## Michael D. Bordo, Owen F. Humpage, and Anna J. Schwartz

Print publication date: 2015

Print ISBN-13: 9780226051482

Published to Chicago Scholarship Online: September 2015

DOI: 10.7208/chicago/9780226051512.001.0001

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# (p.375) Appendix 2 Empirical Method for Assessing Success Counts

Source:
Strained Relations
Publisher:
University of Chicago Press

# A2.1 Introduction

This appendix explains the empirical methodology that we use in chapters 5 and 6 to evaluate US intervention during the floating exchange-rate period. It draws heavily on Bordo, Humpage, and Schwartz (2012). Following a methodology developed in Humpage (1999, 2000), we define three success criteria based on the correspondence between intervention and subsequent exchange-rate movements and count the number of observed successes under each criterion.1 Then we test to see if counts exceed, or fall short of, a number that might occur randomly given the near-martingale nature of daily exchange-rate changes. A count that is statistically different from random suggests that US intervention has value as a forecast of near-term exchange-rate patterns and conveys information useful for price discovery.

Bordo, Humpage, and Schwartz (2012) also present further empirical results for this sample. They test to see if various factors, including the amount and frequency of interventions and whether the intervention was coordinated, affect the probability of success. They find that larger interventions increase the probability of success, but no other factor does so.

This appendix proceeds as follows: The next section defines our three success criteria, explains our data, and describes some key underlying assumptions. Section 3 evaluates our success counts assuming that successes are hypergeometric random variables. Table A2.1, which does not appear in the body of this book, provides results for the entire 1973 to 1995 sample period. Tables A2.2 and A2.3 provided a summary of results for intervention against German marks and Japanese yen respectively for key subperiods of our sample. Tables A2.4 through A2.9 provide the detailed results for those (p.376) subperiods from which we constructed the abbreviated tables that appear in chapters five and six.

# A2.2 Success Counts

We evaluate the success of US foreign-exchange operations using two specific criteria and a general criterion that incorporates the first two. In all of the definitions that follow, It designates US intervention on day t, with positive and negative values being sales and purchases of foreign exchange, respectively. St is the opening (9:00 a.m.) spot bid for foreign exchange in the New York market on day t measured in foreign-currency units per US dollar, and Δ‎St = St+1St. The change in the exchange rate from the opening on day t to the opening on day t+1 brackets US interventions on day t.2 The target exchange rate is either German marks per dollar or Japanese yen per dollar, and It consists only of the corresponding intervention, that is, dollars against German marks or dollars against Japanese yen.

Our first binomial success criterion (SC1) counts an official US sale or purchase of foreign exchange on a particular day as a success (SC1 = 1) if the dollar appreciates or depreciates, as the case may be, over that same day:

(1)
$Display mathematics$

Our second success criterion (SC2) scores an intervention as a success (SC2 = 1) if the United States sells foreign exchange and the dollar continues to depreciate, but does so by less than over the previous day. Likewise, this criterion counts intervention as a success if the United States buys foreign exchange and the dollar continues to appreciate, but does so by less than over the previous day. (For completeness, we include Δ‎St = 0 in this criterion.)

(2)
$Display mathematics$

Our general success criterion (SC3) incorporates SQ and SC2. Accordingly, an intervention sale of foreign exchange on a particular day is successful (SC3 = 1) if the dollar appreciates or if it depreciates by less than on the previous day. A corresponding rule holds for dollar purchases of foreign exchange.

(3)
$Display mathematics$

(p.377) We measure success over a single day, which some may find unduly restrictive (Goodhart and Hesse 1993; Fatum and Hutchison 2002). Despite the narrow window, the chance that we might fail to count an intervention as successful because the appropriate exchange-rate movement occurred beyond the opening on day t + 1 seems remote. Chang and Taylor (1998), Cheung and Chinn (2001), and Dominguez (2003), among others, suggest that exchange markets begin to respond to intervention within minutes or hours, not days. Likewise, a majority of central bank officials in Neely’s (2001) survey contended that exchange rates reflect the full effects of intervention within hours. Alternatively, by keeping the window narrow, we may count an intervention as a success even though the exchange-rate change that led us to that conclusion subsequently disappears. Opening the event window beyond a single day to limit this problem, however, quickly causes overlap among interventions, making inferences about the likelihood of an intervention’s success impossible.

We assume, as in Dominguez (2003, 34), that US monetary authorities base a decision to intervene on day t only on past information about exchange rates. We believe this to be an accurate characterization of how US policymakers generally reach their decision to intervene, although the desk may sometimes adjust the amount of an intervention in response to market reactions (Neely 2001; Baillie and Osterberg 1997). If exchange-rate changes and interventions are jointly determined on day t, our counts could contain a bias (Neely 2005).

Although we do not model a specific transmission mechanism for intervention, we assume that intervention operates through an expectations channel. We are testing to see if US monetary authorities have an informational advantage that they impart to the market through their interventions (Popper and Montgomery 2001). If central-bank intervention does indeed impart new information to the market, private traders will immediately incorporate it into their exchange-rate quotes. This information may be positive; that is, the market may interpret the intervention in the manner that the central bank intends. Alternatively, this information may be negative; that is, the market may react to an intervention in the opposite manner than the central bank desires. Our tests look to uncover this behavior.

# A2.3 Evaluation: How to Read the Tables

Following Henriksson and Merton (1981) and Merton (1981), we evaluate our success counts under the assumption that the number of successes is a hypergeometric random variable. The hypergeometric distribution seems appropriate because it does not require individual interventions to be independent events and does not depend on a presumed probability of an individual success. To apply the Henriksson and Merton methodology, we must consider intervention sales and purchases of foreign exchange separately.

(p.378) Our null hypothesis compares the actual and the expected success counts. We reject the null and conclude that intervention has positive forecast value if the success count exceeds the expected number by two standard deviations. In this case, a private dealer could profit on average by trading with the Federal Reserve. We reject the null and conclude that intervention has negative forecast value if the actual number of successes lies below the expected number by more than two standard deviations. In this case, private dealers could profit on average by trading against the Federal Reserve. If we cannot reject the null hypothesis, we conclude that the number of successes is not different than a number that could randomly occur given the near martingale nature of daily exchange-rate changes.

This approach also assumes that intervention does not change fundamental macroeconomic determinants of exchange rates. This supposition seems appropriate given that the Federal Reserve routinely sterilizes all US interventions and given the lack of evidence that sterilized intervention works through a portfolio-balance mechanism. The failure of this assumption to hold would bias our results toward finding a high number of successes in any sample.

Table A2.1, which does not correspond to any table in the body of this book, presents our results for the entire sample period, 2 March 1973 through 19 March 1997.3 During these 6,274 business days, the United States intervened on 971 days against German marks and on 243 days against Japanese yen.4 The first intervention against German marks took place on 10 July 1973, and the first intervention against Japanese yen followed on 24 January 1974.

The first column in Table A2.1 lists the success criteria for the German marks (top section) and Japanese yen (bottom section). The second column shows official US intervention purchases and sales. Between 2 March 1973 and 19 March 1997, for example, the United States sold German marks on 469 days and bought German marks on 502 days. The next two columns of data show intervention successes. Of the 469 US sales of German marks, 136, or 29.0 percent, were successful under criterion SQ; that is, each of these 136 interventions was associated with a same-day dollar appreciation. The next two columns show virtual successes. Virtual successes follow the respective success criteria outlined in equations 1 through 3, absent any consideration of intervention. The dollar, for example, appreciated against the German mark—whether or not the United States intervened against marks—on 2,951, or 47.0 percent, of the 6,274 business days in our sample.

The final two columns in table A2.1 refer to the hypergeometric distribution. If successes are hypergeometric random variables, then in a sample of 6,274 observations with a virtual success rate of 47.0 percent, we would expect to observe 221 successes in 469 interventions, purely by chance. The observed number of successes, 136, falls more than two standard deviations below the expected value, implying that the United States had negative (p.379)

Table A2.1 Success counts for US intervention, 2 March 1973 to 19 March 1997

Opening bid quotes

German marks

Total (#)

Intervention successes

Virtual successes

Expected successes (#)

Standard deviation (#)

(#)

(%)

(#)

(%)

Observations

6274

Criterion SC1

Sell marks

469

136

29.0

2,951

47.0

220.6

8

502

192

38.2

3,007

47.9

240.6

9

Total

971

328

33.8

Criterion SC2

Sell marks

469

117

24.9

820

13.1

61.30

4

502

110

21.9

807

12.9

64.57

4

Total

971

227

23.4

Criterion SC3

Sell marks

469

253

53.9

3,771

60.1

282

12

502

302

60.2

3,814

60.8

305

13

Total

971

555

57.2

Japanese yen

Observations

6274

Criterion SC1

Sell yen

94

47

50.0

3,000

47.8

45

5

149

63

42.3

2,836

45.2

67

5

Total

243

110

45.3

Criterion SC2

Sell yen

94

19

20.2

740

11.8

11

1

149

28

18.8

829

13.2

20

2

Total

243

47

19.3

Criterion SC3

Sell yen

94

66

70.2

3,740

59.6

56

6

149

92

61.7

3,665

58.4

87

7

Total

243

158

65.0

forecast value. This value is so low that market participants, who knew when the United States intervened, could have bet against the United States—bought German marks on day t—and made money on average. From an expectations-channel perspective, a US sale of German marks signaled that the dollar would depreciate over the same day as the intervention. Similar results hold for purchases of German marks, implying that the United States had negative forecast value in this case too. The corresponding success counts for US official interventions against Japanese yen, however, were no different than random.

(p.380) In contrast to the results under success criterion SC1, the success counts under SC2, for both US interventions against German marks and Japanese yen, are more than two standard deviations above their expected values, indicating that US interventions had positive forecast value with respect to criterion SC2. When the dollar is depreciating and the United States sells foreign exchange, it is a good bet that the dollar will continue to depreciate, but will do so by less than on the day prior to the intervention. Likewise, when the dollar is appreciating and the United States buys foreign exchange, it is a good bet that the dollar will continue to appreciate, but will do so by less than on the day prior to the intervention.

While the successes under criterion SC2 clearly exceed the expected number, the overall frequency of this type of success is fairly low. Only 23 percent of all US interventions against German marks and 19 percent of all US interventions against Japanese yen were successful under the SC2 criterion.

The final, general success criterion, SC3, combines SC1 and SC2. Generally, we expect that approximately 60 percent of all interventions will be successful under at least one of our success criteria purely by chance. (See the virtual counts under SC3 in table A2.1.) The total number of actual successes under SC3 is—in all but one case—no better than random. The exception is the total for US sales of German marks, which falls more than two standard deviations below the expected number.

# A2.4 Subperiods Appearing in Chapters 5 and 6

Tables A2.2 and A2.3 provides a one-stop comparison of the results for the various subperiods that appear in chapters 5 and 6 and for some more comprehensive time periods. This overall summary informed our conclusions about intervention under floating exchange rates. In tables A2.2 and A2.3, N and P indicate whether intervention had negative or positive forecast value for a designated criterion. An R in the tables indicates that the observed number of successes was no different than the number that we expect purely by chance.

The table cautions that overall conclusions about intervention are not necessarily robust across time periods or across currencies within any time period. Nevertheless, some relatively persistent patterns stand out. First, US intervention in German marks prior to 17 April 1981 universally had negative forecast value (N) with respect to criterion SC1 and universally had positive forecast value (P) with respect to criterion SC2 (see table A2.2). As discussed in chapter 5, during this time period—certainly before 15 September 1977—the United States feared that private traders might interpret an intervention as a sign that the dollar was fundamentally weak and that market participants might bet against the Federal Reserve’s interventions. Our results validate this concern. In addition, US policymakers usually only (p.381)

Table A2.2 A summary of the success counts across time periods, German marks

US intervention against German marks

Success criterion

SC1

SC1

SC2

SC2

SC3

SC3

sell

sell

sell

sell

2 March 73–19 March 97

469

502

N

N

P

P

N

R

2 March 73–17 April 81

391

348

N

N

P

P

N

R

2 March 73–14 September 77

161

176

N

N

P

P

N

R

15 September 77–5 October 79

175

58

N

N

P

P

R

N

8 October 81–17 April 81

55

114

N

N

P

P

R

R

20 April 81–19 March 97

78

154

R

R

P

P

R

R

20 April 81–29 March 85

1

24

N

N

R

P

N

R

1 April 85–29 April 88

33

19

R

R

P

P

R

R

2 May 88–19 March 97

44

111

R

R

R

R

R

R

Notes: N = negative forecast value (observed number of successes falls below the expected number of successes by more than two standard deviations). P = positive forecast value (observed number of successes exceeds the expected number of successes by more than two standard deviations). R = random (observed number of success falls within two standard deviations of the expected number of successes).

Table A2.3 A summary of the success counts across time periods, Japanese yen

US intervention against Japanese yen

Success criterion

SC1

SC1

SC2

SC2

SC3

SC3

sell

sell

sell

sell

2 March 73–19 March 97

94

149

R

R

P

P

R

R

2 March 73–17 April 81

11

31

R

R

R

P

R

R

2 March 73–14 September 77

0

2

(none)

R

(none)

R

(none)

R

15 September 77–5 October 79

10

19

R

N

R

P

R

R

8 October 81–17 April 81

1

10

R

R

R

R

R

R

20 April 81–19 March 97

83

118

R

R

P

P

R

R

20 April 81–29 March 85

0

11

(none)

R

(none)

P

(none)

R

1 April 85–29 April 88

52

20

R

R

P

R

R

R

2 May 88–19 March 97

31

87

R

R

P

R

R

R

Notes: N = negative forecast value (observed number of successes falls below the expected number of successes by more than two standard deviations). P = positive forecast value (observed number of successes exceeds the expected number of successes by more than two standard deviations). R = random (observed number of success falls within two standard deviations of the expected number of successes).

(p.382) hoped to smooth exchange-rate movements over this time period; that is, the United States usually cared more about SC2 than SC1.

Second, US interventions against Japanese yen prior to the Plaza Accord—with few exceptions—seem unsuccessful under each of our three criteria (see table A2.3). Prior to the Plaza Accord, however, the United States rarely intervened against Japanese yen. With so few observations, drawing firm conclusions about the success of US interventions against Japanese yen may be risky. (A similar caveat applies to the interventions against German marks over the 20 April 1981 through 29 March 1985 minimalist period.)

Third, the large US interventions associated with the Plaza and Louvre accords (1 April 1985 through 29 April 1988) and with the US Treasury–led interventions of the very late 1980s and early 1990s, had overall success counts that were not obviously different than previous episodes (see chapter 6). Economists have often regarded the interventions following the Plaza and Louvre accords as highly successful.

Fourth, US interventions lack positive forecast value under success criterion SC3 during every subperiod portrayed in tables A2.2 and A2.3. Our overall finding that fewer than 60 percent of US interventions had positive forecast value seems consistent across time periods and currencies.

Tables A2.4 through A2.9, which follow, contain a complete set of results for each of the subperiods that we discussed in chapters 5 and 6 of the book following the format in table A2.1. In chapters 5 and 6 we present abridged results from these tables. (p.383)

Table A2.4 Success counts for US intervention, 2 March 1973 to 14 September 1977

Opening bid quotes

German marks

Total (#)

Intervention successes

Virtual successes

Expected successes (#)

Standard deviation (#)

(#)

(%)

(#)

(%)

Observations

1184

Criterion SC1

Sell marks

161

45

28.0

541

45.7

74

4

176

67

38.1

560

47.3

83

5

Total

337

112

33.2

Criterion SC2

Sell marks

161

34

21.1

151

12.8

21

2

176

45

25.6

163

13.8

24

2

Total

337

79

23.4

Criterion SC3

Sell marks

161

79

49.1

692

58.4

94

6

176

112

63.6

723

61.1

107

7

Total

337

191

56.7

Japanese yen

Observations

1184

Criterion SC1

Sell yen

0

0

na

524

44.3

0

0

2

2

100.0

478

40.4

1

1

Total

2

2

100.0

Criterion SC2

Sell yen

0

0

na

139

11.7

0

0

2

0

na

181

15.3

0

0

Total

2

0

na

Criterion SC3

Sell yen

0

0

na

663

56.0

0

0

2

2

100.0

659

55.7

1

1

Total

2

2

100.0

Note: This table corresponds to table 5.2 in chapter 5.

(p.384)

Table A2.5 Success counts for US intervention, 15 September 1977 to 5 October 1979

Opening bid quotes

German marks

Total (#)

Intervention successes

Virtual successes

Expected successes (#)

Standard deviation (#)

(#)

(%)

(#)

(%)

Observations

537

Criterion SC1

Sell marks

175

43

24.6

222

41.3

72

4

58

16

27.6

284

52.9

31

3

Total

233

59

25.3

Criterion SC2

Sell marks

175

49

28.0

95

17.7

31

3

58

12

20.7

53

9.9

6

1

Total

233

61

26.2

Criterion SC3

Sell marks

175

92

52.6

317

59.0

103

6

58

28

48.3

337

62.8

36

4

Total

233

120

51.5

Japanese yen

Observations

537

Criterion SC1

Sell yen

10

6

60.0

248

46.2

5

2

19

5

26.3

255

47.5

9

2

Total

29

11

37.9

Criterion SC2

Sell yen

10

1

10.0

72

13.4

1

0

19

6

31.6

68

12.7

2

1

Total

29

7

24.1

Criterion SC3

Sell yen

10

7

70.0

320

59.6

6

2

19

11

57.9

323

60.1

11

3

Total

29

18

62.1

Note: This table corresponds to table 5.3 in chapter 5.

(p.385)

Table A2.6 Success counts for US intervention, 8 October 1979 to 17 April 1981

Opening bid quotes

German marks

Total (#)

Intervention successes

Virtual successes

Expected successes (#)

Standard deviation (#)

(#)

(%)

(#)

(%)

Observations

400

Criterion SC1

Sell marks

55

15

27.3

201

50.3

28

3

114

41

36.0

177

44.3

50

4

Total

169

56

33.1

Criterion SC2

sell marks

55

17

30.9

50

12.5

7

1

114

25

21.9

60

15.0

17

2

Total

169

42

24.9

Criterion SC3

Sell marks

55

32

58.2

251

62.8

35

4

114

66

57.9

237

59.3

68

5

Total

169

98

58.0

Japanese yen

Observations

400

Criterion SC1

Sell yen

1

1

100.0

204

51.0

1

1

10

4

40.0

177

44.3

4

1

Total

11

5

45.5

Criterion SC2

Sell yen

1

0

0.0

44

11.0

0

0

10

1

10.0

49

12.3

1

0

Total

11

1

9.1

Criterion SC3

Sell yen

1

1

100.0

248

62.0

1

0

10

5

50.0

226

56.5

6

2

Total

11

6

54.5

Note: This table corresponds to table 5.4 in chapter 5.

(p.386)

Table A2.7 Success counts for US intervention, 20 April 1981 to 29 March 1985

Opening bid quotes

German marks

Total (#)

Intervention successes

Virtual successes

Expected successes (#)

Standard deviation (#)

(#)

(%)

(#)

(%)

Observations

1,030

Criterion SC1

Sell marks

1

0

0.0

517

50.2

1

0

24

6

25.0

464

45.0

11

2

Total

25

6

24.0

Criterion SC2

Sell marks

1

0

0.0

118

11.5

0

0

24

7

29.2

146

14.2

3

1

Total

25

7

28.0

Criterion SC3

Sell marks

1

0

0.0

635

61.7

1

0

24

13

54.2

610

59.2

14

3

Total

25

13

52.0

Japanese yen

Observations

1030

Criterion SC1

Sell yen

0

0

na

519

50.4

0

0

11

4

36.4

449

43.6

5

1

Total

11

4

36.4

Criterion SC2

Sell yen

0

0

na

102

9.9

0

0

11

5

45.5

142

13.8

2

1

Total

11

5

45.5

Criterion SC3

Sell yen

0

0

na

621

60.3

0

0

11

9

81.8

591

57.4

6

2

Total

11

9

81.8

Note: This table corresponds to table 6.2 in chapter 6.

(p.387)

Table A2.8 Success counts for US intervention, 1 April 1985 to 29 April 1988

Opening bid quotes

German marks

Total (#)

Intervention successes

Virtual successes

Expected successes (#)

Standard deviation (#)

(#)

(%)

(#)

(%)

Observations

805

Criterion SC1

Sell marks

33

11

33.3

349

43.4

14

2

19

8

42.1

421

52.3

10

2

Total

52

19

36.5

Criterion SC2

Sell marks

33

11

33.3

132

16.4

5

1

19

4

21.1

80

9.9

2

1

Total

52

15

28.8

Criterion SC3

Sell marks

33

22

66.7

481

59.8

20

4

19

12

63.2

501

62.2

12

3

Total

52

34

65.4

Japanese yen

Observations

805

Criterion SC1

Sell yen

52

25

48.1

349

43.4

23

3

20

10

50.0

412

51.2

10

2

Total

72

35

48.6

Criterion SC2

Sell yen

52

10

19.2

111

13.8

7

1

20

2

10.0

84

10.4

2

0

Total

72

12

16.7

Criterion SC3

Sell yen

52

35

67.3

460

57.1

30

4

20

12

60.0

496

61.6

12

3

Total

72

47

65.3

Note: This table corresponds to table 6.3 in chapter 6.

(p.388)

Table A2.9 Success counts for US intervention, 2 May 1988 to 19 March 1997

Opening bid quotes

German marks

Total (#)

Intervention successes

Virtual successes

Expected successes (#)

Standard deviation (#)

(#)

(%)

(#)

(%)

Observations

2,318

Criterion SC1

Sell marks

44

22

50.0

1,121

48.4

21

3

111

54

48.6

1,100

47.5

53

5

Total

155

76

49.0

Criterion SC2

Sell marks

44

6

13.6

274

11.8

5

1

111

17

15.3

305

13.2

15

1

Total

155

23

14.8

Criterion SC3

Sell marks

44

28

63.6

1,395

60.2

26

4

111

71

64.0

1,405

60.6

67

6

Total

155

99

63.9

Japanese yen

Observations

2,317

Criterion SC1

Sell yen

31

15

48.4

1,156

49.9

15

3

87

38

43.7

1,064

45.9

40

4

Total

118

53

44.9

Criterion SC2

Sell yen

31

8

25.8

272

11.7

4

1

87

14

16.1

305

13.2

11

1

Total

118

22

18.6

Criterion SC3

Sell yen

31

23

74.2

1,428

61.6

19

4

87

52

59.8

1,369

59.1

51

5

Total

118

75

63.6

Note: This table corresponds to table 6.4 in chapter 6.

## Notes:

(1.) Chaboud and Humpage (2005) and Humpage and Ragnartz (2005) apply this same methodology to Japanese intervention (1991–2004) and Swedish intervention (1993–2002), respectively.

(2.) The United States conducts most US interventions by far in the New York market, but has occasionally placed orders through correspondents in both the European and Far Eastern markets. We cannot isolate these few transactions.

(3.) The United States did not abruptly end its intervention on 19 March 1997. United States interventions began to taper off in the early 1990s. After August 1995, the United States intervened against Japanese yen on 17 June 1998, against euros on 22 September 2000, and again against Japanese yen on 18 March 2011. These last three interventions are the only instances of US intervention during the floating exchange rate era not included in our analysis. Our exchange-rate data determined our sample, which ends on 19 March 1997.

(4.) The United States intervened against some other European currencies during the 1970s and early 1980s, but data on these currencies are not available.