AI and productivity

Martin Baily, Erik Brynjolfsson and Anton Korinek offer a calculation that is more subtle than you might think.  They say 

"The first channel is the increased efficiency of output production. By making cognitive workers engaged in production more efficient, the level of output increases. Economic theory tells us that the effect of a productivity boost in a given sector on aggregate productivity and output is equal to the size of the productivity boost multiplied by the size of the sector (Hulten’s theorem). For instance, if generative AI makes cognitive workers on average 30% more productive and cognitive work makes up about 60% of all value added in the economy (as measured by the wage bill attributable to cognitive tasks), this amounts to a 18% increase in aggregate productivity and output."

The second channel?

"The second channel is the acceleration of innovation and thus future productivity growth. Cognitive workers not only produce current output but also invent new things, engage in discoveries, and generate the technological progress that boosts future productivity. This includes R&D—what scientists do—and perhaps more importantly, the process of rolling out new innovations into production activities throughout the economy—what managers do. If cognitive workers are more efficient, they will accelerate technological progress and thereby boost the rate of productivity growth—in perpetuity. For example, if productivity growth was 2% and the cognitive labor that underpins productivity growth is 20% more productive, this would raise the growth rate of productivity by 20% to 2.4%. In a given year, such a change is barely noticeable and is usually swamped by cyclical fluctuations, but productivity growth compounds. After a decade, the described tiny increase in productivity growth would leave the economy 5% larger, and the growth would compound thereafter. If the acceleration applied to the growth rate of the growth rate as well, then of course, growth would accelerate even more over time."

Let me focus on the first channel.  What is Hulten's theorem?  This is an obvious point, but solved by a brilliant piece of economics.  Quoting from Hulten's paper, Growth Accounting with Intermediate Inputs, Charles R. Hulten, The Review of Economic Studies, Volume 45, Issue 3, October 1978, Pages 511–518, https://doi.org/10.2307/2297252.  

1. ...Productivity change is conventionally defined as the residual growth of real product not

accounted for by the growth of real factor input.

2. but, some inputs are themselves outputs of the productive process: capital and intermediate input. Increased factor efficiency will, in general, lead to increased output, and thus to increases in the quantity of produced inputs available for production.

3. In any post-mortem assessment of the sources of growth, this induced expansionin produced inputs must be recognized as having been the result of productivity change. That is, the growth rate of total factor productivity must be adjusted for the additional input available as a result of the increased factor efficiency. 

4.The present paper studies the interaction of productivity change and intermediate input

What he shows is the link between industry TFP growth in an industry, j, and overall TFP growth, taking account of the induced extra intermediates from TFP in the industry. This is 

TFPG, agg = (PgG)j/(PvV) * TFPGj, industry of gross output

where the TFPGj is the gross output of industry j. The multiple is ratio of gross output in industry j, divided by total value added in the economy.  This multiple adds to something greater than one, but that makes sense, since TFPG in j "spreads out to other industries". 

Finally, what of the above calculation?  If AI is labour augmenting, then it raises the productivity of labour in industry j.  Thus it raises TFPG in j by the share of labour payments in gross output of industry j.  Thus the overall effect, for AI that is labour augmenting, is the labour payments in industry j over total value added, times the labour-augmenting technical progress.  This is how they end up with 60% times 30% over the years it will take to realise the gains.

Who is working class?

 The UK government has announced civil service internships will only be available to those who are working class.  What does this really mean? According to the BBC, applicants will be judged by what jobs their parents did when they were 14.

So what jobs are working class? Again, according to the BBC  this definition is being sorted by the Comission on Social Mobility.  I found this table from The State of the Nation 2024. Table 1, page 25. 

with an interesting footnote "10 Some routine occupations can count as intermediate if the worker is self-employed." 

As an economist, I don't really know how to think about what class someone is. So the following comments in the document interested me.

First, as with many of these indicators wages differ more within the divisions than between the. Page 26 : Sometimes people in lower occupational classes earn more than those in higher occupational classes. For example, speech and language therapists count as higher professionals, NS-SEC 1, because their job requires a first degree for entry and experience-related training, and the practical application of a body of knowledge to instruct others. Yet, their average salary is lower than that of many working-class

occupations, including some  routine manual occupations.

There can also be great variation in earnings within a class. For example,

teaching assistants earn an average of £19,033, and rail travel assistants

earn an average of £36,080, yet both occupations are classified as

‘intermediate’.11 Apart from different salaries, these jobs may also have

very different working conditions.

Second, the treatment of the self-employed.  

And, finally, 2 people doing the same type of work can be in different classes if one is an employee and the other is self-employed since the self-employed tend to be classed as intermediate. For example, a bricklayer who is an employee would be in NS-SEC 7, lower working class, while a self-employed bricklayer would be in NS-SEC 4, intermediate class."

I find it odd that being self-employed means you cannot be working class (the document is unclear to me about tending to be classified, I think this means occupations are classified by the ONS into the headings that this commission then choose to be working class).

So what do the ONS do?  They have 8 "analytic" classes, https://www.ons.gov.uk/methodology/classificationsandstandards/otherclassifications/thenationalstatisticssocioeconomicclassificationnssecrebasedonsoc2010, of which one, the self-employed, class 4 are defined by the social mobility people as intermediate and hence not "working class". 

Source: table 2, here. . ONS, ‘The national statistics socio-economic classification (NS-SEC)’, 2021. 

Other interesting information from the Mobility report

1. the education premium has declined

2. those with the same education, sex and age but coming from different backgrounds have different wage premia

3. in the conclusion they again state the heterogeneity within groups

"For example, children eligible for free school meals (FSM) of Chinese

background perform better than the national average for non-FSM children at key stage

(KS) 2 and KS4 (age 11 and 16 years)."

Which comes from a very striking graph 

Blanket classifications e.g. "working class" don't seem very useful to me.