Try Out a New Macro Model and a New Technology

Greg Hannsgen | May 30, 2012

You wonder what will happen when markets finally start working. How about, for example, a market that changes prices and wages quickly in response to fluctuations in demand? In a mixed economy with a government that tries to provide fiscal stimulus as needed, will it be of help to move toward such fast-adjusting markets? The two interactive diagrams in this post are based on figures 9a, 9b, 10a, and 10b in a Levy Institute working paper of mine called “Fiscal Policy, Unemployment Insurance, and Financial Crises in a Model of Growth and Distribution,” which was issued just this month and posted on the Institute’s site (math content somewhat crucial).

Each of the two figures shows one pathway followed by an imaginary economy. The pathways are computed by simulating a heterodox model, using a set of parameters as well as a starting point for each of the following variables: capacity utilization, public (government) production, the markup on labor costs used by businesses to calculate their prices, and the size of the labor force. As I explain in the paper, my parameter choices are not based on econometric estimates, but rather on a rough sense of what might be reasonable for a developed economy. In a moment, a new technology will give you a chance to see the impact of varying one of these assumed numbers. In fact, this post represents the first use on this blog of Wolfram’s interactive cdf format. You’ll need a free cdf reader and browser plug-in, which are downloadable at this link, if you don’t already have them.

The pathway shown in the figure just below is followed by public production, capacity utilization, and the markup. As shown, the pathway leads gradually upward in the figure toward an endless orbit called a “limit cycle.” The stabilizing effects of fiscal policy seem to be creating a steady, repeated elliptical pattern.
[WolframCDF source=”” CDFwidth=”435″ CDFheight=”468″ altimage=””]

Now, move the lever above the diagram to the right by clicking and dragging with your mouse (or similar move with a touchpad or whatever hardware you have). As you move the lever to the right, you are increasing a parameter that controls the speed at which the markup changes in response to high or low levels of customer demand.
Move the lever just a little more to the right and you may find that you are a little less happy. What happens as the speed parameter is increased is that the economy’s pathway gradually changes until there is a relatively sudden vertical jump in the middle and much higher markup levels at the end—which means a bigger total rise in capital’s share.
The next pathway is the one followed by a second group of three variables during the same simulation. This second group includes: money, the government deficit (surpluses are negative numbers in this figure), and the employment rate (total work hours divided by total hours supplied). Here is the figure:
[WolframCDF source=”” CDFwidth=”435″ CDFheight=”404″ altimage=””]

Once again, feel free to move the lever at the top of the picture from left to right and back using your mouse or other device, observing how the pathway changes. Please be sure to notice that when the lever is all the way to the right, the pathway begins with an outward spiral, leading to a new inward spiral, and finally an employment “crash” of sorts that occurs as the center of the second spiral is reached. This occurs after the markup has reached very high levels, as seen in the earlier diagram. Big changes can occur in an economy with very little warning, just when things seem to be stabilizing!

Future applications of the cdf technology on this blog are potentially varied and might include, for example, figures that allow one to toggle between two different types of fiscal-policy rules. In future posts, I may revisit the model depicted in these figures and comment on its implications for some of the economic issues of the day.

(Images/cdf’s slightly revised October 3, 2012)


8 Responses to “Try Out a New Macro Model and a New Technology”

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  1. Comment by David Chester — June 4, 2012 at 6:05 am   Reply

    How many independent variables of money flow does this model contain?
    Is there some way of illustrating the various money flows, by means od a block diagram with interconnections?
    Without this it is not possible to comapre the MMT model used here with earlier Keynesian attampts to determine how our social system works.

    • Comment by Greg Hannsgen — June 4, 2012 at 9:26 am   Reply

      The 5 such independent money-flow variables would be capacity utilization (the variable “u” in the paper), public production divided by the capital stock (p), unemployment benefits for public-sector workers (puc) and private-sector workers (uc), and the profit rate (pi). The wage-income variables, in turn, flow from capacity utilization and public production. Tax revenues are determined by total income, with the tax rate (the Greek letter “tau”) being the same on all types of income. In addition, as part-owner of the capital stock, the government receives a fixed percentage of profits. The government deficit (df) is determined by these dividend receipts, as well as public production, unemployment-benefit costs, and tax revenues (with the government’s interest costs determined by the bond-demand parameter and the interest rate, which are fixed). The goods-demand variables, one for investment and one for consumption–which are not actual money flows–are determined by after-tax wages and other after-tax incomes.
      In this blog reply, I’ve mentioned the profit rate as one of five independent money-flow variables, but the working paper counts the markup variable (m), and not the profit rate (pi), as one of the 5 state variables of the system, with pi determined by m, together with capacity utilization (u). The sizes of the public- and private-sector labor forces are also independent variables, but of course they are not money flows. They help to determine the unemployment rate, and hence unemployment benefit payments (uc and puc). In sum, the five independent money flow variables discussed in the previous paragraph can be obtained from the five independent state variables mentioned in the paper (p, u, m, lf, and plf).
      I am answering without having thought about this long this morning and hope I have this all right. In case you haven’t looked at it yet, I should also mention that the “flow-of-funds” table near the back of the paper may also be of help in getting a complete picture of the model’s variables and how they relate to one another. More variables, such as the interest rate, could be made to move independently in a more detailed version of the model. You raise an important question indeed. Thanks.

  2. Comment by David Chester — June 7, 2012 at 9:02 am   Reply

    Thanks for your straight-forward answer. So many economists imagine that they don’t need to think in such terms when responding to questions!

    I have been modelling the complete and general macroeconomy for a single country, with the aim of better understanding how it works. For the exchange of every type of goods or service or valuable document there is a corresponding money flow in the reverse direction. Then when I take all the possible kinds of role-players, namely Landlords, Capitalists, Producers, Householders (and workers), Banks and Government, I find that a total of 19 mutual flows occur between them. This model is of the aggregate flow quantities to and friom these 6 role-players, who then function as if they contained all the assorted parts of the many people that behave in these specified ways.

    An illustration of this model with all of its flows named and given algebraic symbols is to be found in Google Images: DiagFuncMacroSyst.pdf .

    May I suggest that until the MM Theory is made sufficiently broad so as to include all of these functions, that there is no chance for it to be sufficiently useful and convincing. Only then will the MMT contenders (including yours truely) manage to influence the finance departments of the many faltering policy-making national governments, to wake up and become effective!

    • Comment by Greg Hannsgen — June 7, 2012 at 2:17 pm   Reply

      Thanks, I intend to look at your model. I appreciate your desire to see a model that breaks sectors down more finely. Personally, I intend at some point to work on the financial/monetary side of the model in my WP, which would involve giving more thought to the role of banks. On the other hand, I hope those who look at my work won’t be too insistent on comprehensiveness, as models and papers become large quickly with the addition of new sectors, and a policy issue can often be looked at in the context of a fairly simple framework. In fact, the questions at hand can be obscured if one does not keep the focus of a particular study somewhat narrow. Also, I think, there is sometimes a lack of good theory and/or data to work with. For example, one wonders how to model the total market value of equities as part of a detailed financial sector. Or, how about the market–or price-setting mechanism–for oil? Or the nonprofit sector, which contains numerous US schools, colleges, universities, hospitals, and more? Of course, I feel that one must always be ready to offer an apology for the many simplifications and shortcomings in a macro model like the one in my paper. In this case I certainly do, but hope you find some insights and/or ideas that will be of help to you.

  3. Comment by What Are the Post Keynesians Up To? « Multiplier EffectOctober 2, 2012 at 1:00 pm   Reply

    […] documents, which allow one to experiment with the model, along with links to the paper, appear in this May post.  A somewhat skeptical Marc Lavoie, Fred Lee, and Sunanda Sen asked questions during the Q and A. […]

  4. Comment by beowulf — October 2, 2012 at 8:11 pm   Reply

    That’s interesting. The simplest way to implement this is James Meade’s idea of pegging payroll tax rate inversely to unemployment rate. It’d make sense to put FICA’s whole 15.3% on the employer side (they and but not the employees gets a tax deduction for it anyway). The difference between normal rate and 100% tax holiday rate would be $900 billion or so (in both decreased labor costs and tax revenue).

    Add capital share to the wage tax base and you’re a hop, skip and a jump from a subtraction method VAT. if you then add to that an excess profits tax, you’d have an economy-wide iteration of the IMF’s proposed bank Financial Activities Tax (with the horrible acronym FAT). We could replace the Financial Insurance Contributions Act (FICA) tax with the Financial Insurance Activities Tax, or to be a bit redundant, the FIAT tax. :o)

    • Comment by Greg Hannsgen — October 5, 2012 at 10:32 am   Reply

      If your point is that tax system assumed in the model (which is of course explained in more detail in the working paper) is not close to the current US tax system, or that of most countries in the world, you are right. As mentioned in the concluding section of the working paper, it would be helpful to conduct some explorations with other assumptions about tax rates and the tax code. For example, in light of the current debate about tax reform, it might be interesting to look at the effects of having different rates for different types of income. Also, though, the tax rate for the version of the model shown in the CDFs now online is 20 percent on all income, with profits included in the taxable income of the K-sector (which includes both wealthy households and firms). I have assumed that interest and wages are also taxed. In subsequent simulations, when I add unemployment benefits to the “5D model,” I also increase the tax rate to 22 percent, as the economy becomes somewhat unstable unless taxes are increased at least somewhat. (The unemployment benefits themselves are assumed not to be part of the tax base. The exact 22-percent figure is somewhat arbitrary.) A few of these latter simulations (with unemployment benefits) are illustrated with static images in Figures 11a, 11b, 12a, 12b, 13a, and 13b at the back of the working paper. On the other hand, like the simulations shown in the CDFs, the “2D model” simulations illustrated in figures 2 through 6 in the working paper all use the 20 percent tax rate.

      Does the government actively change its spending to stabilize the economy shown in the CDFs in this post, you might ask, given the lack of unemployment benefits? Stabilization in the illustrated simulations is done solely with a rule that makes the rate of change of public-sector output a function of current public-sector output and capacity utilization. The scheme mentioned in the comment might well also have a stabilizing effect, though of course, it would be different in a number of ways from the policy rule used in the simulations illustrated in the post.

      The particulars of all of the simulations done for the working paper (including the parameter values, such as tax rates) are outlined in the Section 6 and the appendix. (Please keep in mind that the working paper is intended mostly for a somewhat technical audience of economists, though I hope others find it of interest. I will try to keep explanations here on the blog much less technical.)

      Thanks for the comment.

  5. Comment by Asymptosis » Modeling the Price Mechanism: Simulation and The Problem of TimeDecember 1, 2012 at 3:04 pm   Reply

    […] made me think about a Greg Hannsgen post from last May on the Levy Economics Institute’s Multiplier Effect blog, a post I’ve […]

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