Is market liquidity less resilient after the financial crisis? Evidence for US Treasuries

Abstract

Understanding market liquidity resilience, i.e. the capacity of liquidity to absorb shocks, of United States Treasuries is crucial from a financial stability standpoint. The conventional resilience measure has limitations due to the use of the liquidity level. We propose a new complementary approach to analyze resilience based on liquidity volatility. For this purpose, we focus on the link between returns volatility and liquidity volatility, which is a relatively unexplored field. We fit a bivariate conditional correlation (CC-) GARCH model for the 10-year bond returns and five liquidity indicators from January 2003 to June 2016 to analyze persistence and spillovers between these variables in a parsimonious way. We find that after the crisis, spillovers between liquidity volatility and returns volatility are higher, feedback loops are more likely and volatility persistence is lower, which is consistent with a lower resilience. Our results help to explain recent episodes of high volatility in this market.

Highlights

• •The usual liquidity resilience measure based on liquidity levels has limitations.
• •We propose a new approach to analyze resilience based on liquidity volatility.
• •To this end, we study the link between returns volatility and liquidity volatility.
• •We fit a CC-GARCH model for US 10-year bonds returns and five liquidity indicators.
• •Our findings are consistent with a lower liquidity resilience after the crisis.

1. Introduction

Market liquidity is the ease with which market participants can buy or sell securities without affecting their prices (Elliot, 2015)1 and plays a central role from a financial stability standpoint. First, impaired market liquidity makes securities trading more difficult by increasing funding costs. Also, a lack of liquidity is a well-known shock amplifier.2 In recent years, market liquidity has received growing attention given its apparent decline in some markets, such as the United States (US) Treasury debt market (Fender and Lewrick, 2015). Some authors link this likely liquidity deterioration to recent significant structural changes in several markets, including Treasuries (IMF, 2015).3 Indeed, some recent episodes of heightened volatility in the US Treasury markets such as the so-called “taper tantrum” in the second quarter of 2013, the October 2014 “flash crash”, or even the volatility spike linked to the coronavirus crisis in March 2020 have been associated with liquidity strains in this bond market. Those events demonstrated that liquidity strains also affect the most liquid markets, even under benign market conditions, and increased the fear of further volatility spikes (IMF, 2015; Nguyen et al., 2020).

A better understanding of the US Treasury debt market liquidity is crucial, since a severe deterioration of this market could pose a threat to financial stability. As it is the most liquid fixed income asset, liquidity strains would likely feed through to other markets.4 Besides, illiquidity bouts affect critical functions of US Treasury debt, traditionally perceived as a safe haven for investors, a source of high-quality collateral and a key instrument of monetary policy (Anderson et al., 2015; Thornton, 2018) and distort the functioning of the financial markets.

Our objective is to analyze if liquidity resilience, rather than the liquidity level, of the US Treasury debt has deteriorated after the great financial crisis (GFC) of 2007–2009. From a financial stability perspective, the main concern about liquidity is not the level itself but its resilience. The concept of liquidity resilience is linked to the ability of market liquidity to withstand shocks. In a non-resilient market, a state of high liquidity can suddenly transform into one of low liquidity in response to a shock (IMF, 2015). Therefore, the evolution of liquidity level can be different from that of liquidity resilience. Even apparently sound markets with ample liquidity such as US Treasuries can be prone to evaporation. Thus, although low liquidity is a leading indicator of low liquidity resilience during periods of financial stress, in normal times, higher liquidity levels can support the illusion of resilient liquidity and induce excessive risk taking (Clementi, 2001).

The conventional liquidity resilience measure is the speed of recovery of the liquidity level after one shock (Degryse et al., 2005; IMF, 2015). Although this approximation is intuitive and easy to fit by VAR-type models, it has limitations due to the fact that it relies on the liquidity level. To begin with, the market liquidity level is not easy to quantify. In fact, liquidity is an unobservable variable that embodies several heterogeneous characteristics (Sarr and Lybek, 2002). Accordingly, a large number of indicators have been proposed to monitor this multidimensionality. This plethora of indices sometimes provide different signals and do not allow for an unequivocal assessment of how liquidity conditions evolve (Broto and Lamas, 2016). The lack of empirical evidence on the existence of the recent liquidity strains based on the main liquidity level indicators of US Treasuries (Adrian et al., 2017a) illustrates this weakness. Besides, the standard resilience measure depends on the equilibrium liquidity level to be recovered after one shock. In the case of the Treasury bond market, recent structural changes have surely modified this fundamental level to be reached by liquidity (Joint Staff Report, 2015). In other words, the level that ensures that the market is resilient affects the standard measure based on the mean-reverting speed of the liquidity level.

Given these limitations of the liquidity level in the standard analysis of resilience, we propose a new complementary approach where liquidity volatility, rather than liquidity level, becomes the key variable to characterize resilience. To this end, we fit a bivariate model of the family of constant conditional correlation (CC-) GARCH models by Bollerslev (1990) as proposed by Nakatani (2010). We use this model to relate the volatility of five liquidity measures to returns volatility of the 10-year on-the-run US Treasury note. This model approach allows to analyze the ability of liquidity to absorb shocks through the study of the impact of market volatility on liquidity volatility (and vice versa).

The economic intuition behind our methodology is as follows. Volatile dynamics in liquidity lead to lower resilience. If liquidity is resilient, its volatility will scarcely react to shocks. This lack of reaction after shocks will lead to non-significant spillover coefficients, which is related to the fact that liquidity maintains certain capacity to absorb shocks. On the contrary, in a non-resilient scenario, liquidity volatility will deteriorate and spike hand in hand with the shock, which would create illiquidity bouts. Therefore, the empirical results will exhibit significant spillover coefficients. As the model simultaneously fits liquidity volatility, returns volatility and their spillovers, shocks can be either return shocks or liquidity shocks. Thus, in practice, when both spillover coefficients are significant the model allows to empirically characterize if there is a feedback-loop between both variables. Apart from the analysis of spillovers, the use of second order moments also permits us to reach conclusions on the volatility persistence of shocks. Thus, a low volatility persistence estimated by the model will be consistent with the occurrence of liquidity and financial spikes that tend to go back to normal soon.

Our new approach complements the conventional measure of liquidity resilience. Since our focus is on liquidity volatility rather than on its level, the limitations of this latter indicator do not affect our model. In our setting, spikes in liquidity volatility, resulting from past shocks in liquidity or in returns, simply expose investors to potential adverse liquidity environments, raising liquidity risks accordingly. It is worth clarifying that our bivariate GARCH models should not be interpreted as a new liquidity resilience measure, but as a tool to better understand resilience. For this purpose, our approach contributes to the literature on the link between returns' volatility and liquidity volatility, instead of that of liquidity level, which is a relatively unexplored field.

Our results are consistent with a lower liquidity resilience of the 10-year note than before the GFC. Returns of the 10-year note and liquidity volatility measures are more volatile than before the crisis. Spillover estimates, which quantify if financial volatility is fed by liquidity volatility, and vice versa, have also increased in recent years. Thus, liquidity volatility reacts in a more acute way to shocks and this heightened liquidity volatility also impacts on financial volatility. We also show stronger feedback loop effects between liquidity volatility and returns volatility after GFC. On a more positive note, volatility recoveries are faster than before the crisis given its lower persistence. This means that, after the GFC, more shifting market conditions in the US Treasury market can be explained by a less resilient market liquidity with a lower capacity to absorb shocks, although other factors might be contributing to this trend. Our results help to explain the occurrence of recent episodes of heightened volatility in the markets, which have been disruptive but short-lived in nature, and accompanied by liquidity strains (IMF, 2015).

The rest of the paper is organized as follows. After the Introduction, Section 2 briefly reviews the literature on the link between liquidity and financial volatility. Section 3 describes the five US Treasuries liquidity indicators that we model in the resilience analysis. In Section 4 we present our empirical model to analyze the relationship between both variables. Section 5 summarizes the main results. Finally, section 6 concludes.

2. Market liquidity and financial volatility: a literature overview

The close ties between the level of market liquidity and financial volatility are well documented in the literature. There are two main theoretical explanations. On the one hand, according to the mixture of distribution hypothesis, price volatility and liquidity, proxied by trading volumes, should be positively correlated because of their dependence on the rate of information flow. This explanation justifies the positive correlation between price volatility and volumes found empirically by Clark (1973) and Tauchen and Pitts (1983).5 On the other hand, the sequential information arrival hypothesis of Copeland (1976) states that there is a positive correlation between trading volume and price volatility in a sequential manner, as once new information arrives at the markets, intermediate equilibriums occur prior to the final equilibrium, which leads to significant lead-lag relationships between the information flow and the returns.

Regarding the empirical literature, most studies that link returns volatility and liquidity levels fit GARCH-type models. The pioneering work by Lamoureux and Lastrapes (1990) analyze the volatility of 20 traded stocks through a univariate GARCH model where the daily trading volume is an exogenous regressor in the variance equation.6 Since then, univariate and multivariate GARCH models alike have been broadly used to study the link between market liquidity and volatility in different asset classes, while model specifications have been enriched over time—see Frank et al. (2008), Chuang et al. (2012), Ribeiro et al. (2017), Chundakkadan and Sasidharan (2019) or Nguyen et al. (2020), among others—.7 As in these empirical works on the link between returns and liquidity level, we also fit a GARCH-type model.

Although the literature on the link between the liquidity level and financial volatility is extensive, previous studies on the relationship between liquidity volatility and returns volatility are scarcer. However, these few works illustrate that liquidity volatility also matters for financial volatility. For instance, Akbas et al. (2011) conclude that there is a positive correlation between the volatility of liquidity and expected stock returns. If liquidity is very volatile and fluctuates within a wide range, investors may be exposed to a relatively higher probability of low liquidity at the time of selling the asset. Therefore, risk-averse investors will require a premium for holding stocks with high liquidity volatility. In this vein, Fall et al. (2019) argue that investors ask larger premiums for holding illiquid portfolios. On the contrary, Chordia et al. (2001) document a negative relationship between both variables using volumes as liquidity indicators. Additionally, Nguyen et al. (2020) propose a joint model of liquidity and volatility for US Treasuries. They develop a “liquidity-at-risk” measure and conclude that extreme illiquidity events are more correlated with extremely high volatility episodes than the usual liquidity level–volatility correlation. Likewise, Gong et al. (2018) document tail dependence of returns and bid-ask spreads in a stock index futures market. Finally, Jiang et al. (2011) explore unexpected returns in the US Treasury market and link these “jumps” to shocks in market liquidity, or variations in liquidity indicators. These papers use volumes or alternative liquidity measures in their specifications. We contribute to this little explored branch of the literature as we exploit liquidity volatility to analyze liquidity resilience.

3. Market liquidity measures

3.1. Selected market liquidity indicators

Next, we analyze the market liquidity level of US 10-year Treasuries. This analysis poses at least two difficulties. First, market liquidity is not an observable variable. Second, the concept of market liquidity entails several dimensions, so that various proxies are needed to capture all the relevant features. According to Sarr and Lybek (2002), a liquid market should have five characteristics, namely tightness, immediacy, efficiency, depth and breadth. Tightness refers to transaction costs, which are low in liquid markets, whereas immediacy characterizes those markets where trades are executed quickly and in an orderly manner. In an efficient market, prices rapidly adjust to new equilibrium levels once unbalances or new information arrive.8 Finally, depth is linked to the number of orders, while breadth allows orders to flow with a minimal impact on prices, even if they are large.

Given the heterogeneous characteristics behind the definition of market liquidity, a large number of indicators have been proposed to monitor these aspects (see Sarr and Lybek, 2002). We focus on five indicators, one per each feature of market liquidity, to cover the five dimensions. Three of them are based on prices, while the remaining two measures consist of quantities or a combination of prices and quantities. Table 1 provides further details about their construction and interpretation.

Table 1.

Market liquidity measures.

Market liquidity measures	Definition	Aspect of liquidity	Interpretation	Source	Frequency
Roll (1984)	$\begin{array}{c}\text{Estimation of the effective bid}-\text{ask spread }\\ \text{based on the covariance of returns over two consecutive days.}\\ \text{Covariances are computed over sample periods of three months}\end{array}$	Tightness	$\begin{array}{c}\text{Wider spreads imply that transaction costs}\\ \text{are higher and market liquidity is lower}\end{array}$	Bloomberg	Daily
Daily range	Absolute difference between high and low prices each day	Immediacy	$\begin{array}{c}\text{Spikes reflect that the market is less able to}\\ \text{absorb new orders }(\text{less liquidity})\end{array}$	Bloomberg	Daily
Market efficiency coefficient (MEC)	$\begin{array}{c}\text{Variance of weekly returns to variance of daily returns.}\\ \text{Variances are computed over sample periods of three months}\end{array}$	Efficiency	$\begin{array}{c}\text{Proxy for market efficiency. If close to }1\text{,}\\ \text{then prices of a security or asset are able }\\ \text{to move fast to their new equilibrium}\end{array}$	Bank of America Merril Lynch	Daily
Volume	Average daily transactions, in USD	Depth	Lower volume reflects poor liquidity conditions	$\begin{array}{c}\text{Federal Reserve Bank of New York}\end{array}$	Weekly
Amihud (2002)	Absolute return to trading volume	Breadth	Price concession needed to execute trades	$\begin{array}{c}\text{Bloomberg }(\text{FINRA})\\ \text{Bank of America Merril Lynch}\\ \text{Federal Reserve Bank of New York}\end{array}$	Weekly

We analyze tightness, immediacy and market efficiency with metrics based on prices. First, we proxy tightness with the estimation of the effective bid-ask spread proposed in the seminal work by Roll (1984), which follows this expression,

$$L_R=2\sqrt{-\mathrm{C}\mathrm{o}\mathrm{v}(r_t,r_{t-1})},$$ (1)

where r _t is the percentage return on the US 10-year Treasuries, which is given by,

$$r_t=100\times (\mathrm{\Delta }\ln p_t),$$ (2)

where p _t is the bond price in t and Δ is the difference operator. The intuition behind L _R is based on the fact that in an efficient market the underlying value of an asset fluctuates randomly, whereas trading costs introduce negative serial dependence in market price changes. This indicator is more representative of real transaction costs in a market than other widely used indicators like the quoted bid-ask spread. The reason for this is that the measure by Roll (1984) is an estimation of the effective spread, defined as the execution price and the midpoint of bid and ask quotes. Nevertheless, the covariance of price changes is frequently positive, so that L _R might become a noisy estimator even in relative large samples (Harris, 1990). Subsequently, several authors have proposed alternative measures that outperform L _R estimation of transaction costs, such as the high and low prices spread estimator of Corwin and Schultz (2012) or the indicator by Abdi and Ranaldo (2017) calculated from daily close, high and low prices.9 After several proofs with Corwin and Schultz (2012) and Abdi and Ranaldo (2017) measures for the trading costs, we discard them due to convergence problems. Besides, the measure by Abdi and Ranaldo (2017) provides more accurate estimates of trading costs than Roll (1984) for the less liquid securities. For highly liquid assets, such as US Treasuries, the new measure barely improves the Roll (1984) estimator.

Second, we use the daily range, denoted as L _DR, as a measure of immediacy. We calculate this as the difference between the highest and lowest price in a day. This a dispersion measure that contains information on market liquidity. Thus, the daily range widens when bonds are thinly traded in the markets and orders execution is poor, that is, when liquidity is lower. The use of the daily range or similar measures as liquidity proxies is not new in the literature (see, for instance Pu (2009) or Schestag et al. (2016)).10 Third, we analyze market efficiency with the Market Efficiency Coefficient (MEC), L _MEC. The MEC is a ratio between the variances of two returns with different time spans, that is,

$$L_{MEC}=\mathrm{V}\mathrm{a}\mathrm{r}(R_t)/(\mathrm{V}\mathrm{a}\mathrm{r}(r_t)\times 5),$$ (3)

where R _t are weekly returns, whereas r _t are daily returns. This indicator is close to one in efficient, liquid markets, whereas substantial departures from unity reveal lower liquidity. The intuition behind L _MEC is that price movements are more continuous in liquid markets. That is to say, if new information affects equilibrium prices, the transitory changes to that price are minimal in efficient markets. See Sarr and Lybek (2002) or Gabrielsen et al. (2011) for further details on the interpretation of the MEC coefficient.

With regard to measures that require quantities, we use the trading volume, V _t, to analyze market depth. The volume is the amount of securities traded per period (in US dollars). Finally, we study breadth through the indicator proposed by Amihud (2002), given by,

$$L_A=\frac{\left(r_t\right)}{V_t},$$ (4)

which is the ratio of the absolute return in the market to the trading volume, V _t. Sudden spikes in L _A suggest that the market is not able to suitably absorb a given amount of trading orders, so that market breadth will be impaired. By construction, this measure is more volatile than the trading volume, V _t.11

3.2. The data

Fig. 1 represents the five liquidity measures, together with the daily returns of the 10-year on-the-run Treasury note. Due to data constraints, L _R, L _DR and L _MEC are daily, whereas volumes and the Amihud (2002) ratio are weekly. Price data are provided by Bloomberg Generic dataset, which is Bloomberg's market consensus price for government bonds. We obtain volumes from the Primary Dealers' release of the Federal Reserve Bank of New York (FRBNY). The release compiles volume data for US Treasuries with a remaining term to final maturity from seven to eleven years, so that the trading volumes include not only the 10-year note but also other securities.12 However, our measure is representative, as the bulk of trading activity is carried out in the 10-year on-the-run note.13 With regard to the Amihud (2002) ratio, L _A, we use trading volumes in the denominator, whereas we obtain absolute returns from an index by Bank of America that summarizes prices of all outstanding Treasury issues within a similar maturity sector for the numerator.14 Table 1 summarizes data sources.

Fig. 1.

Daily returns of the US 10-year Treasury note and five market liquidity measures.

The sample period runs from January 2003 to end-June 2016, so that the sample size is 3465 trading days and 692 weeks for daily and weekly indicators, respectively. We also focus on the pre-crisis period, from January 2003 to May 2007, and the post-crisis period, from April 2009 to June 2016, to gain an insight into liquidity dynamics in periods of calm. We date the beginning of the crisis in June 2007 coinciding with the first evidence on problematic subprime mortgages and mortgage-related securities, more specifically, when two Bear Stearns hedge funds with large holdings of subprime mortgages run large losses.15 We consider the end of the crisis in April 2009, after the QE program was launched and expanded in March 2009, which also coincided with an agreement of the G20 on a global stimulus package, which helped to stabilize the markets.

According to Fig. 1, all indices but the MEC exhibit a severe deterioration of market liquidity during the GFC, around 2008:Q3 and 2009:Q1. Since then, market liquidity has recovered, but liquidity indicators fluctuate in a different way than in the pre-crisis period. By construction, price-based measures, i.e., L _R, L _DR and L _MEC, are more erratic and exhibit more volatility spikes than volume-based indicators. These bouts of illiquidity are more frequent after the financial crisis. Volumes rapidly recovered after the GFC, but since mid-2013 they have steadily declined. All in all, in the post-crisis period, the five liquidity indices have fluctuated in a non-homogeneous way, so that it is difficult to clearly characterize a market liquidity recovery through Fig. 1.16 This problem is a result of the inherently diverse nature of market liquidity indicators.17

To gain greater insight into liquidity dynamics after the crisis, Table 2 reports the mean and standard deviation of the five indicators in the pre-crisis and post-crisis periods. The average transaction costs and daily range are slightly higher in the post-crisis period, which suggests that market liquidity conditions could have worsened. In this same vein, average daily trading volume dropped below pre-crisis levels, and the Amihud ratio, L _A, stabilized at higher levels. The MEC ratio, however, shows more benign liquidity conditions in the most recent period, as it stands closer to the unity. All averages during the pre-crisis period and the post-crisis period are significantly different, as shown by the t-test for equal means. Standard deviations of the five indicators are significantly higher post-crisis than pre-crisis. Finally, Table 3 shows the pairwise correlations of the five liquidity indicators. Since correlations are generally low, our measures illustrate the multidimensional nature of the concept of market liquidity.

Table 2.

Descriptive statistics of market liquidity indicators.

		LR	LDR	LMEC	V	LA
Mean	Total	0.281	0.553	0.828	11.591	2.967
	Pre-crisis	0.244	0.487	0.812	11.621	2.287
	Crisis	0.399	0.795	0.729	11.609	4.537
	Post-crisis	0.274	0.532	0.863	11.567	2.990
	t-test	−2.889∗∗∗ (0.004)	3.932∗∗∗ (0.000)	−2.441∗∗ (0.015)	2.336∗∗ (0.020)	−3.692∗∗∗ (0.000)
SD	Total	0.305	0.343	0.533	0.281	3.085
	Pre-crisis	0.246	0.287	0.482	0.230	1.858
	Crisis	0.432	0.477	0.404	0.312	5.889
	Post-crisis	0.290	0.306	0.585	0.300	2.475
	F-test	0.714∗∗∗ (0.000)	0.881∗∗ (0.018)	0.678∗∗∗ (0.000)	0.587∗∗∗ (0.000)	0.563∗∗∗ (0.000)
Observations	Total	3465	3465	3465	692	692
	Pre-crisis	1132	1132	1132	227	227
	Crisis	471	471	471	93	93
	Post-crisis	1862	1862	1862	372	372

Notes: L_R is the transaction costs indicator by Roll (1984), L_DR is the daily range, L_MEC denotes the market efficiency coefficient, V is trading volume expresed in logarithms and L_A stands for the Amihud (2002) ratio. The pre-crisis period runs from January 2003 to May 2007, whereas the post-crisis period covers the time from April 2009 to June 2016.t-test and F-test denote a test for the equality of means and variances, respectively, in the pre-crisis and in the post-crisis period. p -values in parentheses. ∗∗∗, ∗∗, and ∗ refer to significance at 1%, 5% and 10% level.

Table 3.

Correlation matrix of five market liquidity indicators.

	Total sample						Pre-crisis period
	LR	LDR	LMEC	V	LA		LR	LDR	LMEC	V	LA
LR	1					LR	1
LDR	0.211∗	1				LDR	0.174∗	1
LMEC	−0.306∗	−0.060	1			LMEC	−0.148∗	−0.087	1
V	0.012	0.103∗	0.012	1		V	0.052	0.149∗	−0.014	1
LA	0.134∗	0.627∗	−0.030	−0.260∗	1	LA	0.073	0.477∗	0.042	−0.223∗	1
	Crisis period						Post-crisis period
	LR	LDR	LMEC	V	LA		LR	LDR	LMEC	V	LA
LR	1					LR	1
LDR	0.234∗	1				LDR	0.112∗	1
LMEC	−0.540∗	−0.020	1			LMEC	−0.344∗	−0.009	1
V	−0.040	−0.136	−0.299∗	1		V	0.016	0.239∗	0.108	1
LA	0.189	0.763∗	0.019	−0.411∗	1	LA	0.038	0.463∗	−0.067	−0.224∗	1

Notes: L_R is the transaction costs indicator by Roll (1984), L_DR is the daily range, L_MEC denotes the market efficiency coefficient, V is trading volume expresed in logarithms and L_A stands for the Amihud (2002) ratio. The pre-crisis period runs from January 2003 to May 2007, whereas the post-crisis period covers the time from April 2009 to June 2016. ∗ refer to significant pair-wise correlations at 5% level.

4. Market liquidity resilience: empirical model

To study liquidity resilience in the US Treasury market we propose a bivariate model to analyze simultaneously both liquidity volatility and returns volatility. Liquidity volatility serves as a proxy for the uncertainty of the liquidity level. We also incorporate US Treasuries returns volatility in the model to analyze its interlinkages with liquidity volatility. If liquidity is resilient to stressed conditions, it will scarcely respond to shocks and more volatile markets will barely impact liquidity volatility. On the contrary, in a non-resilient liquidity scenario, higher market volatility will affect liquidity volatility, which could also react in a feedback loop.

Therefore, we model two dependent variables,

$${\mathbf{Y}}_t=\left(\begin{array}{c}{r}_t\\ \mathrm{\Delta }{L}_t\end{array}\right),$$ (5)

where r _t are daily returns and ΔL _t is the first difference of each of the five liquidity indicators, calculated on a daily basis for L _R, L _DR and L _MEC, and on a weekly basis for V and L _A.18 Treasuries' returns of the models for V and L _A are also weekly, $r_t^w$.19 Table 4 summarizes the main statistics for these variables. All series are asymmetric and/or have excess kurtosis. Box-Pierce Q-statistics for higher order serial correlation suggest the presence of conditional heteroskedasticity in both returns and first differences of liquidity indicators, which evidences the suitability of a GARCH-type model.

Table 4.

Descriptive statistics of US 10-year bonds' returns and market liquidity indicators.

	Total sample							Pre-crisis period
	rt	$r_t^w$	ΔLR	ΔLDR	ΔLMEC	ΔV	ΔLA	rt	$r_t^w$	ΔLR	ΔLDR	ΔLMEC	ΔV	ΔLA
Mean	0.005	0.105	0.000	0.000	0.000	0.002	−0.009	−0.011	0.059	0.000	0.000	0.000	0.005	−0.031
SD	0.505	0.889	0.107	0.388	0.355	0.216	3.922	0.424	0.743	0.083	0.343	0.324	0.211	2.428
Maximum	4.085	3.743	1.760	3.844	9.064	0.894	40.873	1.519	2.469	0.778	1.578	5.412	0.894	7.013
Minimum	−2.176	−3.321	−0.928	−3.469	−3.067	−0.708	−37.141	−2.143	−2.410	−0.475	−1.531	−2.381	−0.548	−6.081
Skewness	0.081∗∗	0.018	1.162∗∗∗	0.291∗∗∗	10.521∗∗∗	0.093	0.424	−0.379∗∗∗	−0.073	0.981∗∗∗	0.166∗∗	8.390∗∗∗	0.100	0.157
Kurtosis	5.718∗∗∗	4.035∗∗∗	39.952∗∗∗	10.882∗∗∗	241.581∗∗∗	3.378∗∗∗	31.378∗∗∗	4.896∗∗∗	3.684	18.629∗∗∗	5.470	147.136∗∗∗	3.834∗∗∗	3.249∗∗∗
Observations	3465	692	3464	3464	3464	691	691	1132	227	1131	1131	1131	226	226
Q(10)	52.743∗∗∗	18.475∗∗∗	41.314∗∗∗	721.100∗∗∗	338.250∗∗∗	97.757∗∗∗	155.260∗∗∗	11.082	19.481∗∗∗	20.301∗∗∗	281.160∗∗∗	123.960∗∗∗	21.892∗∗∗	67.671∗∗∗
Q2(10)	394.790∗∗∗	201.650∗∗∗	9.100	756.220∗∗∗	75.621∗∗∗	27.895∗∗∗	172.780∗∗∗	73.986∗∗∗	30.528∗∗∗	9.466	182.970∗∗∗	31.826∗∗∗	7.098	19.679∗∗∗
	Crisis-period							Post-crisis period
	rt	$r_t^w$	ΔLR	ΔLDR	ΔLMEC	ΔV	ΔLA	rt	$r_t^w$	ΔLR	ΔLDR	ΔLMEC	ΔV	ΔLA
Mean	0.038	0.273	0.002	0.000	−0.001	−0.002	0.103	0.006	0.091	−0.001	0.000	0.000	0.001	−0.023
SD	0.714	1.267	0.154	0.568	0.200	0.232	7.345	0.487	0.855	0.105	0.357	0.400	0.215	3.414
Maximum	4.085	3.743	1.760	3.844	2.168	0.730	40.873	2.032	3.014	1.180	2.289	9.064	0.573	13.671
Minimum	−2.177	−2.586	−0.928	−3.469	−0.853	−0.708	−37.141	−2.104	−3.321	−0.869	−1.422	−3.067	−0.577	−9.076
Skewness	0.567∗∗∗	0.072	2.451∗∗∗	0.426∗∗∗	3.506∗∗∗	0.143	0.400	−0.204∗∗∗	−0.190	0.019	0.173∗∗∗	10.804∗∗∗	0.078	0.085
Kurtosis	5.593∗∗∗	2.899∗∗∗	44.313∗∗∗	12.256∗∗∗	44.537∗∗∗	4.164∗∗∗	18.461∗∗∗	3.970∗∗∗	3.902∗∗∗	23.451∗∗∗	5.634∗∗∗	237.926∗∗∗	2.842∗∗∗	3.858∗∗∗
Observations	471	93	471	471	471	93	93	1862	372	1862	1862	1862	372	372
Q(10)	34.049∗∗∗	9.975∗∗∗	12.485∗∗∗	105.160∗∗∗	36.364∗∗∗	15.715∗∗∗	27.355∗∗∗	20.436∗∗∗	15.186∗∗∗	27.830∗∗∗	352.400∗∗∗	180.670∗∗∗	83.498∗∗∗	113.560∗∗∗
Q2(10)	15.454	31.653∗∗∗	0.709	113.540∗∗∗	14.456	19.670∗∗∗	22.390∗∗∗	279.560∗∗∗	29.313∗∗∗	23.702∗∗∗	229.760∗∗∗	39.639∗∗∗	23.688∗∗∗	34.890∗∗∗

Notes: r_t and $r_t^w$ are the daily and weekly 10-year bond returns, respectively. L_R is the transaction costs indicator by Roll (1984), L_DR is the daily range, L_MEC denotes the market efficiency coefficient, V is trading volume expresed in logarithms and L_A stands for the Amihud (2002) ratio. All liquidity indicators are expressed in first differences, Δ. Q(10) is the Ljung-Box Q-statistic (with 10 lags) and Q²(10) is the Ljung-Box Q-statistic (with 10 lags) for the squared returns. ∗∗∗, ∗∗, and ∗ refer to significance at 1%, 5% and 10% level.

Specifically, our baseline model is a bivariate ECCC-GARCH (Extended Constant Conditional Correlation GARCH) model as proposed by Nakatani (2010) and Jeantheau (1998), which belongs to the family of conditional correlation (CC-) GARCH models by Bollerslev (1990). The main advantage of the specification by Nakatani (2010) for our resilience analysis is that it allows to analyze volatility transmission among the variables of the model. That is to say, whereas in a standard CCC-GARCH specification the conditional volatility would be modeled as a combination of its squared innovations and volatility, Nakatani (2010) considers that conditional volatility also depends on those squared innovations and volatilities of other equations, while keeping the conditional correlation structure constant. Therefore, our proposed bivariate model enables to study the simultaneous impact of higher liquidity volatility on financial volatility and that of financial volatility on liquidity volatility. This approach is more realistic than previous models where the level of market liquidity affects financial volatility exogenously (see, for instance, Lamoureux and Lastrapes, 1990).

We choose the CCC-GARCH, which forces conditional correlation to be constant over time, instead of DCC-GARCH (Dynamic Conditional Correlation GARCH) as in our case there is no gain in the use of a DCC model. The DCC-GARCH model is estimated in two steps. In the first step parameters in the variance equations are estimated, while in the second step dynamic correlations are fitted. As our main focus is on volatility spillovers, which are estimated from the variance equations in the first stage, we rule out a DCC-GARCH specification. Besides, as shown in Table 5 , tests based on Engle and Sheppard (2001) suggest that our bivariate dataset has constant conditional correlations rather than time-varying ones since the null hypothesis of constant conditional correlation cannot be rejected for almost all liquidity indicators and sample periods.

Table 5.

Tests of constant conditional correlation (Engle and Sheppard, 2001).

	Full sample		Pre-crisis period		Post-crisis period
ΔLR	5.734∗	(0.057)	0.030	(0.985)	8.847∗	(0.012)
ΔLDR	1.657	(0.437)	0.455	(0.797)	0.276	(0.871)
ΔLMEC	0.010	(0.995)	0.064	(0.968)	0.824	(0.662)
ΔV	0.065	(0.968)	0.005	(0.997)	5.226∗	(0.073)
ΔLA	0.519	(0.772)	1.895	(0.388)	0.700	(0.712)

Notes: Engle and Sheppard (2001) test for the null hypothesis of constant correlation in a DCC-GARCH model for 10-year US Treasury returns (log difference of prices) and the first difference, denoted by Δ, of each of the five liquidity indicators (namely, L_R is the transaction costs indicator by Roll (1984), L_DR is the daily range, L_MEC denotes the Market efficiency coefficient, V is trading volume expresed in logarithms and L_A stands for the ratio proposed by Amihud (2002)). p-values in parentheses. ∗ refers to significance at 10% level.

As usual in the empirical finance literature, we first prewhiten the dependent variables with AR and VAR filters,20

$${\mathbf{Y}}_t={\mathbf{A}}_0+{\mathbf{A}}_1{\mathbf{Y}}_{t-1}+\cdots +{\mathbf{A}}_i{\mathbf{Y}}_{t-i}+{\mathbf{\varepsilon }}_t,$$ (6)

where ${\mathbf{\varepsilon }}_t={\left[{\varepsilon }_{1t},{\varepsilon }_{2t}\right]}^{\prime }$ and ɛ _t ∼ N(0, Ω). Conditional variance equations follow this expression,

$$\begin{array}{ccc}{\mathbf{\varepsilon }}_t& \mid & I_{t-1}\sim N(0,{\mathbf{D}}_{t}R{\mathbf{D}}_t)\\ {\mathbf{D}}_t& =& diag\{\sqrt{h_{it}}\}\\ {\mathbf{h}}_t& =& \mathbf{C}+{\mathbf{A}\mathbf{\varepsilon }}_{t-1}^{(2)}+{\mathbf{B}\mathbf{h}}_{t-1}\end{array}$$ (7)

where R is the constant conditional correlation matrix, D _t is a diagonal matrix with the conditional variance of returns, h _1t, and liquidity, h _2t, C is a (2 × 1) vector, A and B are (2 × 2) matrices, and ${\mathbf{\varepsilon }}_t^{(2)}={\left[{\varepsilon }_{1t}^2,{\varepsilon }_{2t}^2\right]}^{\prime }$. If both A and B are diagonal, this ECCC-GARCH model collapses into the CCC-GARCH model of Bollerslev (1990). Specifically, our conditional variances follow the proposal by Nakatani (2010) and are given by,

$$\begin{array}{ccc}{h}_{1t}& =& c_1+{\alpha }_{11}{\varepsilon }_{1t-1}^2+{\alpha }_{12}{\varepsilon }_{2t-1}^2+b_{11}{h}_{1t-1}+b_{12}{h}_{2t-1}\\ h_{2t}& =& c_2+{\alpha }_{22}{\varepsilon }_{2t-1}^2+{\alpha }_{21}{\varepsilon }_{1t-1}^2+b_{22}{h}_{2t-1}+b_{21}{h}_{1t-1}\end{array}$$ (8)

where, apart from the determinants of the conditional variance of univariate GARCH models, this specification enables us to describe the impact of liquidity volatility on returns volatility through coefficients α ₁₂ and b ₁₂, and that of returns volatility on liquidity volatility, through coefficients α ₂₁ and b ₂₁. Spillovers to financial volatility, h _1t, can be the result of past shocks of both liquidity measures, α ₁₂, and/or of higher liquidity volatility in (t − 1), b ₁₂. In the same vein, shocks in returns and returns volatility might influence liquidity volatility through h _2t. That is, since the model simultaneously fits returns volatility and liquidity volatility and their spillovers, shocks can be either return shocks or liquidity shocks.

The estimated spillover coefficients serve us to infer conclusions on liquidity resilience. If liquidity is resilient, it will withstand shocks and spillovers to liquidity volatility will not be significant. On the contrary, if liquidity is non-resilient, liquidity volatility will react and spike in response to shocks and spillover coefficients will be significant. These spillover coefficients can also characterize feedback loops between both variables, as a return shock could translate into more uncertain liquidity conditions (and vice versa) simultaneously. If present, these feedback effects are consistent with a lower liquidity resilience, as they will cause further difficulties for liquidity to absorb shocks. The model disentangles whether these interlinkages between returns volatility and liquidity volatility have grown after the GFC as well as the causality direction.

As usual in GARCH-type models, the estimates of α ₁₁ + b ₁₁ and α ₂₂ + b ₂₂ provide a measure of volatility persistence, so that if this sum is close to one, high volatility tends to be followed by high volatility. In our analysis of resilience, a lower persistence after the crisis as proxied by this sum of coefficients has a positive interpretation as this fact is consistent with the occurrence of liquidity and financial spikes that tend to go back to normal soon.

We estimate all parameters simultaneously in R with the ccgarch package of Nakatani (2014) by maximizing the log-likelihood function of this model. As initial values in the estimation process we choose univariate GARCH estimates for diagonal elements of A and B and values slightly above zero for the non-diagonal elements. The modulus of the largest eigenvalue of A + B matrix is constrained to be strictly less than one to ensure positive and stationary variances (Nakatani, 2010).21

5. Results

Next we analyze whether market liquidity has become less resilient after the GFC. We fit the model in equations (6), (7), (8) for the returns, r _t, and the first differences of the five liquidity measures, L _R, L _DR, L _MEC, V and L _A. We estimate the model for the pre-crisis period, from January 2003 to May 2007, for the post-crisis period, from April 2009 to June 2016, as well as for the full sample. Table 6, Table 7, Table 8 report the estimates of the model for the three periods, respectively. Our main interest is in the two calm periods before and after the GFC, as we do not want the outcome of our models to be driven by the financial crisis episode.

Table 6.

Estimates of the model for the pre-crisis period, from January 2003 to May 2007.

	ΔLR	ΔLDR	ΔLMEC	ΔV	ΔLA
c1	0.000 (0.001)	0.000 (0.000)	0.009 (0.088)	0.000 (0.053)	0.000 (0.014)
c2	0.001 (0.018)	0.000 (0.019)	0.086∗∗∗ (0.028)	0.006 (0.037)	0.062∗∗ (0.031)
a11	0.029 0.199	0.006 0.017	0.073∗∗∗ 0.004	0.043 0.851	0.000 0.006
a22	0.180∗∗∗ (0.001)	0.000 (0.001)	0.005 (0.366)	0.104∗∗∗ (0.010)	0.001 (0.110)
a12	0.011 (0.778)	0.013 (0.187)	0.001 (0.878)	0.017 (4.277)	0.011 (0.019)
a21	0.009 (0.024)	0.029 (0.048)	0.003 (0.203)	0.000 (0.134)	0.247∗∗ (0.108)
b11	0.950∗∗∗ (0.008)	0.980∗∗∗ (0.017)	0.752∗∗∗ (0.038)	0.901∗∗∗ (0.004)	0.932∗∗∗ (0.205)
b22	0.273∗∗ (0.123)	0.755∗∗∗ (0.177)	0.002 (3.990)	0.468 (0.642)	0.928∗∗∗ (0.098)
b12	0.510∗∗∗ (0.008)	0.024 (0.051)	0.255 (0.638)	0.961∗∗∗ (0.024)	0.000 (0.794)
b21	0.008 (0.133)	0.056∗∗ (0.023)	0.005 (0.007)	0.013 (0.075)	0.001 (0.043)
LogL	−757.872	−479.1963	−801.5718	−143.8205	−648.3826
T	1131	1131	1131	226	226
Q1(10)	3.745	4.124	3.279	7.992	4.679
Q2(10)	5.352	5.517	1.325	3.675	9.739
$Q_1^2(10)$	6.038	3.955	10.823	4.897	5.007
$Q_2^2(10)$	1.689	7.274	0.339	12.752	13.171
λ(ΓC)	0.995	0.999	0.827	0.976	0.984
λ(ΓC⊗C)	0.993	0.998	0.694	0.956	0.968

Estimation results of the conditional variances of a bivariate ECC-GARCH model (Nakatani, 2010):

$$\begin{array}{ccc}{h}_{1t}& =& c_1+{\alpha }_{11}{\varepsilon }_{1t-1}^2+{\alpha }_{12}{\varepsilon }_{2t-1}^2+b_{11}{h}_{1t-1}+b_{12}{h}_{2t-1}\\ h_{2t}& =& c_2+{\alpha }_{22}{\varepsilon }_{2t-1}^2+{\alpha }_{21}{\varepsilon }_{1t-1}^2+b_{22}{h}_{2t-1}+b_{21}{h}_{1t-1}\end{array}$$

where h_1t is the conditional volatility of 10-year US Treasury returns (log difference of prices) and h_2t the conditional volatility of the first difference, denoted by Δ, of each of the five liquidity indicators (namely, L_R is the transaction costs indicator by Roll (1984), L_DR is the daily range, L_MEC denotes the Market efficiency coefficient, V is trading volume expresed in logarithms and L_A stands for the ratio proposed by Amihud (2002)). See Section 2 for further detais on these indexes; LogL denotes the value of the log likelihood function; Q(10) denotes the Ljung-Box Q-statistic (with 10 lags) for the standardized residuals; Q²(10) denotes the Ljung-Box Q-statistic (with 10 lags) for the squared standardized residuals; λ(Γ_C) and λ(Γ_C⊗C) denote the stationarity and the fourth-order moment conditions, respectively; Standard errors in brackets; ∗∗∗, ∗∗, and ∗ refer to significance at 1%, 5% and 10% level; Estimates of the equations for trading volumes and for the Amihud (2002) ratio are based on weekly data.

Table 7.

Estimates of the model for the post-crisis period, from April 2009 to June 2016.

	ΔLR	ΔLDR	ΔLMEC	ΔV	ΔLA
c1	0.003 (0.002)	0.000 (0.014)	0.011∗ (0.006)	0.003 (0.208)	0.224 (0.445)
c2	0.002 (0.015)	0.011 (0.023)	0.023 (0.031)	0.022 (0.054)	0.168 (0.104)
a11	0.032 (0.311)	0.053∗∗ (0.021)	0.037∗∗∗ (0.004)	0.114 (1.180)	0.033∗∗∗ (0.005)
a22	0.338∗∗∗ (0.001)	0.012 (0.010)	0.003 (0.026)	0.122∗∗∗ (0.012)	0.030 (2.445)
a12	0.315 (0.937)	0.001 (0.539)	0.008 (0.140)	0.729 (7.945)	0.002 (0.043)
a21	0.013 (0.024)	0.032 (0.095)	0.352∗∗∗ (0.038)	0.002 (0.093)	0.000 (1.096)
b11	0.921∗∗∗ (0.004)	0.874∗∗∗ (0.022)	0.849∗∗∗ (0.235)	0.823∗∗∗ (0.003)	0.542∗ (0.325)
b22	0.057 (0.113)	0.606∗ (0.358)	0.010 (0.057)	0.147 (0.368)	0.844∗∗∗ (0.211)
b12	0.477∗∗∗ (0.005)	0.232∗∗∗ (0.064)	0.145∗∗ (0.066)	0.816∗∗∗ (0.007)	0.002 (5.509)
b21	0.008 (0.091)	0.040∗∗ (0.018)	0.025∗∗∗ (0.008)	0.000 (0.055)	0.908∗∗∗ (0.028)
LogL	−683.436	−1377.649	−1509.98	−321.7579	−1270.723
T	1861	1861	1861	371	371
Q1(10)	5.799	5.334	6.644	3.561	1.709
Q2(10)	12.658	9.701	21.184	7.764	16.681
$Q_1^2(10)$	12.204	9.743	11.855	13.343	8.289
$Q_2^2(10)$	4.000	2.678	0.558	5.852	6.420
λ(ΓC)	0.982	0.974	0.948	0.941	0.885
λ(ΓC⊗C)	0.966	0.953	0.901	0.912	0.785

Estimation results of the conditional variances of a bivariate ECC-GARCH model (Nakatani, 2010):

$$\begin{array}{ccc}{h}_{1t}& =& c_1+{\alpha }_{11}{\varepsilon }_{1t-1}^2+{\alpha }_{12}{\varepsilon }_{2t-1}^2+b_{11}{h}_{1t-1}+b_{12}{h}_{2t-1}\\ h_{2t}& =& c_2+{\alpha }_{22}{\varepsilon }_{2t-1}^2+{\alpha }_{21}{\varepsilon }_{1t-1}^2+b_{22}{h}_{2t-1}+b_{21}{h}_{1t-1}\end{array}$$

where h_1t is the conditional volatility of 10-year US Treasury returns (log difference of prices) and h_2t the conditional volatility of the first difference, denoted by Δ, of each of the five liquidity indicators (namely, L_R is the transaction costs indicator by Roll (1984), L_DR is the daily range, L_MEC denotes the Market efficiency coefficient, V is trading volume expresed in logarithms and L_A stands for the ratio proposed by Amihud (2002)). See Section 2 for further detais on these indexes; LogL denotes the value of the log likelihood function; Q(10) denotes the Ljung-Box Q-statistic (with 10 lags) for the standardized residuals; Q²(10) denotes the Ljung-Box Q-statistic (with 10 lags) for the squared standardized residuals; λ(Γ_C) and λ(Γ_C⊗C) denote the stationarity and the fourth-order moment conditions, respectively; Standard errors in brackets; ∗∗∗, ∗∗, and ∗ refer to significance at 1%, 5% and 10% level; Estimates of the equations for trading volumes and for the Amihud (2002) ratio are based on weekly data.

Table 8.

Estimates of the model for the full sample.

	ΔLR	ΔLDR	ΔLMEC	ΔV	ΔLA
c1	0.012∗∗∗ (0.003)	0.001 (0.001)	0.001 (0.008)	0.045 (0.146)	0.016 (0.013)
c2	0.001 (0.017)	0.002 (0.017)	0.001 (0.028)	0.005 (0.040)	0.025 (0.028)
a11	0.043 (0.079)	0.032∗∗∗ (0.010)	0.032∗∗∗ (0.002)	0.093 (0.528)	0.065∗∗∗ (0.001)
a22	0.316∗∗∗ (0.001)	0.009∗∗ (0.004)	0.000 (0.006)	0.023∗∗ (0.010)	0.054 (0.196)
a12	0.000 (0.529)	0.008 (0.405)	0.000 (0.251)	0.028 (5.704)	0.000 (0.001)
a21	0.017 (0.032)	0.038 (0.115)	0.000 (0.103)	0.001 (0.074)	0.183∗∗∗ (0.049)
b11	0.842∗∗∗ (0.004)	0.957∗∗∗ (0.019)	0.960∗∗∗ (0.014)	0.844∗∗∗ (0.002)	0.909∗∗∗ (0.336)
b22	0.265∗∗∗ (0.067)	0.407 (0.351)	0.963∗∗∗ (0.141)	0.802∗ (0.426)	0.915∗∗∗ (0.032)
b12	1.383∗∗∗ (0.004)	0.013 (0.108)	0.008 (0.052)	0.036∗∗∗ (0.005)	0.000 (0.589)
b21	0.005 (0.074)	0.151∗∗∗ (0.017)	0.011∗∗∗ (0.002)	0.000 (0.032)	0.110∗∗∗ (0.041)
LogL	−1188.359	−2616.47	−3233.109	−626.485	−2355.404
T	3464	3464	3464	691	691
Q1(10)	7.948	6.931	7.948	6.331	0.702
Q2(10)	5.693	10.203	5.693	12.949	6.835
$Q_1^2(10)$	11.436	10.541	11.436	21.527∗∗	17.796∗∗
$Q_2^2(10)$	4.456	3.873	4.456	5.281	6.874
λ(ΓC)	0.964	0.996	0.964	0.937	0.980
λ(ΓC⊗C)	0.940	0.995	0.940	0.896	0.965

Estimation results of the conditional variances of a bivariate ECC-GARCH model (Nakatani, 2010):

$$\begin{array}{ccc}{h}_{1t}& =& c_1+{\alpha }_{11}{\varepsilon }_{1t-1}^2+{\alpha }_{12}{\varepsilon }_{2t-1}^2+b_{11}{h}_{1t-1}+b_{12}{h}_{2t-1}\\ h_{2t}& =& c_2+{\alpha }_{22}{\varepsilon }_{2t-1}^2+{\alpha }_{21}{\varepsilon }_{1t-1}^2+b_{22}{h}_{2t-1}+b_{21}{h}_{1t-1}\end{array}$$

where h_1t is the conditional volatility of 10-year US Treasury returns (log difference of prices) and h_2t the conditional volatility of the first difference, denoted by Δ, of each of the five liquidity indicators (namely, L_R is the transaction costs indicator by Roll (1984), L_DR is the daily range, L_MEC denotes the Market efficiency coefficient, V is trading volume expresed in logarithms and L_A stands for the ratio proposed by Amihud (2002)). See Section 2 for further detais on these indexes; LogL denotes the value of the log likelihood function; Q(10) denotes the Ljung-Box Q-statistic (with 10 lags) for the standardized residuals; Q²(10) denotes the Ljung-Box Q-statistic (with 10 lags) for the squared standardized residuals; λ(Γ_C) and λ(Γ_C⊗C) denote the stationarity and the fourth-order moment conditions, respectively; Standard errors in brackets; ∗∗∗, ∗∗, and ∗ refer to significance at 1%, 5% and 10% level; Estimates of the equations for trading volumes and for the Amihud (2002) ratio are based on weekly data.

Spillovers from financial volatility to liquidity volatility, as approximated by ${\hat{b}}_{21}$, have increased substantially. As stated in Table 6, this coefficient is significant only for L _DR in the pre-crisis period, whereas Table 7 indicates that after the crisis ${\hat{b}}_{21}$ also becomes significant for the models with L _MEC and L _A. Therefore, after the GFC liquidity volatility spikes hand in hand with financial shocks, which implies that liquidity has a lower absorbing capacity of shocks.

The impact of liquidity volatility on financial volatility can be analyzed simultaneously through ${\hat{b}}_{12}$. According to Table 6, in the pre-crisis period this coefficient is only significant for the models with L _R and V, whereas, as shown in Table 7, in the post-crisis period all estimates for b ₁₂ except that for L _A are significant and different from zero. Nevertheless, the Amihud ratio, L _A, is weekly, which might make spillover identification more difficult. Therefore, financial volatility reaction to liquidity volatility shocks is higher after the GFC. This higher liquidity news impact on stock returns effect can lead to more volatility spikes that, in turn, simultaneously impact on liquidity volatility and hinder liquidity resilience. Indeed, in the aftermath of the GFC spillovers are significant in both directions for L _DR and L _MEC. This means that for the models with the daily range and the MEC, we identify a feedback loop between liquidity volatility and price uncertainty. Specifically, higher liquidity volatility translates into higher financial volatility and the other way around, so that the more unstable liquidity is, the more volatile returns are, and vice versa. These increasing simultaneous spillovers between both variables imply a lower liquidity resilience after the GFC.

Besides, according to Table 7, the estimates for b ₁₂ tend to be larger and more significant than those for b ₂₁, except for the model for the Amihud ratio, L _A, which suggests that liquidity volatility dominates these dynamics. Thus, liquidity volatility not only reacts to returns volatility, but also plays a major role in exacerbating financial volatility. This result supports our approach based on a simultaneous analysis of returns volatility and liquidity volatility, as a univariate model approach to characterize resilience through the reaction of liquidity volatility to financial shocks would have ignored these coinciding effects. This outcome complements that of Fleming and Remolona (1999) and Fleming and Piazzesi (2005), who state that depth, which we approximate by volumes, tends to disappear prior to economic news announcements.

Table 8 reports the estimates for the full sample. In line with the post-crisis outcome, spillovers from financial volatility to liquidity volatility, which are identified in the post-crisis period though ${\hat{b}}_{21}$ for the model specifications with L _DR, L _MEC and L _A, are also significant for the complete sample. However, and as in the results for the pre-crisis period in Table 6, the coefficient for b ₁₂ is only significant for the models with L _R and V. That is, some of the feedback loop effects between liquidity volatility and price uncertainty that we identify for the post-crisis period in Table 7 would not hold for the entire sample, as they would be hidden by the dynamics of the series during the pre-crisis and the crisis periods.

Moreover, according to the estimates of α ₁₁ and b ₁₁ in Table 6, Table 7, returns volatility of the US Treasuries became less persistent after the financial crisis. Persistence of financial volatility, which is approximated by ${\hat{\alpha }}_{11}+{\hat{b}}_{11}$, is lower in the post-crisis period for all liquidity indicators except for the estimates with L _MEC, although these coefficients are not significant. These results suggest that after the GFC calm periods last less than before the crisis. We reach similar conclusions on the persistence of liquidity volatility as ${\hat{\alpha }}_{22}+{\hat{b}}_{22}$ also diminish after the crisis for all liquidity indicators, except for the model with L _MEC, also with non-significant coefficients. That is to say, this is a positive result in terms of liquidity resilience as this lower persistence than before the GFC in both returns and liquidity volatility indicates that volatility will return to low levels more quickly than in the past. 22

Our results are in line with previous works by some central banks on the changing pattern in volatility after the crisis in different markets. For instance, the ECB (2016) observes a lower persistence of stock market volatility after the announcement of asset purchase programs in the US and the euro area by means of time-varying estimates of GARCH (1,1) parameters, whereas the BoE (2015) estimates a range of asymmetric GARCH models for UK equity and credit markets to conclude that financial volatility has become more sensitive to news after the crisis.

Important financial stability considerations arise from our findings. Higher feedback effects between financial volatility and market liquidity in the aftermath of the GFC imply that financial shocks coexist with liquidity strains, which in turn exacerbate market reaction and limits liquidity capacity to absorb shocks. On a more positive note, episodes of high volatility are less prolonged, as implied by lower volatility persistence, potentially reducing the severity of financial strains, which is positive for financial stability. In any event, our results suggest that the market liquidity of US Treasuries has become less resilient even with apparently sound liquidity. Our assessment on liquidity resilience is helpful to explain the occurrence of the volatility episodes that this key market has witnessed in recent years, such as the October 2014 “flash crash”, which have been intense but short-lived in nature, and characterized by severe liquidity strains.

Poorer liquidity resilience might be related to some recent structural changes in the markets, such as the lower presence of market makers, or the existence of large and concentrated holdings by institutional investors (IMF, 2015). Moreover, the rise of electronic platforms and new trading strategies, such as automatic trading and high-frequency trading, could have prompted more unstable liquidity conditions as well (Joint Staff Report, 2015). From a regulatory perspective, some specific features of the Basel III capital framework, such as the introduction of the leverage ratio, could have contributed to the decline of liquidity provision by bank-dealers (Adrian et al., 2017b). Besides suffering from serious data limitations, the quantification of the impact of these drivers on the link between market liquidity and financial volatility exceeds the scope of this paper.

6. Conclusions

In this paper, we analyze market liquidity resilience, i.e. its ability to absorb shocks, of the US 10-year Treasury bonds given its relevance from a financial stability perspective. The conventional liquidity resilience measure, defined as the mean-reverting speed of the liquidity level after one shock, has limitations due to the fact that it relies on the liquidity level measurement. We propose a new complementary approach where liquidity volatility, rather than the liquidity level, becomes the key variable to characterize resilience.

First, we choose five market liquidity indicators, which do not show an unequivocal drop in liquidity in the aftermath of the GFC. Then, we fit a bivariate CC-GARCH model as proposed by Nakatani (2010) for US 10-year Treasury returns and the first difference of the liquidity measures from January 2003 to June 2016. This model approach allows to evaluate liquidity resilience, as it is useful for understanding the dynamics of returns volatility and liquidity volatility, their interactions, as well as volatility persistence. Our bivariate GARCH models should not be interpreted as a new liquidity resilience measure, but as a tool to better understand resilience through the relatively unexplored link between liquidity volatility and financial volatility that complements the standard quantification.

According to our results, despite apparently sound liquidity, market liquidity resilience has deteriorated after the GFC. Spillovers from liquidity volatility to returns volatility and vice versa have become more intense and feedback loops more likely, which may aggravate turmoil episodes and signals a lower capacity of liquidity to absorb shocks. That being said, the volatility of both returns and liquidity is less persistent than in the past. Therefore, while liquidity volatility and returns volatility could suddenly increase, they will also tend to recover faster than in the past. These results help to explain some of the crash-type episodes that the US Treasury bond market has witnessed in recent years, short-lived in nature and characterized by liquidity strains.

Our results have important financial stability implications regarding the pivotal position of US Treasury debt as a safe asset. These new market liquidity dynamics are also relevant for the liquidity buffer of banks and other institutions. Further research to understand the drivers of this lower liquidity resilience, which are probably related to ongoing structural changes in this market, is needed to guide policy responses that reinforce the market liquidity resilience.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.