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October 21, 2022
Viewing the Wage Growth Tracker through the Lens of Wage Levels
One of the most popular features of the Atlanta Fed's Wage Growth Tracker is its depiction of median year-over-year wage growth of four different wage levels (wage quartiles). Unfortunately, the sample size of each quartile for a month is quite small, and thus the median wage growth for each quartile is noisy. For that reason, the Tracker shows changes by wage quartile only as a 12-month moving average. However, although the averaging smooths out a lot of the month-to-month noise in the series, it also means that the series have a substantial lag in showing wage growth changes across quartiles.
Instead, I have produced a cut of the wage growth data by wage level that can show a three-month moving average, which gives a better near-term picture of wage growth trends. The restriction, however, is that rather than using four wage groups, I put the average wage-level data (that is, the average of a person's reported wage in the current month and their reported wage a year earlier) into two groups: those whose average wage is above the median and those whose average wage is below the median. Essentially, I split the distribution of average wages in half.
Chart 1 plots the resulting three-month moving average of the two groups' median wage growth.
As you can see, median wage growth has been elevated since 2020 for workers across the wage distribution. But for workers in the bottom half of the wage distribution, median growth has been especially high during the last year. High wage growth for lower-paid workers aligns with numerous anecdotal reports suggesting that worker shortages since the pandemic have been especially acute in industries that pay below-average wages, such as leisure and hospitality.
Chart 1 allows another interesting observation: in the years leading up to the pandemic, the median wage growth of those in the lower half of the wage distribution was typically a bit above those in the upper part of the distribution. This was a period when the labor market was also tight, although much less so than it is today. Chart 2, which shows the sum of employment and job openings relative to the size of the available labor force, makes clear the divergence in the degree of overall labor market tightness today versus prior to the pandemic.
By this measure, though the gap has narrowed a bit in recent months, labor demand remains well above its supply, and this gap has been putting upward pressure on wages across the spectrum.
The Wage Growth Tracker series for the two wage groups is available now in the downloadable spreadsheet here and will be updated with October data after the Current Population Survey micro data for October is released, which usually occurs about a week after the US Bureau of Labor Statistics issues its labor report.
October 20, 2022
The Atlanta Fed's Early Career Visitor Program Workshop: A Synopsis
On September 9, 2022, the Federal Reserve Bank of Atlanta hosted the Early Career Visitor Program Workshop, organized by Salome Baslandze, Simon Fuchs, Indrajit Mitra, and Veronika Penciakova. The purpose of the program is to offer early- and mid-career researchers the opportunity to spend several months visiting the department. The program, an innovative addition to the existing landscape of offerings across the Federal Reserve System, provides a unique opportunity for researchers in the early part of their careers to spend some time at a regional Reserve Bank, and for Atlanta Fed's Research Department to strengthen ties with new generations of policy-oriented economists. The program also supports our policy-making process by keeping us in touch with new theoretical, quantitative, and empirical methods in the profession. The workshop brought together participants in the Atlanta Fed's 2021 Early Career Visitor Program with an aim to foster active exchange and discussion among economists on a wide range of topics. Tao Zha from the Atlanta Fed opened the conference by welcoming the participants. He talked about our unprecedented times and the challenges policymakers face in light of high inflation, government debt, and ongoing macroeconomic shocks. He also discussed the importance of high-quality research in informing policymakers.
Yuhei Miyauchi from Boston University presented his in-progress research (coauthored with with Elisa Giannone, Nuno Paixão, Xinle Pang, and Yuta Suzuki) titled "Living in a Ghost Town: The Geography of Depopulation and Aging." This project explores the dynamics of aging and depopulation across different regions within a country and how this process affects welfare across regions and generations. Using spatially disaggregated data from Japan for the last 40 years, he documents that depopulation and aging have progressed more rapidly in less populous areas. This empirical pattern is primarily driven by the youths' net outmigration. Motivated by this evidence, the author develops a dynamic life-cycle spatial equilibrium model of migration decisions. The model matches the historical spatial population changes in Japan and projects future spatial patterns of depopulation and aging. A key take-away from this project is that abstracting from endogenous migration decisions over the life cycle and their effects on local economies substantially biases the projected spatial patterns of demographic changes and welfare.
Wookun Kim from Southern Methodist University presented his joint work with Changsu Ko and Hwanoong Lee, "Heterogeneous Local Employment Multipliers: Evidence from Relocations of Public Entities in South Korea." The authors exploit a variation in public-sector employment from an episode of the relocations of public-sector entities and estimate local employment multipliers. The estimated multiplier is positive and persistent over time: an introduction of one public sector employment increases the private sector employment by one unit, with employment growth in the services sector driving this increase in private sector employment. The authors document that the effect of public employment on private employment is highly localized. In addition to changes in private employment, the relocations of public-sector employees led to a positive net inflow of residents into the treated neighborhood. Examining the variation in the extent of public employment shock across different relocations, the paper identifies heterogeneous local employment multipliers and provides evidence that the extent of public sector shocks and different types of relocation shape this heterogeneity. Their results imply that local employment multipliers tend to be higher in areas with predetermined characteristics that allow faster and larger general equilibrium responses to take place after the public sector shock.
Maya Eden from Brandeis University presented her work titled "The Cross-Sectional Implications of the Social Discount Rate." In her research, Eden asks, how should policy discount future returns? The standard approach to this normative question is to ask how much society should care about future generations. The author establishes an alternative approach, based on the social desirability of age-based redistribution. The social discount rate is below the market interest rate only if it is desirable to increase the consumption of the young at the expense of the old. Along the balanced growth path, small deviations of the social discount rate from the market interest rate imply large welfare gains from redistributing consumption across age groups.
Boyoung Seo from Indiana University presented her work, "Racial Differences in Prices Paid for Same Goods," coauthored with Andrew Butters and Daniel Sacks. The authors document that Black non-Hispanic households pay 2.0 percent higher prices than white non-Hispanic households, and Hispanic households pay 0.8 percent higher prices for physically identical products. This difference suggests that conventional measures of racial income differences understate real racial income inequality. Differences in income, demographics, or education do not explain the racial price gap. Instead, it is entirely explained by three factors: Black non-Hispanic and Hispanic households buy smaller packages with higher unit prices, benefit less from coupons, and live in places where prices tend to be high. The place-based price differences appear driven not by supermarket presence but by differences in carrying and transportation costs.
Abdoulaye Ndiaye from New York University presented "Bonus Question: How Does Incentive Pay Affect Wage Rigidity?," a paper coauthored with Meghana Gaur, John Grigsby, and Jonathan Hazell. Wage rigidity occupies a central role in models of macroeconomic fluctuations. However, recent work shows that wage rigidity is not sustained in equilibrium with appropriately calibrated idiosyncratic shocks. Indeed, individual wages frequently adjust in response to both idiosyncratic and aggregate shocks in the data. Many of these fluctuations result from movements in nonbase compensation such as bonuses, which most existing models are ill-equipped to study. The authors study whether and how flexible incentive pay affects macroeconomic fluctuations. They develop a general model of dynamic contracting, in which firms offer contracts to workers to give them incentives to supply costly effort that is otherwise unobservable by the firm. In this class of models, the first-order response of firm value to exogenous shocks is summarized by the direct effect of the shock on firms' objective function and constraints—the envelope theorem, which examines the effects of changes in certain variables, would hold that the indirect effects of the shock on wage payments and effort are not value-relevant. The authors consider the implications of this result both theoretically and quantitatively for the two fields that most commonly rely on wage rigidity to generate macroeconomic fluctuations: labor search and New Keynesian business cycle theory.
Yu Xu from the University of Delaware presented his work, titled "Ambiguity and Unemployment Fluctuations" and coauthored with Indrajit Mitra. The authors analyze the consequences of ambiguity aversion in the Diamond-Mortensen-Pissarides (DMP) search and matching model. Their model features a cross-section of workers whose productivity is the sum of an aggregate component and a match-specific component. Firms are ambiguity averse towards match-specific productivity. The model delivers two insights. First, ambiguity aversion substantially amplifies unemployment rate volatility. Second, a part of the high value of leisure required by the canonical DMP model to generate realistic unemployment rate volatility can arise from fitting a model missing ambiguity aversion to data generated in an environment where agents are ambiguity averse.
The workshop organizers hope that participants found the diverse array of presentations thought provoking as they progress in their careers as researchers, and that the discussions contributed to their professional and intellectual development.
July 13, 2022
Rounded Wage Data and the Wage Growth Tracker: An Update
In an earlier Policy Hub: Macroblog post, I noted that the US Census Bureau had announced that it planned to make changes to the Current Population Survey Public Use File (CPS PUF). Those changes, part of the Enhanced Disclosure Protection program, included the rounding of the reported wage data in a way that would have a dramatic impact on the usefulness of the Atlanta Fed's Wage Growth Tracker.
The Census Bureau subsequently revised its plans and has proposed a different rounding method described here, to be introduced in February 2023 . This Macroblog post looks at the new method's potential impact on the Wage Growth Tracker. It also considers another of the Census Bureau's other proposed changes to the CPS PUF.
So, for example, $19.99 an hour would become $20, whereas $19.95 an hour would be unchanged. Also, $999 a week would be rounded to $1,000, while $995 would be unchanged.
How much impact would this revised scheme have had on the Wage Growth Tracker if it had been used in the past? The following chart plots three versions of the Wage Growth Tracker time series. The blue line is the published Wage Growth Tracker using unrounded data. The gray line is the Tracker based on the original proposal and described in the earlier Macroblog post. The orange line is the Tracker based on the revised rounding rules. The following table summarizes the current proposed rounding rules:
The chart makes clear that the impact on the Wage Growth Tracker under the current proposed method for rounding is much smaller than the original proposal. While the revised method holds some impact, the basic time series properties of the historical Wage Growth Tracker remain largely intact. The largest difference between the Wage Growth Tracker based on the current proposal and the Tracker computed using unrounded wage data is 0.13 percentage points, the average difference is −0.002 percentage points, and the mean absolute difference is 0.03 percentage points.
No approach is perfect, though, and one quibble I have with the current proposal is that the rounding schemes for reported hourly and weekly wages are not very consistent. For example, for someone who usually works 40 hours a week (the most commonly reported workweek), rounding an hourly wage less than $20 to the nearest $0.05 should be the same as rounding a weekly wage less than $800 to the nearest $2. But the current proposal rounds a weekly wage less than $800 to the nearest $5 instead. For someone reporting a wage of between $20 and $39.99 an hour, the proposed rounding to the nearest $0.25 equates to rounding a 40-hour weekly wage between $800 and $1,599 to the nearest $10. However, the current proposal rounds a weekly wage between $800 and $1,000 to the nearest $5, and a weekly wage above $1000 to the nearest $25. Finally, for someone reporting an hourly wage of $40 or more, the proposed rounding to the nearest $0.50 equates to a 40-hour weekly wage of $1,600 or more rounded to the nearest $20. But the proposal rounds a weekly wage of $1,600 or more to the nearest $25.
The preceding analysis suggests that a more consistent method would be to round a weekly wage less than $800 to the nearest $2, a weekly wage between $800 and $1,599 to the nearest $10, and a weekly wage above $1,600 to the nearest $20.
This alternative rounding method reduces the impact on the Wage Growth Tracker series relative to the current proposal by about one-third. Specifically, the mean absolute difference between the unrounded Tracker series and the series based on the currently proposed rounding scheme is 0.03 percentage points, versus 0.02 percentage points using my alternative. The largest difference is 0.09 percentage points, and the average difference is 0.002 percentage points.
For the CPS PUF, the current proposal has another aspect relevant to the Wage Growth Tracker: the future computation of topcoded earnings data. Currently, a threshold hourly wage that varies with hours worked is used to determine if an hourly wage is topcoded. For weekly earnings the threshold is $2884.61 ($150,000 a year). However, these threshold values have not changed since 1998, and because of generally rising nominal wages over time this has led to the topcoding of more wage observations each year (see here for more discussion of this issue). The Wage Growth Tracker's calculations exclude topcoded wage values because their inclusion would be computed as zero wage change—artificially pulling median wage growth lower.
The current proposal would instead compute a dynamic topcode value that varies in a way that would result in the top-coding of only the highest 3 percent of earnings each month. Although that change means more observations to use to compute the Tracker, those observations will come from a part of the wage distribution that might exhibit quite distinct wage growth properties. For example, wage growth tends to be lower for people at the end of their careers than at the start, and if the highest wages are mostly from people with relatively low wage growth, median wage growth could be pulled lower. Unfortunately, without access to the historical wage data that are not topcoded, constructing a counterfactual to explore the impact of this proposed change is simply not possible. Perhaps someone at the Census Bureau will explore the impact this change has on the properties of the wage growth distribution.
The Census Bureau is seeking comments on the Enhanced Disclosure Protection proposals through July 15, 2022. If you have any suggestions on any aspect of the proposal, send an email to ADDP.CPS.PUF.List@census.gov. I will be sending them a copy of this post for their consideration.
February 3, 2022
Rounded Wage Data and the Wage Growth Tracker
The US Census Bureau recently announced some changes it plans to make this year to the Current Population Survey Public Use File (CPS PUF). Here at the Atlanta Fed, we use data from the CPS PUF to construct the Wage Growth Tracker, and one of the planned changes will significantly affect the tracker. Specifically, a person's usual weekly or usual hourly earnings, which are unrounded currently, will be rounded.
The Wage Growth Tracker bases its results on the median, or middle, observation in the distribution of percent wage changes for a sample of individuals linked between the current month and the same month a year earlier. The Wage Growth Tracker time series has yielded useful insight into the rapidly shifting dynamics of the labor market in the wake of COVID-19, especially as compositional effects have distorted wage data. It's also helped economists and policymakers understand which income levels were seeing the greatest growth and that job switchers were finding the most wage gains.
How will the rounding of wage data affect the Wage Growth Tracker? The announced CPS PUF rounding rules vary by wage level and are different if the earnings are reported on an hourly or weekly basis. (You can see more details here .) Most people in the CPS report earnings on an hourly basis, and most wage observations range from $10 to $99.99 an hour. Under the rounding rules those earnings will be rounded to the nearest dollar. So, for example, if someone reports making $14.50 an hour, that wage will be rounded to $15, while workers reporting a wage of $15.40 an hour will also have that wage rounded to $15.
One implication of the rounding rules is that it will make no wage change appear more common than it currently is. To illustrate, suppose someone's pay went from $14.50 to $15.40 an hour. The rounding rules would show no change in the person's wage (both would be recoded as $15) even though that person's actual wage increased by 6.2 percent. Chart 1 shows what happens to the proportion of zero wage changes if the rounding rules were applied to the CPS PUF earnings data used to construct the Wage Growth Tracker from 1998 to 2021.
As you can see, during the Great Recession, when labor demand was especially weak, about 17 percent of wage growth observations based on unrounded earnings data were zero. But if the rounding rules had been applied back then, more than 25 percent of wage growth observations would have been zero.
Obviously, this change is a big deal for the Wage Growth Tracker. When more than a quarter of the observations are zero near the middle of the wage change distribution, it is very likely that the median observation will also be zero. This effect is evident in chart 2, which compares the median Wage Growth Tracker series using unrounded earnings data with what it would have been if the rounded data had been used.
Clearly, if the rounding rules had been in place in the past, the Wage Growth Tracker time-series would be a much less useful indicator of wage growth or labor market trends.
So, what to do? It turns out that the rounding rules don't affect all summary measures of wage growth as much as they affect the median measure. For example, as chart 3 shows, the mean—or average—wage growth comes out of the rounding changes essentially unaffected.
Unfortunately, not only is the average higher than the median, because wage growth varies greatly across individuals (the monthly sample standard deviation is typically around 25 percent), you can also see that both of the average wage growth series are much more variable month to month than the median series using unrounded data. Indeed, the robustness to variability in the underlying wage change data is a primary reason why the Atlanta Fed's Wage Growth Tracker is based on median rather than average wage growth.
But there is potential solution. Borrowing from the research on using trimmed means of price change data to construct measures of inflation that are robust to extreme price changes, I was able to construct a trimmed-mean wage growth series using the rounded data that has broadly similar properties to the (median) Wage Growth Tracker series constructed from unrounded data. Specifically, for each month's sample, I excluded the bottom 20 percent of wage growth observations (that is, the largest percent wage declines) and the top 25 percent (the largest percent increases) and computed the average of the remaining data. (Note that the trimming is asymmetric because more of the large wage changes tend to be increases than decreases, which is also why the average is higher than the median in the previous chart.)
Chart 4 shows the trimmed-mean series constructed using rounded earnings data, along with the (median) Wage Growth Tracker series that uses unrounded data. I would describe this trimmed-mean series as a reasonable (though not perfect) approximation of the Wage Growth Tracker series (something we could have used if we only had rounded earnings data in the past).
When the January 2022 CPS PUF data become available in February, we will produce the trimmed-mean version of the overall Wage Growth Tracker and add it to the Atlanta Fed's Wage Growth Tracker data set. We are currently exploring if a similar approach will produce useful alternatives to the Wage Growth Tracker for other ways to view the data, such as those for job switchers versus job stayers, or by average wage level. Watch this space for updates.
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