Are Sleepy Punishers Really Harsh Punishers? Comment on Cho,Barnes,and Guanara (2017)

Cho, Barnes, and Guanara (2017) analyzed criminal sentencing by U.S. federal judges in the years 1992 through 2003. Controlling for case covariates, they estimated that “sentences rendered on sleepy Mondays”—Mondays immediately following the start of daylight saving time, when the night from Saturday to Sunday is shortened by 1 hr—“were approximately 5% longer than those rendered on [the immediately preceding and subsequent] Mondays” (p. 243). Cho et al. estimated that so large a difference would arise by chance with a probability of only 0.5% if judges tended to render equal sentences on those three Mondays (i.e., p = .005). Cho et al. interpreted this finding as evidence that sleep-deprived judges punish more harshly than judges who have not been sleep deprived.

This Commentary raises three concerns about Cho et al.’s analysis and conclusions. First, Cho et al. reported results from a model that differed from the model described in their article. The latter model is theoretically superior but yields a nonsignificant result. Second, even the model used by Cho et al. yields a much smaller, nonsignificant coefficient if one accounts for judges’ choice whether to impose any prison time at all, as is standard in the sentencing literature. Third, new data from 2004 through 2016 show not even a trace of a sleepy-Monday effect. Table 1 summarizes all four models mentioned thus far (Models 1, 2, 4, and 7) along with several models providing robustness checks (Models 3, 5, 6, and 8), and the remainder of this Commentary discusses these eight models in more detail. At the outset, it is worth noting that Cho et al.’s result depends entirely on their model: As reported in their note 3, a model without their control variables did not yield a statistically significant estimate of a sleepy-Monday effect.

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Table 1.

Description of the Models and Coefficients for the Sleepy-Monday Effect

Specification	Model 1 a b = 0.061* (0.023)	Model 2 b = 0.052 (0.027)	Model 3 b = 0.039 (0.023)	Model 4 b = 0.011 (0.038)	Model 5 b = 0.023 (0.017)	Model 6 b = −0.004 (0.006)	Model 7 b = −0.027 (0.028)	Model 8 b = −0.000 (0.007)
Dependent variable	ln(1 + s)	ln(s)	ln(s)	ln(1 + s)	ln(s)	s > 0	ln(s)	s > 0
Sentences of zero length included?	No	No	No	Yes	No	Yes	No	Yes
Ethnicities included in the sample	Non-Hispanic	All ethnicities	All ethnicities	Non-Hispanic	All ethnicities	All ethnicities	All ethnicities	All ethnicities
Races included in the sample	White, Black	White, Black	All races	White, Black	All races	All races	All races	All races
Citizenship of sample	U.S.	U.S.	All countries	U.S.	All countries	All countries	All countries	All countries
Sentencing days in the sample	3 Mondays	3 Mondays	3 Mondays	3 Mondays	All days of the year	All days of the year	All days of the year	All days of the year
Sentencing years in the sample	1992–2003	1992–2003	1992–2003	1992–2003	1992–2003	1992–2003	2004–2016	2004–2016
All controls from Cho et al. included? b	Yes	Yes	Yes	Yes	Yes	Yes	No; only trial included	No; only trial included
Other controls	—	—	Hispanic, U.S. citizenship	—	Hispanic; U.S. citizenship; age squared; number of dependents; and fixed effects of Offense Level × Criminal History, day of the week, month, year, offense type, and whether any statutory minimum appliedc	Hispanic; U.S. citizenship; age squared; number of dependents; and fixed effects of Offense Level × Criminal History, day of the week, month, year, offense type, and whether any statutory minimum appliedc	Fixed effects of judge, lead charge, day of the week, month, and year	Fixed effects of judge, lead charge, day of the week, month, and year
Treatment of district effect	Random-effects slopes and intercept	Random-effects slopes and intercept	Random-effects slopes and intercept	Random-effects slopes and intercept	Fixed effect	Fixed effect	Fixed effect	Fixed effect
Clustered SEs used?	No	No	No	No	Clustered at judicial district	Clustered at judicial district	Clustered at judicial district	Clustered at judicial district
Model type	HLM	HLM	HLM	HLM	Linear	Linear	Linear d	Linear d
N	2,985	3,836	6,296	3,781	431,517	521,611	737,637	907,450
Data source	Cho et al. e	USSC	USSC	Cho et al.e	USSC	USSC	TRAC	TRAC

Note: In all models, s (sentence length, in months) was right censored at 470, as in Cho, Barnes, and Guanara (2017). Standard errors of the sleepy-Monday coefficient are given inside parentheses. HLM = hierarchical linear model; USSC = U.S. Sentencing Commission; TRAC = Transactional Records Access Clearinghouse.

a

Model 1 was an exact replication of Model 2 in Cho et al. (Model 2 of their Table 1). ^bThe controls Cho et al. used were as follows: sentencing year (trend); criminal-history fixed effect; offense level; trial; multiple-convictions indicator; and defendant’s age, gender, race (Black, White), education (non–high school graduate, high school graduate, some college, or college graduate). ^cFor details, see Yang (2015). ^dThe model was estimated using the REGHDFE software written by Correia (2017). ^eThe data used, and provided to me, by Cho et al. originated from the USSC but contained fewer observations than are available directly from the USSC.

*

p < .01.

Examination of the data revealed, and personal correspondence with the authors confirmed, that Cho et al. reported estimates from a model that excluded Hispanic defendants (one third of the sample) and transformed the dependent variable, sentence length (s), into ln(1 + s). By contrast, their article did not mention this exclusion and invoked the “log transformation,” ln(s) (p. 243). Cho et al.’s data also contained fewer observations than are available from the source of their data, the U.S. Sentencing Commission (USSC). Transparency aside, these deviations from the article’s description are theoretically indefensible. In particular, the use of ln(1 + s) instead of ln(s) cannot be justified as a means to keep sentences without prison time (i.e., s = 0) in the sample because Cho et al. excluded such observations anyway (as discussed later in this Commentary), and this transformation is mathematically inconsistent with both Cho et al.’s interpretation of their estimate of the sleepy-Monday effect as percentage change and their stated goal of generating a normally distributed variable. ¹ The deviations are consequential, as a comparison of Models 1 and 2 in Table 1 demonstrates. Model 1 is the model whose results are reported in Cho et al.; it uses their data and the ln(1 + s) transformation. Model 2 is the model actually described in their article; it uses all the data available from the USSC, does not exclude Hispanics, and uses the ln(s) transformation. The estimated sleepy-Monday effect in Model 2 is 15% smaller than the effect in Model 1 and not statistically significant at the 5% level (p = .057). ²

Increasing the precision of the estimates of the sleepy-Monday effect only weakens the result. Cho et al. excluded foreign defendants and defendants whom the USSC classified as neither White nor Black, but this exclusion unnecessarily reduced their sample size and thus precision and power because any differences in the sentencing of such defendants are not plausibly related to the sleepy-Monday effect. ³ Including these observations reduces the standard error for the sleepy-Monday effect by 15% relative to Model 2. But it also reduces the coefficient itself by 25%, such that the p value rises to .087 (see Model 3 in Table 1). Various other modeling choices made by Cho et al. are defensible but arguably not optimal. As an alternative, Model 5 employs the linear regression setup of Yang (2015), which uses more data while being more robust. ⁴ This approach shrinks the standard error by an additional 28%, but also shrinks the coefficient by an additional 41%, such that the p value rises to .16.

Beyond quibbles about p values, Cho et al.’s result would have been dramatically different if they had not excluded the 18% of cases in which judges refrained from imposing prison time. Defendants in such cases usually receive probation, but in any event are better off than if they were serving time in prison. Consequently, any measurement of sentencing harshness is incomplete without considering these cases, and the sentencing literature routinely takes them into account (e.g., Steffensmeier & Demuth, 2000, whom Cho et al. cited repeatedly to justify other modeling choices). Leaving these cases in the sample by itself eliminates the sleepy-Monday effect, irrespective of the issues identified in the previous paragraphs. In Model 4, which is identical to Model 1 except that it includes sentences of zero length, the sleepy-Monday coefficient is approximately zero. Similarly small, nonsignificant estimates of the sleepy-Monday effect are obtained in variations of Model 4, including variations that use raw sentence length or a binary imprisonment indicator as the dependent variable or the samples of Models 2, 3, or 5; Table 1 summarizes one such variation, Model 6, which uses Yang’s (2015) approach.

In any event, even if some alternative model produced a “significant” result, it is by now widely understood that such post hoc tinkering with the same data leads to invalid inference. Moreover, models using new data for 2004 through 2016 (Models 7 and 8 in Table 1) show that judges were less harsh on sleepy Mondays than on neighboring Mondays during those years. Although the USSC publicly discloses only the year of sentencing for sentences imposed after 2003, the Transactional Records Access Clearinghouse (TRAC) has obtained exact dates through Freedom of Information Act requests. When all relevant covariates available from TRAC are controlled for (Model 7), the estimated sleepy-Monday coefficient for log sentence length in 2004 through 2016 is negative and has a 95%-confidence upper bound of 0.028 (which would correspond to a 2.8% increase in sentence length). ⁵ Model 8 shows that prison sentences were also negligibly rarer on sleepy Mondays than on other days during 2004 through 2016.

These results strongly suggest that sleepy punishers are not harsh punishers, at least not to the extent claimed by Cho et al. On a methodological level, this discussion illustrates the impact of modeling choices such as sample restrictions and variable transformations, underlining the need for very close attention to such choices.