The Smith-Welch decomposition

As was seen in Figure 3, the gender wage gap in Estonia has not remained constant over time, though it has always been at a comparatively high level. It is particularly notable that significant changes have occurred over the business cycle, and during the Great Recession the gender wage gap fell by several percentage points while the subsequent recovery saw it return to its previous levels. In the following section, the nature of those changes will be examined to see how far they were due to changes in the composition of employees in terms of their characteristics and to what extent they were due to returns to those characteristics.

The method used here is that proposed by Smith and Welch (1986, 1989), which goes beyond decomposing the differential between the mean wages of

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two groups in the labour market (in their case blacks and whites) to decom-posing the change in that differential over time.¹¹

The following description of the method is based on the exposition by Jann (2005). Consider the following log-linear model for the wages of individuals belonging to the group ∈ 1,2 at time period ∈ 1,2 :

= ′ + (10)

where is the wage for group g at time t, is the vector of characteristics for that group and time period, and is an error term with ( ) = 0. The difference in log wages between the two groups in a given time period can then be decomposed as

= − = −

= ( − ) + ( − )

+ ( − ) ( − )

= + + = E + C + EC

(11)

where y denotes group mean log wage, x denotes the vector of group means of characteristics, and the d operator denotes differences between the groups. The intergroup differential in the mean log wage is thus decomposed into three components attributable to differences in endowments (denoted E) of pro-ductive characteristics; differences in coefficients (C), or returns (in the Mincer sense) to those characteristics; and the interaction of endowments and coeffi-cients (EC). The first component, E, indicates the part of the wage gap that would arise in the absence of intergroup differences in coefficients, meaning the change in the mean wage of group 2 that would occur if the group attained the level of endowments of group 1. Likewise the second component, C, is due to differences in endowments and represents the change in the mean wage of group 2 that would arise if the latter’s level of endowments were fixed but its coefficients became identical to those of group 1. The third term, EC, is an interaction term reflecting the combined contribution of differences in both endowments and coefficients.

The decomposition in (11) concerned differences between the two groups in a single time period. Looking next at the change in the wage differential from the first period to the second, the difference between the two time periods is expressed as follows:

− = − + −

+ − = + + (12)

11 Although the original application by Smith and Welch (1986) focused on the change of the black-white wage differential over time, the method can likewise be applied to decompositions of wage differentials in different countries, as pointed out by Jann (2005).

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where d is again the time difference operator. The change in the wage differ-ential can thus be expressed as the sum of changes in each of the three components in (11). Note that each of the components is a function of both endowments and coefficients, and thus can in turn be decomposed into components:

= − + ′ −

+ − ′ −

= − + ′ −

+ − ′ −

= − + ′ −

+ − ′ −

(13)

As seen in (13), each of the changes in the components of the wage gap is expressed as three additive components; these are, in order, the change in the component due to changes in endowments, the change due to changes in coefficients, and the change due to the interaction of changes in both endow-ments and coefficients.

The Smith-Welch decomposition is applied to two time periods, looking at how the gender wage gap of 2009 had changed from 2005, and how that of 2014 compared to that of 2009. The time periods are chosen so as to encompass the business cycle, as 2005 preceded the recession, 2009 was during the recession and 2014 was the post-recession period. This enables us to examine the nature of the changes that occurred in the wage gap over the recession and the subsequent recovery.

The results of the decomposition of the change in the gender wage gap from 2005 to 2009 are presented in Table 3. The overall log wage gap was smaller in the recession year than it was before the recession. The largest change in the different components of the wage gap was the decrease in the part of the wage gap attributable to the coefficients of characteristics, i.e. the unexplained gap.

This contrasts with the single-equation estimates (Figure 18 on p. 68) and with the results of the Oaxaca-Blinder decomposition (Figure 19 on p. 69), which do not indicate a decrease in the unexplained part of the gender wage gap. This is probably due to differences in the decomposition method, as the gap here is decomposed into three components – the endowment (explained), coefficient (unexplained) and interactive (both endowments and coefficients) components.

Further, the dE, dC and dEC components of the changes in the original components E and C indicate that changes in both the explained and unex-plained gaps were primarily due to the changes in the coefficients. This indic-ates that the change in the gender wage gap in the recession from the pre-recession period is due to changes in returns to characteristics rather than in the composition of those characteristics among the employed.

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Table 3. Smith-Welch decomposition of the change in the gender wage gap, 2009 compared to 2005.

Decompositions of individual differentials:

D E C EC

2005 2.450 –0.002 2.448 0.004

2009 0.833 –0.009 0.867 –0.026

Difference in (components of) differentials:

–1.617 –0.007 –1.581 –0.029

Decomposition of difference in differentials:

D E C

dE –0.0071 0.0026 –0.0096

dC –1.5808 0.0243 –1.6051

dEC –0.0294 –0.0152 –0.0142 Source: Estonian Labour Force Survey, author’s calculations.

The changes from 2009 to 2014 mirror those from 2005 to 2009 (see Table 4):

the overall gender wage gap increased and the change occurred mostly in the unexplained component. As above, the changes in the unexplained component were mostly due to changes in returns to characteristics.

These results suggest that the changes in the gender wage gap that occur over the business cycle operate through differential changes in the remuneration of men’s and women’s characteristics, rather than through changes in employ-ment resulting in fewer differences in men’s and women’s average character-istics. It would therefore be interesting to study further what the phenomena are that lie behind such changes. One possible explanation would be that there are differences in men’s and women’s acceptance of proposed wage reductions during the recession, perhaps due to gender differences in tolerating the risk of losing a job, confidence in the ability to find a new job, or some other reason.

The differences in men’s and women’s downward nominal wage rigidity during the recession will be explored further in Study III.

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Table 4. Smith-Welch decomposition of the change in the gender wage gap, 2014 compared to 2009.

Decompositions of individual differentials:

D E C EC

2009 0.833 –0.009 0.867 –0.026

2014 2.170 –0.017 2.184 0.003

Difference in (components of) differentials:

1.337 –0.008 1.317 0.028

Decomposition of difference in differentials:

D E C

dE –0.0077 –0.0135 0.0058

dC 1.3169 –0.0055 1.3224

dEC 0.0281 0.0050 0.0231

Source: Estonian Labour Force Survey, author’s calculations.