On-Line Technical Appendix – Specification and Pooling Pretests
for “Market Fairness: The Poor Country Cousin of Market Efficiency”
Access at (http://dx.doi.org/doi:10.1007/s10551-015-2964-y)
A.1. Endogeneity and Overidentifying Restrictions
Like all overidentified instrumental variable models, ours must overcome two potential
specification biases that often trade off against one another. First, one must test whether the excluded
regressors are valid (exogenous) instruments. We perform two types of endogeneity pretests: a) the
Hausman specification test of a single suspected endogenous variable, the order-to-trade ratio (OTR) –
the number of order instruction messages divided by the number of trades, and b) the χ 2 test of 2SLS
residuals against the entire set of reduced-form instruments. Table 1, Panel A shows an illustration of the
Hausman test for the endogeneity/exogeneity of the order-to-trade ratio which makes use of the
consistency property of 2SLS estimates. From an OLS reduced-form for OTR in London and another in
Paris, we obtain OTR residuals, labelled OTRr. We then introduce OTRr into the 2SLS specification of
the structural equation (3) for the determinants of algorithmic trading (AT) which includes the OTR raw
values. Since the OTR residuals are statistically insignificant (t-scores = 0.67 and 1.15) and therefore
uncorrelated with CTR, we conclude OTR is exogenous as an instrument. That is, the OTR message
traffic-to-trade ratio is a valid instrument for the cancellation-to-trade ratio CTR, our proxy metric for
algorithmic trading.1
Table 1, Panel B shows our second endogeneity pretest. Here, the 2SLS
residuals from structural equation (1) for MTC are regressed on the instruments and control variables in
the reduced-form of the full system. The nR2 statistic from this regression is distributed χ2. This test is
then repeated for each dependent variable in both London and Paris. As shown, all these test statistics are
insignificant at 1%, 5%, and even at 10%. So, the proposed set of instruments and control variables are
jointly not endogenous in any of the equations in the (1) – (3) simultaneous structural equation system.
1
Reversing roles, CTR is not a valid instrument for OTR (the metric Henderschott, Jones, and Menkveld (2011)
employ to proxy HFT), and that is why we endogenize CTR.
In addition to pretesting the validity of the proposed instruments, it is
also important to test the pseudo R-squared of the reduced-form (𝑅̅2) to assess the strength or weakness of
the chosen set of instruments (Murray 2006, 2011). Weak instruments inhibit the ability of instrumental
variable (IV) estimation to overcome the simultaneity bias of OLS. Hahn and Hausman (2005) show that
in the case of overidentified models, the simultaneity bias remaining in IV parameters is proportional to:
(a) the dependent variable error’s covariance with the instrument, (b) (1-𝑅̅2) from the reduced-form, and
(c) the number of instruments employed. So, specification bias is magnified in IV estimation by either
too few adequate instrumental variables or by too many, if they remain jointly weak.
We test the null hypothesis that at least one of the instrumental variables excluded to
identify an equation is strong enough to render the IV procedure useful. We employ Stock-Yogo (2005)
critical values for the null hypothesis of the 2SLS bias exceeding 10, 20, 30% of the OLS bias. Table 1,
Panel C displays these Stock-Yogo F test results for each estimated structural equation separately as well
as the analogous multi-equation Cragg-Donald statistic for the simultaneous system (Cragg and Donald
1993). Our instrumental variables reject the null at 95% for dependent variables MTC, Spread and AT,
reducing the bias in the OLS estimates by wide margins.2 Specifically, in 11 of 12 cases the F test of
restrictions is able to reject the Stock-Yogo null hypothesis that the 2SLS parameters are more than 10%
biased relative to the OLS parameters. Using the Cragg-Donald statistic for the MTC-Spr-AT
simultaneous equation system, the MTC system’s instrumental variables are again strong, especially in
London. Having confirmed the strength and validity of our IV specifications for MTC, Spread and AT
model structure, we proceed to 2SLS and 3SLS estimation.
A.2. Pooling Tests
A.2.1. LSE versus Euronext-Paris
Radically different market designs existed throughout the last decade in London versus Paris.
The Stock-Yogo test is quite different for the Information LEAKAGE (IL) dependent variable. The IL system’s
IVs are universally weak with all three Cragg-Donald statistics (unreported but available from the authors) well
below the Stock-Yogo critical values for rejecting bias in excess of 30%. In this case, IV weakness is a serious
issue, and as a result the parameters on the endogenous variables in the IL-Spr-AT model may be unreliable.
2
2
The London Stock Exchange is a hybrid of dealer and electronic limit order books that are fully revealed
to brokers and investors, combined with worked principal agreements (WPAs) that print when the dealer
accepts the batch order. In stark contrast, NYSE Euronext-Paris is a fully electronic limit order book,
only partially revealed to investors, with prints of constituent parts of batch orders for non-index stocks
whenever liquidit𝑒́ provideurs work their excess inventory into the continuous order flow. In addition,
during the pre-MiFID1 period (2003-2007), few Euronext-listed security transactions could execute
outside the consolidated limit order book of the national exchange in Paris whereas LSE-listed securities
also executed in cross-listings throughout Europe and the U.S. Consequently, we split our sample
between London and Paris, and each equation (1)-(3) as well as the system as a whole was then tested for
the pooling restriction. The fairness equation for MTC cannot be validly pooled across London and Paris
with a Wald test F statistic of 7.74, significant at 99%. Similarly, the Spread equation cannot be validly
pooled with an F statistic of 3.62, significant at 95%. The AT equation can be pooled. Even in the topdecile stocks, again the MTC, LEAKAGE, and Spread equations cannot be validly pooled across London
and Paris at 95%.
Finally, recalling that we hypothesize simultaneity and correlated cross-
equation disturbances in the fairness, spreads, AT equations (1)-(3), we check for structural change
between the LSE and Euronext Paris system estimations. Using Wald tests, we conclude that in both the
full sample and the top decile subsample, the MTC, Spreads, and AT equations cannot be validly pooled
across London and Paris at 99%. The same is true for the LEAKAGE, Spreads, and AT system of
equations at 95%. We therefore proceed to model fairness-efficiency relationships separately for the
London and Paris markets.
A.2.2. Pre-and Post-MiFID1 Regulatory Regimes
The passport rule and the MTF’s high speed
trading platforms ushered in by MiFID1 greatly facilitated the execution of AT strategy. Exhibit 2
displays the absence of trend in the cancel-to-trade (CTR) ratio before the MiFID1 regulatory regime
came into force in November 2007. AT accelerated immediately afterwards and trended ever higher for
the next several years.
Supporting evidence of this possible regime change is also
available from millisecond remainder analysis. Hasbrouck and Saar (2013) argue that automated trading
3
system patterns should be classified as ATs if they are programmed to access and revisit the market
periodically, potentially in order to “slice and dice” institutional orders. Dividing each second into 1000
equal-sized buckets, they identified very frequent order entries immediately following the start of the
second, and less strong though prevalent order entries immediately following the half-second. These
periodicities are much longer than the sub 20ms latency within which ATs can react. Our own
millisecond remainder analysis in Aitken, Harris, McInish, Aspiris, and Foley (2012) for the years 20072011 indicates that precisely such AT patterns now exist that did not exist prior to the implementation of
MiFID1 in late 2007.
We
therefore
conducted
a
careful
analysis of whether the parameters of the efficiency-fairness-AT model are stable across the apparent
regime change. On the one hand, we note that the estimated determinants of Spreads and AT are
qualitatively identical before and after MiFID1. A Wald test of the simultaneous system indicates that the
entire 3SLS model of MTC-Spread-AT in Tables 2 and 3, Panel A (for London) can be validly pooled
over the pre and post-MiFID1 time periods. Paris is a bit of a different story. In unreported results
available from the authors, MTC in Paris was initially reduced by greater AT but not post-MiFID1.
Leakage in Paris was not initially reduced by greater AT but was so reduced, especially in the most liquid
stocks, post-MiFID1. These interaction effects of AT with the regulatory regime change show up as the
on-again, off-again pattern of AT-improved and MiFID1-worsened fairness effects for Paris in the
summary of our findings in Exhibit 4. Again, MiFID1 may have induced regulators in Paris to be keener
on enforcing some securities laws rather than others.
4
Table A.1 Specification Pretests of Endogeneity and Overidentifying Restrictions
We report four sets of specification pretests: two for endogeneity and two for instrument strength/
weakness. The Hausman specification test in Panel A fails to reject the null hypothesis that a suspect r.h.s.
variable in the algorithmic trading (AT) equation -- a normalized metric of message traffic known as the orderto-trade ratio (OTR) -- is exogenous by testing the residuals from a reduced-form estimation of OTR in the
second-stage structural equation for the cancellations-to-trade (CTR) ratio, our proxy measure of AT. Using
another implication of the consistency of large sample 2SLS, Panel B tests nR2 from the residuals of the 2SLS
structural equations for manipulation at the close (MTC), Spread, and AT, respectively, regressed against the
entire set of the r.h.s. variables in the first-stage reduced-forms. The chi-squared test statistic fails to reject the
null hypothesis of exogenous instruments and control variables in each of our three equations.
The final specification pretest concerns the strength/weakness of the instrumental variables. Using StockYogo (2005) statistics as critical values for the first-stage reduced-form’s F statistic, we reject at 95% the null
hypothesis that the 2SLS parameter bias is more than 10% of the OLS parameter bias for 11 of 12 sets of
instruments and control variables in the MTC, Spr, and AT equations. These instruments are strong. The
opposite is true of the information leakage (IL) equation; those instruments are weak. The Cragg-Donald
statistic tests this same hypothesis for the maximum likelihood simultaneous equations system. Again, the MTC
system’s instrumental variables are strong, especially in London. In contrast, the IL system’s IVs are universally
weak.
Panel A – Hausman 2SLS Specification Test of Order-to-Trade Ratio (OTR)
AT Equation
London (Adjusted R2 = 0.936, F = 189.9)
̂𝑡 - 0.36log𝑆𝑃𝑅
̂𝑡 + 0.28logOTRt + 0.29logOTRrt +…
logCTRt=2.05+ 0.11logStdt - 0.709 RecovFeet - 0.02log𝑀𝑇𝐶
(0.66)
(-5.75)†
(-0.10)
(-0.44)
(1.99)**
( 0.67)
2
Paris (Adjusted R = 0.951, F = 288.0)
̂𝑡 + 0.06log𝑆𝑃𝑅
̂𝑡 + 0.63logOTRt + 0.29logOTRrt + …
logCTRt = 1.94 + 0.28logStdt
- 0.19log𝑀𝑇𝐶
(0.29)
(-0.55)
(0.24)
(5.29)**
(1.15)
Panel B –Endogeneity Test for Full Set of Instrumental and Control Variables
2SLS residuals regressed on
London
MTC
QSpread
AT
2
2
nR ~ χ (95% c.v. = 16.92)
7.53
2.11
0.34
IVs and control variables
Paris
2
2
nR ~ χ (95% c.v. = 15.51)
0.15
5.21
1.26
Panel C –Test of Instrumental Variable Strength/Weakness
95% Critical Values for
London
Paris
2SLS Bias > 10/20/30%
London Excluded
Paris
Excluded
of OLS Bias
All IVs IVs Only All IVs IVs Only
2SLS Single Equations
Stock-Yogo (2005) c.v.
F statistic of the Restrictions
MTC Equation
10.27/6.71/5.34
45.23** 15.04** 12.78** 10.78**
Spr Equation
9.08/6.46/5.39
93.27** 26.69** 40.11**
5.77**
AT Equation
9.08/6.46/5.39
79.32** 14.04** 100.81** 14.19**
IL Equation
9.08/6.46/5.39
2.79
3.10
1.45
1.12
Max Likelihood System
MTC Equation
Spr Equation
AT Equation
Stock-Yogo (2005)
10.22/6.20/4.73
9.92/6.16/4.76
9.92/6.16/4.76
5
Cragg-Donald statistic
33.45**
29.01**
5.49**
0.16
6.19**
3.65