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. Author manuscript; available in PMC: 2019 Dec 13.
Published in final edited form as: J Empir Leg Stud. 2019 Jan 7;16(1):26–68. doi: 10.1111/jels.12208

Table 2:

DiD Regression Analyses: Effect of Damage Caps on Imaging Test Rates

No
 Patient * Zip
 Physician * Zip
Patient or Physician FE
 (1)
 (2)
 (3)
 (4)
 (5)
 (6)
 (7)
 (8)
 (9)
Dependent Variable Any Stress Test MRI CT Any Stress Test MRI CT Any Stress Test MRI CT
Panel A: Simple DiD
Damage cap dummy 4.04*** 1.48 3.92** 5.30*** 3.05** 6.38** 0.99*** 0.42 1.21*
(1.44) (1.21) (1.45) (1.32) (1.35) (2.72) (0.34) (0.32) (0.63)
Male 0.02*** −0.02*** −0.01*** 0.005*** −0.001*** 0.0003**
(0.001) (0.001) (0.001) (0.0002) (0.0001) (0.0001)
White 0.01*** 0.02*** 0.02*** −0.001*** 0.0001 −0.0003
(0.001) (0.001) (0.001) (0.0002) (0.0001) (0.0003)
Black −0.005*** −0.002* 0.01*** −0.001*** −0.001*** −0.001**
(0.002) (0.001) (0.002) (0.0002) (0.0002) (0.0005)
Hispanic 0.01*** 0.01*** 0.03*** 0.0003 0.001*** 0.001*
(0.002) (0.003) (0.003) (0.0002) (0.0001) (0.001)
Fraction of population age −0.14* −0.19 −0.12 −0.08 −0.28** −0.30 0.04 0.04 0.06
65–74 (0.08) (0.11) (0.11) (0.08) (0.13) (0.25) (0.03) (0.04) (0.05)
Fraction age 75–84 0.19 0.06 −0.04 0.06 0.10 0.43 −0.03 −0.03 −0.005
(0.11) (0.14) (0.23) (0.17) (0.18) (0.33) (0.04) (0.04) (0.07)
Fraction age 85+ −0.16 0.29 0.26 −0.04 0.40* 0.68 −0.02 −0.02 0.09
(0.34) (0.19) (0.37) (0.43) (0.21) (0.60) (0.09) (0.06) (0.16)
Fraction white −0.08* 0.14*** 0.30*** −0.04 0.04 0.54** −0.03 0.04** 0.05*
(0.04) (0.05) (0.06) (0.06) (0.06) (0.22) (0.02) (0.02) (0.03)
Fraction black −0.20*** 0.16*** 0.34*** −0.18* 0.09 0.68*** −0.05* 0.03* 0.08**
(0.07) (0.05) (0.09) (0.09) (0.07) (0.24) (0.03) (0.02) (0.03)
Fraction male −0.01 −0.30*** −0.48*** −0.002 −0.44*** −0.58*** 0.04 0.03 −0.05
(0.11) (0.06) (0.13) (0.14) (0.09) (0.19) (0.05) (0.02) (0.08)
Fraction Hispanic 0.10*** −0.02 −0.03 0.06** −0.002 −0.01 0.02** −0.03*** −0.08***
(0.03) (0.02) (0.03) (0.03) (0.02) (0.06) (0.01) (0.01) (0.02)
Fraction below poverty line 0.01 0.002 0.04* 0.01 −0.0003 0.05** −0.0003 −0.001 0.02
(0.02) (0.01) (0.02) (0.01) (0.02) (0.02) (0.005) (0.004) (0.01)
Unemployment rate 0.04 0.02 0.06 0.03 −0.0005 0.08* 0.01 −0.005 −0.01
(0.03) (0.02) (0.04) (0.03) (0.02) (0.04) (0.01) (0.01) (0.01)
Fraction of population −0.03 −0.03 0.09* −0.06 −0.01 0.18* −0.01 0.01 0.05**
disabled (0.05) (0.04) (0.05) (0.04) (0.05) (0.11) (0.01) (0.01) (0.02)
Ln(population) 0.01* 0.02*** 0.04*** 0.01 0.02*** 0.06*** 0.0003 0.003 0.01**
(0.01) (0.01) (0.01) (0.01) (0.01) (0.02) (0.003) (0.002) (0.003)
Physicians/1,000 −0.00** 0.001 0.003 −0.003* 0.001** 0.0005 −0.001** −0.001** −.00005
population (0.001) (0.001) (0.002) (0.002) (0.001) (0.003) (0.0004) (0.0003) (0.001)
Ln(household median 0.02*** 0.001 0.001 0.02*** −0.01 −0.003 0.003* −0.0001 −0.002
income) (0.005) (0.01) (0.01) (0.005) (0.01) (0.01) (0.001) (0.002) (0.003)
Medicare penetration −0.02* −0.02*** −0.008 −0.02 −0.03*** −0.01 −0.01*** −0.01*** −0.005*
(0.01) (0.01) (0.01) (0.01) (0.01) (0.02) (0.003) (0.002) (0.003)
(Medicare penetration)2 0.01 0.01 −0.04** 0.003 0.02 −0.05 0.02*** 0.01 0.01
(0.02) (0.01) (0.02) (0.03) (0.02) (0.04) (0.005) (0.005) (0.01)
Constant 0.06 0.05 −0.04 −0.04 0.20*** −0.07 0.02 −0.03 0.01
(0.05) (0.05) (0.08) (0.08) (0.06) (0.21) (0.03) (0.02) (0.04)
R2 0.05 0.03 0.11 0.36 0.34 0.41 0.11 0.11 0.11
Observations 13,524,405 13,524,405 13,524,405 11,559,309 11,559,309 11,559,309 65,438,019 65,438,019 65,438,019
Panel B: Distributed Lags
Cap adoption year or after 2.80** 1.10 2.55** 3.11** 2.40* 4 43*** 0.46* 0.32 0.64*
(1.10) (1.16) (1.23) (1.14) (1.36) (1.49) (0.23) (0.29) (0.34)
Cap Year 1 or after 0.64 −0.71 −0.50 1.34 −0.56 0.81 0.50 0.10 0.57
(1.11) (0.85) (0.92) (1.38) (0.91) (1.55) (0.30) (0.28) (0.43)
Cap Year 2 or after 0.43 1.12 0.15 −0.37 0.90 0.77 0.20 0.18 0.04
(0.83) (0.75) (1.45) (0.86) (0.74) (1.63) (0.18) (0.11) (0.34)
Cap Year 3 or after 0.61 −0.21 2.06 1.39 0.01 2.56 0.09 −0.35** 0.13
(0.64) (0.60) (1.43) (0.84) (0.87) (1.67) (0.23) (0.15) (0.72)
Cap Year 4 or after 0.621 1.65 2.35 0.12 1.48 3.32 0.29 0.43 1.50***
(1.06) (1.17) (1.63) (0.99) (1.08) (2.49) (0.21) (0.29) (0.46)
Sum of coefficients 5.09** 2.94* 6.61*** 5.59** 4.22** 11.89*** 1.56*** 0.69* 2.88***
(1.86) (1.49) (1.95) (2.10) (1.90) (3.89) (0.52) (0.39) (0.94)
R2 0.04 0.03 0.10 0.36 0.34 0.40 0.11 0.11 0.11
Observations 14,057,920 14,057,920 14,057,920 12,020,886 12,020,886 12,020,886 67,952,511 67,952,511 67,952,511
Percentage change +5.3% +3.4% +3.5% +5.8% +4.8% 6.3% +10.2% +3.2% +6.7%

Notes: Panel A: Simple DiD. DifFerence-in-difFerences regressions of dummy variables for whether a patient had the indicated test in a given year. Damage cap dummy =1 in New-Cap states, in years with a cap in effect. We drop cap adoption year.

Panel B: Distributed lags. Distributed lag regressions of dummy variables for whether a patient had the indicated test in a given year. Variable for “cap adoption year and after” =1 for treated states in cap adoption year and after; 0 otherwise. Variable for “cap Year n and after” = 1 is similar but turns on in Year n after cap adoption.

Both panels: Regressions use linear probability model. Coefficients on cap-related variables are multiplied by 1,000, to provide predicted effect of cap on annual rates per 1,000 patients. Regressions include indicated covariates, patient age dummies (for each year of age, from 65 on), 17 dummy variables for elements of Charlson comorbidity index, and year dummies. Regressions (l)–(3) include zip code FE. (4)–(6) include patient * zip FE (which absorb gender, race, and ethnicity). Regressions (7)–(9) include physician * zip FE. Sample period is 1999–2011. We drop IL and GA from treatment group for 2010 on due to cap reversals in 2010. Standard errors, clustered on state, in parentheses.

*, **, ***

indicates statistical significance at the 10 percent, 5 percent, and 1 percent level. Significant results, at 5 percent level or better, in boldface. Percentage change is relative to base rate in 2002 for new-cap states.