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1. • A significant educational expansion. Between 2002 and 2015 the fraction of workers who completed high school increased from 30.6% to 51.4%, while the fraction with a college degree doubled from 6.7% to 13.6%.
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2. • Large declines in poverty rates. The poverty rate, measured as the fraction of individuals living on less than $4 USD per day (at PPP), halved from 37.6% in 2002 to 18.6% in 2016.
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3. • Modest decreases in income inequality. The Gini coefficient of the per-capita household income decreased 8.4% between 2002 and 2017, from 0.58 to 0.53. Still, the income distribution of the country remains among the most unequal ones in the world.
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4. • Number of hires. This variable measures the number of workers hired by the firm over the 2003–2017 period. To compute this variable, I only consider hires with a monthly contract and hired at a salary above the federal minimum wage. This sample restriction makes the analyses of the firm random sample comparable to the analyses of the new-hires sample.
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5. • Significant declines in the informality rate. Between 2002 and 2015, the share of salaried workers in informal-sector jobs declined from 36.2% to 22.4% according to the legal definition and from 55.2% to 42.7%, according to the productive definition.
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34. Figure A2: Distribution of monthly earnings in four Brazilian datasets Panel A. Household Survey (PNAD) 0M 1M 2M 3M 4M 5M Number of workers 0 500 1000 1500 2000 2500 3000 3500 Monthly earnings (in R$) Panel B. Labor Force Survey (PME) 0M 2M 4M 6M Number of workers 0 500 1000 1500 2000 2500 3000 3500 Monthly earnings (in R$) Panel C. Population Census 0M 1M 2M 3M 4M Number of workers 0 500 1000 1500 2000 2500 3000 3500 Monthly earnings (in R$) Panel D. Social Programs Registry 0M 0.5M 1M 1.5M Number of workers 0 500 1000 1500 2000 2500 3000 3500 Monthly earnings (in R$) Salary divisible by: 10 50 100 500 1000 Other Note: This figure shows the distribution of monthly earnings in the dataset listed in the panel title.
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35. Figure A3: Histogram of the share of workers in each firm hired at a round salary Panel A. All firms 0.00 0.10 0.20 0.30 Fraction of firms 0.00 0.25 0.50 0.75 1.00 Share of new employees hired at a round number Panel B. Firms that hired five or more workers in the sample 0.00 0.10 0.20 0.30 Fraction of firms 0.00 0.25 0.50 0.75 1.00 Share of new employees hired at a round number Note: These figures show a histogram of the share of workers in each firm hired at a round-numbered salary in the firm random sample. Panel A shows the histogram for all firms. Panel B shows the histogram for the subset of firms that hired at least five workers during 2003–2017.
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36. Figure E1: Comparison of parametric and non-parametric counterfactual distributions 0k 50k 100k 150k 200k Number of contracts 500 1000 1500 2000 2500 3000 3500 Contractual monthly earnings (in R$) Global polynomial (7th-degree) Local polynomial (7th-degree) Note: This figure compares the counterfactual earnings distribution using two different approaches. The red line denotes the counterfactual earnings distribution using a global 7th-degree polynomial. The blue line denotes the counterfactual distribution using a local 7th-degree polynomial. The grey dashed line around the local polynomial denotes the 95% confidence interval.
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37. Figure E2: Robustness of the counterfactual distribution to alternative specifications Panel A. Robustness to polynomial degree 0k 50k 100k 150k 200k Number of contracts 500 1000 1500 2000 2500 3000 3500 Contractual monthly earnings (in R$) Degree: 5 6 7 8 9 10 Panel B. Robustness to kernel choice 0k 50k 100k 150k 200k Number of contracts 500 1000 1500 2000 2500 3000 3500 Contractual monthly earnings (in R$) Kernel: Uniform Normal Epanechnikov Triangle Note: This figure shows how the counterfactual earnings distributions estimated using a local polynomial approach changes when varying the polynomial degree (Panel A) and the type of kernel (Panel B). See Appendix E for details on how I estimate the counterfactual distribution.
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38. Figure F2: Difference in the number of contracts around salaries divisible by 100 Panel A. Share of contracts just below and just above each side of the round salary Average just below = 0.479 Average just above = 0.521 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Share of contracts 500 1000 1500 2000 2500 3000 3500 Contractual monthly earnings (in R$) Just below the round salary Just above the round salary Panel B. Regression Discontinuity estimates β̂r’s from equation (F2) Average RD coefficient -15 -10 -5 0 5
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39. Figure F6: Distribution of contracted salaries and kinks in the income tax schedule during 2015 Changes in the marginal tax rate 0k 100k 200k 300k 400k 500k Number of contracts 1000 1500 2000 2500 3000 3500 4000 4500 5000 Contractual monthly earnings (in R$) Salary divisible by: 10 50 100 500 1000 Other Note: This figure shows the distribution of contracted salaries in the new-hires sample during 2015. Red dashed lines indicate kinks in the personal income tax rate during 2015. To construct this figure, I first group workers in R$1 bins and then count the number of workers in each bin. Workers whose contracted salary is a round number are denoted with colored markers. The figure only displays workers with earnings above the minimum wage and below R$3500 (which roughly corresponds to the 99th percentile of the distribution of earnings above the minimum wage). See Appendix D for the sample restrictions.
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64. Panel B shows the fraction of contracted salaries divisible by 10, 100, and 1000 in the new-hires sample (blue bars) and the fraction that would be observed if the distribution of the last digits of salaries were uniform (red bars). The figure excludes workers hired at the minimum wage. See Appendix D for the sample restrictions.
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77. The datasets are the 2013 Brazilian Household Survey (Pesquisa Nacional por Amostra de Domicílios, abbreviated PNAD), the 2013 Brazilian Labor Force Survey (Pesquisa Mensal de Emprego, abbreviated PME), the 2010 Brazilian Population Census (Censo Demográfico) and the 2013 Social Programs Registry of Individuals (Cadastro Único). I focus on the monthly earnings of full-time employed workers aged 18–65. I exclude workers employed by public-sector firms and individuals that work without remuneration.
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78. The firm will continue refining its estimate of the fully-optimal salary as long as the 29 The optimal wage is a continuous variable, so the firm can learning the decimals of the fully-optimal wage following the same logic just described. Salaries with cents are rare in the data, which probably reflects the fact that the gain from learning the decimal digits is small. marginal benefit of learning an additional digit is greater than the marginal optimization cost. Observe that learning further digits of the fully-optimal wage shrinks the mispricing wedge at a decreasing rate. If the initial estimate is equal to the fully-optimal wage up to the nearest 1000, the error from not learning the second digit is at most 500, the error from not learning the following digit is at most 50, and the error from not learning the final digit is at most 5.
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79. The x-axis in each panel is a firm’s fraction of new employees hired at a round-numbered salary during 2003–2017. The variable on the y-axis of each graph is listed in the panel title. Markers depict means in five percentage point bins. Lines are predicted values from a linear regression on the plotted points.
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80. This test is analogous to one conducted by Dube et al. (2020) using observational data. Intuitively, in the presence of a left-digit bias, workers with salaries close to, but below, a round number would be more likely to leave a firm to pursue a better wage than workers earning a round salary or a salary just above it. A problem with separation rates is that the separations might be driven by firms exiting the market, as opposed to workers leaving because they found a better match. In the data, I observe whether the employer or the employee initiated the separation. Thus, I estimate worker resignation rates (i.e., worker-initiated separations) in the vicinity of round salaries.
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81. To quantify the missing mass, I follow Kleven and Waseem (2013) and select the narrowest manipulation region consistent with the data. To illustrate how the approach works, Appendix Figure E3 shows how the counterfactual distribution, excess mass (Panel A), and missing mass (Panel B) around R$3000 are estimated. 30 The shape of the counterfactual is robust to the polynomial degree (Appendix Figure E2, Panel A) and the type of kernel (Appendix Figure E2, Panel B). All specifications include minimum wage dummies to improve the fit of the counterfactual density at the minimum wage.
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82. Whynes, D. K., Z. Philips, and E. Frew (2005). Think of a number. . . any number? Health Economics 14(11), 1191–1195.
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83. Without loss of generality, assume that wages can have at most four digits.28 Suppose, furthermore, that the firm’s initial estimate of the fully-optimal wage is such a wage rounded to the coarsest round number. In this case, the fully-optimal wage rounded to the nearest 1000, w1000. By paying τ100, they can learn the second digit of the optimal wage and offer the optimal wage rounded to the nearest 100, w100. After learning the second 28 In the new-hires sample, less than one percent of all salaries are equal or greater than R$10,000 (i.e., have more than four digits).
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42. Market Power Effects on Worker-Employer Network Formation in Evolutionary Labor Markets with Adaptive Search. (1999). Tesfatsion, Leigh.
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43. Do Scientists Pay to Be Scientists?. (1999). Stern, Scott.
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47. Cohort Effects and Returns to Seniority in France. (1995). MARGOLIS, David.
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