Econ 100b

Created 4/30/1996
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Lecture Eighteen

Term Structure; Tobin's q; Summary of IS-LM
(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

March 4, 1996

Using the IS-LM Model for Reading the Wall Street Journal
Term Structure
IS-LM Summary


Using the IS-LM Model for Reading the Wall Street Journal

An odd thing happened the last time Alan Greenspan testified before congress...

Longest-term interest rate: 30-year bond rate up from 6.03% to 6.47% in the four market days surrounding the testimony, from Friday to Wedneday.

Think about that: 6.47% - 6.03% = 0.44%, times 30 years = 13.2%. Everything in 2025 was just marked down in price by some 13%. A huge shift in relative values.

Why did this happen? Not completely sure: supply and demand in the bond market. But people doing the selling (and people watching the bond market) said that they saw two reason:
First, Greenspan more-or-less dismissed the chance of a recession in the near future...
Second,Greenspan's Humphrey-Hawkins testimony provided an occasion for people to reevaluate their views on future government policy, and what they saw was a much lower chance of a deficit reduction deal, of the spending cuts and tax increases that would bring the deficit back into balance.

Why should these changed expectations of future policy change interest rates now?

Begin with what policy will be in the future. A lower deficit means either that G is down, or T is up (and thus that consumption is down). A chance of recession means a chance that investment demand will fall--hence that I will fall. All of these pull the IS curve in and to the left. Thus before Alan Greenspan's testimony, people were expecting a good chance that at some time in the relatively near future the IS curve would shift sharply in and to the left.

But people weren't expecting it to end there. The Federal Reserve is not a houseplant--and while they may dislike inflation more than most of the rest of us do, they also dislike unemployment. Expectations were that there was a good chance that (a) this inward shift of the IS curve would, when it happened, be offset by a sharp reduction in interest rates, as the Federal Reserve sought to push the economy down the IS curve and so offset the incipient recession that the fall in investment demand, and/or the deficit-reduction package, had produced.

So people were expecting a good chance of Federal Reserve action to push interest rates much lower in the relatively near future. And this Alan Greenspan took away.

Term Structure

Why did Alan Greenspan's statements--which had much more of an impact on private-sector expectations than he had thought they would have--change interest rates today? Because of the term structure of interest rates:

Recall that investors face a choice:
Buy and hold a long-term bond
Buy a short-term bond; hold it to maturity; then buy another short-term bond:


(Interest Rate on Long-Term Bond) = (Average Interest Rate on Today's and Tomorrow's Short-Term Bonds) + (Risk [or Term] Premium)

Hence expected reductions in future short-term interest rates tomorrow cause lower current long-term interest rates today. And something like the tone of Greenspan's testimony that--and here we get somewhat convoluted--reduces the expected chance of future declines in short-term interest rates raises long-term interest rates today.

The Stock Market

Let's think about the future stream of corporate profits. Corporate profits are heavily procyclical: higher output Y means higher profits (because of ample fixed costs). Either corporate profits are paid out to investors in stocks as dividends, or they are reinvested in the business--used to buy capital goods that add to the firm's productive power. Hence in a very real sense all of corporate profits are the "property" of shareholders: either they are paid out directly to shareholders, or they are retained and used to buy capital goods that will further boost profits--and dividends--in the future.

So how, if you had a given set of expectations, would you go about trying to pin a value on the stock market--trying to figure out how much you should be willing to pay for a representative basket of stocks (something like the Dow-Jones average of 30 industrial securities);

DJ = (Next year's corporate earnings) + (Corporate earnings two years from now) + ...

But since earnings are strongly procyclical:

DJ is proportional to (Some Average of Future Y)

But there is an alternative to investing in stocks--investing in bonds. When interest rates are high and bond prices are low, you can get returns exceeding stocks for a while by investing in bonds. Hence the higher are interest rates, the lower are stock prices:

DJ proportional to (Average Future Y)/((Interest Rate) + (Risk Premium))

Tobin's q

Now let's look at the Wall Street Journal financial markets summary. This morning's was for Friday:

DJIA .......... 5536.56 .. + 50.94
S&P 500 .................. + 0.62%
Nasdaq Composite.......... - 1.27%
Tokyo (Nikkei 225)........ - 0.52%
London (FT 100) .......... + 0.28%
30-Yr Treasury Yield...... 6.36% (down from 6.47%)
Japanese yen (per US$) ... 105.20
German mark (per US$)..... 1.4725

Three domestic stock price indices (one, the Nasdaq, heavily weighted toward small, and today high-tech, companies) showing gains of one percent or so...

Two foreign stock indices (and two interest rates) that we will delay thinking about until after the midterm.

And the 30-year Treasury yield: in this case down from 6.47% to 6.36%.
Suppose the risk premium on stocks is about four percent per year; then a one-tenth of one percent fall in the Treasury yield reduces the "required rate of return" on stocks by about one percent.

And note that the DJIA rose by about one percent, and the S&P 500 by a little less. The rough coincidence of these magnitudes is no accident.

Opposite proportional changes in interest rates and stock prices; suggests shifts in expectations of monetary policy (and thus real interest rates) with no shift in expected output--thus market changes its view of how strong the economy, but assumes Federal Reserve is going to act to neutralize any rise or fall in private spending.

Interest rates rise and stock prices fall: expectations of monetary tightening, and increased likelihood of a recession.

Interest rates rise and stock prices rise: positive IS shock: higher spending, higher money demand, and higher interest rates in the future:

IS-LM Summary

(1) Y = C + I + G

(2) Sp = DEF + I(r)

(3) C(Y-T) = c0 + c'(Y-T)

(4) I(r) = I0 - Ar

(5) Y = c0 + c'(Y-T) + I0 - Ar + G

(6) (1 - c')Y = c0 + G - c'T + I0 - Ar

(7) Y = (c0 + I0)/(1-c') + DEF/(1-c') + T - Ar/(1-c')

(8) M/P = L(i, Y) = eY - fi

(9) i = (e/f)Y - (M/P)/f

Suppose we put equations (7) and (9) together--under the assumption that i = r-- what do we get? We get (10):


But note that anything like equation (10) depends on the i = r assumption: which is broken regularly

(11) p = E(p) + (1/a)(Y-Y*)

where p is the rate of inflaton, and E(p) is the expected rate of inflation. But usually we will write this Phillips Curve in terms of unemployment, and usually make the assumption that next year's expected inflation is last year's actual inflation:

(12) pt = pt-1 + B(U*t - Ut)

where U is the unemployment rate and U* is the "natural" rate of unemployment


Econ 100b

Created 4/30/1996
Go to
Brad De Long's Home Page

Professor of Economics J. Bradford DeLong, 601 Evans
University of California at Berkeley
Berkeley, CA 94720-3880
(510) 643-4027 phone (510) 642-6615 fax