The "Dead Man Walking model" is indeed now a typical growth model. Interestingly, it is now, of course, comparing the study in the Standardökomie but actually used models. The Wikipedia are sure thankfully, a good and quick overview without having to pass through the same massive economy-browsing.
First I would like to quote the characteristic Conclusion of the above article: "This formula is from the International Monetary Fund in its 2005 study used the investment behavior, he speaks of." Standard neoclassical growth model, "although most of the equations are tautological, that is. apply to very different growth models, including the Harrod-Domar model. "
Well, what about now because of this tautological-standard neoclassical "universal" model of growth that the basis of fact Decisions for the world economic system?
First we look at the model in the usual notation in there:
(1) Y_t = (1 + g) * Y_ (t-1)
(2) I_t = (1 + g) * I_ ( t-1)
(3) k_t = (1 + g) * K_ (t-1)
this case, the variables are defined as follows: Y is the gross domestic product, equal to GDP. I, the gross investment and K is the capital stock. The quantity g is the annual growth of GDP. _t The index is always the last reference year, _ (t-1) then of course the respective previous year.
From these equations then drawn important conclusions that finally in the so-called coefficient of capital efficiency, Eng. productivity of debt: i * = culminates I_t / k_t = ..., ie gross investment per assets or liabilities.
pictures speak a thousand words so here are two images of the identical circumstance. Once the image (source Wikipedia ), the monetary experts would be expected from the above formula, really:
And now the picture to the very official data from the U.S. Census Office (Source: SWARMUSA ) in fact is true:
them fails because of what? Although our two different graphs scaled logarithmically so above official version of what the drama of the effect even more strongly suppressed. Well, at first it is powerful in any case up, down at second, however powerful! As is probably something wrong cruel. For the upper panel is what make our economic and political manager than iron scale for their decisions.
Why is this so problematic that it can be seen when the classical derivation of the growth model of the International Monetary Fund, once translated into the notation of DMWM:
(1 ') B_t = (1 + pw) * B_ (t-1)
(2 ') pn * a_t = (1 + pw) * pn * A_ (t-1)
(3 ') a_t = (1 + pw) * A_ (t-1)
These are the classic formulas in our DMWM notation. The significance of the variables B (GDP), A (assets = liabilities), pn (investment), look at the contribution DMWM , value the contribution to economic growth pw economy on my homepage.
Even the establishment of these equations, one sees the two errors of the classics: The first simplifying assumption that all sizes with the same rate g (this is our pw) grow. Well, in simplified models are not to condemn, in principle, but one must always consider in determining whether such a simplification appropriate and practicable. But a simple look at the growth rates of GDP and assets over a longer period shows that this is made impossible to fulfill:
The growth rates are clearly different. But even without the knowledge of the graph, it is extremely risky to incorporate such a simplifying assumption here. For every banker is clear that the capital owners always want to have something more than economic growth alone would give. And then the inevitable onset of increasing spread, not least because of the compounding effect, is really no secret.
But it gets even worse: The three equation, now is a system of equations are derived from the other conclusions. But we see immediately that the system is singular, because equation (2) and (3) are not independent but only differ by a factor that can be easily ausdividieren. The implications of (in this case not) singular equation systems are always dubious, to say the very least. Mathematically, they are in principle as senseless as inadmissible.
really need to see the singularity of the equation system already, if you look at the simplification of the growth coefficient g look. Because it has the experience is contradictory that the interest rate equal to the cash economy is economic growth, for it is generally higher and higher , as in this picture:
Secondly, the use of an identical g in (1) and (3) predicts that GDP and capital stock permanently the same size . have Because otherwise, grows or shrinks exponentially each other stronger. And then necessarily the g different. One could now assume as naughty, just that only the portion of the capital stock will bear interest from GDP would actually needed, and the rest just not enough to save the system of equations. But of course everyone knows that all capital will be remunerated, not only what is really needed for investment in the real economy. Such a contradiction in terms is symptomatic of a singular equation systems.
The problem is precisely at this point is that the equations of the GDP and capital stock are considered to be independent and not interactive. This can not work, and it is to actually see even if you try to justify the equality of all three G's. But it looks at the latest, when the wonderfully sounding totally independent same growth equation
(1 ') Y_t = (1 + g) * Y_ (t-1) = Y_ (t-1) + g * Y_ (t- 1)
(3 ') k_t = (1 + g) * K_ (t-1) = K_ (t-1) + g * K_ (t-1)
describes in which (with DeltaT = 1 year) is completely equivalent differential equation:
(1 ') dY / dt = g * Y
(3') dp / dt = g * K
The course has a simple solution, that is simply
(1 ') Y (t) = Y0 * exp (g * t)
(3') K (t) = K0 * exp (g * t)
grow that both variables independently, except for ever any size. Latest on this point would have noticeable to the utter stupidity of the model. If you know it with the modeling but just does not, then get there to do them the only sensible idea, namely that the equations (1) and (3) must be linked. For first principle applies
(1 ') Y_t = a * f (Y_ (t-1)) + b * g (K_ (t-1))
(3') k_t = c * h (K_ (t- 1)) + d * j (Y_ (t-1))
But since we can assume a linear behavior, we write
(1 ') = a * Y_t Y_ (t-1) + b K_ * ( t-1)
(3 ') k_t = c * K_ (t-1)) + d * Y_ (t-1)
It looks now so similar, as in the classics, but now comes the important step where the water leaves the economy: Since GDP usually Financed capital grows, you can set a = 0. While it can grow out of itself, but in its own juice, for example by increasing the work force, which is hardly slow. (Moreover, it is still not even want to examine what we are but just the mischief did the classics. They have b = 0, and because of its simplicity, was equal to d also.) So we write correctly:
(1 ') Y_t = b * K_ (t-1)
(3') k_t = c * K_ (t-1)) + d * Y_ (t-1)
Now the equations are in fact coupled correctly. Now we lack only the unknown b, c, d. The principle can also re-function of many influencing factors , including in particular f (t, b, c, d, Y, K). At this point, but we can now actually make some useful simplifications. And, we have the equation Leave right now by a bumbling difference equation in a mathematically more nutritious differential equation:
(1 ') dY / dt = b * K
(3') dK / dt = c * K + d * Y
Well, obviously the economic savings rate d is ps, which of course also increases the capital stock. Remain b and c. The obvious reasons are now out of the same size, but opposite, and represent the net or gross investment ratio pn (net or gross, depending on whether one is from capital or GDP view considered). So
(1 ') dY / dt =-pn * K
(3') dK / dt = pn + ps * K * Y
pn pn as a function of time (t) is now only the basis of experience adequate to model, see for example our DMWM, and you're done.
The difference between the expected and actual falsely present capital effectiveness, is more than a marginality. because this will overestimate the effectiveness of the time huge capital injections into the economy of the United States and Europe by far. It is believed therefore that is rock solid, that the function (3) would have to feed vigorously, so that automatically the function (2) increases and it follows that it would grow the function (1), GDP. Now, however, are even function (3) and (2) singular, and thus the entire edifice fell.
In truth, the coefficient of capital efficiency i *= dY / dK or = dB / dA in our notation. And since holding times tends to be larger than dB, and dB is now zero or even negative in the medium term, the excessive capital injections into the present, contrary to its intention to totally counter-productive.
Do you know the saying: "Mother, there are more guests than expected bulk 'but even more water in the soup."? Well, there are not just people tired, if you just tipped a bucket of water in the soup. And if at some point half the world starving, and they then have a grandson who wants to learn no absolutely math, then tell him: "Dear child, half the world is starving because there are people like you are not happy Math made ". That helps a lot, I can promise, however.
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