Four times they call it a "coding error"

From WSJ: Reinhart, Rogoff Admit Excel Mistake:

Herndon, Ash and Pollin accurately point out the coding error that omits several countries from the averages in figure 2.

If you're not so hot with Excel, I guess you could call it a "coding" error. It's a goddam click-and-drag mistake, that's all it is. An embarrassingly amateurish mistake.

Here's the thing: When they selected the values for a list of 20 countries, they missed the last five values. Konczal has a screen clip:
New link for the Konczal post, 25 April 2018

See the dark blue rectangle with a dot in each corner? Column L, rows 30 to 44. That's a "range" of cells that somebody used in a calculation.

What calculation? Lower right corner, Cell L51, the calculation begins with an equal sign and takes the average value of the cells in the dark blue box.

The blue box should have gone all the way down to row 49. If it did, it would have included one more actual value. Would it have made much difference? I don't know. But the cell-selection would have been right, at least.

If I made a mistake like that in a spreadsheet at work, the boss would somehow figure it out right away and I'd get reamed for it, fairly. And then we would go back to work. So should y'all now.


Having gone back to work myself, the focus of this post changes.

Last December, in Simulacron: Make that three trends I showed this graph of inflation-adjusted GDP with three different trend paths:

Graph #1: Stages of the slowdown in real growth

I wrote:

By the fourth quarter of 2007 when real GDP reached 13.3 trillion, blue trend GDP was 17 trillion, more than 25% greater.

Twenty-five percent.

In the "R&R Admit" post linked at the top, Reinhart and Rogoff write:

It is utterly misleading to speak of a 1% growth differential that lasts 10-25 years as small. If a country grows at 1% below trend for 23 years, output will be roughly 25% below trend at the end of the period, with massive cumulative effects.

Twenty-five percent. Reinhart and Rogoff got this one right, guys.

Give 'em a break.

// 10:54 pm Update:

Come to think of it, the Gross Federal Debt fell from over 90% of GDP in the late 1940s to just over 30% in 1974, skidded along the bottom until 1981, and then started going up:

Graph #2: Gross Federal Debt as a Percent of GDP

According to Graph #1, the economy grew with vigor until the Federal Debt reached a low point. And then, with Federal debt at a low, the economy lost its vigor. And for the three decades since the early 1980s the economy grew about 1% slower than in the three decades before the early 1980s.

So according to these two graphs, one could say it was the lowness of the Federal debt that caused the slowdown in economic growth.

And as Reinhart and Rogaine point out, a long period of 1% slower growth has "massive cumulative effects".

What everybody seems to miss in all of this, is that when the Federal debt was high in the early years of Graph #2, private debt was at a low point. Today the Federal debt is high again, and private debt is also at a high point.

In the early years, accumulated private debt did not interfere with private sector growth. Today it does.

Ya just gotta laugh

From WSJ's Reinhart-Rogoff Response:

On a cursory look, it seems that that Herndon Ash and Pollen also find lower growth when debt is over 90%...

Wrong Problem

Background post: Economic Performance: The Record.

Old Krugman, May 24, 2010, 3:31 pm:

Did The Postwar System Fail?

I’ve been posting about the contrast between the popular perception on the right that America had slow growth until Reagan came along, and the reality that we did fine pre-Reagan, in fact better; see here, here, and here.

I went looking there, there, there, and at my regular hangout.

May 22, 2010: Krugman paraphrases Richard Green, saying "growth has actually been slower since the big rightward shift circa 1980." And he shows a graph of median family income suddenly slowing down circa 1968.

May 23, 2010: Same graph, and this note: "...if you look at income per hour it’s actually worse than the median income."

May 24, 2010: Well, here's something:

Scott Sumner says that I’m wrong about taxes, regulation, and growth, because although American growth has slowed since deregulation and all that, the growth has been better than we might have expected.

We can try to parse whether that’s true — but in any case it’s not a response to my original point. That was about the claim, quite common on the right, that the US economy was stagnant until Reagan did away with those nasty New Deal policies...

So then, Sumner:

For those of you not old enough to remember 1980, let me explain... There was garbage piling up in the streets of London. Britain had been the sick man of Europe for decades, growing far more slowly than Germany, France and Italy. The US wasn’t doing as badly, but certainly wasn’t doing that well either. We had also been growing much more slowly than Europe and Japan...

Krugman makes the basic mistake of just looking at time series evidence, and only two data points: US growth before and after 1980. Growth has been slower, but that’s true almost everywhere. What is important is that the neoliberal reforms in America have helped arrest our relative decline...

...neoliberal reforms lead to faster growth in real income, relative to the unreformed alternative.

Yep: Scott Sumner says American growth has slowed since deregulation and all that, but that the growth has been better than we might have expected otherwise had.

Then, finally, some meat. Sumner says:

The neoliberal revolution occurred precisely because growth was slowing almost everywhere in the 1970s and 1980s, and after 1980 growth slowed the most in those countries that reformed the least.

And this:

I am not denying that growth in US living standards slowed after 1973, rather I am arguing that it would have slowed more had we not reformed our economy.

As for myself, I'm not denying that Supply Side economics helped boost the supply side. I'm just saying it didn't solve the problem.


On a related note, I have a problem with Scott Sumner's analysis. Growth was slowing in the 1970s, Sumner says.

Sure, because the Fed kept creating recessions to slow things down. Because of the inflation.

But the problem was not that growth was slow. Slow growth was a policy goal in the 1970s. If growth was slowing in the 1970s, it was a policy success. It is utterly wrong to turn that around now and pretend that slow growth was the problem.

Sumner is analyzing the wrong problem. They all are.

John Law's Financial System... It sounds oddly familiar

From Famous First Bubbles (PDF, 1990, 20 pages) by Peter M. Garber:

John Law's Financial System

Both the Mississippi and South Sea Bubbles can be best understood in the context of the monetary theory and system created by John Law. Law is not well-known today, but Schumpeter (1954, p.295), for example, is unreserved in praising him: "He worked out the economics of his projects with a brilliance and, yes, profundity which places him in the front ranks of monetary theorists of all times."

Law (1705) sketched a monetary theory in an environment of unemployed resources. In such an environment, he argued (1760, pp. 190-91), an emission of paper currency would expand real commerce permanently, thereby increasing the demand for the new currency sufficiently to preclude pressure on prices.

From the Journal of Economic Perspectives -- Volume 4, Number 2 -- Spring 1990. Via Reddit, submitted by timhuge. (Highlighting mine.)

Jim Tankersley: "Is slow growth America’s new normal?"

At the Washington Post, Jim Tankersley:

Still, many economists, even the ones holding to the “bad luck” story, agree that something has changed in the economy post-recovery; our fireballer, they say, appears to have lost some speed on his fastball permanently. The easiest way to see that is in prices... Prices aren’t rising very fast, even with aggressive monetary easing, but the fact that they aren’t falling probably suggests the demand void — the untapped potential in the economy — isn’t as big as forecasters once thought.

No.

First of all, the argument is based on prices. As if economists understood the forces that drive prices. Tankersley tells the same old "demand-pull" story, the same story you get everywhere from Friedman and Schwartz to Bill Mitchell. But demand-pull stopped being the correct story just about the time Friedman and Schwartz published their book in 1963.

To understand what drives prices now, you have to think cost-push. You have to figure in the cost of finance. You have to allow for the drag, allow for the sluggishness created by the cost of finance. And then you have to allow for all the policy fixes put in place since stagflation arose in the 1970s, fixes that mostly reinforced the problem.

To say that prices aren’t falling "suggests the demand void ... isn’t as big as forecasters once thought" oversimplifies the problem immensely. To say the least.

// Coincidentally related: Analyzing the present

Dunno how I missed this...

Previously, comparing the real non-Federal deficit to the size of the economy, I missed the fact it was as low in the early 1990s as it was before the mid-1960s:

Graph #1: Change in Debt Other Than Federal (Adjusted for Inflation) Relative to Real GDP

The economy was good then, in the 1950s and '60s.

After the 1986-1992 decline, the trend turned around and the economy was good again in the 1990s. Until those deficits got too big, again. And just to be clear, we're not talking Federal deficits here. We're talking everybody else's deficits.

People always say bigger is better. But with debt and deficits, bigger is more costly.

And "costly" means trouble for growth.

Average it is, then

How does FRED think? When you take a time series that's given in "quarterly" values and you change the aggregation to "annual" values, how does that work exactly?

In particular, I'm thinking of the GDP Deflator. You know: the one where the 2005 value is 100, making it easy to compare prices of other years.

GDPDEF, FRED's GDP Deflator, defaults to quarterly values. So, which of the four quarters of 2005 has the value 100??? None of them, as it turns out:

Graph #1

Second quarter is a little low, third quarter is a little high. First and fourth are worse. I figured as much. It's gotta be the annual numbers that will turn up the special value that has to be there.

But when you look at FRED's GDPDEF page and change the aggregation from quarterly to annual, an option field appears asking whether you want average, sum, or end of period aggregation. Three ways to turn the four quarterly values into the value 100. Which method will work?

I was pretty sure that "sum" would take the four values from 2005 -- all of them in the neighborhood of 100 -- and add them together to give me a result in the neighborhood of 400. And yes, that is what happens. So the "sum" option is not the one.

We are left with two options: the average of the four values, or the last of the four. When you switch quarterly data to annual aggregation, FRED defaults to average aggregation. So I figured that one would give me the value 100. But just to be sure, I plotted the data both ways:

Graph #2: Aggregation by Average of Values (blue) and by Last of Values (red)
Click Graph for FRED Source Page

The second set of red and blue of bars, second from the left, shows the blue bar right there at 100.0, and the red bar higher. For me, this confirms that the well-known GDP Deflator value 100, at FRED at least, is the average of the quarterly values.

I downloaded the numbers, just to be sure. The value for 2005 is 99.993. Close enough for government work. Funny thing, though: It's off by double-o-seven.

Analyzing the present

I got to the middle of page 2 of Christopher A. Sims' Paper Money (PDF, 40 pages) before I had my first reaction: He is analyzing how the economy works now, rather than how we got into this situation.

I don't think his is a productive approach.


Yes, actually: analyzing how the economy works now. You can see it in the opening sentence of the paper's Abstract:

Drastic changes in central bank operations and monetary institutions in recent years have made previously standard approaches to explaining the determination of the price level obsolete. Recent expansions of central bank balance sheets and of the levels of rich-country sovereign debt, as well as the evolving political economy of the European Monetary Union, have made it clear that fiscal policy and monetary policy are intertwined. Our thinking and teaching about inflation, monetary policy and fiscal policy should be based on models that recognize fiscal-monetary policy interactions.

Well, maybe, it'll be useful if it leads to an improved analysis of how we got into this situation, so that we can understand what's wrong with where we are today.


Skipping to the conclusion. Sims writes:

The kinds of models that have been the staple of undergraduate macroeconomics teaching, with price level determined by balance between “money supply” and “money demand”, and money supply described using the “money multiplier”, are obsolete and provide little insight into the policy issues facing fiscal and monetary authorities in the last few years. There are relatively simple models available, though, that could be taught in undergraduate and graduate courses and that would allow discussion of current policy issues using clearer analytic foundations.

Existing models are "obsolete", he says. They "provide little insight into the policy issues facing fiscal and monetary authorities". Sims prefers different models, ones that better describe how the economy seems to operate in the years since the crisis.

I cannot emphasize enough how wrong this is. If we base policy on current conditions, we are accepting current conditions as normal. But these are abnormal conditions. The fact that policy has so far failed to rectify the situation, and that the abnormal has continued on now for several years, does not make the abnormal normal.

It's up to you, I guess. If you want to accept higher unemployment and lower GDP growth as normal, then you will choose to look at things the way Christopher Sims looks at things. But if you want to fix those problems, then you need to look at the economy when it was good and see what changes there have been since that time, and try to work out an explanation along those lines.

// Coincidentally related: Jim Tankersley: "Is slow growth America’s new normal?"

Seeing for myself

I looked before at the Econbrowser guest post The Myth of 'Jobless Recoveries' by Laurence Ball (Johns Hopkins University), Daniel Leigh (IMF) and Prakash Loungani (IMF).

Since then I found Kurt Annen's Visual BASIC code for calculating Hodrick Prescott values. So now I can try again to duplicate the graphs from the Econbrowser post, and maybe learn more about them.

From that post:

Using annual U.S. data from 1948 to 2011, we find that the Okun’s Law has a coefficient of –0.4 or –0.5, with an R² in the neighborhood of 0.8. Chart 1 illustrates the fit of the estimated Okun’s Law by plotting the unemployment gap (the gap between unemployment and the natural rate) against the output gap (output relative to potential). The relationship is very tight. No year is a major outlier in the graphs.

Chart 1. United States: Okun’s Law, 1948-2011 (Annual data) (Natural Rates Based on Hodrick-Prescott (HP) Filter with λ = 100)

NOTE: In the Econbrowser article the text reads "...a coefficient of –0.4 or –0.5, with an in the neighborhood of 0.8." Something is obviously missing between the words "an" and "in". I tracked down Laurence Ball at IDEAS, clicked the IMF link to paper, opened the PDF Okun's Law: Fit at 50?, and searched it for the phrase "coefficient of –0.4". Yup, what's missing is "R-squared", given in the PDF as capital R with an overbar, followed by a superscript 2. So I inserted that into the Econbrowser excerpt.


I went to FRED for "annual" data on "unemployment" and "output". Retrieved the seasonally adjusted Civilian Unemployment Rate UNRATE and seasonally adjusted Real Gross Domestic Product GDPC1. For both I selected "annual" data and the default aggregation method, "average". Used Excel to calculate the Hodrick Prescott values and figure the gaps -- the differences between the FRED values and the HP values. Created a scatterplot showing gap versus gap:

Graph #2

Well I'll be darned. The chart's a good match. I got my axes the wrong way around from Chart 1, but the data points are definitely grouped along the trend line, and I even got an R² comparable to the 0.8 reported in the Econbrowser post. And no major outliers.

Huh.

Okay. What I'm looking at is the difference of output values from their trend, versus the difference of unemployment values from their trend. I have to think about it a while.


Two points.

1. On my graph, the unemployment gap values range roughly from 2 to -2, or a difference of four percentage points. And the output gap values range roughly from 4 to -4, a difference of 8 percentage points. Roughly, the change in output is twice the change in unemployment. This agrees with Okun's law.

2. The output gap for this exercise is assumed to be the difference between inflation-adjusted output, and the trend of that output. In other applications, the output gap is taken to be the difference between inflation-adjusted output and potential output, which is not the same as the trend of realized output.

According to CBO's A Summary of Alternative Methods for Estimating Potential GDP (PDF),

Statistical filters (such as centered moving averages, bandpass filters, the Hodrick-Prescott filter, and the Kalman filter) are often used to extract the trend from GDP directly. These methods do not generally use Okun’s law...

Having actually used the HP filter now two or three times, having seen it for myself, I understand this better and I see it applies to the work of Laurence Ball et al. Ball's work is *not* circular because he uses an alternative to CBO's calculation, one that does not use Okun's law.

And yet, as the CBO paper states:

There are many ways to estimate the trend in GDP (and other economic data) as well as to compute the economy’s productive potential. Some methods rely on purely statistical techniques. Others, such as CBO’s method, rely on models guided by economic theory. Many methods used to compute potential output do not benchmark their trends to inflation or any independent measure of capacity and therefore cannot be interpreted as estimating the level of maximum sustainable output. That is, they provide a measure of trend output but not potential output.

If we, Laurence Ball and I, are not measuring the output gap as the difference from potential output, then we are likely understating the size of the gap.

If there is a long-term trend of decline in realized GDP, as I believe, then there may be a long-term increase in the size of the output gap that we are understating.


Thought about it. Given the actual unemployment we've had over the years, it is reasonable to draw a "trend line" that minimizes the actual variations, and helps us picture the general trend. Likewise output.

And then is is interesting to compare the differences-from-trend of unemployment against the differences-from-trend of output. This is what we see in the above graphs. There is nothing circular in the arithmetic, that I can see. And the correlation appears to be strong.


Regarding the second graph in the Econbrowser post, we read:

Our finding of a stable Okun’s Law is robust to various methods of measuring short-run movements in output and unemployment. We try alternatives to the Hodrick Prescott (HP) filter. We also estimate the relationship in “changes”, that is between the change in the unemployment rate and the change in (log) output, which does not require using the HP or any other filter. The relationship holds for quarterly as well as annual data. Chart 2 shows the tight fit between actual unemployment and the estimate based on Okun’s Law. Some residuals are evident during the early years of the Great Recession, for which Ferrara and Mignon provide some conjectures.

Chart 2. United States: Actual and Fitted Unemployment Rate, 1948Q2-2011Q4. Notes: Figure reports fitted unemployment rate from Okun specification estimated on quarterly data in levels with two lags and natural rates based on Hodrick-Prescott filter with λ = 100.

Trying to get clear on what they're saying. This part is easy: "Chart 2 shows the tight fit between actual unemployment and the estimate based on Okun’s Law." In this case, they definitely *are* using Okun's law to determine "fitted" unemployment.

The note below the graph refers to "levels with two lags" which must be some specific detail of the calculation, but the meaning escapes me.

The note below also refers to "natural rates based on Hodrick-Prescott". Rates, plural, so I think they figured HP trends for both output and unemployment, and used these somehow in their calculation. Then Okun's law comes into play. Working it backwards, they use the output gap to estimate unemployment. They call this estimate "fitted" unemployment, and they compare it to "actual" unemployment in their graph.


Okay. I think I figured out a way to estimate unemployment numbers using Okun's law and the HP trends. In my post (linked at the top) I wrote:

To figure potential output, the Congressional Budget Office uses the unemployment gap. They take that gap and stretch it to fit over actual output. That gives them the output gap. The output gap looks like the unemployment gap by design

I'll do the same thing now, but reverse the direction. First I'll figure the HP trends for unemployment and GDP. Then I'll take the difference of GDP and its trend, shrink it by half -- that's the Okun's law part -- and add it to the unemployment trend, then use the result for my estimated unemployment numbers. Now it's simple.

Graph #4

Holy crap! It's a really good match.

Okay, again: Take the discrepancy between RGDP and its HP trend, shrink it by half per Okun's law, and add it to the unemployment HP trend. That's the red line. The blue line is FRED's UNRATE.

What I've learned:
1. The HP trend calc is a really good trend calc.
2. Laurence Ball's "output gap" is the difference between RGDP and its trend, without regard for inflation or the Phillips curve which play a role in the CBO calc. Ball's output gap is based on the trend of realized RGDP, not on Potential Output. This is a significant difference, but I now think not relevant to Ball's Econbrowser post.
3. Laurence Ball's calc is *not* circular, and it *is* interesting.


On Graph #4, the blue line is above the red line when actual unemployment is higher than the estimate. The blue line is lower when actual unemployment is lower than the estimate.

We like low unemployment. We like the blue line low.

Looking at Graph #4, I see two periods where the blue line is clearly below the red line for more than a very brief period. Those periods are 1960-1964 approximately, and 1994-2000 approximately. Those were both periods of exceptionally good economic growth, so we should expect the unemployment to be relatively low in those times. We should expect the blue line to be relatively low in those times.

I decided to look at the discrepancy between the two lines. I subtracted the blue line from the red. This gives me the "error" of the unemployment estimate, relative to realized unemployment.

Graph #5

For the most part, the error is within plus or minus half a percentage point. Not bad.

//

The Excel file containing my graphs and calcs is available for download from Google Drive.

Note that the file contains Kurt Annen's Hodrick-Prescott filter in Visual Basic code, and also some routines I use for formatting my graphs. If your security settings are reasonable, when you open the file Excel will warn you of a potential problem because the file contains VB code.

Excel doesn't know there's a problem. It only knows there could be a problem.

Excel lets you disable the code and open the file. But with the code disabled, the H-P filter calcs won't work and the whole thing will probably be garbage. So maybe you don't care to mess with it. But anyway, the file is available if you want.