Symmetry approach

To get a quantitative estimate about the extent of downward nominal wage rigidity, then a counter-factual distribution has to be constructed. There are several ways of doing this. One way is to introduce one additional assumption:

A6: The counter-factual distribution of the wage change distribution is symmetric around its median (Beissinger & Knoppik, 2001, p. 392). If other assumptions are also fulfilled, then the right side of the wage change

dis-tribution can be used to derive the shape of the left side of the disdis-tribution. The basic idea behind the symmetry approach is that in a symmetric counter-factual, the right side of the factual distribution can be considered to be the mirror image of left side of counter-factual distribution. Thus it follows that if the probability mass on the left side of the factual is smaller than on the right side of the factual distribution, then this could be considered as a sign of nominal wage rigidity.

The idea was first introduced by Card & Hyslop (1997), who use real wage change distributions as the basis for their example. If the counter-factual probability density function of real wage changes is symmetrical and median centred, then it can be shown that (Card & Hyslop, 1997, p. 85):

= 1 − (2 + ) − (− ) (2–6)

where sut is the fraction of workers affected by downward nominal rigidity at period t, ( ) is factual cumulative distributions function of real wage changes, mt is the median, is the rate of inflation at period t, and − and exclude the mass point at − and (Card & Hyslop, 1997, p. 85). The intuition behind this equation is that if distribution is symmetric then the share of observations below the inflation rate in the distribution of real wage growth should be equal to the share of observations above twice the median plus the inflation rate.

Equation (2–6) and (2–2) are versions of the symmetry approach based respectively on real and nominal wage change distributions. Thus the LSW sta-tistic is also an application of the symmetry approach.

The discussion about the appropriateness of the symmetry approach has been quite intensive (e.g. McLaughlin (1999), McLaughlin (2000), Lebow et al.

(2003)) and it has been used in several papers, mostly in the form of the LSW statistic.

Most of the papers dealing with downward nominal wage rigidity use several methods for assessing the existence and size of wage rigidities. In order to avoid duplication, the following sections will provide a more detailed description of the dataset only if this has not been done in previous chapters.

Card & Hyslop (1997) use the symmetry approach on the US Current Popu-lation Survey data from 1979–1993 and find that during the high infPopu-lation period (1979–1982) downward nominal wage rigidity affected 5.4%–7.3% of hourly rated non-job changers, depending on the year. The estimates for the low inflation period (1983–1993) were between 9.7% and 13.5% (Card & Hyslop, 1997, p. 93).

McLaughlin (2000) uses the data from the Panel Study of Income Dynamics (PSID) from 1971–1992. For all workers the share of people affected by nomi-nal wage rigidity is 7.9% (McLaughlin, 2000, p. 18). Values for selected sub-groups are listed in Table 2.

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Table 2. Symmetry test statistics from Panel Study of Income Dynamics 1971–1992

Subgroup LSW statistic

Textiles, Apparel, & Leather 9.7%

Paper, Printing, & Publishing 7.6%

Chemicals, Petroleum, & Rubber 6.9%

Transportation 6.9%

Communications & Utilities 7.8%

Wholesale Trade 4.3%

Retail Trade, Entertainment & Recreation 11.4%

Finance, Insurance, & Real Estate 6.6%

Business & Repair Services 7.7%

Personal Services 16.1%

Health Services 8.1%

Education 5.9%

Other Professional Services 8.5%

Public Administration 5.6%

Source: McLaughlin, 2000, pp. 18–20

However, it has to be kept in mind that several of the results were not consistent with other indicators of skewness, for example the result for union participation.

Beissinger & Knoppik (2001) use the German micro-data from Institut für Arbeitsmarkt und Berufsforschung Beschäftigtenstichprobe from 1975–1995.

They calculate the LSW indicator and find that a symmetry approach for all workers shows that 4.8% of wage cuts could have been considered as not enacted because of nominal wage rigidity. When they differentiated between workers and salaried employees, the figures were 4.6% and 6.8% respectively (Beissinger & Knoppik, 2001, pp. 399–402).

Dwyer & Kenneth (2000) perform the same kind of exercise on Australian data for 1987–1999 and show that the LSW statistic is 15.75% (Dwyer &

Kenneth, 2000, p. 12).

Kuroda & Yamamoto (2003) analyse Japanese data from 1993–1998 and find the LSW statistic’s value to be 12% for men working full time, when calculated from a full time regular monthly salary. Annual earnings data yielded an LSW statistic of 11%. For women the figure was 7% for both monthly and yearly earnings. However, they did have at their disposal also the wages of part-time female workers and from their hourly wages they found a shortage of wage cuts of nearly 40% when compared with the equivalent part of the right side of wage distribution (Kuroda & Yamamoto, 2003, pp. 24-25).

Lebow, Saks & Wilson (2003) use data from the US Bureau of Labor Statistics’ employment cost index from 1981–1999 and find that the LSW statistic is 13.2% (Lebow, Saks, & Wilson, 2003, p. 11). This is somewhat higher than the results obtained by Lebow in cooperation with other co-authors using the US PSID data from 1971–1988 and showing the LSW statistic for wage and salary earners to be 6.8% (Lebow, Stockton, & Wascher, 1995). Lebow, Saks & Wilson explain the difference primarily with different inflation regimes.

Iregui, Melo, & Ramírez (2009) use Colombian company level registry data filed by companies with the Superintendencia de Sociedades from 1999–2006.

The sample covers 1517 companies for white collar workers and 781 for blue collar. The analysis concentrated on companies where employees had a permanent contract and during the period there was no interruption in the payment of wages. Government employees, the self-employed and people working in micro-companies were also excluded. As a measure of wages, the average wage across companies is used. They conclude that there is a 7.8%

shortage of observations of below zero wage change for blue collar workers and a 7.5% shortage for white collar workers (Iregui, Melo, & Ramírez, 2009).

The assumption of the symmetric counter-factual has received quite heavy criticism, mainly because empirical work seems not to support the hypothesis of symmetry. One way to test this is to search for symmetry near the median.

Assuming that observations above zero are not affected by downward nominal rigidity, meaning there are no menu costs, then the left side of the distribution from zero to median must be symmetric to the right side of the distribution from median to twice the median. If there are menu costs, this test has to be modified so as to exclude observations in the neighbourhood of zero.

Such tests have been performed by several authors (e.g. McLaughlin (1999) for PSID data, Beissinger & Knoppik (2000) for IABS data). If the underlying counter-factual distribution is skewed for reasons other than nominal wage rigidity, then the LSW statistic will overestimate the share of not-enacted wage cuts. Both the articles mentioned here found that the symmetry assumption is not fulfilled.

This leads us to the histogram-location approach, which can also give easily interpreted quantitative estimates of downward nominal wage rigidity and does not use the often criticised assumption of symmetry.

Table 3. Summary of results from the symmetry approach Article Country Survey typeSubjects Obs.Time frame Compensation type used in analysis ResultsConclusion Card & Hyslop (1997) USA Individual survey Job stayers (based on industry and occupation data), no minimum wage earners. ca 25 000 per year 1979– 1993 Hourly workers: hourly wages.

Downward nominal wage rigidity affected between 6.2% and 13.85% of hourly rated job stayers Confirms the existence of DNWR McLaughlin (1999) USA Individual survey

Employed household heads (from 1971) and spouses (from 1979) who reported wage or salary and stayed employed (based on tenure) in the same job 34 633 in total 1971– 1992 Hourly workers: straight time hourly wage; Salaried worker:salary 7.89% shortage of observations of below zero wage change (4.11% shortage when observations of zero wage change are excluded).

Confirms the existence of DNWR. However, the symmetry of the counter-factual is rejected. NB! Author draws different conclusion! McLaughlin (2000) USA Individual survey

Employed household heads (from 1971) and spouses (from 1979) aged 18–70 who reported wage or salary and stayed employed (based on tenure) in the same job, no self- employed34 637 in total 1971– 1992 Hourly workers: straight time hourly wage; Salaried worker:salary Overall 7.9% shortage of observations of below zero wage change.

Confirms the existence of DNWR. However, the symmetry of the counter-factual was rejected. NB! Author draws different conclusion!

Article Country Survey typeSubjects Obs.Time frame Compensation type used in analysis ResultsConclusion Beissinger & Knoppik (2001)GermanyIndividual registry data Job stayers (except women, unpaid family workers, highly skilled workers, civil servants, the self-employed, and employees who do not pay social security contributions) in West Germany aged 25–65 who maintained a job during two consecutive years full time and whose other characteristics remain unchanged.

487 507 observatio ns for workers and 121 458 observatio ns for salaried employees1975– 1995 Gross earnings including fringe benefits (no information on hours worked)

For workers: There is a 4.6% shortage of observations of below zero wage change For salaried employees: There is a 6.8% shortage of observations of below zero wage change All employees: There is a 4.84% shortage of observations of below zero wage change Confirms the existence of DNWR. Lebow et al. (2003) USA Employer survey

Private non-farm sector of the economy (excluding households and the self employed). Data characterizes jobs, not individuals. 5000 per year1981– 1999 Straight-time hourly wage and salary costs, including commissions (does not distinguish between hourly wage and salary). Total compensation excluding legally- required benefits The data are calculated as the average of the workers working in each specific job.

Wages and salaries: There is a 13.2% shortage of observations of below zero wage change Benefits: There is a 9.9% shortage of observations of below zero wage change Total compensation: There is a 8.9% shortage of observations of below zero wage change Confirms DNWR. Overall compensation less rigid than wages and salaries.

Article Country Survey typeSubjects Obs.Time frame Compensation type used in analysis ResultsConclusion Dwyer & Kenneth (2000) Australia Employer survey Data from 700 companies for MCED survey. More than 450 different jobs. The data of workers who did not change job between surveys. Data characterise jobs, not individuals.80 000 all together1987– 1999 Base pay is as annual salary excluding allowances or additional payments. No data on hours worked.

Base pay: There is a 15.5% shortage of observations of below zero wage change

Confirms DNWR. However, assumption of symmetry is violated. Kuroda & Yamamoto (2003) Japan Individual survey

Japanese females residing nationwide and husbands of those females in the sample who are married. Age group 24– 34 Excluding: the unemployed, those working in family businesses, the self- employed, job movers, and workers whose overtime hours changed.1292 per year1994– 1998 Regular monthly salary, annual earnings and hourly earnings Regular monthly salary: There is a 11% shortage of observations of below zero wage change: – men: 12% – women: 7% Annual earnings: – men: 11% – women: 7%Confirms DNWR.

Article Country Survey typeSubjects Obs.Time frame Compensation type used in analysis ResultsConclusion Iregui et al. (2009) Colombia Company level registry data Firms that reported the payment of wages to workers with permanent contracts throughout the period Study excludes the self- employed, government employees, and small- scale companies. Data on company, not individual level.

1517 companies for white collar workers, 781 for blue collar1999– 2006 Companies' average wage by skill types and industry Blue collar: There is a 7.8% shortage of observations of below zero wage change White collar: There is a 7.5% shortage of observations of below zero wage change Confirms DNWR. Wages of blue collar workers are slightly more rigid than those of white collar workers

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