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CDF up-date: A new interactive dynamical system with government debt

First, a return to the topic of functionality of CDFs on this site. (CDFs come in two forms: web-embedded and downloadable, free-standing files.) In performing maintenance on this blog, I have taken down an embedded jumbo CDF that was not running with the Firefox browser. Experimentation with other browsers indicate that some cannot at present read pages on this site that contain embedded CDFs, at least on my computer. Remember the free CDFPlayer program by Wolfram, which enables one to read the downloadable versions of all CDFs on this blog. The downloads are available on this page of the site. Just download. After opening, you must click on the “enable dynamics” button to permit interactive features to be usable. You are watching the CDFPlayer program recompute the dynamics for each combination of parameter values that you select with the levers. We apologize for problems viewers may have experienced with functionality.


Here is a new CDF to try, right on today’s post (link to downloadable version). Fans of nonlinear dynamics will note that it models the emergence of a cycle through what is known by mathematicians as a Hopf bifurcation. The horizontal coordinate displays government spending and production, while the vertical axis measures private-sector output. Move the top lever, which controls the exact fiscal policy rule used, and the system moves back and forth between a cycle and a stable equilibrium. The other lever moves a parameter the governs demand for government bonds as a percentage of the capital stock. The system is being recomputed over and over as you shift the levers. Experimenting, one finds that this second lever changes the location of the stable equilibrium or cycle. As an alternative, you can think of bond holders gradually changing their holdings of net claims against the government as time passes. The cycle, when it appears, seems to be stable for any position of the lower lever. Watch, however, for pathways that may be headed out-of-bonds, to negative values of government spending and production. The model takes into account the direct effects of asset holding as well as the effects of interest income on consumption spending. The stable results of course depend on the non-changeable numbers underlying the model, which fall within certain assumed bounds.

In the model, the government is generating or retiring net liabilities at all times. The second lever simply adjusts the portion of existing liabilities that are held in interest-bearing bonds, rather than money–a decision made by those who have wealth to invest.  Within the government sector, the central bank sets the interest rate and lets wealth-holders make this choice, through offsetting open-market trades. Such a system exists where the government has its own currency and does not try to peg its value to gold, another currency, etc. The emphasis on the point that government spending generates liabilities is from SFC economics and MMT (modern monetary theory); the idea that government-issued monetary liabilities adjust to demand (endogenous high-powered money) while the notion that the interest rate on government debt is set by policymakers is an idea espoused since the 1970s by the modern post-Keynesian school of economics, among others. I mention the latter school partly because of the approach of September’s International Post Keynesian Conference in Kansas City.

You might let me know (at mail at greghannsgen dot org) how the interactive features are working in your favorite browser program. If you have not installed the CDFPlayer, you will–assuming things are working right–see a static image that will direct you to a download page at the Wolfram site. Remember, Firefox seems to be working best to display the actual CDFs. If only the frozen replacement image appears, the CDFPlayer can be downloaded by clicking on it. Only this free program is needed to unleash the full computing power of a Mathematica kernel on CDFs. The CDFs on this site were launched using the same company’s Mathematica program, which can for example take a pretty complicated derivative.

All in all, the CDF combines nonlinear dynamics in two continuous variables, SFC concepts, a previously published post-Keynesian fiscal policy model, MMT, and more. Among other things, it allows one to observe robustness of the resulting dynamics to a range of quantitative assumptions. note: corrections were made to the post around 3:50 pm EDT the day of posting to indicate that the CDF shown above included some direct effects of bond holdings on consumption spending.


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