- 7. AKM firm effects • For each year in the reform sample t (i.e. the four years pre-reform), take the universe of prime-age workers from year t − 10 to t. Before 1982, take 1972 as the earliest year.
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- Change (Pct Pts) 10000 15000 20000 25000 30000 Nom. Earnings in Base Year Replacement Rate Change Realized RR Change (e) Placebo 2000: 1998-9 vs. 1999-2000; 1Yr 0 5 10 15 Wage Growth (dw/w) 10000 15000 20000 25000 30000 Nominal Earnings in Base Year Wage Growth '98-'99 Wage Growth '99-'00 Difference (f) Placebo 1999: 1996-8 vs. 1998-2000; 2 Yr 0 5 10 15 20 Wage Growth (dw/w) 10000 15000 20000 25000 30000 Nominal Earnings in Base Year Wage Growth '96-'98 Wage Growth '98-'00 Difference Note: The figure plots additional results related to the analysis in Figure 4. We provide a description at the beginning of this Appendix Section (B).
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- Change (Pct Pts) 5000 10000 15000 Nom. Earnings in Base Year Benefit Change (db/w) Predicted Wage Effects One-Year Effects (dw/w) Two-Year Effects (dw/w) Note: The figure plots reform-induced replacement rate changes and wage effects for the 1989 reform. Observations are binned by their base year (1988) earnings percentile on the x-axis. The 1989 reform increased replacement rates below the 19th percentile as indicated by the green line. The dashed orange line indicates the wage growth that the 1989 reform would induce in the calibrated bargaining model with a wage-benefit sensitivity of 0.39.
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- Change (Pct Pts) 5000 10000 15000 Nom. Earnings in Base Year Replacement Rate Change Realized RR Change (e) Placebo 1988: 1986-7 vs. 1987-8; 1Yr 0 5 10 15 20 Wage Growth (dw/w) 5000 10000 15000 Nominal Earnings in Base Year Wage Growth '86-'87 Wage Growth '87-'88 Difference (f) Placebo 1987: 1984-6 vs. 1986-8; 2Yr 0 10 20 30 40 Wage Growth (dw/w) 4000 6000 8000 10000 12000 14000 Nominal Earnings in Base Year Wage Growth '84-'86 Wage Growth '86-'88 Difference Note: The figure plots additional results related to the analysis in Figure 5. We provide a description at the beginning of this Appendix Section (B).
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- Figure 6: 1985 Reform: Benefit Changes and Wage Effects 0 2 4 6 8 10 Change (Pct Pts) 10000 15000 20000 25000 Nom. Earnings in Base Year Benefit Change (db/w) Predicted Wage Effects One-Year Effects (dw/w) Two-Year Effects (dw/w) Note: The figure plots reform-induced replacement rate changes and wage effects for the 1985 reform. Observations are binned by their base (1984) year earnings percentile on the x-axis. The 1985 reform increased replacement rates above the 61st percentile as indicated by the green line. The dashed orange line indicates the wage growth that the 1985 reform would induce in the calibrated bargaining model with a wage-benefit sensitivity of 0.39.
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- Figure 7: 1976 Reform: Benefit Changes and Wage Effects -10 0 10 20 Change (Pct Pts) 2000 2500 3000 3500 4000 4500 Nom. Earnings in Base Year Benefit Change (db/w) Predicted Wage Effects One-Year Effects (dw/w) Two-Year Effects (dw/w) Note: The figure plots reform-induced replacement rate changes and wage effects for the 1976 reform. Observations are binned by their base year (1975) earnings percentile on the x-axis. The 1976 reform increased replacement rates below the 6th percentile as indicated by the green line. The dashed orange line indicates the wage growth that the 1976 reform would induce in the calibrated bargaining model with a wage-benefit sensitivity of 0.39.
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- Figure A.1: Additional Results: 2001 Reform (a) Wage Growth: 2000-2001 vs. 1999-2000; 1 Yr 0 5 10 15 Wage Growth (dw/w) 10000 15000 20000 25000 30000 Nominal Earnings in Base Year Wage Growth '99-'00 Wage Growth '00-'01 Difference (b) Wage Growth: 2000-2 vs. 1998-2000; 2 Yr 0 5 10 15 20 Wage Growth (dw/w) 10000 15000 20000 25000 30000 Nominal Earnings in Base Year Wage Growth '98-'00 Wage Growth '00-'02 Difference (c) Realized vs. Predicted Benefit Change; 1 Yr -1 0 1 2 3 4 Change (Pct Pts) 10000 15000 20000 25000 30000 Nom. Earnings in Base Year Replacement Rate Change Realized RR Change (d) Realized vs. Predicted Benefit Change; 2 Yr -1 0 1 2 3 4
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- Figure A.2: Additional Results: 1989 Reform (a) Wage Growth: 1987-8 vs. 1988-9; 1 Yr 0 5 10 15 20 Wage Growth (dw/w) 5000 10000 15000 Nominal Earnings in Base Year Wage Growth '87-'88 Wage Growth '88-'89 Difference (b) Wage Growth: 1986-8 vs. 1988-90; 2 Yr 0 10 20 30 40 50 Wage Growth (dw/w) 5000 10000 15000 Nominal Earnings in Base Year Wage Growth '86-'88 Wage Growth '88-'90 Difference (c) Realized vs. Predicted Benefit Change; 1 Yr 0 2 4 6 8 Change (Pct Pts) 5000 10000 15000 Nom. Earnings in Base Year Replacement Rate Change Realized RR Change (d) Realized vs. Predicted Benefit Change; 2 Yr 0 2 4 6 8
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- Figure A.4: Additional Results: 1976 Reform (a) Wage Growth: 1974-5 vs. 1975-6; 1 Yr 0 10 20 30 40 Wage Growth (dw/w) 2000 2500 3000 3500 4000 4500 Nominal Earnings in Base Year Wage Growth '74-'75 Wage Growth '75-'76 Difference (b) Wage Growth: 1973-5 vs. 1975-7; 2 Yr 0 20 40 60 80 Wage Growth (dw/w) 2000 2500 3000 3500 4000 4500 Nominal Earnings in Base Year Wage Growth '73-'75 Wage Growth '75-'77 Difference (c) Realized vs. Predicted Benefit Change; 1 Yr 0 5 10 15 20 Change (Pct Pts) 2000 2500 3000 3500 4000 4500 Nom. Earnings in Base Year Replacement Rate Change Realized RR Change (d) Realized vs. Predicted Benefit Change; 2 Yr 0 5 10 15 20 Change (Pct Pts) 2000 2500 3000 3500 4000 4500 Nom. Earnings in Base Year Replacement Rate Change Realized RR Change Note: The figure plots additional results related to the analysis in Figure 7. We provide a description at the beginning of this Appendix Section (B).
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- Figure A.5: Overview of Non-Parametric Results with Gross UI Benefit Changes (a) 1976 Reform -10 0 10 20 Change (Pct Pts) 2000 2500 3000 3500 4000 4500 Nom. Earnings in Base Year Benefit Change (db/w) Predicted Wage Effects One-Year Effects (dw/w) Two-Year Effects (dw/w) (b) 1985 Reform 0 5 10 15 Change (Pct Pts) 10000 15000 20000 25000 Nom. Earnings in Base Year Benefit Change (db/w) Predicted Wage Effects One-Year Effects (dw/w) Two-Year Effects (dw/w) (c) 1989 Reform 0 2 4 6 8 10 Change (Pct Pts) 5000 10000 15000 Nom. Earnings in Base Year Benefit Change (db/w) Predicted Wage Effects One-Year Effects (dw/w) Two-Year Effects (dw/w) (d) 2001 Reform -2 0 2 4 6
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- For Æ = 0.1 (micro estimates from rent sharing), u ≈ 7% (consistent with the calibration postseparation) and η = 0.72 (e.g., Shimer, 2005), we obtained a calibrated benchmark for the wage-benefit sensitivity of 1−0.1 1+0.1 1 0.72 0.93 0.07 ≈ 0.32.71 Moreover, higher unemployment u increases the macro sensitivity almost exactly as a higher Ä increases the micro sensitivity, which generalizes the implications of whether the sensitivity differs in the local unemployment rate, a prediction we test in Section 5.1. Therefore, our quantitative and structural benchmark for the wage-benefit sensitivity carries over to a macro context with equilibrium adjustment and perfectly segmented labor markets for the treatment group and the control group.
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- Table 3: Wage Effects at Two-Year Horizon: Difference-in-Differences Regression Design 2-Year Earnings Effects (1) (2) (3) (4) (5) (6) Placebo: 3 Yr Lag-0.007-0.025-0.001-0.001-0.003 0.007 (.021) (.021) (.025) (.024) (.022) (.022) Treatment Year-0.007 0.007-0.027-0.022-0.022-0.027 (.031) (.031) (.032) (.03) (.026) (.026) Base-Year Average 14.364 14.364 14.364 14.364 14.364 14.364 Pre-p F-test p-val 0.752 0.241 0.966 0.962 0.878 0.742 R2 .103 .125 .14 .16 .305 .332 N (1000s) 5039 5039 5038 5038 4434 4433 Mincerian Ctrls X X X 4-Digit Ind.-Occ. FEs X X X Firm-Year FEs X X Note: See Table 2 table note.
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- The information needed to translate a given value added rent sharing elasticity into the point estimate for Æ therefore requires strong assumptions or empirical knowledge about b. Measuring the level of the worker’s flow valuation of nonemployment b (and thus surplus b = MPL − b) is difficult even for an average household (see, e.g., Chodorow-Reich and Karabarbounis, 2016). z includes unemployment benefits but also any utility differences between the employed and unemployed state, or other income. z MPL−z is similarly elusive and related to the fundamental surplus in Ljungqvist and Sargent (2017), which is MPL MPL−z ). Identifying Æ off level shifts in p rather than percentage shifts eliminates the complications arising from elasticities, .
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- The red circles indicate the wage effects that the reform induced at the one- and two-year horizon. The reform was implemented in June 1976 and the one- and two-year horizon effects refer to wage growth from 1975 to 1976 and 1977, respectively. We calculate wage effects at the percentile level by calculating wage growth experienced by individuals in that percentile and subtracting the wage effect that a given percentile experienced in a placebo pre-period two years or three years before the reform for the one- and two-year wage effects, respectively. We then normalize the wage effect to zero in the lowest percentile that did not experience a reform-induced replacement rate change in 1976, denoted by the vertical dashed line. Section 4.2 provides more information. Figure 8: Scatter Plots of Wage Growth and Unemployment Benefit Changes (a) One-Year Horizon -2 0 2 4 6 8
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- The red circles indicate the wage effects that the reform induced at the one- and two-year horizon. The reform was implemented in June 1989 and the one- and two-year horizon effects refer to wage growth from 1988 to 1989 and 1990, respectively. We calculate wage effects at the percentile level by calculating wage growth experienced by individuals in that percentile and subtracting the wage effect that a given percentile experienced in a placebo pre-period two years or three years before the reform for the one- and two-year wage effects, respectively. We then normalize the wage effect to zero in the lowest percentile that did not experience a reform-induced replacement rate change in 1989, denoted by the vertical dashed line. Section 4.2 provides more information.
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- The red circles indicate the wage effects that the reform induced at the one- and two-year horizon. We calculate wage effects at the percentile level by calculating wage growth experienced by individuals in that percentile and subtracting the wage effect that a given percentile experienced in a placebo pre-period two years or three years before the reform for the one- and two-year wage effects, respectively. We then normalize the wage effect to zero in the highest percentile that did not experience a reform-induced replacement rate change in 1985, denoted by the vertical dashed line. Section 4.2 provides more information.
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- The results presented in these panels are the same as in panels (a) and (b) except all years are lagged by one or two to estimate the effect the placebo effects. For 1976, we cannot run this placebo check because we do not have enough years of pre-period social security records; these two panels are therefore missing for 1976.
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- The role of z vs. b. While we intentionally define z (the flow utility of the worker while bargaining, perhaps not containing b for, e.g., an incumbent worker) separately from b (the nonemployment payoff, contained in N), the original authors and the follow-up literature (see, e.g., Hall and Milgrom, 2008; Christiano et al., 2016; Hall, 2017) set both to be the same, and thus explicitly include unemployment benefits in z = b. But these authors are interested in new hires and their wage responses; our setting also studied incumbent workers, whose z is unlikely to contain b but rather reflect a default, previous wage. Somewhat in tension to the model however, we do not find evidence for new hires’ out of unemployment to exhibit large wage sensitivity.
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Van Reenen, J. (1996). The Creation and Capture of Rents: Wages and Innovation in a Panel of UK Companies. The Quarterly Journal of Economics 111(1), 195–226.
- Venn, D. (2012). Eligibility Criteria for Unemployment Benefits. OECD Social, Employment and Migration Working Papers, No. 131..
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- Wage Growth (dw/w) 10000 15000 20000 25000 Nominal Earnings in Base Year Wage Growth '82-'83 Wage Growth '83-'84 Difference (f) Placebo 1983: 1980-2 vs. 1982-4; 2Yr 0 5 10 15 20 Wage Growth (dw/w) 10000 15000 20000 25000 Nominal Earnings in Base Year Wage Growth '80-'82 Wage Growth '82-'84 Difference Note: The figure plots additional results related to the analysis in Figure 6. We provide a description at the beginning of this Appendix Section (B).
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- Wage Growth (dw/w) 10000 15000 20000 25000 Nominal Earnings in Base Year Wage Growth '83-'84 Wage Growth '84-'85 Difference (b) Wage Growth: 1982-4 vs. 1984-6; 2 Yr 0 5 10 15 Wage Growth (dw/w) 10000 15000 20000 25000 Nominal Earnings in Base Year Wage Growth '82-'84 Wage Growth '84-'86 Difference (c) Realized vs. Predicted Benefit Change; 1 Yr 0 2 4 6 8 10 Change (Pct Pts) 10000 15000 20000 25000 Nom. Earnings in Base Year Replacement Rate Change Realized RR Change (d) Realized vs. Predicted Benefit Change; 2 Yr 0 2 4 6 8 10 Change (Pct Pts) 10000 15000 20000 25000 Nom. Earnings in Base Year Replacement Rate Change Realized RR Change (e) Placebo 1984: 1982-3 vs. 1983-4; 1Yr 0 2 4 6 8
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- Wage Growth (dw/w) 34 36 38 40 42 Age Wage Growth '87-'88 Wage Growth '88-'89 Difference Two Year Earnings Growth 0 5 10 15 Wage Growth (dw/w) 34 36 38 40 42 Age Wage Growth '86-'88 Wage Growth '88-'90 Difference Note: These figures plot average earnings growth by age from 1987-1988 and 1989-1989 (the year the PBD extension went into effect). Consequently, they mirror the non-parametric analysis for the replacement rate reforms presented in the first two panels of A.1-A.4. Figure A.16: Difference in Difference Coefficient Estimates One Year Earnings Growth -1 -.8 -.6 -.4 -.2 0 .2 .4 .6 .8 1
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- Wage-Benefit Sensitivity 1983 1984 1985 1986 1987 1988 Placebo Years Treated Year Note: These figures report results from estimating a specification similar to Equation (33) but replacing the reform-induced benefit changes with an indicator for being ages 39-42 in 1988 (treated by the PBD reform) and adding age-specific fixed effects. We include the same controls included in specification (4) in table 2.
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- Wage-Benefit Sensitivity 1983 1984 1985 1986 1987 1988 Placebo Years Treated Year Two Year Earnings Growth -1 -.8 -.6 -.4 -.2 0 .2 .4 .6 .8 1
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Weber, C. E. (2014). Toward Obtaining a Consistent Estimate of the Elasticity of Taxable Income Using Difference-in-differences. Journal of Public Economics 117, 90–103.
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