Automation and inequality with taxes and transfers

Abstract

Declines in low-skill labour shares are reviewed, and a stylised model is constructed to examine their determinants and future implications. A retrospective analysis of US shocks suggests that technological change has contributed more to raising income inequality and the wealth to GDP ratio than other changes. An anticipated future twist away from low-skill labour toward the capital, combined with population growth, risks high unemployment rates. Productivity growth at twice the pace since 1990 limits this, though inequality persists. Analysis shows that a generalisation of the US ‘earned income tax credit’ system with consumption tax outperforms alternatives of the ‘universal basic income’.

1 INTRODUCTION

Prominent trends in global economic performance that have emerged in the past three decades include slowing growth in total factor productivity in advanced economies, most notably during the first decade of the millennium (Eichengreen et al., 2017; Lo & Rogoff, 2015; Taylor & Tyers, 2017), declines in rates of return on investment and long-maturity bond yields (Rachel & Summers, 2019; Summers, 2014, 2016) and the tendency for the new income and wealth that has been generated to have been captured by high-level professional and capital-owning households (Alvarez-Cuadrado & El-Attar Vilalta, 2018; Piketty & Zucman, 2014; Rognlie, 2015). It is unsurprising that these three trends are related (Pichelmann, 2015) and that they depend, at least in part, on technical changes in the period (Gordon, 2014, 2015) and the recent surge in automation and robotics (Lankisch et al., 2019).

In the early 2000s, levels of real net investment in the advanced economies began to decline. Other things equal, these slower rates of capital accumulation would have slowed the uptake of embodied technology and the growth of total factor productivity (TFP). Indeed, TFP stagnated quite suddenly across the OECD around this time and there has since been little sign of resurgent growth. At the same time, the steady decline in the share of the low-skilled in value-added throughout the OECD and the transitional economies has been widely noted (Autor et al., 2017; Bloom et al., 2018; OECD, 2012; Trott & Vance, 2018).11 The complementary rise in the capital share of income is the prime focus of Piketty (2014), Piketty and Zucman (2014) and Rognlie (2015). Applications to China include those by Fleisher et al. (2010), Zhou and Song (2016), Kanbur et al. (2017) and Zhou and Tyers (2019). Most recently, an associated concern has been with the poor OECD levels of real-wage growth in the post-Global Financial Crisis (GFC) era (Bishop & Chan, 2019; Schwellnus, 2019).

Explanations posited for these observations include East Asian comparative growth and trade,22 The roles of China, and Asian trade more generally, in US labour market performance in the 2000s are explored by, among others, Pierce and Schott (2012), Autor et al. (2013), Arora et al. (2015), Acemoglu et al. (2016) and Tyers (2015). the rise of the property rights component of intangible capital (Kho et al., 2016), the interaction between IT development and the diminution of competition within IT-intensive oligopolies (Autor, 2017; Eeckhout, 2019; Ezrachi & Stucke, 2016; Moazed & Johnson, 2016) and the wider displacement of workers by increasingly intelligent machines (Abeliansky et al., 2020; Acemoglu & Autor, 2011; Acemoglu & Restrepo, 2015; Autor, 2016; Harris et al., 2018; Krenz et al., 2018; Susskind, 2017; Susskind & Susskind, 2015).

In this expanding literature, it is possible, loosely, to separate the views of ‘techno’ pessimists and optimists. Some pessimism emerges from Gordon (2014, 2015), who sees the major gains in capital-embodied productivity in the past and, in effect, recognizes what has become known as the ‘Solow paradox’,33 Acemoglu et al. (2016) note Robert Solow's comment in his 1987 New York Times Book Review article: “… what everyone feels to have been a technological revolution, a drastic change in our productive lives, has been accompanied everywhere, including Japan, by a slowing-down of productivity growth, not by a step up. You can see the computer age everywhere but in the productivity statistics.” the obvious spread of information technology (IT) in the face of its apparent lack of evidence in productivity statistics. This dark side sees the potential for automation to threaten the role of employment in distributing income.44 Key contributors include Brynjolfsson and McAfee (2011), OECD (2012), Goos et al. (2014), Hemous and Olsen (2014), Avent (2016), Prettner (2017) and Baldwin (2019). Particularly ardent pessimists see artificial intelligence (AI) as necessitating an inevitable “singularity” by which human influence over technology will cease (Barrat, 2013; Kurzweil, 2005; Nordhaus, 2015) and machines that are so adaptable that they will drive almost all workers out of the production process (Susskind, 2017). As Ford (2015, 2016) suggests, the issue is not that we may no longer have ‘broad-based’ innovation; it is that modern innovation may no longer procure broad-based prosperity, leading to low-skill workers becoming the ‘precariat’ (Das, 2016a, 2016b).55 Another dark side of the IT revolution, not addressed in this paper, is that information and communications technologies and connectedness force professionals and workers into multiple related tasks, weakening the gains from the prior division of labour (Harford, 2018; Mark, 2015).

By contrast, techno-optimists see immense potential for productivity and lifestyle improvements from the further expansion of modern IT, AI and robotics. Mokyr (2013) and Mokyr et al. (2015) argue that, technology anxiety notwithstanding, we are on the cusp of a new era of progress in innovation that will provide an unprecedented boost to productivity. Since such strong increases in productivity are yet unobserved, we focus on other determinants of performance and the evident technical bias against low-skill labour.

To examine the roles of this bias in historical and continuing trends in performance, and what fiscal responses governments might offer to control its undesired effects, we develop an elemental, stylised general equilibrium model calibrated on the US economy. The model features multiple households and a technology specification that allows the separation of changes in total factor productivity on the one hand and factor bias on the other. We use the model in two related exercises. The first is a retrospective analysis of income inequality in the United States. The second is a prospective analysis that examines scenarios characterised by differing assumptions about technological change, population growth and fiscal policies.

We begin by summarising the evidence on total factor productivity and factor bias in key OECD countries since 1990. The model is then applied to construct a decomposition of observed changes in that period. Changes in real disposable incomes, the income inequality between three represented households and the economy's wealth to GDP ratio is examined in response to changes in factor abundance, total factor productivity, factor bias, the relative cost of capital goods, labour force participation rates and the progressivity of the tax system. Technological change, featuring bias away from low-skill labour, emerges as the dominant explanators of the rise in inequality in that period.

The model is then subjected to a set of prospective shocks over a further two decades to examine the effects of further changes in factor bias, population growth and its composition,66 With respect to changes in population and its skill structure, we offer a stylised examination of the future consequences detailed empirically by Bloom et al. (2018). and TFP. Unemployment at unprecedented rates emerges as a possibility, made worse by the anticipated population increment if its skill content remains low. In this context, a minimum real wage, combined with transfers to support the unemployed is compared with flexible wages with ‘earned income tax credits’. Alternate financing for both systems includes taxes on capital income and consumption.77 These policy responses are also explored in a different modelling context by Prettner and Strulik (2019). They emphasise skill acquisition in a solely prospective analysis. The earned income tax credit system emerges as superior, in combination with increased taxation of consumption expenditure. In the end, however, much depends on the rate of TFP growth. If it is weak and the ‘Solow paradox’ persists, there will be no politically feasible escape from increased transfers. If it is strong, inequality will continue to increase, but the prospect of rising unemployment or declining real consumption wages is avoidable.

Section 2 reviews data on technical change and income distribution in key advanced economies while Section 3 describes the general equilibrium framework used to conduct the analysis. Section 4 offers the decomposition analysis for the case of the United States over 1990–2016 and Section 5 addresses prospective shocks and their distributional consequences. Section 6 then concludes.

2 TECHNOLOGY, FACTOR SHARES AND INEQUALITY IN ADVANCED ECONOMIES

That income inequality has risen across the OECD countries since the 1960s is clear from Figure 1. To examine how much this rising trend in income inequality is driven by the technical change, we first investigate changes in measured TFP and factor payment shares. Two striking trends emerge: a slowdown in TFP growth and a twist in shares away from low-skill labour. We then examine the dispersion of wage incomes in the United States in search of complementary patterns.

FIGURE 1

Income Gini coefficients, key OECD countries

Sources: Unless otherwise stated, OECD Income Distribution Database (OECD, 2015). The single continuous series is from the US Census Bureau, Current Population Survey, Annual Social and Economic Supplements.

 

2.1 Technology indicators

The slowdown in TFP growth is clear in Figure 2, which shows the turning point following which TFP stagnated to have been during the early 2000s, prior to the GFC. This is true on average for the OECD and, as shown in Figure 2, for key individual economies, including the United States, Great Britain (the UK) and Australia. The UK had taken the lead in TFP growth early on, in part because of its specialisfation as a delivery centre for services to the European Union (EU). The United States caught up during its IT boom in the 1990s. Australia's comparatively rapid uptake of IT raised the efficiency of its services, so that its productivity also surged in this period. These three regions out-performed the OECD as a whole, though all began to stagnate before the GFC.

FIGURE 2

Total factor productivity, 1970–2014 (United States, United Kingdom, Australia, OECD overall)

Source: Penn World Tables, international comparisons of production, income and prices, version 9.0. TFP is the portion of output change not explained by the quantities of inputs used in production and is reported at constant national prices (2011 = 1). We normalise the data to set TFP in 1970 at unity.

 

Changes after 1995 in the shares of expenditure by producers on capital, low-skill labour and skill are examined in Figure 3 for the United States, the United Kingdom, Australia and the OECD as a whole. The low-skill labour share of value-added is that of payments to ‘medium- and low-skilled’ persons. The skill share is that of payments to high-skilled persons. For the OECD as a whole and all the individual regions listed, the low-skill labour share declined significantly, from 42% to 35% across the OECD. By contrast, there was a surge in the skill share over this period, from 20% to 25% across the OECD. Capital shares rose more modestly, from 38% to 40% across OECD, so the major beneficiaries of the incremental factor bias were professional workers.

FIGURE 3

Value-added shares of primary factors, OECD and selected economies 1995–2008

Source: Socio Economic Accounts, World Input Output Database, 2013 Release (Timmer et al., 2015).

Note: The capital share is calculated as the share of payment for capital in value-added; labour share is the share of payment to medium- and low-skilled persons in value-added; skill share is the share of payment to high-skilled persons in value-added. Labour skill types are classified on the basis of educational attainment levels as defined in the International Standard Classification of Education (ISCED): low-skilled (ISCED categories 1 and 2), medium-skilled (ISCED 3 and 4) and high-skilled (ISCED 5 and 6). Capital compensation is derived as a residual and defined as gross value-added minus labour income. Hence, it is the gross compensation for capital, including profits and depreciation allowances. Because of its derivation as a residual, it reflects the remuneration for capital in the broadest sense. This does not include only traditional reproducible assets such as machinery and buildings, but it also includes nonreproducible assets. Examples are mineral resources and land, intangible assets (such as R&D knowledge stocks, software, databases, brand names and organisational capital) and financial capital. 

2.2 Dispersion in real-wage incomes

The modern literature exploring the determinants of wage dispersion in advanced economies expanded during the late 1980s following the deterioration in the labour market performance of low-skill US and European workers. Surveys grounded in the Stolper-Samuelson Theorem, have been offered, early on by Wood (1994), and recently by Gozgor and Ranjan (2017), Wood (2018) and by Zhou and Bloch (2019). The early empirical studies focussed on the links between trade and US labour market performance (Berman et al., 1994; Borjas & Ramey, 1994; Bound & Johnson, 1992; Leamer, 1996). These studies were driven by the observed rise in the skill premium from the late 1980s, seen in the early 1990s in Figure 4. Each contributor sought to apportion blame for the dispersion between trade with developing countries (particularly ‘outsourcing’) on the one hand and labour-saving technical change on the other, with all attributing at least part of the effect to trade.

FIGURE 4

Trends in real worker incomes in the United States

Source: Mean incomes in constant 2015 US dollars by educational attainment based on Table P-18—Educational Attainment, people 25 years old and over by mean income and sex, 1991 to 2015, the US Bureau of the Census.

Note: Cumulative percentage changes are shown relative to 1991 means. These are adjusted for price inflation, money earnings for working males and females (aged 25 and above) by educational cohort in terms of the highest level of education attained. Changes along the y-axis are log changes (which approximate percentage changes), smoothed to three-year moving averages to eliminate occasional annual volatility. Less than high school and some high school workers correspond to low-skill workers; high school grad and some college correspond to medium-skill workers; college grad and more than college correspond to high-skill workers. 

Complementary global general equilibrium studies also emerged in that period, beginning with Krugman (1995) and proceeding to the decomposition studies by Tyers and Yang (1997, 2000) and Francois and Nelson (1998). Both studies suggested that strong growth in developing countries that are trading partners had been net welfare improving in the developed economies and that technical change was more important than trade in determining labour market outcomes.88 Somewhat later a similar conclusion is drawn from dynamic global modeling by McKibbin and Woo (2003).

As can be seen from Figure 4, later in the 1990s the heat came out of this debate temporarily when the US IT boom stabilised the level of dispersion and lifted all real-wage incomes. It was again resurgent after China's accession to the WTO in 2001. China's growth surged thereafter and it came to dominate global trade in manufacturing. The new literature noted that the performance of all US worker occupation groups (bar the top one per cent) deteriorated after 2000 (Haskel et al., 2012; Pierce & Schott, 2012). This is consistent with the final trends in Figure 4, which show a further widening in the dispersion of real worker incomes and deteriorating low-skill worker performance.

These trends appear consistent with the aggregate changes in the US levels of population, employment and its human capital stock to emerge from the Penn World Tables (Feenstra et al., 2015), illustrated in Figure 5. Relative to the path of population growth, these show a slowing in the rate of human capital accumulation after 1990 and in total employment after 2000. More recently, the economic stories that help explain these trends combine more detailed characterisation of job tasks with greater roles for trade and competition behaviour than had been considered in the earlier literature.99 See, for such explanations, Helpman et al. (2010), Autor et al. (2013), Ezrachi and Stucke (2016), Moazed and Johnson (2016), and Autor et al. (2017). Earlier work had also shown that product differentiation could limit the penetration of external terms of trade shocks to domestic labour markets (Tokarick, 2005), and wage distribution effects were shown to depend on capital-skill complementarity (Tyers & Yang, 2000; Winchester & Greenaway, 2007).

FIGURE 5

Population, human capital and employment in the United States (indices 1990 = 100)

Source: Penn World Tables (Feenstra et al., 2015). The human capital index is based on years of schooling and returns to education; see ‘Human Capital’ in PWT9.

 

2.3 The suffering ‘middle’ and the increasing income disparity between the highly skilled and others

The trend toward comparatively poor labour market performance of workers in the middle-skill levels was noted early on by Gregory (1993) for the United States and Australia, and more recently by Acemoglu and Autor (2011) and Autor (2016). Table 1 presents the changes in skill earnings gaps in OECD economies from the year 2002 to the year 2014. Overall, the gap between high- and medium-skill earnings widened and that between medium- and low-skill earnings narrowed, which suggests the twist was in the dispersion of earnings between high-skill persons and the combined medium- and low-skill group. This is consistent with Autor's assertion that it is workers of medium skill that have been most vulnerable to automation and outsourcing and the assertion of Beaudry et al. (2017) that the penetration of automation into the advanced professional sector is causing highly trained professionals to compete in the middle-skill range.

TABLE 1. Earnings gaps between skill groups as % of income to the low-skilled (full-time 25- to 64-year-old employees)

	Low to medium skill (as % of low-skill earnings)		Medium to high skill (as % of low-skill earnings)
	2002	2014	2002	2014
Australia	22	14	28	32
Germany	30	..	33	..
Korea	41	14	31	33
United Kingdom	47	32	39	36
United States	52	37	48	50
OECD	28	23	40	47

• Note: Data on mean incomes are not available. Earnings by skill (or education levels) refer to mean annual earnings of full-time for 25- to 64-year-old employees. Earnings gaps between medium-skilled and low-skilled employees are calculated as the difference between mean earnings of medium-skilled employees and low-skilled employees relative to mean earnings of low-skilled employees; earnings gaps between high-skilled and medium-skilled employees are calculated as the difference between mean earnings of high-skilled employees and medium-skilled employees relative to mean earnings of low-skilled employees. The skill levels are based on the International Standard Classification of Education (ISCED, 2011). Low (skills) corresponds to less than upper secondary ISCED levels 0, 1, 2 (Less than primary, primary and lower secondary education). Medium (skills) corresponds to upper secondary and postsecondary nontertiary ISCED levels 3 (including partial level completion), and ISCED 4 (Upper secondary and postsecondary nontertiary education). High (skills) corresponds to tertiary ISCED levels 5, 6, 7 and 8 (short-cycle tertiary education, bachelors or equivalent level, masters or equivalent level, doctoral or equivalent level).

Source: Authors' calculations based on data from OECD Employment Outlook, 2014 and 2016.

To reflect the above-growing wage gap between the highly skilled and the combined-medium-and-low skilled, our modelling below distinguishes just two groups: the high-skilled and the rest, which henceforth we refer to as the ‘low-skill’ group.

3 MODELLING THE ECONOMY-WIDE CONSEQUENCES OF AUTOMATION

A calibrated, single product, real general equilibrium structure is used that has three-household groups, a complete financial market and a detailed fiscal structure that includes three types of income taxes and transfers. The modelling is comparative static, constructed to simplify the analysis of jumps over extended periods. We chose this structure to avoid the many complications of full, transitional dynamics, since it nonetheless offers the means to do useful decomposition analysis and forecasting.1010 The comparative static modelling requires shocks to the capital stock while also calculating levels of annual investment. We did not link these dynamically because we simulate changes over quite long periods, when the connection between new levels of investment and the new capital stock is more obscure. Moreover, the accumulation of physical capital is only one of a number of sources of intertemporal change. Opting for full dynamics would require endogenizing the supply of skill, or human capital accumulation, and the technology, via R&D expenditure. At least in looking retrospectively, when we know factor inputs at the beginning and end of a period of analysis, this is unnecessary.

On the supply side, there are three primary factors with low-skill labour (L) defined as a partially unemployed variable factor. In standard model closures, the stocks of physical capital (K) and skill (S) are exogenous and fully employed. We use a formulation of the technology that allows for the separation of factor bias shocks from TFP shocks, to ensure that bias shocks can be considered separately from neutral TFP shocks that ‘raise all boats’.

The three households own differing shares of the three primary factors and have different consumption behaviour, dependent on current and expected future disposable income and a common bond yield, derived to clear the financial market. We use a reduced form consumption equation that is digested not only from a common utility function but also from the embedding of that function in separate intertemporal optimisation problems that involve consumption and saving choice. This consumption equation is a generic form that follows from the first-order conditions emerging from the intertemporal optimisation problem.

Different household elasticities of consumption demand to current and expected future real incomes ensure that the marginal utility of consumption is higher in the poorer than in the richer households. Households operate at different income and consumption levels, so the elasticity of current real consumption to income is smaller for wealthier households and hence that their marginal propensities to save are higher.

3.1 The supply side

There have been many approaches to the representation of automation in technology. Ours stems from the recent work of Aghion et al. (2019). For them, real gross domestic product is a CES combination of goods. They build on the task-based approach of Zeira (1998), which offers a crude substitution of capital for labour at the task level. They further point out that the simple Cobb–Douglas combination of capital and labour works where automation has the effect of raising the elasticity of output to capital.

Consider the case where there are two primary factors, combined via a CES production function to calculate the real volume of output in period t:

$$$$ {y}_t={A}_t{\left[{\alpha}_t^{1-\rho }{K}_t^{\rho }+{\left(1-{\alpha}_t\right)}^{1-\rho }{L}_t^{\rho}\right]}^{\frac{1}{\rho }}, $$$$(1)

where K is capital, L is labour, α_t is the fraction of goods that have been automated in period t and the elasticity of substitution between factors is 1/(1 + ρ) with −1 < ρ < 1. From this, the elasticities of output to factor input are:

$$$$ {\beta}_{Kt}=\frac{\partial {y}_t}{\partial {K}_t}\frac{K_t}{y_t}={\alpha}_t^{1-\rho }{A}_t^{\rho }{\left(\frac{K_t}{y_t}\right)}^{\rho },\kern1em {\beta}_{Lt}=\frac{\partial {y}_t}{\partial {L}_t}\frac{L_t}{y_t}={\left(1-{\alpha}_t\right)}^{1-\rho }{A}_t^{\rho }{\left(\frac{L_t}{y_t}\right)}^{\rho } $$$$(2)

In period t, then, production behaviour can take the simpler Cobb–Douglas form:

$$$$ {y}_t={B}_t{K}_t^{\beta_{Kt}}{L}_t^{\beta_{Lt}}, $$$$(3)

where B is a calibrated constant and automation can be represented by changes in the elasticities, β, which depend on the shares of automated products. The difficulty that then arises is that shocks to the elasticities alter both initial and final output levels. Factor bias shocks and TFP therefore interact.1111 For example, when the TFP coefficient is held constant, a rise in the elasticity of output to capital input (and a commensurate reduction in the elasticities to labour and skill) changes initial output in a direction that depends on the levels of factor use. We adjust for this so that output, and implied TFP, is neutral to bias “twists”. To (1) allow for the independent consideration of factor elasticities and total factor productivity, (2) separate raw labour from skill and (3) retain constant returns to scale, we adopt a ‘relative Cobb–Douglas’ formulation.

$$$$ \frac{y}{y_0}=\theta {\left(\frac{L}{L_0}\right)}^{\beta^L}{\left(\frac{S^K}{S_0^K}\right)}^{\beta^S}{\left(\frac{K}{K_0}\right)}^{1-{\beta}^L-{\beta}^S}, $$$$(4)

where y₀, L₀, $$$ {S}_0^K $$$ and K₀ are the initial levels of output and inputs of low-skill labour, skill and capital. A total factor productivity parameter, θ, is included, along with a set of factor shares, β, and to do this in such a way that the initial output is unaltered.

Technology shocks that result in pure factor bias have no net effect on the level of output, but they strongly affect the marginal products and hence drive changes in primary factor rewards.1212 In effect, shocks to factor shares alone adjust the initial level of total factor productivity, so that the question becomes, how different would the economy have been had the factor shares been at their post-shock levels? In the complete model, however, such shocks do not necessarily hold output constant, since this depends on whether real-wage rigidities cause changes in unemployment, directly affecting output through labour use. A pure-bias change against raw labour, that advantages capital, can then be represented simply as a decline in β^L. In the complete model, this raises the real reward of capital at the expense of labour. Total factor productivity shocks require only a change in θ.

The marginal products are then:

$$$$ {\mathrm{MP}}^L={\beta}^L\frac{y}{L},\kern1em {\mathrm{MP}}^S={\beta}^S\frac{y}{S^K},\kern1em {\mathrm{MP}}^K=\left(1-{\beta}^L-{\beta}^S\right)\frac{y}{K}. $$$$(5)

The real production wages of unskilled and skilled workers depend conventionally on the corresponding marginal products:

$$$$ w=\frac{W}{P^P}={\beta}^L\frac{y}{L},\kern1em {w}^S=\frac{W^S}{P^P}={\beta}^S\frac{y}{S^K}. $$$$ (6)

Here, the upper case wages are nominal (expressed relative to the numeraire, the GDP price), and the lower case wages are real (expressed relative to the producer price, P^P).

3.1.1 Output, GDP and prices

The real volume of output, y, is distinguished from nominal GDP, Y = P^Yy, where P^Y is the GDP price level (deflator).1313 In this real model, “nominal” refers to prices relative to the model numeraire, which is arbitrary but is chosen to be the GDP price P^Y. The producer price, P^P and the consumer price level, P^C, vary relative to this value in response to shocks. Direct and indirect tax revenues, T^D and T^I, and transfers to households, T^R, play key roles in the formulation. In this context, the GDP price, P^Y, and the producer price, P^P, would be the same were it not for indirect taxes. In their presence we have:

$$$$ Y={P}^Yy={P}^Py+{T}^I,\kern1em \mathrm{so}\ \mathrm{that}\;{P}^Y={P}^P+\frac{T^I}{y}. $$$$(7)

GDP at factor cost (or producer prices), Y^FC, is the total of direct payments to the collective household in return for the use of its factors. Nominal GDP is then

$$$$ Y={Y}^{FC}+{T}^I,\kern1em {Y}^{FC}=C+\left[{T}^D-{T}^R-\alpha {W}_0\left(F-L\right)\right]+{S}^P. $$$$(8)

This is the standard disposal identity for GDP or the collective household budget. C is the total value of final consumption expenditure, including indirect taxes paid, S^P is private saving and the term in square parentheses is direct taxation net of transfers to households (the latter including nonspecific transfers, T^R, and unemployment benefits at a fraction, α, of the initial low-skill wage). L is low-skill employment and F is the low-skill labour force. These aggregates of consumption, taxation and saving are broken down into household components once the populations of household groups are formulated.

3.1.2 Population and participation

The three separate households, h, are defined based on factor ownership. The first has income dominated by production labour, the second by skill and the third by capital. Because few households depend on only one factor of production, the three are defined based on the stylised factor ownership shares, s_hf, offered in Table 2. The low-skill and skilled labour forces depend not only on these ownership shares but also on separate participation rates. All three households supply low-skill workers and skills but at different participation rates, $$$ {\lambda}_{Lh} $$$ and $$$ {\lambda}_{Sh} $$$ (defined here as the ratios of participating, full-time equivalent, worker-years to populations). The links between the low-skill and skilled labour forces and the three-household populations are then:

$$$$ {N}_h=\frac{s_{hL}L}{\lambda_{Lh}}+\frac{s_{hS}{S}^K}{\lambda_{Sh}}. $$$$(9)

TABLE 2. Stylised household factor ownership shares used in modelling

Households	Primary factors
	Low-skill labour	Skill	Physical capital
Low income	0.95	0.01	0.10
Professional	0.04	0.70	0.20
Capital owning	0.01	0.29	0.70
All households	1.00	1.00	1.00

• Source: These are highly stylized but representative of data on wealth shares from Boshara et al. (2015) and Schneider and Tavani (2016).

This level of detail in labour supply is required not only for labour market equilibrium but also for the eventual construction of Lorenz curves. Apart from their significance for labour supply and real wages, changes in unemployment and participation rates influence welfare via dependency ratios within each household group.

3.2 The demand side

Central to the demand side in any economy-wide model is the financial market, which equates saving to investment. Here investment depends on the expected after-tax yield, or the rate of return on the installed capital net of depreciation and capital tax, adjusted for sovereign risk, r^ce. This has a number of components. First, since only the after-depreciation component of capital income is taxed, after-tax capital income is:

$$$$ {Y}_{KN}=\left(1-{t}^K\right)K\left({P}^P{\mathrm{MP}}_K-{P}^K\delta \right), $$$$(10)

where $$$ {P}^K $$$ is the price of capital goods,1414 In this single product model the product and capital goods prices are separated by a single parameter: $$$ {P}^K=\gamma {P}^P $$$. This allows shocks to represent the relative cheapening of capital goods over time as their information technology content rises. t^K is the ad valorem capital income tax rate and δ is the depreciation rate. The rate of return net of both tax and depreciation is then:

$$$$ {r}^c=\frac{\left[{P}^P{\mathrm{MP}}_K-{t}^K\left({P}^P{\mathrm{MP}}_K-{P}^K\delta \right)\right]}{P^K}-\delta . $$$$(11)

The expected form of this rate is then:

$$$$ {r}^{ce}={r}^c\left(\frac{\varphi^0}{\varphi}\right), $$$$ (12)

where the interest premium factor, $$$ \varphi $$$, permits consideration of the effects of changes in the fiscal balance on the sovereign risk premium. A deteriorating fiscal balance causes investment to be less attractive.

$$$$ \varphi ={\varphi}^0{\left[\left(\frac{G}{T}/\frac{G_0}{T_0}\right)\right]}^{\phi }, $$$$(13)

where $$$ \phi $$$ is a positive elasticity indicating sensitivity to sovereign risk.

The demand for investment financing depends on the ‘Tobin's Q like’ ratio of the expected rate of return on installed capital, $$$ {r}^{ce} $$$ and a domestic market-clearing bond yield or financing rate, $$$ r $$$. These differ so long as the economy is not in a financial steady state.

$$$$ \frac{I^D}{I^0}={\left(\frac{r^{ce}}{r}\right)}^{\varepsilon^I}, $$$$(14)

where $$$ {\varepsilon}^I $$$ is a positive elasticity. This investment demand is then matched by a supply of saving that incorporates the government's fiscal position:

$$$$ {I}^D={S}^D={S}^P+\left({T}^D+{T}^I-G\right), $$$$(15)

where T^D and T^I are, respectively, direct and indirect tax revenues, S^P is private saving and G is the total of all the government's expenditures, including those on goods and services, G^X, transfers to households, T^R, and unemployment benefits, which are paid at a fraction, α, of the initial nominal low-skill wage, W₀. Thus:

$$$$ G={G}^X+{T}^R+\alpha {W}_0\left(F-L\right),\kern1em {T}^R={\sum}_h{T}_h^R,\kern1em {T}_h^R={t}_h^R{YN}_h, $$$$(16)

where F is defined in (8) as the total low-skill labour force, $$$ {t}_h^R $$$ is the proportion of GDP that is paid out to household h, per capita (the fundamental constant underlying transfers), and N_h is the household population.

Calibration of the financial market is facilitated by the assumption that the initial database has the steady-state property that the net rate of return is initially the same as the market bond yield: $$$ {r}_0^{ce}=r $$$. Thus, the financial market-clearing condition endogenizes r by equating the value of the domestic investment, $$$ {I}^D $$$, which represents the sum of all domestic long-maturity asset issues, with demand for those assets in the form of net (private and government) savings.

For each household, h, aggregate consumption expenditure, C_h, is a nominal sum, but real consumption behaviour is motivated by current and expected future real disposable incomes and the real interest rate. We detail the taxation and accounting relations required to arrive at household and national disposable incomes in Appendix 1. For real consumption behaviour we resort to a reduced form that readily accommodates calibrated behavioural elasticities. Real consumption, (lower case) c_h, is represented as depending negatively on the after-tax real return on savings (the home bond yield, r) and positively on both current and expected future real disposable income:

$$$$ {c}_h=\frac{C_h}{P^C}={A}_h^C{\left(\frac{r}{1+{t}^K}\right)}^{-{\varepsilon}_h^{CR}}{\left(\frac{Y_h^D}{P^C}\right)}^{\varepsilon_h^{CY}}{\left(\frac{Y_h^{De}}{P^C\left[1+{\pi}_h^{Ce}\right]}\right)}^{\varepsilon_h^{CY}}, $$$$(17)

where household nominal disposable income is $$$ {Y}_h^D $$$, its future expectation is $$$ {Y}_h^{De} $$$ and the expected inflation rate of the consumer price level is $$$ {\pi}^{Ce} $$$.1515 There is no money-driven inflation in this model but expectations can be formed of a future increase in the consumption tax rate that would raise P^C relative to P^P and P^Y. The elasticities, ε, differ across households as indicated in Appendix 2. The consumer price level is marked-up over the producer price level by the power of the consumption tax, which is levied at the rate t^C, $$$ {P}^C=\left(1+{t}^C\right){P}^P $$$. This yields consumption tax revenue:

$$$$ {T}^I={t}^C{P}^P\sum \limits_h{c}_h. $$$$(18)

3.2.1 Private saving

Households receive factor incomes amounting to GDP at factor cost, Y^FC. Their disposal of nominal income is this sum less direct tax, net of transfers to households and the unemployed, as detailed in Appendix 1. Private saving differs across households. It is what remains after consumption expenditure (gross of indirect taxes) is further deducted from disposable income.

$$$$ {S}^P=\sum \limits_h\left[{Y}_h^D-{C}_h\right] $$$$(19)

Since total consumption expenditure, inclusive of consumption tax, is.

$$$$ C=\sum \limits_h{C}_h={P}^C\sum \limits_h{c}_h={P}^P\left(1+{t}^C\right)\sum \limits_h{c}_h, $$$$(20)

and total disposable income, Y^D, is as defined in Appendix 1, aggregate private saving can also be written consistent with (8) as:

$$$$ {S}^P={Y}^D-C=\left[Y-{T}^I-{T}^D+{T}^R+\alpha {W}_0\left(F-L\right)\right]-C. $$$$ (21)

3.2.2 Government and total domestic saving

This is government revenue less government expenditure, both measured net of direct transfers to households and the unemployed. Total domestic saving is then the sum of private and government savings where government saving is $$$ {S}^G={T}^D+{T}^I-{T}^R-{G}^X-\alpha {W}_0\left(F-L\right) $$$.

$$$$ {S}^D={S}^P+{S}^G=Y-C-{G}^X. $$$$(22)

3.2.3 The product balance

Product balance stems from a version of the expenditure identity in real volume terms:

$$$$ y=\frac{I+{G}^X}{P^P}+\sum \limits_h{c}_h, $$$$(23)

where the final term is the sum of real consumption across the households. Neither investors nor the government pays indirect taxes on their expenditure and so the price they face for the home product is the producer price, P^P.

3.2.4 Welfare and inequality

For distributional analysis, taking household and total disposable incomes, $$$ {Y}_h^D $$$ and Y^D, from Appendix 1, the household shares of disposable income and population are:

$$$$ {s}_h^{YD}={Y}_h^D/{Y}^D,\kern1em {s}_h^N={N}_h/\sum \limits_{i=1}^H{N}_i,\kern1em \forall \kern0.5em h\in \left(1,H\right). $$$$ (24)

Our measure of group welfare is real disposable income at consumer prices, $$$ {V}_h={Y}_h^D/{P}_C $$$, since this indexes the volumes of current and potential future consumption on which group utility depends. We code into the model a three-group Gini coefficient, first by calculating the area under the three-household Lorenz curve:

$$$$ {A}_L=0.5\;\left[{s}_{Lh}^N{s}_{Lh}^{YD}+{s}_{Sh}^N\left(2{s}_{Lh}^{YD}+{s}_{Sh}^{YD}\right)+{s}_{Kh}^N\left(1+{s}_{Lh}^{YD}+{s}_{Sh}^{YD}\right)\right], $$$$(25)

so that the corresponding Gini coefficient is then.

$$$$ {G}^C=2\left(0.5-{A}_L\right). $$$$(26)

3.2.5 Financial wealth

The growth path of the US economy has not been in a steady state for three decades, with asset prices inflating relative to product prices by at least six percentage points per year on average.1616 This is readily concluded from a comparison of the path of a broad index of stock prices, such as the Wilshire Capital Price Index, and the US CPI, since 1990. This implies growth in financial wealth relative to GDP, which we posit is due generally to growth in realised rates of return relative to financing rates and, more fundamentally, to the cheapening of new IT-intensive capital relative to other goods and a rise in saving supply due to income concentration in comparatively high-saving households. Financial wealth is simply represented as the present value of an infinite stream of real dividends, r^ceK (recalling that r^ce is the expected real, net rate of return on installed capital from Equation 12), discounted at the current financing rate, r. The variable of interest is the ratio of the real present value of financial wealth to real GDP:

$$$$ {W}^F/y=\left(\frac{r^{ce}}{r}\right)\left(\frac{K}{y}\right) $$$$(27)

3.3 Parameters, database and operation

A complete list of the behavioural parameters used in the model is provided in Appendix 2, Table A1. The model is structured to resemble the US economy in 2016. The database is built on national and government accounts and financial data for that year. The model code and working software are available on request from the authors.

A particularly important element of the database concerns the assets of all three represented households: low income, professional and capital owning. The ownership shares of each, across low-skill labour, skill and physical capital, are detailed in Table 2. Most notably, the low-income and professional households do have some capital assets, mainly in the form of housing, and the capital-owning households do offer some low-skill and high-skill labour.

3.3.1 Operation and closures

The model is of the applied general equilibrium type, comprising a set of nonlinear equations. In its structure, all variables are potentially endogenous or exogenous depending on the ‘closure’ chosen. This means that when we have n variables with m equations with n > m, changes in the closure are derived by choosing the set of n-m variables to be rendered exogenous (unchanged or shocked in any solution). We detail the closures required to undertake the experiments for Sections 4 and 5, below, in Table A2.

4 SIMULATING US GROWTH AND INEQUALITY FROM 1990

Our first application is to begin with the model database representation of the economy in 2016 and to use the observed changes occurring in the period 1990–2016 to construct a back-cast to 1990. The purpose of this is so we can then use the model to decompose the back-cast and attribute contributions to inequality to separate components of change in that period. The particular changes introduced are to the volumes of factor use and population levels, TFP, factor bias, the relative cheapness of capital, reduced income tax progressivity and labour force participation. The extensive literature on the drivers of US income inequality frequently highlights these variables (Bargain et al., 2015; Benzell et al., 2015; Kaymak & Poschke, 2016; Lin & Tomaskovic-Devey, 2013; Rubin & Segal, 2015; Saez, 2017; Saez & Zucman, 2016).

Central to our historical analysis are changes in factor shares, which we plot in Figure 6, and which show the continuous decline in the low-skill labour share discussed previously. The corresponding growth in the skill share moderates after 2000, suggesting that the substitution for high-skill jobs has slowed and that automation is encroaching on skill demand as well (Autor, 2016; Beaudry et al., 2017). Associated with this is evidence of a modest growth trend in the capital share.

FIGURE 6

Factor shares of value-added in the United States

Source: Authors' calculations based on the Penn World Tables (Feenstra et al., 2015) and Socio Economic Accounts, World Input Output Database, 2013 Release (Timmer et al., 2015), along with employment and wage data from FRED. Solid lines indicate historical data. Broken lines indicate extrapolations used in the prospective analysis.

 

Other key changes in this period include declines in labour force participation and in rates of direct taxation. Labour force participation, as a proportion of the population, fell from 51% to 49% since 1990, which seems modest, but this disguises a much larger fall amongst the low-skilled. When rising participation rates amongst professionals are accounted for (Tracey & Fels, 2016) we estimate that low-skilled participation fell by four percentage points, reducing the earning power of low-income households.

Notwithstanding widespread discussion of the Reagan and GW Bush tax cuts, as favouring high-income earners, the evidence on federal tax rates from the Congressional Budget Office suggests only moderate declines in effective rates of tax on incomes to skill and capital.1717 Since our analysis concludes with data for 2016 it does not account for the further reductions in corporate and high-income tax rates introduced with the Trump 2017 tax reforms. Our estimated rates are illustrated in Figure 7. We also consider the well-known decline in the cost of physical capital relative to other goods, which favours investment and income from physical capital, the latter having important implications for the fiscal balance. We list the complete set of 1990–2016 shocks applied to the model in Table 3. When all these shocks are imposed collectively, the consequences for each household's share of population and disposable income can be compared across the two periods, as in Table 4, yielding the three-household Lorenz curves illustrated in Figure 8.

FIGURE 7

Approximate effective federal tax rates, US %

Source: Authors' calculations based on revenues from Congressional Budget Office (2017) and tax bases from the World Input–Output Database (Timmer et al., 2015). Capital consumption from FRED is deducted from gross capital income to form the capital income tax base, and estate tax revenue is added to other capital tax revenue. The low-skill and high-skill income tax bases are payments to these factors recorded in the Input–Output Database. Payroll tax revenue is added to that from household income taxes, which are then split on the assumption that the low-skill rate, inclusive of payroll tax, has averaged 15%.

 

TABLE 3. Decomposition of past aggregate performance changes in the United States: Forward shocks from 1990 to 2016^{a a} The decomposition is achieved by shocking these variables individually and collectively. All shock variables are available for intermediate years, and some intermediate shocks are illustrated graphically.

Variable shocked, 1990 to 2016	Shock, % change
Factor use
Low-skill labour	6.4
Skill	91.3
Capital	79.0
Total factor productivity	24.2
Factor shares
Low-skill labour	−38.4
Skill	21.4
Capital	10.6
Cheaper capital relative to goods	−16.9
Power of income tax rates
Low-skill labour income	1.0
Skill income	−1.1
Capital income	−1.2
Government saving (negative)^b ^b This is a shock to the fiscal deficit, measured relative to the GDP price, P^Y.	9.5
Labour force participation rates^c ^c The changes in participation rates affect the per capita measures in the modelling. They are inferred from the skilled participation results of Tracey and Fels (2016) and the overall participation rate series from FRED.
Low-skill labour	−7.9
Skill	13.3
Unemployment rate	−6.4

• ^a The decomposition is achieved by shocking these variables individually and collectively. All shock variables are available for intermediate years, and some intermediate shocks are illustrated graphically.
• ^b This is a shock to the fiscal deficit, measured relative to the GDP price, P^Y.
• ^c The changes in participation rates affect the per capita measures in the modelling. They are inferred from the skilled participation results of Tracey and Fels (2016) and the overall participation rate series from FRED.

Sources: Factor use, factor share and total factor productivity changes are from Socio Economic Accounts, World Input Output Database, 2013 Release (Timmer et al., 2015) and the Penn World Tables Database (Feenstra et al., 2015). The relative capital goods price compares capital with GDP prices from FRED and the tax rates are interpretations from IMF, World Economic Outlook Database and Pomerleau and Lundeen (2014).

TABLE 4. Household population and disposable income shares, 1990 and 2016^{a a} These represent changes in shares in response to the shocks listed in Table 3. They provide the basis for the Lorenz curves in Figure 8 and the period change in the Gini coefficient.

Shares of totals, %	Households
	Low income	Professional	Capital owning
Population 1990	76	18	6
2016	69	22	9
Disposable income 1990	37	28	35
2016	27	34	39

• ^a These represent changes in shares in response to the shocks listed in Table 3. They provide the basis for the Lorenz curves in Figure 8 and the period change in the Gini coefficient.
• Source: Model database and back-cast simulation to 1990.

FIGURE 8

Simulated three-household Lorenz curves, 1990 and 2016 (This summarises the results of the simulated response of the economy to the collective shocks indicated in Table 3. It mirrors the shares indicated in Table 4)

Source: Solutions to the model described in the text.

 

4.1 Decomposition of inequality determinants 1990–2016

Here we use the model to decompose the aggregate and distributional changes in the US economy that emerge from our back-cast into components due to the different determinants of change across the period. The shocks to the variables listed in Table 3 are imposed, both individually and collectively, allowing the contribution of each to be separately quantified. We summarise the results in Table 5. The major contributors to the changes in GDP and real disposable income are, not surprisingly, factor use and total factor productivity. While the considerable relative expansion in both the supply and use of skill militates toward greater income equality, the shift in factor shares outweighs it. These effects, plus falling participation rates in the low-income household and reduced tax rates on professional and capital incomes, cause the model to predict a 2016 Gini coefficient that is higher by 10% (Table 5).

TABLE 5. Decomposition of aggregate performance changes in the United States—1990 to 2016^{a a} All but the final column show forward % changes from 1990. Changes in the rate of return and the financing rate are percentages of original rates, not percentage points.

Per cent change 2016 over 1990	Factor use	TFP	Factor shares	Cheaper capital	Fiscal deficit	Lower tax rates	Participation and unemployment	Total effects	Av growth rate, %/year
Real gross investment and saving	61.5	50.2	24.8	16.7	−5.3	3.6	0.8	152	4.5
Net real rate of return	−44.1	63.0	19.3	64.9	0.0	−0.1	0.7	104	3.4
Real financing interest rate	−44.6	8.9	−4.7	8.3	1.1	−1.0	0.0	−31.9	−1.8
Real consumption low-skill wage^b ^b Real consumption wages are nominal wages defined initially relative to the GDP price, P^Y, divided by the consumer price, P^C, also defined relative to P^Y.	37.6	14.9	−38.4	0.0	0.0	0.0	−0.4	13.7	0.6
Real consumption high-skill wage^b ^b Real consumption wages are nominal wages defined initially relative to the GDP price, P^Y, divided by the consumer price, P^C, also defined relative to P^Y.	−27.3	29	21.5	0.0	0.0	0.0	0.2	23.8	1.0
Real disposable income	71.5	23.8	0.0	−0.3	0.0	0.8	0.1	96.0	3.3
Real GDP	70.4	24.2	0.0	0.0	0.0	0.0	0.3	94.9	3.2
Real per capita disposable income	37.3	23.6	−0.4	−0.4	0.0	0.7	−6.8	54.0	2.1
Gini coefficient	−22.1	0.3	25.3	−0.2	0.0	1.1	5.3	9.6	0.4
Financial wealth/GDP	75.5	16.5	25.4	63.0	−5.1	3.5	0.2	179.0	5.0

• ^a All but the final column show forward % changes from 1990. Changes in the rate of return and the financing rate are percentages of original rates, not percentage points.
• ^b Real consumption wages are nominal wages defined initially relative to the GDP price, P^Y, divided by the consumer price, P^C, also defined relative to P^Y.
• Source: Back-casting using the model described in the text.

We summarise the corresponding decomposition of real incomes by household in Table 6. These results show even more clearly that the drag on the real disposable income of the low-income household is dominated by the change in factor bias. This household is the only one to lose from changes in factor bias and, also, the only one to lose from changes in participation rates and tax rates. Even though this technical change most favours skilled workers, the growth in real disposable income is greatest for the capital-owning household, principally because this household gains most from the comparatively high rate of capital accumulation and disproportionately from the rise in TFP.

TABLE 6. Decomposition of household income changes in the United States—1990 to 2016^{a a} All but the final column show forward % changes from 1990.

Per cent change 2016 over 1990	Factor use	TFP	Factor shares	Cheaper capital	Lower tax rates	Participation and unemployment	Total effects	Av growth rate, %/year
Real disposable income^b ^b Disposable income is defined relative to the GDP price, P^Y, and it is here divided by the consumer price, P^C, also defined relative to P^Y.
Low income	52.5	17.7	−24.9	0.0	−1.2	−0.2	43.9	1.7
Professional	87.4	27.9	15.5	−0.1	3.4	0.3	134	4.1
Capital owning	78.8	26.9	12.9	−0.8	2.1	0.3	120	3.8
Total	71.5	23.8	0.0	−0.3	0.8	0.1	96.0	3.3
Real disposable income per capita
Low income	44.0	17.5	−25.2	−0.1	−1.1	−10.9	24.2	1.0
Professional	−12.7	27.6	15.1	−0.2	1.9	17.8	49.5	1.9
Capital owning	−19.3	26.7	12.5	−0.6	1.2	0.2	20.6	0.9
Total	37.3	23.6	−0.4	−0.4	0.7	−6.8	54.0	2.1

• ^a All but the final column show forward % changes from 1990.
• ^b Disposable income is defined relative to the GDP price, P^Y, and it is here divided by the consumer price, P^C, also defined relative to P^Y.
• Source: Back-casting using the model described in the text.

4.2 The counterfactual: The path with and without tech bias

By subdividing the back-cast shocks and constructing depictions of the economy for selected years since 1990 it is possible to chart a simulated course through 2016. We then construct a counterfactual path, such that there is no change in factor bias beyond 1990. All the other shocks from Table 3 apply in their sub-period versions, including those to TFP. The results from this exercise are shown in Figure 9. They illustrate the significance of tech bias in the path of the economy and, in particular, in the paths of inequality, the welfare of the low-income household and the wealth to GDP ratio. The results suggest that, in the absence of tech bias since 1990, and assuming the same level of TFP growth in its absence, the Gini coefficient would actually have fallen and the real consumption low-skill wage would have risen by two-thirds.

FIGURE 9

Decomposition results: Key effects of tech bias in the US

Source: Back-casts from 2016 using the model described in the text.

 

The ratio of financial wealth to GDP is an alternative inequality measure in that it contrasts trends in the value of capital, mostly owned by the wealthier households, with those in national income. Real financial wealth grows with the accumulation of physical capital and with changes in the valuation of that capital that is based on expectations (Equation 27). Relative to GDP, the results suggest that this measure has increased considerably since 1990 and that a substantial contribution to this growth has been due to the bias component of technical change. As chosen techniques have become less intensive in low-skill labour, due to innovation, trade and competition changes, expected rates of return on capital have grown. Yet, at the same time, increased concentration of income in the high-saving households has tended to raise saving and suppress financing rates, raising discounted present values.

5 IMPLICATIONS OF PROSPECTIVE AUTOMATION IN THE UNITED STATES

In looking ahead we construct a ‘central’ projection over two decades to 2035, around which we examine the paths of different inequality outcomes and their fiscal implications. We list the elements of this projection in Table 7. To begin with, changes in labour supply are projected by imposing the baseline UN population projection, with 90% of the population expansion accruing to the low-skill household and 10% to the skilled. We hold constant labour force participation rates, defined on populations. The level of capital use is endogenous and allowed to expand so as to keep the expected rate of return on capital constant. When factor bias continues to increase this puts upward pressure on the rate of return on capital and sees the capital stock expand, also raising capital income and inequality.

TABLE 7. ‘Central’ projection shocks for the United States: 2016 to 2036^{a a} These shocks are chosen as ‘central’ to the prospective analysis. Unlike the retrospective analysis, there are no shocks to the relative price of capital goods, which is anticipated to be affected by a slowing of Moore's Law and the consolidation of the global IT sector into oligopolies, fiscal balance and participation rates. Anticipation of the latter two would be arbitrary and beyond the scope of this analysis.

Variable shocked, 1990 to 2008	Shock, % change
Population^b ^b These population shocks are consistent with UN-projected growth of the US population to 366 million by 2036, with 10% of increment in the professional category.
Low income household	15.3
Professional household	5.4
Total factor productivity^c ^c The central total factor productivity increment assumes a continuation of the average growth rate of productivity between 1990 and 2016, according to the Penn World Tables (Feenstra et al., 2015).	18.1
Factor shares^d ^d The projected changes in shares are as per Figure 6.
Low-skill labour	−30.8
Skill	0.0
Capital	13.7
Depreciation rate^e ^e The depreciation rate is shocked upward in the prospective analysis because of the expectation that, as the proportion of the capital stock comprising IT equipment rises, rates of obsolescence will also rise. For this purpose, the links between the overall depreciation rate (the ratio of capital consumption to the capital stock, from FRED), the rate of TFP growth and the low-skill labour share are explored econometrically. The results endorse a rise from 4% to 6% over two decades.	50.0

• ^a These shocks are chosen as ‘central’ to the prospective analysis. Unlike the retrospective analysis, there are no shocks to the relative price of capital goods, which is anticipated to be affected by a slowing of Moore's Law and the consolidation of the global IT sector into oligopolies, fiscal balance and participation rates. Anticipation of the latter two would be arbitrary and beyond the scope of this analysis.
• ^b These population shocks are consistent with UN-projected growth of the US population to 366 million by 2036, with 10% of increment in the professional category.
• ^c The central total factor productivity increment assumes a continuation of the average growth rate of productivity between 1990 and 2016, according to the Penn World Tables (Feenstra et al., 2015).
• ^d The projected changes in shares are as per Figure 6.
• ^e The depreciation rate is shocked upward in the prospective analysis because of the expectation that, as the proportion of the capital stock comprising IT equipment rises, rates of obsolescence will also rise. For this purpose, the links between the overall depreciation rate (the ratio of capital consumption to the capital stock, from FRED), the rate of TFP growth and the low-skill labour share are explored econometrically. The results endorse a rise from 4% to 6% over two decades.

The projection has TFP growing at the same annual rate as was achieved during 1990–2016 and, to reflect technical bias, factor shares are extrapolated as illustrated in Figure 6. No growth is introduced in the skill share to reflect a possible stand-off between the encroachment of automation on professional employment on the one hand and the creation of new professional jobs on the other (Autor, 2016; Beaudry et al., 2017).1818 It is worth noting that in the prospective analysis we assume that skill share is unchanged, but skill supply is increased in the form of a tenth of the population increment projected by the UN. The rise in the capital share is then a residual. The only other projected change is in the depreciation rate, which we raise from four to six per cent on the expectation that the rise in the IT proportion of the capital stock will increase the overall rate of obsolescence.1919 As indicated by Rognlie (2014), US Bureau of Economic Analysis data suggests that the depreciation and obsolescence rates for IT equipment and software are 18% and 43%, respectively. Because the relative price of IT capital services has been falling, its share of capital value has grown only moderately, but its share of capital volume continues to grow rapidly. It is the latter that has the most implications for the average rate of depreciation, and indeed for factor demand behaviour. We implement this ‘central’ projection under five alternative closures, in all of which there are changes to taxes, transfers and government expenditure on goods and services, but fiscal balance is constrained to be unchanged.

5.1 Projection with no policy change

Here there are no changes in tax rates and there is downward rigidity of real, low-skill wages, reflecting minimum wage laws. The results for this case are shown in the first column of Table 8. Most notably, worker displacement raises the unemployment rate to 18% and the Gini coefficient increases from 0.48 to 0.52. There is a considerable net improvement in household real income, by 39%, with the low-income household enjoying an improvement by a much smaller 11%. This overall improvement raises government collections at constant rates of tax, which makes affordable a rise in transfers, including unemployment benefits, from 8.1 to 10.6% of GDP. This considerable overall prosperity gain also raises the financial wealth to GDP ratio from 3.5 to 4.7. The increasingly stark differences in performance between the low-income and the other households, combined with the extraordinary unemployment levels, suggest the need for corrective policy changes.

TABLE 8. Prospective changes with automation in the United States—‘Central’ projection, 2016–2036^{a a} All columns refer to results from the central prospective shocks listed in Table 7. Model closures differ by column. In all cases, unemployment benefits are paid at 60% of the low-skill wage, and there is a flow of transfers over and above this that is, in the first column, at 2016 rates. Fiscal balance is retained throughout, with government spending on goods and services endogenous to tax receipts net of transfers in the first column only. In the remaining cases, government spending on goods and services is fixed, with either the capital income or consumption tax rate made endogenous.

Changes	No policy change	Policies to stabilise the Gini coefficient
		Minimum wage and transfers, incremental financing by		Earned income tax credits, incremental financing by
		Capital tax	Consn tax	Capital tax	Consn tax
Ending unemployment rate, %	17.5	20.2	20.2	4.9	4.9
Real consumption wage,^b ^b Real consumption wages are nominal wages defined initially relative to the GDP price, P^Y, divided by the consumer price, P^C, also defined relative to P^Y. %	0.4	0.5	−1.3	−18.4	−19.6
Capital use, % change	30.3	17.4	28.9	27.2	37.6
Real disposable income^c ^c Real disposable income is at the consumer price, P^C. per capita, % change
Low income	10.5	20.8	25.1	31.2	35.1
Professional	31.9	21.5	23.0	30.8	32.1
Capital owning	41.7	23.7	31.7	34.7	41.9
Total	39.1	31.2	37.6	42.1	47.8
% point change in
Capital tax rate	0.0	17.3	0.0	14.5	0.0
Consn tax rate	0.0	0.0	7.1	0.0	5.9
Ending transfers/GDP, %	8.2	11.6	12.1	13.9	14.3
Ending unemplt benefit/GDP, %	2.4	2.9	2.8	0.5	0.5
Ending total benefits/GDP, %	10.6	14.5	14.9	14.5	14.8
Real GDP, % change	34.4	27.3	32.9	36.8	41.8
Ending Gini coefficient level	0.52	0.48	0.48	0.48	0.48
Ending financial wealth/GDP	4.7	3.4	4.6	3.7	4.8

• ^a All columns refer to results from the central prospective shocks listed in Table 7. Model closures differ by column. In all cases, unemployment benefits are paid at 60% of the low-skill wage, and there is a flow of transfers over and above this that is, in the first column, at 2016 rates. Fiscal balance is retained throughout, with government spending on goods and services endogenous to tax receipts net of transfers in the first column only. In the remaining cases, government spending on goods and services is fixed, with either the capital income or consumption tax rate made endogenous.
• ^b Real consumption wages are nominal wages defined initially relative to the GDP price, P^Y, divided by the consumer price, P^C, also defined relative to P^Y.
• ^c Real disposable income is at the consumer price, P^C.
• Source: Projections using the model described in the text.

5.2 Transfers to stabilise inequality

The next step is to consider the expansion of transfers to the low-income household sufficiently to hold constant the Gini coefficient at its 2016 level. This is readily achieved via the model closure change indicated in Table A2 in Appendix 2, which is that the Gini coefficient is made exogenous while one of the tax rates is then endogenous to indicate the source of funding. We consider funding from two sources. The first option is a rise in the capital income tax rate, which reflects the dictum that governments should tax the robots (or their owners).2020 This comment stems famously from Bill Gates in an interview with Quartz: https://qz.com/911968/bill-gates-the-robot-that-takes-your-job-should-pay-taxes/. The second is the imposition of a federal tax on consumption expenditure. In each case, nominal government expenditure on goods and services is retained exogenous, along with the fiscal deficit.2121 The fiscal deficit, and expenditure on goods and services, are held constant in real terms (relative to the GDP price, P^Y); not relative to GDP. Rises in transfers are then financed from increases in the respective tax rates.

Both taxes cause negative multiplier effects in this application. In the case of financing from an increased rate of capital income tax, there is downward pressure on the net real rate of return and so the endogenous capital build-up is smaller, cutting aggregate demand and the employment of elastically supplied low-skill workers.2222 This single-economy analysis of the effects of capital tax financing is generalised in a global model, so as to account for the “race to the bottom” issue (Lehmann et al., 2014), by Tyers and Zhou (2018). This, in turn, requires a larger transfer to the low-skill household and therefore a further increase in the capital income tax rate. And so on. In the case of the consumption tax, a rise in its rate directly increases the required scale of transfers to low-skill households to stabilise the Gini. This rise in transfers then requires a further increase in the consumption tax rate and so on.

We list the results in the second and third columns of Table 8. They indicate that this multiplier effect is considerably more serious in the case of the capital income tax than it is with the consumption tax. The capital income tax curtails overall growth substantially and a rate increase of 17 percentage points is required. By contrast, the consumption tax alternative requires only seven percentage points and, while maintaining the Gini, it restores the original levels of performance in terms of capital, GDP and welfare growth. In both cases, the scale of transfers, almost all to the low-income household, rises from eight per cent to almost 15% of GDP. Financing from a consumption tax therefore seems less distortionary, maintaining the Gini while allowing considerably superior aggregate performance. This finding provides model-based simulation evidence for the argument in chapter 7.4 in Prettner and Bloom (2020), which is that consumption taxes are more effective in redistribution and, at the same time, less distortive than alternatives like robot taxes or other direct taxes.

5.3 Broadening the ‘Earned Income Tax Credit’ system

The alternative to allowing workers to be displaced at minimum wages and supported in unemployment via transfers is to keep them working at market-driven lower wages but to offer compensatory transfers. In practice, this system is operational in the United States, directed particularly at families with children (IRS, 2017). We model a broadening that combines a simultaneous relaxation of minimum wage laws with transfers that are conditional on employment and sufficient to stabilise the Gini coefficient. Once again, the fiscal deficit and government expenditure on goods and services are set as exogenous and the transfers are financed by either a rise in the capital income tax rate or a rise in the consumption tax rate. The results are summarised in the final two columns of Table 8.

This policy option is superior to that with a minimum low-skilled wage because employment is larger and so, therefore, is the expected rate of return on physical capital, thus raising the eventual capital stock, output and income. The transfers, mainly to the low-income household, are larger in this case, but unemployment benefit payments are smaller, leaving the total benefits paid at around the same percentage of GDP. Indeed, the imposed transfers due to all four interventionist options add little more than four percentage points of GDP to government revenue and expenditure. Here again, financing of the associated transfers from the tax on consumption expenditure, rather than capital income, is the source of further gains. The negative multiplier effect of the consumption tax, once again, proves smaller than for the capital income tax. Overall, then, the earned income tax credit system, with additional transfers financed by consumption tax, proves the superior option in response to further declines in the low-skill share of income and to population growth that is heavy in low-skill workers.

5.4 Sensitivity to departures from the ‘central’ projection

Because our central projection is merely an extrapolation of trends in factor shares, population and productivity, it offers only one narrow perspective on future developments. Here we examine variations around it in these three directions. The results are summarised in Figure 10, which has the ‘central’ projection results indicated by diamond markers. Not surprisingly, the results are most sensitive to TFP growth. Since this ‘lifts all boats’, strong growth in it can be sufficient to eliminate low-skill worker displacement, if not inequality. Nonetheless, the necessary TFP increase would need to be around 35%, implying roughly twice the TFP growth rate achieved between 1990 and 2016. More concerning is the prospect of a continuation of the poor productivity performance of the last decade. This could lead to a very negative outcome for the economy as a whole, along with unemployment rates over 30%. Still worse is the possibility that this poor productivity outcome is combined with a larger decline in the low-skill share of income and population growth that supplies predominantly low-skill workers.

FIGURE 10

Sensitivity to departures from the central projection (These graphs represent sensitivity to changes in factor shares, the composition of the population increase and total factor productivity of the ‘central’ projection shocks documented in Table 8. In all simulations, the closure is as for the first column of that table, reflecting no policy change. Minimum low-skill wage rates apply with flexibility upward when the unemployment rate is at its lower bound of 4.9%. The per cent changes are shown for all variables except the rate of unemployment. The actual level of the unemployment rate is shown in percentage points.) (Per cent changes in noted variables, no policy change case)

Source: Solutions to the model described in the text.

 

6 CONCLUSION

For key OECD countries, changes in the choice of technique since 1990 are first reviewed, highlighting implications for productivity and factor bias. The productivity slowdown in the early 2000s is noted along with the already widely discussed shift in factor shares away from low-skill labour toward skill and the smaller and more recent shift toward physical capital. An elemental three-household general equilibrium model, with considerable fiscal detail and a technological specification that allows independent shocks to total factor productivity and factor bias, is then used in decomposition analysis. This quantifies the links between real income growth, income inequality and the wealth to GDP ratio on the one hand and changes in factor abundance, total factor productivity, factor bias, the relative cost of capital goods, labour force participation and the progressivity of the tax system on the other. In an application to the United States, changes in factor bias are shown to have been the primary cause of the observed increase in inequality between 1990 and 2016.

The widely anticipated future twist away from low-skill labour toward capital is then examined, in combination with expected changes in population and its skill composition. With downward rigidity of low-skill wages, the potential is identified for unemployment to rise to extraordinarily high levels, with possible exacerbation from low-skill intensive population growth and productivity growth that is no greater than that achieved since 1990. Indeed, the results suggest that productivity growth at twice the pace since 1990 would be needed to constrain unemployment, though even this would not slow the continued rise in inequality. The superior policy response is shown to be a generalisation of the US ‘earned income tax credit’ system, with financing from taxes on consumption, rather than capital income.

ACKNOWLEDGEMENTS

Thanks for assistance with the literature review is due to Alex Dixon and Grace Taylor. For useful comments and discussions, we also thank Markus Brueckner, Peter Dixon, Bob Gregory, Warwick McKibbin, Ivan Roberts, John Simon and Xiaobo Zhang, along with participants in seminars at the UWA Business School and the Melbourne Centre for Policy Studies. In addition, we are particularly grateful to two anonymous reviewers, whose meticulous comments led to our reshaping of the paper. The model used is solved using the Gempack software. Open access publishing facilitated by Australian National University, as part of the Wiley - Australian National University agreement via the Council of Australian University Librarians. [Correction added on 7 May 2022, after first online publication: CAUL funding statement has been added.]

APPENDIX 1: TAXATION AND DISPOSABLE INCOME

These materials augment the presentation of the model's analytics in Section 3 of the text.

Direct tax

Constant marginal direct tax rates, t^L, t^S and t^K, apply to all low-skill labour, skill and capital income, respectively. Bearing in mind that taxation of capital income is after depreciation (6), total direct tax revenue is:

$$$$ {T}^D={t}^L\kern0.1em WL+{t}^S{W}^S{S}^K+{t}^KK\left({P}^P{\mathrm{MP}}_K-{P}^K\delta \right). $$$$(A1)

Indirect tax revenue, T^I, depends on consumption and it emerges in the text via (15).

Household disposable income and consumption

Disposable income, for each household, takes the form:

$$$$ {\displaystyle \begin{array}{l}{Y}_h^D={s}_{hL}\left[\left(1-{t}^L\right) WL+\alpha {W}_0\left(F-L\right)\right]+{s}_{hS}\left(1-{t}^S\right){W}^S{S}^K\\ {}\kern2em +{s}_{hK}\left(1-{t}^K\right)K\left({P}^P{MP}_K-{P}^K\delta \right)+{T}_h^R,\kern1em \forall h,\end{array}} $$$$(A2)

where $$$ {T}_h^R={t}_h^R{N}_hY $$$ is a direct transfer to the household from government revenue, with $$$ {t}_h^R $$$ the transfer rate to household h per unit of group population, N_h, and per unit of nominal GDP.2323 The expression (A2) is more complex if the labour force participation rates, as defined in (6), of low-skill workers, $$$ {\lambda}_{Lh} $$$, are unequal across households and, similarly, if participation rates of skilled workers, $$$ {\lambda}_{Sh} $$$, are unequal across households. The simpler expression is offered here since this is not the case in this analysis. The participation rates within skill groups and across households are kept equal in the experiments conducted, although the rates differ between skill groups and may be differently shocked. Total disposable income is the sum of $$$ {Y}_h^D $$$ across households, which is also GDP at factor cost (household primary income) less total direct taxes, plus net transfers from the government to households and the unemployed: $$$ {Y}^D=\sum \limits_h{Y}_h^D={Y}^{FC}-{T}^D+{T}^R+\alpha {W}_0\left(F-L\right) $$$. Since, from (5), GDP at factor cost is full GDP less net indirect tax revenue, this can be written as

$$$$ {Y}^D=Y-{T}^I-{T}^D+{T}^R+\alpha {W}_0\left(F-L\right). $$$$(A3)

Disposable income measures at the household and national levels are then important determinants of consumption at the national and household levels, as indicated in (15) in the text.

APPENDIX 2: MODEL PARAMETERS AND OPERATION

TABLE A1. Key parameters, representing the United States in 2016

	US
Depreciation rate^a ^a The depreciation rate is the ratio of capital consumption to the capital stock, from FRED.	0.04
Production factor shares^b ^b Value-added shares are based.
Labour, β^L	0.180
Skill, β^S	0.415
Capital, β^K	0.405
Initial household consumption volume shares^c ^c Initial consumption value shares are used to calibrate consumption structure of the model database.
Low income	0.35
Professional	0.33
Capital owning	0.32
Initial household saving rates^d ^d Initial household saving rates are from disposable income. These emerge from the calibration and are indicative of embodied behaviour but do not remain constant in response to shocks. , %^c ^c Initial consumption value shares are used to calibrate consumption structure of the model database.
Low income	−2.5
Professional	22.7
Capital owning	34.5
Income tax rates (revealed) on^e ^e These income tax rates are ‘revealed’ in the sense that they are derived from the collections reported by the Congressional Budget Office and the tax bases implied by the model database.
Labour income, t^L	0.150
Professional income, t^S	0.250
Capital income, t^K	0.050
Indirect (consumption) tax rate, t^C	0.140
Unemployment benefit ratio, α	0.60
Transfer rates/GDP, $$$ {t}_h^R={T}_h^R/Y $$$, %
Low income	5.6
Prof income	1.6
Capital owning	0.0
Elasticities^f ^f Consumption elasticities are consistent with a variety of estimates in use in other models, both of marginal propensities and elasticities (including McKibbin & Wilcoxen, 1995 and Jin, 2011).
Consumption, c to r, ε^CR
Low income	0.02
Prof income	0.10
Capital owning	0.20
Consumption, c to Y^D, ε^CY
Low income	1.05
Prof income	0.98
Capital owning	0.90
Investment, Ii to r^Ci/ri, ε^Ii	1.00
Premium to G/T, ϕi	0.20

• ^a The depreciation rate is the ratio of capital consumption to the capital stock, from FRED.
• ^b Value-added shares are based.
• ^c Initial consumption value shares are used to calibrate consumption structure of the model database.
• ^d Initial household saving rates are from disposable income. These emerge from the calibration and are indicative of embodied behaviour but do not remain constant in response to shocks.
• ^e These income tax rates are ‘revealed’ in the sense that they are derived from the collections reported by the Congressional Budget Office and the tax bases implied by the model database.
• ^f Consumption elasticities are consistent with a variety of estimates in use in other models, both of marginal propensities and elasticities (including McKibbin & Wilcoxen, 1995 and Jin, 2011).

TABLE A2. Closures: choices of exogenous variables^{a a} Closures vary in the prospective analysis, as noted in the discussion of results.

Long run equilibrium analysis
Labour market
Back-casting to 1990
Endogenous: low-skill wage, W
Exogenous: employment of low-skill workers, L
Prospective shocks
Exogenous: nominal production wage, W
Endogenous: Employment of low-skill workers, L
Fiscal policy
Back-casting to 1990
Exogenous net government saving after transfers, S^G
Tax and transfer rates exogenous and shocked
Government expenditure endogenous to retain S^G
Prospective shocks
Exogenous: net government saving after transfers, S^G
Exogenous government expenditure on goods, G
Exogenous Gini coefficient
Endogenous: power of either
Consumption tax rate, τC, or
Capital income tax rate, τK

• ^a Closures vary in the prospective analysis, as noted in the discussion of results.