Is the US Printing Too Much Money?

The Federal Reserve, the central bank of the US, has the power to print money. The US has just been through the Financial Crisis of 2007-2008. As a result of the Financial Crisis, the US Federal government has gone into debt both to maintain operations in the face of decreased tax revenue and to stimulate the economy. The Federal Reserve could simply print money to erase the Federal Debt but the fear is that printing money will lead to inflation. 

In this post, I look at this issue using statistical models based on Complex Systems Theory and World-Systems Theory. The models show that the US has not printed too much money (but could at some point in the future and has at times in the past) and that the money supply has historically had little to do with inflation as measured but the Consumer Price Index (CPI). Other forces in the world-system are at work here, not just the policies of the US Federal Reserve.

Printing money has been a contentious issue throughout US History and the current episode is no different (if you want to read in more detail type Is the US printing too much Money into the Google search engine). Monetary theory is also a contentious area in macroeconomics. If I tried to summarize  the area, you would instantly stop reading this post. 

Let me just mention one theory that is easy to understand and applies to the question at hand (most monetary theory doesn't). The theory is Milton Friedman's k-percent rule. Simply put, the central government should increase the money supply at some fixed percent, the k-percent. Contrast Friedman's theory to Keynesian counter-cyclical policy: the money supply should be increased during recessions to stimulate the economy and decreased after the recession to prevent inflation. The problem with each of these theories is "how much." How much should k-percent be or how much should the money supply be increased during a recession and decreased afterwards?

The "how much" question could be rephrased in a way that would be understandable to Stock Market Analysts who used technical analysis. The figure above is the US M1 Money supply (the definition of the money supply that is under government control) taken from the Financial Forecast Center (FFC). It includes actual data starting in April 2012 and a forecast that starts in 2015. The forecast is made using artificial intelligence techniques, not economic theory. A simple form of technical analysis would just connect the high and the low points for M1 over a period of time (the dashed green and blue lines). The argument is that if M1 goes outside this range, it is changing too much. Using this form of analysis, what tends to scare analysts (the red arrow in the graph) is when M1 increases rapidly as it did after Dec-2014. A problem with the graph above is its limited historical scope. We'd really like to look further back to set reasonable ranges and decide how M1 has fluctuated historically. In any event, the FFC is forecasting a peak in M1 for 2015.

The figure above shows M1NS (M1 not seasonally adjusted) from the Federal Reserve. We can see that the money supply expanded during the Dot-com Bubble but remained fairly flat until 2009. Why did M1 increase during the Dot-com Bubble and what would have happened had continued increasing (line A) rather than flattening out until 2010? Were the sharp increases in the money supply (lines B and C) after the Financial Crisis justified or something to be feared? And, what are the dashed green, red, and blue lines in the figure?

The dashed green and blue lines are the 98% bootstrap prediction intervals for the dashed red line, which is the attractor path for M1. The attractor path is the simulated time path of M1 derived from a state space model of the US economy. It shows what M1 would have been (a fictional line) without random shocks (the black line is the fact line). The attractor path is the line to which M1 will return without random shocks. The conclusion is that from before 1980 until 2000, M1 was too high. After 2000, until 2012, M1 was too low. As of 2012, M1 was right on the attractor path; if it stays there increasing at k-percent per year, M1 will be just right and it cannot be said that the US is printing too much money.

Now let's look at the US Inflation Rate as measured but the Consumer Price Index (CPI). The graph above is another forecast from the Financial Forecast Center (FFC), this time looking at the rate of change in the CPI. There have been a lot of increases and decreases in the CPI since Apr-12. Each increase (solid red arrow) could have been used by commentators to trigger fears of inflation. Technical analysis shows that the swings are increasing but have never peaked much over 2% while the FFC forecast is for essentially zero inflation after Dec-2014. Had the US been printing too much money and had all that money printing created inflation, we should have seen it here and we don't.

The forecast above is for CPIAUCNS (CPI for All Urban CoNSumers), again from the Federal Reserve. In this case, the model is forecasting the level of the CPI not the rates of change. It's very easy to see that the CPI is on the attractor path and well within the 98% prediction intervals, unlike the M1. You can pick particular blips (for example the red arrow) and become worried about inflation but the blips are random variation, all within probable ranges. 

The fact that the dynamics of M1 and the CPI are very different means they are being driven by different forces. The M1 is best explained by the state of the US economy and the CPI is best explained by the state of the World system. This should make some sense since the US is a globalized economy that controls its currency through the Federal Reserve and is at the same time the hegemonic leader of the World-system. These issues seem to escape most monetary models and economic models of inflation.

NOTE: In case you are wondering how good the state-space models are at predicting M1 one-month into the future (the typical criteria for econometric models), the forecast graph is presented below.

The models do an excellent job with very tight prediction intervals, getting wider of course into the future. The two models used for the forecasts are the USL20 model and the WL20 model. The USM1 models is here and the US CPI model is here. Explanations for how to use the models are available here.

QUESTIONS FOR FUTURE POSTS:

1. What are the forces in the US Economy and the World System that drive monetary policy?
2. Why was the M1 too high during the Dot-com Bubble and too low afterwards?
3. During the Financial Crisis of 2007-2008, M1 growth was pretty flat. Was the US Federal Reserve trying to pop the Subprime Mortgage Bubble?
4. What would be a reasonable value for Friedman's k-percent? In 2015, the annualized growth rate of the M1 attractor was about 5%. Should the value of k-percent increase, decrease or stay the same in the future?
5. What are the forces in the World System that drive inflation?
6. Did the US recently go through a Debt Crisis similar to ones in Europe and Latin America?
7. Would harsher Austerity Policies produced a better or worse outcome in the US? Are stronger Austerity Policies needed in the future? 
8. What about the performance of Federal Reserve policy instruments such as the Fed Funds Rate?
9. What about the behavior of interest rates and the Zero Lower Bound problem?

Peak Oil Forecast and Global Warming

Peak Oil is the point where the rate of petroleum extraction starts declining because the resource is being exhausted.  US domestic Peak Oil production was reached in 1970. World oil production may have peaked in 2011, but it is too early to establish that as fact. In this post, I will forecast World oil production using the WL20 model to see whether the model thinks the World system has reached Peak Oil.

If you've "peaked" at the graphic above you probably can determine that the answer will be "Yes"! However, there's much more at stake here than the simple conclusion, however controversial, that we have reached Peak Oil.

After seeing my Global Warming forecast (here), one of my readers wondered whether anyone had combined Peak Oil models and Global Warming models. He reasoned, correctly, that the  WL20 model was capable of exploring the link between Peak Oil and Global Warming. This post will explore that relationship.

The underlying theoretical model linking Peak Oil and Global Warming is pretty simple: (Oil Production) -> (CO2 Emissions) -> (Global Warming). You might disagree with this linear causal model, but assume for the moment that it is correct. Then, anything that reduces oil production, like Peak Oil, will reduce Global Warming. My Global Warming forecast (here) shows Global temperature peaking sometime between 2040 and 2060. My Peak Oil Forecast above shows that oil production has reached its peak and is likely to collapse entirely around 2040. The result would seem to confirm the simple theoretical model, but how are these two forecasts related within the WL20 model?

The WL20 model model is a state-space model with three state variables (these state variables were not imposed on the model a priori but were the result of the statistical analysis): the first state variable measures overall growth in the World system; the second state variable measures declining biodiversity; and, the third state variable measures increasing resource constraints in the commodity markets related to the Ecological Footprint. The three state variables are interrelated: increasing biodiversity is related to declining global temperature while  increased resource extraction through commodity markets and overall economic growth are related to positive increases in global temperature.

The early peak in oil production is just one of a number of negative feedback loops within the model. The negative feedback loops limit overall growth in the World system around 2040 (see the WL20 state-variable forecast here). Global temperature takes a few more decades to peak after that, but it is really the end of overall growth, not just Peak Oil, that eventually limits global temperature growth, at least in the WL20 model.

There seem to be very few studies that have pursued the link between Peak Oil and Global Warming possibly because there are many alternative, high-carbon sources of energy (tar sands and synfuel from coal being two examples) that could be substituted for oil. Others, such as Amory Lovins (here) have argued that "Efficiency is cheaper than fuel" and will, for economic reasons, eventually limit emissions along with cheaper green energy. The WL20 model is capable of making projections of economic efficiency, a topic I will have to return to in a future post. The difficulty with the "substitution" argument is the important extent to which the entire World system is built on the oil economy. Even though we switched from a coal- to an oil-based economy in the 20th Century, it's not clear that the next energy conversion will be that easy given the larger scale of the present World system.

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The prediction of Peak Oil was initially made by M. King Hubbert, a Shell geoscientist who died in 1989. The Hubbert curve or Hubbert peak for the World system is displayed above (from this source). His forecast, based on logistic curve modeling, predicted that the peak in World oil production would occur in the year 2000. It serves as a warning that no forecasting model can really see into the future. The models are simply attempts to explore the future implications of the data and models available when the forecast was made.

Using the WL20 Package

The WL20 (W stands for World and L20 stands for Late 20th Century) package is an aggregate, state-space model of the World system. It contains 14 variables thought to be important to measuring the state of the World system, to include population growth, urbanization, commodity markets, carbon emissions, global temperature, biodiversity, globalization and the Ecological Footprint.

Unlike other World models, such as the DICE model, the Wonderland Model, or the System Dynamics World Models, WL20 was not derived from purely theoretical considerations. Rather, it was based on a 1979 paper by R. E. Kalman titled A system-theoretic critique of dynamic economic models. In the paper, Kalman argues that, until complex social systems are better understood, it is important to work from

data -> model

rather than from first-principle, theoretical considerations. In this approach, the primary emphasis is the selection of the data to describe the system followed by the use of state-space models to describe the dynamic behavior of the system. There is some theory used to make the selection of data that I have already discussed (here) and will discuss more fully in a future post. This post will concentrate on the computing details of the model.

The WL20 state-space model was estimated using the dse package (here) and the matlab package (here) in the public domain (it's free) R statistical language (here). Documentation, procedures and the WL20 model are available here.  They should be downloaded to a directory on your computer with the absolute path described by W (see below). The remainder of this post describes how to use the WL20 model using the R statistical language.

When you start R on your computer, the R console window will display the version number, copyright information and platform. On my computer:

R version 2.14.2 (2012-02-29)

Copyright (C) 2012 The R Foundation for Statistical Computing

ISBN 3-900051-07-0

Platform: i386-apple-darwin9.8.0/i386 (32-bit)

A number of  commands that you might find useful will also be displayed

R is a collaborative project with many contributors.

Type 'contributors()' for more information and

'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or

'help.start()' for an HTML browser interface to help.

Type 'q()' to quit R.

To use the WL20 package,  the dse and matlab packages must also be installed (use the "Package Installer" menu choice and be sure to check the box marked "Install Dependencies" after you get the list of "CRAN (binaries)", you can then select matlab and dse and click "Install Selected"). You can then run R and enter the commands below in the R console window (the > is the R prompt). 

> W <- "a character string describing the working directory location"

> setwd(W)

> source("LibraryLoad.R")

> load(file="ws_procedures")

> load(file="WL20v3_model")

> WL20.est

The first two commands assign and set the working directory to the file folder where you have downloaded the WL20 package. For example, on my computer, W is set to:

> W <- "/Users/georgepa/Desktop/R/Papers/WL20 v3/"

The next command will source the dse and matlab packages (if you get error messages, these packages have not been installed properly). The two load commands load the ws (world system) procedures and the model (if you get error messages here, you have probably not specified W properly). The final command displays the state-space model matrices for the WL20 model. These matrices are defined in the dse documentation that you can display with the following command:

> help(SS)

Data for the WL20 model were gathered from a number of sources, but mostly from the Earth Policy Institute's Data Highlights (here). The complete list of the data sources is available in the documentation (Appendix F, here). You can look at the first few lines of the data set using the following commands:

> head(WL20.data)

          N   OIL  QA GWP P.Wheat. P.Oil.  TEMP   CO2 Carbon

[1,] 2555.0 10.42 631 7.4     1.89   1.71 13.83 311.3   1630

[2,] 2597.5 11.73 655 7.9     2.03   1.71 13.98 311.7   1767

[3,] 2641.2 12.34 680 8.3     1.93   1.92 14.04 312.2   1795

[4,] 2686.2 13.15 705 8.6     1.89   2.01 14.12 312.7   1841

[5,] 2732.5 13.74 730 8.9     1.98   2.11 13.91 313.2   1865

[6,] 2780.0 15.41 759 9.4     1.81   2.11 13.92 313.7   2043

     TotalFootprint    Earths WorldGlobal LivingPlanet    URBAN

[1,]       5.292910 0.4597521    23.37150     1.000000 705.4807

[2,]       5.493554 0.4797747    23.94942     1.002878 730.5622

[3,]       5.694199 0.4997972    24.52735     1.005581 756.4242

[4,]       5.894843 0.5198197    25.10527     1.007935 783.1143

[5,]       6.095488 0.5398423    25.68320     1.009766 810.6524

[6,]       6.296133 0.5598648    26.26112     1.010900 839.0286

The data set runs from 1950 to 2008, which you can verify with the following commands:

> start(WL20.data)

[1] 1950    1

> end(WL20.data)

[1] 2008    1

There are commands in the dse package that you can use to evaluate this model. For example:

> roots(WL20.est)

[1] 1.0000000+0.000000i 0.9982313+0.027957i 0.9982313-0.027957i

[4] 0.9140820+0.000000i

attr(,"class")

[1] "roots"

displays the eigenvalues of the system matrix. The first eigenvalue (1.0000000+0.000000i) is unity because the model includes a constant. The other eigenvalues are all less than unity and have imaginary parts indicating that the model is stable but cyclical.

You can also check the model fit using:

> tfplot(WL20.est)

The results are displayed above. The dotted line displays the fitted values (one step ahead predictions) and the solid lines display the actual state variables.

The WL20 model has three state variables labelled W1, W2 and W3 in the graphic above. The state variables were constructed using Principal Components Analysis (PCA). The measurement model from the PCA is displayed with the following command:

> measurementModel(WL20.index)

               N        OIL          QA         GWP  P.Wheat.

[1,]  0.28446020  0.2711239  0.28207253  0.28243781 0.2362789

[2,] -0.01609311  0.2410390  0.09853503 -0.14131911 0.4113772

[3,] -0.11117409 -0.2412009 -0.08825703  0.02134276 0.4610974

         P.Oil.       TEMP         CO2      Carbon TotalFootprint

[1,] 0.24295530  0.2514421  0.28373276  0.28328608      0.2752374

[2,] 0.06595202 -0.2352280 -0.09832577  0.09252815      0.1816798

[3,] 0.71181845  0.1901141 -0.02009544 -0.09553557     -0.2925719

         Earths WorldGlobal LivingPlanet       URBAN

[1,]  0.2787654  0.28189899  -0.18387870  0.28400812

[2,]  0.1484351 -0.09256627   0.77050207 -0.08681005

[3,] -0.2311710 -0.09431697  -0.05760175 -0.07067596

The rows of this matrix display the weights used to calculate W1, W2 and W3. The weights were constructed from standard scores of the input data. The weight attached to each indicator variable for each state variable are displayed in the columns. By construction, the state variables are independent and uncorrelated.

The pattern of the weights indicated that W1 measures overall secular growth in the World system (this can also be seen from the time plot of W1 above). The second measure is most heavily weighted on the Living Planet Index (0.77050207), wheat prices (0.4113772), oil production (0.2410390) and the Ecological Footprint (number of Earths used by the World System, 0.1484351). The W2 state variable thus measures biodiversity. Finally, the W3 state variable is weighted most heavily on oil prices (0.71181845), wheat prices (0.4610974), Total Ecological Footprint (-0.2925719), and oil production (-0.2412009). The W3 state variable thus measures the effect of commodity markets and the Ecological Footprint.

> WL20.index$measurement$output$fraction.variance

 [1] 0.8740847 0.9413934 0.9725388 0.9864508 0.9949011 0.9980068

 [7] 0.9987371 0.9993400 0.9997902 0.9999405 0.9999802 0.9999923

[13] 0.9999986 1.0000000

Taken together, the World system state variables explain 97% of the variation in the underlying indicators.

One important use of the WL20 model is to forecast future states of the World system. The following commands create and display a 100 year forecast of the state variables:

> f <- forecast(WL20.est,horizon=100)

> tfplot(f)

The results of the forecast, displayed above, indicate that growth in the World system is expected to peak between 2040 and 2050 (W1)  associated with continuing losses of biodiversity (W2) and increasing pressure on commodity markets (W3). You can obtain the entire forecast to use as input to there times series models with the following command:

> fx <- merge.forecast(f)

The WL20 forecast and the time series are already available to you as data files named WL20.f and WL20.fx, respectively. 

I have already used forecasts from the WL20 model to predict global climate change and other indicators (here and here). In future posts, I will make the forecasting models models available as state-space models that can also be loaded into your R workspace and run on your machine.

TECHNICAL NOTE: In the Kalman article (here), emphasis is placed on the importance of observability and controllability in the selection of state space models. For the WL20, these two features can be checked with the following commands:

> observability(WL20.est)

[1] 2.5510918 2.2200285 1.8375940 0.6061376

> reachability(WL20.est)

Singular values of reachability matrix for noise:  2.424642 2.20612 1.628193 1.202821e-16 

The commands display the singular values of certain state-space matrices (use help for more information). If all the singular values are greater than zero, the model is both observable and controllable. The WL20 model is completely observable but might not be totally controllable (the 1.202821e-16 principal value is effectively zero). 

World Impact Forecasts

In the 3F blog, I have been primarily using state space models to make macro forecasts for the world system and countries within that system. The approach is a dynamic realization of ImPACT models developed by the Human Environment Program at Rockefeller University (here) in an article by Waggoner and Ausubel (2002). ImPACT models include the Kaya Identity used by the IPCC and the EIA and the I=PAT identity used for studying population growth impacts (here). Included in the class of ImPACT models is the neoclassical economic growth model (see note below) which has been used by William Nordhaus and Resources for the Future (here) to make climate change forecasts.

Whether or not state space models provide better forecasts than ImPACT models is an open question. The advantage of ImPACT models is that they can be calculated by hand. The disadvantage is that, as explained below, ImPACT models do not include feedback effects.

The directed graph above describes the causality underlying ImPACT models. Under long-run, full employment conditions, population growth (N) leads to greater aggregate production (Q)--more people mean more workers and, as long as the workers are fully employed, more workers mean more output and more demand. Output creates greater energy consumption (E). Energy consumption leads to greater CO2 emissions. And finally, great CO2 emissions leader to increases in global temperature (T).

The extent of these changes depends on the values of the lower case letters, called coefficients or intensive variables (the upper case letters are the extensive variables). In equation form:

T = N*(Q/N)*(E/Q)*(CO2/E)*(T/E) = N*q*e*c*t

where T is global temperature, N is global population, Q is world GDP, E is primary energy consumption, CO2 is global CO2 emissions, q = Q/N per-capita output, e = E/Q energy intensity of production, c = CO2/E carbon intensity of energy and t = T/CO2 is the climate sensitivity to radiative forcing.

The ImPACT formulation is very general. For example, if you think that CO2 emissions have no impact on global temperature, you can set t=0. In other words, if you can provide values for [N,q,e,c,t] then you can make global climate change forecasts using a hand calculator.

There are two problems with such forecasts: (1) you need to come up with reasonable values for population growth and for the other intensive variables (discussed below) and (2) you have to assume that there are no system feedbacks (for example from environmental degradation to population growth or to agricultural production). Said another way, will the intensive variables change over time?

Discussions of energy emissions or global temperature change all seem to rely on the assumption that population growth, energy intensity, and emissions intensity will all decrease over time and decrease enough to make up for increases in per capita GDP (improving standards of living). Generally, the climate sensitivity parameter is assumed to be constant.

Coming up with values for intensive variables in ImPACT models is thus yet another forecasting problem. Below I provide business-as-usual (BAU) forecast for each intensive variable using the WL20 model (data definitions are available in Appendix F). World population forecasts from the United Nations can be found here.

The BAU forecast for real per capita GWP (Gross World Product) is displayed above. Values in 2100 (the usual end-point of long-run forecasts) range anywhere from about 0.02 to 0.09 with a mid-range value of about 0.05 - 0.06.
The BAU forecast for energy intensity in millions of tons of oil equivalent is more difficult to forecast. Energy intensity will not go to zero as predicted by the model so values between 50 and 150 for e = E/Q would seem reasonable.
The BAU forecast for emission intensity (atmospheric CO2 concentrations in ppmv) is displayed above. Values seem to be stabilizing around 0.05.
Finally, BAU forecasts for climate sensitivity (degrees C) provide another surprise. Rather than being a constant as assumed by the IPCC, there would appear to be an observable time trend where climate sensitivity is decreasing. The decrease over time is possibly the result of feedback mechanisms. It is certainly not zero as assumed by global warming skeptics.

The observed trends in energy intensity and climate sensitivity might suggest that using ImPACT models to make long-run projections is an uncertain business. Since imPACT models are identities (true by definition), my suggestion would be to use ImPACT models to make the following types of assertions: (1) if other things remain equal, an increase in population growth would have the following impacts on production, carbon emissions and global temperature or (2) changes in intensive variables necessary to limit global warming to 2 degrees C would involve limiting per capita income growth or reducing energy intensity or decreasing carbon intensity.

NOTE: Neoclassical Economic Growth Models are a form of ImPACT model, which can be demonstrated using directed graphs.

In the standard neoclassical growth model, full employment and growth in autonomous technical change (A) drive growth in output. The Capital Stock, K, is an endogenous variable based on saving from output, K(t) = K(t-w) + ( sQ - d K ) where d is depreciation and s is saving.
Using graph theoretic rules, endogenous variables can be eliminated from the model. Technological change can also be endogenized assuming learning by doing. These two assumptions result in the graph above.

The neoclassical growth model is thus equivalent (nonparametrically) to a dynamic version of the ImPACT model displayed in the graph above.