained by past NGDP growth. To get a better idea of what the relationship looked like, I also plotted the predicted values of NGDP versus the actual values:

While the intercept is not statistically significant different from zero, the slope is 1, with standard error of 0.10, suggesting that the model does do a reasonable job of estimating actual NGDP. So does this data prove NGDP is sticky, making instantaneous NGDP expectation adjustment impossible?

As with most economic questions, the answer is "not necessarily". Perhaps NGDP is sticky because of certain nominal frictions in the economy, such as staggered wage contracts or menu costs. These traits, while they endow nominal shocks with real effects, also mean that nominal levels in the economy have momentum. If wages are suppressed for extended periods of time, the economy would be able to stay at higher levels of aggregate activity for longer. Alternatively, information itself can be sticky. So even if economic agents stand at the ready to change prices and to be flexible, they don't observe economic conditions quickly enough, acting in a way that creates nominal momentum.

A first pass analysis would suggest that these frictions would fundamentally limit the ability of NGDPLT to achieve stability. If elevated current NGDP always predicts elevated future NGDP, then there would be no way for a central bank to credibly commit to quick NGDP corrections.

However, given some recent discussion of Milton Friedman's thermostat, we have to ask if this result is regime dependent. Take inflation for a concrete example. The Federal Reserve has, for most of its recent history, targeted the rate, not the level of inflation. What this means is that if the Fed overshoots one year, there's no expectation for the Fed to compensate with lower than normal inflation for the next year. There's no expectation for monetary policy to correct the elevated inflation, which allows all the frictions mentioned above to keep inflation persistent. But if there's an expectation that the Fed will engage in corrective policy as in level targeting, then inflation may not be as persistent. Higher inflation today would actually predict lower inflation tomorrow as the central bank quickly acts to restore the original price level trend. Applied to NGDP targeting, if people perceived that current NGDP growth was higher, they would have an expectation that future NGDP growth would be slower. They could then act on that expectation and quickly restore trend NGDP. We could also test this hypothesis by testing if inflation or NGDP autocorrelations are higher in rate targeting countries than level targeting countries. However, I do not know of any central banks that have a formal committment to any kind of level targeting, so I'm not sure how robust my results would be.

This discussion of autoregressions and NGDP stickiness is also an instance where the Lucas critique defends the effectiveness of monetary policy. While I can run a multiple regression and find "evidence" that NGDP growth is sticky, because my arguments are not microfounded I have no theoretical reason for why NGDP growth would stay sticky in a level targeting regime. So to fully understand how nominal persistence can affect NGDP targeting, we need a microfounded model that can analyze the intertrelated process of nominal frictions, policy and expectation formation: a hole that market monetarists must be able to fill.

Levels and Rates to Fill the NGDP Data Gap

An implementation of levels and rates to quickly estimate NGDP growth

An important problem with NGDP targeting is data frequency. NGDP data only comes in every quarter, and is also subject to large revisions. This is one of the stronger arguments against NGDP targeting, as the lack of data makes it hard for the market to check that policy makers are hitting their targets. Expectations don't always match reality, so it's important to have a concrete and frequently updated data source to monitor the economy.

Evan, in his musings on level and rate targeting, offers a theoretically robust alternative in the current world of flexible inflation targeting. From his post (my emphasis):

Third, given a mixed rate/level targeting regime, the Fed has what should be the rate and what should be the level backward. In the long run, the Fed has almost no control over the unemployment rate, yet almost total control over the price level; in the short run, it does have some control over real variables such as unemployment. Given those constraints, it makes far more sense to level-target the variable which the Fed controls in the long and short runs, i.e. the price level, and to rate-target the variable over which the Fed has some control in the short run, i.e. change in nonfarm payroll employment or quarterly real output growth.:

As I commented before, such an arrangement would be aligned with Okun's law, which states that year over year falls in unemployment is approximately equal to year over year real GDP growth minus 3. As a result, in Evan's formulation, the combination of change in unemployment and the change in the price level would approximate an NGDP target. His other alternative, nonfarm payroll employment, is what I want to test in this post.

Armed with the requisite FRED data, I looked to see if I could find a simple econometric relationship between YoY NGDP growth, YoY nonfarm employment growth, and YoY Headline CPI growth. In other words, I tested the relationship:

NGDP Growth = a*Inflation + b*%ΔEmployment + Constant + Error

As I'm interested in how the rule would help guide policy in the most recent "Great Recession", I calibrated the data on pre-crisis, 1948-2006  data and then saw how the model predicted NGDP growth "out of sample" for 2007-2012. It turns out that nonfarm payroll, inflation, and NGDP do form a rather tight relationship (note that I use headline inflation. Core inflation does not substantially change the conclusions). The precise rule that I get from the calibration is:

NGDP Growth = 0.517*Inflation + 1.083*%ΔEmployment + 2.968

But if we're looking for a more general, simpler rule of thumb, we can approximate it to:

NGDP Growth = 0.5*Inflation + 1*%ΔEmployment + 3

From here, we can compare the time series of the simple approximation to actual NGDP growth.

We can easily see that the measure does quite well throughout the historical period. I've already divided the graph as Marcus Nunes does for each central banking "regime", and it's clear that the composite measure exhibits the same trends as Marcus shows in his NGDP graphs.

What you do see is that, even in the out of sample period, the time series match up well. Around the end the composite measure does spike to 6% while actual NGDP growth is around 4%. However, in spite of that differential, the rule still makes very good out of sample predictions for the 2007-2012 time period:

Interestingly enough, the regression coefficient has been around one, which means there's an approximate one to one relationship between actual NGDP growth and the composite measure. About 80 percent of the variance in the composite measure is explained by the variance in NGDP growth. Of course, the relationship is not perfect, but it's really quite amazing how well the out of sample prediction holds up. So before the Fed establishes an NGDP futures targeting regime to help with the data availability problem, it can still use monthly available statistics such as CPI and changes in nonfarm payroll to approximate an NGDP target. When actual NGDP data comes out, that quarterly data can be checked against the composite measure. The higher data frequency would help cement in the Fed's credibility as the regime could be checked, thereby smoothing and enabling a transition to a full fledged NGDP level targeting regime.

P.S. While playing with the data, a statistically significant relationship between inflation and employment growth emerges. 95 confidence interval on the slope returns (0.04, 0.22). Pseudo-Philips Curve, anyone?

1970's Sumner-time Stagnation

Recently, Scott Sumner and Karl Smith have debated to what extent was the 1970's an era characterized by "stagnation" (AS shock), or just overexpansionary monetary policy. For Scott, much this debate seemed to be about retelling the stories that we learned in introductory economics. Scott reframes the issue in terms of above trend nominal GDP growth, and, along with other data about the labor markets, argues that the decade of inflation came about not because of stagflation or supply shocks, but rather because of overly loose monetary policy.

From the most basic AS/AD perspective, robust real growth in the 1970's is no indication that there was no stagnation. Given the accelerated NGDP growth, real GDP growth should have been higher, for reasons ranging from money illusion to sticky wages to sticky prices. In other words, the higher rates of nominal change meant that a short run equilibrium with higher real growth could be maintained. Had NGDP growth been slower, then we would not have been able to squeeze 3.2% RGDP growth out of the economy. In short, I disagree with the statement that:

I think Karl and I would both agree that (whether or not there was stagflation during the 1970s) under 5% NGDP targeting there definitely would not have been any stagflation."

Is there any reason for this? Scott's argument presupposes that you can decouple nominal growth from real growth. So when he says:

Growth was normal, and inflation was very high.  Rapid growth in AD explains roughly 100% of the inflation during the 1970s.  There was no stagflation, just inflation.

He presupposes the high real growth was not explained by the higher inflation. While, in the long run, higher inflation does not lead to a permanently higher level of growth, there is still a positive relationship between inflation and output in the short run. In introductory terms, this trade-off is the aggregate supply curve, and the correlation arises from increases in aggregate demand. If the high level of aggregate demand is the reason why inflation is high, the high level of AD is also the reason output is high. I don't see how they can be separated.

There are also many places one can look for data to support this hypothesis. The first is the classic shifting of the Philips curve. If the Philips curve moved outwards in the 1970's era, that meant you needed a higher level of inflation to reach any given unemployment rate. If the unemployment rate is a proxy for real growth, then this directly leads to the conclusion that higher levels of inflation allowed higher levels of real growth.

However, Scott prefers to focus on real GDP ("I had thought the word ‘stagflation’ meant high inflation plus slow output growth (due to slow growth in AS.)"), and on this issue the data still suggests that the higher NGDP growth could not be disentangled from the higher RGDP growth. The first graph is a scatterplot of 1960's data, with NGDP YoY growth on the x-axis, and RGDP YoY growth on the y-axis.


The following grpah is a scatterplot of 1970's data, with the same x and y axis data.

Looking at these two graphs, one can see that the relationship between NGDP and RDGP was very tight in both periods. While correlation does not prove causation, it's hard to think of any theoretical mechanism that could have decoupled NGDP from RGDP in either period.. Another interesting note is that the x-intercept of the 1970's data is much larger than the 1960's data. This suggests that you needed a higher level of nominal growth to hold RGDP steady in the 1970's than you needed in the 1960's. the 1970's was suffering from an overall supply shock relative to the 1960's.

As an interesting corollary to all of this, given the lack of a long-run relationship between higher nominal and real growth, you need accelerating nominal growth to prevent real growth from falling down. In a sense, in addition to the positive relationship between the first derivatives of NGDP and RGDP, there should also be a  positive relationship between the second derivatives of NGDP and RGDP.

Notably, these correlations are even stronger than the first two graphs. This lends more evidence to the argument that, had the Fed decided to decrease YoY NGDP growth, RGDP would have taken a hit. For all the power that lies within expectations, they can't take away all of the pain away from a NGDP disinflation.

What seems unexplained is why the 1970's slope is higher (with greater than 95 confidence) than the 1960's slope. If agents adapt, the same increase in NGDP growth should result in a lower increase in RGDP growth. By that theory, the 1970's slope should be less than the 1960's slope. This will be an interesting topic for future investigation.

Correlations Across Time - NGDP and Bond Yield Edition

There's a lot of interest in using futures to help determine expectations: TIPS spreads are used to forecast expected inflation, 10-year bond yields are used to forecast expected NGDP growth, and in Scott Sumner's market monetarist nirvana the central bank would use NGDP futures to help forecast NGDP growth exactly.  The central bank would then only worry about that one expectation, vastly simplifying monetary policy.

In this post, I want to focus in on the NGDP growth and bond-yield correlation.  David Beckworth offers pretty convincing evidence that bond yields are highly correlated with NGDP growth forecasts:

Forecasting can be a bit inaccurate, so Lars Christensen  has a very nice graph showing how the 10 year bond yield has been tightly coupled with the year to year growth in NGDP in any given year.

But how do these correlations or trends change throughout time?  From the FRED data, I computed foward looking NGDP growth in 10-year windows from the second quarter of 1964 to the first quarter of 2002.  I then computed the correlation between actual NGDP growth and the bond yield in 10 year windows for each date, with 19 quarters of the window before the given date and 20 quarters of the window after the given date.  With the correlation, I also computed the OLS regression slope for the regression of bond yield as the explanatory variable and NGDP growth as the response variable.  It turns out that the NGDP growth and  the bond yield have had a very tight correlation in recent windows, but that this was not always the case.



On the graph in the second half of the 1970's (which would have been the correlations between the data from 1970 to 1985 on the NGDP growth from 1980 to 1995), we can see that there is actually a negative correlation between the bond yield and NGDP growth.  This likely could have been the result of tightening by the Federal Reserve in the 1980's in response to the oil shocks.  As a result, NGDP was pushed down against expectations, thereby creating a negative correlation.  The correlation is stronger in recent times, as the 1997 data point includes data from 2012, but still the correlation is not as strong as the one Beckworth and others find for forecasters.

Another interesting point to note in recent times is that although the correlation between NGDP growth and bond yield has been fairly high, , the OLS coefficient is rather low.  Bond yield does predict NGDP growth, but not in a one-to-one relationship.  In the most recent window, a 1% increase in bond yield predicted a 0.47% increase in NGDP growth.  What's interesting about the OLS coefficient that the correlation hides is that the OLS coefficient has been increasing in recent history.  I'm still not quite sure what that means, but I feel it should have important implications for the safe assets hypothesis and expectations of future economic growth.

Take-the-Best Statistical Model

Why do we do multiple regression?

Multiple regression is the workhorse of econometrics.  Almost every empirical paper in economics relies on it, and it also forms the basis for a large majority of political science research.  But is this a valid model for prediction?  How sensitive are the results?

As it turns out, the answer is "very".  Multiple regression is sensitive to a host of issues, including normality, linearity, and low error data.  But if the real world doesn't always fit these assumptions, why do we try to use the model to predict the real world?  One thing to notice when reading the empirical papers is that they often tell you that a certain coefficient is statistically significant, but rarely does one see a given confidence interval for that coefficient.  Of course, listing confidence intervals for every coefficient, especially when there are so many, is quite cumbersome.  Yet this convenient omission often leads us to be too confident about our estimates.  How much do we really know?

Behavioral economists have long criticized this model of human decision making because there's no feasible way that we can run a regression in our head and then make a decision.  At least, I know I don't.   Although many of my friends may have used excel spreadsheets to decide where to go to college, they did not end up basing their decision on some kind of complex regression model.  It's just too computationally intractable for everyday use.

Furthermore, one key problem of multiple regression is ecological validity.  We know that the regression model predicts the sample pretty well, but does it predict the future with any accuracy?  Especially if the future is highly variable and uncertain, why should we trust our Gaussian methods that are highly sensitive to outliers? According to Gerd Gigerenzer, the most accurate rules are often not the high powered intensive statistics methods.  Rather, fast and frugal algorithms that actually limit the information they evaluate can create more accurate results.

One of the prototypical fast and frugal algorithms Gigerenzer describes is Take the Best.  While multiple regression would look at all the data and perform various tests on individual data's contribution to the dependent variable, Take the Best does a sequential evaluation of a list of key determinants.  For example, multiple regression would decide between two restaurants by looking at all the data: food quality, wait time, location, parking spots.  It would then weight each input carefully according to an equation, and then look at the results of the equations for the two restaurants.  Whichever restaurant returns the higher value is the restaurant that's chosen.  On the other hand, Take the Best would look at whether the food quality gap is high.  If so, then pick the restaurant with better food.  If the gap is not high enough, move on to the next rule and repeat this simple process.  Computationally, this would require M+1 evaluations, which is in linear time and computationally quite tractable.

Gigerenzer applied this heuristic to predicting Chicago high school dropout rates.  Given two high schools and all the associated statistics: attendance rate, proportion of low income students, social science test scores, and more, what's the most accurate way to predict which high school had a higher dropout rate?   Gigerenzer and his fellow researchers took half the population of schools and built a Take the Best model and a multiple regression model to explain the data.  No surprise, multiple regression did better, predicting over 70% of the pairs correctly while Take the Best only managed around 65%.  Yet when the two models were tested on the other half of the population, Take the Best had about a 60% accuracy rate and multiple regression barely manged around the low 50%'s.

Surprising?  Gigerenzer in Gut Feelings explains:

But why did ignoring information pay in this case? High school dropout rates are highly unpredictable-in only 60 percent of the cases could the better strategy correctly predict which school had the higher rate, (Note that 50 percent would be chance.) Just as a financial adviser can produce a respectable explanation for yesterday's stock results, the complex strategy can weigh its many reasons so that the resulting equation fits well with what we already know. Yet, as Figure 5-2 clearly shows, in an uncertain world, a complex strategy can fail exactly because it explains too much in hindsight. Only part of the information is valuable for the future, and the art of intuition is to focus on that part and ignore the rest. A simple rule that relies only on the best clue has a good chance of hitting on that useful piece of information.

Looking backwards can hurt; you might end up blindsided by what the future can hold. The data might show trends that are only valid for the sample, and not the population as a whole.  Your results won't be ecologically valid if all the data is taken into consideration.  Especially since correlations change substantially over time, Gaussian methods are more likely to offer the pretense of knowledge than knowledge itself.

This has massive policy implications.  From Gigerenzer:

According to the complex strategy, the best predictors for a high dropout rate were the school`s percentage of Hispanic students, students with limited English, and black students-in that order. In contrast, Take the Best ranked attendance rate first, then writing score, then social science test score. On the basis of the complex analysis, a policy maker might recommend helping minorities to assimilate and supporting the English as a second language program. The simpler and better approach instead suggests that a policy maker should focus on getting students to attend class and teaching them the basics more thoroughly. Policy, not just accuracy, is at stake.

Yet with these policy issues at stake, it's surprising that fast and frugal algorithms aren't used more in economics research.  One disadvantage of take the best is that it doesn't give much quantitative accuracy.  It only tells which value is higher, but not by how much.  But how much does that matter?  While multiple regression may give more statistically significant coefficients, do we really have the power to tune the economy that much?  Even the best of natural experiments don't result in parameters that don't change through time.  Romer and Romer beautifully estimate tax elasticity, but how arrogant would a person need to be to build our entire tax policy based on an estimation from an almost 80 year old data set?  DSGE quantitative accuracy is such a joke that peripheral ad-hoc models are needed to make them even somewhat useful.

These alternative statistical tools are likely to add much to our insight of models.  The development of robust heuristics will be critical in a complex world, in which calculation becomes increasingly difficult and Gaussian methods increasingly fragile.

Correlations Across Time: How Stable are the Curves?

What is the Philips curve, and how do we know it's there?   It was originally discovered by Irving Fisher in 1926 when he noted the negative correlation between inflation and unemployment.  Of course, he was not the first to realize this connection between prices and employment, as Hume commented on this exact issue almost 200 years before:

In my opinion, it is only in the interval or intermediate situation, between the acquisition of money and the rise in prices, that the increasing quantity of gold or silver is favourable to industry. . . . The farmer or gardener, finding that their commodities are taken off apply themselves with alacrity to the raising of more. . . . It is easy to trace the money in its progress through the whole commonwealth; where we shall find that it must first quicken the diligence of every individual, before it increases the price of labour

For this reason, Milton Friedman often said that modern macroeconomics has made it just one derivative past Hume.  Instead of just focusing on the first derivative and changes in the price level, we now look at the second derivative and changes in the inflation rate.

Robert Hall took this one step further in his 1986 exposition on efficient monetary policy and, instead of looking at one more derivative, looked at one more parameter.  Instead of just looking at the levels of unemployment and inflation, he theorized on the relationship between the volatility of the two variables.  He hypothesized the existence of an efficient policy frontier, a trade-off between price stability and unemployment stability that would prevent both variables from settling down in the face of periodic random shocks.

But have either of these correlations held throughout time?  The Philip's curve worked originally very well in the 1960's to 1980's, but then broke down as stagflation struck and expected inflation shifted the "stable" Philip's curve.  Thus, there seems to be a severe issue with measuring the Philip's curve; where should one start and end the observation window?  The analysis can easily become utterly meaningless, as:

To see how meaningless correlation can be outside of Mediocristan, take a historical series involving two variables that are patently from Ex­ tremistan, such as the bond and the stock markets, or two securities prices, or two variables like, say, changes in book sales of children's books in the United States, and fertilizer production in China; or real-estate prices in New York City and returns of the Mongolian stock market. Measure correlation between the pairs of variables in different subperiods, say, for 1994, 1995, 1996, etc. The correlation measure will be likely to ex­hibit severe instability; it will depend on the period for which it was com­puted. Yet people talk about correlation as if it were something real, making it tangible, investing it with a physical property, reifying it. The same illusion of concreteness affects what we call "standard" deviations. Take any series of historical prices or values. Break it up into subsegments and measure its "standard" deviation. Surprised? Every sample will yield a different "standard" deviation. Then why do people talk about standard deviations? Go figure. 

Note here that, as with the narrative fallacy, when you look at past data and compute one single correlation or standard deviation, you do not notice such instability (Taleb, The Black Swan, my emphasis).

So, in this post, I want to look at the time series data and see how the correlation evolves over time.  This is important for both the Philip's curve and the efficient policy frontier, as one can see if either of those relationships actually holds across all time periods.

Monthly CPI and unemployment data are obtained from the St. Louis Federal Reserve website, and variabilities for each variable are measured by the standard deviation of the past year's worth of observations.  Correlations were then calculated in five year windows, such that a correlation coefficient on month t is the correlation between the variables of interest in months t-59 to t.  As the concept of a standard deviation is a bit abstract and not well understood, I took the logarithms of the standard deviations, to allow an explanation in terms of percentage increases in one variable leading to percent increases in another.

Below is a tool to gain a qualitative understanding of the evolution of the correlations.  Red denotes high numbers (strong positive correlation), while green denotes low numbers (strong negative correlation).  The black lines mark every 10 years to give a sense of scale in the colorful "time series".

As expected, the correlation coefficients fluctuated throughout history. For the Philips curve, old Keynesian theory would predict a negative correlation.  However, if there's a supply shock, both inflation and unemployment move in the same direction.  This makes sense as the two major supply shocks in recent history were the negative aggregate supply oil shock in the mid 1980's, as well as the positive aggregate supply shock in the 1990's.

With this in mind, we see that the Philip's curve relationship was actually quite stable up until the 1990's.  Although the oil price shock did force the correlation positive for a short period, it quickly reverted to a negative value.  However, from about 1990 on, the correlation between unemployment and inflation became consistently, if only weakly, positive.  Since both inflation and unemployment rose in that time period, this is another piece of evidence that suggests much of the aggregate supply gains in the 1990's were steadily reversed in the 2000's.

However, the relationship between the two volatilities was not as clear cut.  A log-log regression of the unemployment volatility versus the inflation volatility over the entire 60 years yields a slope of 0.44, with a 95% confidence interval between 0.346 and 0.540, suggesting that 1% increase in inflation volatility resulted in about a 0.44% increase in unemployment volatility.  Yet this general correlation masks the variance.  Around the 1980's and 2010, the correlation was incredibly positive, while in the 1970's and 2000's the correlation is very negative.

From this, general conclusions can be made.  First, policy is not efficient.  Even if there were an efficient policy frontier, we're not on it.  The many zones of positive correlation indicate that there's much more monetary policy can do to limit volatility in the two variables.  Second, that there are interesting things going on with transmission mechanisms that would cause uncertain inflation to translate to uncertain output.  Third, if there are severe risks to inflation volatility, it may be in our interest to lower unemployment volatility as well.  Moderating the relationship between these two variables may become one of the biggest benefits of NGDP targeting, as uncertainty along the Philips curve may cause movement towards higher levels of volatility.

What is with inflation expectations? Analysis from Cleveland Fed Data

After working with TIPS data in a previous post, I became more interested in the relationship between inflation expectations and actual inflation over time.  Generally, as per a paper by Mankiw, Reis, and Wolfers, inflation expectations can be highly contentious, with uncertainty among Economists especially high in times of crisis.  However, even though the data suggests that inflation expectation are well correlated with past inflation, the hypothesis of rational expectations and inflation predictions is a bit more uncertain.  In the Mankiw et al. study, the short term predictions of the Michigan, Livingston, and Survey of Professional Forecasters seemed reasonably accurate; how does this accuracy carry over to longer term measures of inflation expectation?

However, since the TIPS data does not go back very far, I used the Cleveland Fed's inflation expectation data instead.  And as per some comparative analysis between the two measures, the Cleveland Fed data can be more descriptive in times of major change, which is when the stability of expectations is the most important.  From the CPI data, I calculated the actual inflation over the future timeframe of the expectation, and then associated this inflation rate with each month's inflation expectation data starting from January 1982.  Thus, for the 5-Year inflation expectation data for January 1982, the actual inflation was the average annual inflation from January 1982 to December 1986.  These two numbers formed a point.  I then took 60 of these points (five years), and used them to calculate a Pearson's r-value, a measure of the correlation between the two values.  For example, the set of data beginning with a point in January 1982 includes the inflation data from December 1992 to make the last calculation for actual inflation.  The movements of the different correlations are plotted below:

What is immediately apparent is that the stability of the relationship changes with time.  During the second half of the 80's, expectations matched reality quite well, with an r-value of over 0.9 for the 5 year expectation data.  This seems to match the rational expectations proposition that the expectation should be the reality.  However, beginning with the 90's, the correlation between inflation expectations and actual inflation became more negative.  What is striking is that the correlation kept on going down, reaching almost -0.8 with the 5 year expectation.  The correlation is consistent with the r value of about -0.73 with the TIPS data, lending credibility to the fact that Cleveland Fed predictions are theoretically robust.

What is more interesting than the correlations are the slopes; an increase in expected inflation predicts how much of an increase in actual inflation over the future period?  The data is graphed below.  A value of 1 means that for every percentage point increase in inflation expectations in a period, the actual inflation in the corresponding term is 1 percentage point higher.

Before looking at the actual numbers, what should we expect the slope to be?  In a world of perfect rational expectations, in which , the slope should be one.  Although there may be error, the expectation should, on average, match reality.  In the world of an inflation targeting central bank (with or without rational expectations), the slope should be 0, as actual inflation should always gravitate towards a constant.  This analysis of central banks is supported by comparisons between US (non-inflation targeting) and UK and Swedish (inflation targeting) central banks.  Below are both the time series of the slopes, as well as box and whisker plots showing the distributions of the slopes.

As can be seen from the time series, the slopes don't stay constant.  Rather, they jump around, with the 1-Year slope value substantially more volatile than the 5 or 10 year slopes.  In spite of this, the median of the slopes do lie around zero.  However, their distributions are skewed right, with the outliers mostly coming from the mid 1980's to the early 1990's time period, which was the time after the brunt of the Volcker disinflation.  The amazing convergence of measures at that time suggest it has something to do with people adjusting to a new monetary regime.  It is as if, in the transition to the fight against inflation, people were able to accurately predict the new stable regime, creating the high correlation as people lowered their expectations of inflation.  Later, as the regime became stable, the correlation became weaker as noise gained a proportionally larger effect.

But then what explains the negative slopes in more recent times?  One interpretation is that they're statistical anomalies: the 1 year data goes much farther and, while it does have a few blips into negative slope, they revert back to mildly positive relatively quickly.  Given this volatility, we will have to wait for more data to try to evaluate the impact of the regime on inflation and their expectations.