## 2.1–3.3, 4.1–5.3 — Data sources, empirical strategy, AEL, event-study, identification, and results

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### Danish registry data and sample construction
- Danish National Hospital Register (Landspatientregisteret/LPR) contains nation-wide data on all hospital interactions since 1995, including a 4-digit ICD10 main/action diagnosis code, co-diagnoses, patient type (inpatient, outpatient, ER), start- and end-date of treatment, hospital and department, and treatments/operations/examinations.
- Hospital data linked via unique personal identifier to tax- and labor market registers to observe detailed work history and all hospital interactions for the full population of Danes aged 25-59 years from 1995 to 2015.
- Final dataset includes earnings, transfer income, municipality, marital status, wealth, spousal earnings and wealth, education, occupation and socioeconomic status; education-specific local labor market statistics constructed at municipality level.
- Analysis focuses exclusively on in-patient hospital admissions.
- Index admission definition and sample:
  - “Index” admission = first non birth/pregnancy related inpatient hospital admission for at least 3 years.
  - Labor-market outcomes followed 3 years prior to, during, and 3 years following the treatment year.
  - Total of 1.1 million index hospitalizations in the data.
  - For descriptive comparisons authors also present statistics for: all observed inpatient admissions (one hospitalization per year per person), individuals aged 25-59 once hospitalized in 1998-2012, and a control group of individuals who don’t experience any index admission.
  - Roughly 1/3rd of all observed hospitalizations for the specified ages and years are index admission observations.
  - Index-admission patients are on average 0.4 years younger compared to those with any inpatient admission.
  - Pre-admission labor force participation:
    - index-admission sample: 0.915
    - all inpatient admissions sample: 0.68
    - control group: 0.82
  - Both index and all-inpatient groups experience participation drops of:
    - roughly four percentage points in the hospitalization year,
    - another three percentage points in the following year.
  - Mortality rates are slightly lower in the index-admission subsample.
- Expanded-sample note:
  - “All admissions” sample: observed total of 3.1 million non-birth related index admission observations of patients born in Denmark aged 25-59 in 1998-2012.

### Institutional context (Denmark)
- Universal, tax-financed health care with the vast majority of hospitals publicly owned; private hospitals accounted for less than 2% of total hospital expenditures during 1998-2012.
- Government spending on healthcare increased by 30% from 2000 to 2010, mainly driven by hospital expenditures.
- Hospital financing based on politically fixed budgets accounting for patient mix heterogeneity.
- Structural reform in 2007 merged 16 counties into 5 regions; fewer but larger hospitals than in countries such as the U.S.; mergers and closures since the 1990s concentrated hospitals.
- Patient choice:
  - since 1993 patients can freely choose among somatic hospitals if capacity;
  - since 2002 patients can choose state-financed private hospital treatment if public-hospital waiting times exceed 2 months before 2007 and 1 month after.
- Approximately 91% of patients in the sample period are admitted to hospitals in the same region where they live.

### Descriptive labor-market patterns around admissions (illustrative event regressions)
- Descriptive linear model: yi,t = Xi,t β + γt + ∑_{−5≤r≤5} δr + εit, with controls Xi,t including age, gender and education, and a 10% random subsample of non-index individuals used as control group (δ normalized to 0).
- Disease illustrations (Clinical Classification Software groups): intervertebral spondylosis, acute cerebrovascular disease, breast cancer, fracture of the lower limb.
- Intensive margin = log(earnings) including only positive earnings; extensive margin = dummy for positive earnings (dead individuals included with zero earnings).
- Key descriptive δ coefficients:
  - Intervertebral spondylosis:
    - intensive-margin decline in earnings of 8%, halved to a 4% decline 3 years after admission.
    - labor force participation drops by 12%.
  - Acute cerebrovascular disease:
    - intensive-margin decrease in earnings of 12%.
    - labor force participation drop of almost 20%.
  - Breast cancer:
    - intensive-margin decrease of 5%.
    - steady decline in labor force participation mounting to a 14% decrease five years after admission.
  - Fracture of the lower limb:
    - intensive-margin earnings drop of 8%, almost fully recovered after 3 years.
    - labor force participation permanently decreased by 7%.
- Pattern: intensive-margin drops tend to recover (especially for less severe diseases); extensive-margin responses continue to decline for all diseases.
- Time heterogeneity: re-estimating by admission cohorts (2000-2002, 2003-2004, 2005-2007, 2008-2010) using log(earnings + 1 DKK) shows:
  - Intervertebral spondylosis: 2008-2010 loss only borderline significantly smaller than 2000-2002.
  - Breast cancer and acute cerebrovascular diseases: patients much better off in later periods compared to early 2000s.
- Hospital heterogeneity (illustrative): pre-hospitalization trends similar across hospitals for acute cerebrovascular disease, but vastly different post-hospitalization earnings losses across hospitals.

### Adjusted Earning Losses (AEL): definition, intuition, and measurement
- Quality of hospital h: q_h = E[y_h | r ≥ 0] − E[y_0 | r ≥ 0], referred to as “Adjusted Earning Losses” (AEL).
- Interpretation: percentage change in yearly normalized earnings (compared to mean pre-hospitalization levels) expected to occur over 3 years from hospital admission.
- Identification assumption: after controlling for extensive patient-, case-, and local-level characteristics, hospital selection is not driven by residual unobservable heterogeneity.
- Empirical sample and restrictions for AEL estimation:
  - All inpatient “index” admissions in Denmark during 1998-2012, divided into five three-years periods; each period estimated separately.
  - Analysis restricted to the 31 largest hospitals; diagnoses with less than 100 observed index admissions in 1998-2012 excluded.
  - Only Danish-born patients aged 25-59 at hospitalization included.
- Main outcome: post-hospitalization earnings in years r with 0 ≤ r ≤ 3 relative to admission, measured as share of mean earnings in the 3 years prior to the index admission (“normalized earnings”).
- Estimating equation:
  - y_{i,r} = q_{h,t} + X_{i,r} β_t + φ_{d,t} + ∑_{0≤r≤3} δ_{r,dg,t} + ε_{i,r}
  - q_{h,t}: time-varying hospital fixed effects (AEL estimates)
  - φ_{d,t}: time-varying main-diagnosis fixed effects
  - δ_{r,dg,t}: disease-group specific evolution of earnings around hospitalization
- Controls X_{i,r} include extensive pre-hospitalization socio-economic characteristics, co-diagnoses, interactions with outpatient/ER visits, fixed effects for all co-morbidities and calendar year, and education-specific local labor market controls.
- Averaged sample size: an average of 21 thousands observations per hospital per time period (each admission relates to 4 observations since dead patients’ earnings are assumed zero).
- Empirical Bayes Adjustment applied to correct AEL estimates for measurement error (municipality-clustered standard errors used to estimate variance of hospital fixed effects and allowing the mean of “true” quality to be a function of hospital size).

### Distribution of AEL and back-of-the-envelope savings
- Substantial heterogeneity in hospital quality across all time periods.
- AEL average (across the five periods) standard deviation: 1.05 percentage points.
- An inpatient admission in the lowest-ranked hospital is associated with an additional decrease in annual labor earnings of 4.2 percentage points, on average, compared to the highest-ranked hospital.
- Hospital heterogeneity:
  - larger for early sample period (1998/2000),
  - constant between 2001 and 2009,
  - lower for latest period (2010/2012) partly due to reduction in number of hospitals (only 22 active at end of sample).
- Hospital quality positively correlated over time; correlation between AEL and its lag (three-year period scale): 0.59 (approximately 0.84 yearly).
- Patients treated at below-median hospitals would on average have earned an additional 0.7% of pre-hospitalization earnings for (at least) four years if treated at a hospital with median estimated quality, corresponding to an estimated loss of (at least) 6,400 DKK (approximately 960 USD).
- Back-of-the-envelope aggregate savings from raising below-median hospitals to median quality:
  - Savings_t = ∑_{h: q_h < q_med} [ (q_med − q_h) × (N_{ht} × Ȳ_{ht} × 4) ], where N_{ht} is number of non-pregnancy related inpatient admissions of patients aged 25-59 in year t at hospital h, and Ȳ_{ht} is mean earnings the year before hospitalization for those patients.
- Estimated implication: if all hospitals had at least median quality, the Danish economy would save on average almost one billion DKK (approximately 140 million USD) in foregone earnings each year, or 60 million DKK (or 9 million USD) per year per hospital.
- Notes on conservatism: inpatient-only focus, four-year horizon, exclusion of smaller hospitals and patients outside 25-59, wage growth abstracted, some productivity losses may be borne by employers; study lacks data to quantify cost of improving low-AEL hospitals.

### Event-study approach and government transfers (section 3.3)
- Event-study estimating yi,r = αi + γt + ∑−3≤r≤3,r≠−1 δr + εit separately for patients admitted to hospitals in top and bottom third of AEL ranking.
- Outcome used: government transfers (sickness benefit, cash assistance, unemployment benefit) rather than earnings because AEL is estimated with normalized earnings.
- Findings on transfers:
  - Transfers increase sharply from the year of hospital admission onwards, indicating substitution from labor earnings to government-provided insurance.
  - Pre-admission dynamics: patients admitted to different hospitals follow exactly the same dynamics before admission.
  - Post-admission differences: patients admitted to high-quality hospitals receive significantly less transfers from the year of admission onwards; difference persists over time.
- Confidence intervals: 95% confidence intervals based on municipality-clustered standard errors.
- Robustness: results similar when defining high/low-quality hospitals as top/bottom half or quartile and when including a control group of non-hospitalized individuals.

### Within-hospital heterogeneity and correlation with traditional measures (sections 3.4–3.5)
- Chapter-specific AEL (qh,ch) estimation yields average correlation across chapter-specific AEL measures: 0.14.
- AEL for acute non-deferrable conditions has correlation 0.52 with AEL estimated for all conditions.
- Correlation with Risk-Adjusted Mortality (RAM) and Risk-Adjusted Readmission (RAR) for acute non-deferrable conditions:
  - AEL (acute non-deferrable) correlation with RAM: -0.29 (p−value= 0.001).
  - AEL (acute non-deferrable) correlation with RAR: -0.13 (p−value= 0.118).
  - AEL (acute non-deferrable) correlation with RAM in other results: -0.51 (p−value= 0.000) and with RAR: -0.14 (p−value= 0.047) in another reported comparison.
- AEL and RAM/RAR together explain limited share of variation:
  - Correlation between actual AEL and AEL predicted by RAM and RAR via linear regression: 0.32 in one place and 0.52 in another; RAM and RAR explain only 3 percent of the variation of AEL when AEL estimated with all index admissions.
- External ranking comparison (Spearman):
  - Correlation between 2011 “Dagens Medicin” ranking and AEL-based ranking: 0.27 for 2007/2009 period and 0.15 for 2010/2012 period.
- Interpretation: AEL contains substantial additional information beyond mortality and readmission measures, particularly for non-acute conditions.

### Identification concerns and validation strategies (Section 4 overview)
- Two main endogeneity concerns:
  1. Selection on unobservable patient severity (best hospitals may treat sicker patients → downward bias).
  2. Local heterogeneity (hospitals near “better” patients or amenities admit more resilient patients → upward bias).
- Mitigation via controls and institutional features:
  - Extensive controls include main diagnosis, co-morbidities, past medical history, socio-economic variables, local labor market controls.
  - Danish context: fewer and larger hospitals, broader catchment areas, and each hospital in main sample serves neighborhoods across income deciles.
- Validation approaches:
  - a) Instrumental variables using patients’ home location (Church District) as instrument for hospital choice.
  - b) Analysis of patients admitted far from home (acute non-deferrable admissions at non-common hospitals).
  - c) Additional checks adding controls; AEL heterogeneity remains.

### Instrumental variables and non-common hospital analysis (sections 4.1–4.2)
- Alternative regression: yi,r = α·q̂h,t + Xi,rβt + φd,t + ∑0≤r≤3 δr,dg,t + ηi,r, pooling five periods.
  - Interpretation of α: α = 0 → estimated quality uninformative; α > 0 → higher-measured-quality hospitals decrease economic impact; α = 1 → OLS consistent.
- Instrument: patient neighborhood (Church District) as instrument for hospital AEL; motivated by >70% of patients admitted to the “common” hospital for their neighborhood and condition.
- IV result: α neither statistically nor economically different from 1 in neighborhood-instrument IV (reported column (1) of Table 2): being admitted to a higher AEL hospital decreases economic impact as predicted by equation (3).
- Caveat: IV validity requires patient location affects post-hospital earnings only through hospital choice.
- Non-common hospital (acute non-deferrable admissions treated outside local common hospital) OLS (column (2) of Table 2):
  - α ≈ 1.2, implying admitted to a better hospital significantly decreases earnings cost of hospitalization.
  - Cannot reject α = 1 at 10% level (p−value= 0.21).
- Alternative specification (equation (8)) adding neighborhood-estimated common-hospital quality ̂q_{n,dg,t}:
  - OLS results column (3) of Table 2: α = 1.39; θ (neighborhood quality effect) not different from zero.
  - Conclusion: hospital of admission, not where patients live, matters for economic impact; no evidence AEL driven by neighborhood-level unobservables.

### Robustness to observable covariates and selection checks (Section 4.3–4.4)
- Sequential inclusion of six ordered sets of controls (from main disease fixed effects to full controls of equation (3)) shows:
  - R-square rises monotonically as controls added.
  - AEL heterogeneity (standard deviation and range) higher in regressions with fewer controls, then stabilizes once comorbidities, education, and pre-hospitalization occupation included (range ≈ 4 percentage points; standard deviation ≈ 1 percentage point).
  - Inclusion of additional income and wealth controls increases R-square by more than a third but does not diminish AEL heterogeneity.
- Exercise comparing susceptibility to purposeful selection (correlation with share of out-of-region patients for non-acute/deferrable conditions):
  - AEL correlation = 0.13, p−value = 0.13
  - RAM correlation = -0.16, p−value = 0.08
  - RAR correlation = -0.04, p−value = 0.64
  - Interpretation: AEL not more prone to selection biases than traditional metrics.
- Caveats noted by authors:
  - Additional selection issues may remain (e.g., hospital quality affecting care-seeking/timing).
  - Diagnostic coding capacity could correlate with quality.
  - IV recovers effects for “marginal” patients whose hospital selection depends on home location; very sick patients who travel may not be fully captured.

### Time trends: decline in labor cost of hospitalizations (Section 5)
- Model (equation (9)) estimates changes in labor market consequences across year-groups (1998-2000, 2001-2003, 2004-2006, 2007-2009, 2010-2012) with extensive controls and individual fixed effects.
- Outcome measures:
  - Extensive margin: dummy indicator for earnings larger than 50,000 DKK; extensive-margin cost measure = δ_{r=3}×yg (third year following index admission).
  - Intensive margin: log earnings conditional on earnings > 50,000 DKK; intensive-margin cost measure = δ_{r=1}×yg (first year following index admission).
- Disease-level results (extensive-margin participation drop 3 years after hospitalization):
  - Acute cerebrovascular disease:
    - 1998-2000: 19% dropped out of labor force 3 years after hospitalization.
    - 2010-2012: 6% dropped out.
  - Spondylosis (spinal degeneration):
    - 1998-2000: 13% dropped out.
    - 2010-2012: 11% dropped out.
  - Other severe conditions with roughly 10% drop: poisoning by other medications and drugs, poisoning by psychotropic agents, alcohol-related mental disorders, multiple sclerosis.
- Mortality’s role:
  - Excluding dead individuals:
    - Acute cerebrovascular disease: 14% of surviving patients dropped out 3 years after hospitalization in 1998-2000, versus 9% in 2010-2012.
    - Changes in mortality drive more than half of estimated change for acute cerebrovascular disease; much smaller share for less severe diseases.
- Intensive-margin patterns:
  - Intensive-margin costs generally smaller than extensive-margin costs.
  - Overall decrease over time but less steady than for extensive margin—consistent with more individuals remaining in labor force but with lower earnings.
- Accumulated 3-year change (equation (10)):
  - Accumulated Change = ∑_{r=1}^3 δr,yg=2010−2012 − ∑_{r=1}^3 δr,yg=1998−2000
  - For most significant disease changes:
    - Decline in accumulated extensive-margin severity: roughly 7–27 percentage points (disease-specific).
    - Decline in accumulated intensive-margin severity: around 4–6 percentage points.
- Disease-specific notable improvements:
  - Lung cancer: largest improvement—accumulated decline in labor force participation during 3 years following hospitalization decreased by 27 percentage points from 1998-2000 to 2010-2012.
  - Cancer-related diseases (secondary malignancies, breast, colon) show especially large declines.
  - Acute cerebrovascular disease: accumulated decline of 20 percentage points on extensive margin and 10% on intensive margin.
  - Acute myocardial infarction (AMI): change of 15 percentage points on extensive margin and 8% on the intensive margin (as reported).
  - Little or no significant decline for benign neoplasm of uterus, varicose veins of lower extremity, abdominal hernia.
- Aggregate/weighted averages (weighted by number of patients during 1998-2012):
  - Average accumulated 3-year decline in participation rates following hospitalization decreased by 8.8 percentage points from 1998-2000 to 2010-2012.
  - Average accumulated 3-year intensive-margin earnings decline following hospitalization dropped by 4.9 percentage points.
  - Total change (sum of intensive and extensive margin changes) = 13.6 percentage points.
  - Corresponds to:
    - Average decline in labor force participation costs of a hospitalization of 50%.
    - 25% reduction in corresponding intensive-margin earnings costs.

### Interpretation and attribution to healthcare improvements (Section 5.3 and robustness)
- Interpretation: sizeable reduction in labor market costs of hospital admissions between 1998 and 2012 suggests strong improvements in quality of healthcare treatments; likely drivers include advancements in medical technology and improvements in Danish hospitals’ systems.
- Alternative contributors: healthier population behaviors, labor market changes, reforms targeting sick-leave and disabled employment, and cultural changes may contribute.
- Flex-job scheme robustness check:
  - Flex-job scheme (introduced 1998) provides wage subsidies to partly disabled individuals.
  - Counterfactual worst-case (all flex-job participants on full disability with 0 earnings) yields slightly larger declines in both intensive- and extensive responses, implying flex-job scheme unlikely to drive observed improvements.
  - Participation rates for index-admission patients:
    - Hospitalized in 2000: 0.4% participated in 1999 and 1% in 2001.
    - Hospitalized in 2011: 3.3% participated in 2010 vs. 3.7% in 2012.
- Conservative lower-bound attribution exercise:
  - Decompose change in labor costs for diagnostic group dg: ΔLC(dg) = ΔTQ(dg) + ΔLM(severity(dg)).
  - Assign minimum observed ΔLC(dg) across dg in each severity class to ΔLM(severity) to bound non-treatment factors.
  - Empirical results:
    - Total 3-year accumulated labor costs declined by 13.6 percentage points.
    - With severities split into 3 equally large groups, 8.8 percentage points come from health care improvements.
    - With 5 groups, 7.7 percentage points come from health care improvements.
    - With 10 groups, 5.3 percentage points come from health care improvements.
  - Conservative lower bound: improvements in healthcare quality alone caused labor costs of a hospitalization to decrease by at least 5.3 percentage points.

### Robustness tables and additional simulation evidence
- Key robustness coefficients (reported):
  - AEL of Admission Hospital coefficients:
    - Column (1) IV: 1.003*** (standard error 0.0263)
    - Column (2) OLS: 1.199*** (standard error 0.250)
    - Column (3) OLS (top 31 hospitals): 1.387** (standard error 0.277)
  - Observations reported: 3,113,831; 59,912; 52,186 respectively. R-squared: 0.165; 0.243; 0.242. Standard errors clustered at municipality level. Significance: *** p<0.01, ** p<0.05, * p<0.1.
- Expanded hospital sample (60 hospitals) findings:
  - Average standard deviation of AEL is 1.2 percentage point.
  - An inpatient admission in the lowest-ranked hospital associated with additional decrease in annual labor earnings of 5.1 percentage points, on average, compared to the highest-ranked hospital.
- Simulation of IV under endogenous selection (G parameter):
  - When no endogenous selection (G = 0), αIV = 1.
  - When G > 0 (better hospital admits more resilient patients) average αIV < 1.
  - When G < 0 (better hospital admits sicker patients) average αIV > 1.
  - OLS mechanically equals 1 for αOLS across simulations; q̂1 biased unless G = 0.

### Additional descriptive statistics (selected)
- Table 1 selected means by r = -1, r = 0, r = 1 (various samples):
  - Mean earnings examples: 204,742; 201,737; 196,661; 327,639; 313,750; 307,559; 301,963.
  - Mean log earnings (earn > 50,000): 12.48; 12.49; 12.53; 12.68; 12.69; 12.70; 12.70.
  - Share w/ earn > 50,000: 0.678; 0.642; 0.611; 0.915; 0.872; 0.840; 0.82.
  - Share alive: 1.000; 0.984; 0.966; 1.000; 0.989; 0.981; 0.97.
  - Mean age: 42.83; 43.84; 44.84; 42.42; 43.42; 44.40; 42.38.
  - # Observations examples: 3,104,532; 3,104,632; 3,099,490; 1,098,162; 1,113,321; 1,111,576; 3,312,609.
- Table A.1 (robustness alternative sample) highlights:
  - Column (1) IV: AEL of Admission Hospital = 1.012*** (standard error (0.0223)), Observations = 3,727,345, R-squared = 0.165.
  - Column (2) OLS: AEL of Admission Hospital = 1.199*** (standard error (0.223)), Observations = 71,396, R-squared = 0.237.
  - Column (3) OLS: AEL of Admission Hospital = 1.374** (standard error (0.223)), Observations = 69,471, R-squared = 0.185.

- Figures described include event studies, AEL distributions, scatterplots of AEL vs RAM/RAR, cumulative distributions of hospital size, and simulation results (as summarized above).

*Source: wpiea2019173-print-pdf — 2.1 Data Sources; sections 3.3–5.3 and appendices as provided.*

### 2.1  Data Sources

### 2.1  Data Sources

### Danish registry data and linkage
- The Danish National Hospital Register ("Landspatientregisteret"/LPR) contains nation-wide data on all hospital interactions since 1995.
- Available information includes a 4-digit ICD10 main/action diagnosis code and other related co-diagnoses, patient type (inpatient, outpatient, ER), start- and end-date of treatment, and the hospital and hospital department.
- The data also contain information on the treatments, operations and examinations conducted.
- Using a unique personal identifier, hospital data are linked to tax- and labor market registers to observe detailed work history and all hospital interactions for the full population of Danes aged 25-59 years from 1995 to 2015.
- Final dataset includes extensive labor market and demographic variables: earnings, transfer income, municipality, marital status, wealth, spousal earnings and wealth, education, occupation and socioeconomic status.
- Education-specific local labor market statistics (e.g., unemployment, median income) are constructed at the municipality level from the full-population data.
- Analysis in this study focuses exclusively on in-patient hospital admissions.

### Sample construction and "index" admissions
- To mitigate co-morbidities affecting treatment outcomes, the sample is restricted to “index”-admissions.
- An “index” admission is defined as the first non birth/pregnancy related inpatient hospital admission for at least 3 years.
- Labor-market outcomes are followed 3 years prior to, during, and 3 years following the treatment year.
- The data contain a total of 1.1 million index hospitalizations.
- For descriptive comparisons the authors also present statistics for:
  - a sample including all observed inpatient hospital admissions (one hospitalization per year per person),
  - individuals aged 25-59 once hospitalized in 1998-2012,
  - a control group of individuals who don’t experience any index admission during the observed years.
- Roughly 1/3rd of all observed hospitalizations for the specified ages and years are index admission observations.
- Index-admission patients are on average 0.4 years younger compared to those with any inpatient admission.
- Pre-admission labor force participation:
  - index-admission sample: 0.915
  - all inpatient admissions sample: 0.68
  - control group: 0.82
- Both index and all-inpatient groups experience participation drops of:
  - roughly four percentage points in the hospitalization year,
  - another three percentage points in the following year.
- Mortality rates are slightly lower in the index-admission subsample.
- Note: restricting to index-admissions reduces representativeness because the control group includes both very poor health (too many inpatient hospitalizations to have an index admission) and very good health (no non-birth related inpatient admission during the period).

### Institutional context (Denmark)
- The Danish health care system is universal and provides free and equal access to health care for all citizens.
- Health care expenses are primarily tax financed; the vast majority of hospitals are publicly owned.
- During 1998-2012, private hospitals accounted for less than 2% of total hospital expenditures.
- Government spending on healthcare increased by 30% from 2000 to 2010, mainly driven by an increase in hospital expenditures.
- Hospital financing is based on politically fixed budgets that account for heterogeneity in patient mix.
- Following a structural reform in 2007, 16 counties were merged into 5 regions.
- Compared to countries such as the U.S., there are fewer but larger hospitals in Denmark; mergers and closures since the 1990s further concentrated hospitals.
- General practitioners often act as gatekeepers; residence determines a “default” hospital, but:
  - since 1993 patients can freely choose among somatic hospitals if the requested hospital has capacity;
  - since 2002 patients can choose state-financed treatment at private hospitals if public-hospital waiting times exceed 2 months before 2007 and 1 month after.
- Approximately 91% of patients in the sample period are admitted to hospitals in the same region where they live.

### Descriptive labor-market patterns around admissions
- Descriptive linear model estimated for illustrative purposes:
  - yi,t = Xi,t β + γt + ∑_{−5≤r≤5} δr + εit
  - Dependent variable: a labor market outcome of individual i at year t.
  - Controls Xi,t: age, gender and education; γt denotes calendar-year fixed effects.
  - For index admissions, subscript r denotes year relative to admission year where r = 0 is admission year.
  - A 10% random subsample of non-index individuals (1995-2015) used as control group with δ normalized to 0.
- Four disease types illustrated (grouped by Clinical Classification Software, CCS): intervertebral spondylosis (spinal degeneration), acute cerebrovascular disease, breast cancer and fracture of the lower limb.
- Intensive margin: outcome = log(earnings) including only positive earnings observations.
- Extensive margin: outcome = dummy for positive earnings for all observations; dead individuals included with zero earnings.
- Key descriptive findings (δ coefficients; intensive = log earnings, extensive = participation):
  - Intervertebral spondylosis:
    - intensive-margin decline in earnings of 8%, halved to a 4% decline 3 years after admission.
    - labor force participation drops by 12%.
  - Acute cerebrovascular disease:
    - intensive-margin decrease in earnings of 12%.
    - labor force participation drop of almost 20%.
  - Breast cancer:
    - intensive-margin decrease of 5%.
    - steady decline in labor force participation mounting to a 14% decrease five years after admission.
  - Fracture of the lower limb:
    - intensive-margin earnings drop of 8%, almost fully recovered after 3 years.
    - labor force participation permanently decreased by 7%.
- Intensive-margin drops tend to recover (especially for less severe diseases); extensive-margin responses continue to decline for all diseases.
- Time heterogeneity: re-estimating the model by admission cohorts (2000-2002, 2003-2004, 2005-2007, 2008-2010) using log(earnings + 1 DKK) shows disease-specific improvements over time:
  - Intervertebral spondylosis: 2008-2010 loss only borderline significantly smaller than 2000-2002.
  - Breast cancer and acute cerebrovascular diseases: patients much better off in later periods compared to early 2000s.
- Hospital heterogeneity (illustrative): allowing δ coefficients to vary by admitting hospital shows pre-hospitalization trends similar across hospitals for acute cerebrovascular disease, but vastly different post-hospitalization earnings losses across hospitals (e.g., hospitals A and D worse than B or C). These descriptive results do not control in detail for patient characteristics or local labor markets.

### Adjusted Earning Losses (AEL) — definition and intuition
- Quality of hospital h defined as difference in earnings realized after treatment at hospital h and at a reference hospital 0:
  - q_h = E[y_h | r ≥ 0] − E[y_0 | r ≥ 0]
- q_h referred to as “Adjusted Earning Losses” (AEL).
- Interpretation: since dependent variable is normalized earnings, the quality measure is interpreted as the percentage change in yearly earnings (compared to mean pre-hospitalization levels) expected to occur over 3 years from the hospital admissions.
- Identification assumption: after controlling for extensive patient-, case-, and local-level characteristics, hospital selection is not driven by residual unobservable heterogeneity (e.g., unobserved severity).

### Empirical strategy for estimating AEL
- Sample: all inpatient “index” admissions in Denmark during 1998-2012 (see Section 2.1).
- Sample divided into five three-years periods; each period estimated separately.
- Analysis restricted to the 31 largest hospitals; patients with diagnoses with less than 100 observed index admissions in 1998-2012 are excluded.
- Include only Danish-born patients aged 25-59 at hospitalization.
- Main outcomes: post-hospitalization earnings in years r with 0 ≤ r ≤ 3 relative to admission, measured as share of mean earnings in the 3 years prior to the index admission (“normalized earnings”), allowing joint consideration of extensive and intensive margins.
- Notation: h = hospital, d = main diagnosis (4-digit ICD10), t = one of five three-year periods.
- Estimating equation:
  - y_{i,r} = q_{h,t} + X_{i,r} β_t + φ_{d,t} + ∑_{0≤r≤3} δ_{r,dg,t} + ε_{i,r}
  - q_{h,t}: time-varying hospital fixed effects (AEL estimates)
  - φ_{d,t}: time-varying main-diagnosis fixed effects
  - δ_{r,dg,t}: disease-group specific evolution of earnings around hospitalization
- Controls X_{i,r} include:
  - pre-hospitalization individual socio-economic characteristics: percentile of earnings distribution, earnings growth, decile of own assets, decile of spouse’s wealth and spouse’s earnings interacted with gender, gender, age, education, marital status, occupation, socioeconomic status the year before hospitalization;
  - number of co-diagnoses related to index admission;
  - interactions with public healthcare system: number of non-pregnancy related outpatient and ER visits and number of pregnancy related inpatient, outpatient, and ER visits the same year and 3 years before;
  - fixed effects for all co-morbidities registered in discharge data and calendar year fixed effects;
  - education-specific local labor market controls: unemployment rates, non-in-labor-force rates, earnings levels for individuals with same education level within the municipality, and share of individuals receiving disability benefits in the municipality.
- Averages after dropping missing values: an average of 21 thousands observations per hospital per time period (each admission relates to 4 observations since dead patients’ earnings are assumed zero).
- Empirical Bayes Adjustment implemented to correct AEL estimates for measurement error (algorithm following Chandra et al. [2016], with differences: municipality-clustered standard errors used to estimate variance of hospital fixed effects and allowing the mean of “true” quality to be a function of hospital size rather than location).

### Distribution of AEL and back-of-the-envelope savings
- Substantial heterogeneity in hospital quality across all time periods.
- AEL average (across the five periods) standard deviation: 1.05 percentage points.
- An inpatient admission in the lowest-ranked hospital is associated with an additional decrease in annual labor earnings of 4.2 percentage points, on average, compared to the highest-ranked hospital.
- Hospital heterogeneity:
  - larger for early sample period (1998/2000),
  - constant between 2001 and 2009,
  - lower for latest period (2010/2012); partly due to reduction in number of hospitals (only 22 active at end of sample).
- Hospital quality positively correlated over time; correlation between AEL and its lag (three-year period scale): 0.59 (approximately 0.84 yearly).
- Patients treated at below-median hospitals would on average have earned an additional 0.7% of pre-hospitalization earnings for (at least) four years if treated at a hospital with median estimated quality, corresponding to an estimated loss of (at least) 6,400 DKK (approximately 960 USD).
- Back-of-the-envelope aggregate savings from raising below-median hospitals to median quality:
  - Savings_t = ∑_{h: q_h < q_med} [ (q_med − q_h) × (N_{ht} × Ȳ_{ht} × 4) ]
  - N_{ht}: number of non-pregnancy related inpatient admissions of patients aged 25-59 in year t for hospital h.
  - Ȳ_{ht}: mean earnings the year before hospitalization for patients in N_{ht} at hospital h in year t.
- Estimated implication: if all hospitals had at least median quality, the Danish economy would save on average almost one billion DKK (approximately 140 million USD) in foregone earnings each year, or 60 million DKK (or 9 million USD) per year per hospital.
- Notes on conservatism of this estimate:
  - Focus on inpatient admissions only.
  - Better healthcare might lead to savings beyond four years.
  - Smaller hospitals and patients outside 25-59 excluded.
  - Wage increases over time abstracted from.
  - Some productivity losses might be borne by employers rather than reflected in employees’ earnings.
- The study does not have data to quantify the cost of improving the quality of low-AEL hospitals.

*Source: wpiea2019173-print-pdf — 2.1 Data Sources*

### 3.3  Event-Study Approach

### 3.3 Event-Study Approach

### Event-study design
- Estimation strategy: event-study design estimating
  - yi,r = αi + γt + ∑−3≤r≤3,r≠−1 δr + εit (equation (4)), estimated separately for patients admitted to hospitals in the top and bottom third of AEL ranking (within their admission time period).
- Dependent variable choice rationale:
  - Because AEL is estimated with normalized earnings, earnings cannot be used as the outcome for equation (4) due to mechanical correlation with the quality ranking.
  - Focus instead on the amount of transfers from the government received by the patient (sickness benefit, cash assistance, unemployment benefit).

### Outcome: government transfers
- Transfers are related to both labor outcomes and patients’ health status but are not used to estimate AEL.
- Parameters δr capture evolution of transfers before and after index admission, controlling for patient fixed effects.
- Confidence intervals reported: estimated coefficients plotted with 95% confidence intervals based on municipality-clustered standard errors.

### Findings on transfers and pre-trends
- Transfers increase sharply from the year of hospital admission onwards, signaling substitution from labor earnings to government-provided insurance.
- Pre-admission dynamics: patients admitted to different hospitals follow exactly the same dynamics before hospital admission.
- Post-admission differences:
  - Patients admitted to high-quality hospitals receive significantly less transfers from the year of admission onwards.
  - The difference between high- and low-AEL hospital patients persists over time.
- Robustness notes:
  - Estimation of equation (4) requires an additional assumption due to multicollinearity: coefficients of two consecutive years (2000 and 2001) set equal.
  - Alternative estimation including a control group of non-hospitalized individuals yields similar results (see referenced Figure A.2).
  - Results are similar if high- and low-quality hospitals are defined as top/bottom half or quartile of the AEL ranking.

### Within-hospital heterogeneity (section 3.4)
- AEL can be estimated by ICD10 chapter to produce chapter-specific AEL qh,ch (equation (3) estimated separately by chapter) pooled over time.
- Correlations across diagnostic chapters:
  - Average correlation coefficient across chapter-specific AEL measures is 0.14.
  - AEL estimated only for acute non-deferrable conditions has a 0.52 correlation with AEL estimated for all conditions.
- Interpretation: while better hospitals are on average better across conditions, substantial within-hospital quality heterogeneity exists.

### Correlation with traditional measures (section 3.5)
- Risk-Adjusted Mortality (RAM) and Risk-Adjusted Readmission (RAR) computed for acute non-deferrable conditions via probit:
  - Pr(Di = 1) = Φ(γh,t + Xiβt + φd,t) (equation (5)), with controls Xi similar to those used for AEL estimation but excluding extremely detailed socio-economic controls.
  - RAM and RAR recovered as derivatives of estimated probabilities with respect to hospital dummies, Empirical Bayes Adjustment applied, period-specific averages subtracted.
- Correlations and explanatory power:
  - AEL (acute non-deferrable) correlation with RAM: -0.29 (p−value= 0.001).
  - AEL (acute non-deferrable) correlation with RAR: -0.13 (p−value= 0.118).
  - Correlation between actual AEL and AEL predicted by RAM and RAR via linear regression: 0.32.
  - RAM and RAR explain only 3 percent of the variation of AEL when AEL estimated with all index admissions.
- External ranking comparison:
  - Spearman rank correlation between 2011 “Dagens Medicin” ranking and AEL-based ranking:
    - 0.27 for the 2007/2009 period.
    - 0.15 for the 2010/2012 period.
- Interpretation: AEL contains substantial additional information beyond mortality and readmission measures, especially for non-acute conditions.

### Identification and selection concerns (Section 4 overview)
- Two main endogeneity concerns identified in hospital quality measurement:
  1. Selection on unobservable patient severity: best hospitals might treat a disproportionate share of the sickest patients (downward bias).
  2. Local heterogeneity: hospitals located near unobservably “better” patients or different local amenities could admit more resilient patients (upward bias).
- Data and institutional context mitigating concerns:
  - A large set of controls included (main diagnosis, co-morbidities, past medical history).
  - Danish institutional features: fewer and larger hospitals, larger travel distance differences, more homogeneous population.
  - Empirical fact: each hospital in the main sample serves at least one neighborhood in each decile of the income distribution.
- Validation approaches used:
  - a) Instrumental variables using patients’ home location as instrument for hospital choice to address selection on severity.
  - b) Analysis of a subsample of patients admitted far from home (acute non-deferrable admissions at non-common hospitals) to address local heterogeneity concerns.
  - Additional checks: AEL heterogeneity remains after adding more controls; correlation between hospital quality and share of outside-the-region patients similar for AEL and RAM for deferable and non-acute conditions.

### Instrumental variables and non-common hospital analysis (sections 4.1–4.2)
- Alternative regression framing:
  - yi,r = α·q̂h,t + Xi,rβt + φd,t + ∑0≤r≤3 δr,dg,t + ηi,r (equation (6)), pooling five time periods, where q̂h,t is the estimated AEL.
  - Interpretation of α:
    - α = 0: estimated quality uninformative (captures patient mix only).
    - α > 0: higher-measured-quality hospitals decrease economic impact of admission.
    - α = 1: OLS estimates consistent with main specification (3), OLS not biased by selection.
- Instrument construction and IV results:
  - Location (patient neighborhood / Church District) used as instrument for hospital AEL, motivated by the fact that more than 70% of patients in the sample are admitted to the “common” hospital for their neighborhood and condition.
  - IV estimate: α is neither statistically nor economically different from 1 in the neighborhood-instrument IV (reported in column (1) of Table 2): being admitted to a higher AEL hospital decreases the economic impact exactly as predicted by equation (3).
  - Caveat: IV validity requires that patient location affects post-hospitalization earnings only through hospital choice; remaining local unobserved heterogeneity could invalidate IV.
- Acute non-deferrable admissions at non-common hospitals (equation (7)):
  - Sample: patients treated outside their local common hospital with acute non-deferrable condition (weekend-admissions share within 0.02 of two-sevenths).
  - Specification includes neighborhood fixed effects τn: yi,r = α·q̂h,t + Xi,rβt + τn + φd,t + ∑0≤r≤3 δr,dg,t + εi,r (equation (7)).
  - OLS estimate on this subsample (column (2) of Table 2): α ≈ 1.2, implying being admitted to a better hospital significantly decreases the earnings cost of hospitalization.
    - Statistical test: cannot reject α = 1 at 10% confidence level (p−value= 0.21).
  - Interpretation: results provide no strong evidence that local heterogeneity substantially biases AEL compared to traditional measures.

*Source: IMF working paper chapter text (sections 3.3–4.2 as provided).*

### section 3, we consider the alternative specification:

### wpiea2019173-print-pdf - section 3, we consider the alternative specification:

### Alternative specification and local heterogeneity (equation (8))
- Model (8): yi,r = α·̂qh,t + Xi,r βt + θ·̂qn,dg,t + φd,t + ∑0≤r≤3 δr,dg,t + ϵi,r
- Interpretation: ̂qn,dg,t is the estimated quality of the “common” hospital for patients of neighborhood (Church District) n and diagnostic group dg in period t. If AEL captures local heterogeneity (patients’ unobserved characteristics or presence of better GPs) rather than hospital quality, patients from “better” neighborhoods should show better earnings even when treated outside the local hospital.
- Sample focus: acute admissions at non-common hospitals.
- OLS results (column (3) of Table 2):
  - α = 1.39
  - θ is not different from zero (no systematic effect of neighborhood-estimated common-hospital quality on outcomes when patients are treated elsewhere)
- Conclusion:
  - It is the hospital where patients are admitted—and not where they live—that matters for the economic impact of hospitalization.
  - No evidence that AEL estimates are affected by patients’ heterogeneity clustered at the local level.
  - Lack of correlation between estimated hospital quality and earnings dynamics of patients from the same area when admitted elsewhere supports a hospital-quality interpretation of AEL.

### AEL heterogeneity and observable covariates (Section 4.3)
- Concern: most variance of normalized earnings remains unexplained; AEL heterogeneity could reflect omitted patient-level factors rather than hospital quality.
- Approach: evaluate joint changes in OLS coefficients and R-square as controls are sequentially added (six ordered sets of controls; each set is a superset of the previous).
  - Sixth set includes all controls of equation (3).
  - First set includes only main disease fixed effects.
  - Second group adds pre-hospitalization income (linear and square) and fixed effects for age, gender, marital status, and year.
  - Third group adds detailed controls for comorbidities, education, and pre-hospitalization occupation.
- Re-estimate equation (3) pooling years and plot R-square, AEL standard deviation, and AEL range across specifications (Figure 8).
- Findings:
  - R-square rises monotonically as controls are added.
  - AEL heterogeneity (standard deviation and range) is higher in regressions one and two (when controls have little explanatory power).
  - Once controls for comorbidities, education, and pre-hospitalization occupation are included, both range and standard deviation stabilize around 4 and 1 percentage points respectively.
  - Inclusion of additional controls (percentile of income, patients and spouses wealth) increases R-square by more than a third but does not diminish AEL heterogeneity.
- Interpretation:
  - While unobserved heterogeneity affecting hospital selection cannot be fully eliminated, these exercises mitigate the concern that AEL heterogeneity merely captures unobserved patient characteristics rather than hospital quality.

### Robustness, selection issues, and comparisons to traditional metrics (Section 4.4)
- Main takeaways:
  - Selection issues are unlikely to significantly bias quality measures if unobserved heterogeneity is homogeneous across neighborhoods.
  - Estimates of equation (8) show local heterogeneity does not significantly affect results, supporting a quality interpretation of AEL heterogeneity.
  - AEL heterogeneity is robust to inclusion of a large set of controls.
- Caveats:
  - Additional selection issues may be present (e.g., local hospital quality may affect decision to seek care or timing of care).
  - Diagnostic coding capacity of hospitals could be correlated with quality, affecting comparability.
  - Instrumental variable approach recovers effects for “marginal” patients whose hospital selection depends on home location; the very sickest patients might travel to best hospitals irrespective of location, so estimates may not capture those hospitals’ ability to treat very sick patients.
- Exercise comparing susceptibility to purposeful selection:
  - Correlations with the share of out-of-region patients (for non-acute and “deferrable” conditions):
    - AEL correlation = 0.13, p−value = 0.13
    - RAM correlation = -0.16, p−value = 0.08
    - RAR correlation = -0.04, p−value = 0.64
  - Interpretation: this exercise suggests AEL is not more prone to selection biases than traditional metrics (RAM, RAR, mortality rates).
- Recommendation: future research should adopt alternative empirical designs to further test labor market outcome–based measures of healthcare quality.

### Empirical strategy for labor market costs over time (Section 5.1)
- Data and sample:
  - All inpatient “index” hospital admissions in Denmark during 1998-2012, plus a 10% control group of individuals without any index admissions during the same period.
  - Diagnostic grouping: >9,000 4-digit ICD10 codes aggregated into 271 diagnostic groups; analysis uses the 150 groups with most observations (covering 97.5% of total index admission observations; each group covers more than 850 index-observations).
- Model (equation (9)):
  - yi,t,yg = αi + Xi,t β + γt + ∑−3≤r≤3,r≠−1 δr×yg + ϵi,r,t
  - αi: individual fixed effects
  - Xi,t: controls including age fixed effects, municipality- and education-specific unemployment rates and log median earnings in year t, share on disability benefits in municipality in year t, dummies for age categories at hospitalization, manual labor indicator in r = −1, fixed effects for outpatient admissions and ER visits in previous three years, fixed effects for number of co-diagnoses, and fixed effects for ICD10 chapter of primary co-diagnosis
  - γt: calendar-year fixed effects
  - δr×yg: time-relative-to-hospitalization fixed effects interacted with year-group of treatment (year-groups: 1998-2000, 2001-2003, 2004-2006, 2007-2009, 2010-2012). Reference r = −1.
- Outcome measures:
  - Extensive margin: dummy indicator for earnings larger than 50,000 DKK. Extensive-margin cost measure = δr=3×yg (third year following index admission).
  - Intensive margin: log earnings conditional on earnings > 50,000 DKK. Intensive-margin cost measure = δr=1×yg (first year following index admission).
- Identification: change in labor market consequences of a disease = difference in δr×yg for r > 0 across year groups.

### Results: disease-level evolution (Section 5.2)
- General pattern:
  - Decline in estimated severity over time for most diseases (negative labor participation consequences decrease for later year groups), often steadily and with an apparent acceleration over time.
- Examples (extensive-margin participation drop 3 years after hospitalization):
  - Acute cerebrovascular disease:
    - 1998-2000: 19% of patients dropped out of the labor force 3 years after hospitalization.
    - 2010-2012: 6% dropped out.
  - Spondylosis (spinal degeneration):
    - 1998-2000: 13% dropped out.
    - 2010-2012: 11% dropped out.
  - Other severe diseases (roughly 10% drop): poisoning by other medications and drugs, poisoning by psychotropic agents, alcohol-related mental disorders, multiple sclerosis.
- Mortality contribution:
  - When excluding dead individuals:
    - Acute cerebrovascular disease: 14% of surviving patients dropped out 3 years after hospitalization in 1998-2000, versus 9% in 2010-2012.
    - Interpretation: changes in mortality rates drive more than half of the estimated change in labor participation drop for acute cerebrovascular disease; mortality explains a much smaller share for less severe diseases.
- Intensive-margin patterns (δr=1×yg, first year log-earnings conditional on >50,000 DKK):
  - Intensive-margin costs are generally smaller than extensive-margin costs.
  - Overall decrease over time observed, but less steady than for extensive margin—consistent with more individuals remaining in the labor force but with lower earnings.
  - Scatter of intensive vs extensive margins (Figure 12) shows ordering similarity across margins and larger declines in extensive-margin severity between 1998-2000 and 2010-2012.
- Accumulated 3-year change (equation (10)):
  - Accumulated Change = ∑_{r=1}^3 δr,yg=2010−2012 − ∑_{r=1}^3 δr,yg=1998−2000
  - Figure 11 confirms larger declines on the extensive participation margin compared to the intensive log-earnings margin.
  - For most significant disease changes:
    - Decline in accumulated extensive-margin severity: roughly 7–27 percentage points (disease-specific).
    - Decline in accumulated intensive-margin severity: around 4–6 percentage points (more constant).
- Disease-specific notable changes:
  - Lung cancer: largest improvement—accumulated decline in labor force participation during 3 years following hospitalization decreased by 27 percentage points from 1998-2000 to 2010-2012.
  - Cancer-related diseases (secondary malignancies, breast, colon) show especially large declines.
  - Acute cerebrovascular disease: accumulated decline of 20 percentage points on extensive margin and 10% on intensive margin.
  - Acute myocardial infarction (AMI): change of 15 percentage points on extensive margin and 8% on the extensive margin (as reported).
  - Little or no significant decline: benign neoplasm of uterus, varicose veins of lower extremity, abdominal hernia.
- Aggregate/weighted averages (weighted by number of patients during 1998-2012):
  - Average accumulated 3-year decline in participation rates following hospitalization decreased by 8.8 percentage points from 1998-2000 to 2010-2012.
  - Average accumulated 3-year intensive-margin earnings decline following hospitalization dropped by 4.9 percentage points.
  - Corresponds to:
    - Average decline in labor force participation costs of a hospitalization of 50%.
    - 25% reduction in corresponding intensive-margin earnings costs.
  - Total change (sum of intensive and extensive margin changes) = 13.6 percentage points.

### Discussion and interpretation (Section 5.3 and Conclusion)
- Interpretation:
  - Sizeable reduction in labor market costs of hospital admissions between 1998 and 2012 suggests strong improvements in quality of healthcare treatments.
  - Likely drivers: advancements in global medical technology (new drugs, devices) and improvements in Danish hospitals’ system.
- Alternative contributors and limits:
  - Healthier population behaviors (e.g., less smoking, better diet) could increase resilience and contribute to observed improvements.
  - Labor market changes may affect evolution of economic losses associated with hospital admissions.
  - Appendix C investigation finds no evidence that the introduction of the “flex-job” scheme in 1998 explains the improvements.
- Conservative estimate of healthcare contribution:
  - Under the assumption that non-healthcare factors depend only on severity and not on nature of disease, a conservative estimate implies at least 40% of the estimated change is due to improved healthcare treatment over time.
- Methodological contribution:
  - Introduces “Adjusted Earning Losses” (AEL) as a novel measure of hospital treatment quality based on mitigation of labor market consequences of diagnosis.
  - Data linkage: universe of hospital admissions in Denmark to tax data on labor market outcomes for working-age population in Denmark from 1995- (continuation of data description in the source).

*wpiea2019173-print-pdf - section 3, we consider the alternative specification:*

### 2015. This allows us to measure the labor market consequences of any hospitalization,

### wpiea2019173-print-pdf - 2015. This allows us to measure the labor market consequences of any hospitalization,

### Methodology and measurement
- Measure: patients’ “normalized earnings” that allow combining intensive and extensive margins [Kleven et al., 2018].
- Sample construction:
  - All patients who experience their first non-pregnancy related inpatient admission in four years.
  - Observed total of 3.1 million non-birth related index admission observations of patients born in Denmark aged 25-59 at the time of hospitalization in year 1998-2012 (sample referred to as “all admissions”).
  - Index admission sample: subsample of patients who experience the first observed non-pregnancy related inpatient hospital admission for at least 3 years.
  - Control group: 10% random sample of everyone who didn’t experience an index admission, with similar birth-year and age restrictions as in the index-admission sample.
- Estimation: A hospital’s Average Earnings Loss (AEL) is estimated (see equation (3) in source). Instrumental variables (IV) and OLS specifications are used:
  - Column (1): IV with neighborhood (Church District) dummies as instruments; sample: All.
  - Column (2): OLS with neighborhood fixed effects; sample: Non-deferrable acute not at “Common” hospital.
  - Column (3): OLS with neighborhood quality substitutêq_{n,dg,t}; sample restricted to top 31 hospitals.
- Outcomes:
  - Intensive margin: log(earnings) excluding non-positive earnings.
  - Extensive margin: dummy for positive earnings (earnings > 50,000 DKK).

### Heterogeneity in AEL across hospitals and diagnoses
- There is significant heterogeneity in the labor cost of a hospitalization across different hospitals.
- Point estimate: a 4 percentage point difference in lost earnings between the best and worst hospital, all else equal.
- AEL is positively correlated with traditional quality measures (risk-adjusted mortality and readmissions) but contains substantial additional information.
- Within-hospital heterogeneity: positive but low correlation between a hospital’s abilities to treat patients admitted with different diagnoses, indicating substantial within-hospital heterogeneity.
- Expanded hospital sample (60 hospitals, covering 98% of inpatient admissions) findings:
  - Average standard deviation of AEL is 1.2 percentage point.
  - An inpatient admission in the lowest-ranked hospital is associated with an additional decrease in annual labor earnings of 5.1 percentage points, on average, compared to the highest-ranked hospital.

### Bias concerns and identification checks
- Two main identification concerns:
  1. Patients unobservably sicker select into better hospitals, generating downward bias on estimated quality of good hospitals.
  2. Unobserved patient characteristics unevenly distributed across geographic regions bias estimated quality of hospitals in unobservably "good"/"bad" neighborhoods.
- Mitigation:
  - Controls include a broad range of patient characteristics (argued broader than previous papers).
  - Two complementary empirical strategies test whether admission to a higher quality hospital (by estimated AEL) leads to positive causal effects on post-admission earnings.
  - Both tests suggest the above concerns are not biasing the estimated quality measure in any significant way.
- Robustness table notes:
  - AEL of Admission Hospital coefficients:
    - Column (1) IV: 1.003*** (standard error 0.0263)
    - Column (2) OLS: 1.199*** (standard error 0.250)
    - Column (3) OLS (top 31 hospitals): 1.387** (standard error 0.277)
  - Observations reported: 3,113,831; 59,912; 52,186 respectively.
  - R-squared: 0.165; 0.243; 0.242 respectively.
  - Standard errors clustered at the municipality level. Significance: *** p<0.01, ** p<0.05, * p<0.1.

### Time trends: decline in labor cost of hospitalizations (1998-2012)
- Documented significant decline in labor cost of hospitalizations over time.
- Measured as accumulated change in the three years following admission.
- Average declines across diseases (accumulated over three years):
  - Extensive (participation): decline of 8.8%.
  - Intensive (earnings conditional on working): decline of 4.9%.
  - Total change in estimated labor costs: 13.6 percentage points.
- Relative reductions:
  - Average reduction of extensive margin labor market costs of about 50%.
  - 25% reduction of the intensive-margin labor cost of a disease.
- Figures and event studies illustrate heterogeneity over time, across hospitals, and by disease group for:
  - Labor supply responses (intensive and extensive margins).
  - Estimated labor force participation loss three years after hospitalization by disease and year of treatment (150 most frequent disease groups).
  - Estimated earnings loss in year r=1 by disease and year of treatment (150 most frequent disease groups).
  - Change in accumulated labor market cost of a hospitalization by disease group, 1998-2001 to 2010-2012 (r∈{1,2,3}).

### Additional descriptive and sample statistics
- Table 1 (selected descriptive statistics; means by r = -1, r = 0, r = 1):
  - Mean earnings: 204,742; 201,737; 196,661; 327,639; 313,750; 307,559; 301,963 (various sample columns shown in source).
  - Mean log earnings (earn > 50,000): 12.48; 12.49; 12.53; 12.68; 12.69; 12.70; 12.70.
  - Share w/ earn > 50,000: 0.678; 0.642; 0.611; 0.915; 0.872; 0.840; 0.82.
  - Share alive: 1.000; 0.984; 0.966; 1.000; 0.989; 0.981; 0.97.
  - Mean age: 42.83; 43.84; 44.84; 42.42; 43.42; 44.40; 42.38.
  - # Observations: 3,104,532; 3,104,632; 3,099,490; 1,098,162; 1,113,321; 1,111,576; 3,312,609.
- Table 2 sample notes:
  - Sample (1) All; (2) Non-deferrable acute not at “Common” hospital; (3) Non-deferrable acute not at “Common” hospital (top 31 hospitals).

*Source: wpiea2019173-print-pdf - 2015. This allows us to measure the labor market consequences of any hospitalization,*

### 0.68 in this sample, see Figure A.6.

### wpiea2019173-print-pdf - 0.68 in this sample, see Figure A.6.

### AEL versus traditional measures (RAM, RAR)
- For acute non-deferrable conditions, AEL has a correlation of -0.51 with RAM (p−value= 0.000).
- For acute non-deferrable conditions, AEL has a correlation of -0.14 with RAR (p−value= 0.047).
- The correlation between the actual AEL and the predicted values (obtained regressing AEL on RAM and RAR) is 0.52: half of the variation in AEL cannot be explained by mortality and readmission rates.
- Robustness exercises of section 4 produce similar results (see Table A.1 and Figure A.8).

### Location IV: Simulation (endogenous selection and heterogeneous hospital quality)
- Model setup and estimation:
  - Two hospitals: hospital1 with quality q1>0 and hospital0 normalized to 0.
  - Patient i normalized earnings when admitted to hospital h: Yi = c0 + q1·1_{h=1(i)} + εi (equation 11).
  - Hospital choice: 1_{h=1(i)} = 1 ⇐⇒ Φ(ηi + c1·1_{n=A(i)} + G·εi) > 1/2, where Φ(·) is the standard normal CDF.
  - c1>0 means neighborhood A is more likely to go to hospital1. G disciplines endogenous selection: G=0 (no selection), G<0 (better hospital admits sicker patients), G>0 (better hospital admits more resilient patients).
  - Researcher estimates q̂h by OLS on equation (11); then uses patient location 1_{n=A(i)} as an instrument for q̂h to obtain αIV, with OLS estimate αOLS.
- Simulation parameters and procedure:
  - Set q1 = 1 and choose arbitrary values for other parameters.
  - Grid for G: from −0.3 to 0.3.
  - Simulate the model 200 times for each G, compute q̂1, αIV, and αOLS and plot the sample average.
  - Parameter values used: c0 = 1, c1 = .5, N = 20,000, ε and η distributed as iid standard normal.
- Simulation findings (Figure A.9 summary):
  - Solid line: average AEL estimate q̂1. OLS recovers true parameter only when G = 0. When G < 0, q̂1 underestimates true q1 because hospital1 treats sicker patients. When G > 0, q̂1 overestimates true q1.
  - Stars: αOLS, mechanically equal to 1 for all simulations.
  - Dotted line: average αIV. When no endogenous selection (G = 0), αIV = 1. When G > 0 (q̂1 > q1), average αIV < 1 (admission effect smaller than OLS-predicted). When G < 0 the opposite holds.

### Labor market reforms and the decline in economic costs of hospital admissions
- Flex-job scheme (introduced 1998) hypothesis and counterfactual:
  - Flex-job scheme provides wage subsidies to partly disabled individuals.
  - Counterfactual robustness check: assume all flex-job participants would instead be on full disability benefits with 0 earnings (worst-case).
  - Result: under this counterfactual, estimates show slightly larger declines in both intensive- and extensive labor market responses following hospitalization; thus the flex-job scheme is unlikely to drive the observed improvement.
- Participation rates in flex-job program for index-admission patients:
  - For index-admission patients hospitalized in 2000: 0.4% participated in the program in 1999 and 1% in 2001.
  - For index-admission patients hospitalized in 2011: 3.3% participated in 2010 vs. 3.7% in 2012.
- Other potential contributors:
  - Other labor market regulations targeting the sick, reforms aimed at decreasing sick leave, improved health, and cultural changes (e.g., perceptions of how sick one should be to not work, employer pressure) could explain part of the change.
  - These factors may vary across disease severity but are expected to have the same effect across diagnostic groups conditional on severity.
- Back-of-the-envelope lower bound attribution to treatment quality:
  - Define change in labor costs for diagnostic group dg: ΔLC(dg) = ΔTQ(dg) + ΔLM(severity(dg)) (equation 12).
  - For each severity class, attribute the minimum observed ΔLC(dg) across dg in that severity class to ΔLM(severity) (equation 13), assuming ΔTQ(dg) ≥ 0.
  - Empirical results:
    - Total 3-year accumulated labor costs declined by 13.6 percentage points over the period.
    - With severities split into 3 equally large groups, 8.8 percentage points come from health care improvements.
    - With 5 groups of severities, 7.7 percentage points come from health care improvements.
    - With 10 groups, 5.3 percentage points come from health care improvements.
  - Conservative lower bound: improvements in healthcare quality alone have caused labor costs of a hospitalization to decrease by at least 5.3 percentage points.

### Additional Tables (Table A.1: Robustness of AEL - Alternative Sample)
- Dependent variable: Normalized earnings (columns reported with Estimator = IV, OLS, OLS).
- Key coefficient: AEL of Admission Hospital
  - Column (1) (IV): 1.012*** (standard error (0.0223))
  - Column (2) (OLS): 1.199*** (standard error (0.223))
  - Column (3) (OLS): 1.374** (standard error (0.223))
- AEL of “Common” Hospital in column (3): -0.116 (standard error (0.212))
- Fixed effects and controls:
  - Church District FEs and Controls indicated across columns as reported in table header.
- Observations:
  - Column (1): 3,727,345 (Sample: All (top 60 hospitals))
  - Column (2): 71,396 (Sample: Non-deferrable acute not at “Common” hospital)
  - Column (3): 69,471 (Sample: Non-deferrable acute not at “Common” hospital)
- R-squared:
  - Column (1): 0.165
  - Column (2): 0.237
  - Column (3): 0.185
- Notes on specifications (as in table):
  - Column (1): estimates y_{i,r} = α·q̂_{h,t} + X_{i,r}β + η_{i,r}, q̂_{h,t} instrumented with neighborhood (Church District) dummies; labor earnings normalized by average earnings during the three years before hospital admission.
  - Column (2): estimates y_{i,r} = α·q̂_{h,t} + τ_n + X_{i,r}β + ε_{i,r}; includes full set of neighborhood fixed effects; sample restricted to non-deferrable acute admissions not at the most common hospital among similar patients.
  - Column (3): estimates y_{i,r} = α·q̂_{h,t} + θ·q̂_{n,dg,t} + X_{i,r}β + ε_{i,r}; neighborhood fixed effects replaced with q̂_{n,dg,t}, the estimated quality of the most common hospital for patients from same neighborhood and diagnosis.
  - Standard errors clustered at the municipality level. Significance: *** p<0.01, ** p<0.05, * p<0.1.

### Additional Figures (summary of figure content)
- Figure A.1: Number of non-pregnancy related hospital records by type (raw data).
- Figure A.2: Event study of AEL and transfers from government to patients; effects by hospital quality terciles/quarters; includes 95% confidence intervals.
- Figure A.3: Event study of hospital quality (AEL or RAM) and labor earnings (logs and levels); stratified by hospital quality and pre-hospitalization earnings deciles.
- Figure A.4: Cumulative distribution function of hospital size (non-elderly inpatient index admissions); panels for all hospitals, largest 31, largest 60.
- Figure A.5: Descriptive statistics of AEL for alternative hospital sample: standard deviation, range, and number of hospitals by period.
- Figure A.6: Scatterplot of AEL present versus previous period (lag), pooled years, AEL normalized by period-specific average.
- Figure A.7: Scatterplots of AEL against RAM, RAR, and predicted values from regressing AEL on RAM and RAR; pooled years and period-normalized measures.
- Figure A.8: Range and standard deviation of AEL estimates with R-squared of regression used to estimate hospital quality as progressively larger sets of controls are included.
- Figure A.9: Results of simulated IV model described above: solid line = average q̂1, dotted line = average αIV, stars = average αOLS over 200 simulations per G value.

*Source: wpiea2019173-print-pdf - 0.68 in this sample, see Figure A.6.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019173-print-pdf.pdf_