Category Archives: gdp forecast

Money Picked Up From Sidewalk

It took nearly a month after we first pointed it out, but someone has taken advantage of a unique investment opportunity that we identified with the options for the S&P 500's quarterly dividend futures!

And because they did, we now have a better and more up-to-date picture of how much S&P 500 companies are expected to collectively pay out in dividends to investors in 2018-Q2, where in this case, we can now show how much the expectations for dividends to be paid out in this upcoming quarter have changed thanks to a combination of improved organic corporate earnings and, perhaps more significantly, the effect of the permanent corporate income tax cuts passed in late December 2017.

Future Quarterly Dividends per Share Expected for the S&P 500 in 2018-Q2 and 2018-Q3, 21 December 2017 through 7 March 2018

The sudden change in the CME Group's S&P 500 quarterly dividend futures came on 5 March 2017, which vaulted slightly ahead of the bottoms-up dividends per share estimate indicated by IndexArb, which is how we were able to identify that a trading opportunity existed in the first place. In jumping from $12.70 per share to $13.20 per share, the CME Group's dividend futures for the S&P 500 in 2018-Q2 are now communicating that investors stand to collect an additional 50 cents per share in that future quarter compared to what the dividend futures had been indicating since at least mid-December 2017.

We believe that this particular opportunity existed because the CME Group's quarterly dividend futures for the S&P 500 have been trading on very thin volumes. Their annual quarterly divided futures for the S&P 500 see more action, where the mismatch between the S&P 500's projected annual dividends per share for 2018 and the sum of their projected quarterly dividend futures for the S&P 500 for 2018 also confirmed the existence of the trading opportunity.

In terms of real money, the 50 cent per share increase in projected S&P 500 dividends means that investors will collectively rake in upwards of $4.47 billion more in dividends during the second quarter of 2018 than they were expecting prior to the passage of the Tax Cuts and Jobs Act of 2017. Altogether, the updated dividend futures project that S&P 500 companies would pay out over $118 billion in dividends during 2018-Q2. Or since we're talking about dividend futures, over the period from the end of the third Friday of March 2018 through the end of the third Friday of June 2018. And there's still lots of time between now and Friday, 15 June 2018 for dividends payouts in 2018-Q2 to change further.

Now that the "easy" money on the sidewalk for the S&P 500's 2018-Q2 dividend futures has been picked up, we'd be remiss if we didn't point you another interesting opportunity to pick up some other money that's figuratively lying on the sidewalk - only this opportunity won't cost you a dime, because its really a contest. It's Hypermind's Nominal GDP Prediction Market, where your goal is to predict what the U.S. economy's growth rate for nominal GDP (or real GDP plus inflation) will be at the time that Hypermind's currently available future contracts for its NGDP prediction market expire in either April 2018 or in April 2019.

If you're interested, check out Hypermind's description of how it works (click each of the different icons at the top of the page), along with Scott Sumner's recent description of how thinly traded those particular futures have been. Like us with the S&P 500 quarterly dividend futures and our use of that data to project the actual trajectory of the S&P 500, he has ulterior motives in promoting the NGDP prediction market, but like us, they're the good kind!

Polling Results: The Over and the Under for the Upcoming National GDP Revision

Updates! Scroll down....

Nearly a month ago, we presented our "most likely" prediction for how the U.S. Bureau of Economic Analysis will revise the U.S.' Real Gross Domestic Product on Friday, 29 July 2016.

Let's recap what we forecast, picking things up from after we described how we went from estimating the "maximum potential" size of the revision to the "maximum likely" size of it, before we drilled down to what we think will be the "most likely" amount by which real GDP will be revised through the fourth quarter of 2015:

Previously Reported and Revised Real GDP, 2005-Q1 Through 2015-Q4, per BEA Regional Data released on 2016-06-14, Revised to Account for 'Overseas' GDP, with Date Correction - was 14 June 2015, now corrected to 14 June 2016 - previous chart here: https://2.bp.blogspot.com/-EzKqOVcLGC4/V2XJce71MhI/AAAAAAAANkk/uxCWYmwSK98c6baRUFRi1-NmNArdwz1qgCLcB/s1600/Political-Calculations-2016-GDP-Revision-Projection-spanning-2005Q1-to-2015Q4.png

But the "maximum likely" revision of -1.4% of previously reported GDP through 2015-Q4 is not the "most likely" size of the upcoming revision to the nation's GDP will be, because the BEA's plans for the revision of the national level GDP data will only cover the period from 2013-Q1 through 2016-Q1.

That means that it will miss the discrepancy that opens up in 2012-Q3 and 2012-Q4 between the just-revised state level GDP and previously indicated overseas federal GDP and its previously recorded national level GDP. That discrepancy is just over $55.1 billion in terms of constant 2009 U.S. dollars in 2012-Q4, which itself is over 24% of the full $225.7 billion discrepancy that our previous calculations indicates between the pre-revised national level real GDP and the post-revised state level GDP data through 2015-Q3.

Because the BEA won't be including that $55.1 billion portion of the discrepancy from 2012, the "most likely" size of the revision that it will report at the end of July 2016 is therefore -1.1%, which is 24% less than the "maximum likely" revision of -1.4% we previously calculated.

After the BEA's annual revision of GDP for the 50 states and the District of Columbia on 14 June 2016, there is only one factor left that can affect the amount by which the BEA will actually revise the nation's total real GDP next week - the contribution of overseas federal military and civilian government activities, or as we've described it, the "hidden GDP of war".

There are three scenarios in how that one factor can play out:

  1. If that contribution is greater than what the BEA has previously indicated, the amount by which real GDP through 2015-Q4 will be adjusted will be smaller. So instead of being reduced by 1.1% as we've projected to be "most likely", it would instead be reduced by a smaller percentage, or in the very unlikely case that contribution is much, much greater, real GDP through 2015-Q4 could be adjusted upward. For this scenario to occur, it would mean that the U.S. government was much more engaged in fighting wars overseas in a way that adds to the nation's GDP than it has previously indicated. This is the "under" scenario.
  2. If that contribution is less than that the BEA has previously indicated, the amount by which real GDP through 2015-Q4 will be adjusted downward will be larger, going in the direction of what we calculated would be the maximum likely revision. For this scenario to occur, it would mean that the U.S. government was engaged in less "productive" military and civilian government activities overseas than it has previously indicated. This is the "over" scenario.
  3. If the contribution is the same as what the BEA has previously indicated, then we'll see the "most likely" scenario we calculated be the actual result. Real GDP through 2015-Q4 would be decreased by about 1.1% from the level that was recorded earlier this year on 29 March 2016. This might be considered the "null" scenario.

To make that question more interesting, we asked our most dedicated readers [1] to click through and answer a SurveyMonkey poll, which we've now closed. The results of that poll are presented in the following chart.

SurveyMonkey Poll Results

As you can see, our poll produced a 40-40-20 split. 40% of the poll participants indicated they thought Scenario #1 was more likely, 40% predicted Scenario #2 would be a reality, and 20% believed in the Scenario #3 "no change from our forecast outcome" outcome.

While those results seem nearly split down the middle, what they really indicate is that the majority of the poll participants believe that the actual adjustment to real GDP through 2015-Q4 will be different from our "most likely" forecast for the size of the July 2016 national revision. What is equally split down the middle is the direction in which it will be adjusted, with no clear collective prediction emerging from our poll.

Where is Philip Tetlock when you need him?

Notes

[1] We had problems with generating working code to embed the survey directly in our post, so we were stuck with providing a link for readers to click through to participate in the survey. That's the sort of hassle that only the most dedicated readers would endure, so we greatly appreciate the extra effort on the part of all the participants who registered their own prediction for how this one aspect that will affect the actual size of the upcoming GDP revision. Thank you!

Update 27 July 2016: This is so cool! We had an extended contact today with an analyst who works for the BEA, who wanted to know more about how we came up with our estimate of how real GDP would change using the BEA's recently revised regional account data.

That was fantastic timing, because we just happened to have our spreadsheet open because we were updating it with state level GDP data from 2016-Q1 that was just released today.

In going over that material, we discovered a problem that threw off our calculations, with the effect that the results we had obtained weren't matching what they were getting from 2014-Q3 onward in replicating our analysis. We were able to trace the problem back to the GDP deflator that we used to convert nominal GDP data to inflation-adjusted "real" data, where we were multiplying the nominal data by the GDP deflator data for the national level data (the data whose revision is set to be published on Friday, 29 July 2016) instead of the GDP deflator data that applies for the aggregate 50 states plus Washington DC, which just happened to be in the spreadsheet column next to it.

After we made the appropriate correction, all our results from 2014-Q3 onward snapped into place and all results matched, from the period from 2005-Q1 through 2014-Q2, where there was never any problem, and now from 2014-Q3 through 2015-Q4! The following chart shows the latest and greatest for what we expect from Friday's GDP revision based only on the state level GDP revision from June!

Previously Reported and Revised Real GDP 2005-Q1 Through 2015-Q4 (Updated 27 July 2016)

As for the outcome of the analysis, the error we made with using the incorrect GDP deflator overstated the amount by which real GDP is likely to be revised by 0.5% of GDP, so instead of the maximum likely change of -1.4% that we had previously calculated, the maximum amount by which national GDP might change as a result of the revisions the BEA has made to its GDP data for the 50 states plus Washington DC is -0.9%, with the maximum discrepancy now taking place in 2013-Q3. This data is indicated in the chart above by the dark-green line.

But since the BEA's national revision will cover the period from 2013-Q1 to the present, the revision of the national level GDP will not include the now-confirmed $55 billion discrepancy that opens up between the national GDP data and the national aggregate state level GDP in 2012. We are therefore now estimating that the most likely revision that will be made to the national GDP data on Friday, 29 July 2016 will be an adjustment of -0.6% in 2013-Q3. This data is indicated in the chart above by the bright red line (and the blue arrow at 2013-Q3).

We'd like to thank everyone who provided their useful assistance in getting to this point - in terms of collaborative effort, this has been one of the biggest projects we've had the pleasure of working on since launching Political Calculations. It's always exciting when we get to break brand new ground and do analysis that was never possible before, and we appreciate your shared enthusiasm!

On a final note, if you happened to have come across this post by way of Econbrowser, you might want to pass along information back to the author who pointed you in this direction that their observations have been described as "not relevant". We're pretty sure that particular author hears that a lot ....

There's more that we'd like to be able to discuss on the topic of the upcoming national-level GDP revision, but that will have to wait until after that data is released. Until then, what you see above represents the most that anyone can reasonably glean about what the revision will look like based only on data that is already available to the public.

Update 29 July 2016: The verdict is in! The chart below shows the revisions in national level real GDP from 2013-Q1 through 2015-Q4....

Previously Reported and Revised Real GDP, 2005-Q1 through 2015-Q4 (29 July 2016)

Compared to our final pre-revision prediction from 27 July 2016, we were off by 0.1% of GDP through 2015-Q4, where we had previously projected no change.

More significantly however, national-level real GDP was increased by 0.2% of its previously reported figure in 2013-Q3, where the aggregate GDP data for the 50 states and the District of Columbia had instead indicated that a 0.6% of GDP decline for that quarter was most likely. That means that the amount of GDP that the U.S. generated in that quarter from Overseas Federal Military and Civilian Government Activities was revised to be significantly much higher than the BEA had previously indicated, in effect, adding an additional 0.8% of GDP on top of what the BEA now indicates was generated within the actual territory of the United States.

We'll dig deeper into the national-level GDP revision periodically over the next several weeks!

Finally, our congratulations to the 40% of respondents in our poll who chose the "under" scenario - well done!

How U.S. GDP Will "Most Likely" Be Revised in July 2016


How much will U.S. GDP most likely be revised when the U.S. Bureau of Economic Analysis publishes its annual revision to the nation's real GDP on 29 July 2016?

We started working on that question last Thursday, the day after the BEA released its revision of GDP data for the individual 50 states and the District of Columbia, when we identified the "maximum potential" size of the revision to be a -2.0% decline from its value that was recorded at the end of 2015.

We updated that post two days later to take into account the contribution to national GDP from the U.S. government's overseas military and civilian activities, which add to the GDP contributed by the 50 states and the nation's capital to be equal to what the BEA should report for the nation's entire GDP. (Although we did that work last Friday, we only just featured that contribution to national GDP in the period from 2005-Q1 through 2015-Q3 yesterday.)

We then used that information along with the BEA's just-revised data for the individual 50 states plus DC to determine the "maximum likely" size of the upcoming revision to the nation's real GDP. The chart below reveals what we found.

Previously Reported and Revised Real GDP, 2005-Q1 Through 2015-Q4, per BEA Regional Data released on 2016-06-14, Revised to Account for 'Overseas' GDP, with Date Correction - was 14 June 2015, now corrected to 14 June 2016 - previous chart here: https://2.bp.blogspot.com/-EzKqOVcLGC4/V2XJce71MhI/AAAAAAAANkk/uxCWYmwSK98c6baRUFRi1-NmNArdwz1qgCLcB/s1600/Political-Calculations-2016-GDP-Revision-Projection-spanning-2005Q1-to-2015Q4.png

But the "maximum likely" revision of -1.4% of previously reported GDP through 2015-Q4 is not the "most likely" size of the upcoming revision to the nation's GDP will be, because the BEA's plans for the revision of the national level GDP data will only cover the period from 2013-Q1 through 2016-Q1.

That means that it will miss the discrepancy that opens up in 2012-Q3 and 2012-Q4 between the just-revised state level GDP and previously indicated overseas federal GDP and its previously recorded national level GDP. That discrepancy is just over $55.1 billion in terms of constant 2009 U.S. dollars in 2012-Q4, which itself is over 24% of the full $225.7 billion discrepancy that our previous calculations indicates between the pre-revised national level real GDP and the post-revised state level GDP data through 2015-Q3.

Because the BEA won't be including that $55.1 billion portion of the discrepancy from 2012, the "most likely" size of the revision that it will report at the end of July 2016 is therefore -1.1%, which is 24% less than the "maximum likely" revision of -1.4% we previously calculated.

Our "most likely" estimate assumes however that the BEA's estimates of the contribution to national GDP from the U.S. government's overseas military and civilian activities will not greatly change from what it has previously indicated. Should the BEA revise its estimates of this component of nation real GDP, the actual size of the BEA's upcoming revision to the national GDP will entirely depend upon how that single factor might change.

In the case that it turns out that more GDP than previously indicated was generated through supporting the U.S. government's various overseas activities, the actual magnitude of the revision will be smaller than what we've now indicated the "most likely" size of the revision to be, and vice versa for the opposite scenario.

So if you want to place your bets on the over or under, all you need to do is to take your best guess as to just how much more or less of the nation's real GDP has been generated through supporting the U.S. government's activities overseas than what the BEA has previously indicated. To make it interesting, we've set up an online survey where you can put in your two cents and also find out what the consensus is for all those who have answered that single question!



Predicting the Next Debt-Bubble Pop Recession

Last week, economist Steve Keen went on record to predict that Australia's economy would fall into recession in 2017.

In doing that, Keen made a back-of-the-envelope calculation linking changes in the rate of private sector debt growth available with real economic growth available via an Excel spreadsheet.

We were intrigued by the math, so we've converted the spreadsheet math into the simple tool below, in which anyone can play with the numbers to predict how a nation's economic growth might change over the next year based on just a handful of factors.

The default numbers apply for the years 2016 and 2017 for Keen's Australia example, but you're more than welcome to substitute the numbers that apply for other nations or years of interest. If you're reading this article on a site that republishes our RSS news feed, please click here to access a working version of this tool!

GDP and Private Sector Debt Data
Input Data Values
Current Nominal Gross Domestic Product
Current Nominal GDP Growth Rate [%]
Current Total Private Sector Debt
Current Nominal Credit Growth Rate [%]
Projected Nominal Credit Growth Rate [%]
Inflation Rate [%]

Projected Future Economic Conditions
Calculated Results Values
Nominal Aggregate Demand Growth Rate [%]
Real Aggregate Demand Growth Rate [%]

In the tool above, "Current Nominal Credit Growth Rate" is the rate at which private sector debt increased from the previous period to reach its current value. The "Projected Nominal Credit Growth Rate" is the rate that would apply in the future period under consideration.

The reason why changes in the rate at which private sector debt grows would have predictive power for future economic performance comes down to why people in the private sector of the economy take on debt in the first place. It is because they reasonably expect to have sufficient income in the future where they will be able to make payments without significant problems.

As such, the forward-looking expectations that influence decisions to take on debt in the private sector, and consequently economic growth as a result, serve a similar role to what the expectations for earning dividends in the future do for setting the current and projecting the future value of stock prices. The math involved is certainly very similar.

As for Steve Keen's recession call for Australia, we should caution that he has been famously wrong before, particularly with respect to Australian housing prices, yet at the time he made that ill-fated prediction, the impact of China's massive economic stimulus on the strength of Australia's resource-exporting economy was an unknown factor. China's stimulus worked to significantly boost Australia's economy in 2009 and 2010, helping the nation to avoid falling into recession at that time, which in turn, also helped sustain housing prices.

The rapid deceleration of China's economy today as the remnants of that previous stimulus effort evaporate provides a good argument in support of why a recession in Australia's future has become increasingly likely at this time.

It will be interesting to see what factors might intervene to either forestall or accelerate that scenario. Having gone 25 years without an official period of recession, Australia certainly has lived up to its reputation as the "Lucky Country" through this point in time.

Update 30 March 2016 9:46 PM EDT: Steve Keen e-mails a clarification - the output variables in the tool above have been reidentified as nominal and real aggregate demand growth rates rather than as GDP growth rates. It's a subtle difference, but a distinct one that better describes the tool's output!

Previously on Political Calculations

Sydney Harbor - Source: http://www.export.gov/australia/

Slitting the Greeks’ Throats Deeper

Ruins of Theater at Delphi and Remains of Temple of Apollo - if you don't know why this image is relevant to our forecast of the future for Greece's economy, you should brush up on your ancient history!  Source: https://www.cia.gov/library/publications/the-world-factbook/photo_gallery/gr/photo_gallery_B1_gr_44.html

We have been following the negotiations between Greece's new government leaders and the nation's European creditors with some interest as the nation would seem to be diving headlong into defaulting on its debt interest payments at the end of June 2015. Last week, we finally got the details for how each of these parties propose to both cut the Greek government's spending and by how much they would hike Greece's taxes through 2016.

As best as we can tell, Greece's economy is about to be struck with another body blow regardless of which bailout proposal might go forward as the stage is set for tragedy, no matter what.

But you don't have to take our word for it. Since we're the ones who built the tool that calculated, with uncanny mathematical precision, how the tax hikes and spending cuts approved by previous Greek government leaders and the nation's major creditors wrecked the Greek economy by ensuring that the nation would fall into deep depression, we're going to do that same math all over again.

The first set of numbers we'll be using in this exercise represent the tax and spending changes that Greek Prime Minister Alexis Tsipras' government has proposed to accept as a condition for receiving a new bailout, which were reported in The Guardian, and which Grumpy Economist John Cochrane featured on his blog. Totaling the detailed expected tax collections and spending cuts by year presented in the table above, we obtained the following hard numbers proposed for each in both 2015 and 2016:

23 June 2015 Greek Government Proposal for Tax Hikes and Spending Cuts
Tax Collections [millions of Euros] 2015 2016
Value Added Tax Hikes 680 1,360
Corporate Tax Hikes 945 815
Retirement and Pension "Social Contribution" Hikes 350 800
Other Tax Hikes 320 397
Total Proposed Tax Hikes 2,295 3,372
Spending Cuts [millions of Euros] 2015 2016
Retirement and Pension Cuts 60 300
Defense Cuts 0 200
Total Proposed Spending Cuts 60 500

We'll also use the OECD's 2014 estimate of Greece's GDP of 179,080.6 million Euros as the baseline reference from which we'll forecast how Greece's GDP will change as a result of the Greek government's tax and spending proposals and we'll set the amount of quantitative easing that the European Central Bank might adopt at 0, which will give us an idea of the total amount of fiscal drag that the current Greek government would appear to be ready to impose on the Greece's economy.

The default data in our tool below is set up with the data for 2015, where we'll use the results for that year to repeat the calculations as they would apply for the proposed tax hikes and spending cuts in 2016. If you're reading this article on a site that republishes our RSS news feed, click here to access a working version of our tool!

GDP and "Input Shocks"
Input Data Values
Nominal GDP for the Previous Period [millions]
Change in Expected National Government Tax Collections [millions]
Change in National Government Spending [millions]
European Central Bank Net Quantitative Easing [millions]
Fiscal Policy Multipliers (Estimated Range)
Government Spending (0.6-0.7)*
Government Taxes (-3.0)
Quantitative Easing (0.8-1.0)
* If unemployment rate ≥ 7.5%. Multiplier is 0.5 if unemployment rate < 7.5%.

Individual Effects of Fiscal and Monetary Policies Upon GDP
Calculated Results Values
Effect of Change in Government Spending on GDP [millions]
Effect of Change in Government Taxes on GDP [millions]
Effect of Change in Monetary Policy on GDP [millions]
Combined Effects of Fiscal and Monetary Policies Upon GDP
Combined Effects on GDP [millions]
Estimated GDP for Next Period [millions]

Without any quantitative easing specifically targeting the Greek economy on the part of the European Central Bank to offset the negative consequences of the Greek government's proposed tax hikes and spending cuts for 2015, we can reasonably expect Greece's economy to contract by about 3.9% in 2015, with its GDP falling to 172,159.6 million Euros. Using that GDP number and substituting the Greek government's proposed 2016 tax hikes and spending cuts, we can reasonably expect that Greece's economy will further contract by an additional 6.0% from that lower level to 161,743.6 million Euros in 2016. Altogether, the Greek economy would be 10% smaller in 2016 than it was in 2014.

And that would be the consequences to Greece's economy that Greece's own government has proposed to accept as a condition for continuing to be allowed to borrow money from its international creditors. The situation for Greece's economy would be even worse under the counterproposal offered by those parties, who would have Greece increase its Value Added Tax collections by up to 1,789 million Euros in 2015 and up to 1,838 million Euros in 2016 (1% of the GDP they project for Greece in those years), while also boosting the amount of Greek defense cuts to 400 million Euros in 2016.

Adjusting the numbers in our tool above to reflect 3,404 million Euros worth of tax hikes in 2015 (still coupled with 60 million Euros of spending cuts) would have Greece's GDP in 2015 fall to 168,832.6 million Euros. In 2016, with an additional 3,850 million Euros of tax hikes paired with 700 million Euros of spending cuts, Greece's GDP would fall to 156,862.6 million Euros - a 12.4% reduction from 2014's GDP figure.

Crowds gather as hundreds of thousands of dollars in “Scrip Money” are burned. The notes were issued after the bank had closed. April, 1933. Local Identifier: 306-NT-177.567C Source: http://unwritten-record.blogs.archives.gov/2014/10/29/black-tuesday-85-years-gone-by/

The reason why the negative impact on Greece's GDP is set to be so large is because the proposed conditions for receiving a new bailout to avoid a Greek default on its debt are so heavily weighted toward tax hikes over spending cuts, where tax hikes outweigh spending cuts by roughly a 10-to-1 ratio. The negative impact to the nation's GDP would be considerably less if the ratio were reversed - as it stands, they might as well burn the bailout money they receive as part of the deal being negotiated because they won't get any benefit from it.

The wild card in our analysis is the Quantitative Easing (QE) program that the European Central Bank might adopt to offset these negative impacts within Greece. The question is whether they are capable of working QE within just Greece itself to specifically offset the negative impacts that would be caused by their tax-dominant austerity plan within that nation. If not, the ECB would have to apply their QE programs across Europe as a whole where their efforts would have to be much, much, much bigger to be able to reach enough into Greece to avoid it falling even deeper into economic depression.

Neither option seems likely at present. Especially since the international creditors, made up of the European Central Bank (ECB), the International Monetary Fund (IMF) and the European Union (EU), actually seem to be intent on breaking both Greece's economy and the democratically-elected Greek government. And even more especially after the Greek government called to put the creditors' bailout measure up for a public referendum on Sunday, 5 July 2015, prompting the creditors this past weekend to cut off Greece's available lines of credit and thereby guaranteeing its default on 30 June 2015.

The international creditors' strategy at this point would not appear to have anything to do with genuinely resolving Greece's debt and economic problems, which they have been party to creating. They're trying to send a message to others in Europe who might threaten their supremacy by challenging them, where it seems that Greece is to be the example of what they mean will happen whenever they say "or else".

Why else would they reject Greece's proposal, in which the Greeks offered to slit their own economic throats and slash their own GDP by 10%, to instead demand that the Greeks slit their own throats even deeper and slash their GDP by 12.4% as a condition of keeping their IV drip of credit hooked up?

We can only conclude that things other than common economic sense are motivating the parties in this deal.

How Greece Got Here, or Rather, Previously on Political Calculations

We've been periodically monitoring Greece's deteriorating fiscal situation for a number of years. Here's our previous analysis, presented in chronological order.