J-PAL has been awarded a three-year grant to promote Research Transparency and Reproducibility. One primary component of this grant is to facilitate the reproducibility of 36 studies through pre-publication reanalyses, a new attempt to conduct code replications of research before it gets published.
The Fall 2017 round of applications for J-PAL’s Research Transparency Graduate Student Fellows will close at 11:59 pm EST on Friday, June 30, 2017. This is an exciting opportunity for graduate students who are excited about research transparency and development economics and are seeking additional funding.
The fellowship program offers financial support (tuition assistance of up to $12,000 and a stipend of $13,000) for one semester (approximately 4.5 months) for current PhD students. While preference will be given to students from economics programs, graduate students from other disciplines with strong quantitative and programming skills (STATA, R etc.) are very welcome to apply.
During the fellowship, students will work with J-PAL’s affiliated professors from dozens of universities around the world, re-analyzing RCTs from scratch (starting with the creation of the data set from “raw survey” data, up to production of the final econometric analysis included in the working papers).
You can find this fellowship announcement on J-PAL’s website. If you have questions, please contact James Turitto at firstname.lastname@example.org.
Finance academics have started to take replication studies seriously. As hundreds of factors have been documented in recent decades, the concern over p-hacking has become especially acute. In a pioneering meta-study, Harvey, Liu, and Zhu (2016) introduce a multiple testing framework into empirical asset pricing. The threshold t-cutoff increases over time as more factors have been data-mined. A new factor today should have a t-value exceeding 3.
Reevaluating 296 significant factors in published studies, Harvey et al. report that 80-158 (27%-53%) are false discoveries. Two publication biases are likely responsible for the high percentage of false positives. First, it is difficult to publish a negative result in top academic journals. Second, more subtly, it is difficult to publish replication studies in finance, while in many other disciplines replications routinely appear in top journals. As a result, finance and accounting academics tend to focus on publishing new factors rather than rigorously verifying the validity of published factors.
Harvey (2017) elaborates the complex agency problem behind the publication biases. Journal editors compete for citation-based impact factors, and prefer to publish papers with the most significant results. In response to this incentive, authors often file away papers with results that are weak or negative, instead of submitting them for publication. More disconcertingly, authors often engage in, consciously or subconsciously, p-hacking, i.e., selecting sample criteria and test procedures until insignificant results become significant. The outcome is an embarrassingly large number of false positives that cannot be replicated in the future.
We conduct a massive replication of the published factors by compiling a largest-to-date data library with 447 variables. The list includes 57, 68, 38, 79, 103, and 102 variables from the momentum, value-versus-growth, investment, profitability, intangibles, and trading frictions categories, respectively. We use a consistent set of replication procedures throughout. To control for microcaps (stocks that are smaller than the 20th percentile of market equity for New York Stock Exchange, or NYSE, stocks), we form testing deciles with NYSE breakpoints and value-weighted returns. We treat a variable as a replication success if its average return spread is significant at the 5% level.
Our replication indicates rampant p-hacking in the published literature. Out of 447 factors, 286 (64%) are insignificant at the 5% level. Imposing the t– cutoff of 3 per Harvey, Liu, and Zhu (2016) raises the number of insignificance to 380 (85%).
The biggest casualty is the liquidity literature. In the trading frictions category, 95 out of 102 variables (93%) are insignificant. Prominent variables that do not survive our replication include Jegadeesh’s (1990) short-term reversal; Datar-Naik-Radcliffe’s (1998) share turnover; Chordia-Subrahmanyam-Anshuman’s (2001) coefficient of variation for dollar trading volume; Amihud’s (2002) absolute return-to-volume; Acharya-Pedersen’s (2005) liquidity betas; Ang-Hodrick-Xing-Zhang’s (2006) idiosyncratic volatility, total volatility, and systematic volatility; Liu’s (2006) number of zero daily trading volume; and Corwin-Schultz’s (2012) high-low bid-ask spread. Several recent friction variables that have received much attention are also insignificant, including Bali-Cakici-Whitelaw’s (2011) maximum daily return; Adrian-Etula-Muir’s (2014) intermediary leverage beta; and Kelly-Jiang’s (2014) tail risk.
The much researched distress anomaly is virtually nonexistent. Campbell-Hilscher-Szilagyi’s (2008) failure probability, the O-score and Z-score in Dichev (1998), and Avramov-Chordia-Jostova-Philipov’s (2009) credit rating all produce insignificant average return spreads.
Other influential but insignificant variables include Bhandari’s (1988) debt-to-market; Lakonishok-Shleifer-Vishny’s (1994) five-year sales growth; several of Abarbanell-Bushee’s (1998) fundamental signals; Diether-Malloy-Scherbina’s (2002) dispersion in analysts’ forecast; Gompers-Ishii-Metrick’s (2003) corporate governance index; Francis-LaFond-Olsson-Schipper’s (2004) earnings attributes, including persistence, smoothness, value relevance, and conservatism; Francis et al.’s (2005) accruals quality; Richardson-Sloan-Soliman-Tuna’s (2005) total accruals; and Fama-French’s (2015) operating profitability, which is a key variable in their 5-factor model.
Even for significant anomalies, their magnitudes are often much lower than originally reported. Famous examples include Jegadeesh-Titman’s (1993) price momentum; Lakonishok-Shleifer-Vishny’s (1994) cash flow-to-price; Sloan’s (1996) operating accruals; Chan-Jegadeesh-Lakonishok’s (1996) standardized unexpected earnings, abnormal returns around earnings announcements, and revisions in analysts’ earnings forecasts; Cohen-Frazzini’s (2008) customer momentum; and Cooper-Gulen-Schill’s (2008) asset growth.
Why does our replication differ so much from the original studies? The key word is microcaps. Microcaps represent only 3% of the total market capitalization of the NYSE-Amex-NASDAQ universe, but account for 60% of the number of stocks. Microcaps not only have the highest equal-weighted returns, but also the largest cross-sectional standard deviations in returns and anomaly variables. Many studies overweight microcaps with equal-weighted returns, and often together with NYSE-Amex-NASDAQ breakpoints, in portfolio sorts.
Hundreds of studies use cross-sectional regressions of returns on anomaly variables, assigning even higher weights to microcaps. The reason is that regressions impose a linear functional form, making them more susceptible to outliers, which most likely are microcaps. Alas, due to high costs in trading these stocks, anomalies in microcaps are more apparent than real. More important, with only 3% of the total market equity, the economic importance of microcaps is small, if not trivial.
Our low replication rate of only 36% is not due to our extended sample relative to the original studies. Repeating our replication in the original samples, we find that 293 (66%) factors are insignificant at the 5% level, including 24, 44, 13, 38, 81, and 93 across the momentum, value-versus-growth, investment, profitability, intangibles, and trading frictions categories, respectively. Imposing the t-cutoff of three raises the number of insignificance to 387 (86.6%). The total number of insignificance at the 5% level, 293, is even higher than 286 in the extended sample. In all, the results from the original samples are close to those from the full sample.
We also use the Hou, Xue, and Zhang (2015) q-factor model to explain the 161 significant anomalies in the full sample. Out of the 161, the q-factor model leaves 115 alphas insignificant (150 with t<3). In all, capital markets are more efficient than previously recognized.
Kewei Hou is Fisher College of Business Distinguished Professor of Finance at The Ohio State University. Chen Xue is Assistant Professor of Finance at University of Cincinnati. Lu Zhang is the John W. Galbreath Chair, Professor of Finance, at The Ohio State University. Correspondence about this blog should be addressed to Lu Zhang at email@example.com.
Abarbanell, J. S., & Bushee, B. J. (1998). Abnormal returns to a fundamental analysis strategy. The Accounting Review, 73, 19-45.
Acharya, V. V., & Pedersen, L. H. (2005). Asset pricing with liquidity risk. Journal of Financial Economics, 77, 375-410.
Adrian, T., Etula, E., & Muir, T. (2014). Financial intermediaries and the cross-section of asset returns. Journal of Finance, 69, 2557-2596.
Amihud, Y. (2002). Illiquidity and stock returns: Cross-section and time series evidence. Journal of Financial Markets, 5, 31-56.
Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2006). The cross-section of volatility and expected returns. Journal of Finance, 61, 259-299.
Avramov, D., Chordia, T., Jostova, G., & Philipov, A. (2009). Credit ratings and the cross-section of stock returns. Journal of Financial Markets, 12, 469-499.
Bali, T. G., Cakici, N., & Whitelaw, R. F. (2011). Maxing out: Stocks as lotteries and the cross-section of expected returns. Journal of Financial Economics, 99, 427-446.
Bhandari, L. C. (1988). Debt/equity ratio and expected common stock returns: Empirical evidence. Journal of Finance, 43, 507-528.
Campbell, J. Y., Hilscher, J., & Szilagyi, J. (2008). In search of distress risk. Journal of Finance, 63, 2899-2939.
Chan, L. K. C., Jegadeesh, N., & Lakonishok, J. (1996). Momentum strategies, Journal of Finance, 51, 1681-1713.
Chordia, T., Subrahmanyam, A., & Anshuman, V. R. (2001). Trading activity and expected stock returns. Journal of Financial Economics, 59, 3-32.
Cohen, L., & Frazzini, A. (2008). Economic links and predictable returns, Journal of Finance, 63, 1977-2011.
Cooper, M. J., Gulen, H., & Schill, M. J. (2008). Asset growth and the cross-section of stock returns, Journal of Finance, 63, 1609-1652.
Corwin. S. A., & Schultz, P. (2012). A simple way to estimate bid-ask spreads from daily high and low prices. Journal of Finance, 67, 719-759.
Datar, V. T., Naik, N. Y., & Radcliffe, R. (1998). Liquidity and stock returns: An alternative test. Journal of Financial Markets, 1, 203-219.
Dichev, I. (1998). Is the risk of bankruptcy a systematic risk? Journal of Finance, 53, 1141-1148.
Diether, K. B., Malloy, C. J., &Scherbina, A. (2002). Differences of opinion and the cross section of stock returns, Journal of Finance, 57, 2113-2141.
Fama, E. F., & French, K. R. (2015). A five-factor asset pricing model, Journal of Financial Economics, 116, 1-22.
Francis, J., LaFond, R., Olsson, P. M., & Schipper, K. (2004). Cost of equity and earnings attributes, The Accounting Review, 79, 967-1010.
Francis, J., LaFond, R., Olsson, P. M., & Schipper, K. (2005). The market price of accruals quality, Journal of Accounting and Economics, 39, 295-327.
Gompers, P., Ishii, J., & Metrick, A. (2001). Corporate governance and equity prices, Quarterly Journal of Economics, 118, 107-155.
Harvey, C. R. (2017). Presidential address: The scientific outlook in financial economics. Journal of Finance, forthcoming.
Harvey, C. R., Liu, Y., & Zhu, H. (2016). …and the cross-section of expected returns. Review of Financial Studies, 29, 5-68.
Hou, K., Xue, C., & Zhang, L. (2015). Digesting anomalies: An investment approach. Review of Financial Studies, 28, 650-705.
Jegadeesh, N. (1990). Evidence of predictable behavior of security returns. Journal of Finance, 45, 881-898.
Jegadeesh, N. & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. Journal of Finance, 48, 65-91.
Kelly, B., & Jiang, H. (2014). Tail risk and asset prices. Review of Financial Studies, 27, 2841-2871.
Lakonishok, J., Shleifer, A., & Vishny, R. W. (1994). Contrarian investment, extrapolation, and risk, Journal of Finance, 49, 1541-1578.
Liu, W. (2006). A liquidity-augmented capital asset pricing model. Journal of Financial Economics, 82, 631-671.
Richardson, S. A., Sloan, R. G., Soliman, M. T., & Tuna, I. (2005). Accrual reliability, earnings persistence and stock prices, Journal of Accounting and Economics, 39, 437-485.
Sloan, R. G. (1996). Do stock prices fully reflect information in accruals and cash flows about future earnings? The Accounting Review, 71, 289-315.
In a recent post (“Open data for the busy researcher”), Richard D. Morey suggests an easy way to share data. The hardest part is getting started. The following steps make it easy to “ease in” to the process of making your data available.
“Create an OSF page for the project. If you’ve never used OSF before, you may have to create an account, but this is easy. If you need help, there are guides.”
“Add a README file describing the project (perhaps title and abstract, and, importantly, your contact information). Say that the data/materials for the project will be placed there, and in the meantime, people who want access to the data/materials should contact you. This is a “stub” OSF page, awaiting your later additions.”
“Add the link to this OSF page in your manuscript (perhaps in the author note). Write something like “Information about obtaining data and materials underlying this paper can be found at X.” where X is your OSF page’s URL.”
“When you have time — hopefully before the paper is formally published — populate the OSF page.”
“To do everything I’ve described above takes only a few minutes, at most, except for the last step. Consider the worst case scenario: you forget to upload the materials/data. Then a curious researcher simply emails you as would be typical, and asks you for it. The link to the OSF page points to your contact information, so nothing is lost.”
[From the article “Science Needs a Solution for the Temptation of Positive Results” by Aaron E. Carroll at The New York Times/The Upshot website]
“Science has a reproducibility problem. … As long as the academic environment has incentives for scientists to work in silos and hoard their data, transparency will be impossible. As long as the public demands a constant stream of significant results, researchers will consciously or subconsciously push their experiments to achieve those findings, valid or not. As long as the media hypes new findings instead of approaching them with the proper skepticism, placing them in context with what has come before, everyone will be nudged toward results that are not reproducible.”
In our AER Papers and Proceedings paper, “Assessing the Rate of Replications in Economics” we try to answer two questions. First, how often do economists attempt to replicate results? Second, how aware are we collectively of replication attempts that do happen?
Going into this project, the two of us were concerned about the state of replication in the profession, but neither of us really knew for sure just how bad (or good) it might be. To get a better handle on the problem, we set out to quantify just how often results produced in subsequent work spoke to the veracity of the core insights in empirical papers (even if this was not the main goal of the follow up work).
We couldn’t answer this for all work ever done, so we needed to limit the exercise to a meaningful subsample. To do this we chose a base set of papers from the AER’s 100th volume, published in 2010. This volume sample therefore represented important, general-interest ideas in economics, and gave all the papers at least 5 years since publication to accrue replication attempts.
We wanted to be fairly comprehensive on the fields we included, but we also wanted to focus on “replication” in a very broad sense: had the core hypothesis of the previous paper been exposed to a retest and incorporated into the published literature? But this broad definition led to a problem on the coding, as we wanted the reader of each volume paper to be an expert in the field providing his or her opinion on whether something was a replication. To solve this, we put together a group of coauthors who possessed expertise across of an array of fields (adding James Berry, Rania Gihleb, and Douglas Hanley to the project).
Assigning the volume papers by specialty, we read through and coded just over 1,500 papers citing one of the 70 empirical papers in our volume sample. For each paper we coded our subjective opinions on whether each was a replication and/or an extension for one of the original paper’s main hypotheses. Alongside this, we also coded more-objective definitions on the relationship of the data in each citing paper to the original, allowing us to compare our top-level replication coding to the definitions given by Michael Clemens.
The end results from our study indicate that only a quarter of the papers in our volume sample were replicated at least once, while 60 percent had either been replicated or extended at least once. While the replication figure is still lower than we would want, it was higher than we expected. Moreover, the papers that were replicated were the most important papers in our sample: Every single volume paper in our sample with 100 published citations had been replicated at least once. Given 50 published citations, the paper was more likely to have been replicated than not. While the quantitative rates differ slightly, this qualitative result is replicated by the findings in the session papers by Daniel Hamermesh and Sandip Sukhtankar (examining very well-cited papers in labor economics, and top-5/field publications in development economics, respectively.)
While the replication rates that we found were certainly higher than we initially expected, one thing that we discovered from the coding exercise was how hard it was to find replications. Our coding exercise was an exhaustive search within all published economics papers citing one of our volume papers. In total we turned up 52 papers that we coded as a replication, where the vast majority of these were positive replications. But of these 52, only 18 actually explicitly presented themselves as replications. Simply searching for a paper with a keyword such as “replication” isn’t enough, as many of the replications we found were buried as sub-results within larger papers, for which the replication was not the main contribution.
This hampers awareness of replications. Though one might expect that knowledge of replications is better distributed among the experts within each literature, in a survey we conducted of the volume-paper authors and a subsample of the citing authors, the main finding was substantial uncertainty on the degree to which papers and ideas had been replicated.
Certainly the profession could do a far better job in organizing replications through a market design approach. In a companion paper to this one that we wrote with Muriel Niederle, we set out some modest proposals for better citation and republication incentives for doing so. But much, much more is possible.
Lucas Coffman is a Visiting Associate Professor of Economics at Harvard University. Alistair Wilson is an Assistant Professor of Economics at the University of Pittsburgh. Comments/feedback about this blog can be directed to Alistair at firstname.lastname@example.org.
– Berry, James , Lucas Coffman, Rania Gihleb, Douglas Hanley and Alistair J. Wilson. 2017. “Assessing the Rate of Replication in Economics” Am. Econ. Rev P&P, 107 (5): p.27-31
– Coffman, Lucas, Muriel Niederle and Alistair J. Wilson. 2017. “A Proposal to Incentivize, Promote, and Organize Replications” Am. Econ. Rev P&P, 107 (5): p.41-5
– Clemens, Michael. 2017. “The Meaning of Failed Replications: A Review and Proposal.” J. Econ. Surv. 31 (1): p.326–42
– Hamermesh, Daniel S. 2017. “What is Replication? The Possibly Exemplary Example of Labor Economics.” Am. Econ. Rev P&P, 107 (5): p.37-40.
–Sukhtankar, Sandip. 2017. “Replications in Development Economics” Am. Econ. Rev P&P, 107 (5): p.32-6
The Replication Network is proud to announce that we are now listed on the American Economic Association’s website, Resources for Economists on the Internet (RFE), edited by Bill Goffe at Penn State University. We are listed under “Data / Journal Data and Program Archives / Replication Studies”. You can find us by clicking this. Of course, that would be rather pointless since you are already here!
“A form of replication that has received not much attention yet is what I will call concurrent replication. The basic idea is this. A research group formulates a hypothesis that they want to test. At the same time, they desire to have some reassurance about the reliability of the finding they expect to obtain. They decide to team up with another research group. They provide this group with a protocol for the experiment, the program and stimuli to run the experiment, and the code for the statistical analysis of the data. The experiment is preregistered. Both groups then each run the experiment and analyze the data independently. The results of both studies are included in the article, along with a meta-analysis of the results.”
Various Elsevier associates then discuss how they see these problems being addressed. Given the huge role that Elsevier plays in academic publishing, their view of the problems of scientific research/publishing, and their ideas regarding potential solutions, should be of interest. To read more, click here.
Observed power (or post-hoc power) is the statistical power of the test you have performed, based on the effect size estimate from your data. Statistical power is the probability of finding a statistical difference from 0 in your test (aka a ‘significant effect’), if there is a true difference to be found. Observed power differs from the true power of your test, because the true power depends on the true effect size you are examining. However, the true effect size is typically unknown, and therefore it is tempting to treat post-hoc power as if it is similar to the true power of your study. In this blog, I will explain why you should never calculate the observed power (except for blogs about why you should not use observed power). Observed power is a useless statistical concept. –Daniël Lakens from his blog “Observed power, and what to do if your editor asks for post-hoc power analyses” at The 20% Statistician
Is observed power a useless statistical concept? Consider two researchers, each interested in estimating the effect of a treatment T on an outcome variable Y. Each researcher assembles an independent sample of 100 observations. Half the observations are randomly assigned the treatment, with the remaining half constituting the control group. The researchers estimate the equation Y = a + bT + error.
The first researcher obtains the results:
The estimated treatment effect is relatively small in size, statistically insignificant, and has a p-value of 0.72. A colleague suggests that perhaps the researcher’s sample size is too small and, sure enough, the researcher calculates a post-hoc power value of 5.3%.
The second researcher estimates the treatment effect for his sample, and obtains the following results:
The estimated treatment effect is relatively large and statistically significant with a p-value below 1%. Further, despite having the same number of observations as the first researcher, there is apparently no problem with power here, because the post-hoc power associated with these results is 91.8%.
Would it surprise you to know that both samples were drawn from the same data generating process (DGP): Y = 1.984×T + e, where e ~ N(0, 5)? The associated study has a true power of 50%.
The fact that post-hoc power can differ so substantially from true power is a point that has been previously made by a number of researchers (e.g., Hoenig and Heisey, 2001), and highlighted in Lakens’ excellent blog above.
The figure below presents a histogram of 10,000 simulations of the DGP, Y = 1.984×T + e, where e ~ N(0, 5), each with 100 observations, and each calculating post-hoc power following estimation of the equation. The post-hoc power values are distributed uniformly between 0 and 100%.
So are post-hoc power analyses good for nothing? That would be the case if a finding that an estimated effect was “underpowered” told us nothing more about its true power than a finding that it had high, post-hoc power. But that is not the case. In general, the expected value of a study’s true power will be lower for studies that are calculated to be “underpowered.”
Define “underpowered” as having a post-hoc power less than 80%, with studies having post-hoc power greater than or equal to 80% deemed to be “sufficiently powered.” The table below reports the results of a simulation exercise where “Beta” values are substituted into the DGP, Y = Beta × T + e, e ~ N(0, 5), such that true power values range from 10% to 90%. A 1000 simulations for each Beta value were run and the percent of times recorded that the estimated effects were calculated to be “underpowered.”
If studies were uniformly distributed across power categories, the expected power for an estimated treatment effect that was calculated to be “underpowered” would be approximately 43%. The expected power for an estimated treatment effect that was calculated to be “sufficiently powered” would be approximately 70%. More generally, E(true power| “underpowered”) ≥ E(true power|“sufficiently powered”).
At the extreme other end, if studies were massed at a given power level, say 30%, then E(true power|“underpowered”) = E(true power|“sufficiently powered”) = 30%, and there would be nothing learned from calculating post-hoc power.
Assuming that studies do not all have the same power, it is safe to conclude that E(true power| “underpowered”) > E(true power|“sufficiently powered”): Post-hoc “underpowered” studies will generally have lower true power than post-hoc “sufficiently powered” studies. But that’s it. Without knowing the distribution of studies across power values, we cannot calculate the expected value of true power from post-hoc power.
In conclusion, it’s probably too harsh to say that post-hoc power analyses are good for nothing. They’re just not of much practical value, since they cannot be used to calculate the expected value of the true power of a study.
Bob Reed is Professor of Economics at the University of Canterbury in New Zealand and co-founder of The Replication Network. He can be contacted at email@example.com.
Hoenig, John M., & Heisey, Dennis M. (2001). The abuse of power: The pervasive fallacy of power calculations for data analysis. The American Statistician, Vol. 55, No. 1, pp. 19-24.