## Answer Outline for Econ 302 Exercise Set 2

Course Instructor: Leigh Tesfatsion
Date: 13 February 1996

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SECOND TAKE-HOME EXERCISE SET [9 Points Total]      L. Tesfatsion
DUE DATE:  Tuesday, Feb 13, 9:30 A.M.          Econ 302/Spring 96

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EXERCISE 2.1 [3 Points]:   Hall and Taylor, Chapter 2, ANALYTICAL
Exercise Number 8, page 64.

PART a): Is the U.S. running a current account surplus or
deficit?

ANSWER OUTLINE FOR PART a): The U.S. current account CA is in
#deficit# by \$12,000 since U.S. imports consist of one Toyota
Tercel worth \$12,000 while U.S. exports are zero.  In algebraic
terms,

CA = - \$12,000.

PART b): For each of the financial transactions described in the
Hall and Taylor statement of the exercise, explain the effect
the transaction has on the U.S. capital account.  What is the
sum of the current account and the capital account balances?

following observation is of use.  By definition, Japanese
#net# lending to the U.S. is given by

(1)    [Japanese lending to U.S.]  -  [U.S. lending to Japan] ,

or equivalently,

(2)    [Japanese claims against U.S.] - [U.S. claims against Japan].

Consequently, Japanese #net# lending to the U.S. #increases#
either if Japanese lending to the U.S. #increases# or if U.S.
lending to Japan #decreases#.  An increase in Japanese net
lending to the U.S. represents, by definition, an increase in
the U.S. capital account KA.
Also, note that dollars are legal tender in the U.S. in the
sense that, by law, dollars must be accepted when offered in
payment of debt.  Consequently, dollars are a liability of
(i.e., a claim against) the U.S. government.  Similarly, yen are
a liability of (i.e., a claim against) the Japanese government.

Transaction (i):  Japan has increased its claims against the
U.S. in the form of a \$12,000 increment to its U.S. bank
account, with no change in the claims of the U.S. against Japan.
[In effect, Japan has lent \$12,000 to the U.S. consumer in
exchange for a financial asset in the form of a deposit to a
bank account.] By (2), Japanese #net# lending to the U.S. has
thus increased by \$12,000, implying that the U.S. capital
account KA registers a \$12,000 #surplus# from this exchange.
Combining this with Part a), the sum of the current account and
the capital account is #zero#:

CA  +   KA   =   - \$12,000  +   \$12,000   =   0.

Transaction (ii): The U.S. has decreased the amount of its
claims against Japan by \$12,000 by reducing its deposit account
in Japan by \$12,000, and there has been no change in the amount
of Japanese claims against the U.S.  Consequently, using (2),
the #net# lending of Japan to the U.S. has increased by \$12,000,
implying the U.S. capital account registers a \$12,000 surplus
from this exchange.  Combining this with Part a), the sum of the
current account and capital account is #zero#.

Transaction (iii):  Japan has increased its claims against
the U.S. by its purchase of U.S. Treasury bills worth \$12,000,
whereas the claims of the U.S. against Japan are unchanged.
Consequently, the answer to (iii) is the same as for (i).

Transaction (iv):  The U.S. has decreased the amount of its
claims against Japan by \$12,000 since an amount of yen worth
\$12,000 held by a U.S. (American) foreign exchange trader has
now been paid to Japan.  On the other hand, there has been no
change in Japanese claims against the U.S.  The answer for (iv)
is thus the same as the answer for (ii).

-----------------------------------

NOTE: The MacroSolve plots and tabulations referred to in the
Outline on Closed Reserve in Heady 368.

EXERCISE 2.2 [3 Points]:   Hall and Taylor, Chapter 2, MACROSOLVE
Exercise Number 2, page 65.

IMPORTANT CORRECTION:  Hall and Taylor incorrectly omit V = [net
factor and transfer payments] in the accounting identities stated
in parts a) and b) of this exercise.  Corrected statements for
Parts a) and b) are given below.  Also, note that the MacroSolve
data labelled "savings" represents PRIVATE savings for the U.S.,
and the MacroSolve data labelled "investment" represents private
gross investment for the U.S.

PART a) CORRECTED:

First, explain intuitively rather than algebraically why it
must always be the case that, in realized terms, private savings
equals investment plus the government deficit plus net exports
plus net factor and transfer payments.  In algebraic terms:

(*)     S`p   =   I   +   [Gov't Deficit]   +   NE   +   V  .

Second, using the MacroSolve data for savings (which
represents U.S. #private# savings), for investment, for the
government deficit, and for net exports, all expressed as
percentages of GDP, confirm for 1930-1993 that savings are
approximately equal to the sum of investment plus the government
deficit plus net exports.  STUDENTS SHOULD APPEND TABULATIONS
AND PLOTS FOR THIS MACROSOLVE DATA TO THEIR TURNED IN EXERCISE
SETS.

NOTE: By accounting definition, the difference between private
savings and the sum of investment, the government deficit, and
net exports is net factor and transfer payments from abroad.
Empirically for the U.S., net factor and transfer payments from
abroad are a very small percentage of GDP.  However, statistical
measurement errors may also cause measured savings to diverge
from the measured sum of investment, the government deficit, and
net exports.

ANSWER OUTLINE FOR PART a): An algebraic demonstration that
the accounting identity

(**)       S`p   +   S`g   +   S`r   =    I

must hold is given in Hall and Taylor, Chapter 2, pages 50-52.
Substituting into (**) the definitions S`g = -[Gov't Deficit] and
S`r = -[NE+V], one obtains relation (*).

Intuitively, relations (*) and (**) each simply reflect the
fact that the funds to finance investment must come from
somebody's savings (i.e., somebody's nonconsumed income), and
the three possible sources of savings are private savings,
public (government) savings, and savings supplied by the rest of
the world.

Tabulations for U.S. (private) savings, investment, the
government deficit, and net exports (all as a percentage of GDP)
should be obtained using MacroSolve.  Year by year, these
tabulated data show that private saving S`p as a percentage of
GDP is approximately equal to the sum of investment, the
government deficit, and net exports as a percentage of GDP,
implying that the residual V is an insignificant percentage of
GDP for the U.S.

Another way to see this is to use the MacroSolve
"statistics" routine to output the mean values for S`p/GDP and
for [I+DEF+NE]/GDP over 1930-1993.  These mean values each come
out to be 15.2 percent.

PART b) CORRECTED:  According to relation (*), private saving
and investment should be positively related (given everything
else remains the same), the government budget deficit and
investment should be negatively related (given everything else
remains the same), net exports and investment should be
negatively related (given everything else remains the same), and
net exports and the government deficit should be negatively
related (given everything else remains the same).
Graph each relationshop using annual U.S. data from 1930 to
1993.  Historically, have these relationshops existed?  In
particular, do the data support the argument that government
deficits "crowd out" investment in the sense that times of high
government deficits tend also to be times when investment is
low?  Are high government deficits correlated with low net
exports in the sense that times of high government deficits tend
also to be times when net exports are low?

HINT: In addition to eye-balling the data plots, check out
the "correlation statistic" provided by MacroSolve (under
"Statistics") whenever two time-dated variables are plotted
together.  By construction, the correlation statistic must lie
between -1 and +1; and a positive correlation statistic
indicates that the two variables tend to move #together# over
time whereas a negative correlation statistic indicates that the
two variables tend to move in #opposite# directions over time.

ANSWER OUTLINE FOR PART b):  In actuality, other things never
"remain the same."  However, using the MacroSolve data plots
(appended to the closed reserve copy of this answer outline),
the following observations can be made by simply "eye-balling"
the plots.

First, investment and savings appear to be #weakly#
positively related, in the sense of moving up and down together.
Second, the government budget deficit and investment appear to
be rather #strongly# negatively related, in the sense of moving
in opposite directions---this is evidence of crowding out.
Third, net exports and investment appear to be #weakly#
negatively related.  Fourth, net exports and the government
deficit appear to be moderately negatively related.

These informal conclusions drawn from simply looking at the
data plots can be more formally tested by checking out the
correlation statistic provided by MacroSolve (under "Statistics")
whenever two time-dated variables are plotted together.  By
construction, the correlation statistic must lie between -1 and +1;
and a positive correlation statistic indicates that the two
variables tend to move #together# over time whereas a negative
correlation statistic indicates that the two variables tend to move
in #opposite# directions over time.

The correlation statistic between investment and savings is
0.07 (weakly positive); the correlation statistic between the
government deficit and investment is -.73 (strongly negative);
the correlation statistic between investment and net exports is
-0.05 (weakly negative); and the correlation statistic between
the government deficit and net exports is -0.30 (moderately
negative).

TECHNICAL REMARK (NOT REQUIRED):

How is correlation defined?  To explain by example, let
s(T) denote savings as a percentage of GDP for year T and let
i(T) denote investment as a percentage of GDP for year T.  Let
s* denote the mean of s(T) over the 64-year period from T=1930
to T=1993, that is,

s(1930) + s(1931) + ... + s(1993)
s*   =    ----------------------------------  ;
64

and similarly, let i* denote the mean of i(T) from T=1930 to
T=1993.  Then the "covariance" between s and i over this
64-year period is defined to be

[s(1930) - s*][i(1930) - i*] + ... + [s(1993) - s*][i(1993 - i*]
----------------------------------------------------------------
64

Thus, the covariance between s and i is a sum of a bunch of product
terms, one for each year T from T=1930 to T=1993, measuring whether
s and i tend to deviate from their mean in the #same# direction
(giving a positively signed product term) or in #opposite# directions
(giving a negatively signed product term).  The correlation statistic
for s and i from T=1993 to T=1993 is then just this covariance
statistic appropriately normalized to lie between -1 and +1.

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EXERCISE 2.3 [3 Points]: Hall and Taylor, Chapter 3, ANALYTICAL
Exercise Number 3, page 85.

On January 1, 1995, the government creates a million new jobs.
Only those currently without jobs may apply.  The new jobs
attract 3 million applicants, half of whom would not otherwise
by looking for work in January.

PART a): Is the labor force for January changed from what it
would have been in the absence of the new jobs?  By how much?

By definition, the labor force for January is the number of
persons at least 16 years of age either working or looking for
work in January (more precisely, during the survey week in
January).

applicants from people who are not working #and who otherwise
would not have been looking for work#.  Consequently, none of
these 1.5 million people would have been counted in the labor
they are counted in the labor force for January because they are
seeking work.  It follows that the labor force in January has
increased over what it would have been by 1.5 million people.

PART b): Assuming that without the new jobs the labor force
would have been 100 million and the unemployment rate 6 percent,
what will the unemployment rate for January now be?

By definition, the unemployment rate for January is given by

the number of unemployed in January
(3)           -----------------------------------   .
the labor force in January

By assumption, #without# the job announcement, the labor force in
January would have been 100 million and the unemployment rate
for January would have been given by .06, i.e., by 6 percent.
Consequently, using (3), in the absence of the job announcement
one has

the number of unemployed in January
(4)           -----------------------------------   =   .06  ,
100 million

which gives

(5)  the number of unemployed in January  =  .06  x  100 million

=  6 million.

#With# the job announcement, however, it follows from Part a)
that the labor force in January is given by

(6)   100 million  +   1.5  million    =     101.5 million .

previous Jan      change in Jan
labor force        labor force
due to job
announcement

Moreover, #with# the job announcement, the number of unemployed
is given by

(7)  6 million       +     1.5  million       -       1 million ,

unemployed before    people newly attracted     number of new
the announcement     into the labor force       jobs created

i.e., the number of unemployed is given by 6.5 million. Thus,
#with# the job announcement, the unemployment rate for
January is

6.5 million
(8)               ---------------    =   .064 .
101.5 million

That is, the creation of 1 million new jobs actually leads to a
measured #increase# in the unemployment rate for January from 6
percent to 6.4 percent.

This perverse effect is due to the accounting convention
that people not actively seeking work are not counted as part of
the labor force.  The job announcement, by attracting such
people back into the labor force, has actually decreased the
#percentage# of the labor force with jobs even though the
overall #number# of people with jobs has increased.

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