Appendix: Using the Fieller Method to Construct Confidence Intervals for PI Functions

The estimated values of PFDEPi,t–l that set the PI functions equal to 0 are given by:

PIFj=ΔDEPi,tljFi,tl=0{PFDEPi,tl=(βF^+βdF^)(γF^+γdF^)ifj=PFPFDEPi,tl=βF^γF^ifj=OTHER;

where β^ and γ^ are estimates of β and γ, respectively. Following Hirschberg and Lye (2007, 2010), 100 · (1–α)% confidence intervals (CI) for the empirical PI functions are defined by:

CI=(βF^+γF^.PFDEPi,tl)±tα/2.σβF2^+2.Cov^(βF,γF).PFDEPi,tl+PFDEPi,tl2.σγF2^ifj=OTHER;CI=[(βF^+βdF^)+(γF^+γdF^).PFDEPi,tl]±tα/2.σ^(βF+βdF)2+2.Cov^(βF+βdF,γF+γdF).PFDEPi,tl+PFDEPi,tl2.σ^(γF+γdF)2ifj=PF.

In the previous expressions, σ^βF2,σ^γF2, and Cov^(βF,γF) are estimates of the variances and the covariance corresponding to βF^ and γF^. Similarly, σ^(βF+βdF),2σ^(γF+γdF)2, and Cov^(βF+βdF,γF+γdF) are estimates of the variances and the covariance corresponding to (βF^+βdF^) and (γF^+γdF^):

σ^(βF+βdF)2=σ^βdF2+σ^βdF2+2.Cov^(βF,βdF);σ^(γF+γdF)2=σ^γdF2+σ^γdF2+2.Cov^(γF,γdF);Cov^(βF+βdF,γF+γdF)=Cov^(βF,γdF)+Cov^(βF,γdF)+Cov^(βdF,γF)+Cov^(βdF,γdF).

Numerical calculations are based on robust estimation of the variance-covariance matrix of regression coefficients.

Aggregate PI Funcion: in this case the aggregate PI function is non-linear and the Filler method cannot be applied directly. However, we can obtain confidence intervals associated with linear approximations to the PI function at each point PFDEPi,t–l.

We approximate the PI function βF + (βdF + γF) · PFDEP + γdF · (PFDEP)2 around the point PFDEP.

The slope of the linearized function is given by: βdF+γF+2.γdF.PFDEP¯; and its intercept is given by:

βFγdF.PFDEP2¯. Hence, the linear approximation to the function can be written as follows:

ΔDEPi,tlFi,tl[βFγdF.PFDEP¯2]+[βdF+γF+2.γdF.PFDEP¯].PFDEPi,tl.

Applying the Fieller method, a 100 · (1–α)% confidence interval (CI) for the (linearized) PI function at the point PFDEP is given by:

CI=[(β^Fγ^dF.PFDEP2¯)+(β^dF+γ^F+2.γ^dF.PFDEP¯).PFDEP¯]±tα/2.σ^(βFγdF.PFDEP¯2)2+2.Cov^(βFγdF.PFDEP¯2,βdF+γF+2.γdF.PFDEP¯).PFDEP¯+PFDEP¯2.σ^(βdF+γF+2.γdF.PFDEP¯)2;
where σ^(βFγdF.PFDEP2¯)2=σ^βF2+σ^γdF2.PFDEP¯42.PFDEP¯2.Cov^(βF,γdF);σ^(βdF+γF+2.PFDEP¯)2=σ^βdF2+σ^γF2+σ^γdF2.(4.PFDEP¯2)+2.Cov^(βdF,γF)+4.PFDEP¯.[Cov^(βdF,γdF)+Cov^(γF,γdF)];andCov^(βFγdF.PFDEP¯2,βdF+γF+2.γdF.PFDEP¯)=Cov^(βF,βdF)+Cov^(βF,γF)+PFDEP¯.Cov^(βF,γdF)PFDEP¯2.[Cov^(γdF,βdF)+Cov^(γdF,γF)]PFDEP¯3.σ^γdF2.

PI Functions for Analysis of Banks’ Connection to the Pension Fund Industry:

Confidence intervals for the PI functions of pension fund depositors on connected banks (CONNECTi = 1) are given by:

CI=[(βF^+βdF^+φdF^)+(γF^+γdF^+βdF^).PFDEPi,tl]±tα/2.σ^(βF+βdF+φdF)2+2.Cov^(βF+βdF+φdF,γF+γdF+τdF).PFDEPi,tl+PFDEPi,tl2.σ^(γF+γdF+βdF)2.

Confidence intervals for the PI functions of pension fund depositors on unconnected banks are obtained as before.

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1

For a database documenting the high frequency and intensity of systemic banking crises in the period 1970-2007, see Laeven and Valencia (2008). On the connection between government guarantees and market discipline, see for example Demirguc-Kunt and Huizinga (2004) and Demirguc-Kunt and Detragiache (2002).

2

A broader definition would also include situations where depositors demand higher interest rates in response to a deterioration in fundamentals—see Berger (1991) and Martinez Peria and Schmukler (2001). Our goal is to compare the disciplining behavior of pension funds and other depositors; but we have no data on interest rates earned on pension fund deposits.

3

Exposure to the government sector is a highly relevant bank fundamental in the case of Argentina. The study period includes a banking crisis and a protracted sovereign debt crisis. Thus, we interpret high provision of government financing by a bank as a fundamental weakness—a high exposure to sovereign default risk.

4

We date the beginning of the Argentine banking crisis at the end of January of 2001, when time deposits in the banking system reached a peak. Note that all pension fund deposits were in the form of time deposits.

5

Martínez Pería and Schmukler (2001) point out advantages of the single equation approach: (1) it permits a market discipline test in cases where a lack of actual bank failures precludes an estimation of the probability of failure, and (2) it allows one to study specifically which fundamentals are affecting depositor behavior the most.

6

From an institutional perspective, Calomiris and Powell (2000) provide a detailed account of regulatory developments aimed at establishing discipline during the 1990s.

7

Central references in the literature on pension fund governance are Clark (2000 and 2004). Catalán (2004) offers an early discussion of conflicts of interest between pension funds and banks in Latin America.

8

Conflicts of interest within universal banks include those associated with bank lending/underwriting; sell side analysis/underwriting; analysis/brokerage; and asset management/underwriting; Mehran and Stulz (2007) offer an excellent literature review. Conflicts within the mutual fund industry are reviewed by Mahoney (2004). Ljungqvist et. al. (2007) show that institutional investors moderate conflicts in sell-side research.

9

Specifically, we select variables based on previous studies of depositor discipline in Argentina, in particular Martinez Peria and Schmukler (2001) and Barajas and others (2007).

10

The numerator of NGOVB is calculated as bank holdings of government bills and bonds, and loans to the non-financial public sector (net of government deposits) denominated in both domestic and foreign currency. The numerator of PROFIT is calculated as monthly before-tax profits. The numerator of LIQ includes gold and cash assets and reserves (required and voluntary) denominated in domestic and foreign currency; it excludes government bills and bonds as well as private sector assets.

11

A standard measure of sovereign default risk, the EMBI+, was below 400 basis points in the first semester of 1998. Since a recession started in the second semester of 1998, the EMBI+ increased over time and reached the 600-700 basis points range in the second semester of the year 2000. After the beginning of the banking panic, the EMBI+ increased sharply in March of 2001, and crossed the 1000 basis point barrier in July. See Mussa (2002) for an account of macroeconomic developments in Argentina in this period.

12

During the study period, banks owned 80 percent of the Pension Fund Management Companies; the remaining ownership was divided among insurance companies, labor unions, and non-financial companies.

13

By January of 2001, pension fund deposits were distributed as follows: 86 percent were fixed-rate deposits denominated in pesos; 4.5 percent were fixed-rate deposits in foreign currency (2.6 percent in US dollars and 1.9 percent in euros); 6.5 percent were floating-rate deposits in pesos; and 3.5 percent were peso-denominated deposits embedding early withdrawal options.

14

PRODUCTION is the index of industrial production. Regarding the stock market price index, it is widely used as a leading indicator of future macroeconomic conditions. The variable MERVALNB is a stock market price index that excludes stocks of publicly traded banks to prevent an endogeneity problem in our regressions.

15

The variable FISCAL was calculated as the ratio of monthly overall fiscal balances multiplied by 12 and divided by annual nominal GDP.

16

On theoretical grounds, the relation between size and market discipline is ambiguous and complex. First, a “too big to fail” problem could weaken the market discipline exerted on big banks relative to small banks. In the case of Argentina, however, the capacity of the government to bailout banks was severely constrained by the widespread dollarization of deposits and the currency board monetary regime. Second, large depositors could account for a larger share of deposits in big banks than in small banks—wealthy families, corporations, and institutional investors could prefer to do business with big banks that offer a broader set of financial and support services. In such case, large banks would be subject to more strict discipline than small banks.

17

Constant terms and fixed effects coefficients are not reported in Tables 2 and 3.

18

Strictly, according to our analysis of the disciplining behavior of non-pension fund depositors, we reject the “no discipline” hypothesis when the share of pension fund deposits is low, but we cannot reject it when the share of pension fund deposits is sufficiently high.

19

This interpretation is consistent with previous results in the empirical banking literature in emerging market economies; see Barajas and Steiner (2000).

20

Specifically, regressions (1) and (2) in Table 2 report F-tests on the joint significance of the variables DUM—these tests compare an “unrestricted” regression that includes the variables DUM against a “restricted” regression that includes a single constant term. Regressions (3) and (4) in Table 2 report F-tests on the joint significance of the bank and depositor specific fixed effects—such tests compare an “unrestricted” regression that includes the fixed effects against a “restricted” regression that includes the variables DUM.

21

Note that the numbers correspond to the weighted average calculations shown in Table 4.

Market Discipline and Conflicts of Interest Between Banks and Pension Funds
Author: Mr. Adolfo Barajas and Mr. Mario Catalan