Saturday, July 22, 2017

How does growth affect volatility?

Friday, July 21, 2017

How volatility is calculated

Wednesday, July 19, 2017

Low volatility, interrupted by periods of high volatility

Under the heading Possible end in Wikipedia's Great Moderation article, we read that some economists have said the Great Recession brought an end to the Great Moderation. Some, but not all. According to the article,

Todd Clark has presented an empirical analysis which claims that volatility, in general, has returned to the same level as before the Great Recession. He concluded that while severe, the 2007 recession will in future be viewed as a temporary period with a high level of volatility in a longer period where low volatility is the norm, and not as a definitive end to the Great Moderation.

I thought that was interesting. I looked up the link the article provides to a paper by Mr. Clark. In his opening, Todd Clark writes:

This article conducts a detailed statistical analysis of the putative rise in volatility and its sources to assess whether the Great Moderation is over. The article concludes that, over time, macroeconomic volatility will likely undergo occasional shifts between high and low levels, with low volatility the norm.

Writing in 2009, Clark said the Great Moderation will probably continue, interrupted by periods of high volatility.

Very interesting. Clark's view of the future is compatible with mine:

Tuesday, July 18, 2017

A Greater Moderation

While making my recent graphs of RGDP per Capita trends, I noticed that the trend line after 2007-2009 completely hides the data from the 2009-2016 period. First I was worried about creating confusion because the data points were not visible. Then I started thinking about "volatility".

I avoided the confusion (I hope!) by bringing the data line to the foreground and making it dotted. But I was left thinking about the volatility. So now I'm making the dotted line continuous again and putting it back behind the red lines where it is partly hidden by them.

I also made the black line thicker this time so you can see it behind the red:

Graph #1
You can see white space between the black and red in the early years. Not so much white between them since the 1970s. None since the mid-1980s. And then after the 2007-2009 gap in the red lines, the black would completely disappear behind the red if the black line wasn't thick. After 2007-2009, the volatility is gone!


Using quarterly data for RGDP per Capita, selecting subsets for effect, and looking at the standard deviation of the subsetted data, yes: Volatility has decreased more, since the crisis:

Graph #2
Not sure why people think moderation of economic growth is a good thing.

Monday, July 17, 2017

You are here

Graph #1

Saturday, July 15, 2017

(again, shorter)

It seems there are two ways to think about how things will look if the decline continues. This is the wrong way:

Graph #1: Showing the Most Recent Trend Continuing
If we stay on track with the 2009-2016 trend, by the year 2100 RGDP per Capita will reach the level it would have reached by 2050 if we had stayed on track with the 1949-1973 trend.

But Graph #1 does not show the continuation of decline. It shows only the continuation of the low-growth trend that resulted from the decline. The decline is the change in the rate of growth, from 2.4% to 2.1% to 1.34% and, unless things change, to a growth rate lower than 1.34% in the foreseeable future. And then again. That is the decline.

This is the right way to look at the decline:

Graph #2: A Continuing Decline in the Rate of Growth

Monday, July 10, 2017

The Future of Real GDP per Capita

Scott Sumner says "the neoliberal reforms after 1980 helped growth". He writes:

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

One may wonder how much more the economy might have slowed if not for those reforms. Perhaps here we have an answer: 0.76% more.

Graph #1: Natural Log of Real GDP per Capita (black) with Trend lines
2.4% Annual Trend Growth Rate for 1949-1973
2.1% Annual Trend Growth Rate for 1974-2007
1.34% Annual Trend Growth Rate for 2009-2016
Trend growth slowed 0.3% annual after 1973, from 2.4% to 2.1%. When the effects of the neoliberal reforms (or whatever) failed after 2007, trend growth slowed an additional 0.76%, falling to a 1.34% annual rate. The combined decline in the trend growth rate is 1.06%, more than a full percentage point below the 1949-1973 rate.

Based on these numbers, Sumner's story says growth would have slowed 1.06% without the neoliberal reforms, but instead slowed only 0.3% because those reforms were put in place.

In Sumner's next post after the one I quoted above, he considers the question Why did growth slow after 1973? His answer echoes that of Robert Gordon, who says "the life-altering scale of innovations between 1870 and 1970 cannot be repeated." An empty explanation.

Scott Sumner adds to Robert Gordon's story, diluting the meaning with extra words. "Here’s what I think happened," Sumner says:

There were a few underlying technological developments in the late 19th century that dramatically affected living standards in the 1920-70 period, when they were widely adopted in advanced economies. I would certainly include electric power and the internal combustion engine. I also think indoor plumbing is underrated. Imagine having to rely on outhouses in cold climates... Many key products were first invented in the late 1800s or early 1900s (electric lights, home appliances, cars, airplanes, etc) and were widely adopted by about 1973. No matter how rich people get, they really don’t need 10 washing machines. One will usually do the job. So as consumer demand became saturated for many of these products, we had to push the technological frontier in different directions. And that has proved surprisingly difficult to do.

Well, they had indoor plumbing in ancient Rome. But Scott Sumner's "surprisingly difficult to do" tells us no more than Robert Gordon's "cannot be repeated". The question "Why?" remains. And then, "Why 1973?"

More to the point, Sumner's explanation does not account for the second slowdown, the 2007-2009 slowdown. He has a different story for that one. Not enough money, he says. Print more money, he says. Increasing the Fed's balance sheet from 800 billion to 4.5 trillion was not enough, he says.

Two slowdowns, two explanations. But we don't need two explanations. "One will usually do the job."

The greatest weakness in Sumner's story is a weakness he shares with almost all modern-day economists: His argument is a hodgepodge of unrelated tales. In this case, a lack of invention after 1973, plus saturated demand, plus a difficult technological frontier. But then after 2007, tight money was the problem: 4.5 trillion, and still too tight.

The question "Why?" remains.

There is no "big picture" any more, no one overall theory that explains what's wrong with the economy. There has been no big picture since Keynes was rejected by the moderns. Only a hodgepodge of unrelated tales.

What's wrong with our economy is the excessive accumulation of private debt. That was the problem in 2007-09, and in 1973-74, and before, and since. One problem. One problem that never gets better and always gets worse. One problem, ignored by economists who know which side their bread is buttered on.

I can never resist the opportunity to criticize Scott Sumner's economics. But that's not what this post is about. This is not about the decline of economics. It's not even about the reasons for the decline of economic growth. This post is only about how big the decline of growth has been, and how things will look if the decline continues.

It seems there are two ways to think about how things will look if the decline continues. This is the wrong way:

Graph #2: Showing the Most Recent Trend Continuing
If we stay on track with the 2009-2016 trend, by the year 2100 RGDP per Capita will reach the level it would have reached by 2050 if we had stayed on track with the 1949-1973 trend.

But this graph does not show the continuation of decline. It shows only the continuation of the low-growth trend that resulted from the decline. The decline is the change in the rate of growth, from 2.4% to 2.1% to 1.34% and, unless things change, to a growth rate lower than 1.34% in the foreseeable future. That is the decline.

This is the right way to look at the decline:

Graph #3: A Repeating Decline in the Rate of Growth
Two factors affect the up-and-down on this graph: the changing slope of the red lines, and the drop after each red line stops. Two factors affect the left-and-right: the length of the red lines, and the duration of the gap between the red lines. Obviously I made these things up.

The black dots indicate the original source data. After the black dots die out in 2016, it's all just a guess. The last five red lines, including the one that started in 2009, are each shown as 20-year trends. You could change them if you want.

The gaps between the red lines, each is one year longer than the gap before. The gap you can't see (1973-74) is one year. And the 2007-2009 gap is two years. These are actuals. I stuck with the pattern and made the next gap three years, and the next gap four years, and like that. You can change them if you want.

If you change these things, you will stretch the graph out, left-to-right, or shorten it, left-to-right. But you won't change the up-and-down pattern. To change the up-and-down pattern you have to change the growth rates (the slopes of the red lines) or the drops after the red lines stop, or both. You can change those too, if you want, but you should be realistic.

The red line slopes 0.3% less after 1974 than before. Hard to see. After 2009 it slopes 0.76% less than before. Those are actuals. I was going to keep making the number bigger for the future slopes, but I decided against it. Instead, I went with the 0.76% additional decline each time. No one knows what those actuals will turn out to be, but assuming the most recent actual change each time provides a realistic picture.

For the vertical drop at the end of each red line, I did something similar: Each drop is the same size as the 2007-2009 drop. That's as realistic as I can be here, estimating the future.

// The Excel file

Thursday, July 6, 2017

Real GDP per Capita growth: Three Trends

The previous post shows Real GDP with lines that represent growth trends for three different time periods. The topic of the post was the relation between economic growth and population growth.

But come to think of it, RGDP varies when population varies, and a change in population growth would change the trend of RGDP. So I want to take another look at the changes in Real GDP growth trends, this time excluding the changes in population. To do it, I'll look at Real GDP per Capita.

I'll make some other changes, too. Rather than using "billions of 2009 dollars" and showing the numbers on a "log scale", I'll get "log values" from FRED and plot them normally. That eliminates the Log Scale Axis Labels problem I had last time. And because the values are logged, the trends will be straight lines rather than exponential curves. So I can use Excel's "linear" trendline option and keep things nice and simple.

I'll use annual values instead of quarterly, to reduce the work involved. The purpose of the graph is to get a general idea about how the trends have changed, and the annual values are good enough for that. Annual frequency with "end of period" aggregation because, for GDP, it just seems right.

Here's my data source:

Graph #1: Natural Log of Real GDP per Capita, 1947-2016
In order to define trend regions, I divided the dataset into three sections. The break points between sections are so arbitrary they made me hesitate -- hesitate enough to miss a day's posting. But then, missing a day's posting got me working again, "arbitrary" be damned.

I'm ending the first section at 1973 and starting the second at 1974. I'm ending the second section at 2007 and starting the third at 2009. In each case the section ends at a relative high value and the next section begins at a relative low. To be consistent, I started the first section at the relative low in 1949.

Because of these decisions, not all the data points are used to determine the trends. The data points not used are shown in black on the following graph; the points that are used create three separate red lines which represent the source data for the three trend calculations:

Graph #2: Subsetting the Data for Determination of Trends
Once the data was split up into subsets, adding trend lines was easy.

For the next graph, the data not used is not shown. The data that is used is shown in black. And the trend lines are red. The year values are not shown, as adding those values messes up the trendline equations:

Graph #3: Determining the Trends
This one's a little hard to read because the trend lines are too long. I'll fix that, below.

The equation for the first period (1949-1973) shows a slope of 0.024, indicating 2.4% annual growth. For the second period (1974-2007) the equation indicates 2.1% annual growth. And for the third period (2009-2016) the equation indicates a 1.34% annual growth rate.

For both the second and third periods the R-Squared value is 0.9889, pretty close to 1.0. For the first period, R-Squared is somewhat lower, at 0.9571. As I understand it, this means the first-period trend line is somewhat less accurate than the other two. The trend line doesn't match the data as well.

I want to suggest a reason for the mismatch: The first period was not part of the so-called "Great Moderation". The Great Moderation was a time of moderate variability in the data. (The "standard deviation" was less.) With less variability in the source data of the later periods, the trend line should be a better match. And we find that it is. So I think the lower R-Squared of the first period is a result of the fact that the data values varied more in that period, and not that there is something wrong with the trend.

I took the three trendline equations from Graph #3 and changed them to display more decimal places, for greater accuracy when I use those equations to create my own lines. Making my own lines to show the trends gives me greater control over where the lines start and end. Also, I can show the years on the x-axis without messing up the trends.

Graph #4: Three Trends of RGDP per Capita
This graph looks lot like the "three trends" graph for Real GDP in the previous post. But this graph shows that even when the changes in population are set aside, long-term decline of economic growth is evident.

// The Excel file

Tuesday, July 4, 2017

Does GDP growth influence population growth?

For 22 years beginning in 1952, the economy grew at something like a 4% annual rate. For 24 years beginning in 1984, the economy grew at something like a 3% annual rate. And for all the years since 2009, the economy has grown at something like a 2% annual rate:

Graph #1
Assume it is true that population growth influences economic growth. Suppose it is also true that economic growth influences population growth, and look at the graph.

The graph shows the beginning of a very long long-term decline.

// The Excel file

Monday, July 3, 2017

Why is he talking about population?

Why population? Because, to my mind, apart from fiddling with immigration policy and such, population growth responds primarily to economic conditions. Population growth slowed in the 1930s? Because the economy was slow. Population growth picked up in the 1950s? Because the economy picked up.

I don't see it on my graphs, but I want to suggest that the U.S. population growth (not counting immigrants) has been in decline since 1980 because the U.S. economy has been in decline since that date. Or maybe the date should be 1974. Or maybe the 1960s.

Can't see it on the graphs because the data from before 1960 is not comparable.

Such a decline in population growth would be evidence of economic decline. Come to think of it, so is the argument that we need to increase immigration in order to boost economic growth. Or maybe that last one is just evidence of the decline of economic argument.

But if the "natural" rate of population growth (which excludes immigration) has declined in response to a declining economy, then the correct response would be to reverse the economic decline. To reverse the decline of population growth by increasing immigration is the wrong response. It camouflages the economic problem and confuses the economic analysis. It does not solve the economic problem.

That's why I'm talking about population.

Sunday, July 2, 2017

The "Natural Rate" of Population Growth?

The population growth rate graph, again:

Graph #1: A Natural Rate of Population Growth?
I put a line on there in red, suggesting what looks to me to be a "natural" rate of population growth since the 1960s, or anyway a rate from which the actual rate is sometimes disturbed and to which it apparently desires to return.

Don't be outraged; it's just an impression.

Anyway, when I look at the blue line after 1960 I see what looks like one particularly large and long-lasting disturbance:

Graph #2: A Large Disturbance beginning around 1990
For some reason, I had in mind that this large disturbance was a result of immigration as opposed to the other thing. I don't know why I thought immigration, but I did. For the longest time.

Maybe I read it somewhere, and then forgot. Anyway, I finally tracked it down and yes, it looks like immigration caused that disturbance. The next graph is part of an image presented by weforum:

Graph #3: from World Economic Forum
There looks to be a pretty consistent uptrend since about 1950 on this graph. But just around 1990 there is one particularly large spike. It shows a tripling, from about 600 thousand to about 1800 thousand immigrants, and it attributes the spike to "IRCA legislation".

I looked it up. IRCA is the Immigration Reform and Control Act of 1986. So yeah, immigration in this case. But I still see it as a disturbance or deviation from the "natural" tendencies which arise as an outgrowth of economic conditions.

Saturday, July 1, 2017

Population growth responds to economic conditions

It is often argued that the economy's performance depends upon population growth. No doubt, but economic forces typically work in both directions and, if that is true, then it is also true that population growth depends upon the economy's performance.

Googling us population historical data excel turns up World Population Data (3) as the first result. Their population.xls file contains a worksheet named US Population Data - Filled in which will serve my purpose. The initial notes say

Before 1960, 10 year census data was filled in assuming constant annual growth during that decade. From 1960, Current Population Survey estimates are used.

So the data for the time of the Great Depression time is not perfect, but I probably won't find anything better. They provide this graph:

Graph #1: From the Population.XLS file
You can easily see a slowdown of population growth from 1930 to 1940. That's gotta be a result of the Great Depression. Malthusian. Here is a plot of the growth rate:

Graph #2: Population Growth Rates, based on the data from Graph #1
You can see the low of the 1930s, a low which supports the view that population growth responds to economic conditions. And you can see the high of the 1950s, likely in part a result of the improved economic conditions of that time.

Diane J. Macunovich writes:

Many factors can influence a couple’s decision to have a child, but a large body of work suggests that economic factors—especially women’s wages and young adults’ relative income—have played a major role in U.S. fertility trends. “Relative income” refers to a person’s earning potential relative to his or her desired standard of living.

If your "desired standard of living" is high, you might be inclined to put off having children and instead devote more time to your career. That would tend to push the economic trend and the population trend in opposite directions. No doubt it's a factor.

I think more in terms of our expected standard of living -- low during the Great Depression, high after a victorious end of WWII. These would tend to push the economic trend and the population trend in the same direction.

Both tendencies exist, no doubt. But it seems to me that major events (like the Great Depression and the end of World War Two) would give a general push in one direction or another. People do always have their own goals and their own desires, but for a large number of people these would tend to average out. So the general trend of population growth in an economy like ours must be subject to the push of major economic events.