Lecture Eleven
About the IS and LM Curves
(Economics 100b; Spring 1996)
Professor of Economics J. Bradford DeLong
601 Evans, University of California at Berkeley
Berkeley, CA 94720
(510) 643-4027 phone (510) 642-6615 fax
delong@econ.berkeley.edu
http://www.j-bradford-delong.net
February 14, 1996
Happy Valentine's Day
Where Is the IS Curve?
Why Is the IS Curve Where It Is?
The Keynesian Cross
Where Is the LM Curve?
Why Is the LM Curve Where It Is?
IS-LM Since 1971
Happy Valentine's Day
Where Is the IS Curve?
Where is the IS curve?
- In real interest rate, output space; the U.S. IS Curve in 1995
was at ($6.7 trillion; 4%)
- In real interest rate, unemployment space; the U.S. IS Curve
in 1995 was at (5.5%, 4%)
What is Y*?
- Somewhere between 5 and 7 percent of unemployment...
- Somewhere between $6.6 trillion and $6.9 trillion of output...
What is the slope of the IS curve?
- Alan Greenspan: 1% is to $150 billion
- Other model estimates: 1% is to $75 billion
So it runs from ($6.7, 4%) to ($6.4, 8%) to ($7.0, 0%)
Uncertainty about location of the IS curve...
Uncertain about the value of Y*...
Why Is the IS Curve Where It Is?
Start with:
Y = C + I + G
--with planned expenditure equals production equals income, which as
we know is the same as:
S_{p} = DEF + I(r)
equilibrium in the loanable-funds market, or the equalization of
savings with planned investment.
We have the consumption function:
C(Y-T) = c_{0} + c'(Y-T)
And let's think of an investment function:
I(r) = I_{0} - Ar
Substitute back into the national income identity:
Y = c_{0} + c'(Y-T) + I_{0} - Ar +
G
Rearrange terms:
(1 - c')Y = c_{0} + G - c'T + I_{0} - Ar
Y = (c_{0} + I_{0})/(1-c') + DEF/(1-c') + T -
Ar/(1-c')
We see here:
- A term involving the "intercepts" of the consumption and
investment functions: the higher up are the consumption and
investment functions--the higher are the"exogenous" components of
consumption and investment--the higher is output going to be for
any given level of Y.
- A term involving the deficit--the higher the deficit, the
higher is output.
- A term (that I wish would go away) corresponding to the
size of government (the "T" term). An expansion of
the size of government (keeping the deficit fixed) will tend to
push C down by less than it pushes G up, and tend to
make a higher level of total output and employment consistent with
S_{p} = DEF + I(r), consistent with equilibrium in
the loanable funds market
- A term showing the effect of higher interest rates on
depressing investment and "cooling off" the economy.
- A fraction 1/(1-c') -- the inverse of 1 - MPC -- that appears
just about everywhere. This fraction is called the
multiplier
The Keynesian Cross
Where does this multiplier come from?
We can see where it comes from in the math. It comes from the fact
that consumption--on the right hand side of equation #?--is a
function of income, so that when we substitute the consumption
function into the equation we get a Y on the left-hand side and a
-c'Y on the right hand side, and collecting terms gives us a (1-c')Y
on the left-hand side, so we have to divide everything by (1-c').
But you may find this explanation less than fully helpful; less than
fully intuitive. So let me give another--the so-called Keynesian
Cross.
Plot expenditure--what people, firms, and governments will spend, on
the vertical axis, and income on the horizontal axis. Hold the
interest rate fixed. Start with government--spending invariant to the
level of income. Add investment--also not affected by changing levels
of income.
Add consumption--upward sloping--marginal propensity to consume.
Equilibrium where expenditure equals income. Circular flow.
Suppose we boost investment. Shift the C+I+G line as a function of Y
upwards by an amount DI.
At current Y, expenditure greater than income. So move up--then over.
But the first increment to income, the DI, is not sufficient to
restore equilibrium. Why? Because the boost to income has also
increased planned consumption, because of the upward-slope
imparted to C+I+G from the consumption function, the fact that
households do not save everything out of income but spend some on
consumption goods.
So we have:
DI + (DI)(c') + (DI)(c')^2 + (DI)(c')^3 + (DI)(c')^4 + (DI)(c')^5+
... a lot more similar terms which together add up to:
DI/(1-c')
Where Is the LM Curve?
Why Is the LM Curve Where It Is?
Details of money demand...
These days money demand pretty elastic...
Lots of substitute ways to spend purchasing power...
Hence surprisingly big moves in quantity of liquidity needed to have
a material effect on output or interest rates...
- Does this play a role in the Federal Reserve's preference for
interest-rate targetting? Not sure...
Conversely, surprisingly large moves in IS curve produce
relatively little interest rate action...
IS and LM Since 1971
A potted history of where the IS-LM model says that we have been
since the early 1970s. Long and variable lags. Differences between
short-term and long-term interest rates; between real and nominal;
trend growth of the economy; shifting trend growth.
Flatten all these out by looking at unemployment rates and at
last-year's short-term real interest rate...
What do we see?
- 1971-1973: An economy with a 5.9% unemployment rate
with which we would be happy, but they then were not (thinking
that structural plus cyclical unemployment amounted to 4%);
inflation a bit high; bipartisan agreement to impose various
price-control and -restraint programs while easing monetary
policy; riding down the IS curve to 1973, with what we would now
see as high output and very low real interest rates.
- 1973-1975: First oil shock. In the wake of the
1973 Arab-Israeli War OPEC tripled the world price of oil. Effects
twofold (a) burst of inflation, and (b) collapse in
investment--strong shift of IS curve to the left; Federal Reserve
responds to burst of inflation and fears of a truly deep recession
by raising interest rates, but roughly only as much as inflation
rose.
- 1975-1978: IS curve moves back to the right as more
businesses are willing to invest at new relative prices once it
becomes clear that the recession is not going to be deep or
prolonged. Falls in inflation lead the Federal Reserve to lower
nominal interest rates by about as much as inflation falls (thus
shifting the LM curve out to the right as well). But well before
the economy had reached what people then saw as full employment,
inflation began to accelerate.
- 1978-1982: The Volcker deflation. Faced with what he
feared would become unstable accelerating double-digit inflation,
the Federal Reserve under chairman Paul Volcker contracts monetary
policy. The economy rides up the IS curve to 1982, where
real interest rates are at levels unseen since the Great
Depression--and unemployment is at levels unseen since the Great
Depression as well. Inflation falls rapidly.
- 1982-1989: The expanded federal deficits created by
Reagan-era tax cuts shift the IS curve out to the right; the
Federal Reserve responds to falling inflation by easing monetary
policy as well; the shift in monetary policy dominates--for most
of the 1980s unemployment and real interest rates drift
downward as repeated policy stimulations fail to re-start
inflation.
- 1989-1992: Fears of another Iraqi-driven oil shock and
other factors pull the IS curve back to the left. The Federal
Reserve responds too slowly--or so we now see in retrospect--and
the economy enters a recession.
- 1992-1994: Repeated monetary easing pushes the economy
down and to the right as it rides down the IS curve once again,
heading for full employment.
- 1994-1995: As the economy reaches what the Federal
Reserve guesses to be "full employment," monetary policy is
tightened slightly to keep strong investment demand from pushing
the economy back into the inflationary-spiral region; the Federal
Reserve pursues the elusive concept of a "soft landing."
ÿ