This is a guest post by Lukas Freund. Lukas is a PhD candidate in economics and Gates scholar at the University of Cambridge and a doctoral fellow with the Klaus Murmann Foundation. His research focuses on the intersection between macroeconomic policy, inequality and technological change. He blogs at https://lukasfreund.wordpress.com.

The Solow Paradox

If robots are taking our jobs, then why is productivity growth so slow? Over the past couple of years, numerous people, both inside and outside economics, have raised some variant of this question. To paraphrase Robert Solow‘s famous quip: Why can you see robots everywhere but in the productivity statistics? This blog post surveys some of the attempts to resolve this so-called productivity (or “Solow”) paradox, i.e., why despite seemingly ubiquitous technological progress, official productivity statistics do not seem to reflect this.

I delineate five hypotheses, some which are competing while others are potentially complementary. These hypotheses point, respectively, (1) to exaggerated hopes about the real-world impact of the technologies we see around us; (2) to delays in their impact; (3) to the mismeasurement and understatement of the effects of these technologies; (4) to the growth of zero-sum activities that partially offset the influence of innovation on productivity; and, finally, (5) to sectoral reallocation dynamics that may likewise have an effect on aggregate productivity statistics running counter to the influence of innovation within sectors.

While the first two involve difficult forecasting exercises, and while most studies cast doubt on the role of mismeasurement, I present some evidence that the shift of workers to sectors with lower productivity levels—possibly those where zero-sum activities are important—may have constituted a drag on aggregate productivity levels. However, since this likely applies only to some countries—notably the USA—but not to others—the UK being an example—whereas the productivity slowdown is a global phenomenon, such reallocation effects can at most represent one factor among several that explain the productivity paradox.

What Is Productivity and Why Does It Matter?

Before diving into the five hypotheses, let us take a step back to ask: what is productivity and why does it matter? In essence, productivity statistics describe how efficiently an economy (or an industry or a firm etc.) produces goods and services; productivity thus relates a particular set of inputs to a particular set of outputs.

One particularly important productivity metric, which the rest of this article will focus on, is labour productivity. The basic idea—simplifying somewhat—is straightforward: we add up an economy’s total output, and then divide it by the number of people in employment (or the hours they have worked).[1] The UK Office for National Statistics has an excellent handbook providing further details to the interested reader (also see footnote 1).

Labour productivity matters for our standard of living, for employment and wages, for fiscal sustainability, and much more. As Paul Krugman once wrote: “Productivity isn’t everything, but, in the long run, it is almost everything.” To illustrate, with productivity growth of 2% p.a., the average standard of living will double roughly every 35 years, but with a growth rate of 1% p.a., this happens only every 70 years.

The Global Productivity Slowdown 

In view of this, the chart below is deeply worrying: it shows that following an acceleration in the late 1990s and early 2000s, productivity growth has slowed down severely. This trend can be observed in most countries, especially rich ones; shown are the USA, the UK and Germany. Moreover, there is robust evidence (e.g. by Cette, Fernald and Mojon (2016)) that the slowdown began before the Great Recession and the Eurozone crisis, meaning that it does not merely reflect the “hangover” from these crises.

Both a slowdown in capital deepening (an increasing amount of capital per worker) and TFP seem to be contributing to slower labour productivity growth. To many, including economists, this slowdown seems paradoxical: for is the world around us not full of remarkable examples of new technologies—signs that we are entering a Second Machine Age, as Erik Brynjolfsson and Andrew McAfee have argued?

Source: OECD, author’s calculations.

Notes: 5-Year centered moving average of annual percentage growth (log difference). Labour productivity is measured as GDP per hour worked.

Exaggerated Hopes—Or Are We Just Too Impatient?

The academic literature has pointed to a host of explanations to reconcile apparently transformative technological change with disappointing productivity statistics. The exaggerated hopes hypothesis states that the impacts of the technologies highlighted by “techno-optimists”—such as CRISPR, machine learning, or 3D printing—are in fact not that pervasive or significant.

Perhaps the most frequently cited proponent of this view is Robert Gordon, who in his 2014 book The Rise and Fall of American Growth argued that productivity growth has been in long-run decline, with the IT-driven acceleration of 1995-2004 (clearly visible in figure 1) being a one-off aberration. For Gordon, the technology revolution that drove growth in the first half of the 20th century “is without peer, completely different than what happened before or since”: smartphones and AI are just not as important as the arrival of electricity or of cars and airplanes. This may be because “ideas—and in particular the exponential growth they imply—are getting harder and harder to find” (Bloom et al. (2018)).

A variant on this “techno-pessimist” position holds that at least some of the most ubiquitous new technologies (think computers and mobile phones) actually makes us less productive. This could potentially offset some of the productivity-enhancing contributions of other technical improvements. Thus, Dan Nixon of the Bank of England notes that in addition to the direct impact of distractions on the amount of effective time spent working (e.g. ‘cyberslacking‘), habitually distracted minds may also reduce our effectiveness during the hours we work.[2]

Optimists such as Erik Brynjolfsson and co-authors, on the other hand, argue that lags are likely the best explanation of the paradox. In other words, the transformative impact of new technologies will be real, but it takes time to manifest. This is, firstly, because it takes time to build the stock of new technology (i.e., implementation lags) and, secondly, because the installation of complementary capital, both tangible and intangible, is necessary to obtain the full benefits of each new technology (i.e., restructuring lags).

Both the “exaggerated hopes” and the “lags” hypotheses are intuitively appealing—and each side can marshal some quantitative evidence—but, ultimately, both rely on forecasting what technologies will emerge going forward and how significant their impact will be. It may seem sensible, hence, to remain epistemically modest—a luxury that, e.g., officials having to forecast pension liabilities do not have!—and to focus, in the first instance, on trying to understand what has happened so far.

All A Fluke? The Role of Mismeasurement

In this spirit, it is possible that true productivity growth in recent decades has been mismeasured and under-stated in official statistics. This could be because statistics do not incorporate enough of an adjustment for the ever-increasing quality[3] or because many of the fastest-diffusing technologies since the early 2000s—like smartphones, online social networks, and downloadable media—involve consumption of products that are time-intensive but do not impose a large direct monetary cost on consumers. As such, they do not significantly affect measured output (which, recall, is the number in the numerator of the labour productivity statistic), regardless of their impact on human welfare; a recent IMF staff report explains this in great clarity and detail.

However, while this case is prima facie plausible, a whole host of recent studies present evidence suggesting that (increasing) mismeasurement is not the primary explanation for the productivity paradox. For one thing, if we are to explain a slowdown in measured productivity growth, it is not sufficient to point towards mismeasurement of, say, the gains from innovation in IT-related goods and services. Instead, mismeasurement would need to have become more prevalent than in preceding decades. However, David M. Byrne and co-authors argue that in the US, at least, mismeasurement of IT hardware was already significant prior to the slowdown and that, in fact, the mismeasurement effect was larger in the period 1995-2004 than in the period since. One reason is that although mismeasurement has worsened for some types of IT, this is more than offset by the fact that the domestic production of such goods has declined (we will revisit the importance of considering composition and reallocation effects in a different context below).

Meanwhile, Nakamura et al., who use an experimental methodology that values “free” digital content through the lens of a production account, find that TFP would grow faster by approximately 0.07 percentage points per year from 2005 to 2014 if this value was included in GDP. These figures are meaningful, but relatively small. More generally, as Chad Syverson explains in this excellent interview with the Richmond Federal Reserve Bank, the magnitude of the productivity slowdown is simply too large to believe that mismeasurement can account for it. Moreover, Nakamura et al. document a similar valuation of “free” content (e.g. print newspapers) in the period 1995 to 2005, implying that their account also does not rationalize a slowdown of productivity growth.

A third line of thought involves an important philosophical component: what are our economic statistics supposed to capture? For it is conceivable that GDP and productivity growth, as measured by national statistical agencies, truly have slowed yet welfare has continued to increase due to the growing availability, for example, of free digital products. For instance, Feldstein (2015) argued that “low growth estimates fail to reflect the innovations in everything from healthcare to Internet services to video entertainment that have made life better during these years”.

However, such a line of reasoning does not, eo ipso, imply that productivity, as hitherto defined, is mismeasured. It would mean that rapid technological progress has rendered GDP a less meaningful indicator of the underlying pace of technological change and of human welfare. But it is a matter of judgement whether we ought to react to such a development by, say, making technical adjustments to the way we measure GDP in order to account for more internet services in productivity estimates, because we think they matter for human welfare.[4] In particular, one downside of such an approach is that this could render GDP a less useful indicator for other purposes, e.g., for judging the tax base that governments can draw on to pay for social services, infrastructure, defence, debt service and repayments, and any other government function. Moreover, it is not possible to simply add an estimate of the value of free digital services to household consumption, say, because in the national accounts production and consumption have to balance.

A more advisable approach might be to have multiple indicators and recognise their respective limitations. This perspective accepts that nominal GDP is a measure of production, specifically market and near-market production, valued at market prices, and need not coincide with welfare.[5] Indeed, the discrepancy between welfare and GDP is not new: water yields massive welfare given its essential role in sustaining life, but (in most countries), water is abundant and therefore carries a low price, such that the consumption of water, valued at market prices, is small. Similarly, many of the benefits from smartphones and digital services are, conceptually, non-market: “Consumers are more productive in using their nonmarket time to produce services they value,” as Byrne et al. put it.

Creative and Distributive Activities

A fourth perspective holds that new technologies have already had an impact, but their effect on productivity growth is limited because of dissipative efforts to attain or preserve them. This is an important point made in a recent, insightful lecture by Adair Turner: he highlighted the growth of zero-sum activities: activities that are, in the terminology used by Roger Bootle, “distributive” in their impact on total prosperity, rather than “creative”. That is, in these jobs, people compete for a share of the economic cake, yet their activity does not add to the sum total of goods and services available for consumption. Importantly for our purposes, zero-sum activities have an arbitrary impact on GDP and productivity statistics, depending solely on measurement conventions (in particular, whether they go into the intermediate or final goods basket; see also footnote 8 of Turner’s lecture).

Turner gives a list of examples—cyber criminals and cyber defence experts, tax accountants and tax lawyers, financial regulators and compliance officers, but also, say, the positional aspect of good education, fashion design, etc.—that suggest this hypothesis could be important. It is difficult to assess the quantitative relevance of this factors with precision, but it is potentially large: if over 25 years, zero-sum activities grew from 20% of economic activity to 30%, with 50% of zero-sum activity reflected in GDP but 50% not, measured productivity growth would equal 1.77% even if every activity in the economy, considered in itself, enjoyed 2% p.a. productivity improvements.

It’s Not All About Innovation: The Role of Sectoral Allocation Effects

Finally, Turner’s speech and long-standing economic theory alike highlight the role of sectoral reallocation effects: “Total productivity growth is as much driven by the productivity and productivity growth potential of the sectors into which workers move, as in the sectors where jobs are automated away,” Turner notes.

The basic underlying mechanics of this effect are well articulated by Timothy Lee: “As innovation has pushed down the cost of certain types of products (mostly durable goods such as televisions, furniture, and clothing), Americans have used the savings to spend more on other things—especially education, health care, child care, and housing—where productivity growth has been much slower. Over time, low-productivity sectors have become a larger share of the economy, while high-productivity goods production has become a smaller share. And an economy dominated by industries with low productivity growth is going to grow slowly.”[6]

This argument goes back to William Baumol’s (1967) analysis of unbalanced growth, whereby productivity growth is higher in the “progressive” (manufacturing) sector than in the “nonprogressive” (services) sector of the economy, but, due to labour market competition and mobility across sectors, wages grow more or less at the same rate in both sectors.[7] Baumol argued that as more weight is shifted to the more slowly progressing sector, the economy’s growth rate declines and eventually converges to zero. Nordhaus (2008) calls this the “Growth Disease”.[8]

In assessing this hypothesis, it is important to keep in mind that even within Baumol’s framework it is not necessarily the case that stagnant industries have rising shares of total output, and that this will tend to reduce overall growth in productivity and living standards.[9] Fortunately, though, we can use accounting methods to decompose historical labour productivity growth into three distinct effects (details are given in the appendix): the focus of technology optimists is typically on the within-sector effect (WSE) that reflects the impact of productivity growth within individual sectors on aggregate productivity (think robots in car factories, fast computers in finance, etc.). However, there are also two types of effects arising from movements of workers across sectors. The static reallocation effect (SRE) captures the impact of the reallocation of employment from less productive to more productive sectors (i.e., it arises from sectoral differences in productivity levels). The dynamic reallocation effect (DRE or “Baumol Effect”) describes the impact of reallocating employment into sectors with different productivity growth rates. This dynamic detracts from aggregate productivity growth when labour moves towards (away from) a sector with low (high) labour productivity growth.

Figure 2, which is based on sector-level data from the Groningen 10-sector database for the USA over the period 1950-2009 shows the evolution of aggregate labour productivity growth and the three components over time.[10] The crucial lesson is that, in the USA, the dynamic reallocation effect has historically represented some drag on the economy, albeit a relatively small one. Notably, though, the static reallocation effect has turned from positive to negative over the past few decades. Together, the SRE and DRE imply that even if productivity within sectors has continued to grow, employment shifts across sectors can partially explain the productivity paradox (consistent with the evidence presented elsewhere). Although this is only a first, high-level look at the data, it suggests that it is only the static effect that helps explain a decline in overall growth: the DRE has not become more negative over the past two decades, hence it does not play a major role in explaining the slowdown. Finally, and this is entirely conjectural, it is possible that the detraction coming from the SRE partially reflects the growth of zero-sum activities discussed above.

Although the USA plays the most important role in the global economy, in assessing the arguments advanced by Turner and Lee, it is insightful also to consider a number of other countries—especially because the productivity slowdown appears to be global. Based again on the Groningen database, and using the same methodology, it appears that in the UK, reallocation effects have detracted from aggregate growth (figure 3)—yet this component has declined in significance since the 1990s. Indeed, according to Goodridge et al (2015) (who use a different dataset), in 2009 it turned, and has remained, positive. Accordingly, reallocation effects (and especially the dynamic components) deepen the productivity paradox in the UK, unlike in the US case.

Meanwhile, in Japan (figure 4), reallocation effects have always positively contributed to aggregate growth, but this boost to growth has slowed down over time, albeit very gradually: this helps, albeit in a limited fashion, explain the slowdown, however, for reasons that are different from those in the USA (the German case seems yet again different[11]).

Reallocation Effects Matter—But They Are Not The Whole Story

The takeaway from this analysis is, therefore, that sectoral allocation effects can potentially help reconcile the simultaneity of rapid innovation in individual sectors, on the one hand, and the measured productivity slowdown at the aggregate level, on the other. But whether this is the case (sign), to what extent (magnitude), and for what reasons varies across countries. This view is consistent with the observation (about the within-sector component) of Acemoglu et al. (2014), who report that there is little evidence of faster productivity growth even in IT-intensive industries, and that this is particularly true after the late 1990s. In other words, although such insightful thinkers as Adair Turner, whom I greatly admire, seem confident in our ability to explain away the paradox, it strikes me that we have at most made a first few steps in that direction.

Source: Groningen 10-Sector Database, author’s calculations.

Notes: Annualised rolling 5-year growth rates (the annualisation means that WSE, SRE and DRE do not exactly add up to LP-agg). Labour productivity is measured as real value added per person engaged.

 

Source: Groningen 10-Sector Database, author’s calculations.

Notes: Annualised rolling 5-year growth rates (the annualisation means that WSE, SRE and DRE do not exactly add up to LP-agg). Labour productivity is measured as real value added per person engaged.

Source: Groningen 10-Sector Database, author’s calculations.

Notes: Annualised rolling 5-year growth rates (the annualisation means that WSE, SRE and DRE do not exactly add up to LP-agg). Labour productivity is measured as real value added per person engaged.

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Appendix

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Footnotes

[1] The primary alternative measure is called “total” (or “multi-“) factor productivity (TFP). TFP seeks to capture not only the efficiency with which labour inputs are employed but instead describes how efficiently and intensely all the inputs into production are utilized—in that sense, it is the more ambitious productivity metric. Which measure is preferably has been the subject of extensive debates, but there are good reasons to think that both measures have their place. This article focuses solely on labour productivity for two reasons. First, compared to total factor productivity, labour productivity is relatively more straightforward to measure. Notably, we can compute it directly using readily available estimates of value added and labour inputs. By contrast, TFP is typically retrieved as a residual by subtracting the contribution of growth in the capital–labour ratio from labour productivity growth. This is often done within the framework of a Cobb-Douglas aggregate production function and requires more assumptions as well as more data than calculating labour productivity. Second, labour productivity is closely related to current living standards (notably real wages) which is typically the primary normative concern underlying discussions about the productivity paradox.

[2] On the role of changing habits and character traits in accounting for slowing growth, see also Tyler Cowen’s The Complacent Class.

[3] As the UK Office for National Statistics explains: “In order to reflect changes in real values of inputs and outputs, measures of productivity should take quality changes in both into account. This is usually achieved by ensuring that the price indices used for deflation are adjusted for these quality changes. At the most basic level, volume measures are regarded as a combination of quantity and quality.”

[4] Remarkably, the connection between standard measurements of output and human well-being was contentious very early. Thus, Simon Kuznets in a report to the US Congress in 1934 stated that “the welfare of a country can scarcely be inferred from a measure of national income.”

[5] Of course, GDP is a relevant component of any statistical approximation of living conditions but it should only be one among many; the same applies to productivity statistics based on GDP.

[6] Note that Lee’s account implicitly incorporates non-homothetic preferences, a mechanism that was not part of Baumol’s original theory but is common in the literature on structural transformation (e.g. Kongsamut et al., 2001).

[7] Baumol died last year. I like this little story retold in the NYT obituary penned by Patricia Cohen: “Asked by the economist Alan Krueger in 2000 where his blockbuster ideas came from, Professor Baumol said he was always looking for a theory to explain any given human phenomenon, and if he were lucky, his speculation would turn out to be right. “And sometimes I’m very lucky,” he continued, “and I turn out to be totally wrong. Because when I turn out to be totally wrong, that’s when the best ideas come out.””

[8] Baumol’s main focus was on the so-called “Cost Disease”. Due to asymmetric growth, unit costs and prices rise much faster in the tertiary sector than in the secondary sector. At the same time, demand for certain services, like health care and education for instance, is hardly price-elastic. Hence, even if real production in both sectors develops proportionately, an increasing share of total expenditures will be channelled into stagnant service industries which are mainly financed by taxes and social contributions.

[9] As Nordhaus (2008) explains, Baumol’s growth disease occurs when sectors with relatively slow productivity growth also have rising nominal output shares; whether this will be the case depends on the interaction of rising relative prices and declining relative outputs. In particular, the Baumol growth disease occurs when sectoral substitution elasticities are below unity (complementarity). Considering AI technologies, for instance, a drag to due sectoral reallocation is more likely if product demand for the sectors with the largest productivity gains through new technologies such as AI is sufficiently inelastic. In this case, these sectors’ shares of total expenditure will shrink, shifting activity toward slower-growing sectors and muting aggregate productivity growth through the Baumol effect. But as Brynjolfsson et al (2017, footnote 14) note, it is unclear what the elasticities of demand are for the product classes most likely to be affected by AI. If anybody knows of a study addressing this question, please do let me know.

[10] Dietrich Vollrath has conducted a similar exercise (for the USA); I use a slightly different decomposition, as detailed in the appendix.

[10] I have also used Eurostat data to look at post-reunification Germany. The TRAD decomposition assumes that real output is measured using fixed-base Laspeyres and Paasche price indices, but most official statistics, including those from Eurostat (as far as I could see), now rely on chained indices. I have therefore used the Generalized Exactly Additive Decomposition (GEAD) formula presented by Tang and Wang (2004), which is applicable in such a context, but add the caveat that the interpretation of the individual terms is not quite the same as for the TRAD decomposition. The results for Germany tell yet another story, with reallocation effects representing a persistent boost to overall labour productivity growth and not helping to explain the overall slowdown. That said, Elstner et al (2017) come to the opposite conclusion, albeit using different data and (yet another) a different decomposition. As I have not been able to access their data or calculations yet (and put together mine quite quickly), I will leave it at this footnote for now.