月曜日, 5月 06, 2019

A DSGE model of MMT






Modern Monetary Theory for Mainstream Economists (English Edition) [プリント・レプリカ] Kindle版
William Heartspring (著)2019
Contents What Questions To Ask About MMT? 5 Is MMT Just Accounting or Simple Matter of Consistency? 5 MMT Understanding of a Monetary Economy 6 MMT Understanding of Fiscal and Monetary Policy 6 Why MMT Rejects Mainstream Economic Language 7 MMT: Taxes Are How People Come to Use Money 7 Functional Finance 8 Vertical and Horizontal Money 8 Revisiting the Fundamental Principle of MMT 9 What Should Be the Baseline Framework? 10 What Does MMT Give Up? Where Misunderstandings Come From 10 A DSGE model of MMT 13 Financial Instability Hypothesis 17

Conclusion 19 Appendix: from [Future Horizons of Economics] 23 Stock-flow consistency of DSGE models 23 BKER model 24 Evaluation of New-Keynesian liquidity traps 27


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.


おまけ
モズレー
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.