Friday, November 30, 2012

Attenuating the Long Wave

Graph #1: Velocity and the Interest Rate
Click Graph for FRED Source Page
Shows part of a long wave, up and down. All during the long wave there are business cycles, one after another. Those are the little ups and downs visible in both the red and blue lines.

On the way up the long wave, the business cycle pattern is much more evident in the red line than the blue. But on the way down the long wave, the business cycle pattern is strongly visible in both lines.

The most significant difference between the red and blue lines seems to occur between the years 1990 and 2000. Velocity fell much less than the FedFunds rate early in that decade, and stayed higher for the rest of the decade when economic performance was unusually good.

If there is a second most significant difference between the lines, it seems to be between the years 1960 and 1970 -- another decade of unusually good economic performance. Or perhaps I should say the early years of those ten were unusually good, until inflation flared up. But then, the separation between the two lines happens in the early years of that decade. The gap closes by 1967.

It's odd, though. During the good years on the way up the long wave, the red line runs high. During the good years on the way down, the red line runs low.

This is what we want to do. We want to "capture" those two good periods of economic performance and repeat them. We want to design a business cycle synchronized with a shortened and properly managed long wave.

The "up" side of the long wave will last as long as the concurrent business cycle. Interest rates will lead velocity on the way up. The "down" side will last as long as the following business cycle, and interest rates will lead the way down.

We attenuate the long wave, cutting off the highs and lows with a coordinated policy that works perhaps like a bandpass filter for the economy.

Thursday, November 29, 2012

Simulacron: Let me repeat that

Real GDP growth was faster in the years before 1980 than it was in the years since. This is true even though we ignore 2008 and after, when growth got even worse. The numbers I have are 3.798% annual growth for 1947-1979, and 3.072% for 1980-2007.

I used exponential growth trends to estimate what real GDP would have been in the years since 1980, if the faster growth of the earlier years continued. The graph below compares the outcome of this improved growth (shown in blue) with the outcome we actually got (red).

Graph #1: Better Growth Reduces Debt
The red line is the Gross Federal Debt as a percent of nominal GDP, the debt graph everybody shows. The blue line is Gross Federal Debt (reduced by the extra tax revenue generated by the faster-growing economy) divided by nominal GDP that is larger because of the faster growth: Less than one percentage point faster growth.

Wednesday, November 28, 2012

Simulacron: Growth and the Federal Debt

Had some trouble with Federal debt numbers. Didn't trust my results. Thought it might be a confusion of quarterly data and annual-versus-quarterly rates of change. Downloaded the numbers from FRED again, this time annual numbers.

Graph #1:Developing the Trend Calcs
Blue is RGDP early (1947-1979). Red is RGDP late (1980-2007). Exponential trend equations are provided by Excel.

Graph #2: RGDP Fitted to the Trend Lines
The red trend line is the actual RGDP trend, before 1980. The green trend line is the actual RGDP trend since 1980 (and before the financial crisis). RGDP (blue) hugs the trend lines.

Graph #3:RGDP Since 1980 boosted to the Early Trend. Compare Graph #2.
For the years since 1980, I took the RGDP numbers, divided by the green-trend number and multiplied by the red-trend number to simulate continuation of the Early Trend in RGDP growth. This boosts RGDP and pushes the blue line up.

Graph #4: A Difference since 1980, due to faster the GDP growth of Graph #3.
Thats DEBT, Gross Federal DEBT, not REBT thank you very much.
I used the "boosted" RGDP numbers to calculate high-performance NGDP numbers. The blue line shows Gross Federal Debt relative to actual NGDP. The red is lower since 1980 because the high performance NGDP values are bigger.

NOTE: The difference shown on Graph #4 is due to the difference in Early-Trend and Actual NGDP numbers. All of the change is in the denominator. In Graph #5, I change the debt.

Graph #5: A Faster Growing Economy Generates More Tax Revenue
GDP is income. When GDP grows faster, income goes up. When income goes up, tax revenue goes up. Faster GDP growth since 1980 produces more tax revenue. I take this extra tax revenue and apply it to debt and deficits. Doing this brings the Gross Federal Debt down from the red line to the blue line -- from 15000 billion dollars to less than 6000 billion.

Next, Graph #6 combines the high-performance NGDP denominator of Graph #4 with the high-performance reduced-debt numerator of Graph #5.

Graph #6: Better Growth Reduces Debt
The red line is the Gross Federal Debt as a percent of nominal GDP, the debt graph everybody shows. The blue line is Gross Federal Debt reduced by the extra tax revenue generated by the faster-growing economy, divided by nominal GDP that is larger because of the faster growth.

The blue line here assumes everything is as it was since 1980, except that RGDP growth continued at its pre-1980 rate.

// UPDATE: I forgot to link to the Excel file. Preview or download the file here:

Tuesday, November 27, 2012

Simulacron: Backtrackin'

When I got started on these Simulacron posts, it seemed redundant to show this graph

Graph #1: Excel's Exponential Formulas for the Early and Late Periods

among the others in my post of the 25th. Redundant.

But now it becomes important to show the exponential trend formulas generated by Excel. And to know the growth rates of the two periods.

Early Period, 1947Q1 - 1979Q4: 3.735% annual rate

Late Period, 1980Q1 - 2007Q4: 2.9775% annual rate

A difference of about 0.7575% -- less that one percent annual.

Monday, November 26, 2012

Simulacron: Federal Revenue and Spending

Yesterday we explored the trends of economic growth in the years between World War Two and the financial crisis of 2008. Two trends: a little faster before 1980, and a little slower since. How would things have looked, if the faster trend continued? Here's what I have so far:

Graph #1: If GDP growth since 1980 continued at a pre-1980 pace...

Graph #2: ... Federal revenue would have been higher...

Graph #3: ... and Federal spending would have been a smaller share of GDP.

Federal spending fell relative to GDP between 1980 and 2000. If excessive Federal spending was the reason GDP growth was slow, then economic performance should have improved when Federal spending fell.

As economic performance improved, the actual (blue) line would have moved closer and closer to the simulated (red) line on Graph #3. The fact that this did not happen is evidence that excessive Federal spending is *NOT* the reason GDP growth is slow.

Federal spending bottomed out at 18.8% of NGDP-actual in 2000, then rose to between 20 and 21% for the 2001-2007 period. But spending fell to 16.7% of NGDP-simulated in 2000, and remained below 18% until 2008. That's as low as it was in the golden years of the 1960s!

Yet economic performance after 2000 was miserable. Even before the financial crisis, economic performance after 2000 was miserable. Why did economic performance not improve while Federal spending remained so remarkably low?

The answer is obvious: It is not Federal spending that hinders economic growth.

The Excel file containing these graphs and the numbers behind them is available to view and download.

Sunday, November 25, 2012

Simulacron: The Keynes-Reagan Shift

From John Boehner's

“The reason it [the economy] isn’t doing better is quite simple – excessive government spending."

The Freeman: What Spending and Deficits Do by Henry Hazlitt:

The greater the amount of government spending, the more it depresses the economy. Government spending:

...volumes of research have shown that excessive government spending that causes chronic budget deficits is one of the most serious drags on economic dynamism.

The standard argument against government spending is that it hinders economic growth. It drags on economic dynamism. It depresses the economy. It is the reason the economy isn’t doing better. It certainly gets repeated a lot.

William A. Niskanen, Reaganomics:

"Only by reducing the growth of government," said Ronald Reagan, "can we increase the growth of the economy."

And how do we measure government spending?

PolitiFact Virginia: Mark Warner, 17 April 2011:

"Right now we are spending at an all-time high, close to 25 percent of our GDP [is] being spent on the federal government. But our revenues are at an almost all-time low of about 15 percent [of GDP]."

Center on Budget and Policy Priorities: Federal Spending Target of 21 Percent of GDP Not Appropriate Benchmark for Deficit-Reduction Efforts:

Over the 40 years from 1970 through 2009, revenues averaged a little over 18 percent of GDP, and expenditures averaged nearly 21 percent of GDP.

Paul Krugman: The Truth About Federal Spending:

The fact is that federal spending rose from 19.6% of GDP in fiscal 2007 to 23.8% of GDP in fiscal 2010.

The yardstick for government spending is GDP.

The yardstick for government spending is GDP. But GDP is the thing that is not growing. The yardstick is shrinking. And this is what we use to measure Federal spending.

The shrinking yardstick creates the appearance of excessive Federal spending growth. But what is the truth? Is Federal spending growing excessively? Or does it only seem that way because the yardstick is shrinking?

Has anyone ever addressed this question? To my knowledge, no.

The argument for cutting government spending is that the spending hinders economic growth. And we know that GDP growth is slow. But slow GDP growth is not evidence that government spending is the cause of slow GDP growth.

What is the evidence?

We know that GDP is not growing fast enough. They say government spending is to blame. And their proof is that government spending is growing relative to GDP. The proof is that government spending is growing faster than the thing that is not growing fast enough.

I went back and forth for two days, trying to determine where to show the trend-change in my "trend of real GDP" numbers. Finally I decided to go with 1980.

Growth is exponential. Real (inflation-adjusted) GDP, shown in red on Graph #1, closely follows the exponential trend line shown in black:

Graph #1: Real GDP (Quarterly) 1947-2007 and Exponential Trend

But take a closer look. For the first half, the left half of the graph, the red line is on the black line or above it. In the second half, the red line is on the black line or below it.

In the first half of the graph, the red line starts out slightly below the trend line but gains on it. In the second half, the red line ever so gradually falls below the trend. And I should point out, this graph stops in 2007. The graph stops before the financial crisis of 2008 and the recession of 2009 and the large fall of RGDP below trend that occurred at that time. This graph doesn't show that.

In the first half, the graph shows, economic performance was better than trend. In the second half economic performance was worse than trend. I therefore decided to split the data into two halves, and calculate the trend of each half separately.

I plotted the early years and late years as separate lines, then had Excel put exponential trend lines on them. Then I used the exponential formulas Excel came up with, and calculated the trend values as numbers so I could work with the numbers. Graph #2 shows black trend lines based on the numbers I calculated from those formulas.

Graph #2: Early Period (red) and Late Period (blue) with Calculated Trends
The X-Axis numbers here are "count of quarters" (quarterly data)
Notice that the early years RGDP (red) hugs its trend line more closely than on Graph #1. So does the late years RGDP. What happened is, the two trend lines here are a little different than the one trend line on Graph #1.

I took out the RGDP data so I could look at the trend lines. I scaled the two trend lines so they start at the value 100, and I showed them both for both halves of the graph. After 60 years or so, the late years trend (red) increases from 100 to about 700. The early years trend (blue) increases from 100 to 950 or so, nearly 1000.

Graph #3: Two Different Trend Lines

Now we're getting there. I re-scaled the late (red) trend and showed it starting at 1980, when the trend actually slowed. The faster-rising early (blue) trend I showed both early (as it occurred) and late (for comparison to the red trend line).

Graph #4:The Late Trend of RGDP Growth (red) Shown as it Occurred.
The Early Trend (blue) Shown Early and Late for Comparison.
As before, the blue trend reaches near 1000 by the end. The red line reaches higher than before, above 800 now instead of only 700, because the red line got a free ride on the blue line for 30 years.

Also, the separation of the red and blue lines is smaller on Graph #4 than #3 because #4 shows 30 years of late trend instead of 60.

What I have developed here is a growth index. It is similar to a price index that economists might use to convert between "real" and "nominal" values. But this index can be used to convert "late period" RGDP values to values fitted to the "early period" trend. I'll be doing that tomorrow. Here's a peek:

Graph #5: RGDP values (red) fitted to the Early Period Trend (blue)

Graph #5 shows the slower pace of real GDP growth that has been a focus of concern since the time of Reagan or before. It will be interesting to work with these higher values that are based on pre-1980 growth. They will make a larger denominator when we look at "Federal spending relative to GDP" and when we look at "Federal tax dollars relative to GDP" and when we look at "Federal debt relative to GDP'.

And that's just for starters.

The Excel file containing these graphs and the numbers behind them is available to view and download.

Saturday, November 24, 2012

Exponential Trends in Real GDP (3): Simulacron

On Thanksgiving day I wrote

Thornton says there was "a marked increase in [Federal] expenditures relative to GDP" beginning in the early 1970s. Fine. But economic performance dropped in the early 1970s. The marked increase in expenditures relative to GDP was a result of the decline in GDP growth.

I'd like to test that hypothesis. And now I know how to do it. This graph is from mine of the 20th:

Graph #1: Early Trend (green), Actual Trends (red), RGDP Values (blue)

In green, the latter years of the graph show a continuation of the early years' real GDP trend. In red is the more laggard latter years' actual trend. In blue you see the RGDP values from which the trends arise.

For the latter years I want to take the RGDP number, divide out the red trend value, and multiply by the green trend value. This will simulate higher values for real GDP in the latter years, based on the performance of the early years.

Then we can look at Federal spending and Federal revenue and such, relative to this simulated improvement of economic performance. We will be able to see what would have happened if -- if the inflation of the 1970s didn't lead to the suppression of economic growth since the 1980s. Would Federal spending still have increased, relative to the bigger GDP? How much would Federal revenue have increased, if we maintained the superior growth of the early period? And then with increased revenue, with less call for social spending because economic performance was better, and with a bigger denominator, what would have happened to Federal debt, relative to GDP?

Interesting questions.

Back in July I looked at the economy's performance in a series of graphs on RGDP growth. Here is Graph #3 along with remarks from that post:
Graph #3: Growth Rate from 1947 to Plotted Year (blue)
and Growth Rate from Plotted Year to 2011 (red)
The higher line here, the blue line, shows compound annual growth rates of Real GDP, the compound rate being figured from 1947 to each year plotted. The first three points on the blue line of Graph #3 show the compound annual growth rates for the periods 1947-48, and 1947-49, and 1947-50. Each subsequent point shows the compound growth rate of a longer period. The general trend shows decline.

At the right, the last blue point shows the rate for the full 1947-2011 period.

The general trend shows decline. The early years are "splashy" because few years are considered. But the blue line shows a peak right around 1967, and all downhill thereafter.

That's where I want to make my trend break, right around 1967. I want to look at the trend up to that point, and compare it to the trend since that point. It would be nice to push the date back a couple years, to 1965 maybe. That would get the whole of the "Great Inflation" out of the early trend and into the late trend.

I have to break this up into a series of posts. I need to go slow and check my work. Tomorrow I'll take a better look at where to put the break in the exponential trend.

Friday, November 23, 2012

Thornton: "the U.S. deficit/debt problem began during the early 1970s when the government started to increase spending significantly without a corresponding increase in tax revenue"

I showed this graph in the early post yesterday as Graph #4:

Graph #1: Federal revenues (red) lag GDP (green) more than Federal spending (blue) leads GDP.
I called it a "conceptual view" because it's not really a comparison of the Federal numbers to the GDP. GDP is by itself on the right-hand scale. So I got up in the middle of the night to redo the graph. I want to compare the Federal numbers to 20% of GDP:

Graph #2: All on the Left Scale, and Not on a Log Scale
Click Graph for FRED source page

Before 1970 the three lines run tight together. After 1970 Federal revenue (the red line) drops down a bit from the others; and after 1974 it drops down more. Federal spending (the blue line) runs tight beside GDP÷5 until the recession-induced blip of 1975, and tight again until 1980.

It does appear that the government "started to increase spending significantly" faster than the trend of GDP -- but not until 1980 and after. Not "during the early 1970s" as Daniel Thornton says. Definitely not "around 1970".

For proper analysis of the problem, it makes a world of difference.

Thursday, November 22, 2012

An Excel Tutorial by Chris Georges of Hamilton College

Found a nice 10-page PDF, Graphing and Data Transformation in Excel.

It's pretty inviting. If you've been looking for a way "in" to Excel, give this PDF a shot.

Happy Thanksgiving.

"The U.S. Deficit/Debt Problem: A Longer-Run Perspective"

For the last 40 years we have been told over and over and over again that the Federal debt and deficits are proof government spending is excessive. They are not proof.

Daniel Thornton
Vice president and economic adviser
Federal Reserve Bank of St. Louis
The Economic Research division of the St. Louis Fed offers an intro page on Daniel L. Thornton's The U.S. Deficit/Debt Problem: A Longer-Run Perspective (PDF). The intro page presents the abstract of the paper:

The U.S. national debt now exceeds 100 percent of gross domestic product. Given that a significant amount of this debt is the result of governmental efforts to mitigate the effects of the financial crisis, the recession, and the anemic recovery, it is tempting to think that the debt problem is a recent phenomenon. This article shows that the United States was on a collision course with a major debt problem for nearly four decades before the financial crisis.

Oh, I agree! I think it is a great insight... Well no, not really. I think it is painfully obvious that the Federal debt was growing long before the crisis. Really, Perot was talking about Federal debt in 1992, and before him Reagan was talking about Federal debt in 1980. So nobody -- nobody at the Fed, and nobody outside the Fed, either -- should be thinking that the Federal debt suddenly became a problem at the time of the financial crisis. Oh, well. The abstract continues:

In particular, the debt problem began around 1970 when the government decided to significantly increase spending without a corresponding increase in revenue.

Yeah yeah, the problem began long ago.

But wait a minute. What does Thornton say? "The debt problem began around 1970 when the government decided to significantly increase spending without a corresponding increase in revenue." The Federal debt problem arose right around the end of the Golden Age, when the government decided to increase its spending. Really?

Quick look:

Graph #1: Federal Government Total Expenditures  (Log Scale)

... I dunno. I see a slow-down from 1980 to 2000 all right, but before 1980 looks to me like a straight line. Wiggly, sure, but straight. And a straight line on a log-scale graph means a constant rate of growth. Means there was no decision to "significantly increase spending". Quick look, mind you.

What I think, it wasn't that there was a decision to "increase" Federal spending. I think things were growing, population, GDP, Federal spending all were growing. And there was a presumption that a straight-line increase (like the 1960-1980 trend on Graph #1) was a baseline that did not count as an "increase". And I think that was a perfectly reasonable thing to think.

And then what happened was, the Golden Age ended, and GDP started falling behind its baseline trend. Unemployment started going up:

Graph #2: Unemployment hits bottom, 1968-1970

Federal revenues (red) started falling off, ever so slightly at first:

Graph #3: Federal Government Total Expenditures (blue)
Federal Government Current Receipts (red)
1960-1990, Log Scale

Okay. Granted, it's hard to see clearly whether Federal spending increased or Federal revenues fell off. Gimmie a break, I'm telling ya what I think. I think revenues started falling off. I think the source of the Federal deficits was that revenues started falling off. Not that "the government decided to significantly increase spending" relative to trend.

These are small changes, subtle differences. If I have sufficiently motivated myself, then soon I will take a closer look at the growth patterns of Federal revenue and spending, and come up with something more definitive. But I shouldn't have to do that. Daniel Thornton should have done it already.

Hey, here is one more look at Federal spending (blue) and Federal revenue (red) on a log chart, this time with nominal GDP shown as well (green, right scale):

Graph #4: Federal revenues (red) lag GDP (green) more than Federal spending (blue) leads GDP.
In this conceptual view we see Federal revenues falling off, and not Federal spending growth, as the chief contributor to the deficits.

NOTE: It may well be that the Federal deficits increasingly fail to have the intended (Keynesian) effect. In other words, stimulus spending does not work as well as expected. The value of the fiscal multiplier has fallen. This is a view more often expressed by "conservative" economists (I think) than by "liberal" ones. But I think there is something to it. Nevertheless, it remains wrong to say that "the government decided to significantly increase spending".

From Thornton's PDF:

The analysis here shows that the U.S. deficit/debt problem began during the early 1970s when the government started to increase spending significantly without a corresponding increase in tax revenue. This article also analyzes various aspects of government revenues and expenditures to better understand the different elements of the debate...

(Page 441.) Thornton continues:
The conclusion that the United States was on a collision course with a debt problem is supported by a simple analysis of government revenues and expenditures as a percent of GDP. Figure 3 presents government spending and revenue as a percent of GDP from 1950 through 2010. The black and blue dashed lines denote the average federal government revenue and expenditures, respectively, as a percent of GDP from 1950 through 1969. The figure shows that after 1970 both revenues and expenditures increased on average relative to the previous two decades; however, revenue increased marginally, while expenditures increased significantly...

Figure 3 shows, however, that tax revenue as a percent of GDP increased from 17.5 percent of GDP to 20.6 percent of GDP from 1993 to 2000. This increase is associated with the tax increases introduced in 1993. Revenue subsequently decreased following passage of the Economic Growth and Tax Relief Reconciliation Act of 2001 (EGTRRA; a.k.a. the George W. Bush tax cuts). The decline in tax revenue relative to GDP between 2000 and 2003 was likely due in part to the 2001 recession; 2007 tax revenue as a percent of GDP was at or above the 1950-69 average level during the 2006-08 period. The marked decline in revenue as a percent of GDP during the 2009-11 period is likely due to the financial crisis and the accompanying recession. Hence, while the Bush tax cuts may have been a contributing factor to the deficit after 2001, this analysis suggests that the average deficit from 1970 to 2007 was largely due to a marked increase in expenditures relative to GDP: The ratio of debt to GDP was 57 percent in 2000 and increased to only 64 percent by 2007. Hence, most of the increase in the debt over the entire 1970-2007 period occurred because the government spent much more than it collected in taxes—about $6 trillion more.

I quoted quite a lot here, because Thornton's conclusion is important. That conclusion again: "Hence, most of the increase in the debt over the entire 1970-2007 period occurred because the government spent much more than it collected in taxes."

Okay. It is true that if you spend more than you receive, you increase your debt. If A is less than B, then A minus B is less than zero. It is a mathematical fact, yes. But it is not a "because". It is not an explanation. And it is not "proof".

Why was A less than B? Why did the Federal government spend more than it received? What happened? These are the important questions.

Thornton says there was "a marked increase in expenditures relative to GDP" beginning in the early 1970s. Fine. But economic performance dropped in the early 1970s. The marked increase in expenditures relative to GDP was a result of the decline in GDP growth. Meanwhile, the accepted view at the time called for increased government spending when GDP growth slows, as a way to boost economic growth.

The proper question is not Why did the government choose to spend "much more than it collected in taxes"? The proper question is Why did GDP growth falter?

The rising cost of interest, a result of our ever-increasing reliance on credit, drove up the financial cost of production. This cost drew income away from labor, causing a subtle decrease in the growth of demand. That same cost drew profit away from productive ("nonfinancial") enterprise, undermining the incentive for productive sector growth. And that same cost boosted the profit of the financial sector, enhancing the incentive for financial sector growth. Policy encouraged all of this, on the grounds that credit use is always good for growth.

GDP faltered because of our excessive reliance on credit. Federal spending increased when GDP faltered, and Federal revenue declined. Thus, the Federal debt and deficits.

I find it most disturbing that the people who should be looking into such things, people like Daniel Thornton, are instead busy overlooking them.

Wednesday, November 21, 2012

"Updated Summary of NIPA Methodologies" versus Nick Rowe

From: Survey of Current Business (Online) November 2012, Bureau of Economic Analysis, Volume 92 Number 11:
Updated Summary of NIPA Methodologies (PDF)

The data and methods used to prepare current-dollar and real estimates of GDP as well as current-dollar estimates of gross domestic income, reflecting the 2012 annual NIPA revision.
From the PDF:
Updated Summary of NIPA Methodologies

The Bureau of Economic Analysis (BEA) has recently improved its estimates of current-dollar gross domestic product (GDP), current-dollar gross domestic income (GDI), and real GDP as part of the 2012 annual revision of the national income and product accounts (NIPAs). The sources of data and the methodologies that are now used to prepare the NIPA estimates are summarized in this report...

Estimates of real GDP

BEA uses three methods to estimate real GDP: the deflation method, the quantity extrapolation method, and the direct valuation method. These methods and the source data that are used for estimation are listed in table 2.

The deflation method is used for most components of GDP. A quantity index is derived by dividing the current-dollar index by an appropriate price index that has the base year—currently 2005—equal to 100. The result is then multiplied by 100.

The quantity extrapolation method uses quantity indexes that are obtained by using a quantity indicator to extrapolate from the base-year value of 100.

The direct valuation method uses quantity indexes that are obtained by multiplying the base-year price by actual quantity data for the index period. The result is then expressed as an index with the base year equal to 100.

For most components of GDP, they divide the actual (so-called nominal) number by a price index. They divide the price change out of the number in order to get a quantity-of-output number. They start with the actual-price output number, divide by a price number, and take the result to be "real" output.

I'm not saying it is wrong to do this. I'm just pointing out that they do it. I'm sure that for most components of GDP, there is no other practical way to do it. Okay?

So now, here's what Nick Rowe said:

Places like Statistics Canada measure *both* NGDP and RGDP to calculate P. P is the "derived" value, in practice.

But according to the NIPA PDF, they do not do it the way Nick Rowe says. For most components of GDP, according to NIPA, RGDP is the derived value. Not P.

Nice to know.

Tuesday, November 20, 2012

Exponential Trends in Real GDP (2): Trend 20, Shift 10, Repeat

This is Graph #4 from mine of the 18th:

Graph #1: Early Trend (green), Actual Trends (red), RGDP Values (blue)

The green line is the RGDP trend for the years 1947-1977, continued out for 60 years.

The red line shows two RGDP trends: the 1947-1977 trend for the first 30 years, and then the 1977-2007 trend for the next 30 years. Real growth was slower in the second half, as the separating lines show.

In order to check the validity of my calculations for the earlier post, I added the blue line -- FRED's values for "GDPC1", which we can call "Real GDP" or "RGDP". I was pleased to see the blue line run close to the red line for the whole 60 years shown on the graph. Oh -- not happy that RGDP growth slowed down, no. But happy that my arithmetic turned up a pretty good match.

But look again at the second half, the right half of the graph where the red and green lines separate. For that whole 30 years, the blue line is almost always below the red. The RGDP numbers are almost always below the trend I show.

My bad. I figured trends as described previously, for the 1947-1977 and 1977-2007 periods. Those are 31-year periods, start to finish. Then when I plotted the exponential trends, I used 30-year periods. Didn't think it through beforehand. I'm doing that now.

What I should have done is to make the first half of my red line 31 years long, not 30. And I should have started the second half at the 31st year, not the 30th. That would have pushed the second half of my red line one year more to the right. It would have moved the red line closer to the "middle" of the blue line. That would have given me a better picture of the second-half trend. Oops.

I am not alone in thinking that the "golden age" after World War Two ended in 1966. That's earlier than is often said, but I see it on lots of graphs.

I am also not alone in thinking that the general uptrend of RGDP growth has been slowing. I think, consistently slowing. I suggested as much before, imagining a graph without the growth suppression of the Great Inflation time, and without the Supply-Side fixes that came after the Great Inflation. "We might have seen the three lines spread more equally apart," I wrote, "suggesting the unrelenting decline of economic growth."

So now I want to look at the RGDP trend up to 1966 -- the best trend, I expect -- and compare it to later trends. Overall, I expect to see the the uptrends showing less "up" as time goes by.

FRED's start-of-data is 1947, so my first trend will be based on the years 1947-1966. Now that's an actual 20-year trend. Count the years, if you like.

In order to make my trend lines comparable, I will use 20-year periods for each trend I figure. And I will let Excel figure the trends for me. Exponential trends, as before: Trends of growth.

I will end each trend ten years after the previous one. So my second trend runs from 1957 to 1976. My third runs from 1967 to 1986. And so on. At the end I'll have a few years left over, so I'll use a 20-year trend that ends with the most recent data. That'll be 2011, as I am using annual (not quarterly) data, to simplify my life.

So that's the plan. Now I have to create the graph.

I created graphs in Excel, one per sheet as before, added exponential trend lines, and put the resulting trend formula in the upper-right corner on each graph. Everything is contained in the ExpoTrends#2.xls file.

After I had all the graphs in place I went back and used the trend formulas to generate trend numbers (in the third column on each worksheet). These numbers are values for points on the exponential trend line. I'll use them to re-create the trend lines all in one graph, and leave out the original source data.

I added a line to each graph, using these trend values. I figured if I could *see* this new line, then it's not in the same place as Excel's trend line, and I have to check my work. I had to fix the first one; after than they all came out good.

I gathered all the exponential trend numbers on Sheet1. I entered the formulas again: more work but less confusion than trying to copy them from six other pages. So the checking I did previously doesn't mean the numbers on Sheet1 are good. But I did compare the first and last expo values on Sheet1 with the first and last "third column" values of each of the six sheets. All good. (But feel free to check my work.)

Graph #2: Variation in Real GDP Trends
The two highest trend lines here are the two oldest 20-year periods plotted. The one lowest trend line is the most recent: the 20-year period ending with the most recent annual data. The other three trend lines (blue, green, and a pink one that just peeks out beneath the green one) fall between the others chronologically as well as vertically.

It's not a perfect, regular decline in economic performance. But it is without question a continuing decline in economic performance. So when somebody shows you one of these straight-line trends cutting through the RGDP numbers...

Graph #3, source: Marcus Nunes

... do not hesitate to point out that the RGDP numbers were going up (relative to that trend) until 1966 or so, and have been declining (relative to that trend) since the '70s.

Kinda puts the recent large decline in perspective, don't you think?

Monday, November 19, 2012

Eyeballing-in some trend lines

I am pretty sure now that the graph in my 4 AM post is by Alexander Gloy of Lighthouse and SilverIsTheNew, and that the host for guest-posting was Zero Hedge.

I am particularly interested in the dotted black line on the graph, the "marginal utility of debt" line. Here is the same graph again, with some blue trend-lines eyeballed in, quick and dirty:

There is an uptrend in my trend line from the mid-1980s to the early 1990s, which corresponds perfectly with the downtrend in the red line.

What policy needs to do is more of the thing that makes the blue line go up and the red line go down.