## Sunday, May 31, 2015

### Seasonality, Measurement, and First Quarter U.S. GDP

After the latest revisions to U.S. real GDP by the Bureau of Economic Analysis (BEA), the estimate for real GDP growth in the first quarter of 2015, seasonally adjusted at an annual rate, was -0.7%. So, have we entered a recession or what? In answering that question, we can learn something about how GDP is measured, and how seriously we want to take GDP measurement and the interpretation of quarterly real GDP growth rates.

Real GDP in the United States since the beginning of 2007 looks like this:
If you focus on what's happened since the end of the last recession, in 2009Q2, you'll notice that GDP has not grown in every quarter. Indeed, if we focus just on the quarterly growth rates in the first quarter, we get:

2010Q1: 1.7%
2011Q1: -1.5%
2012Q1: 2.3%
2013Q1: 2.7%
2014Q1: -2.1%
2015Q1: -0.7%

So, the average first-quarter growth rate since the end of the recession has been 0.4%, while the average growth rate over that period was 2.2%. This might make you wonder whether there is something funny going on with the seasonal adjustment of the data. The same thought occurred to Glenn Rudebusch et al. at the S.F. Fed, and they showed that, in fact, there is residual seasonality in the real GDP time series. They ran the supposedly-seasonally-adjusted real GDP time series through Census X-12 (a standard statistical seasonal adjustment filter), and came up with an estimate of first-quarter 2015 real GDP growth that was 1.6 percentage points higher than the reported number at the time (before the latest revisions). Apparently the BEA has been made aware of this problem, and is working on it.

Why do we have this problem? In the United States, the collection of economic data is a decentralized activity, conducted by several government agencies. The Bureau of Labor Statistics collects labor market and price data (why the consumer price index is a labor statistic I'm not sure), the Fed collects financial data, the Congressional Budget Office collects data on government activity, and the Census Bureau collects demographic data. Finally, the Bureau of Economic Analysis collects data for the National Income and Product Accounts (NIPA), and international trade statistics. It's this hodgepodge of data collection that makes FRED useful (shameless advertising), as FRED puts all of that data together (plus much more!) in a rather user-friendly way.

When the BEA constructs an estimate for real GDP, it uses as inputs data that comes from other sources, including (I think) some of the other government statistical agencies listed in the previous paragraph. Some of the data used by the BEA as inputs has been seasonally adjusted before it even gets to the BEA; some has not been adjusted. What the BEA does is to seasonally adjust all the inputs, and then construct a real GDP estimate. It might be surprising to you, as it is to me, that the resulting GDP estimate could exhibit seasonality. But, behold, it does. Maybe somebody can explain this for us.

As economists, what we would like from the BEA are estimates of real GDP that are both seasonally adjusted and unadjusted, for reasons I'll discuss in what follows. But given how the BEA currently does the data collection, that's impossible, and the BEA reports only seasonally adjusted real GDP. It might help if we had a single centralized federal government statistical agency in the United States, but if you have ever dealt with Statistics Canada, you'll understand that centralization is no guarantee of success. Statistics Canada's CANSIM database is the antithesis of user-friendliness. Go to their website and do a search for anything you might be interested in, and you'll see what I mean. For example, the standard GDP time series go back only to 1981, and the standard labor market time series to 1990. Why? Statisticians in the agency have decided that GDP prior to 1981, for example, is not measured consistently with post-1981 GDP, so they don't splice together the post-1981 data and the pre-1981 data. You have to figure out how to do that yourself if you want a long time series.

Getting back to seasonal adjustment, why do we subject time series data to this procedure? Many time series have a very strong seasonal component, for example, monthly housing starts:
That's not too bad, as we can eyeball the raw time series and roughly discern long-run trends, cyclical movement, and the regular seasonal pattern. But try getting something out of the monthly percentage changes, where the seasonal effects dominate:
However, if we take year-over-year (12-month) percentage changes, we get something that is more eyeball-friendly:
That's not unrelated to what seasonal adjustment does. If you're interested in the details of seasonal adjustment, or want to acquire your own seasonal adjustment software, go to the Census Bureau's website.

As macroeconomists or macroeconomist policymakers, if we're making use only of seasonally-adjusted data, we're throwing away information. Basically, what we're getting is the executive summary. I don't think we would like it much, for example, if the government provided us only with detrended time series data - detrended using some complicated procedure we could not reverse-engineer - and wouldn't provide us with the original time series. I have not been able to find much recent work on this, but at one time there was an active (though small) research program on seasonality in macroeconomics. For example, Barsky and Miron wrote about seasonality and business cycles, and Jeff Miron has a whole book on the topic. Is the seasonal business cycle a big deal? It's hard to tell from U.S. data as, again, the BEA does not appear to provide us with the unadjusted data (I searched to no avail). However, Statistics Canada (though they fall down on the job in other ways) publishes adjusted and unadjusted nominal GDP data. Here it is:
So, you can see that the peak-to-trough seasonal decrease in nominal GDP in Canada is frequently on the order of the peak-to-trough decrease in nominal GDP in the last recession. Barsky and Miron found that the seasonal cycle looks much like the regular business cycle we see in seasonally adjusted data, in terms of comovements and relative volatilities. So, the seasonal ups and downs are comparable to cyclical ups and downs, in terms of magnitude and character. Not only that, but these things happen every year. In particular, we get a big expansion every fourth quarter and a big contraction every first quarter. That raises a lot of interesting questions, I think. If seasonal cycles look like regular business cycles, why isn't there more discussion about them? There are macroeconomists who get very exercised about regular business cycles, but they seem to have no interest in seasonal cycles. How come?

Aside from seasonality, what else could be going on with respect to first-quarter 2015 U.S. real GDP? A couple of years ago, the Philadelphia Fed introduced an alternative GDP measure, GDP-Plus. As we teach undergraduates in macro class, there are three ways we could measure gdp: (i) add up value-added at each stage of production, for every good and service produced in the economy; (ii) add up expenditure on all final goods and services produced within U.S. borders; (iii) add up all incomes received for production carried on inside U.S. borders. If there were no measurement error, we would get the same answer in each case, as everything produced is ultimately sold (with some fudging for inventory accumulation), and the revenue from sales has to be distributed as income. In most countries, we don't actually try to follow approach (i), but there are GDP measures that follow approaches (ii) and (iii). In the U.S. we call those GDP (actually a misnomer, as it's really gross domestic expenditure) and GDI (gross domestic income). Over a long period of time, the two measures look like this:
You can see that for long-term economic activity, it makes little difference whether we're looking at GDP or GDI. Over short periods of time, it does make a difference:
You can see in this last chart that the differences in quarterly growth rates could be large. Note in particular the first quarter of 2015, where GDI goes up and GDP goes down.

The GDP-Plus measure, developed by Aruoba et al., uses signal extraction methods to jointly extract from GDI and GDP the available information that is useful in measuring actual GDP - treated as a latent variable. The most recent GDP-Plus observation is +2.03% for first-quarter 2015. So that's another indication that the BEA estimate, at -0.7%, is off.

Further, the recent labor market information we have certainly does not look like labor market data for an economy at the beginning of a recession. Employment growth has been good:
Weekly initial claims for unemployment insurance, relative to the labor force, are at an all-time low:
And the unemployment rate is at 5.4%, the same as in February 2005, in the midst of the housing market boom.

So, it would be hard to conclude from the available data that a recession began in the first quarter of 2015 in the U.S. But, I think the more you dig into macroeconomic data, and learn the details of how it is constructed, the more skeptical you will be about what it can tell us. Most macro data is contaminated with a large amount of noise. We can't always trust it to tell us what we want to know, or to help us discriminate among alternative theories.

1. "If seasonal cycles look like regular business cycles, why isn't there more discussion about them? There are macroeconomists who get very exercised about regular business cycles, but they seem to have no interest in seasonal cycles. How come?"

Because the pattern is REGULAR. The folks who are impacted by seasonal variations in GDP are e.g. farmers and construction workers and they can deal with it (and people in retail business can also expect holiday extra sales).

During recessions on the other hand people get unemployed UNEXPECTEDLY. And while standard micro theory tells us that while unemployed people are not at their labour supply optimum they should enjoy their extra leisure actually asking people tells us that they hate being unemployed (even ignoring the immediate consumption impacts like e.g. not being abel to pay off a house).

The whole reason macro exists (the real world cares about outcomes and not the intellectual games of acaedmics ) is to help alleviate and dampen the effects of the business cycle.

1. Well, a recession is not as predictable as the holiday season or summer, but everyone knows recessions happen. So, given your line of reasoning, people could plan for recessions just as the farmers and construction workers can plan for the down season. On the other hand, presumably unemployment in the down season is just as painful for the construction worker as it is for people unemployed during a recession. The fact that seasonal fluctuations are predictable in fact could give you a greater case for intervention to smooth the seasonal cycle. For example, Milton Friedman liked to make the case that we shouldn't smooth business cycles because of uncertainty about the length and depth of recessions. That case goes away for seasonal cycles.

So, if we think we should intervene to stabilize business cycles, why shouldn't we intervene to counteract the "overheating" of the economy in the fourth quarter, and the lackluster performance in the first quarter?

2. Farmers can and do smooth their incomes over the year just like people on a salary smooth their income over a month. No need for public help of any kind. That would be preposterous as there is no insurance against totally predictable events. Insurance does not exist in a deterministic world.

Farmers are not unemployed during spring and winter. They just receive their income during summer/autumn. It is as if somebody who receives a salary did not receive it monthly but only for three monthy per year.
Everybody would ideally like to receive his income as a constant stream (even folks on a salary, getting your income daily would be superior to receiving it monthly) and I don't deny that there are as a result of that TECHNOLIGICAL income pattern for farmers some mild wealth issues. These wealth issues can be significant in the Third World (we all read Stiglitz's sharecropping paper) but are insignificant in the First World.
The larger issue for farmers is their ordinary business risk, influenced by weather and so on.

I don't see how receiving income during a few months due to technological reasons is a market failure. Christmas is also no market failure, retail can deal very well with the income hike in December.

Unemployment during recessions on the other hand is a gigantic market failure. Private unemployment insurance does not exist due to adverse incentivze problems and as unemployment caused by a recession is a structural risk (a privat player would not like to insure against personal risk due to the above mentioned moral hazard so he could only insure against firm-specific unemployment) it is not insurable by a private player. This is why we have public unemployment insurance.
In addition to that we use monetary policy and during liquidity traps also fisal policy to get us quicker out of the underemployment equilibria.

To end it poignantly, people during the Great Recessions had no issues with harvest being only during a few months. They had issues with not having any job for the entire year. And to be blunt, I have no idea why we have to discuss such obvious issues.

3. Seems you're contradicting yourself. People who are seasonally unemployed should be left on their own to self-insure - there's no market failure. But when people are unemployed in a recession, the government should step in to insure them - the market failure is obvious.

"And to be blunt, I have no idea why we have to discuss such obvious issues."

You don't know how funny that is - on many dimensions.

4. I just told you that farmers are not unemployed just because they receive income only once per year. And people in retail certainly are not unemployed when it is not Christmas. Tell me where the market failure is.

I mean it is not like I do not understand what this is all about. It is not really about claiming that seasonal variations in GDP are horrible but about claiming what demand denying Lucas disciples always do: that the effects of the business cycle are neglibile and that we should not do anything about it.

5. I'm not claiming anything. Just asking questions. Don't get hot and bothered.

6. Anonymous, but unemployment also exhibits seasonal variation! It is not just the income that varies.

7. Aside from your good nature, it would be very easy to conclude that you are being intentionally obtuse. Anonymous' point, I believe, is that, while they may share characteristics, there are very substantial differences between seasons and business cycles. In particular, while they both are cyclical the timing and duration of the seasons is so much more predictable than business cycle components. This is not to say there is no variation in seasons but that variation is much smaller. Another difference is that it is much more difficult to know exactly who will be impacted by a recession and to what degree.

These are essential differences - especially when trying to determine the approach to ameliorating their impacts.

For example, for the most part, not only is the timing and duration of the winter relatively defined, the occupations that are most sensitive to the winter season are, as well. Therefore, it makes eminent sense that those occupations would price the impact into their costs and/or find alternative sources of income for the winter. (Think landscapers that plow snow.) OTOH, the vast majority of us working stiffs have no way of knowing when the next recession will hit, how long it will last and what the specific impact will be on ourselves. Yes, we should (if we can) set aside some savings to help in the event that we are impacted severely. But since neither we or our employers/clients nor our neighbors or their employers/clients nor our cousins or their employers/clients know when, whether or how we, our neighbors or cousins (let alone our employers/clients) will be impacted, it is nearly impossible to build that expectation into our cost. (Not to mention the asymmetrical leverage that generally applies in the labor market.) Therefore, it makes absolute sense that ameliorating this situation would be a collective solution.

8. "it would be very easy to conclude that you are being intentionally obtuse."

The truth is that I really don't have a strong opinion on this. I'm interested in what people might say - maybe I can learn something.

"This is not to say there is no variation in seasons but that variation is much smaller."

That's certainly not the case for Canadian nominal GDP in the chart above. And we can look at time series for the U.S. for which we have adjused and unadjusted data. For example, employment shows substantial seasonal variation. You could do a calculation, for example, of variability around trend for seasonal and cyclical components of the time series. If you eyeball the employment series, the peak-to-trough decrease in seasonal employment looks to be about a third of the peak-to-trough drop in employment during the previous recession, and about the same order of magnitude as in the recession previous to that. So I would not characterize the seasonal variation as "much smaller." And this is happening every year.

"it is much more difficult to know exactly who will be impacted by a recession and to what degree."

That's not correct. As Barsky and Miron show, the seasonal cycle looks like the business cycle. Basically, in a recession, we know who is going to be affected, just as we know who is going to be affected in slow seasons.

"..it makes eminent sense that those occupations would price the impact into their costs and/or find alternative sources of income for the winter."

So why wouldn't the same be true for firms and workers, for example, in the consumer durables sector? Why don't they price in the probability of a recession, and plan for alternative sources of income in the recession? And why are you limiting this to market work? People can substitute into home production too.

Just like anonymous, you seem to be very confident about how the market works for the seasonal cycle, but not for the business cycle. And the predictability of the seasonal cycle would seem to make this a more logical venue for government intervention.

9. If you're going to take things out of context, it makes it difficult to have a discussion with you. For instance, my first comment you highlighted:

"This is not to say there is no variation in seasons but that variation is much smaller."

Was clearly referring to the timing and duration of the seasons. Not the level of employment.

You make similar contextual distortions with most of the other cited comments - as you did with anonymous. This tends to make it seem like you're more interested in scoring rhetorical points than understanding the other person's argument. The intentionally obtuse option is looking more likely ...

Not hot and bothered but disappointed.

I'll look up Barsky and Miron. Going in, I'm skeptical that they can show that Business Cycle unemployment is as predictable as seasonal. But even if it is, there is still the matter of predictability of the seasons (timing and duration) versus business cycles. I can tell you with a fairly high degree of certainty within weeks when the next winter will begin and end. And the winter after that. And the winter after that. etc. I'll miss a couple but not by that much. What level of certainty do you have in predicting when and how long the next recession will be? How about the next?.

10. Dear Disappointed,

I hope you understand that I'm just trying to key you into which parts of your argument I'm discussing. I'm only trying to figure out what you're trying to say. Taking someone "out of context" is when we edit their comments so as to alter the meaning. In this case, everyone can see what you said, and what I said, so it's not an issue. You're not exactly a model for clarity, so don't blame me if you think I'm misunderstanding you.

"I'm skeptical that they can show that Business Cycle unemployment is as predictable as seasonal."

That's not quite it. The issue is what a seasonal cycle looks like, and what a business cycle looks like. Barsky/Miron characterize the data as telling us that comovements and relative volatility look similar in the seasonal cycle and the business cycle. It's not a question of predictability. We know that business cycle turning points are hard to predict, but the arrival of January is easy to predict.

"What level of certainty do you have in predicting when and how long the next recession will be?"

There are many events about which I am uncertain, and for which the market provides me no insurance, or will not fully insure me. Yet I think I can self-insure against those events - by making arrangements with my family and friends, and through my savings behavior - to make allowances for those events, in the same ways you're claiming the seasonal workers can make allowances. I still think you're not making a good case.

"This tends to make it seem like you're more interested in scoring rhetorical points..."

I'm not just playing games with you here. I'm taking you seriously.

11. "So why wouldn't the same be true for firms and workers, for example, in the consumer durables sector? Why don't they price in the probability of a recession, and plan for alternative sources of income in the recession? And why are you limiting this to market work? People can substitute into home production too."

So far we have had two balance sheet recessions. Before the Great Depression this event was unknown and afterwards the probability was unknown. Now you could claim that these are 'once per 80 year# events but it would obviously be ludicrous to infer the probability of a balance sheet recessions from a sample of the size 2.
Furthermore well-known economist like Bob Lucas claimed during the naughties that we have solved the problem of preventing such nasty depressions so if we had rolled with his advice we would have wrongly assumed a probability of zero.

Furthermore it is clear that seasonal employment is just that. I know folks who work in such occupations and they have a second job during the winter. I (and they) don't see the problem with that.
Recessions on the other hand are obvious malfunctions of capitalism. Here in Spain youth unemployment has been and still is around 50% for quite some time. That's not just millions of people who wanna work but can find no work and the obvious immediate sufferings that follow from that. There are in addition to that massive hysteresis effects; young folks get no on the job training and the human capital stock will rise far slower (compared to the no-austerity scenario).

12. "So far we have had two balance sheet recessions."

I've heard people use the term "balance sheet recession" but I'm not sure what they mean. I might guess that this would be a recession in which financial factors are important. But was there ever a recession in which financial factors were not important? Surely, a typical feature of recessions is that there are more defaults, banks are stressed, lending declines, there is deleveraging, etc. The Great Depression and the Great Recession certainly stand out in terms of the degree of financial stress, But, for example, the 1981-82 recession, people seem to agree, had something to do with monetary policy. Surely that worked through the financial system, don't you think?

"I know folks who work in such occupations and they have a second job during the winter. I (and they) don't see the problem with that."

1. Apparently the folks you know are not representative. In U.S. data, at least, there is a significant seasonal in the unemployment rate, the labor force participation rate, and in employment. I'll write another post on this. It looks like a large fraction of seasonal workers don't find work on the off-season. Some of them search, and some drop out of the labor force.

2. Why you "don't see a problem with that" is the question I'm asking. You are very concerned with the business-cycle unemployed, and business cycle fluctuations in GDP, but you're indifferent to the plight of the seasonally unemployed.

13. This might help anonymous get it. I have a friendly relationship with almost everyone working at the super marker where I do my shopping. Every year I see a similar pattern. After the holidays, hours are cut and though everyone knows it will happen, no one knows how the manager will decide whose to cut more. Maybe this is already priced into the salary, but it still hurts when it happens, enough for my friend Ann, among others, who works at the deli section to complain to me about it. So I don't see much difference relative to what happens during the non-seasonal business cycle.

14. "2. Why you "don't see a problem with that" is the question I'm asking. You are very concerned with the business-cycle unemployed, and business cycle fluctuations in GDP, but you're indifferent to the plight of the seasonally unemployed."

I could also accuse you of being indifferent to the plight of people who are unemployed due to the Great Recession. But let's cut this nonsense and talk about actual employment-enhancing policies.

I am of course for ordinary macro tools, monetary policy during normal times and fiscal policy while we are at the ZLB, do deal with business cycle unemployment. I am also sympathetic to the Post Keynesian notion that there is a constant slack in the labour market, e.g because of monopsony power of firms, and the resulting idea that we should have constant stimulus but also sceptical as this is not researched enough.

But this has obviously nothing to do with seasonally unemployed (except for the last idea). As most of them have low incomes if they are unemployed during a large part of the year conventional tax/subsidy changes in favour of low incomes, e.g. Friedman's negative income tax, in general low income tax rates and low incomes plus financing of social security via the income tax system (like in Scandinavia) instead of via pseudo-taxes on labour, should help them. The additional benefit is obviously the resulting reduction of income inequality.

I am also sympathetic of seemingly radical ideas like the suggestion that the public sector should be the employer of last resort (this can be viewed in context with the above-mentioned New Keynesian "constant slack" idea). Obviously the disadvantage of such a policy would be the incentive problems it raises so the trade-off between reducing unemployment and these incentive problems has to be carefully evaluated before such a radical idea is implemented.

What policies do you consider employment-enhancing for the seasonally unemployed ?

About the 81/82 recession, you are right that it was due to financial issues but I don't think (not sure though, would have to check the data) that deleveraging was as significant as during the two balance sheet recession.
As far as I know the normal definition of a balance sheet recessions is that private players are very busy deleveraging so firms don't invest, consumers don't spend and banks don't lend (and due to the latter monetary policy might have less traction). As usual in econ, it is a vague, qualitative definition as deleveraging is always a part of a recession.

I totally agree with you that finance is the key. The mainstream notion that price rigidity is a significant inefficiency is strange to say the least.

16. "I totally agree with you that finance is the key. The mainstream notion that price rigidity is a significant inefficiency is strange to say the least."

I agree completely with that. But some of your other policy prescriptions seem to come from thinking about a world with price rigidity. For example, if the monopsony power of firms is a problem, then there are conventional remedies that have nothing to do with "constant stimulus." Not clear why you want, for example, to have permanently higher government spending (or lower taxes) to correct the distortion.

17. Carlos is a typical uninformed noneconomist -- he is "sympathetic" to ideas that fail empirically but, in his worldview, should nevertheless be true. I don't know how you can handle these nuts, Steve.

18. "Carlos is a typical uninformed noneconomist -- he is "sympathetic" to ideas that fail empirically but, in his worldview, should nevertheless be true. I don't know how you can handle these nuts, Steve."

We have just conducted a large scale experiment in Europe which showed that mainstream macro is correct: during a recession contractionary fiscal policy is indeed contractionary.

So much about who is informed, who is an economists and what works empirically.

2. Steve,

Good blog. Measurement is far from perfect.

The difference in GDI and GDP is particularity interesting. The BEA adds about 5% of GDP to proprietors income (a component of of GDI) so that the statistical dependency is near zero on average. The Italians add on a lot more for unreported income to GDI than does US. There is also money laundering which increases income without increasing product.

Given measurement problems, my assessment is that the US economy is on a a balanced growth path, which is about 11% lower than the balanced growth path for the pre-2008 policy regime. Absent a policy regime change, expect about 2.5% real growth for the year.

E. C. Prescott

1. I was looking at the Canadian data. They construct GDI and GDP in such a way that, in the accounting, the bottom line is the same. In the GDI calculation, there is an item called "statistical discrepancy," which I assume is the same as the difference between GDP and GDI, as it would be measured in the U.S. But that statistical discrepancy is small relative to the difference between GDP and GDI in the U.S. Unless the Canadians are better at measurement, I'm not sure what's going on there.

3. "why the consumer price index is a labor statistic I'm not sure"

Because it was commissioned in order to determine appropriate wage increases (and is still used in that way in, for example, union wage escalation clauses).