I’ve been Head of School at Kingston University London for over 18 months now, but these things do take time: last Wednesday I gave my inaugural Professorial lecture to an audience of about 200 people. My screenrecording video of the talk is below. Click here to download the Powerpoint slides; Minsky crisis model; Minsky Loanable Funds model; Minsky Endogenous Money model; Private Debt levels (6 countries); Private Credit growth (6 countries); USA Private Debt change & Unemployment; Private Debt Acceleration & Asset Prices.
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Instead of, “Brazil cans carnival as recession bites”, they should invite Pope Francis and have the party anyway!
http://www.ft.com/cms/s/0/b97905eab5db11e583589a82b43f6b2f.html#axzz3xTzTGWSN
http://im.ftstatic.com/content/images/be875529767543d8b461b304410398c2.img
Here is the direct link to the photo in the FT article if you hit the article limit.
The multiplication and quotient rules can be put in a different form that derives your identities from the first ones. This is a neat math trick. By using a formula for F’/F. One can prove it by using the multiplication rule and dividing it by the term, F. Or use natural log to split product terms into sums and differentiating.*
Say, F=abc/[de]
Then the multiplication rule gives this for, F’/F. [exponent 1 for numerator terms]
F’/F=a’/a + b’/b + c’/c – d’/d – e’/e.
Positive terms for numerator terms and negative terms for denominator terms.
Example using, d=D/Y
d’/d=D’/DY’/Y
Now you can do it easily for the wages share and debt ratio equations.
The other equations yield the alpha and beta terms. Because alpha=a’/a and beta=N’/N. Where a is labor productivity and N is population. Alpha and beta are the instantaneous growth rate relative to the numerator.
This is like an instantaneous percent change.
This make juggling this kind of instantanious change ratio easier.
Much easier proof using natural log. Other way is a lot of work for more terms.
F= abc/[de]
ln F = ln a + ln b +ln c –ln d –ln e
because ln ab=ln a +ln b and ln a/b = ln aln b
Now take the derivative, noting that, [ln x]=x’/x.
Correction:
Now take the derivative, noting that, [ln x]´=x’/x.
Not ´ means time derivative.
Should have typed:
Note ´ means time derivative.
Labor productivity is defined as with this equation, a=Y/L or equivalently Y=aL.
Examples of the othre two equations using the mathematical tool for F’/F: *
1. wages_share ? Wages/Output
wages_share’/wages_share = Wages’/Wages – Output’/Output
and
2. Emloyment rate ? Employment/Population ? Output/(Labor_Productivity*Population
ion )
(Y=aL thus L=Y/a) This corrects a typeo at 4m:15s.
We can now directly derive from the algebra equation:
Emloyment rate’/Emloyment rate = Output’/Output – Labor_Productivity’/Labor_Productivity – Population’/Population
(Again nuberator terms are + and denomenater terms are .)
Also the definitions of the following exponential growth rates are:
?=Labor_Productivity’/Labor_Productivity=a’/a
and
?=Population’/Population
Using those to replace terms above gives:
Emloyment rate’/Emloyment rate = Output’/Output – (? + ?)
or ?’/ ?=Y_Real’/Y_Real – (? + ?)
*https://en.wikipedia.org/wiki/Quotient_rule See Alternative Proof section.
Corrected for greek letters and defined as sign that did not show. Defined as was replaced with an equal sign.
Examples of the othre two equations using the mathematical tool for F’/F: *
1. wages_share = Wages/Output
wages_share’/wages_share = Wages’/Wages – Output’/Output
and
2. Emloyment rate = Employment/Population ? Output/(Labor_Productivity*Population
ion )
(Y=aL thus L=Y/a) This corrects a typeo at 4m:15s.
We can now directly derive:
Emloyment rate’/Emloyment rate = Output’/Output – Labor_Productivity’/Labor_Productivity – Population’/Population
(again nuberator terms + and denomenater terms )
Also the definitions of the following exponential growth rates are:
alpha=Labor_Productivity’/Labor_Productivity=a’/a
and
beta=Population’/Population
Using those to replace terms above gives:
Emloyment rate’/Emloyment rate = Output’/Output – (alpha + beta) ,
Emloyment rate’/Emloyment rate = Output’/Output – (labor_productivity growth + Population growth),
or ?’/ ?=Y_Real’/Y_Real – (alpha + beta)
*https://en.wikipedia.org/wiki/Quotient_rule See Alternative Proof section.
Missed a few, all corrected I hope:
Examples of the othre two equations using the mathematical tool for F’/F: *
1. wages_share = Wages/Output
wages_share’/wages_share = Wages’/Wages – Output’/Output
and
2. Emloyment rate = Employment/Population = Output/(Labor_Productivity*Population
ion )
(Y=aL thus L=Y/a) This corrects a typeo at 4m:15s.
We can now directly derive:
Emloyment rate’/Emloyment rate = Output’/Output – Labor_Productivity’/Labor_Productivity – Population’/Population
(again nuberator terms + and denomenater terms )
Also the definitions of the following exponential growth rates are:
alpha=Labor_Productivity’/Labor_Productivity=a’/a
and
beta=Population’/Population
Using those to replace terms above gives:
Emloyment rate’/Emloyment rate = Output’/Output – (alpha + beta) ,
Emloyment rate’/Emloyment rate = Output’/Output – (labor_productivity growth + Population growth),
or lambda’/ lambda=Y_Real’/Y_Real – (alpha + beta)
*https://en.wikipedia.org/wiki/Quotient_rule See Alternative Proof section.
https://en.wikipedia.org/wiki/Logarithmic_differentiation
Under applications section it coveres products and quotients.
Conclusion:
The reason I mentioned this math tool, was that it seemed to greatly simplify putting together Goodiwn´s, Keen´s cycle models.
It is quicker and more strait forward than using the usual product and quotient rules for derivatives.
Here is an example applied to Goodwin in section 2.2.
http://www.systemdynamics.org/conferences/2005/proceed/papers/WEBER196.pdf
“The eyes of the financial and economic worlds are now fixed on China, with focus predominantly on Chinese stock markets and the country’s GDP figures. A fascinating perspective was provided last week in the leafy borough of Kingston upon Thames. The university there has recruited the Australian Steve Keen as head of its economics department, and it was the occasion of his inaugural lecture. Keen was one of the few economists to highlight the importance of private sector debt before the financial crisis began in 2008.
The title of the lecture itself was exciting: “Is capitalism doomed to have crises?” Judging by the beards and dress style of the audience, many may have expected a Corbynesque rant. Instead, we heard an elegant exposition based on a set of nonlinear differential equations.
Private sector debt is the sum of the debts held by individuals and companies, excluding financial sector firms like banks. Keen pointed out that, in the decade prior to the massive crash of 1929, the size of private debt relative to the output of the economy as a whole (GDP) rose by well over 50 per cent.
The increase from the late 1990s onwards meant that debt once again reached dizzy heights. In ten years, it rose from being around 1.2 times as big as the economy to being 1.7 times larger. This may seem small. But American GDP in 2007 was over $14 trillion. If debt had risen in line with the economy, it would have been about $17 trillion. Instead, it was $24 trillion, an extra $7 trillion of debt to worry about.
Japan experienced a huge financial crash at the end of the 1980s. The Nikkei share index lost no less than 80 per cent of its peak value, and land values in Tokyo fell by 90 per cent. During the 1980s, private sector debt rose from being some 1.4 times as big as the economy to 2.1 times the size.
In China, in 2005, the value of private debt was around 1.2 times GDP. It is now around twice the size. Drawing parallels with the previous experiences of America and Japan, a major financial crisis is not only overdue but it is actually happening. And Keen suggests there is still some way to go.
So is it all doom and gloom? Up to a point, Lord Copper. High levels of private sector debt relative to the size of the economy do indeed seem to precede crises. But there is no hard and fast rule on the subsequent fall in share prices.
Japanese shares fell 80 per cent and have not yet recovered their late 1980s levels. In the 1930s, US equities fell 75 per cent, and took until 1952 to bounce back. In the latest financial crisis, they fell by 50 per cent but are even now above their 2007 high.
Equally, output responds to these falls in completely different ways. In the 1930s, American GDP fell by 25 per cent, compared to just 3 per cent in the late 2000s. Japan has struggled, but never experienced a major recession. Still, Keen’s arguments leave much food for thought.”
http://www.cityam.com/232702/chinaisdrowninginprivatesectordebttheresnotellinghowthisonewillend?ITO=sidebartopcomment