Conversion-forcing security calls: Wealth transfers revisited

Conversion-forcing security calls: Wealth transfers revisited

CONVERSION-FORCING WEALTH TRANSFERS L. PAICE FIELDS, SECURITY CALLS: REVISITED ERIC L. MAIS, and WILLIAM T. MOORE ABSTRACT We reexamine eviden...

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CONVERSION-FORCING WEALTH

TRANSFERS

L. PAICE FIELDS,

SECURITY

CALLS:

REVISITED

ERIC L. MAIS, and WILLIAM

T. MOORE

ABSTRACT We reexamine evidence of wealth effects on various classes of security holders due to calls of convertible bonds and preferred stocks. Significant average devaluations of common equity documented in previous research are found in our sample and, unlike earlier studies, evidence is reported of a significant wealth transfer from common stockholders to senior security holders upon announcement of calls of convertible bonds. Thus, for convertible bond calls, some of the adverse price reaction for common stocks is gained by senior claimants.

I.

INTRODUCTION

Negative equity valuation effects of conversion-forcing calls of convertible bonds have been found in repeated studies since first examined by Mikkelson (198 1, 1985). And calls of convertible preferred stocks appear to affect equity values adversely as well (Mais, Moore, & Rogers, 1989). Potential reasons for the negative effects are many: lost tax shields in the case of bond calls (Mikkelson, 1981, 1985), intra-firm wealth transfers from stockholders to senior security-holders (Mikkelson, 1981) information signalling (Harris & Raviv, 1985) voting rights dilution (Stulz, 1988), agency costs of free cash flow (Jensen, 1986), and recently, liquidity costs (Mazzeo & Moore, 1992).

Direct all correspondence to: Dr. William T. Moore, College of Business Administration, University of South Carolina, Columbia, SC 29208. L. Paige Fields, Department of Finance and Real Estate, College of Business, University of Arizona, Tucson, AZ 867214001; Eric L. Mais, College of Business Administration, Department of Finance, University of Hawaii, Honolulu, HI. International Review of Economics and Finance, 4(l): 17-27 Copyright 0 1995 by JAI Press Inc. ISSN: 1059-0560 All rights of reproduction in any form reserved.

17

L. PAICE FIELDS,

ERIC L. MAIS,

and WILLIAM

T. MOORE

The notion that wealth transfers between stockholders and bondholders could explain the negative stock price reaction was examined but not supported by Mikkelson (1981). Since that time some developments have come about that suggest that reconsidering this possibility is worthwhile. We now know that calls of convertible preferred stocks lead to negative stock price reactions and these events may result in wealth transfers, the same as for convertible bond calls. Thus, the population of events in which intra-firm wealth transfers may be expected is larger than previously suspected. Methods for detecting abnormal performance for securities that trade infrequently have been developed since the mid- 198Os, thus the absence of support reported byMikkelson (198 1) may be attributed to the method he used to test for wealth transfers. The study is in the spirit of that of Kalay and Shimrat (1987) in which equity issue announcements are examined for information effects extending to non-equity securities, and Travlos (1987) in which bond price reactions to takeover bid announcements are estimated in order to detect wealth transfers. Kalay and Shimrat (1987) find that issuing firms bonds suffer negative equity issue announcement effects, consistent with the information-release hypothesis. Travlos (1987) finds that bidding firms’ bonds lose value when takeover bids are announced, inconsistent with the wealth transfer hypothesis. The article is arranged as follows. We offer a brief summary of the empirical record on announcement effects of convertible calls in Section II. In Section III we describe the data and the test design. The findings are reported in Section IV. We show that our samples of convertible bond and preferred stock call announcements exhibit significant average common stock price effects of -3.37 percent and -1.42 percent, respectively, similar to results reported by Mikkelson (198 1) for bond calls and Mais, Moore, and Rogers (1989) for preferred calls. Reactions of nonconvertible bond and preferred stock prices to the combined set of calls around the announcement dates average -0.28 percent for bonds and 0.37 percent for preferred stocks, neither significantly greater than zero at reasonable levels. Although the mean price reactions are small and statistically insignificant, we find that senior security price reactions reflect some gains at shareholders’ expense due to convertible bond calls, though not due to preferred calls. Thus, there is limited evidence that some types of recapitalization decisions result in wealth transfers among security holders. The findings are summarized in Section V.

II.

THE EMPIRICAL

RECORD ON CONVERSION-FORCING

CALLS

Since Mikkelson’s (1981, 1985) pathbreaking research we have been faced with the seemingly anomalous result that voluntary actions by managers, that is, convertible bond calls, result in equity devaluations.’ Recent findings of Mais, Moore, and Rogers (1989) indicate that convertible preferred stock calls have a similar effect. Forced conversion of bonds or preferred stock may convey management’s pessimism since conversion substitutes a variable cash flow stream, common dividends, for a fixed stream, preferred dividends or coupon payments (Ross, 1977). This is predicted to trigger a negative equity valuation effect and a non-positive effect on senior (nonconvertible) securities. A call announcement may also reveal that future earnings are not expected to be sufficient to motivate eventual voluntary conversion, thus a call may have a negative effect on equity value and a non-positive effect on senior security values for this reason as well (Harris & Raviv, 1985).2

Conversion-Forcing

19

Security Calls

Jensen (1986) predicts a negative effect on firm value due to conversion-forcing calls since replacing fixed claims (preferred dividends or coupon payments) with variable cash flows (common dividends) may induce or exacerbate the agency problem of free cash flow. Some convertible security holders may prefer not to have newly converted common shares in their portfolios, thus following calls, ultimate buyers must be found for the new shares (Mazzeo & Moore, 1992). In response to anticipated selling pressure, dealers lower bid and ask quotes to attract buyers and deter sellers. Stock prices rebound following calls as the temporary mismatch in supply and demand disappears; thus Mazzeo and Moore (1992) predict a negative short-run common stock price reaction and no reaction for senior (nonconvertible) securities. The explanations summarized thus far all predict negative stock price reactions to convertible security calls and non-positive price reactions for senior (nonconvertible) securities. Plausible scenarios exist, however, for convertible security calls to result in positive price reactions for senior securities. Mikkelson (1981) suggests that senior security holders may benefit from conversion-forcing calls of subordinated issues because (1) reductions in financial leverage generally reduce the magnitude of potential wealth transfers from senior security holders to common stockholders, a manifestation of the agency problem among competing classes of claimants (Jensen & Meckling, 1976) and (2) expropriation incentives are reduced to the extent senior claims are reduced in magnitude. Another source of wealth transfer, also pointed out by Mikkelson (1981), is that calls of convertible bonds and preferred stocks result in changes in relative priority of outstanding claims. In the event bankruptcy results in less than strict application of absolute priority in settling claims, conversion of subordinated claims may benefit senior debtholders to the detriment of stockholders, and there is ample evidence that absolute priority is violated frequently (see Eberhart, Moore, & Roenfeldt, 1990, for example). Observed negative stock price reactions could be driven by virtually any combination of the various explanations cited above. But only the latter explanations, those having to do with wealth transfers due to agency problems and priority rule violations, predict negative stock price reactions and positive reactions of senior security prices.

III.

DETECTING

PRICE EFFECTS

ON NON-EQUITY

SECURITIES

We examine nonconvertible, publicly traded debentures and preferred stocks for price reactions to conversion-forcing call announcements. The initial sample consists of 111 convertible bond calls and 58 convertible preferred stock calls examined by Mazzeo and Moore (1992). Their convertible bond call sample was identified in various editions of Moody’s Industrial Manual. Preferred stock calls were identified by searching Standard & Poor’s Compustat data base for firms that reported reductions in preferred stock outstanding. These samples were then screened for announcements in the Wall Street Journal and availability of returns on the Center for Research in Security Prices (CRSP) return tiles. Prices of nonconvertible bonds were taken from the Wall Street Journal and coupon payment information was identified in Moody> Bond Record. Prices and dividend payments for nonconvertible preferred stocks were identified in the Wall Street Journal and Standard & Poor’s Daily Stock Price Record. In order to be included, each security had to have an

L. PAIGE FIELDS, ERIC L. MAIS, and WILLIAM

20

T. MOORE

observable transaction price at least nine times during the period t = -60 to t = -11 relative to the announcement date (t = 0). This selection process resulted in 11 bonds and nine preferreds for the convertible bond call sample, and 11 bonds and nine preferreds for the convertible preferred stock call sample. Mikkelson (1981) examined weekly returns on nonconvertible bonds surrounding 19 announcements of convertible bond calls. During the announcement week his sample exhibits a positive (0.73 percent) return, greater than the average weekly return (0.21 percent) for the 24 weeks surrounding the announcement week. His test statistic (t = 1.53) was insignificant at the 10 percent level, but he acknowledges that “the use of weekly return data may not allow for sufficiently powerful tests to identify a small wealth effect” (Mikkelson, 1981, p. 258). We employ tests using daily returns in order to improve power. To treat the inevitable problem of low trading frequency, hence unobserved daily returns, we follow the technique employed by Hite and Owers (1983), an adaptation of a method suggested by Handjinicolaou and Kalay (1984). The return (Rir(r)) for bond i is measured over T days, beginning on day t-T and ending on day T, as follows:. Pi, + D, (C/365) Q(T) In equation (l),

=

- 1. Pi t_T+ D,_+/365)

(1)

P, = close price of bond i on day t; D, = number of days since last coupon payment date; Ci = annual promised coupon payment for bond i; and T = number of days between the current trade (at t) and the previous

trade (at t-7’). For preferred stock, the T-day return, Rir(~, is determined according to equation (I), but with D, (CJ365) and D,_T (Ci/365) set equal to zero. Abnormal returns (ARit) for bonds and preferred stocks are determined from the mean-adjusted returns model as follows: AR,,

= Ri, (T) - TRi.

(2)

In equation (2), Ri = estimate of mean one-day return from the estimation period (t = -60 to t = -11 for security i, where R;,(T)IT is an unbiased estimate of the one-day return and &r(Z) is from equation (1). Handjinicolaou and Kalay (1984) subtract a matching Treasury bond return from the senior security return to form their version of equation (2) while we follow Hite and Owers (1983) and form abnormal returns according to equation (2). This is justified on the same basis; that is, “we are looking at a much longer time period over which there was no consistent interest rate movement” (Hite & Owers, 1983, p. 423, Note 20). Our call announcement data span 23 years, 1964 through 1986, and events are fairly evenly distributed over the period. Each abnormal return is then standardized according to equation (3):

AR;+ SAR,,

= L . S,,TT

(3)

21

Conversion-Forcing Security Calls

In equation (3) Si = sample standard deviation of abnormal returns for security i during the estimation period. The average abnormal return (AA&) for the sample of securities on day t is given by equation (4).

AAR,

= j$

AR,,. z=

(4)

1

To examine abnormal performance over arbitrary lengths of time, AAR in equation (4) is summed over the time span of interest and the sum is denoted by CAAR, the cumulative average abnormal return. To test hypotheses about CAAR, we calculate the standardized cumulative abnormal return (SCAR) for each security i over the time span from t = rl to r = f2 as in equation (5). r2

SCARi

=

(3

c SARi,/dm. t= t,

The test statistic for N securities is then given by equation (6).

Z = 5 i=

The test statistic (Z) in equation (6) is asymptotically

IV.

(6)

SCAR/$N. 1

unit normal.

TEST RESULTS

Our first empirical task is to confirm the negative average stock price reaction for our two call samples. We estimate the market model over the 200 days ending immediately prior to the beginning of the event period designated as t = -2 1 to t = +20.3 Abnormal returns (ARs), average abnormal returns (AARs), and cumulative average abnormal returns (CAARs) are determined from the market model. Test statistics (Z) for cumulative average abnormal returns are calculated following Mikkelson and Partch (1988) equation (2) page 122.4 This method takes into account autocorrelation in the time-series of abnormal returns induced by use of a single set of market model parameter estimates throughout the estimation period. Results for the samples of 18 convertible bond calls and 18 convertible preferred stock calls are reported in Table 1. For the two-day announcement period, t = - 1,0, calls of convertible bonds result in a CAAR value of -3.37 percent, significant at the 1 percent level (Z = -5.987). Calls of convertible preferred stocks also exhibit a negative announcement effect (CAAR = -1.42 percent), significant at the one percent level (Z = -2.878). Thus our samples are representative of the larger samples examined by Mikkelson (198 1) for bond calls and by Mais, Moore and Rogers (1989) for preferred calls. We examine security price reactions to the combined sample of convertible bond and convertible preferred stock calls initially, then results are presented separately for the two types

L. PAGE FIELDS,

22

ERIC L. MAIS, and WILLIAM

T. MOORE

Table I. Cumulative Average Abnormal Returns (CAAR) and Test Statistics (Z) for Common Stocks during Selected Intervals Surrounding Announcements of Calls of Convertible Preferred Stocks and Convertible Bonds Convertible Preferred Calls’ Interval’

Convertible Bond Calls2

CAAR(%)4

Z

-21 to -12

-3.14

-2.626

-11 to-2

a.08

-0.226

-0.57

-0.460

-1 and 0

-1.42

-2.878

-3.37

-5.987

1 to 10

-1.02

-0.152

1.51

1.184

I1 to20

4.23

-0.152

1.75

1.652

Notes:

MAR(%)

Z

0.11

0.427

1. Sample size = 18; 17 listed on NYSE or ASE, 1 NASDAQ. 2. Sample size = 18; all listed on NYSE or ASE. 3. Day 0 is the Wall Street Journal press date for the announcement. 4. CAARs are based on market model estimates using the equally-weighted Center for Research in Securities Prices (CRSP) Index. Results are similar using the value-weighted CRSP Index.

of security calls. Our full period of analysis includes the span from 10 trading days before the Wall Street Journal announcement (t = 0) to 15 trading days following the announcement. Various segments of the full time span, such as t = - 1,O, will be examined separately. In Table 2 we present cumulative average abnormal returns (CAARs), test statistics (z) from equation (6), and the number of securities for which returns could be calculated for various time spans. In Panel A of Table 2 results are presented for the combined sample of calls of convertible bonds and preferred stocks. For the portfolio of 20 nonconvertible bonds for which returns were observed for the announcement period (t = -1 ,O), the cumulative average abnormal return (CAAR) is -0.53 percent and is not significantly different from zero (Z = -0.722) at any reasonable level. The result is similar for nonconvertible preferred stocks. The portfolio of 18 preferreds for the period t = -1,0 has a CAAR of -0.66 percent, not significantly different from zero (Z = -0.85 1). Following Hite and Owers (1983), we also consider the span of time “around t = 0,” defined at the last trading day prior to t = -1 through the first day on or after t = 0. For the straight bonds this allows us to add two data points, and no observations are gained for the preferred stock sample; all 18 of those observations traded “around t = 0,” from t = -2 (last trading day before t = -1) to t = 0. As is clear in Table 2, the price reactions “around t = 0” are benign for both samples. For bonds, CAAR = -0.28 percent and Z = -0.964 (N = 22). For preferred stocks, CAAR = 0.37 percent and Z = 0.5 14 (N = 18) insignificantly different from zero. Of the 18 observations, eight were negative and 10 were positive, hence the low Z-value is not due to extreme observations. Thus, for the combined set of convertible bond and preferred calls, nonconvertible senior securities’ values are not significantly affected on average. The null finding may be because the economic explanation for price reactions to convertible bond calls differs from that for convertible preferred calls, hence the combined sample of calls may mask the effect on senior securities. In particular, wealth transfers from stockholders due to calls of convertible bonds may differ in severity from those due to calls of convertible preferred stocks. Thus we analyze nonconvertible bond and preferred stock returns around announcements of convertible bond calls separately from convertible preferred calls.

Conversion-Forcing Security Calls

23

Table 2. Cumulative Average Abnormal Returns (CAAR), Test Statistics (Z), and Numbers of Observed Returns (N) for Nonconvertible Bonds and Preferred Stocks During Select Intervals Around Announcements of Calls of Convertible Bonds and Preferred Stocks Nonconvertible Interval

CAAR(%)

Z

Bonds

Nonconvertible N

CAAR(%6)

Preferred Stocks Z

N

A. Combined Sample of Convertible Bond and Preferred Stock ~~11s

to 15

-1.28

-2.55

-1.889

22

-1otoo

-1.36

-1.194

22

-1 too

-0.53

-0.722

20

-0.66

-2t02

-0.40

-0.909

21

-0.66

1 to 15

-1.25

-1.421

21

-1.47

Around 0

-0.28

-0.964

22

0.37

-10

0.19

-0.465

18

0.766

18

-0.85 1

18

1.436 -1.248 0.5 14

18 18 18

B. Convertible Bond Calls -10 to 15

-2.91

-1.082

11

-2.20

-0.352

9

-10 to 0

-2.36

-1.492

11

-0.86

-0.178

9

-1 too

-1.25

-1.569

9

-0.36

-0.461

9

-2 to 2

-0.32

-0.539

10

-1.00

-1.130

9

1 to 15

-0.60

-0.095

11

-1.34

-0.320

9

Around 0

-1.16

-1.475

II

0.89

0.460

9

C. Convertible Preferred Calls -10 to 15

-2.01

-1.564

11

-10 to 0

-0.25

-0.141

11

-I too

0.07

0.48 1

a.36 1.24

-0.305 1.261

9 9

11

-0.96

-0.136

9

-2 to 2

-0.44

0.723

11

-0.32

-0.902

9

1 to 15

-1.93

-1.996

10

-1.60

-1.445

9

0.63

0.180

11

-0.16

Around 0

0.267

9

In Panel B of Table 2 we present CAAR values, test statistics (z), and the number of securities in the various portfolios arranged by time spans for straight bond and preferred stock returns around convertible bond call announcements only. For the nine straight bonds for which observations were available during the period r = -l,O, CAAR = -1.25 percent and the test statistic is Z = -1.569. This value is significantly different from zero at the 12 percent level, thus convertible bond calls may exhibit negative price reactions for some senior securities as well as common stocks. For the period “around f = 0,” the 11 straight bonds exhibit an average price reaction of -1.16 percent, significant at the 14 percent level (Z = -1.475). The straight preferred stocks in our sample exhibit no detectable reaction to calls of convertible bonds. In Table 2, Panel B, we report CAAR = -0.36 percent, and Z = -0.467 for the announcement period, t = -l,O. For the period “around t = 0,” the CAAR value is 0.89 percent and Z = 0.460. Thus, we conclude that straight preferred stocks are not significantly affected on average by convertible bond calls. In Panel C of Table 2 we report results of tests of the effects of convertible preferred stock culls. For the 11 straight bonds in the sample, the CAAR for days t = -1,0 is 0.07 per-

L. PAIGE FIELDS, ERIC L. MAIS, and WILLIAM T. MOORE

24

cent with a Z value of 0.48 1 (insignificant at the 3 1 percent level). The CAAR for straight bonds for “around f = 0” is 0.63 percept and Z = 0.180. Thus, bor ? prices exhibit no detectable average effect from convertible p.:ferred calls. The pattern is the same for straight preferred stocks. For the period t = -l,O, CAAR = -0.96 percent and Z = -0.736. Of the nine observations, four are negative and five are positive. For the period “around t = 0,” CAAR = -0.16 percent and Z = 0.267 (insignificant at 39 percent). Thus, we conclude that straight preferred stocks exhibit no detectable average price reaction to calls of convertible preferred issues. The absence of a positive average price reaction among senior securities does not necessarily rule out wealth transfers. It is possible, for example, that convertible calls convey negative information that depresses firm value, that is, all securities, but transfers of wealth offset the effect for some and accentuate the effect for others. We examine the possibility that wealth transfers occur from common equity to senior securities by estimating the linear model in equation (7). AR,

SENIOR

= PO + p,,$oMMoN

+

P,TYPE,

+ izi

(7)

In equation (7), ARfENtoR and ARCoMMoN are the two-day abnormal returns (t = -1,O) for senior securities and common stocks, respectively, and TYPE = 1 if the senior security is a bond and zero if preferred stock. The senior security abnormal return may be subject to greater measurement error, hence it is modeled as the dependent variable. Equation (7) is estimated by ordinary least squares (OLS) and the results are in Table 3. We provide OLS t-statistics for coefficient estimates and White’s (1980) heteroskedasticity-adjusted t-statistics. In view of the small sample sizes and possible non-normality of the data, we also estimate 9.5 percent confidence intervals for the coefficient estimates using Efron’s (1979) bootstrap. The results in Panel A of Table 3 indicate that prices of senior securities move opposite those of common stocks upon announcement of convertible bond calls; the coefficient estiTable 3. Ordinary Least Squares (OLS) estimation of the model ARSENioR = PO + p, ARiCOMMoN + p2 TYPE, + Ei for calls of conv&tible securities. ARi denotes the 2-day abnormal return, and TYPE = 1 if the senior security is a bond and TYPE = 0 if a preferred stock. 95% Bootstrap Confidence Interval OLS Estimate

OLS t-statistic

A. Results for Calls of 18 Convertible PO

PI

0.0028

White’s t-statistic

Lower Bound

Upper Bound

Bonds 0.27

0.289

-0.0137

0.02 19

-0.2475

-1.44

-2.506

-0.6018

a.0398

I32

a.0246

-2.04

-2.115

-0.0492

-0.0017

R2 = 0.2759

Adj. R2 = 0.1793

B. Results for Calls of 16 Convertible

Preferred Stocks

PO

0.0080

0.81

2.344

PI

0.0940

0.57

1.229

-0.0952

0.27 13

0.0018

0.15

0.178

-0.0146

0.0249

P2

R2 = 0.0268

Adi. R2 = -0.1230

0.0018

0.0154

25

Conversion-Forcing Security Calls mate for E+ is negative

and White’s (1980) t-statistic is -2.506. The 9.5 percent confidence interval based on the bootstrap technique with 1000 iterations is (-0.6018, -0.0398). The coefficient estimate of B, is also negative and significant judging by White’s t-statistic (-2.115) and the bootstrap confidence interval, (-0.0492, -0.0017}, thus preferred stockholders appear to benefit more from the wealth transfer than bondholders. An obvious explanation for this result does not present itself, however we conjecture that the differential price reaction may be due to differences in protective covenants. Calls of convertible preferred stocks exhibit no evidence of wealth transfer judging by Panel B of Table 3. None of the slope coefftcient estimates is significant according to the t-statistics or the bootstrap estimator, and R2 is only 0.0268. Our combined evidence reveals some wealth transfer from common equity to senior security-holders due to calls of convertible bonds, but not to convertible preferred stocks.’

V.

SUMMARY AND CONCLUSIONS

We have examined price behavior of nonconve~ible bonds and preferred stocks around fnms’ announcements to call and force conversion of convertible securities. Our sample selection procedure identified in-the-money calls of convertible bonds and calls of convertible preferred stocks, each associated with significant negative average common stock price reactions. The research question is whether the wealth reduction suffered by equityholders was at least partially the result of a transfer to senior security holders, or the result of info~ation signalling (e.g., Harris & Raviv, 1985), agency costs (e.g., Jensen, 1986), voting rights dilution (e.g., Stulz, 1988), liquidity costs (Mazzeo & Moore, 1992), or some other explanation that supports a negative common stock price reaction and a nonpositive price reaction for senior securities. Using a recently developed statistical methodology for assessing abnormal daily price performance, we find no reliable evidence of positive average reactions of senior securities to either type of call announcement. However, we do find evidence that some of the loss suffered by common stockholders due to convertible bond calls is associated with corresponding gains to senior securityholders. Thus, wealth transfers cannot be ruled out as an explanation for stock price reactions to convertible bond calls.

Acknowledgments The authors are grateful for helpful comments and criticisms from two referees of this journal, and for expert administrative assistance from Ms. Harriet Bradham.

NOTES 1. Another apparent anomaly, reported by Ingersoll (1977), is that firms tend to call convertibles “late,” that is, they call when the convertibles are deep in-the-money. Recent

26

I_. PAICE FIELDS,

ERIC L. MAIS, and WILLIAM

T. MOORE

analysis by Asquith (1992) goes far in resolving the anomaly. He finds that firms call on average four months after the specified delay period has ended, thus the “late” calls are hardly late in terms of time. 2. See also Constantinides and Grundy (1987), Ofer and Natarajan (1987), Campbell, Ederington, and Vankudre (1991), Singh, Cowan, and Nayar (1991) and Cowan, Nayar, and Singh (1992) for variations of the signalling explanation and empirical evidence. 3. We also perform the analysis using the 200-day post-event period (t = +21 to t = 220) for parameter estimation. All results are unchanged. 4. See the notational correction at the end of the December 1988 issue of the Journal of Financial and Quantitative Analysis. 5. Given the small samples, the results could be due to high-influence observations. We calculated leverage for each observation, each model. For convertible bond calls, the highest value was 0.5756, and for preferrred stock calls, 0.3285. They were not deemed to be highly influential points (see, for example, Chatterjee and Hadi (1988)). This was corroborated by calculating Cook’s (1977) D-statistic to detect high influence on the set of coefficient estimates.

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