スティーヴ・キーン『次なる金融危機』
https://nam-students.blogspot.com/2019/04/can-we-avoid-another-financial-crisis.html
危機・不安定性・資本主義――ハイマン・ミンスキーの経済学 2012年12月20日 服部茂幸
CanWeAvoidAnotherFinancialCrisis?(TheFuture of Capitalism)2017Steve Keen
To go from truisms to a model, some additional definitions
・Labour productivity (a ≡Y/L)
・Profit Ⅱ = Y-W-r-D
Some (genuinely) "simplifying assumptions"
・Output is a linear function of the capital stock (Y=K/v)
・Linear Depreciation dK/dt = IG-δ × K
・ Investment in excess of profits is financed by credit dD/dt=IG-п
・Wage change is a linear function of the employment rate ω'/ω=λs×(λ-λz)
・Investment is a linear function of the profit rate iG=πs×(π-πz)
・Constant labor productivity growth rate a; & population growth rate β
Yields simplest possible model of capitalist economy with debt finance...
:2017 Keen
https://unctad.org/divs/gds/dmfas/what/Documents/2017_p2_keen.pdfMinsky’s fundamental insight
★Take 3 undeniably true macroeconomic definitions
• Employment Rate （λ≡L/ N）
• Wages share of GDP （ω≡W / Y）
• Private debt to GDP ratio (d ≡D/Y)
• Differentiate with respect to time
★ Yields three truisms that cannot be reformed away:
•“The employment rate will rise if economic growth exceeds the sum of population & labor productivity growth” • “Wages share of output will rise if wage rises exceeds growth in labor productivity” • “Debt ratio will rise if rate of growth of debt exceeds rate of growth of GDP”…
★Mathematically, with the simplest possible assumptions, it looks like this…
λ(ラムダ)＿The employment rate 雇用率
ω(オメガ)＿Weighting factor on impact of change in the employment rate on wage setting 賃金率
d＿Depreciation rate 減価償却率 、負債率
Π=利潤率
v＿Accelerator relation
α＿Rate of change of labor productivity
β＿Rate of population growth
γ＿Depreciation rate
Ph…＿Linear Phillips curve for Goodwin model
Lo, Wo, ao, No＿＿Initial conditions for Labor, real wage, labor productivity and population in the Goodwin model
D0＿Initial condition for debt in the Minsky model
Parameters for nonlinear Phillips curve in the Minsky model
Parameters for nonlinear investment function in the Minsky model
Initial conditions for financial variables in the monetary Minsky model
Initial conditions for physical variables in the monetary Minsky model
Loan and deposit interest rates, markup coefficient, time constants for bank and household consumption and price setting.
ω＿Weighting factor on impact of change in the employment rate on wage setting
Output is a multiple of the installed capital stock.
Employment is a multiple of output.
The rate of change of the wage is a linear function of the employment rate.
Investment is a linear function of the rate of profit.
Debt finances investment in excess of profits.*
Population and labour productivity grow at constant rates.
1.資本ストックのレベルKは、アクセラレータνを介した年間の生産量Yのレベルを決定します。Y= K/ν。
2.生産水準は労働生産性aを介して雇用水準Lを決定する：L = Y/a。
3.雇用レベルによって、雇用率（人口Nに対するLの比率）が決まります。λ[ラムダ]=L/N
4.雇用率は、フィリップス曲線を介して実質賃金の変化率wを決定する：1/w・dw/dt =（ - c + dλ）。
5.生産量Yから賃金率w×労働力Lを引くと、利益の水準が決まる。 Π= Y - w・L
6.利益は投資を決定します（単純なグッドウィンモデルでは、すべての利益が投資されます）。
7.投資から減価償却費を差し引いたものが資本ストックKの変化率を決定し、モデルを閉じます：dK/dt = I - γ・K。
１資本ストックK→生産量Y→２(労働生産性a→)雇用水準L→３雇用率λ(L/N)
→４(フィリップス曲線Ph→)実質賃金変化率w→５利益水準Π→６投資Ｉ
→７資本ストック変化率dK/dt
4. Modeling Minsky I: the Goodwin model
Minsky’s own attempts to devise a mathematical model of his hypothesis were unsuccessful,4arguably because thefoundation he used—the multiplier-accelerator model—was itself flawed (Keen, 2000, pp. 84–89). Keen (1995) instead usedGoodwin’s growth cycle model (Goodwin, 1967), which generates a trade cycle with growth out of a simple deterministicstructural model of the economy.Goodwin’s model can be expressed as two differential equations in the rate of employment and the wages share of output.I outline it here in terms of absolute values, since this is the form in which the final monetary Minsky model in this paper isexpressed. The basic deterministic causal cycle of the model is:
1.The level of capital stock K determines the level of output per annum Y via the accelerator v: Y =Kv.
2. The level of output determines the level of employment L via labor productivity a: L =Ya.
3. The level of employment determines the employment rate (the ratio of L to population N): =LN.
4.The employment rate determines the rate of change of real wages w via a Phillips curve:1wdwdt= (−c + d · ).
5. Subtracting the wage rate w times labor L from output Y determines the level of profit ˘; ˘ = Y − w · L.
6.Profit determines investment I (in the simple Goodwin model, all profits are invested): I = ˘.
7. Investment minus depreciation determines the rate of change of capital stock K, closing the model:dKdt= I − · K.
With population growth of ˇ percent per annum, labor productivity growth of ˛ percent, and a linear Phillips curverelation of the form Ph()=(−c + d · )(where a and b are constants), the model consists of the following 4 differentialequations in the level of employment, the real wage, labor productivity and population growth:
…
Fig. 2. Cyclical growth in the basic Goodwin model.earnings, firms will borrow to finance investment. An exponential function for the propensity to invest captures the mostfundamental of Keynes’s insights about the behavior of agents under uncertainty: that they behave as if:
the present is a much more serviceable guide to the future than a candid examination of past experience would showit to have been hitherto (Keynes, 1937, p. 214)
Agents thus extrapolate current conditions into the future, a behavior that Keynes elsewhere describes as “unreasoningand yet in a sense legitimate where no solid basis exists for a reasonable calculation” (Keynes, 1936, p. 154). Thus desiredinvestment exceeds profits at high rates of profit, and is less than profits at low rates, because agents extrapolate currentconditions into the future. Similarly, with a nonlinear Phillips curve, wages rise rapidly at high levels of employment andfall slowly at lower levels.The same generalized exponential function is used for both the relationship between investment as a share of output,and the Phillips Curve:GenExp(x, xval, yval, s, min) = (yval− min) · e(s/(yval−min))·(x−xval)+ min (1.2)With suitable parameter values (see Appendix A), the two relationships are as shown in Figs. 4 and 5.A banking sector that finances the gap between desired and investment is then introduced by the simple relationshipthat the gap between desired investment and actual profit causes a change in the level of debt:dDdt= I − ˘ (1.3)Profit is also redefined as output minus the sum of wages plus interest payments:˘ = Y − w · L − r · D
…
6. Endogenous money
Though debt was modeled in the preceding system, money was not explicitly considered, and therefore price dynamicswere absent. To consider these, the model had to be extended to include an explicit monetary sector. The first step here wasto develop a model of an established empirical datum, that credit money is created independently of base money.The pioneering work on this was done by (Moore, 1979, 1983, 1988). Contrary to the standard ‘money multiplier’ modelof credit money creation, where base money is created before credit money, Moore concluded (citing Holmes, 1969), that:“In the real world banks extend credit, creating deposits in the process, and look for the reserves later.” (Alan Holmes,1969, p. 73)Kydland and Prescott concurred, noting that:
There is no evidence that either the monetary base or M1leads the cycle, although some economists still believe thismonetary myth. . . if anything, the monetary base lags the cycle slightly. . . The difference of M2–M1leads the cycle byeven more than M2, with the lead being about three quarters. (Kydland and Prescott, 1990, p. 12)
They further concluded that:
Fig. 7. A dissipative system with breakdown.
The fact that the transaction component of real cash balances (M1) moves contemporaneously with the cycle while themuch larger nontransaction component (M2) leads the cycle suggests that credit arrangements could play a significantrole in future business cycle theory. Introducing money and credit into growth theory in a way that accounts for thecyclical behavior of monetary as well as real aggregates is an important open problem in economics. (Kydland andPrescott, 1990, p. 15)
This open problem was addressed by Graziani (2003, 1989, 1990, 1995) in a manner that clarified the emphasis that Keynes put on the importance of money,＊5 and explained the well-known difficulties that have been encountered in introducingmoney into neoclassical models (Bhattacharjee and Thoenissen, 2007; Gutierrez, 2004; Magill and Quinzii, 1992; Wright,2010). Graziani’s simple but profound principle was that “A true monetary economy must. . . be using a token money” ratherthan a commodity as money, since “an economy using as money a commodity coming out of a regular process of production,cannot be distinguished from a barter economy” (Graziani, 1989, p. 3). From this he derived the proposition that banks, asthe creators of these tokens, must be modeled as separate agents from firms and households, and that all transactions aresingle-commodity, monetary exchanges involving three agents:
any monetary payment must therefore be a triangular transaction, involving at least three agents, the payer, the payee,and the bank. (Graziani, 1989, p. 3)
A model of a monetary production economy thus must (a) have at the minimum three agents; (b) model demand as theflows of a pure monetary token (which motivate counter-flows of commodities and labor) between bank accounts held bythose agents, and (c) allow for the endogenous creation of money by the banking sector.
Table 1.
Steve Keen has developed dynamic disequilibrium models of monetary production that fulfil these conditions (Keen,2009a,b, 2008, 2010), using a technique that combines double-entry book-keeping with systems dynamics. Each column ofa “Godley Table” (named in honor of Wynne Godley; see Godley, 1999; Godley and Lavoie, 2007) is a bank account belongingto a specific class of agent (banker, firm, household), and each row represents financial transactions between these agentsthat either purchase a good or service, or compound, meet or record a financial obligation. The symbolic sum of the operationsin each column then generates the differential equation for that account. In the next section, a simple model of a pure crediteconomy is combined with the preceding Minsky–Goodwin model to generate a monetary model of the Great Moderationand the Great Recession.
＊
5“... as soon as we pass to the problem of what determines output and employment as a whole, we require the complete theory of a monetary economy...For the importance of money essentially flows from its being a link between the present and the future... It is when we have made this transition [to] . . .the real world in which our previous expectations are liable to disappointment and expectations concerning the future affect what we do to-day . . . that the peculiar properties of money as a link between the present and the future must enter into our calculations. . . Money in its significant attributes is,above all, a subtle device for linking the present to the future; and we cannot even begin to discuss the effect of changing expectations on current activitiesexcept in monetary terms.” (Keynes, 1936, pp. 293–294).
#21:1
全体としての産出量と雇用を決めるものが何かという問題に移るやいなや、貨幣経済についての完全な理論が必要となる。
あるいは、おそらく、分割線を定常均衡の理論と移動均衡の理論ここに言う移動均衡の理論とは、将来についての変化する見解が現在の状態に影響を及ぼしうるような体系に関する理論のことであるのあいだに引くこともできよう。というのも、貨幣の重要性は本質的にはそれが現在と将来をつなぐ連環であるところに淵源しているからである。われわれは、資源の異なる用途間へのいかなる配分が、将来に関する見解が不変かつあらゆる点で信頼するに足る世界の中で正常な経済的動機のもとに成立するところの均衡と両立するかを考えることができる。
…
現在と将来をつなぐ連環としての貨幣の特性がわれわれの計算に入って来ざるをえないのは、まさしくわれわれがこのような移行を敢行したときである。
…
貨幣の重要な属性はなかんずくそれが現在と将来をつなぐ精妙な手段だということにあり、貨幣の言葉に翻訳するのでなければ、変化する期待が現在の活動にどのような影響を及ぼすか、議論を始めることさえできない。
………
Appendix A. Appendix
Variable or parameter＿＿＿ Description ＿＿＿Value
v＿Accelerator relation
α＿Rate of change of labor productivity
β＿Rate of population growth
γ＿Depreciation rate
Ph…＿Linear Phillips curve for Goodwin model
Lo, Wo, ao, No＿＿Initial conditions for Labor, real wage, labor productivity and population in the Goodwin model
D0＿Initial condition for debt in the Minsky model
Parameters for nonlinear Phillips curve in the Minsky model
Parameters for nonlinear investment function in the Minsky model
Initial conditions for financial variables in the monetary Minsky model
Initial conditions for physical variables in the monetary Minsky model
Loan and deposit interest rates, markup coefficient, time constants for bank and household consumption and price setting.
ω＿Weighting factor on impact of change in the employment rate on wage setting
3
2 percent p.a
1 percent p.a
1 percent p.a
c=4.8, d = 5
300, 0.95, 1, 300 resp
Lo, Wo, ao, No
0
0
P,A)=GenExp(λ, 0.95, 0, 0.5,-0.01)
I(Tr) -GenExp(Tr, 0.05, 0.05, 1.75, 0)
Byo, BTo, Flo, FDo, HD
Lo, Wo, ao, No, KRO, YRo, P
12,5, 100, 70, 1;3
300, 300, 1,300,900, 300,1
5 percent, 1 percent, 20 percent, 1, 1/26,1
10 percent
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ギリシャ文字の読み方
明るい恒星には，星座の中で明るい順にギリシャ文字のアルファベットの名前がついています。これは，ドイツのヨハン・バイエルが1603年に『ウラノメトリア』という星表を出版した際に，各星座の星の明るい順にこれを割り当てたことが始まりです。以来，α，β，γ....という名前は“バイエル名”とか“バイヤー名”などと呼ばれ，頻繁に用いられるようになりました。
バイエル名は，だいたい明るい順番についていますが，順番が入れ替わっているものもたくさんありますので，注意しましょう。
ギリシャ文字は，以下のように読みます。
| 小文字 | 大文字 | ローマ綴り | 日本での一般的な読み方 | ギリシャ式読み方 | 英語式読み方 |
|---|---|---|---|---|---|
| α | Α | alpha | アルファ | アルファ | アルファ |
| β | Β | beta | ベータ | ベータ | ビータ |
| γ | Γ | gamma | ガンマ | ガンマ | ガマ |
| δ | Δ | delta | デルタ | デルタ | デルタ |
| ε | Ε | epsilon | イプシロン | エプシロン | エプシロン |
| ζ | Ζ | dzeta | ゼータ | ゼータ | ジータ |
| η | Η | eta | エータ | エータ | イータ |
| θ | Θ | theta | シータ | セータ | シータ |
| ι | Ι | iota | イオータ | イオータ | アイオタ |
| κ | Κ | kappa | カッパ | カッパ | カッパ |
| λ | Λ | lambda | ラムダ | ラムダ | ラムダ |
| μ | Μ | my | ミュー | ミュー | ミュー |
| ν | Ν | ny | ニュー | ニュー | ニュー |
| ξ | Ξ | xi | クシー | クシー | グザイ |
| ο | Ο | omicron | オミクロン | オミークロン | オミクロン |
| π | Π | pi | パイ | ピー | パイ |
| ρ | Ρ | rho | ロー | ロー | ロー |
| σ | Σ | sigma | シグマ | シグマ | シグマ |
| τ | Τ | tau | タウ | タウ | トー |
| υ | Υ | ypsilon | ウプシロン | ユープシロン | ユープシロン |
| φ | Φ | phi | ファイ | フィー | ファイ |
| χ | Χ | khi | カイ | キー | カイ |
| ψ | Ψ | psi | プサイ | プシー | プサイ |
| ω | Ω | omega | オメガ | オーメガ | オメガ |
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