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- As robustness tests we also estimate productivity using various other approaches, in particular, Olley and Pakes (1996), Ackerberg, Caves, and Frazer (2015), and Collard-Wexler and De Loecker (2020) and using a translog specication. Following Hsieh and Klenow (2009), we also experimented with using the wage bill as a proxy for labor instead of the number of full-time-equivalent jobs, which captures skill heterogeneity as higher skilled workers tend to get paid higher wages.
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- Cohort-Specic Di-In-Di designs Table D11 show the event studies using the Sun and Abraham (2021) approach for all our main outcomes for the three denitions of superstars.
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- Finally, we also estimated a gross output production function instead of a value-added production function following Gandhi, Navarro, and Rivers (2020). They show that when using proxy variable methods for estimating a gross output production function additional sources of variation in the demand for exible inputs are required. They develop a new non-parametric identication strategy which regresses the exible's input revenue share on all inputs (labor, capital and intermediate inputs) to identify the exible input elasticity. The latter is used to identify the part of the production function that depends on the exible input. A standard proxy variable approach as in Ackerberg, Caves, and Frazer (2015) is then used to identify the remaining coecients on the other inputs.
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- For example, a market might be dominated by a single large retailer and rm i 's are manufacturers (as in the WalMex model of Iacovone et al. (2015)). Or the superstar might be a multinational which has an eective monopoly in its home (foreign) market. Rather than endogenize this market structure we simply take this as given at Stage 0. 30 The upstream market has N rms indexed i = 1;::::;N, where we assume that N is suciently large that we can abstract away from strategic oligopolistic interactions, each of whom produces a single variety. Firms have heterogeneous TFPQ, A, with the high TFPQ rms having lower marginal costs and therefore lower prices and higher output. Output Q is produced with a production function Q = AL where L are competitively supplied labor services 31 and 1: In Stage 1, upstream rms enter the economy and draw A from a known i.i.d. distribution,
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Gandhi, Amit, Salvador Navarro, and David A. Rivers. 2020. On the identication of gross output production functions. Journal of Politcal Economy 128 (8): 29733016.
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- Relationship Capability (RC) This is measured as simply the number of customer rm j0s that a rm i has (following Bernard et al. (2022)). Firm Age The rm's age is computed using the date of incorporation of the rm reported in ORBIS (BvD). 29 The age of the rm is then the year the rm is observed in the data minus the date of incorporation. We dene a young rm as a rm which is less than or equal to ve years old. For 32 rms a negative age is computed, which were checked (and corrected) using the Ocial Gazette of Belgium that provides the business registration details and deed of incorporation. These were typically older rms that changed either their legal status (e.g. into limited liability) or that changed their address.
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