# ANNEX A Production function approach

The production function approach assumes that potential output can be captured by a Cobb-Douglas production function with constant returns to scale (Solow 1957):<sup>15</sup> Yt = AtKtaLt(1-a) , where Yt is potential output, At is potential total factor productivity (TFP), Kt is the potential capital stock, and Lt is potential employment. To extend the sample beyond 2019—the latest available data from Penn World Tables—TFP was recalculated as the Solow residual of output, employment (extended using data from Haver Analytics) and capital (extended using investment data from Haver Analytics and the perpetual inventory method; table 3). Labor and capital shares are the within-country averages of those reported in Penn World Tables. Human capital is not separately accounted for in the production function approach but affects TFP growth and labor supply growth, as described below.

Two of the three components of potential output—potential TFP and potential employment—are proxied by the fitted values from panel regression estimates. The third component, the contribution of capital to potential growth, is assumed to be the same as the contribution of capital to actual growth, as shown in the Penn World Tables (and extended using data from Haver Analytics). This approach yields an unbalanced panel dataset for 30 advanced economies and 64 EMDEs for 1998-2021 (table 4). The same approach, using appropriate assumptions, can be used to project potential growth into the future. These assumptions and the approach for projections for 2022-32 are detailed in Kilic Celik, Kose, and Ohnsorge 2023.

Capital stock data from Penn World Tables 10.0 is used until the latest available year in the dataset (2019 for most countries in the sample). For 2020-21, investment data are compiled from national statistical agencies and Haver Analytics, while the capital stock is estimated from investment data by the perpetual inventory method using historical average depreciation rates.<sup>16</sup> Potential TFP growth is defined as the fitted value of a panel fixed effects regression for 33 advanced economies and 92 EMDEs for 1983-2020 of Hodrick Prescott-filtered trend of actual TFP growth (the Solow residual) on determinants of productivity. These include GDP per capita relative to advanced economies, education (secondary school completion rate), the working-age share of the population, and the five-year moving average real investment growth (as in Abiad, Leigh, and Mody 2007; Bijsterbosch and Kolasa 2010; Feyrer 2007; Turner et al. 2016).<sup>17</sup> To allow for nonlinearities in the productivity dividends

> 15 The potential growth estimates may be biased if the assumption of constant returns to scale is not valid (Dribe et al. 2017). For a detailed discussion of drawbacks of growth accounting, see Dieppe and Kilic Celik (2021). That said, the approach is widely used for its conceptual simplicity and ease of interpretation.

> 16 Implicitly, this approach does not account for the possibility that inefficient investment is written off during downturns. Hence, it may overstate the capital stock during downturns.

> 17 The results are robust to using GDP per capita instead of GDP per capita in percent of advanced-economy GDP per capita. GDP per capita relative to a frontier (advanced economies) is used here to proxy the catch-up effect highlighted in the literature on stochastic frontier analysis (Growiec et al. 2015).

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