Routine-biased technological change and wage inequality: do workers’ perceptions matter?

Abstract

The Routine-Biased Technological Change (RBTC) has been regarded as a relatively novel technology-based explanation of social changes affecting job and wage polarization. In this paper, we investigate wage inequality between routine and non-routine workers along the wage distribution in Italy. Thanks to unique survey data, we can estimate the wage differential using both the actual and the perceived level of routine intensity of jobs to classify workers. We adopt semi-parametric decomposition techniques to quantify the importance of worker characteristics in explaining the gaps. We also employ non-parametric techniques to account for self-selection bias. We find evidence of a significant U-shaped pattern in the wage gap, according to both definitions, with non-routine workers always earning significantly more than routine workers. Results show that worker characteristics fully explain the gap in the case of perceived routine, while they account for no more than 50% of the gap across the distribution in the case of actual routine. Thus, the results highlight the importance of taking into account workers’ perceptions to reduce the set of omitted vaiables when analyzing determinants of wage inequality.

Appendices

Appendix A

See Appendix Tables 3, 4, 5, 6, 7, 8, 9, 10; Figs. 3, 4, 5, 6.

Table 3 The structure of the Routine Task Index

Table 4 Summary statistics for the whole sample and by subjective and objective routinarity

Table 5 Kolmogorov–Smirnov test for comparison between routine and non-routine workers, for both definitions

Table 6 Mincerian wage regression, subjective routine = no

Table 7 Mincerian wage regression, subjective routine = yes

Table 8 Mincerian wage regression, objective routine = no

Table 9 Mincerian wage regression, objective routine = yes

Table 10 Counterfactual decomposition using unconditional quantile regression based on a recentered influence function (RIF)

Fig. 3

Source: OECD Employment Outlook (2017). European Labour Force Survey, Labour force surveys for Canada (LFS), Japan (LFS), Switzerland (LFS), and the United States (CPS MORG)

Job polarization in Europe.

Fig. 4

Observed differences in non-routine/routine workers’ wage distributions

Fig. 5

a, b Actual vs counterfactual wage distribution (using non-parametric estimation). Subjective routinarity (top panel) and objective routinarity (bottom panel)

Fig. 6

Decomposition of differences in distribution using quantile regression (semi-parametric). Subjective routine at the occupational-4 digit level

Appendix B

2.1 Blinder Oaxaca and quantile-regression based decompositions

By means of the Blinder-Oaxaca (B-O) decomposition, a researcher can explain how much of the difference in the mean wage across two groups is due to group differences in the levels of explanatory variables, and how much is due to differences in the magnitude of regression coefficients (Blinder, 1973; Oaxaca, 1973). If N and R are the two groups of non-routine and routine workers, the mean wage difference to be explained $(\Delta \overline{y }$) is simply the difference in the mean wage for observations in those two groups, denoted ${\overline{y} }_{n}$ and ${\overline{y} }_{r}$, respectively:

$$\Delta \overline{y} = \overline{ y}_{n} - \overline{y}_{r}$$

(9)

In the context of a linear regression, the mean wage for group W $=N,R$ can be expressed as $\overline{y}_{W} = \overline{X}^{\prime}_{W} \hat{\beta }_{W}$, where ${\overline{X} }_{\text{W}}$ contains the mean values of explanatory variables and $\hat{\beta }_{W}$ the estimated regression coefficient. Hence, $\Delta \overline{y }$ can be rewritten as:

$$\Delta \overline{y} = \overline{{X^{\prime}}}_{n} \hat{\beta }_{n} - \overline{{X^{\prime}}}_{r} \hat{\beta }_{r}$$

(10)

The twofold approach splits the mean outcome difference with respect to a vector of non-discriminatory coefficients $\hat{\beta }_{R}$. The wage difference in (10) can then be written as

$$\Delta \overline{y} = { }\left( {\overline{X}_{{\text{n}}} - \overline{X}_{{\text{r}}} { }} \right){^{\prime}}\hat{\beta }_{{\text{n}}} + \overline{X^{\prime}}_{{\text{n}}} { }\left( {\hat{\beta }_{{\text{n}}} - \hat{\beta }_{{\text{r}}} } \right) + \overline{X^{\prime}}_{{\text{r}}} \left( {\hat{\beta }_{{\text{r}}} - \hat{\beta }_{{\text{n}}} } \right)$$

(11)

In Eq. (11) the first term is the explained component, while the sum between the second and the third term is the unexplained component.

While the Ordinary Least Squares (OLS) method provides estimates for the conditional mean exclusively, the Quantile Regression (QR) technique allows for the estimation of the whole conditional wage distribution. Moreover, QR estimates capture changes in the shape, dispersion and location of the distribution, while OLS estimates do not. This can be a source of misleading relevant information on the wage distribution for routine and non-routine workers. Put in another way, the QR method (Koenker & Bassett, 1978), seems to be more interesting, and more appropriate in this context: the θth quantile of a variable conditional on some covariates can be accounted for and the effect of those covariates at selected quantiles of the distribution can be estimated.

Being $y_{i}$ the dependent variable and $x_{i}$ the vector of the chosen explanatory variables, the relation is given by:

$$y_{i} = x_{i} \beta \left( \theta \right) + \varepsilon_{i} \,\,{\text{ with }}\,\,F_{\varepsilon }^{ - 1} \left( {\theta |X} \right) = 0$$

(12)

where $\, F_{\varepsilon }^{ - 1} \left( {\theta |X} \right)$ represents the θ^th quantile of ε conditional on x. The estimated θ^th quantile is obtained by solving the following equation:

$$\mathop {\min }\limits_{\beta \left( \theta \right)} \left\{ {\sum\limits_{{\left( {i:y_{i} \ge x_{i} \beta \left( \theta \right)} \right)}}^{N} {\theta \left| {y_{i} = x_{i} \beta \left( \theta \right)} \right| + \sum\limits_{{\left( {i:y_{i} \le x_{i} \beta \left( \theta \right)} \right)}}^{N} {\left( {1 - \theta } \right)\left| {y_{i} = x_{i} \beta \left( \theta \right)} \right|} } } \right\}$$

(13)

and β(θ) is chosen to minimize the weighted sum of the absolute value of the residuals.

Once the QR coefficients have been estimated, the differences at the selected quantiles of the wage distribution between the two groups can be divided into one component based on the differences in characteristics and another based on the differences in coefficients across the wage distribution. As argued by Melly (2005), in the classic Blinder-Oaxaca (B-O) decomposition procedure, the exact split of the average wage gap between two groups is due to the assumption that the mean wage conditional on the average values of the regressors is equal to the unconditional mean wage. In other words, if one chooses to frame the QR with the B-O methodology, he/she will elicit biased results. For this reason, we chose to apply a procedure to single out the two above mentioned components from the decomposed differences at given quantiles of the unconditional distribution. Firstly, the conditional distribution is estimated through the Q; secondly it is integrated over the range of covariates.

Representing with $\hat{\beta } = \left( {\hat{\beta }\left( {\theta_{1} } \right),....\hat{\beta }\left( {\theta_{j} } \right),....\hat{\beta }\left( {\theta_{J} } \right)} \right)$ the vector of quantile regression parameters estimated at J different quantiles $0 < \theta_{j} < 1$ with j = 1,……..J and integrating over all of the quantiles and observations, an estimator of the τ^th unconditional quantile of the (log monthly) wage is given by:

$$q\left( {\tau ,x,\beta } \right) = \inf \left\{ {q:\frac{1}{N}\sum\limits_{i = 1}^{N} {\sum\limits_{j = 1}^{J} {\left( {\theta_{j} - \theta_{j - 1} } \right)1\left( {x_{i} \hat{\beta }\left( {\theta_{j} } \right) \le q} \right) \ge \tau } } } \right\}$$

(14)

where 1(^.) is the indicator function. Thus, the counterfactual distribution can be estimated by replacing either the computed parameters of the distribution of characteristics for routine or non- routine workers. The difference at each quantile of the unconditional distribution can be decomposed into the two above mentioned components as follows:

$$q\left( {\theta ,x^{n} ,\beta^{n} } \right) - q\left( {\theta ,x^{r} ,\beta^{r} } \right) = \left[ {q\left( {\theta ,x^{n} ,\beta^{n} } \right) - q\left( {\theta ,x^{n} ,\beta^{r} } \right)} \right] + \left[ {q\left( {\theta ,x^{n} ,\beta^{r} } \right) - \left( {\theta ,x^{r} ,\beta^{r} } \right)} \right]$$

(15)

The right hand term in the first brackets constitutes the difference in rewards that the two groups of workers receive for their labor market characteristics (i.e. the counterfactual distribution), while that in the second brackets is the effect of differences in labor market characteristics between routine and non-routine workers. This is a semi-parametric-method because the QR framework does not need any distributional assumption, while at the same time allows the same covariates to have an influence all over the conditional distribution.

To estimate the standard errors and confidence intervals, the bootstrap method can be used to replicate the above procedure. In this study 200 replications were performed.