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A. Appendix: Solving transitions

To solve for the transition, we use this algorithm:

  • 1. Guess the whole sequence of interest rates for the financial assets {rtB}t0.

  • 2. Recover all other prices. Because of no arbitrage between financial assets, robots, and capital, we recover the rental rates for capital and robots, {rtK}t0and{rtZ}t0. Using the rental rates, the cost function for the final good, and the fact that the price of the final good is normalized to 1 in every period, we recover wages in each region {wA,t}t≥0 and {wD,t}t≥0.

  • 3. Recover input and output levels. Based on the prices for all inputs, recover ratios of robots and labor from the firm’s first order condition. Using the fact that the stock of labor is constant, recover the stock of capital and robots in each region {Ki,t}t≥0 and {Zi,t}t≥0. Using the production function, find GDP in each period for each region {Yi,t}t≥0. Using the rules of motion for the stock of capital and robots, find investment paths {Ii,tK}t0and{Ii,tZ}t0.

  • 4. Given interest rates and prices, solve for the optimal consumption path for each household as follows:

    • (a) Guess initial consumption level, Ci,0.

    • (b) Recover the rest of the consumption path using the Euler equation from the household’s maximization problem {Ci,t}t≥0.

    • (c) Compute implicit path of financial assets holdings using the budget constraint, {Bi,t}t≥0.

    • (d) Iterate on initial consumption, so that financial asset holdings remain constant in the final steady state.

  • 5. Adjust sequence of interest rates {rtB}t0 to clear the global financial assets market each period.

B. Appendix: Data

Wage data: This data is taken from the Global Wage Report (ILO) and the Conference board.

  • Conference Board: This is nominal data in local currency that has been converted (by the source) using the average annual exchange rate. We convert this to real compensation using the US CPI with 2010 as the base year. It is also converted to real compensation in local currency using countries’ CPI. Wage is hourly compensation costs – this relates to all employees in manufacturing and includes (1) direct pay and (2) employer social insurance expenditures and labor-related taxes.

    • – Direct pay includes all payments made directly to the worker before payroll deductions and consists of two parts: Pay for time worked and directly-paid benefits.

    • – Social insurance expenditures refer to the value of social contributions (legally required as well as private and contractual expenses) incurred by employers in order to secure entitlement to social benefits for their employees; these contributions often provide delayed, future income and benefits to employees.

    • – Labor-related taxes refer to taxes on payrolls or employment. reductions to reflect subsidies), even if they do not finance programs that directly benefit workers.

    • – For EU countries, values before certain years have been disregarded because of discrete jumps in the underlying series. These are as follows with years indicated prior to which data is not considered.

      • ∗ Finland, Italy, Netherlands, Portugal, Spain – 1999

      • ∗ Slovakia, 2009

      • ∗ Estonia, 2011

  • Global Wage Report Data: This source allows us to add more developing economies to the sample. The data is mostly for the manufacturing sector, however for a few countries it is a broader definition – this is indicated below. The data is in local currency and provides information on gross average monthly wages. This is converted to USD using the annual average exchange rate and the deflated using the US CPI. It is also converted to real compensation in local currency using countries’ CPI. Data for 11 countries is taken from the Global Wage Report data from the ILO. This data is sourced from country surveys. Of these 11, data for manufacturing is specifically indicated for 2 (Malaysia and Indonesia), while for 2 it is indicated that agriculture is excluded (Hong Kong and Chile). For the rest it is either not indicated or for all sectors. When several series are provided for a country, the most appropriate one is chosen for the manufacturing sector. Detail are as follows:

    • – For Malaysia two wage series are provided, one for the manufacturing and one for the economy as a whole.

    • – For Indonesia, two series are provided, one of which is relevant for the manufacturing sector. Although both series have a similar trend, the series for the manufacturing sector ends in 2014 and is not imputed for 2015–2016 data for which is available for the national series.

    • – For Chile, three series are available. All of these are all combined to form one. The sector coverage indicates that the series exclude agriculture.

    • – For Hong Kong, one series is provided, and this excludes agriculture.

    • – For Iran, the nominal wage is used. While an index is also provided for manufacturing it is not used. Note that they both indicate a similar growth trajectory.

    • – For Thailand no information provided on sector coverage.

    • – For Vietnam, three series are provided of which the most complete one is taken, and value for 2008 is imputed assuming a linear growth trend between 2007 and 2009. No information is provided on the sector coverage.

    • – The data for Venezuela ends in 2013. After that, another series for an index is provided up to 2014 but the growth rates and trends are different, therefore another year is not imputed based on the additional information. No information provided on sector coverage.

    • – For Colombia, the missing value for the year 2001 is imputed assuming a linear growth trend between 2000 and 2002. No information is provided sector coverage.

    • – For Peru, the most complete series is selected. The missing value for the year 1996 value is imputed assuming a linear growth trend between 1995 and 1997. No information provided for sector coverage.

    • – For Egypt, two series are combined (which are essentially the same but have missing data in the first few or last few years). This series includes agriculture.

Labor data: This data is taken from various sources: OECD, 10-Sector Groningen database, World KLEMS and ILO. Employment is provided in ‘the 2000s up to 2011/2012 mostly. The data is for the manufacturing sector except for ILO which exists for industry – a broader definition that includes the manufacturing sector. Please refer to table for specific country details on which series in selected for each country.

Robot Stock: The data for robot stocks is taken from IFR Robotics which provides the number of robots (operational stock) across countries, sectors and time.31 Observed zeros are actual zeros -implying that zero robots have been reported.32 Mostly, the data begins to take on positive values after 2004/2005, especially for developing economies. A minor imputation is made in the data to address the data anomaly for North America. Specifcally, the data from IFR lumps up USA, Canada and Mexico into one category till 2010. Only after this year, the distinct data is provided. To address this, the ratios for 2011 for each country are applied to historical data.

C. Appendix: Figure

Figure A.1:
Figure A.1:

Real Wages and Robot Density

Citation: IMF Working Papers 2020, 184; 10.5089/9781513556505.001.A999

Note: Data on robots from IFR. Data on employment and wages from multiple sources. See appendix for details.
Table A.1:

Details on Data Selection

article image
Note: “x” indicates the variable that was used for a particular country across the various indicators that were available. For details on comparability see appendix.

We thank Aidar Abdychev, Emre Alper, Ed Buffie, Dominique Desruelle, Anton Korinek, Axel Schimmelpfennig, Preya Sharma, Felipe Zanna, and other colleagues at the IMF, and participants at the INET/IMF conference “Macroeconomics in the age of Artificial Intelligence” for valuable comments and suggestions. We acknowledge funding from the U.K. Department of International Development (DFID)


The otherwise comprehensive set of contributions in Agrawal et al. (2019) contains no chapter focusing on international dimensions.


For general overviews, see Brynjolfsson and McAfee (2014), Ford (2015), and Susskind (2020) and, for a view that there is little new to see here, Mokyr et al. (2015) and Shiller (2019). As Susskind (2019) argues, the ability of various specific, i.e. “narrow”, AIs to substitute for human labor is more relevant to the labor market, and a much more immediate prospect, than the possible role of artificial general intelligence.


”Robots” here and below, unless specifically noted, stands for the full-range of new technologies mentioned above.


In an influential series of papers, Acemoglu and Restrepo (2018a,c,d, 2019a) employ tasked-based models in the spirit of Zeira (1998) to examine the implications of task automation, and the creation of new tasks, for wages and output and the labor market.


Rodrik (2016) discusses developmental implications of earlier waves of automation.


The model, of course, cannot directly speak to all the channels that are discussed in the qualitative literature. For example, the idea of leapfrogging is often raised as a possible benefit for developing countries, while the impact of automation on the viability of a manufacturing led development strategy is viewed as a challenge. See Abdychev et al. (2018) and World Bank (2019) for a broader discussion of these channels.


If, in contrast, the financial account is closed, then capital does not flow “uphill”; on the other hand the developing region loses the main potential benefit from the increases in robot productivity, which is the boost to long-run consumption that follows from the opportunity to accumulate claims on highly-productive robot capital in developed countries during the transition.


See Akerman et al. (2015) on broadband internet and Frey (2019) for a general discussion.


Along somewhat similar lines, Eden and Gaggl (2019) argue that developing countries adopt less IT-intensive technologies because they are less-well-endowed in complementary skilled labor.


This estimate is controversial. See the discussion in Susskind (2020), for example, for a review.


To be clear, the models in the paper consider a much broader range of technologies, including AI and machine learning algorithms and ever-faster related hardware, pervasive data and networks, and robotics per se. Indeed, one of the features of this new technological revolution, as argued for example in Susskind (2020), is that it extends well beyond manufacturing. However, data limitations force us to focus on this narrower concept in this section. Along simliar lines, Acemoglu and Restrepo (2019b) uses similar data for the US to address more general questions.


Using the same robots data for advanced economies, Graetz and Michaels (2018) find that while increased robot use contributed positively to productivity growth and lowered prices, it only reduced low-skilled workers’ employment share, leaving overall employment relatively unchanged. The slopes are similar if we use wages converted to USD using market and PPP exchange rates and when excluding commodity exporters.


Here, we disregard the first two years of reporting for the robot stock data for each country to account for a compliance bias. This bias can be inferred from the fact that some countries witnessed a very rapid increase in robot adoption in the first two years in which data is available, which may be a result of improved data reporting by the country rather than an actual increases in the underlying stock of robots. The slopes are similar if we use wages converted to USD using market and PPP exchange rates and when excluding commodity exporters.


Figure 4 excludes Iran, Argentina and Greece, three outliers where real wages fell significantly, potentially due to sanctions in Iran’s case and the severe economic crises in the others. Excluding these outliers increases the slope of the fitted line significantly to approximately 3. Figure A.1 includes all countries in our sample. Here, the slope of the fitted line is positive, but only marginally greater than 1.


An early version of the one-sector model of this paper appeared in Abdychev et al. (2018)


We use region and economy interchangeably henceforth.


Since there are no adjustment costs to capital or robots stocks and the net rental rate of capital, robots, and financial asset is the same, the holdings of these assets are indeterminate for the household. We assume that households hold all the capital and robots in the country, with the remaining wealth being held as a financial asset. Thus, capital and robots are not mobile across countries. However, this is not a restrictive assumption because households in one region can still invest in robots in the other region by lending resources through financial assets, which can in turn finance the capital and robot investment. In all cases, the return would be the same across assets.


As we show in the next section, with open capital accounts divergence in consumption is mitigated, because the developing region invests in some of the advanced-country robot stock during the transition.


The annex provides details on solving for the transition.


Gross national income is defined as wL + rKK + rZZ + rB (BA – BD).


Bakker et al. (2020) emphasizes the roleof himan capital in explaining lack of convergence in Latin America.


Results are similar if we assume that robots and capital are produced using a Cobb–Douglas aggregate of the two goods.


Our solution algorithm first solves the unconstrained problem, and then checks whether the non-negativity constraint on the solution holds. If the non-negativity constraint does not hold because the quantity produced of one of the goods is negative, the algorithm assumes that production of that good is zero and allocates all the inputs to the production of the other good. For example, with our calibration for this section, we find that Tl is not produced in the developing region (i = D) in equilibrium. For this allocation to be an equilibrium, it must be the case that given factor prices, the marginal/average cost of producing Tl in the developing region is higher than the price of Tl in equilibrium in the world market. This inequality holds in our equilibrium, indicating that there is, in fact, no incentive to produce Tl in the developing region, as doing so would lead to losses.


Furthermore, within each region, the direct effect is larger for good T2 as this sector is more intensive in the robots and unskilled labor composite (1-αk,T2 – αs,T2 > 1-αk,T1αs,T1) . Thus, a doubling in robot productivity will lead to a larger increase in investment in robots and capital in the T2 sector, all else equal.


On the other hand, if robots were to substitute for skilled workers (i.e. if skilled labor were to be the input combined with robots using a CES technology, instead of unskilled labor), then the terms of trade effect would be reversed with the relative price of T2 increasing. See Acemoglu and Restrepo (2018b) for a model where automation can impact high and low skilled workers.


While we assume that capital and robots are produced using good Tl only, the qualitative result does not change if we allow capital to be produced using a Cobb-Douglas aggregate of the two goods. In particular, the price of T2 relative to that of investment will fall as long as investment uses Tl good to some extent.


This result has a flavor of “re-shoring”, in that the higher robot productivity drives some of the production of the low-skill-intensive good to the advanced region.


Allowing for migration of unskilled labor from developing to advanced countries could help mitigate the divergence results.


In a sense the results in this paper are an example of the general phenomenon underscored in Korinek and Stiglitz (2019), which emphasizes the need for redistribution to make everyone better off in the face of technical progress, in general. A key feature in our setting is that large-scale international redistribution is much less plausible than in the domestic context.


This is a proprietary database. Recent papers by Acemoglu and Restrepo this dataset has been used extensively to study demographics and employment in the context of automation in the US.


Consulted IFR data representative.

Will the AI Revolution Cause a Great Divergence?
Author: Cristian Alonso, Mr. Andrew Berg, Siddharth Kothari, Mr. Chris Papageorgiou, and Sidra Rehman