I have been working on a way to endogenize the projection of the capital stock. I needed a way of calculating the capital stock based on other economic data that was available from the Penn World Table. I went down several interesting but unhelpful rabbit holes. I finally found what I needed in Godley and Lavoire (Godley, Wynne, and Lavoire, Marc. Monetary Economics, An Integrated Approach to Credit, Money, Income, Production, and Wealth. Palgrave Macmillan, 2012). They present a system of 4 equations shown below.

K=K_-1+(I_d-DA), where

K= the capital stock in the year of interest

K_-1= the capital stock in the previous year

I_d= the investment in the year of interest

DA= the depreciation allowance in the year of interest

DA=δ K_-1, where

δ= the constant rate of depreciation

K^T=κ Y_-1, where

K^T= the target capital stock for the year of interest

κ = target fixed capital to output ratio

Y_-1 = the GDP for the previous year

I_d=γ (K^T- K_-1)+DA, where

γ= partial adjustment for fixed capital

The Penn World Table provides data for the K, Y, and Id. I was then able to calculate DA, KT, Id, and K using the actual values for K-1, Y-1, and Id for each year from 1950 to 2014. Then by using the error squared between the actual and the calculated GDP, investment, and capital, I was able to estimate values for δ, κ, and γ.

Before I discuss the results, I am also concerned about the logistic projection of the total factor productivity (TFP). The capital stock projection calculated above depends on the calculated GDP which depends on the total TFP. So it makes sense to explore them together. There is some evidence that the TFP growth is slowing, but the logistic curve fit seems to level off too sharply. The first graph shows some results of various TFP projections.

The data is calculated TFP based on actual data. The DICE curves are from Nordhaus. They were adjusted for this version of the Solow equation. The rational model curve seems to be the best fit based on R squared and visually. I got it from my curve fitting software, Curve Expert.

Getting back to the capital stock, when I projected the capital stock I forced the investment/GDP to stay in the range of the data. The second and third graphs show capital stock, and GDP.

As you can see, this results in considerably higher capital stock and GDP projections than the logistic capital stock projection, but still a leveling off. The green line uses the logistic TFP projections and the brown line uses the rational model TFP projection. Of course, any GDP projection depends on how we deal with climate change. My plan is to combine this GDP projection with a DICE based integrated assessment model.

I plan to make this into an easily accessible Excel workbook that allows various combinations TFP and capital stock projections as well as various climate damage models and maximum temperatures. This will take a while so please be patient.

On 8/25/20 below I discussed the global population projection to be used as a measure of available labor. A better choice would be to use employed individuals. I get to that by projecting the percentage of the population employed. Beyond that, it can be augmented by estimating human capital in terms of years of education. I will address these issues later, but first I wanted to discuss the projection of capital stock.

In economics, capital stock consists of the physical assets that help us supply products and services. This includes things like machinery and buildings, but it also includes the infrastructure: such things as the transportation system, the electric grid, and the water supply. The Penn World Table provides this data from 1960 to 2014. I modeled the global capital stock data with a logistic curve. The best-fit midpoint is the year 2036, and the maximum global capital stock is about 2.2 times higher than it is today.

However, the exponential curve is indistinguishable from the logistic curve over the time frame of the data, but the exponential curve has the unfortunate property of increasing at an increasing rate forever. David Attenborough said, “Anyone who thinks that you can have infinite growth on a planet with finite resources is either a madman or an economist.” The capital stock is often measured in dollars, but they are physical assets that need resources to produce and maintain. While this makes a certain amount of sense, it is a rather weak justification. I am working on a way to endogenize capital stock into a model rather than projecting it separately. While I am hopeful this will work, I am not particularly confident. There is little in the literature to provide direction.

I discussed projecting energy use below on 8/11/20. In that post, the focus was on projecting energy intensity. In this post, I provide some context. The combination of lower economic growth and lower energy intensity results in a projected global energy use maximum in about the year 2060. This maximum is only about 15% higher than it was in 2016. By the year 2300, the projected energy use is only 20% of the value in 2016. The projected energy intensity is only 9% of what it was in 2016. Can this be true?

It depends on two other projections. The first is the projection of global GDP. I discussed this below on 8/4/20. I used two approaches. The first one is to analyze the GDP over a very long term, back 2000 years. The second approach to projecting GDP is to use a Solow model and project all the factors (population, percent employed, capital stock, human capital, and total factor productivity). Each of the factor projections has its uncertainties. I discussed the population projection below on 8/25/20 and will discuss the other factors in future posts. In the end, the long-term and Solow model approaches give very similar results which provide a bit more confidence.

The other projection needed is energy intensity in terms of the amount of energy needed for each dollar of GDP. I discussed this below on 8/11/20. This projection seems to be on solid ground at least for the rest of this century.

This projection for energy use is lower than other projects available. Lower energy use is good news for climate change. It will be easier to address climate change if our energy use is lower. However, the energy use projection is based on lower GDP growth which tends to make economic inequality worse. It also tends to make an already unstable economic system more unstable. Fortunately, there are things we can do to reduce economic inequality and instability in the economic system. That will be discussed in future posts.

This week I added a section on excerpts from the book to this website. You can access them from here or the “Excerpts” link above the picture of the front cover on the home page. This will take you to a page with an expanded table of content. So far, there are links for the Preface, the Introduction, and the Index. I plan to add sections from time to time. I hope you find them interesting and informative. Enjoy!

Today a came across an article in Grist, Growing Pains, that echoed many of the decidedly not mainstream points I made in my book like global economic growth has been slowing since the 1960s, economic growth is an aberration in the last 150 years or so that is unlikely to last or be repeated, and green growth and uncoupling of economic growth from energy use are mostly myths. I said, “Wow! Maybe I’m not crazy.” Well, I guess I might still be crazy but at least I have company. In any case, this article provides a good history of the idea that we can’t grow forever and an overview of some recent progress. It starts with the Club of Rome report from the late 1960s and Limits to Growth from the early 1970s and discusses how these were slammed at the time by the press and mainstream economists. Over the last 50 years, these ideas have been explored by a slowly growing group of people. Research on how we can thrive in a low or no growth scenario is slowly making progress and converts. This research appears in smallish, niche journals. Maybe it is time for this thinking to go mainstream.

To project global GDP by calculation from the various factors that are used, projections of those factors are required. The population is a key factor in projecting GDP. Until about 1800 the population growth was very slow. After that, it grew rapidly until about 2000. The latest projections from the U.N. in 2019 go only to 2100. They project an average population of 10.9 billion in 2100 with 95% confidence limits of 9.4 to 12.6 billion. This represents a slowing of population growth. This type of behavior is often projected with a logistic curve. The population logistic curve model uses the existing data plus the 2019 average U.N. projection. The results of the logistic curve fit are a midpoint of 2004, and the maximum is about 13.0 billion. This is 75% higher than where it is today. It projects 11.4 billion for the year 2100, which is within the U.N. confidence limits.

Of course, any projection contains uncertainty. Projecting anything 80 years into the future contains significant uncertainty. Part of the uncertainty is related to the quality of the historical data. This can be described by standard statistical methods. I use Curve Expert software for this purpose. The shaded area shows the 95% confidence limits of where the curve may be. The dashed lines show the 95% prediction limits where individual data points may be.

The latest U.N. projection predicts a world population of 11.4 billion in the year 2100. The 95% confidence limits are 9.6 to 13.2 billion. In 2004 the U.N. projected world population to the year 2300. The medium projection was nine billion in the year 2300. They gave low and high projections of 2.3 to 36.4 billion. What could cause such a wide range? Population projections often make three sets of assumptions: fertility, mortality, and migration.28 The U.N., of course, does a very thorough job of making its projections. For the 2017 projection, it broke the world population into 233 countries and regions. Then it broke each of those into five-year cohorts and by sex. A five-year cohort is a group of people in the same five-year age group. For example, a group of females aged six to ten years. For each cohort in each country or region and sex, it made projections for mortality and migration and fertility for females. It then projected populations for each combination. Finally, it added up all the countries and regions. This produced a projection of the total population. It also projected the number of people in each cohort, sex, and country.

The problem is there is significant uncertainty. This comes from the uncertainty in the projections of fertility, mortality, and migration. Also, the further we project into the future, the greater the uncertainty. To reduce uncertainty, the 2019 projection went only to the year 2100. Also, they used confidence limits instead of a range. Even this is only an effort to quantify the uncertainty. In the end, some things like population projections are difficult to know with much certainty far into the future because human behavior can change unexpectedly or environmental limits may be reached. Yet, it is worth making the best projection we can explore the results.

In the year 2000, I began my climate crisis journey. I was working in the Owens Corning Corporate Research and Development Center as an engineer on the energy-saving effects of cool roofs. Soon the discussion changed to the effect of cool roofs on the climate crisis. Cool roofs are a mild form of geoengineering, the deliberate intervention in the Earth’s natural systems to counteract climate change. They reflect solar energy directly back into space and help cool the planet. I didn’t know much about the climate crisis, so I did some digging. I even made a little spreadsheet climate model getting a feel for how the process worked. Even then, the scientific evidence was convincing. I came to three conclusions. First, the climate crisis was real. Second, we were causing it by emitting CO2 from the burning of fossil fuels, and third, the effects, while uncertain, were very bad. Once one comes to these conclusions, there is a moral imperative to try to do something about it.

So I started working on improving energy efficiency with more urgency and a sense of purpose. Over the years from the 1960s, there had been significant energy efficiency improvements. Yet, energy use continued to increase. I began to wonder what was going on. Soon it became apparent that energy use was related to the size of the economy as measured by GDP. So, I did some work to look at how energy and the size of the economy were related. I looked at the US economy first, but that data was confounded by international trade. We were importing products like steel that required a lot of energy to produce, but that energy use didn’t show up in US data. Untangling the effects of international trade looked nearly impossible, so I avoided it by looking at global data. I soon found that global energy use and GDP were highly correlated and the reason energy use continued to grow was that the economy was growing faster than energy efficiency was improving.

To assess the climate crisis, I needed a projection of global economic growth. What I found was that most projections used some version of exponential growth forever. I had read the Limits to Growth back in college and unlimited growth didn’t make sense to me. I started digging into economic growth. It was a long and convoluted path, but I finally concluded that global economic growth had been slowing since the 1960s and that it would likely stop by the end of this century. This might be kindly called a heterodox idea, or less kindly crazy and blasphemous. It does make the climate crisis a bit easier to manage. If we muster the political will to put an appropriate price on carbon emissions, we can succeed. A modified version of Nordhaus’s DICE integrated assessment model gave me a projected price on carbon emissions that could work.

If low or zero economic growth was our future, I wondered what it would mean. After another long and convoluted path, I concluded that could make economic inequality worse and the financial system more unstable. Reduced inequality is associated with better health and life expectancy, fewer drug problems, lower teenage birth rates, less obesity, less mental illness, fewer people imprisoned, and better social mobility. Of course, more inequality is associated with the opposite of these. With low or zero economic growth, the financial system is always close to a recession and the slightest slowing leads to a recession. Recessions hurt everyone and destroy families who are living on the edge. To thrive in a low growth world, we need an economic system that reduces inequality and improves financial stability. After a long search, I developed a list of not radical but practical policies that could be implemented now to make the economic and financial systems more robust and level the playing field reducing inequality.

So, I wrote this book partly to solidify my ideas, and partly to share the ideas and let them see the light of day. Hopefully, others that read this book will take these ideas and support them, criticize them, improve them and most of all implement them in their improved form.

In earlier posts, I have shown that energy use and GDP are highly correlated and made a long-term projection of GDP. To project CO2 emissions, a projection of energy use is needed. Projecting energy use requires projected energy intensity along with the projection of GDP. Plotting energy intensity versus time shows a nice downward sloping set of data, yet a linear curve fit line crosses zero a little after the year 2100. This, of course, is impossible. We can’t generate GDP with zero or negative energy use. However, it is possible to use an exponential curve fit, which fits the data about as well as a linear fit. This results in a curve that asymptotically approaches zero.

Now, I can multiply the projected energy intensity times the projected GDP to project energy use. This yields some surprising results. The combination of lower growth and lower energy intensity results in a projected energy use maximum in about the year 2050. This maximum is only about 15% higher than it was in 2016.

This is an amazing projection. Can this be true? The energy use maximum happens when economic growth is less than the reduction in energy intensity. Can we continue to reduce energy intensity by the same percentage until 2050 and beyond? There is nothing in the data to suggest we can or we cannot. There are ample opportunities for energy efficiency improvements in buildings and transportation. Buildings, especially old buildings are not very well insulated or sealed against air leakage. Electric cars are coming as batteries become better and less expensive. Internal combustion engines are not very efficient, about 33% compared to electric motors at about 90%. So, the total energy needed to move our cars drops by almost two thirds, if the electricity is generated with renewable sources. As economies continue to become more service-oriented, their energy intensity will drop. All this suggests that continuing energy intensity improvements and reaching peak energy use is possible in the next 30 years.

Addressing the climate crisis requires converting our energy system to renewable energy sources. Because energy use correlates with GDP, we need a projection of GDP far into the future to understand the problem. Most GDP projections assume continued exponential growth. We need a projection that considers the limits we are already up against. I looked at historical data and projected it into the future with these limits in mind. The conclusion is global economic growth has been slowing since the 1960s. This is despite our best efforts to increase GDP. It is likely GDP will double and economic growth will approach zero by the end of this century.

To come to these conclusions I used two different approaches. First, I looked at the long-term global GDP data. There is good data for about the last 60 years. Before that, there are estimates for various years going back 2000 years. This data shows that GDP grew almost imperceptibly until the industrial revolution and then took off dramatically. An exponential curve fits this data very poorly. However, a logistic curve fits it very well. The second approach breaks down GDP into the factors that affect it. These include population, percent employed, capital stock, human capital, and total factor productivity (a measure of technology available). Each of these can be projected. Then GDP can be projected by calculation using the individual projections. This approach gives similar results. Of course, all projections have some uncertainty. Since two different approaches giving similar results is an indication that our future probably looks something like this rather than the exponential projections typically used.

About 60% of Americans feel the same way. What about the 3% of climatologists and 40% of Americans? Minority opinions are not always wrong. So what should we do? We must convert to renewable energy sources eventually. Oil is projected to last 30 to 50 years and coal could last over 100 years. Our choice is to do nothing and risk catastrophe or spend resources now on things we may have been able to delay for decades. Perhaps an example that is familiar to most of us would help clarify our situation. If we buy homeowner’s or renter’s insurance, we pay money every year for something we hope we will never need. We lose the money we pay for insurance. We buy it because we can’t afford to have our home and/or all our stuff destroyed by a calamity, say a fire. In case of a fire, we would still lose our stuff, but we would be financially compensated so we could rebuild and restock our homes. Even if we are among the lucky few who could afford to rebuild and restock our homes without insurance, it is not worth the risk. I view acting on climate change as buying insurance.

Over time, the money saved by spending less to repair the damage caused by climate change will exceed the amount paid to mitigate climate change. It is as if the people of society are making an investment in themselves and their children. We will end up with a more stable climate and save money. To me this sounds like a win- win situation. What do you think?

This means when GDP goes up, energy use goes up by a proportional amount. GDP is a measure of the size of an economy, and global GDP equals the sum of the individual country GDPs. Using this data from 1965 to 2018, I was able to determine that:

Global Energy Intensity declined by about 0.69%/year.

Global Energy use increased by a factor of 3.74.

Global GDP increased by about 3.2%/year in constant dollars.

Energy intensity, in this case, is a measure of the energy needed per unit of GDP. We decrease energy intensity by energy efficiency improvements and decoupling GDP from energy use by moving more of the economy to energy light sectors, like services. You can see that so far we have not decreased energy intensity as fast as the economy is growing. So, energy use grows. And it gets worse. Not only are our efforts at reducing energy intensity not reducing energy use, energy intensity reductions are getting harder to come by. It is a case of diminishing returns. The more we reduce energy intensity the less room there is for improvements. This means that the more the economy grows, the more difficult it becomes to mitigate climate change. Not only do we have to convert or existing fossil fuel energy infrastructure to renewable sources, we have to add more renewable sources to meet the growing energy needs. It also means we need to have estimate of how much economic growth we can expect in this century to get a handle on the scope of mitigation needed.

Here is an excellent overview of income inequality in the US. It touches on many of the of the subjects I discuss in Crazy Climate and Rigged Economies like how US inequality is higher and economic mobility is lower than almost all developed countries, and that it is getting worse. They show how from 1979 to 2016 the real disposable income (adjusted for inflation after taxes and transfers) of the top 1% increased by 226% while the middle 60% increased by 47%. They don’t discuss the long list of social maladies associated with high economic inequality such as worse health and lower life expectancy, more drug problems, more violence, higher teenage birth rates, more obesity and mental illness, more people imprisoned, and lower mobility. Council on Foreign Relations Inequality Overview