Broadband Internet and Income Inequality

A Conceptual Framework – Automation and Jobs

The objective of this section is to present a simple model that links broadband adoption to the Gini index of income inequality. Our intention is not to introduce a model for structural estimation, but rather to illustrate this link in a simple way by a graphical and mathematical expressions.

Acemoglu and Restrepo (2018) provides a task-based framework to describe a production process in a single-sector economy. The author assumes that production is composed of a number of tasks. A task is indexed by z, which is between N − 1 and N. Each task can be produced by capita or labor. When, z < I the task is automated, i.e. produced by capital. On the other hand, when z > I, the task cannot be automated and is only performed by labor.

An increase in I represents a greater automation of task z. An increase of N corresponds to the introduction of new labor with new skills. With Internet adoption, the increase in I and N coexist. The increase in I allows for the replacement of some routine tasks. The increase in N, represented by an increase in new jobs related to the Internet or broadly ICT (Information and Communications Technology).

Figure A1:

Link between broadband internet adoption and Gini index of income inequality.

As shown in Figure A1, the Gini index of income inequality is represented by the surface between the diagonal line (y = x) (in blue) and the convex curve f(x) (in orange). The Gini is calculated by the integral of (x − f(x)) between 0 and 1, i.e. Gini = ∫ 0 1 ( x − f ( x ) ) 1 / 2 d x .

The Internet adoption has potentially two effects in f(x). The first effect is the new tasks effect which makes the curve f(x) more convex by passing through f(x) = x ^b to f(x) = x ^(b+w) with b > 1 (b represents the initial level of the Gini), and w > 0 (w represents the extent of skilled web workers), since ICT tends to benefit employees who are highly skilled and whose skills are complementary to ICT. The second effect is the automation effect for x close to 0. Low deciles between 0 and a, mainly routine workers, are reduced by automation (a reflects the share of routine works replaced by automation). The first effect increases the Gini index and the second effect reduces the Gini index.

New jobs created with the arrival of the Internet are represented as “Web works” in Figure A1. These high income jobs increase the surface between y = x and y = f(x). As a result, the Gini index may rise with these new jobs.

Internet adoption has also reduced some routine tasks. In general, these tasks are basic service jobs and are in the low income decile.^[20]

This reduction decreases the surface between y = x and y = f(x). Internet adoption is giving rise to a new business which is the delivery of e-Commerce goods. The deliverers, who probably used to be routine workers before, can earn more by working more. The latter can contribute to raising the incomes of low deciles.

These two effects co-exist. While the first effect dominates, inequality increases with Internet adoption. While the second effect dominates, inequality decreases with Internet adoption. We can describe these two effects with simple illustrative mathematical expressions.

First effect: as the new jobs make the function f(x) more convex from f(x) = x ^b to f(x) = x ^(b+w), the surface between y = x and y = f(x) increases. It is a matter of simple maths to show that the Gini is increased by 2 w ( b + 1 ) 2 compared to the initial Gini, Gini 0 = ( 1 − 2 b + 1 ) , before the arrival of new Web jobs (i.e. w = 0).

Second effect: the loss of some routine jobs represented by the area of the small triangle at the bottom left for x between 0 and a. This loss makes x take value between a and 1. We could make a variable transformation to express f(x) in f(z) with z = ( x − a ) ( 1 − a ) and z is between 0 and 1 for x between a and 1. So f(z) > f(x), the surface between y = z and y = f(z) decreases, that means the Gini decreases. It is also possible to approximate this effect by a simple calculation without the variable transformation, by performing the integral of (x − f(x)) for x between a and 1 with the assumption of a ≪ 1. The Gini is reduced by ( a 2 − 2 a ( b + 1 ) ( b + 1 ) ) compared to the initial Gini with (a = 0). Depending on the dominance of one of these two effects, the Gini can increase or decrease according to a (loss of routine works due to automation) and w (new skilled Web works). When both effects coexist:

1. the Gini increases if 2 w ( b + 1 ) 2 > ( a 2 − 2 a ( b + 1 ) ( b + 1 ) )

2. the Gini increases if 2 w ( b + 1 ) 2 < ( a 2 − 2 a ( b + 1 ) ( b + 1 ) )

These mathematical expressions are simply illustrative and we do not attempt to calibrate the values of b, a or w by the empirical estimations.

B Graphs and tables

Figure A2:

Central offices and distance to households – illustration from a French department (Belfort).

The squares correspond to central offices and the dots correspond to upgraded central offices to get closer to households.

Source: actualisation du schema directeur d’amenagement numerique de l’Aisne – Volet Infrastructures numeriques – February 2016.

Figure A3:

Broadband subscriptions by technology (million).

Source: authors, using data from the national regulator (ARCEP, 2016).

Figure A4:

Impact of broadband internet uptake in low-income cities.

Source: low-income cities have average income below 16,000 euros in 2001.

Figure A5:

Impact of broadband internet uptake in high-income cities.

Source: high-income cities have average income above 16,000 euros in 2001.

Figure A6:

Impact of broadband internet uptake on department-level income deciles.