This article revisits the relation between current systemic risk measures and macroeconomic shock based. I construct the combined framework of Granger causality test and quantile regressions to investigate the causal effect in a specific quantile.
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The relationship between systemic risk and macroeconomic shock is important for understanding the impact from systemic risk on potential macroeconomic shock. Many systemic risk measures have been developed and tested in different dimensions. Adrian and Brunnermeier (2011), Acharya, Pedersen, Philippon and Richardson (2010), Brownlees and Engle (2011) propose CoVaR, ?CoVaR and MES-BE separately based on institution specific risk. Amihud (2002), Gilchrist and Zakrajsek(2012) construct AIM and GZ measure from the liquidity and credit perspective.
Kritzman and Li (2010), Allen, Bali and Tang (2012) use “turbulence” and CatFin as a value-at-risk measure to describe the extent of systemic risk. Later, Giglio, Kelly, and Pruitt (2016) evaluate the ability of different systemic risk measures to predict shift in macroeconomic downside risk. They find few of the large collection of systemic risk is capable to capture the future macroeconomic shock using predictive quantile regression both nationally and internationally.
The quantile causal effect, which is estimated by means of quantile regressions (Koenker and Baseett 1978) has been used widely in finance area. (Bernanke and Gertler, 1989; Kiyotaki and Moore, 1997; Bernanke, Gertler and Gilchrist, 1999; Brunnermeier and Sannikov, 2010; Gertler and Kiyotaki, 2010; Mendoza, 2010; and He and Krishnamurthy, 2012). Chuang, Kuan, and Lin (2009) investigate the causal relations between stock return and volume based on quantile regressions. They use the Granger non-causality test to check the causal effects in all quantiles.
This paper tries to investigate the causal relations of systemic risk and macroeconomic shock in US from the perspective of conditional quantiles. Instead of predicting the distribution of future macroeconomic shock caused by systemic risk, I examine the past relation between a large collection of systemic risk measures and macroeconomic shock based on the Granger causality test in different given quantiles. There are two goals in this paper.
The first goal is to revisit the relations between different systemic risk measures and macroeconomic shock. The second goal is to explore the extent to effects on macroeconomic shock of each systemic risk. Specifically, I would like to see whether the relation, which between systemic risk and macroeconomic shock, is different in different quantiles and belongs to the skewed right tail distribution.
Granger Causality in Quantiles
The notion of Granger causality captures predictability given a particular information set (Granger, 1969). If the addition of variable X to the given information set ? alters the conditional distribution of another variable Y, and both X and ? are observed prior to Y, then X improves the predictability of Y, and is said to Granger cause Y with respect to ?. Granger originally envisioned the information set ? “be all the information in the universe”, which is not a workable concept.
Thus, I focus on testing Granger causality in different quantiles.
Following Granger (1969), the Granger causality measures whether the random variable x_t happened before dependent variable y_t and helps predict it and nothing else. For a random variable y_t and a set of explanatory variables x_(t-1). The basic structure of Granger causality equation is:
If the equation exists, conditional on x_(t-1), addition of y_(k,t-1) to the information set does not improve predictability of y_t. Otherwise, x_(t-1) Granger causes y_t.
A conventional test may find no causality in mean because the positive and negative quantile causal effects cancel out each other in least-square estimations. Quantile regression, on the other hand, allows us to study the impact of predictors on different quantiles of the response distribution, and thus provides a more complete picture of the relation between y and x.
Given that the distribution is determined by its quantiles, Granger causality test in distribution can be expressed in terms of given quantiles:
More specifically, Y_t is the macroeconomic shock, X_t is the systemic risk, ? is the quantiles of distribution. The hypothesis is ?_?= 0, which means relation at different quantile ranges is the same between systemic risk and macroeconomic shock. F statistics is used to measure the significance.
- Systemic Risk Measures
This section describes the systemic risk measures and provide a brief summary of correlation among measures. There are several dimensions of systemic risk: institution specific risk, comovement and contagion, volatility and instability, liquidity and credit. Aggregated from previous study, each dimension has several different measures.
In total, I use CoVaR, ?CoVaR from Adrian and Brunnermeier (2011), marginal expected shortfall (MES) from Acharya, Pedersen, Philippon and Richardson (2010), and MES-BE, a version of marginal expected shortfall proposed by Brownlees and Engle (2011), Absorption Ratio described by Kritzman et al. (2010), Dynamic Causality Index (DCI) from Billio et al. (2012), International Spillover Index from Diebold and Yilmaz (2009), “turbulence” from Kritzman and Li (2010), CatFin from Allen, Bali and Tang (2012), “volatility” from Giglio, Kelly, and Pruitt (2016), Amihud’s(2002) illiquidity measure, the TED spread (LIBOR minus the T-bill rate), the Gilchrist-Zakrajsek measure of the credit spread (2012).
Since this is a paper based on the replication of the main outcome, 19 systemic risk measures are all obtained from the Stefano Giglio’s website. The time p is from 1926 to 2011.
- Macroeconomic Shock
Though the proxy for macroeconomic shock is still in debate, I define the macroeconomic shock as the innovations to an autoregression in the underlying macroeconomic series according to the literature from Bai and Ng (2008), and Stock and Watson (2012).
Let the monthly Industrial Production Index obtained from the Federal Reserve Board be denoted Y_t. I construct shocks to these series as residuals in an autoregression of the form:
for a range of autoregressive orders, p, and select the p that minimizes the Akaike Information Criterion. This approach purges each macroeconomic variable of predictable variation based on its own lags. For each month t, I estimate the AR and AIC on data only known through t and construct the forecast residual at time t+1 based on these estimates. Shocks are constructed as the residuals between real historical shocks dependent variables and estimated variables.
- Empirical Evaluation
Table 1 reports the correlation among all 19 systemic risk measures in US. Table 2 reports the F-statistics of the Granger causality test for each systemic risk measures at 50th and 20th quantiles respectively. It is obvious more measures show relation when in lower quantiles suggesting the distribution of the macroeconomic shock caused by systemic risk is right tail. Moreover, the measures of financial sector volatility are notably robust in different quantiles.
In this paper, I use the Granger causality test in each quantile to revisit the relation between systemic risk measures and macroeconomic shock. The outcome shows that few of the systemic risk measures capture the macroeconomic shock at the 50th quantile while some of them show potential relation at lower quantile.
In other words, the extent of the relation between systemic risk and macroeconomic shock is different. The systemic risk more informative on macroeconomic shocks’ lower tail
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