https://www.icloud.com/keynote/0ijR6uZ6ikrKf8JzrJlJhuujg | http://nbviewer.jupyter.org/github/braddelong/LSF18E101B/blob/master/Flexprice_Model_and_IS_Curve-Review_and_Problems.ipynb
GSI's have read me the riot act...
We have gone too far too fast, and it is time to pause and do some examples...
The examples I will do start one of the things I am thinking about these days—the one-year anniversary of the Trump-McConnell-Ryan corporate tax cut...
This is nominal investment spending as a share of potential GDP
This is the principal driver of the business cycle
$ I = I_o - I_rr $
The Trump administration and their... I guess I have to call them "tame", or something less polite... economists insisted that the passage of the 2017 corporate tax cut would produce a substantial jump in investment spending, and a substantial acceleration of economic growth.
For example: Robert Barro in December 2017 https://www.project-syndicate.org/onpoint/how-us-corporate-tax-reform-will-boost-growth-by-robert-j--barro-2017-12...
Preview: "Listen up! It's just not happening!" in the words of P!NK:
Robert Barro, Paul M. Warburg Professor, Harvard University https://www.project-syndicate.org/onpoint/how-us-corporate-tax-reform-will-boost-growth-by-robert-j--barro-2017-12
Barro is going through a Solow Growth Model calculation of the effects of last December's 2 trillion wealth transfer that was last December's corporate tax cut:
Barro: Once we know the change in the capital-labor ratio, it is straightforward to estimate the long-run change in real (inflation-adjusted) per capita GDP. The short-run effects can then be inferred by using previous estimates of convergence rates associated with economic growth….
The tax changes raise long-run capital-labor ratios by 25% for non-residential corporate structures and 17% for corporate equipment… [a] long-run level effect… 7%…. If one assumes a capital share of income [α] of 40%, the convergence rate in the neoclassical growth model would be around 5% per year… the growth rate rises in the short run by 0.34% per year…
Let's do the math and unpack what is going on here. And let's move into the flexprice model, because the U.S. economy is near full employment, so we are not talking about a cyclical recovery boosting short-run growth by putting lots of unemployed people to work:
To Your iClickers: What is dY/dK?
⟹ dY/dK = α(Y/K) = 10%
⟹ ΔY = 20 trillion x 0.34% = 70 billion
What is ΔI?
⟹ ΔI = 70 billion/10% = 700 billion
I am not surprised not to see it.
Why not? Because we are talking about a 15 percentage point—temporary—reduction in the taxes on investment. dY/dK = 10%. That is shared between investors, middlemen, workers with market power, managers, and the government. So figure that 15 percentage point is a change in after-tax r of between 0.75 and 1.5 percentage points for your return on investment. And that is simply not large enough to drive such a huge rapid leap in investment spending...
About 10%—consistent with investment incentives that raise the rate of return on investment in the U.S. by 1%-point for ten years...
And this will drive an increase in foreign savings that will drive some—not a lot—of increased investment in America.
As I said before, flexprice model...
Investment needs to be looked at from both the supply and the demand side:
And so we are left, on the supply side, with:
$ΔI = x_εΔε = x_εε_rΔr $
What's going on here? The higher interest rates will induce people to stop buying U.S. exports. People who then earn dollars by selling us imports will have no choice but to invest that money in the United States—and that increased foreign saving will drive higher investment.
$ ΔI = x_εε_rΔr x_ε = 500 ε_r = 10 $
By how much would r have to go up to make $ ΔI = 700 $?
By a lot: A 14% rise in r? A 140% rise in the value of foreign currency?
What does this mean? This means: $ r = r^f $
What must be going on for both of these things to be true? What are they assuming behind the curtain?
⟹ xεΔ = ∞
Keynes: “Now ‘in the long run’ this is probably true. If, after the American Civil War, that American dollar had been stabilized and defined by law at 10 per cent below its present value, it would be safe to assume that n and p would now be just 10 per cent greater than they actually are and that the present values of k, r, and k' would be entirely unaffected. But this long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us that when the storm is past the ocean is flat again…”
Keynes on how hard it is to be a good economist:
But there is more: motivated reasoning, and a failure to take any steps to mark their beliefs to market...
$ Δr = \frac{x_εΔε_o + x_εε_rΔr^f}{I_r + x_εε_r} $
$ Δr = \frac{(500)(0.20) + (500)(10)(.02)}{20000 + (500)(10)} $
$ Δr = \frac{200}{25000} = 0.008 $
$ ΔI = -(20000)(0.008) = -160 $
$ ΔGX = x_εΔε = (500)(0.2 + 10(.02-.008)) = + 160 $
Export manufacturing production recovers...
Reference: Olivier Blanchard, Jonathan D. Ostry, Atish R. Ghosh, and Marcos Chamon (2015): Expansionary or contractionary effects of capital inflows: It depends what kind: "Some scholars view capital inflows as contractionary, but many policymakers view them as expansionary. Evidence supports the policymakers.... For a given policy rate, bond inflows lead to currency appreciation and are contractionary, while non-bond inflows lead to an appreciation but also to a decrease in the cost of borrowing, and thus may be expansionary..."
A bond inflow is: a $ {\Delta}{\epsilon}_o < 0 $
A non-bond inflow (DFI) is:
So holding i constant:
$ {\Delta}Y = {\mu}(x_{\epsilon}{\Delta}{\epsilon}_o - (I_r + x_{\epsilon}{\epsilon}_r){\Delta}{\rho}) $
The key question is: when capital flows in, does it just come by itself or does it bring an increased supply of risk-bearing capacity along with it?
Reference: Basic Model:
$ Y = C + I + G + NX $
$ C = c_o + c_y(1-t)Y $
$ I = I_o - I_rr $
$ G $
$ NX = GX - IM $
$ IM = im_y $
$ GX = x_fY^f + x_{\epsilon}{\epsilon} $
$ {\epsilon} = {\epsilon}_o + {\epsilon}_r(r^f - r) $
$ r = i + {\rho} - {\pi} $
$ MPE = c_y(1-t) - im_y $
$ \mu = \frac{1}{1 - MPE} $
$ A_o = [c_o + I_o + G] + [x_fY^f + x_{\epsilon}{\epsilon}_o + x_{\epsilon}{\epsilon}_rr^f] $
$ Y = \mu(A_o - (I_r + x_{\epsilon}{\epsilon}_r)r) $
The reverse of the effects of capital inflows:
A bond outflow is: a $ {\Delta}{\epsilon}_o > 0 $
A non-bond outflow is:
So holding i constant:
$ {\Delta}Y = {\mu}(x_{\epsilon}{\Delta}{\epsilon}_o - (I_r + x_{\epsilon}{\epsilon}_r){\Delta}{\rho}) $
The key question is: when capital flows out, does it just leave by itself or does it carry risk-bearing capacity away with it?
# calibrating the flexprice model to the U.S. economy today
# consensus parameter values...
Y = 20000
C = 13500
I = 3250
G = 3750
GX = 2500
IM = 3000
NX = GX-IM
I_0 = 3650
I_r = 20000
e_r = 10
x_e = 500
t = 0.15
c_0 = 750
c_y = 0.75
im_y = 0.15
x_f = 0.10
Y_f = 25000
e = 0
r = 0.02
C_calc = c_0 + c_y*(1-t)*Y
I_calc = I_0 - I_r*r
GX_calc = x_f*Y_f + x_e*e_r*e
GX_calc
Lecture Support: http://nbviewer.jupyter.org/github/braddelong/LSF18E101B/blob/master/Flexprice_Model_and_IS_Curve-Review_and_Problems.ipynb
Keynote File: https://www.icloud.com/keynote/0ijR6uZ6ikrKf8JzrJlJhuujg
Real GDP:
Real GDP per Worker:
Investment as a Share of Potential GDP:
Consumption as a Share of Potential GDP:
Gross Exports as a Share of Potential GDP:
Imports as a Share of Potential GDP:
Net Exports as a Share of Potential GDP:
Price Level:
Inflation Rate:
Nominal Short-Term Safe Rate:
Long-Term Real Safe Rate:
Long-Term Risky Real Rate:
Real Exchange Rate (Value of Foreign Goods/Currency):