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New interactive dynamical systems from Kansas City conference

In the wee hours of last Tuesday morning, I returned from the 2016 International Post Keynesian Conference in Kansas City, Missouri, in the United States of course. (Conference webpage for the curious).

My coauthor, Tai Young-Taft of Bard College at Simon’s Rock, and I each presented one paper. I presented a paper dealing with the implications of post-Keynesian theories of money in the setting of a model of the whole economy. I used some interactive CDFs during my presentation to illustrate the effects of changing my quantitative assumptions on the simulated pathways followed by the economy. Wolfram CDF technology is simply a way of creating interactive applets—illustrations with levers, buttons, and the like that allow one to watch the effects of changing the underlying quantitative assumptions. More on CDFs can be found on this page at the Wolfram website. I promised to post these objects quickly.

The work that we presented continues a project begun years ago. The first CDFs for a version of the model were shown in 2012 at an earlier version of the same conference, and results from that initial presentation found their way into a 2014 article in the economics journal Metroeconomica. and into this (free) working paper.

In this post, I present and explain some CDFs from my presentation, “Exogenous vs. Endogenous High-powered Money in Keynesian Monetary Growth Models.” Again, the work was coauthored with Tai. We hope to make the entire paper available free online in the form of a CDF, with the interactive graphics and the text incorporated into one document. A more conventional static document will provide links to online CDFs.

The CDFs are designed to explore the effects of “functional finance,” which among other things entails the use of countercyclical government spending, vs. “sound money,” the use of rules designed to achieve budgetary aims per se. Functional finance is one of the tenets of Modern Monetary Theory (MMT), a topic I discuss here frequently.

Our Policy Rule A is our functional finance alternative, using changes in public spending & production to target capacity utilization, while our Policy Rule B uses the same instrument to target a perfectly balanced budget.

Enter the Post Keynesian School’s argument that the supply of money is endogenous (that is, beyond the control of policymakers) and the central bank interest rate on the other hand is exogenous (set at a chosen rate). Thus, no situation is possible in which the Fed pushes the inflation rate up by insisting that the amount of money held by the public or its growth rate be some certain quantity.

This argument was important in the context of economic debates that were hot during the 1970s. In today’s deflationary economic environment, the putative existence of an too-large or too-small exogenous money supply is still an oft-heard red herring. Complicating matters somewhat, models of growth fluctuations differ on this point. Some researchers tend to assume exogenous and endogenous money almost in turn, as if the choice were somewhat random.

My presentation at the conference looked at the implications of one’s position on this theoretical question—exogenous vs. endogenous money—a matter that is not straightforward to “test” econometrically. Specifically, how does the choice affect the dynamics of the economy? We tried to answer this question in a range of different models. If the economy follows a pathway through n-dimensional space, how do outcomes differ depending on four underlying assumptions?
1) endogenous vs. exogenous money
2) functional finance (policy rule 1) vs. sound money (policy rule 2) as guides to fiscal policy
3) net wealth effects on the spending of the capitalist sector: some vs. none
4) fixed wages, price markups, and labor productivity vs. moving versions of these same variables

We are interested in whether these implications appear to be of economic importance. Many economists from various theoretical perspectives allege that the modeler’s choice of endogenous vs. exogenous money is of little consequence, especially in a growth & distribution model, which is designed to consider long-term outcomes. Hence, to their minds, it is even a somewhat overblown issue. Hence, we hope to bring some simulation evidence to bear on an argument among economists and other policy scholars who otherwise share many of the same goals in their research.

The interactive dynamical systems that follow, which are made with CDF technology, illustrate some consequences of the four modeling choices above, in the context of a post-Keynesian model. We do not illustrate all possible combinations, partly because our work is not finished.

When there are no net wealth effects (#3 answered in the negative) and money is endogenous, the stock of bonds does not figure into the determination of capacity utilization or public production & spending in any way, except that it determines the base on which interest income is calculated. A CDF showing the pathway of the economy can be found at this link. (Some viewing instructions appear below.) The figure uses two variables: p for public production & spending and u for capacity utilization.
CDF URL (in case link fails):
viewing instructions: To look at the CDF, you need only a free log-on at Mathematica Online, which will enable you to view CDFs that I have publicly posted to the Wolfram Cloud. When you click on the link below, you will be given a chance to create a Wolfram ID and password. Posting the CDFs to the Cloud allows people to look at our output on a much wider range of devices and will replace plug-in technology previously used on this site. This page provides CDF viewing advice.

When we switch to the exogenous monetary-growth rule (Rule 2), we get a model in which the interest rate can rise and fall because it is no longer held steady with the help of public-sector bond purchases—of course an inaccurate description of the world in which we live according to our preferred post-Keynesian view.

Of course, the Fed and other central banks do not always implement policies to keep long-term interest rates steady, but short-term paper usually predominates. Long-term interest-rate setting is always open to countries that do not peg their exchange rates to another currency or gold. Moreover, some countries (especially those with developed economies) are able to set both interest and exchange rates for prolonged periods. On the other hand, real-world efforts to set the money supply or its growth rate have consistently failed.

In our first exogenous-money CDF, we use the same fiscal policy rule: Rule 1 with its countercyclical properties and its property of steadying public sector work in relation to the total size of the capital stock. The vertical dimension in the figure is b, bonds outstanding divided by the replacement value of the capital stock. This amount is determined by the portfolio choices of bondholders. Moving the lever helps one get a sense of what might happen as the assumed “taste” for bonds increased.
This CDF is again available online with a free log-in to the Wolfram Cloud.

Next, we retain the same exogenous-money assumption—again, clearly a counterfactual in our view—but replace Policy Rule 1 with the more fiscally conservative “sound money” fiscal policy function (Policy Rule 2). My previous work (see above) has shown that this rule is not stabilizing, but did not entertain the possibility of “crowding out.” Here is a direct link to the CDF.
…and a URL:

The exogenous money figures show rather unstable behavior in both cases. We believe these results speak to the plausibility of exogenous money as part of a model of the actual economy.

As in our first figure, the next CDF again shows the implications of an endogenous money assumption combined with “Fiscal Policy Rule 1.” This time, we add net wealth effects to our equation for private sector production so that there will be some impact—in contrast to our first situation—of the size of the existing stock of bonds held by the wealthy capitalist sector, other than as a base on which interest income is computed. Levers (a.k.a. slider controls) allow one to control (1) the quantity of demanded by securities-holders at the policy-determined interest rate and (2) the fiscal-policy parameter. Click here for the CDF.

Finally, we have a 3D picture of the same system. The variable b (bond holdings relative to the replacement value of the capital stock) is determined by the interaction of a portfolio demand curve with central bank policy. Again, we allow the coefficient in the policy rule to be adjustable. Another lever controls a coefficient that determines what percentage of bond holdings are consumed each year by those wealthy enough to own them in the context of our small model. Can we make the coefficient big enough to matter for the dynamics, yet keep this magnitude consistent with common sense and empirical realism? Clicking a button enables you to monitor the size of this important coefficient. How much does the wealth effect change a picture in which interest-driven spending is the only way bond wealth affects the amount of goods (and labor) sold? Mathematically, a 3D system carries the possibility of chaotic behavior. See the CDF at this link in the Wolfram Cloud.

Please note that: these figures use quantitative assumptions that are not very carefully selected to be representative of analogous quantities in actual economies. However, as one can verify by experimenting with the levers, things are often relatively robust to fairly large changes in assumptions. On the other hand, in a nonlinear model, dynamical behavior can completely change when an assumed number crosses a particular threshold. We hope to tune things up as we complete our work on the two papers. Moreover, our pathways are necessarily conditional on assumed starting points in each figure. Also, the model leaves many things out; our most comprehensive model so far is be developed based on Levy Economics Institute working paper number 839.
Finally, amidst these caveats, we note that since the conference, we have worked out a few bugs and coding errors, yielding pathways that look somewhat (but not radically) different from those in my presentation.

Technical Note: Finally, a word about the use of the Wolfram Cloud as a way of making public some of our CDFs in this post. This step follows announcements by Wolfram that it is moving away from browser plug-in technologies, following wider trends in the tech world. (See this earlier post.) Hence, these CDFs may be visible and interactive on wider array of client platforms, including personal devices, which might use different operating systems, etc. Remember, getting a log-in name and password is free.

Note to fellow Kansas City conference-goers: I hope this post will be of interest to those present at the session and others who attended the conference. Any conference-goers interested in this venture should consider getting in touch with me at Examples include people with CDFs to post or people I met in the two sessions specifically devoted to economic modeling, who might be inspired to comment on this post, or to contribute to an online forum for issues raised by the papers at the conference. Supplementary materials from other presentations could be posted on this site to more broadly disseminate results–as long as they are not spoken for already, of course. Non-conference-related blog submissions would also certainly be considered seriously.

Our sincere thanks go out to those who attended our sessions and those who organized the event, along with others who helped us in Kansas City and along the way in our cross-country trip.


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