I use the Z-SCORE, as dependent variable, to test the bank risk-exposure nexus. It is defined as the 3-year average of the 12 month return on assets (ROA) plus the 3-year average ratio capital to total assets (CAPITALR), divided by the 3-year standard deviation of ROA. This indicator has been extensively employed in the literature to capture the bank risk of insolvency, and to test the market discipline hypothesis in the interbank market (Distinguin et al., 2013; Liedorp et al., 2010). A higher Z-SCORE value indicates a lower probability of bank failure, that is, low-risk bank.

In addition, as measure of bank risk, I employ the reserve for loan losses (RESERVE) defined as the balance at quarter end of provisions for possible credit losses divided by nonperforming loans. A higher RESERVE value indicates a lower probability of bank failure. Similarly, with an inverse relationship with bank risk, I employ nonperforming loans divided by total loans (DOUBTFUL). Dinger and Von Hagen (2009) employ similar variables to measure bank risk.

The key explanatory variable of bank risk is the participation in the interbank market, as a lender or borrower. I employ four variables to measure this participation. First, the ratio of interbank lending to total assets (EXPOSURE1). Second, the ratio of interbank borrowing to total assets (EXPOSURE2). Third, the ratio of interbank borrowing to total deposits (EXPOSURE3). Finally, the ratio of net interbank assets (interbank lending minus interbank borrowing) to total assets (EXPOSURE4). In the former variable, note that negative values indicate that the bank is a net borrower.2

I expect that banks with higher exposure to the interbank market, especially as borrowers, will have lower levels of bank risk. Then, higher values of EXPOSURE1–3 and lower values of EXPOSURE4 should impact positively reducing the bank risk-taking.

Former studies employed measures of the CAMEL rating system (capital adequacy, asset quality, management, earnings and liquidity) to control the effect of EXPOSURE. It is worth noting that the CAMEL indicators frequently are used to capture the bank risk (Tovar-García, 2014).

In this research, capital adequacy is measured with the ratio of capital to total assets (CAPITALR). For asset quality, I use the reserve for loan losses (RESERVE) and nonperforming loans (DOUBTFUL). For management quality, the ratio 12 month managerial expenses to annual average total assets (MANAGEMENT1) and the ratio 12 month managerial expenses to 12 month total income (MANAGEMENT2). Earnings are captured with the 12 month return on assets (ROA) and the 12 month return on capital (ROE). For liquidity, I use the ratio short-term (circulating) assets to total assets (LIQUIDITY1) and the ratio short-term assets to short-term liabilities (LIQUIDITY2).

According to findings in previous empirical studies, bank size is a relevant explanatory variable. Consequently, I approach the size effect using the logarithm of total assets (SIZE), and I analyze bank subsamples.

The summary statistics of the variables can be seen in Tables 1 and 2. As a first step, I reviewed the data to eliminate outliers. I use four subsamples of banks, following the classification of Banxico, as Tovar-García (2012b, 2014). The first subsample includes seven of the largest banks (G7), which usually are a cutoff point in the reports of Banxico. In September 2012, the G7 operated around 92% of interbank lending and around 62% of interbank borrowing. The second subsample includes 14 commercial banks with typical activities, but smaller than the G7. The third subsample includes 9 retail banks, which specialize in transactions with consumers. Finally, the fourth subsample includes seven investment banks, working on the issuance of securities.

Mexican banks present a large dispersion of their characteristics, according to the standard deviations of the bank variables. However, this dispersion diminishes considerably in the bank subsamples. On average, the seven largest banks are around 30 times larger (by total assets) than the rest of banks, and these differences are also appreciable in terms of capital.

The largest proportion of interbank lending and borrowing correspond to the G7, on average, they are net lenders. Conversely, other kinds of banks are net borrowers, especially retail banks, as can be observed in the values of the variable EXPOSURE4. The interbank deposits are more relevant for investment banks than for the rest of banks, as we can expect, because non-investment banks have better positions in the retail deposit market (see EXPOSURE3 in Table 2). The participation as lender in the interbank market is relevant for the G7 and commercial banks (see EXPOSURE1 in Table 2), and the participation as borrower in the interbank market is not relevant for the G7 in comparison to other types of banks (see EXPOSURE2 in Table 2).

On average, Z-SCORE (measure of bank risk) equals 27.9, the G7 and commercial banks are above the mean, that is, they are banks with a low-risk. Conversely, retail and investment banks are below the mean, as we can expect, because of the nature of their portfolios. Investment banks show better positions in the variables RESERVE and DOUBTFUL, but this result must be treated with caution because the sample include only two investment banks, and they have the largest values.

The correlation matrix (see Table 3) shows relevant positive relationships among total assets, capital, and the amount borrowed in the interbank market. These correlations are in line with previous findings about the relevance of the largest banks in the interbank transactions. The measures of exposure to the interbank market show high correlations among EXPOSURE2, 3 and 4, as might be expected, but they show a low correlation with EXPOSURE1, that is, the position as a lender in the interbank market has a low correlation with the position as borrower. The CAMEL indicators present some high correlations among them. Subsequently, in the regression analysis these variables are included with prudence, to avoid multicollinearity concerns. It is noteworthy that I can use these high correlations to check robustness of the results to different indicators of the theoretical variables.

Eq. (2) is used to test the bank risk-exposure nexus. The SYS GMM method is alleviating possible endogeneity concerns, and I lag the explanatory variables by one quarter and include a logarithmic transformation of some variables to achieve linearity and semi-elasticity coefficients.

Bank-Risk can be Z-SCORE, RESERVE or DOUBTFUL, the key explanatory variable is EXPOSURE. It is not possible to enter all the measures of exposure at the same time because of collinearity. Consequently, I include EXPOSURE1 in combination with EXPOSURE2, 3 or 4. LnCAMEL includes, in logarithms, combinations of the indicators of capital adequacy, asset quality, management, earnings and liquidity (taking into account collinearity concerns among them).3 SIZE is controlling bank size and BANK is a dummy variable for each type of bank (G7, commercial, retail and investment), where the G7 is the reference group. Thus, the model controls for other bank characteristics and markets. T is a dummy variable for years4 controlling effects of unspecified macroeconomic and financial market conditions, which are assumed constant across banks.

The fundamental hypothesis of interest is that bank risk is lower for banks with a higher participation in the interbank market. Z-SCORE and RESERVE depend positively upon the level of EXPOSURE1–3 and inversely upon the level of EXPOSURE4, considering that interbank borrowing is the major channel to mitigate the risk-taking. On the contrary, DOUBTFUL depends inversely upon of the level of EXPOSURE1–3 and positively upon the level of EXPOSURE4. This is interpreted as evidence for market discipline induced by other banks in the interbank market.

Table 4 summarizes the main results when the measure of bank risk is Z-SCORE. In columns, there are results of the regressions using the full sample with combinations of the explanatory variables (consequently, they check robustness by replacement). The explanatory variables are in rows and empty cells indicate that the variable was dropped because of collinearity.

It is noteworthy that the dynamic panel is justified because the dependent variables as regressors show statistically significant coefficients at the 1% level. All reported estimations pass both the Sargan and the first order serial correlation tests at conventional significance levels, although the second order serial correlation test shows some problems.

In the columns (1)–(6), only the indicator of exposure as lender (EXPOSURE1) shows some statistically significant coefficients with negative signs. Hence, banks with more exposure to the interbank market as lenders present higher levels of risk. Nevertheless, this result must be treated with caution because other regressions, with other control variables (see columns 1–3), do not support this finding. Moreover, as described above, in the section on descriptive statistics, the largest banks are net lenders, and the individual analysis of the G7 banks does not show evidence in favor of this finding, as will be discussed below.

The other measures of exposure to the interbank market (as borrower) do not have statistical significance (see columns 1–6). Thus, the exposure to the interbank market as borrower does not affect the levels of risk-taking, and these first findings do not support the peer monitoring hypothesis. Note that a few control variables, in specific the CAMEL indicators, enter significantly in the regressions.

The number of banks in each regression diminishes because of data limitations on investment banks (see row N×T in Table 4). The information on the variables RESERVE and DOUBTFUL is available only for two investment banks. As a result, the majority of investment banks are not included in the regressions (1)–(6). I removed RESERVE and DOUBTFUL as control variables, to include these banks in the analysis, and the new results are reported in the columns (7)–(12) in Table 4. Now, most of the exposure variables (EXPOSURE2–4) have statistically significant coefficients with the predicted sign, in favor of the peer monitoring hypothesis. Moreover, the control variables LIQUIDITY and MANAGEMENT enter significantly in the majority of the regressions.

It is interesting to note that in most of the regressions bank size has statistically significant coefficients with a positive sign, so larger banks show lower levels of risk. The dummies for year 2011 and 2012 have positive and significant coefficients in all regressions, as it was expected, because Z-SCORE has a positive trend in the last years.

The dummies for commercial and retail banks enter with negative and statistically significant coefficients. Subsequently, these types of banks have lower levels of Z-SCORE (they are riskier) in comparison with the G7 banks (the reference group). Besides, this indicates that the regression results depend on types of banks. Accordingly, I replicated the regressions by subsamples of banks. Table 5 shows the major findings. The problem of multicollinearity among control variables is higher, but different combinations of control variables showed similar results to those reported in Table 5.5

The regressions by subsamples of banks do not present evidence in favor of the peer monitoring hypothesis. All reported estimations pass the Sargan and the first and second order serial correlation tests, yet the model lost meaning for the G7 banks and investment banks, where practically nothing is explaining the levels of Z-SCORE. In the case of commercial and retail banks, only the dependent variable as regressor has statistical significance.

Consequently, the previous findings about the presence of market discipline in the Mexican interbank market are not robust. The statistical significance of the bank risk-exposure nexus depends on the inclusion of investment banks. Without these banks, as reference, the rest of banks do not show evidence in favor of the peer monitoring hypothesis. Furthermore, the exposure to the interbank market by types of banks (subsamples) does not present a significant relationship with Z-SCORE (bank risk).

These findings also imply that the monitoring activities, if they exist, works from one region (market share or sector) to another, as described by Allen and Gale (2000), probably from the G7 (net lenders) to investment banks. I do not find evidence for peer monitoring from one bank to other bank inside of their banking groups. However, it is worth noting that the results do not indicate that the exposure to the interbank market increases the bank risk.

Table 6 summarizes the main results when the bank risk is approached with RESERVE. In columns, there are results of the regressions using the full sample and subsamples, but I excluded the subsample of investment banks because of data limitations (RESERVE is available only for two investment banks). All reported estimations pass both the Sargan and the first and second order serial correlation tests.

Specifically, the dynamic model is justified for the full sample where the dependent variable as regressor enters with statistically significant coefficients at the 1% level (see columns 1–6 in Table 6). In this case, the measures of exposure to the interbank market (as lender or borrower), in general, have statistical significance, yet with the opposite sign. Banks with higher exposure to the interbank market, especially as borrower, present lower levels of RESERVE, so they are riskier. This is evidence against the peer monitoring hypothesis, and in favor of the contagion hypothesis.

The majority of the control variables enter in the model with statistically significant coefficients, I will not comment further on that to save space. Nevertheless, note that the dummies for types of banks show some significant coefficients with positive signs, suggesting a bias by subsamples of banks, as in the previous model.

Columns (7)–(15) in Table 6 show the estimations by subsamples. For a second time, the EXPOSURE variables do not present significance in any case. This result may imply that the channel of contagion, if it appears, is from one region to another, it is not from one bank to another. Anyway, the peer monitoring is absent.

Table 7 summarizes the main results when the measure of bank risk is DOUBTFUL. All reported estimations pass both the Sargan and the first and second order serial correlation tests. I expect an inverse relationship with exposure to the interbank market because higher values of DOUBTFUL indicate riskier banks.

The results are similar to the RESERVE case. The full sample again shows evidence in opposition to the peer monitoring hypothesis, and in favor of the contagion hypothesis. The coefficients of the EXPOSURE variables, especially as borrower, present statistically significant coefficients with the opposite sign, so banks with larger exposure to the interbank market are riskier. Once more, the regressions by subsamples of banks do not show any significance, and the subsample of investment banks was excluded because of data limitations (DOUBTFUL is available only for two investment banks).

Summarizing, the bank risk-exposure nexus in the Mexican interbank market rejects the peer monitoring hypothesis. With three different measures of bank risk the regression analysis indirectly suggest evidence in favor of the contagion hypothesis, because banks with higher exposure to the interbank market, especially as borrower, present higher levels of risk (lower levels of RESERVE and higher levels of DOUBTFUL). It is important to note that, in general, the regressions by subsamples of banks do not show statistical significance, and this finding can be interpreted as connections from one banking sector to another. These results are robust to different combinations of explanatory and control variables. In particular, the regressions with EXPOSURE2 and EXPOSURE4 show very similar coefficients for the independent variables.

Although, there is no reason to assume that the variables have unit roots and are thus non-stationary, as additional robustness checks, I also estimated the equation 2 using the DIF GMM method, which has a better control on non-stationary variables because the model is in first differences. The results are very similar to those reported in Tables 3–6. In addition, I replicated the regressions using as independent variable the ratio of the indicator of exposure to the corresponding indicator of bank risk (the ratio of exposure to risk-taking). This strategy can reduce the simultaneity problem; however, the regressions presented autocorrelation concerns, yet the major findings are similar (these results are not reported in tables to conserve space).