ANSWER OUTLINE SECOND TAKE-HOME EXERCISE SET [9 Points Total] L. Tesfatsion DUE DATE: Tuesday, Feb 13, 9:30 A.M. Econ 302/Spring 96 --------------------------------- 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? ANSWER OUTLINE FOR PART b): In answering this part, the 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 following answer outline are appended to the copy of this Answer 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. ------------------------------------ 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? ANSWER OUTLINE FOR PART a): 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). The advertisement of the new jobs attracts 1.5 million 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 force for January in the absence of the advertisement but now 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? ANSWER OUTLINE FOR PART b): 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.