Troquel

In addition of the personal and productive characteristics of the workers and their working conditions, other factors also contribute into the variation of individual wages. To analyse that now the study will test this in a more rigorous way and to do this we will look into the existence and scale of inter-industry wage differentials in the Pakistan. To put this differently, this study analyses whether wage disparities may be observed between people employed in different sectors of activity, similar from the point of view of their productive characteristics and their working conditions. The employed methodology is similar to that of Krueger and Summers (1988) as described below, however as pointed out by Haisken-DeNew and Schmidt (1997) that Krueger and Summers (1988) have suggested approximation of the coefficients‟ standard errors in the original regression for the omitted base category, by the standard error of the constant term rather than calculating the standard errors of renormalized coefficients. Thus, the model has been improved to incorporate the methodology for calculating standard errors as suggested by Haisken-DeNew and Schmidt (1997).

The estimation of inter-industry wage differential depends upon the estimation of a wage equation identical to the one described in previous sections (see equation (1)). To start with, the study includes only a constant and the sectoral dummies (Y) according to one and two digits, which is 9 and 41 branches, respectively. The estimated coefficients 𝛼 and 𝜓 _𝑘 (𝑘 =

1, … , 𝐾), are used to identify the wage of the average worker in reference sector and the wage

differential between the average worker in sector k and the average worker in the reference sector, respectively.

Therefore, the wage of the average worker in sector k is obtained by adding 𝛼 and𝜓 _𝑘. The wage of the average worker in economy (i.e. ω) is the average of the wages of the average workers in all sectors (i.e. 𝑤_𝑘, for 𝑘 = 1, … , 𝐾 + 1), weighted by the sectoral employment shares (i.e. 𝑝 _𝑘), to put in other words:

𝜔 = 𝑝 𝑘 𝐾+1 𝑘=1

81 𝑤_𝑘+1 = 𝛼 𝑝 𝑘 = 1 𝑁 𝑝𝑘.𝑖 𝑁 𝑖=1 𝑘 = 1, … , 𝐾 + 1 (3)

Accordingly, the wage differential between the average worker in sector k and the average worker in the economy may be expressed as follow:

𝑑_𝑘 = 𝑤_𝑘− 𝜔 𝑘 = 1, … , 𝐾 + 1 (4)

The above formula gives the gross inter-industry wage differential: 𝑑_𝑘, it does not take account of the sectoral heterogeneity of productive capabilities, working conditions or the household characteristics, for this previous section have estimated „enlarged‟ wage equations, which contains other exogenous variables in addition to the constant and the sectoral dummies (Y). Estimation of these equations provides the inter-industry wage differential between identical individuals, for example from the point of view of their household characteristics. Now given this, the constant no longer corresponds to the wage of the average worker in the reference sector; and the estimation of the values of 𝑑𝑘is slightly different.

Estimation now involves calculation of the average wage differential of all the sectors compared to reference to:

𝜋 = 𝑝 _𝑘

𝐾 𝑘=1

𝜓 _𝑘 (5)

and applying the formulae as:

𝑑𝑘 = 𝜓 𝑘− 𝜋 𝑑_𝐾+1= −𝜋

𝑘 = 1, … , 𝐾 (6)

The standard errors of the original industry coefficients have been adjusted according to Zanchi (1998), in order to test the inter-industry wage differential hypothesis accurately. In other words, the study has transformed the variance-covariance matrix found when estimation equation (1) by OLS as follow:

82

Where H is a ((K+1) × K) matrix constructed as a stack of (K+K) identity matrix and a (1×K) row of zeros, e is a ((K+1)×1) vector of ones, s represents the employment shares of the K

first industries, and 𝑣𝑎𝑟 − 𝑐𝑜𝑣 𝜓 is the original variance-covariance matrix of the industry dummy coefficients. The correct estimates of the standard errors are obtained by taking the square roots of the diagonal elements of this transformed variance-covariance matrix.

The wage differential calculated above in equations (4) and (6) is expressed in log points, as the wage equation is of semi-logarithmic form (equation 1). As pointed out by Reilly and Zanchi (2003) most studies interprets these wage differential as the percentage effect of industry k affiliation on wages, but this interpretation is incorrect as the form of the wage equation is semi-logarithmic. Thus, the estimation will follow the procedure of Gannon and Nolan (2004) to calculate the percentage wage differential.

In order to obtain the wage differential between the wage of the average worker in sector k, (λk) and the wage of worker in the economy (ρ) in percentage terms, we need the following transformation:

𝑣_𝑘 = 𝜆𝑘− 𝜌

𝜌 for k = 1, … , K + 1 8

where

𝜆_𝑘 = exp 𝛼 [1 + (exp 𝜓 𝑘 − 1)] for 𝑘 = 1, … , 𝐾 , 𝜆𝑘+1= exp 𝛼 , and 𝜌 = 𝑝 𝑘𝜆𝑘 𝐾+1 𝑘=1

Equation 8 above provides wage differential for each sector in percentage terms, and ρ is the percentage for the reference sector. When included individual, household and job characteristics in wage equation, the transformation is presented as:

𝑣_𝑘 = exp 𝜓 𝑘 − 1 − 𝐺 for k = 1, … , K (9)

where

𝑣_𝑘+1 = −𝐺 and G = p _k[exp⁡(ψ_k) − 1]

K k=1

83

Once estimated the differential between industries, the overall variability in industry wages can be measured by the standard deviation of the inter-industry wage differential (Teulings and Hartog (1998)). Standard deviation, of values dk, is a synthetic indicator of the dispersion

of the inter-industry wage differential, adjusted for sampling error and weighted by the sectoral employment shares. In algebraic terms, the weighted adjusted standard deviation (WASD) of the dk obtained using following formulae:

𝑊𝐴𝑆𝐷 𝑑_𝑘 = 𝑝 𝑘 𝐾+1 𝑘=1 𝑑_𝑘− 𝐾+1𝑘=1𝑑𝑘 𝐾 + 1 2 − 𝐾+1𝑘=1var(𝑑 𝑘) 𝐾 + 1 + cov(𝑑 𝑘, 𝑑 𝑙) 𝐾+1 𝑙=1 𝑘+1 𝑘=1 𝐾 + 1 2 (10)