The Evolution of the Earnings Distribution in a Volatile Economy: Evidence from Argentina

This paper studies earnings inequality and dynamics in Argentina between 1996 and 2015. Following the 2001–2002 crisis, the Argentine economy transitioned from a low- to a high-inflation regime. At the same time, the number of collective bargaining agreements increased, and minimum wage adjustments became more frequent. We document that this macroeconomic transition was associated with a persistent decrease in the dispersion of real earnings and cyclical movements in higher-order moments of the distribution of earnings changes. To understand this transition at the micro level, we estimate processes of regular wage adjustments within job spells. As the Argentine economy transitioned from low to high inflation, the monthly frequency of regular wage adjustments almost doubled, while the distribution of changes in regular wages morphed from having a mode close to zero and being positively skewed to having a positive mode and being more symmetric.


Introduction
How are workers' fates tied to macroeconomic conditions? Who are the winners and losers as labor markets adjust to economic downturns and subsequent recoveries? And to what extent does the flexibility to adjust vary with macroeconomic conditions as well as throughout the workforce?
The answers to these questions are of great importance for evaluating the welfare consequences of aggregate fluctuations and also for designing economic stabilization tools such as fiscal and monetary policy.
As part of the Global Income Dynamics Project, we address these questions by studying individual labor market outcomes in a large emerging-market economy. Using newly available administrative data, we analyze time trends and cross-sectional heterogeneity in earnings inequality, volatility, and mobility from 1996 to 2015 in Argentina. This period was volatile for the Argentine macroeconomy. The country experienced several severe recessions and a sharp devaluation of its currency, which prompted a switch in the inflation regime. At the same time, there were substantial changes in the role of unions, the minimum wage, and other labor market institutions. The confluence of these events makes Argentina a particularly interesting setting to study worker-level labor market outcomes in the shadow of macroeconomic turbulence.
Our paper is the first to use administrative data from Argentina to document recent trends in earnings inequality, volatility, and mobility. We leverage newly available administrative data from Argentina's social security system, which comprise over 100 million job records over the period from 1996 to 2015. The large-scale administrative data provide a richer picture of the evolution of earnings inequality, volatility, and mobility than has been possible in previous studies. 1 Specifically, we are able to reliably compute the evolution of higher-order (e.g., third and fourth) standardized moments of Argentina's distribution of earnings and earnings changes, akin to a recent study by Guvenen, Ozkan and Song (2014) based on 34 years of U.S. social security records.
Since the administrative data cover only jobs in Argentina's formal sector, we also supplement our analysis with rich household survey data that allow us to validate our findings based on administrative records and also to compare labor market outcomes in Argentina's formal and informal sectors. In addition, a unique contribution of our paper is our leveraging of administrative data to measure the frequency and size of wage adjustments in Argentina during low-and high-inflation regimes, both in the aggregate and across subgroups of workers.
The first part of this paper implements a set of standardized measurement exercises related to 1 Previous studies of the earnings distribution in Argentina have relied on household survey data. See, for example, Cruces and Gasparini (2009), Gasparini and Cruces (2010), and Alvaredo, Cruces and Gasparini (2018). important quantitative differences. Second, we can compare earnings inequality and dynamics between Argentina's formal and informal sectors. As is the case in other emerging economies, the informal sector constitutes an important part of Argentina's economy, with between 29% and 43 % of all employees in our sample working in informal (i.e., not covered by the social security system) jobs over the period we study. Here, we document significant differences in the distribution of earnings between formal and informal jobs, both in levels and also in time trends. 2 The second part of this paper studies a particular aspect of the flexibility of labor market adjustments to macroeconomic conditions by quantifying nominal wage rigidities in Argentina. Frictions that prevent the adjustment of nominal wages are a core ingredient in many macroeconomic models of empirically realistic business cycle fluctuations. For instance, Christiano, Eichenbaum and Evans (2005) highlight staggered wage contracts as one of the most important features needed to match the observed dynamic effect of a monetary policy shock in a New Keynesian model. Similarly, Shimer (2004) shows that wage rigidity can solve the lack of propagation in the Mortensen-Pissarides search and matching model. In the international macro literature, Schmitt-Grohé and Uribe (2016) argue that wage rigidity can explain sharp differences in employment dynamics between fixed and floating exchange rates in a small-open-economy neoclassical model. Given the importance of wage rigidity in modern business cycle theories, extensive studies measure aggregate wages' business cycle properties. While business cycle moments of aggregate wages have been extensively studied, our understanding of the nature of wage rigidity is incomplete without a set of facts about wage setting at the micro level. In this regard, we contribute to a literature that has made important progress on measuring the micro-level behavior of wages (Grigsby, Hurst and Yildirmaz, 2021;Hazell and Taska, 2019;Gertler, Huckfeldt and Trigari, 2020). A key contribution of the current paper is to study Argentina during a volatile economic period from 1996 and 2015, which allows us to link wage dynamics at the micro level to different inflation regimes, with important implications for other developing countries and economies with high (risk of) inflation.
Our analysis adds to our understanding of wage rigidities by presenting facts about nominal wage setting under different inflation regimes. At a first glance of our data, individual wages appear to be changing almost every month, even when inflation is low and aggregate wages remain almost constant. On closer inspection, individual wages exhibit two clear patterns: either they revert to the exact previous nominal value after temporary deviations, or they fluctuate closely around a "regular" wage. Theory in the price-setting literature shows that aggregate price flex-2 In this manner, we contribute to an emerging literature that compares administrative and household survey data in other emerging economies such as Brazil (Engbom, Gonzaga, Moser and Olivieri, 2021) and Mexico (Calderón, Cebreros, Fernández, Inguanzo, Jaume and Puggioni, 2021). ibility depends on the composition of price changes between those of a transitory or a permanent nature (see Eichenbaum, Jaimovich and Rebelo, 2011;Kehoe and Midrigan, 2015;Alvarez and Lippi, 2020). Motivated by this theory, we use methods developed in the pricing literature to construct regular wage changes. We construct regular wages using the Break Test proposed by . This methodology detects breaks in the stochastic process of wages in non-Gaussian wage-setting models. We verify the validity of this methodology by calibrating and simulating a model that matches features of the wage-setting process in the actual data.
Our main finding pertains to the evolution of the frequency of regular wage changes. We find that in periods of low inflation (such as 1997-2001), the average monthly and annual frequencies are 0.09 and 0.64, respectively. Similar results have been found in other countries with low inflation (see, e.g., Grigsby et al., 2021), which provides further support to our methodology for constructing regular wages. In contrast, during the period of high inflation (i.e., 2007-2015), the average annual frequency of wage change rises to 0.95. In addition, the transition from these two inflationary regimes encompasses other differences: the annual frequency of upward wage changes increases from an average of 0.44 to 0.90, while the frequency of decreases plummets from 0.2 to 0.05. Finally, the richness of the data allows us to study the frequency of wage adjustment for a wide set of workers. We find that in periods of low inflation, the frequency of wage changes falls with workers' ages and earnings ranks, and is largely heterogeneous across sectors.
However, as inflation raises, the heterogeneity across workers becomes less pronounced.
Finally, we document a significant difference in the shape of the regular wage change distribution between low-and high-inflation regimes. During the low-inflation period, the distribution of regular wage changes (i) is asymmetric, with a missing mass of negative wage changes, and (ii) exhibits a large spike at positive-small changes. The pronounced asymmetry between positive and negative wage changes is consistent with previous studies analyzing the distribution of wage changes in low-inflation environments (see, e.g., Dickens, Goette, Groshen, Holden, Messina, Schweitzer, Turunen and Ward, 2007;Barattieri, Basu and Gottschalk, 2014;Grigsby et al., 2021). In contrast, during the high-inflation period, the wage change distribution is symmetric around a mean close to the annual inflation rate. The gap between the 50th and 10th percentiles of the change distribution is 22 log points, almost equal to the difference between the 90th and 50th percentiles (21 log points).
The paper is organized as follows. Section 2 describes the data. Section 3 provides the macroeconomic background in Argentina during the period of analysis. Section 4 presents a set of standardized statistics on earnings inequality, volatility, and mobility. Section 5 validates those find-tion about employees' education status. Information about employers includes their four-digit industry code. 5 Employees' anonymized unique identifiers and identifiers for each employeremployee match allow us to track individual workers and formal employment relationships over time. 6 The dataset is representative of the formally employed population at private firms in all sectors and regions and covering all types of contracts (e.g., full-time workers, internships, temporary workers). It contains data from about 130,000 workers in 1996 to 230,000 in 2015. With formal private employment accounting for roughly 30% to 40% of total employment over the period (including independent and self-employed workers), the sample amounts to about 1% of the employed population in any given year.

Sample Selection.
To enhance harmonization and allow meaningful comparisons across countries in the project, we restrict the original dataset according to the following criteria. First, we focus on workers between 25 and 55 years old, a range within which most education choices are usually completed in Argentina and after which workers tend to leave the labor force for retirement. 7 Second, we drop observations with earnings below a threshold to avoid observations from workers without a meaningful attachment to the labor force or with very low earnings, which could skew log-based statistics. Specifically, we discard observations with earnings below what a worker would earn if they were to work part-time for one quarter at the national minimum wage. In Argentina, the minimum wage is set as a monthly wage and is usually revised at the middle of the year. Maximum legal working hours are 48 hours per week, which in an average month amount to 52/12 × 48 = 208 hours. We compute the equivalent hourly minimum wage for Argentina as y h ts ≡ y m ts /208, where y m ts is the minimum wage in year t and month s. The as the average of the three continuous earnings observations, that is, f A (y ijt ) = (1/3) ∑ k=2 k=0 y (i−k)jt . This is a linear transformation of the original data that does not alter the ordering of observations. Therefore, we could identify which observations have been partially pooled. Note that, while using the group's median or mean to replace all observations within each group would generate bunching at the upper tail of the distribution, the procedure applied to our sample still maintains variation across individual earnings at the very top of the distribution, although decreasing their levels. This implies that there will be a (potentially small) downward bias when computing levels at the top 2% of the earnings distribution. However, since there is no specific time trend in the extent of partial pooling and the same linear transformation is applied each month, we do not have any reason to expect a large bias when analyzing changes in the log of top earnings over time. In the analysis of earnings dynamics below, we use all observations, including those that have been partially pooled. 5 To complete information about employers and employees, the Ministry of Labor, Employment and Social Security combines records from SIPA with employers' sector and type information from AFIP, and workers' gender and year of birth from Argentina's Social Security Agency (ANSES). The industry classification was developed by AFIP, closely following a correspondence with the ISIC Revision 4. 6 Employers' identifiers are not included in the sample. 7 Note that the minimum formal retirement age in Argentina is 65 for men and 60 for women.
annual average hourly minimum wage is then y h t = ∑ 12 s=1 y h ts /12. Finally, the threshold is chosen as part-time (24 hours) earnings for one quarter (13 weeks) at the national minimum wage, or y t ≡ y h t × 13 × 24. For future reference, we label the sample with age and minimum earnings restrictions as the CS sample.
In addition to age-and minimum earnings-related criteria, when computing longitudinal statistics, we apply two additional restrictions. First, we consider a subsample of workers for which we can compute 1-year and 5-year earnings changes; we call this the LX sample. Then, we further restrict the LX sample to observations for which we can compute a permanent earnings measure, as defined below; this limits the sample to workers in a given year who have been in the sample for the previous three consecutive years. We label the latter LX + sample.
Variable Construction. For our statistical analysis, we construct several measures of earnings for worker i in year t: 1. Raw real earnings in levels, y it , and logs, log(y it ). We compute real earnings from total annual worker compensation and our measure of CPI inflation.
2. Residualized log earnings, ε it . This measure is the residual from a regression of log real earnings on a full set of age dummies, separately for each year and gender. It is intended to control for trends in earnings across workers at different stages of their life or business cycle.
3. Permanent earnings, P it−1 . They are defined as average earnings over the previous three years, P it−1 = (∑ t−1 s=t−3 y is )/3, where y is can include earnings below y s for at most one year.
4. Residualized permanent earnings, ε P it . These are computed from P it−1 similarly to ε it .
5. 1-year change in residualized log earnings, g 1 it . It is the 1-year forward change in ε it , g 1 it ≡ ∆ε it = ε it+1 − ε it , where earnings must be above y for both years.
6. 5-year change in residualized log earnings, g 5 it . It is the 5-year forward change in ε it , g 5 it ≡ ∆ 5 ε it = ε it+5 − ε it , where earnings must be above y for both years. Summary Statistics. Table 1 presents sample sizes for our different sample selection criteria.
After imposing restrictions on age and minimum earnings for cross-sectional analysis (the CS sample), we are left with around 70% of the sample. When we further restrict the sample for longitudinal analysis involving 1-and 5-year changes, the LX sample reduces to between 41% and 47%. The LX + sample, which reduces to observations between 1999 and 2010, includes between 34% and 38% of the original sample. The percentage of women remains almost identical after the cross-sectional restrictions and slightly decreases after selecting the sample to allow for the computation of 1-and 5-year changes and permanent earnings. Table 2 reports summary statistics of the monthly real earnings distribution in the unrestricted sample. Average monthly real earnings (in 2018 AR$) increased by 34% over the sample period, from AR$11,725 to AR$15,673. There is wide dispersion in earnings, with the 5th and 99th percentiles of the distribution representing on average around 9% and 580% of the mean, respectively.
As we will study in detail below, although there was an overall increase in real earnings over the period, growth was monotonically decreasing in percentiles of the earnings distribution. Real monthly earnings at the 5th percentile grew by 90% between 1996 and 2015, while earnings at the 95th and 99th percentiles increased in real terms by only 14.5% and 2.5%, respectively.

Macroeconomic Variables
In our analysis, we use two additional data series, CPI inflation and the Argentine peso to U.S. dollar nominal exchange rate, which we obtained from INDEC and the Central Bank of Argentina. 8

Background
This section provides a brief description of the macroeconomic context in Argentina during 1996-2015 and relevant institutional features of the labor market, especially those associated with wage setting, such as the role of unions and the minimum wage. To illustrate the macroeconomic context, Panel (a) of Figure 1 displays the cyclical component of real GDP, Panel (b) shows the evolution of inflation, Panel (c) shows the nominal exchange rate, Panel (d) displays the unemployment rate, while Panel (e) displays the formality rate during the period of analysis.

Collective Bargaining Agreements and the Minimum Wage
In addition to the formal sector, Argentina has an informal sector, which represents over one third of all employment. Wages are market based for informal workers, while in the formal sector, they are subject to labor regulations. Below, we briefly describe the role of two institutions that are essential to the process of wage setting in Argentina over the period we study: unions and the minimum wage.

Collective Bargaining Agreements.
A fundamental aspect of wage setting in Argentina is the collective bargaining mechanism. Centralized unions and employers reach collective agreements with force of law, either at the sector or firm level. Agreements at the sector level apply to all formal labor relations associated with a particular sector, irrespective of whether employees have union affiliation. In contrast, firm-level agreements apply only to labor relations within the firm. 9  Once a collective agreement is signed, its rules prevail until they are explicitly modified by a new agreement, even if no new agreement is reached before the original one expires.
During the 1990s, unions' role in the wage setting process was reduced to a minimum. Most agreements were reached at the firm level and included clauses stipulating flexible working conditions rather than wage adjustment clauses. Price stability, a rigid minimum wage, and increasing unemployment discouraged unions from negotiating new agreements under very unfavorable conditions. In this way, unions preserved previously negotiated collective clauses (Palomino and Trajtemberg, 2006). Council became active again, and since then, it has set new levels for the minimum wage with an 10 Eventually, these wage adjustments flattened wage scales by reducing differentials among different categories of workers. Typically, collective bargaining contracts specify a scale of base wages for workers with different occupations and tenure. These scales define the wage over which workers pay taxes and social security contributions and what constitutes non-taxable labor income. 11 The fraction of workers covered by collective agreements changed only slightly, however, from around 82% in 2002 to 85% in 2009. approximately annual frequency, increasing wage floors in collective bargaining between unions and employers. 12 The latter tended to favor the weakest unions, granting their workers a higher wage floor, while stimulating the negotiation of new wage scales for unions with greater bargaining power. Between 2004 and 2015, the minimum wage increased by around 1,225% nominally and by 56% in real terms.

Earnings Inequality and Dynamics in Argentina
This section describes our main results regarding the evolution of earnings inequality, earnings volatility, and earnings mobility in Argentina during the 1996-2015 period, based on the administrative microdata for Argentina's formal sector.

Earnings Inequality
We first document the evolution of different percentiles of the earnings distribution. Then, we describe the implications of this evolution for overall earnings inequality. Finally, we present results regarding the concentration of earnings at the top of the distribution.
The Evolution of the Earnings Distribution. Panels (a) and (b) of Figure 3 present the evolution of percentiles of the earnings distribution of men and women, respectively, normalized by their value in 1996. 13 Over the sample period, there was an overall increase in real earnings across the entire earnings distribution for both men and women. To illustrate this trend, median log real earnings were 56 and 45 log points higher for men and women, respectively, in 2015 relative to 1996. However, the magnitude of the increase was not homogeneous across the distribution.
Instead, the size of the increase was monotonically decreasing in percentiles of the earnings distribution. While the 10th percentile of men's distribution increased by 69 log points, the 90th percentile increased by only 23 log points. Similar trends hold for women. The only exception to this pattern is the dynamics at the top of the earnings distribution, illustrated in Panels (c) and (d) of Figure 3 for men and women, respectively. 14 Not only were the long-run gains experienced at the top the lowest among the reported percentiles, but some percentiles experienced small net gains, or even losses, between 1996 and 2015.
Examples of such small gains or losses include the 99th and 99.9th percentiles of the distribution for men.
In addition to these long-run trends, Figure  14 The size of the CS sample implies that relatively few observations are used to estimate percentiles above the 99th percentile. Given that they are imprecisely estimated, one should be cautious when interpreting our results for percentiles at the very top of the earnings distribution. 15 Using household survey data, Cruces (2005) finds that the impact of fluctuations in total household income during 1995-2002 was three times higher among households in the bottom quintile of the income distribution compared with those in the top quintile, even during periods of positive GDP growth between 1996 and 1998.  Figure 4 show the dynamics of two measures of log earnings inequality for men and women, respectively, the difference between the 90th and 10th percentiles and the standard deviation, scaled by a factor of 2.56, which corresponds to the P90-P10 differential for a Gaussian distribution.
First, in terms of the level of inequality, the earnings distribution for women has been consistently less unequal than the distribution for men. Second, inequality started to decrease sharply after 2002 for both groups of workers. During the 2002-2008 period, the P90-P10 differential decreased from 2.90 to 2.43 for men and from 2.74 to 2.31 for women. Since then, inequality has mildly and similarly increased for both men and women. 16 Panels (c) and (d) of Figure 4 show the contribution of top and bottom inequality as measured by the P90-P50 and P50-P10 differences, respectively, to the aggregate dynamics of inequality. For men, there was a similar decline in top and bottom inequality of 28 and 23 log points, respectively, between 2002 and 2008 when inequality decreased. By contrast, for women, the main contributor to the decline in inequality during the same period was top inequality, which decreased by 26 log points. While, top inequality since 2008 has remained stable or even decreased, bottom inequality has been steadily increasing, especially for men. 17 Cruces and Gasparini (2009) highlight four forces behind the reduction in earnings inequality during 2003-2007: first, the recovery of labor demand, which induced upward pressure on nominal wages and earnings growth of the previously unemployed; second, changes in relative prices favoring labor-intensive industries, who were protected from imports following the devaluation; third, the potential role of decreasing technology adoption, which could have reduced earnings inequality by inducing less substitution of unskilled labor; and fourth, the aforementioned establishment of non-taxable lump-sum increases in formal workers' salaries by the government.

Initial and Life-Cycle Earnings Inequality. Previous literature has documented that earnings
inequality differs significantly over the life cycle (see, e.g., Deaton and Paxson, 1994;Storesletten, Telmer and Yaron, 2004). Figure 5 reports the evolution of top and bottom inequality for 25-yearold workers. Inequality among young workers followed dynamics similar to those as in the overall population: inequality consistently decreased until 2008, particularly at the bottom, and then increased until the end of the sample. The only difference is that the decline in inequality started before 2002, especially for the decline in top inequality. Another pattern worth highlighting is that while younger workers' earnings have lower average dispersion at the top of the distribution (e.g., top-tail inequality measured by the log P90/P50 earnings percentile ratio was 0.84 for 25-year-old men vs. 1.07 for all men), they exhibit slightly higher dispersion at the bottom of the distribution (e.g., bottom-tail inequality measured by the log P50/P10 earnings percentile ratio was 1.63 for 25-year-old men vs. 1.54 for all men).
In Figure 6, we report the evolution of the log earnings P90-P10 differential for four different     these variables, which is equal to (the negative of) the shape parameter of the Pareto distribution.
Two patterns emerge. First, the earnings distribution for men is more fat-tailed than the distribution for women, as captured by the lower shape parameter in 1996 and 2015. Second, over time, the Pareto tail became thinner for both men and women.
Despite the overall decline in inequality at the top of the earnings distribution, there is sub-stantial heterogeneity within the top 1%. Panels (a) and (

Earnings Dynamics
A standard life-cycle model with incomplete markets predicts that idiosyncratic earnings risk is an important determinant of consumption and savings decisions. In what follows, we document the dynamics of the distribution of earnings changes. More specifically, we report the evolution of the dispersion and higher moments of the distribution of the 1-year change in log residual earnings, Dynamics over Time. Figure 7 shows the evolution of the P90-P50 and P50-P10 gaps of the distribution of 1-year residualized log earnings changes, which intend to capture a measure of earnings risk. The first fact to notice is that Argentina's level of earnings risk is higher than the Dynamics by Age and Earnings Rank. Next, we provide facts about the distribution of 1-year earnings changes by age, earnings rank, and gender. To do so, we group workers into three age groups (25-34, 35-44, and 45-55 years) and permanent earnings percentiles over the last three years.
We find that the dispersion of earnings changes is decreasing in age conditional on earningssee Panels (a) and (b) of Figure 9 for results for men and women, respectively. We also find a U-shaped pattern of dispersion by earnings conditional on age. While the decline in permanent 19 Such asymmetry is observed only in the low-inflation period (before 2002), which can explain the lower fluctuation of skewness in the high-inflation period (after 2007). 20 Figures A.11 and A.12 in the Appendix plot the empirical log-densities of 1-and 5-year earnings growth changes. Deviations from normality are evident: the distributions exhibit non-zero skewness and are leptokurtic (i.e., a more pronounced "peak" around zero changes and fatter tails).   earnings at the bottom of the distribution is gradual, the increase in earnings occurs above the 95th percentile and is steep. The overall pattern is similar across gender groups, except for a higher dispersion for men at the bottom of the permanent earnings distribution, irrespective of age.
Panels (c) and (d) of Figure 9 present the Kelley skewness of 1-year earnings changes. We find a more symmetric distribution for men: skewness is mostly positive but close to zero. Also, differences in skewness across earnings and age groups among men are small. In contrast, skewness among women is much more heterogeneous across the earnings distribution: it fluctuates in the [−0.15, 0.15] range, which is much wider than the range of fluctuations for men of [−0.05, 0.10].
Such fluctuations also follow a U-shaped pattern across the earnings distribution, especially those for young women: for women, skewness is positive at the bottom third of the distribution, negative in the second third, and closer to zero for women in the top third.
Regarding the Crow-Siddiqui kurtosis of earnings changes, Panels (e) and (f) of Figure 9 show an inverted U-shape across the permanent earnings distribution. The degree of heterogeneity across the distribution is much more pronounced for men than for women. For the former, there is a steeper increase in kurtosis for older workers at the bottom third of the distribution. For men in the middle and top of the distribution, kurtosis is highest among the youngest workers. We also observe an increase at the bottom of the distribution for women across all age groups, albeit one that is smaller in magnitude. In addition, the decline is more gradual and observed mostly among younger women. First, as expected, the level of earnings volatility is higher across the earnings distribution and age groups. Second, the distribution of the 5-year earnings changes exhibits negative skewness also for men. Finally, the distribution of 5-year earnings changes has thinner tails than that of 1-year earnings changes.

Mobility
In Figure 10, we analyze how earnings dynamics have affected earnings mobility over the life cycle in Argentina. We consider the average rank-rank mobility of permanent earnings over a 10-year period and look at two age brackets, 25-34 and 35-44, for both men and women. Consistent with the compression in the earnings distribution we have documented so far, we see upward (downward) rank mobility below (above) the 40th percentile of the permanent earnings distribution.
Those at the lower end of the distribution exhibit higher mobility. For instance, on average, workers at the 10th percentile of the permanent earnings distribution manage to transition to between the 25th and 30th percentiles after ten years. Women seem to exhibit slightly higher mobility than men and younger workers show higher mobility than their older counterparts for both genders,

(f) Women
Notes: Using residual 1-year earnings changes and the LS + sample, Figure 9 plots the following variables against permanent earnings quantile groups for the three age groups: (

Comparing Data Sources and Economic Sectors
While the SIPA administrative data have several advantages in measuring labor market outcomes, they naturally miss a significant share of Argentina's informal labor market. This section compares the administrative data from SIPA with independent household survey data from the EPH.
We validate cross-sectional statistics in both samples, highlighting similarities and differences between the two data sources. Using the EPH household survey data only, we also compare earnings inequality and dynamics in Argentina's formal and informal sectors over this period.   Notes: Figure 12 shows percentiles of the earnings distribution (Panels (a) and (b)) and measures of earnings dispersion (Panels (c) and (d)), using administrative data from SIPA (Panels (a) and (c)) and household survey data from EPH (Panels (b) and (d)

Comparing the Formal and Informal Sectors in Household Survey Data
There are many differences between Argentina's formal and informal sectors. Chief among them is that informal workers are not covered by formal labor institutions such as the minimum wage, collective bargaining agreements, employment protection, and social security benefits. This raises the important question: How do labor market outcomes compare for workers in Argentina's for-mal versus informal sectors?
To answer this question, Figure 13 replicates the same set of standardized statistics of the distribution of earnings in Argentina separately for workers in the formal and informal sectors. Panels (a) and ( As a result of these dynamics, panels (c) and (d)

Wage Setting under Low and High Inflation
In this section, we document a series of facts pertaining to wage dynamics across workers in Argentina under low-and high-inflation settings. We first describe how we construct regular wages, and thus regular-wage changes, for each worker. Then, we report and discuss various moments based on the distribution of estimated regular-wage changes.

Measurement
In the following analysis, we restrict our attention to total monthly labor compensation-henceforth referred to as "wages"-of workers between 25 and 55 years old in the private sector. Before we measure nominal wage rigidity in our data, we need to address four measurement challenges associated with administrative wage data in Argentina.
First, since SIPA collects data on workers at a monthly frequency, we do not know the exact day their job spells start or end. Owing to this time aggregation problem, we omit the first and last wage of each job spell. Additionally, the last month of the job spell may include severance Notes: Figure 13 shows percentiles of the earnings distribution (Panels (a) and (b)) and measures of earnings dispersion (Panels (c) and (d)) for workers in Argentina's formal sector (Panels (a) and (c)) and informal sector (Panels (b) and (d)), based on household survey data from EPH. Source: EPH, 1996EPH, -2015 payments, so a worker's wage in the last month of a job spell is not necessarily comparable with previous wages. Second, the SIPA dataset features outliers that are incongruent with Argentine labor market policies. Following criteria similar to those in Section 2, we define outliers as the wages of workers who earn less than half of the monthly minimum wage. We drop monthly observations with wages below this threshold. Third, observed wages exhibit slight variations (i.e., cents) in total value (e.g., AR$2,012.75 versus AR$2,013.15) across months, which we discard by rounding monthly earnings to the nearest integer.
The fourth, and most significant, measurement challenge is the presence of transitory deviations from a modal or permanent wage. Theory in the price-setting literature shows that aggregate price flexibility depends on the composition of price changes between those of a transitory or a permanent nature (see Eichenbaum et al., 2011;Kehoe and Midrigan, 2015;Alvarez and Lippi, 2020). In particular, Kehoe and Midrigan (2015) show that aggregate price flexibility depends mainly on price changes that do not revert to their previous nominal value. Intuitively, transitory deviations in prices matter less for aggregate price rigidity as prices revert to their previous value, while the same is not true for permanent changes. For this reason, we distinguish between total wages and "regular" wages and present facts about the latter.

Summary of Methodology.
We construct regular wages within job spells using the Break Test proposed by , which is an adaptation of the Kolmogorov-Smirnov test of the equality of two distributions. The basic idea behind this methodology is to split a wage series into two contiguous subsamples and test whether those subsamples were drawn from the same distribution. The methodology will identify changes in the regular wage series-henceforth referred to as "breaks"-whenever differences between observed wage series before and after a potential break are sufficiently large.
This methodology requires the specification of a threshold value, denoted by K, that determines whether differences in subsamples of wages are large enough to reject the null hypothesis of no break in the series. The appeal of this methodology is that it relies on a single parameter K.
However, there are no standardized critical values to test for this null hypothesis. Therefore, we determine this parameter via a cross-validation exercise based on the estimation and simulation of a structural model of total and regular wage setting. The procedure to determine K follows these six steps: 1. Set up a statistical model for total and regular wages indexed by a vector of parameters θ. Once we obtain a value for K, we apply the Break Test on the actual microdata from Argentina and compute the set of statistics of interest. In addition to the Break Test, we apply three other filters used in the pricing literature to recover regular wages Kehoe and Midrigan, 2015;. Appendix B.4 highlights the advantages of the Break Test over these alternative methods. In addition, we have further analyzed the robustness of our results by computing different critical K values for periods of high and low average inflation.
More specifically, we split job spells according to their start date into two samples: jobs that started before January 2003 and those that started after. Those samples correspond to periods of low and high inflation, respectively. Then, we repeated the same steps described above to each of the two samples. While there are differences in the estimated moments and parameters across periods, we do not find a significant difference in the calibrated critical K values across samples and regular wage statistics analyzed below. 23 The Relevance of Regular Wages. Before documenting our main results, here we show that the dynamics of regular wages capture a significant fraction of the volatility of total wages. Using w t = w T t + w R t , we can decompose the variance of total wages w t as follows: var(w t ) and Paciello (2011) for a similar micro-foundation in the price-setting context. We use moments of total wages suggested by Baley and Blanco (Forthcoming). 23 Table A.5 in the Online Appendix shows the threshold values for the entire sample and the two subsamples. Figures  A.26 and A.27 reproduce Figures 16 and 19, respectively. This decomposition shows that almost 92% of the dispersion in total wages across workers and years is due to the dispersion in their regular wages. Around 6% of the remaining variation stems from the dispersion in transitory wages, while the covariance term captures the roughly 2% remaining variation. Figure 15 presents a similar variance decomposition for 12-month changes in the total wage, ∆w t ≡ w t − w t−12 , and reports the contribution of the variance of the regular and transitory components of wage changes to the overall variance of ∆w t . In periods of low inflation (i.e., between 1996 and 2002), changes in the regular and transitory wage account for 52% and 56% of the overall variation, respectively, with a negative covariance component equal to −9.3%. During the period of increasing inflation after 2002, the contribution of regular wage changes increases to 66%, while that of changes in transitory wages declines to 51%, with a negative covariance term equal to −16.7%. Thus, we conclude that regular wages capture an important component of workers' earnings and their changes, especially in times of high inflation.  Notes: Figure 15 presents the variance decomposition of ∆w t ≡ w t − w t−12 over time, where time t is at the monthly level. The red line with circles shows the variance share due to regular wages and corresponds to var(∆w R t )/var(∆w t ). The blue line with triangles shows the variance share due to residual wages and corresponds to var(∆w t − ∆w R t )/var(∆w t ). Source: SIPA, 1996-2015, and simulations.

Results
This section presents and discusses the main results. We first report the frequency of regular wage changes for the aggregate data under low and high inflation. We then discuss the results across different groups of workers by age, gender, earnings, and sector.

Aggregates
We next provide evidence of the process of regular wage adjustment for the overall population of workers. We present results for the entire period from 1996 to 2015 but also report summary statistics for two subperiods. The first subperiod is from 1997 to 2001, with low annual inflation rates of −0.3% on average. The second subperiod is from 2007 to 2015, with high annual inflation rates of 24.3% on average. We study these periods to focus on the two clear inflation regimes in Argentina while omitting the transition period originated by the 2002 devaluation and the subsequent adjustment of relative prices.  Figure 16, we find that the frequency of wage changes increases with inflation, especially after the large devaluation of the currency and the subsequent (temporary) spike in inflation in 2002. The wide difference between the level of frequencies of wage adjustments pertaining to the high inflation regime (blue circles in the figure) and those corresponding to the low inflation regime (green circles) reflect the relatively high sensitivity of such frequencies to a switch in the inflation regime. Finally, Table A.10 in the Appendix reports the correlation of the frequency of wage changes with inflation, which was 0.67 during the entire sample. However, this correlation is different across inflation regimes: in the low-inflation regime, the correlation was 0.16, while in the high-inflation regime, it was 0.66. This evidence shows strong state dependence of the wage-setting mechanism. 24 24 Figure A.28 in the Online Appendix shows the monthly and annual frequency of total and regular wage changes. A clear pattern holds in the figure; the frequency of annual or monthly wage changes is larger than the frequency of regular wage changes. For example, the monthly frequency of wage changes is around 0.7 during the low inflation period, while the frequency of regular wage changes is 0.13. As in the pricing literature, most wages changes are transitory. For example, Kehoe and Midrigan (2015) shows that the weekly frequency of price change is 0.34, while the Changes in Regular Wages within Job Spells. Despite this sizeable annual frequency of wage changes, it is not the case that in periods of high inflation workers' wages are constantly updated, as the monthly frequency of wage changes increases from 0.09 to only 0.17 across subperiods. To further illustrate this point, Figure A.22 plots the average fraction of months within a year and job spell that experienced a regular wage change relative to the previous month. Before 2002, the average job spell experienced a wage change in 7.5% of the months. For a spell that lasted 12 months, this corresponds to slightly less than a single wage change per year. After 2002, this fraction increased to 14.4%, which means that a worker who kept the same job for 12 months experienced on average slightly less than two wage changes per year.

Seasonality of Changes in Regular Wages.
In addition to affecting how often workers experience wage changes, the level of inflation is associated with different seasonal patterns. Figure   A.23 plots the average frequency of regular wage changes by calendar month for low-and highinflation periods. There are no large seasonal patterns in times of low and stable inflation, except for December, when the average monthly frequency of wage changes is 0.14 (relative to an average of 0.08). Combined with the fact that workers experienced a single change in contractual wages during the year and union bargaining was dormant during this period, this pattern implies that many wage changes reflect idiosyncratic worker-, firm-, or match-level variation, rather than coordinated variation at the time level. Sharper seasonal patterns emerge in times of high inflation, when the monthly frequency of wage changes spikes to 0.35 in June and December, relative to an average of 0.17. This stronger time dependence is consistent with the fact that as inflation increased, unions (i) started playing a more significant role in the adjustment of wages and (ii) were able to negotiate two wage scales within the same contract, with one scale for each six-month period within a year. As a consequence, wage changes became more synchronized and concentrated in July and December. 25 Figure 18 shows the annual frequency of wage increases and decreases. We find that the frequency of upward (downward) wage changes significantly increases (falls) with inflation, from an average of 0.44 (0.20) during the low-inflation period to an average of 0.90 (0.05) during the high-inflation period. As expected, at high inflation rates, weekly frequency of regular price change is 0.029. Similarly,  shows that the monthly frequency of price change is close to one at a monthly frequency, and it decreases to 0.12 for the regular prices. 25 Sigurdsson and Sigurdardottir (2016) find a similar time-dependence pattern for Iceland, with half of the wage increases concentrated in January because of union settlements, while the remaining wage changes were distributed over the year.  The blue line shows least-squares, fitted values for the frequency of 12-month regular wage changes against log(π t ), for π t > 1, and against (π t − 1), for π t ≤ 1. π t is the annual percentage change in the consumer price index. frequent wage increases become the norm, while wage cuts become very rare. 26 26 Figure A.29 in the Appendix plots the frequency of 12-month upward and downward regular wage adjustments against annual inflation. Consistent with Figure 18, we find that both frequencies are highly sensitive to the change in the inflation regime, with the frequency of upward (downward) wage changes significantly increasing (decreasing) between low-and high-inflation regimes. Figure A.29 also shows that the two estimated frequencies notably change In addition to the comovement with inflation, these series seem to respond to the business cycle. This comovement is particularly true during the slowdown in economic activity in 1998 that precipitated the large recession in 2001-2002, when the frequency of wage increases fell from a peak of 0.47 in March 1997 to 0.36 in April 2002. During that same period, the frequency of wage decreases sharply rose from 0.17 to 0.29. It is worth noting that there is a spike in nominal wage cuts before the big drop due to the fact that Argentina entered a recession before the inflation spike-see Figure 1. Notes: Figure 18 shows the frequency of 12-month upward and downward regular wage changes. The shaded area shows the annual percent change in the consumer price index. Decomposition of Wage Inflation. Next, we quantify the relative importance of fluctuations in the frequency of wage changes (i.e., the extensive margin) and the average wage changes (i.e., during the transition period, where we observe high (low) levels of the frequency of upward (downward) wage changes associated with relatively low levels of inflation. 27 Figure A.30 in the Appendix plots the magnitude of regular wage changes against price inflation, including lags of 3, 6 and 12 months for price inflation. In addition to the positive relationship between wage inflation and price inflation, the figure illustrates the improvement of the fit when we include lags for price inflation, especially so during the transition period after the 2002 devaluation and the subsequent adjustment of relative prices. the intensive margin). Following Alvarez, Beraja, Gonzalez-Rozada and Neumeyer (2019), we decompose the average aggregate regular wage change as

Direction of Changes in Regular Wages.
whose variance can be decomposed as The variables Freq  Figure 19 displays the distribution of 12month non-zero regular wage changes across inflation regimes. 28 During the low-inflation period, we find patterns similar to those described in the previous literature despite a 20% drop in output.
First, there is a large spike at zero (omitted from the figure) as 36% of workers do not experience a wage change between t − 12 and t. Second, the distribution is asymmetric: the distribution concentrated 24% of the observations in the [−25%, 0%) range of wage changes, while 48% of the observations fell in the (0%, 25%] range. We also find that during the high-inflation regime, the 28 This exercise is fundamentally different from the statistics presented in the first part of our analysis, which were based on 1-year differences in annualized (residual) earnings. Here, we compute year-on-year changes in regular wages based on monthly earnings. Figure A.20 in the Appendix illustrates these differences. average wage change was similar to the average inflation rate of the period (25%). Also, at higher levels of inflation, the distribution became much more symmetric: the difference between the mass of workers in the [0%, 25%) range of regular wage changes and the mass in the (25%, 50%] range was only 4 percentage points (p.p.), much smaller than the difference of 24 p.p. during the period of low inflation. Thus, higher inflation allows for a higher prevalence of wage cuts in real terms. Low inflation (1997)(1998)(1999)(2000)(2001) High inflation (2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) Notes: Figure 19 plots the distribution of 12-month regular wage changes under low-and high-inflation regimes (1997-2001 and 2007-2015, respectively).

Heterogeneity across Worker Subgroups
The literature that studies price setting has documented considerable heterogeneity in the frequency of price changes across goods (see, e.g., Bils and Klenow, 2004;Nakamura and Steinsson, 2008). Next, we show that while the broad aggregate patterns are prevalent in the overall population, there is also significant heterogeneity in wage adjustment processes across different groups of workers. Figure 20 plots the 12-month frequency of regular wage changes by age, earnings, gender, and sector. In the Online Appendix, Figure A.25 plots the evolution of the average 12month regular wage increases, and Table A  Heterogeneity by Age. We present results for four groups of workers at different points of their lifecycle: workers who are 26, 35, 45, and 55 years old. 29 Several interesting patterns are worth noting. Regardless of the inflation regime, we find that the frequency of wage changes falls with age, especially during the low-inflation period. During this period, the annual frequency was 0.65 for the youngest workers and 0.59 for the oldest workers. However, with high inflation, these differences almost vanish-the frequencies of wage changes increased to 0.95 and 0.94 for these workers.
We also find that, regardless of the inflation regime, average wage increases fall with age. For example, during the low-inflation period, the average regular wage increases for these four groups 29 Since we focus on the frequency of 12-month wage changes and restrict the sample to workers who are between 25 and 55 years old, for the youngest group, we report results for workers who are 26 years old. of workers were: 15.6%, 14%, 12.5%, and 11.7%. In contrast, there are no similar differences across groups in the average regular wage decrease.

Heterogeneity by Earnings.
To analyze the process of regular wage changes by earnings, in each month, we first sort workers according to their average monthly earnings in the preceding 24 months. Then, we group workers by deciles of this earnings measure. Our first finding is that the frequency of wage changes falls with earnings: throughout the entire period, the average annual frequency of regular wage changes for workers in the first and last decile was 0.85 and 0.81, respectively. This difference was more pronounced in the low-inflation period, when the gap in the frequency between workers in the 2nd and 10th deciles was 11 p.p. This gap persisted in the high-inflation period, although smaller in magnitude (4 p.p.). In addition, the comovement between the annual frequency of regular wage changes and inflation also differs across the earnings distribution: in both the low-and high-inflation periods, the correlation between these variables is increasing in earnings.
Workers at the top of the earnings distribution not only had more rigid wages but also experienced wage increases at a lower rate. During the low-inflation period, the probability of a wage increase conditional on a wage change was 0.64 for workers above the median of the earnings distribution, 10 p.p. lower than the probability of a wage increase for workers at the bottom half of the distribution. This difference completely vanished in the high-inflation regime.
Regarding the average size of wage changes, we find an inverted U-shape pattern for average wage increases, especially during the low-inflation regime. According to this pattern, workers in the 1st, 3rd, and 10th earnings decile experienced average wage increases of 12.9%, 7.5%, and 17.1%. A relatively similar pattern is found for the average wage decrease, albeit with a more compressed differential and in the low-inflation period only.
Heterogeneity by Gender. Differences in the wage-setting mechanism between men and women are among the smallest found in the heterogeneity analysis. The average frequency and size of wage changes are virtually the same. There are only two noteworthy differences. First, the probability of an increase conditional on a wage change was higher for women in the low-inflation period (0.74 vs. 0.67 for men). During the same period, the frequency of wage changes for men exhibited a larger correlation with inflation than the one for women (0.53 and −0.12, respectively).

Heterogeneity by Sector.
Although trade unions' presence is ubiquitous in the Argentine labor market, we find substantial heterogeneity in wage-setting processes across sectors. In the interest of space, we present results for a subset of industries representing the degree of potential heterogeneity: agriculture, manufacturing, construction, trade, and education (these sectors capture 57% of formal employment). The most considerable differences in the frequency of regular wage changes manifested in the period of low inflation, when the gap in this measure between the sector with the most flexible wages (agriculture) and the least flexible one (trade) averaged 23 p.p. It is also evident from Figure 20 that a large fraction of this heterogeneity vanished as the economy transitioned into the high-inflation regime. Similarly, the conditional probability of a wage increase exhibits similar differences across sectors. While 79% of wage changes in the agriculture sector were positive between 1997 and 2001, only 58% were positive in the construction sector. Finally, sectoral heterogeneity goes beyond differences in levels during periods of low and high inflation. While some sectors exhibited a large comovement between the frequency of wage changes and inflation (e.g., a correlation of 0.7 in the manufacturing sector), in others, this relationship is more muted (e.g., a correlation of 0.55 in the Education sector). 30 Table A.10 in the Appendix shows the average wage increase by sector, which also exhibits large differences across sectors: while the average increase in the agriculture sector between 1997 and 2001 was 7.1%, the average increase in the Construction sector was 19.6%. As is consistent with results for other workers' groupings, sectoral heterogeneity in the average wage decrease is much smaller (the widest gap between sectors is 2.5 p.p.). However, we do not find any clear relationship between the frequency of wage changes and the size of the increase. For example, the average increase in the construction and education sectors was similar-19.6% and 19.9%, respectively-but the respective frequencies of wage changes were 0.72 and 0.64.

Persistence of Wage Change Regimes
Following Argentina's devaluation and subsequent spike in inflation in 2002, inflation returned to more modest levels for multiple years before starting to trend up again-see Figure 1. In contrast, our estimated (upward and downward) frequencies of regular wage changes in the aggregate and across worker subgroups see a structural break around 2002 but then remain relatively constantsee Figures 16,18,and 20. 31 This raises an interesting question: how can the observation of a temporary spike in inflation be associated with persistent changes in the frequency of regular 30 The latter result highlights the importance of the nature of the labor market for wage setting. Since the education sector operates in an arguably less competitive market, as the government is a large employer in the sector, workers' wages are more insulated from the macroeconomic environment. wage changes? While a fully-specified structural analysis of this question is beyond the scope of the current paper, we want to briefly discuss three candidate explanations for this observation.
The first explanation pertains to a persistent gap between actual and target wages. Due to the high inflation levels of 2002 and initially sticky nominal wages, real wages declined precipitouslysee Figure 3. All else equal, this means that the inflation spike led to greater room for actual wages to increase toward target wages in the future. To the extent that wage changes close only parts of this gap-for example, due to fairness concerns within sectors and employers-a one-off inflation spike could result in an extended period of catch-up between actual and target wages. of earnings inequality coincides with a greater prevalence of centralized wage-setting mechanisms and a significant increase in the minimum wage, among other things. We also document novel facts on wage setting during Argentina's transition from a low-to a high-inflation regime. We find that during the high-inflation regime, the frequency of regular wage changes strongly increased, while exhibiting significant heterogeneity across population subgroups. An interesting avenue for future research is to study the causes of such heterogeneity as well as its macroeconomic consequences.

A.1 Description of Household Survey Data (EPH)
Additional Details on Variable Construction. We first create a dataset at the worker-year level by estimating residual annual earnings based on an aggregation of the (one or two) available observations per worker in each year. 32 Therefore, depending on the individual's appearances in a year, two-quarter or only one-quarter information is used to annualize earnings. We create a variable that identifies the quarter-quarter combinations for individuals within a given calendar year. There are nine possible quarter-quarter combinations: where "Q1", "Q2", "Q3", and "Q4" represent the four quarters of a year and "." represents no matching quarter in the current calendar year.
Next, we transform reported nominal earnings in real terms and in multiples of the prevailing minimum wage. In doing so, we drop observations with average earnings below a thresholdnamely, half the current minimum wage. 33 We then annualize the individual earnings, keeping in mind that the variable of earnings in the quarter of the dataset (labor_income) corresponds to monthly earnings. Annualize differently if individual appears two times or one time in a year. If a given individual appears in two quarters within the same calendar year, then we compute mean real earnings from formal employment as Mean real formal earnings across quarters × Number of quarters working as formal × 6. If a given individual appears in only one quarter within a given calendar year, then we compute mean real earnings from formal employment as Mean real formal earnings in the quarter × 12.
We collapse the data to the individual-year level data with annualized earnings. Note that this means that all quarter-pair observations for a given individual will be collapsed to one observation per calendar year. Sample weights in the survey for up to two quarters are averaged to yield a yearly individual sample weight. Age is rounded up if it changes during the two quarter observations. The collapsed data contain around 70% of the number of observations compared with before, as shown in the last column of Table A.3. Finally, we construct earnings residuals by estimating the following earnings equation for all individuals i of gender G(i) = g and age A(i, t) who appeared in a quarter-quarter combination ("season") S(i, t) in year t separately by gender and year, taking into account yearly individual sample weights: where ε it denotes the earnings residual of interest, log y it is log earnings, α gt is a gender-yearspecific intercept, β gtA is a gender-year-age-specific coefficient on the age indicator 1[A(i, t) = A ], and γ gtS is a gender-year-season-specific coefficient on the season indicator 1[S(i, t) = S ].
Additional Summary Statistics. Table A.1 shows the number of observations in each year-quarter in the raw data.  Table A.2 shows quarter-quarter combinations for the same individual within a given year, based on the rotating panel structure of the EPH household survey data.
Finally, Table A.3 shows the number of observations as we cumulatively apply our selection criteria starting from the raw data.

(b) Selected Income Shares
Notes: Using raw earnings in levels and the CS sample, Figure A.5 plots the following variables against time for the overall population: (a) the share of aggregate income going to each quintile, (b) the share of aggregate income going to the bottom 50%, and top 10%, 5%, 1%, 0.5%, 0.1%, 0.01%. All income shares are normalized to 0 in the first available year. Shaded areas indicate recessions.

(f) Women
Notes: Using residual 1-year earnings changes and the LS + sample, Figure A.14 plots the following variables against permanent income quantile groups for the three age groups: (a)

B.1 A Statistical Model for Total and Regular Wages
The statistical model for total wages is defined at the job-spell level. Total wages are the sum of two components, a transitory wage w T t and a regular wage w R t , so that w t = w T t + w R t . The transitory component captures small deviations or significant but short-lived deviations around a regular wage. The evolution of the regular wage follows a model that combines elements of a fixed cost model (Barro, 1972) and a Taylor model (Taylor, 1980) with unit root shocks to the optimal static wage. We now describe the mathematical formulation for an individual worker. 34 Time is discrete and denoted by t. We normalized time so that the second month of a job spell corresponds to t = 0. Let w * t be a worker's target nominal wage that follows a discrete-time random walk with drift, where η t iid ∼ N (0, σ η ) with its initial value normalized to zero, i.e., w * 0 = 0. Here, π t captures the monthly wage inflation rate, which we construct in two steps. First, we extract monthly seasonality from observed wage-inflation series using a linear regression with calendar-month dummies. Second, we regress these seasonally adjusted changes in wages on a set of age, sector, and gender dummies in addition to time fixed effects. We then recover π t as the predicted time fixed effects from this specification.
With the target wage in hand, we construct the wage gap asw R t = w R t − w * t . We assume that the regular wage is changed whenever the wage gap hits an upper or lower trigger or if the last regular wage adjustment occurred more than T periods before. Under these assumptions, the joint stochastic process of the wage gap and the time elapsed since the last adjustment of the regular wage, denoted by a, follows Here, z t is an auxiliary variable andw − andw + denote the lower and upper bounds of the wage gap that trigger an adjustment of the regular wage, respectively. We assume that the initial regular wage is equal to the target nominal wage; thus, (w R 0 , a 0 ) = (0, 0). Fluctuations in the wage gap come from variations in the nominal target or wage shocks η t . During periods of adjustment in the regular wage,w R t − z t captures the regular wage change. Thus, The transitory component of total wages is modeled as the sum of random transitory deviations across months, denoted by γ t , and another random deviation that captures the payment of 34 See Caballero and Engel (1993) for the original formulation of defining the probability of adjustment using an optimal static target and its application to producer-level employment. See Alvarez et al. (2011) for a micro-foundation in a price-setting context and Baley and Blanco (Forthcoming) for capital producer-level investment. the 13th salary, denoted by φ t . Formally, w T t = γ t + φ t , with γ t ∼ N (0, σ γ ) with probability β 0 with probability 1 − β , and φ t is drawn from a Normal distribution with mean m φ and variance σ φ in June and December and is zero otherwise.

B.2 Model Estimation
We use the simulated method of moments (SMM) to estimate the parameters of the stochastic process of (w R t , w T t ). We match moments of the wage-change distribution at the two-digits sectoral level to account for the pervasive heterogeneity in wage behavior across sectors. Table A.4 reports the estimation results (from rows 1 to 14) for the manufacturing and trade sectors and the average across sectors weighted by sectoral employment. Tables A.5 to A.8 in the Appendix B.6 report the same statistics for all the sectors in the economy.
The set of targeted moments includes the monthly and annual frequencies of wage changes and moments of the distributions of 1-month and 1-year wage changes. Intuitively, moments of the 1-month wage change distribution discipline the dispersion and frequency of transitory changes of total wages, while moments about the distribution of 1-year wage changes inform parameters affecting the regular wage. We select the 1-year moments suggested by the theory in Baley and Blanco (Forthcoming) as sufficient statistics for aggregate wage flexibility (see Corollary three). More specifically, we choose moments reflecting the size (i.e., frequency, mean, and standard deviation of 1-year wage changes) and dispersion (i.e., the third-order coefficient of variation) of wage changes. Intuitively, the size of wage changes identifies the variance of permanent worker-level shocks and the total wage change frequency due to Taylor or fixed cost adjustments. The dispersion of wage changes identifies the composition of the wage change frequency due to wages hitting the adjustment trigger or reaching the maximal date before adjustment.
The statistical model is able to generate the wage-setting patterns observed in the data within sectors. The outcome of the estimation reveals a highly asymmetric adjustment policy toward wage increases for the regular wage. Finally, note that despite the fact that the frequency of total wage changes is 80% in the data (see the row labeled "Share zero 1-month ∆w"), the frequency of regular wage changes is around 10% in the model.

B.3 Regular Wage Construction
In the last step of the measurement exercise, we apply the Break Test to simulated data from the estimated model to compute the model-implied frequency of regular wage changes. We relegate a formal description of the Break Test algorithm to Appendix B.5 and present the main intuition here. The method follows an iterative approach. First, it starts by assuming that there is no break in the wage series within a job spell. Under this assumption, it computes the maximum distance across two sub-series defined by all possible breaks (i.e., by all the dates in the series). If that maximum distance is larger than the threshold K, then the method adds a new break at the date in which the distance is maximized. The method continues these iterations within each resulting sub-series until the maximum distance across all breaks is less than K. Once all the breaks have been identified, we construct the regular wage as the median wage in between breaks and the frequency of regular wage changes as the fraction of regular wages that changed between t − 1 and t. Finally, we calibrate K to match the (known) monthly frequency of wage changes in the model. Table A.4 reports the calibrated values for K. The estimated K ranges from 0.38 to 0.51 across sectors, with a mean of 0.47 across sectors. For comparison, Stevens (2020) recovers K = 0.61 from weekly data on grocery store prices. By construction, the Break Test generates the same modelimplied frequency as regular wage changes. The last two rows evaluate the accuracy of the Break Test. If in the model there is no break in period t, the test correctly identifies no change in regular wages with a probability of at least 0.9. As we show below, most wage changes are concentrated in June and December, two months with particularly large transitory shocks due to the payment of the 13th salary. For this reason, the method cannot always accurately identify the exact date of the break. Intuitively, there is no useful information for the test if a break occurs during months of large transitory shocks. Therefore, the last row of Table A.4 reports the probability of correctly identifying changes in regular wages in a two-month window around an actual change, which is equal to 0.81 across sectors. Panels (a) and (b) of Figure 14 show the log regular wage (blue lines) for Diana and Mario. Inspection of the figures, together with the results of the structural model, suggests that while the break test is not perfect, it captures well the theoretical notion of a regular wage in the data and in the simulated data.

B.4 Robustness
In the paper, we provide a set of facts that rely on the Break Test for the construction of regular wages. Here, we highlight the advantages of this test over three other methods commonly used in the literature (see , for a similar discussion using price data). In particular, we construct series of regular wages following three alternative methods proposed by Nakamura and Steinsson (2008), Kehoe and Midrigan (2015), and . Based on model simulation and inspection of the raw data, we find that the Break Test performs better in constructing series of regular wages- Figure  In addition, we have further analyzed the robustness of our results by computing different critical K values for periods of high and low average inflation. More specifically, we split job spells according to their start date into two subsamples: jobs that started before January 2002 and those that started after. Those samples correspond to periods of low and high inflation, respectively. Then, we repeated the same steps described above to each of the two samples. While there are considerable differences in the estimated moments and parameters across periods, we do not find a significant difference in the calibrated critical K values across samples and regular wage statistics analyzed below. 35 The reason for this result is that there is no significant change in the stochastic process for transitory shocks across periods.
2. Set f t = ∑ L KM j=−L KM I(w t+j non missing, w t+j = w m t )/(2L KM ), where Otherwise .
3. Define w r t with the recursive algorithm 4. Repeat the following algorithm five times: Here, R denotes periods of changes in regular wage: C denotes periods with regular wages: and P denotes periods where the last wage was regular: Blanco (2020) Method. The method drops wage changes with two properties: (i) wage changes preceded and followed by the same wage and (ii) inverse V-shaped wage changes. This method depends on three parameters: K B , P B , and E B . Here, K B describes the number of periods to drop wages changes for wages when they are preceded and followed by the same wage, P B denotes ignored small wage changes, and E B denotes the minimum size to drop an inverse V-shape wage change.
The method works as follows: Observe that t * ∈ F K ⇐⇒ t * + K ∈ F K .
3. Replace ∆w t = 0 for all dates between t * and t * + K, where t * ∈ F K . If K < K B , go to step 1 and set K = K + 1. If K = K B , go to step 3.
4. Replace ∆w t if ∆w t > E B and ∆w i,t+1 < −E B .   (1997)(1998)(1999)(2000)(2001) High inflation (2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) Notes: Panel (a) of Figure A.20 plots the distribution of 12-month regular wage changes within jobs in the low-and high-inflation regimes (i.e. 1997-2001 and 2007-2015, respectively). Panel (b) plots the distribution of 12-month regular wage changes within and across jobs in both regimes. Panels (c) and (d) repeat panel (a) and (b) for total wages. Panels       Notes: Figure A.27 plots the distribution of 12-month regular wage changes under low-and high-inflation regimes (1997-2001 and 2007-2015, respectively). The solid lines plot the distribution of regular wage changes using only one K and the dashed lines plot the distribution of regular wage changes with a K with high and low inflation.  Freq. of 12-month wage increase Freq. of 12-month wage decrease Notes: Figure A.29 plots the frequency of 12-month upward and downward regular wage changes against the annual percentage change in the consumer price index. The blue circles show the frequency of upward changes, while the red squares represent the frequency of downward adjustments. Blue and red lines show least-squares, fitted values for each frequency against log(π t ), for π t > 1, and against (π t − 1), for π t ≤ 1. π t is the annual percentage change in the consumer price index.

(d) 12-month Lags for Inflation
Notes: Figure A.30 plots the average magnitude of 12-month regular wage adjustments against the annual percentage change in the consumer price index. Panel (a) shows the contemporaneous relationship between regular wage inflation and price inflation. Panels (b) to (d) plot regular wage inflation against lags of 3, 6, and 12 months for price inflation. Lines are least-squares, fitted values for the magnitude of 12-month regular wage adjustments against log(π t−j ), for π t−j > 1, and against (π t−j − 1), for π t−j ≤ 1. π t−j is the annual percentage change in the consumer price index at month t − j, for j = 0, 3, 6, and 12.  (1997-2001 and 2007-2015, respectively) and the aggregate and different groups of workers (i) the average frequency of 12-month regular wage changes, (ii) the conditional probability of an increase-i.e., the share of changes that are increases calculated as freq. of increase / (freq. of increase + freq. of decrease), (iii) the average size of annual regular wage increases and decreases (in absolute terms), and (iii) the correlation of the annual frequency of regular wage changes with annual inflation.