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At least since Thomas Piketty's best-selling "Capital in the Twenty-First Century" (2014, Cambridge, MA: The Belknap Press), percentile shares have become a popular approach for analyzing distributional inequalities. In their work on the development of top incomes, Piketty and collaborators typically report top-percentage shares, using varying percentages as thresholds (top 10%, top 1%, top 0.1%, etc.). However, analysis of percentile shares at other positions in the distribution may also be of interest. In this paper I present a new Stata command called -pshare- that estimates percentile shares from individual-level data and displays the results using histograms or stacked bar charts. A shorter version of this paper has been published in The Stata Journal 16(2): 264-300 (see: http://www.stata-journal.com/article.html?article=st0432).

Social desirability and the fear of sanctions can deter survey respondents from responding truthfully to sensitive questions. Self-reports on norm breaking behavior such as shoplifting, non-voting, or tax evasion may therefore be subject to considerable misreporting. To mitigate such misreporting, various indirect techniques for asking sensitive questions, such as the randomized response technique (RRT), have been proposed in the literature. In our study, we evaluate the viability of several variants of the RRT, including the recently proposed crosswise-model RRT, by comparing respondents’ self-reports on cheating in dice games to actual cheating behavior, thereby distinguishing between false negatives (underreporting) and false positives (overreporting). The study has been implemented as an online survey on Amazon Mechanical Turk (N = 6,505). Our results indicate that the forced-response RRT and the unrelated-question RRT, as implemented in our survey, fail to reduce the level of misreporting compared to conventional direct questioning. For the crosswise-model RRT, we do observe a reduction of false negatives (that is, an increase in the proportion of cheaters who admit having cheated). At the same time, however, there is an increase in false positives (that is, an increase in non-cheaters who falsely admit having cheated). Overall, our findings suggest that none of the implemented sensitive questions techniques substantially outperforms direct questioning. Furthermore, our study demonstrates the importance of distinguishing false negatives and false positives when evaluating the validity of sensitive question techniques.

Graphical display of regression results has become increasingly popular in presentations and in scientific literature because graphs are often much easier to read than tables. Such plots can be produced in Stata by the marginsplot command (see [R] marginsplot). However, while marginsplot is versatile and flexible, it has two major limitations: it can only process results left behind by margins (see [R] margins), and it can handle only one set of results at a time. In this article, I introduce a new command called coefplot that overcomes these limitations. It plots results from any estimation command and combines results from several models into one graph. The default behavior of coefplot is to plot markers for coefficients and horizontal spikes for confidence intervals. However, coefplot can also produce other types of graphs. I illustrate the capabilities of coefplot by using a series of examples.

Is Benford’s law a good instrument to detect fraud in reports of statistical and scientific data? For a valid test, the probability of ‘false positives’ and ‘false negatives’ has to be low. However, it is very doubtful whether the Benford distribution is an appropriate tool to discriminate between manipulated and non-manipulated estimates. Further research should focus more on the validity of the test and test results should be interpreted more carefully.

The counterfactual decomposition technique popularized by Blinder (1973, Journal of Human Resources, 436–455) and Oaxaca (1973, International Economic Review, 693–709) is widely used to study mean outcome differences between groups. For example, the technique is often used to analyze wage gaps by sex or race. This article summarizes the technique and addresses several complications, such as the identification of effects of categorical predictors in the detailed decomposition or the estimation of standard errors. A new command called oaxaca is introduced, and examples illustrating its usage are given.

At least since Thomas Piketty's best-selling "Capital in the Twenty-First Century" (2014, Cambridge, MA: The Belknap Press), percentile shares have become a popular approach for analyzing distributional inequalities. In their work on the development of top incomes, Piketty and collaborators typically report top-percentage shares, using varying percentages as thresholds (top 10%, top 1%, top 0.1%, etc.). However, analysis of percentile shares at other positions in the distribution may also be of interest. In this paper I present a new Stata command called pshare that estimates percentile shares from individual-level data and displays the results using histograms or stacked bar charts.

Individuals differ not only in their background characteristics but also in how they respond to a particular treatment, intervention, or stimulation. In particular, treatment effects may vary systematically by the propensity for treatment. In this paper, we discuss a practical approach to studying heterogeneous treatment effects as a function of the treatment propensity, under the same assumption commonly underlying regression analysis: ignorability. We describe one parametric method and two nonparametric methods for estimating interactions between treatment and the propensity for treatment. For the first method, we begin by estimating propensity scores for the probability of treatment given a set of observed covariates for each unit and construct balanced propensity score strata; we then estimate propensity score stratum-specific average treatment effects and evaluate a trend across them. For the second method, we match control units to treated units based on the propensity score and transform the data into treatment-control comparisons at the most elementary level at which such comparisons can be constructed; we then estimate treatment effects as a function of the propensity score by fitting a nonparametric model as a smoothing device. For the third method, we first estimate nonparametric regressions of the outcome variable as a function of the propensity score separately for treated units and for control units and then take the difference between the two nonparametric regressions. We illustrate the application of these methods with an empirical example of the effects of college attendance on women’s fertility.

Lorenz and concentration curves are widely used tools in inequality research. In this article, I present a new command, lorenz, that estimates Lorenz and concentration curves from individual-level data and, optionally, displays the results in a graph. The lorenz command supports relative, generalized, absolute, unnormalized, custom-normalized Lorenz, and concentration curves. It also provides tools for computing contrasts between different subpopulations or outcome variables. lorenz fully supports variance estimation for complex samples.

I introduce the new mgof command to compute distributional tests for discrete (categorical, multinomial) variables. The command supports large-sample tests for complex survey designs and exact tests for small samples as well as classic large-sample X2-approximation tests based on Pearson's X2, the likelihood ratio, or any other statistic from the power-divergence family (Cressie and Read, 1984, Journal of the Royal Statistical Society, Series B (Methodological) 46: 440–464). The complex survey correction is based on the approach by Rao and Scott (1981, Journal of the American Statistical Association 76: 221–230) and parallels the survey design correction used for independence tests in svy: tabulate. mgof computes the exact tests by using Monte Carlo methods or exhaustive enumeration. mgof also provides an exact one-sample Kolmogorov–Smirnov test for discrete data.