- (2019) consider SSA earnings records for men. Second, we use a minimum earnings threshold of 100% of the annualized minimum wage, whereas Sorkin (2018) and Song et al. (2019) set the minimum earnings threshold to 25% of the annualized minimum wage. Third, since we want to include small firms when studying inequality, we do not impose a minimum firm size restriction in the baseline results. By comparison Sorkin (2018) restricts the sample to firms with a minimum of 15 workers in each year (among workers who appear at least twice in the sample) and Song et al. (2019) restrict the sample to firms with at least 20 workers in each year.
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- A key difference from our baseline analysis is that we now focus only on the years 1999 and 2001. Comparing descriptive statistics of our replication sample in row 3 of Table D5 to those reported in Table 1 of Kline et al. (2020), we find that the sample counts for number of observations, movers, and firms are nearly identical, and the estimates of the total variance of daily wages are very close (0.199 compared to 0.206).
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- Estimating firm groups in CRE. Let us now describe how we estimate the firm groups that we use to build the CRE specification. Accounting for the groups allows one to correlate worker and firm effects to mobility patterns, as we will explain in the next paragraph. To estimate the firm grouping {kj, j = 1, ..., J}, we follow Bonhomme et al. (2019) and cluster firms together based on earnings information. For example, using mean log-earnings one can estimate the partition by minimizing J X j=1 nj(Y j â (kj))2 ,
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- Estimation of FE-HO. We follow Andrews et al. (2008). The first step in the estimation procedure is to extract the variance Ï2 of the residual. As noted in the text we use the following expression which provides an unbiased estimator under A2 homoskedasticity: b Ï2 = (NT â N â J)â1 Y 0 (I â A(A0 A)â1 A0 )Y. Importantly, job stayers do not contribute to the estimation of this variance since they only have a single spell observation per individual. This is because the data is in event-study form, if this was not the case one should worry about the fact that the formula assumes away serial correlation within job spells. The next step is to compute the trace formula. When the design matrix A is not too large, we directly invert the matrix and compute: d Bias FEâHO Q = b Ï2 Trace (A0 A)â1 Q .
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- In sum, we conclude that our implementation of the estimators delivers similar results to Kline et al. (2020) on the Italian data once we use a similar sample.
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- In Table D5, we also apply the FE, FE-HO, and FE-HE estimators to our Kline et al. (2020) replication sample. Our implementation of the estimators differs from Kline et al. (2020) in two ways. First, we collapse yearly data to spell level data as described in Appendix A. Second, as in our main analysis, we use only one spell observation per stayer spell rather than assuming errors are uncorrelated over time within stayer spells. This choice matters for FE-HO, but not for FE-HE.
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- To understand the impact of the restrictions made by Sorkin (2018) and Song et al. (2019), we now consider alternative minimum earnings and minimum firm size thresholds: Minimum earnings threshold. As discussed in detail in Subsection 7.5, we examine how our results change when imposing minimum earnings thresholds ranging from 25% to 100% of the annualized minimum wage. When using the 25% threshold, we find that the variance of log earnings is 0.82 (see Table D4). This estimate is higher than the estimate of 0.67 reported in Table 1 of Sorkin (2018), and lower than the estimate of 0.92 reported in Table 3 of Song et al. (2019) for years 2007-2013.
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