A DSGE model of MMT
Despite the warning that a mainstream-style model to understand MMT is potentially a futile business, because MMT would charge that it is the model that is inconsistent, not MMT, in this chapter a DSGE model of MMT would be constructed.
List of variables to be determined Pt ,Ct ,Dt ,rt ,W p t ,L p t ,W g t ,L g t ,Kt+1 for every time t.
Budget constraints of households and a consolidated bank
PtCt + Dt ≤ Mt
where Mt represents amount of high-powered money in an economy,
Ct represents total consumption,
Dt represents monetary amount of debt issued to firms,
Pt represents the price level of all goods. In this economy, there exists only one consolidated bank, and consumers do not trade against each other -consumers purchase goods only from firms, as usual in monetary economy. Debt and shares are placed on equal footing, as banks and households are consolidated. That is, households at time t can only spend from money injected by government -one can think of Mt as determined before an economy at time t operates. After accounting for flows, Mt is expanded as:
Mt = Mt−1 − Pt−1Ct−1 + (rt−1 − 1)Dt−1 + W p t−1 L p t−1 + W g t−1 L g t−1 + X g t−1
where rtDt is interests received for debts,
W p t refers to wage in private firms,
W g t refers to wage in government sector,
L p t refers to amount of labor in private sector and
L g t refers to amount of labor in government sector.
X g t is amount of money externally injected (or taken away by taxes or other means) by government.
Profit of firms Investments It are done by firms only, and firms finance It by debts Dt or their profits Πt. Thus,
Dt = PtIt − Πt
The profit of firms is given by:
Πt = Pt(Ct + It) − W p t L p t − rtDt
High-powered money and sectors together From perspective of government:
Mt = Mt−1 + W g t−1 L g t−1 + X g t−1
Now let us recall:
Mt = Mt−1 − Pt−1Ct−1 + (rt−1 − 1)Dt−1 + W p t−1 L p t−1 + W g t−1 L g t−1 + X g t−1
which means:
PtCt = (rt − 1)Dt + W p t L p t
Thus despite being constrained by Mt, PtCt is equal to wage plus net interests at time t, which would be expected in a non-monetary barter economy.
Production function of a consolidated firm
Ct + It = At(Kt) α (L p t) 1−α
Kt+1 = (1 − δ)Kt + It
Labor demand Wage in labor demand side is set by marginal product of labor:
Wt/Pt = (1 − α)At(Kt) α (L p t) −α
Wage bargaining: wage Phillips curve Wage Phillips curve is given by: Wt/Wt−1 = f Lt Nt, W g t!
where Nt represents total possible amount of labor, assumed to be given.
Lt = L g t + L p t . This potentially creates the Minsky instability factor that MMT additionally emphasizes.
Government sector: traditional and job guarantee Government sets W g t and L g t such that an equilibrium of maximum intertemporal utility of a consolidated household under some objective is chosen. (This is essentially about free government goods S t that government workers produce, which does not affect household’s own decisions as S t is assumed simply to be given by government.) A policy function is not explicitly provided but is given after one obtains equations for private sectors. A government objective can be job guarantee -which would mean L g t = Nt − L p t, and W g t would be set to provide maximum utility. Or a government objective can be zero inflation -for which government controls W g t and L g t as to obtain maximum utility consistent with the objective and results in unemployment.
Investment A firm can attempt to maximize expected intertemporal profit given by:
X∞ t=0 γ tΠt
This gives us another equation mainly related to Kt+1 at each time t.
Household utility maximization Utility at each time is given by Ut(Ct, S t, L p t, L g t) where S t refers to free goods coming from works in government sector. S t does not influence the utility maximization problem. The intertemporal utility maximization problem, subject to the aforementioned budget constraint, is:
max {Ct ,N p t ,N g t ,Dt} X∞ t=0 β tUt
This provides us four equations for each time t related to Ct, N p t, N g t and Dt.
Wrap-up Assuming linearization of equations in this model, we can now see that the model has a unique solution. First, there are nine variables to be determined for each time t -with Kt+1 considered to be one of these variables. Two variables are effectively set by the implicit government objective function -counted effectively as two equations. Four equations are given by the household utility maximization problem. One equation is the wage equation of the labor demand (firm) side. One equation is the wage Phillips curve. The last equation is given by the maximization problem of expected intertemporal profit. 9 = 2 + 4 + 1 + 1 + 1.
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Deadly Innocent Fraud #7: It’s a bad thing that higher deficits today mean higher taxes tomorrow.
Part III: Public Purpose Functions of government are those that best serve the community by being done collectively. These include: The military, the legal system, international relations, police protection, public health (and disease control), public funding for education, strategic stockpiles, maintaining the payments system, and the prevention of “races to the bottom” between the states, including environmental standards, enforcement standards, regulatory standards and judicial standards. What has made the American economy the envy of the world has been that people working for a living make sufficient take-home pay in order to be able to purchase the majority of the goods and services they desire and are produced. And what American business does is compete for those dollars with the goods and services they offer for sale. Those businesses that produce goods and services desired by consumers are often rewarded with high profits, while those that fail fall by the wayside. The responsibility of the federal government is to keep taxes low enough so that people have the dollars to spend to be able to purchase the goods and services they prefer from the businesses of their choice. Today, unfortunately, we are being grossly overtaxed for the current level of government spending, as evidenced by the high level of unemployment and the high level of excess capacity in general. People working for a living are getting squeezed, as they are no longer taking home a large enough pay check to cover their mortgage payments, car payments and various routine expenses, nevermind any extra luxuries.
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