Association Between Supplemental Private Health Insurance and Burden of Out-of-Pocket Healthcare Expenditure in China: A Novel Approach to Estimate Two-Part Model with Random Effects Using Panel Data

Figures & data

Figure 1 Structure of the generalized structural equation model (GSEM) used to estimate the two-part model (TPM) with random effects.

Table 1 Characteristics of Respondents with and Without PHI in CHARLS 2011–2015

	With PHI [480 (1.83%)]	Without PHI [23,821 (98.07%)]	Total [24,301]	p-value
Age (years)	53.9 (7.4)	59.3 (9.0)	59.2 (9.0)	<0.001
Male [N (%)]	251 (53.4)	11,662 (48.9)	11,913 (49.0)	0.055
Rural [N (%)]	229 (48.7)	15,843 (66.5)	16,072 (66.1)	<0.001
Education high school or above	141 (30.0)	2723 (11.4)	2864 (11.8)	<0.001
Mean number of chronic conditions	1.5 (1.5)	1.6 (1.5)	1. 6 (1.5)	0.380
Self-reported health status [N (%)]				<0.001
Excellent	7 (1.6)	199 (1.0)	206 (1.0)
Very good	63 (14.8)	2006 (9.6)	2069 (9.7)
Good	73 (17.1)	2929 (14.1)	3002 (14.1)
Fair	223 (52.2)	11,018 (52.9)	11,241 (52.8)
Poor	61 (14.3)	4695 (22.5)	4756 (22.4)
Income (Chinese ¥)	9633 (20,525)	3927 (18,346)	4035 (18,406)	<0.001
Had any hospitalization in the past year [N (%)]	52 (11.1)	2712 (11.5)	2764 (11.5)	0.815
Had any outpatient visit in the past month [N (%)]	94 (20.4)	4805 (20.5)	4899 (20.5)	0.992
The household had any out-of-pocket medical expenditure [N (%)]	300 (63.8)	13,639 (57.2)	13,939 (57.4)	0.004
Household out-of-pocket medical expenditure as percent of household consumption (percentage points)	6.5 (12.6)	7.9 (15.2)	7.9 (15.1)	0.039

Notes: Results are presented as mean (standard deviation) unless otherwise specified. Repeated responses were pooled.

Abbreviation: PHI, private health insurance.

Table 2 Coefficient Estimates Using the Three Different Methods to Implement TPM Estimation

	First Part			Second Part
	Probit with RE Estimated Separately	Probit Without RE Estimated Using TPM Routine	Probit with RE Estimated Using GSEM	GLM with RE ESTIMATED Separately	GLM Without RE Estimated Using TPM Routine	GLM with RE Estimated Using GSEM
Having PHI	0.185* (0.0720)	0.185* (0.0749)	0.184* (0.0726)	−0.182* (0.0914)	−0.206 (0.105)	−0.241* (0.0959)
Self-reported health fair or above	0.192*** (0.0262)	0.192*** (0.0252)	0.186*** (0.0283)	−0.265*** (0.0356)	−0.221*** (0.0313)	−0.326*** (0.0380)
Living in rural area	−0.0233 (0.0218)	−0.0233 (0.0199)	−0.0222 (0.0218)	0.119*** (0.0314)	0.120*** (0.0303)	0.0515 (0.0347)
Age	0.00602*** (0.00118)	0.00602*** (0.00108)	0.00587*** (0.00135)	0.0259*** (0.00178)	0.0215*** (0.00166)	0.0203*** (0.00197)
Annual personal income (in thousand Chinese ¥)	0.000225 (0.000454)	0.000225 (0.000674)	0.000236 (0.000453)	−0.00738*** (0.00122)	−0.00834*** (0.00120)	−0.00903*** (0.00127)
Ever Had Condition
High blood pressure	0.0806*** (0.0243)	0.0806*** (0.0222)	0.0839*** (0.0247)	0.0473 (0.0333)	0.0184 (0.0316)	0.0133 (0.0363)
Diabetes	0.171*** (0.0425)	0.171*** (0.0376)	0.178*** (0.0436)	0.181*** (0.0528)	0.132** (0.0451)	0.154** (0.0573)
Cancer	0.256* (0.103)	0.256** (0.0868)	0.260* (0.104)	0.396** (0.122)	0.396*** (0.104)	0.353** (0.131)
Lung disease	0.0659 (0.0357)	0.0659* (0.0328)	0.0702* (0.0358)	0.0787 (0.0479)	0.0708 (0.0437)	0.0626 (0.0517)
Heart problem	0.122*** (0.0318)	0.122*** (0.0281)	0.127*** (0.0325)	0.263*** (0.0411)	0.216*** (0.0349)	0.250*** (0.0446)
Stroke	0.124 (0.0672)	0.124* (0.0585)	0.126 (0.0678)	0.143 (0.0847)	0.118 (0.0730)	0.132 (0.0908)
Psychiatric problem	0.207* (0.0928)	0.207* (0.0817)	0.217* (0.0933)	0.278* (0.112)	0.270** (0.0968)	0.246* (0.120)
Arthritis	0.106*** (0.0219)	0.106*** (0.0198)	0.108*** (0.0223)	0.0607* (0.0302)	0.0414 (0.0294)	0.0164 (0.0328)
Dyslipidemia	0.175*** (0.0338)	0.175*** (0.0315)	0.180*** (0.0349)	0.109* (0.0428)	0.0804* (0.0378)	0.0849 (0.0462)
Liver disease	0.216*** (0.0515)	0.216*** (0.0470)	0.222*** (0.0524)	0.174** (0.0641)	0.168** (0.0566)	0.143* (0.0692)
Kidney disease	0.180*** (0.0417)	0.180*** (0.0374)	0.182*** (0.0430)	0.111* (0.0523)	0.0908 (0.0473)	0.0939 (0.0562)
Stomach/digestive disease	0.136*** (0.0240)	0.136*** (0.0214)	0.139*** (0.0248)	0.109*** (0.0329)	0.0443 (0.0301)	0.0578 (0.0358)
Asthma	0.118* (0.0548)	0.118* (0.0495)	0.124* (0.0551)	0.0748 (0.0718)	0.0327 (0.0618)	0.0623 (0.0772)
Memory problem	0.222* (0.0879)	0.222** (0.0788)	0.229** (0.0885)	0.126 (0.102)	0.0776 (0.0809)	0.142 (0.109)
Smoke now	−0.265*** (0.0236)	−0.265*** (0.0216)	−0.261*** (0.0256)	−0.179*** (0.0356)	−0.139*** (0.0362)	−0.216*** (0.0391)
Drink alcohol daily or more often	−0.0801** (0.0305)	−0.0801** (0.0285)	−0.0789** (0.0306)	−0.156*** (0.0448)	−0.114* (0.0473)	−0.217*** (0.0478)
Covariance of random effects	-		−0.00759 (0.0306)	-		−0.00759 (0.0306)
N observations	15,937	15,937	15,937	9373	9373	9373
N individuals	9032	9032	9032	6785	6785	6785

Notes: Standard errors in parentheses. *p < 0.05, **p < 0.01, ***p < 0.001.

Abbreviations: TPM, two-part model; RE, random effect; GSEM, generalized structural equation model; GLM, generalized linear model; PHI, private health insurance.

Table 3 Marginal Effect Estimates Using the Three Different Methods to Implement TPM Estimation

	First Part			Second Part			Total Marginal Effects
	Probit with RE Estimated Separately	Probit Without RE estimated Using TPM Routine	Probit with RE Estimated Using GSEM	GLM with RE Estimated Separately	GLM Without RE Estimated Using TPM Routine	GLM with RE Estimated Using GSEM	TPM with RE Estimated Separately	TPM Without RE Estimated Using TPM Routine	TPM with RE Estimated Using GSEM
Having PHI	0.0699* (0.0272)	–	0.0429* (0.0169)	−0.0265* (0.0133)	–	−0.0237* (0.00946)	–	−0.00755 (0.00929)	−0.0105 (0.00603)
Self-reported health fair or above	0.0724*** (0.00991)	-	0.0433*** (0.00649)	−0.0385*** (0.00528)	-	−0.0320*** (0.00394)	-	−0.00844** (0.00282)	−0.0156*** (0.00246)
Living in rural area	−0.00880 (0.00823)	-	−0.00517 (0.00507)	0.0173*** (0.00458)	-	0.00506 (0.00341)	-	0.00856** (0.00265)	0.00262 (0.00215)
Age	0.00227*** (0.000446)	-	0.00137*** (0.000312)	0.00377*** (0.000280)	-	0.00199*** (0.000198)	-	0.00203*** (0.000149)	0.00136*** (0.000128)
Annual personal income (in thousand Chinese ¥)	0.0000850 (0.000171)	-	0.0000550 (0.000106)	−0.00107*** (0.000178)	-	−0.000888*** (0.000127)	-	−0.000664*** (0.000104)	−0.000541*** (0.0000789)
Ever Had Condition
High blood pressure	0.0304*** (0.00917)	-	0.0195*** (0.00574)	0.00687 (0.00486)	-	0.001303 (0.00356)	-	0.00546* (0.00277)	0.00267 (0.00226)
Diabetes	0.0647*** (0.0161)	-	0.0414*** (0.0101)	0.0263*** (0.00773)	-	0.0152** (0.00562)	-	0.0191*** (0.00410)	0.01330*** (0.00360)
Cancer	0.0965* (0.0390)	-	0.0604* (0.0241)	0.0576** (0.0179)	-	0.0347** (0.0129)	-	0.0447*** (0.00947)	0.0272*** (0.00829)
Lung disease	0.0249 (0.0135)	-	0.0163* (0.00833)	0.0114 (0.00697)	-	0.00615 (0.00508)	-	0.00898* (0.00389)	0.00535 (0.00322)
Heart problem	0.0460*** (0.0120)	-	0.0296*** (0.00755)	0.0383*** (0.00610)	-	0.0246*** (0.00442)	-	0.0235*** (0.00317)	0.0180*** (0.00283)
Stroke	0.0467 (0.0254)	-	0.0294 (0.0158)	0.0208 (0.0123)	-	0.0130 (0.00892)	-	0.0156* (0.00657)	0.0108 (0.00569)
Psychiatric problem	0.0780* (0.0350)	-	0.0506* (0.0217)	0.0404* (0.0163)	-	0.0242* (0.0118)	-	0.0320*** (0.00883)	0.0197** (0.00754)
Arthritis	0.0400*** (0.00828)	-	0.0252*** (0.00516)	0.00882* (0.00441)	-	0.00162 (0.00322)	-	0.00857*** (0.00257)	0.00341 (0.00204)
Dyslipidemia	0.0660*** (0.0128)	-	0.0419*** (0.00808)	0.0158* (0.00624)	-	0.00835 (0.00454)	-	0.0151*** (0.00343)	0.00915** (0.00290)
Liver disease	0.0815*** (0.0195)	-	0.0516*** (0.0121)	0.0253** (0.00935)	-	0.0141* (0.00680)	-	0.0243*** (0.00514)	0.01360** (0.00435)
Kidney disease	0.0682*** (0.0158)	-	0.0424*** (0.00995)	0.0162* (0.00762)	-	0.00923 (0.00552)	-	0.0162*** (0.00425)	0.00974** (0.00353)
Stomach/digestive disease	0.0516*** (0.00909)	-	0.0325*** (0.00572)	0.0159*** (0.00481)	-	0.00568 (0.00351)	-	0.0103*** (0.00264)	0.00661** (0.00222)
Asthma	0.0445* (0.0207)	-	0.0288* (0.0128)	0.0109 (0.0104)	-	0.00613 (0.00759)	-	0.00846 (0.00556)	0.00653 (0.00482)
Memory problem	0.0840* (0.0332)	-	0.0533** (0.0206)	0.0183 (0.0149)	-	0.0140 (0.0107)	-	0.0172* (0.00761)	0.0137* (0.00688)
Smoke now	−0.100*** (0.00896)	-	−0.0609*** (0.00580)	−0.0260*** (0.00523)	-	−0.0212*** (0.00384)	-	−0.0243*** (0.00312)	−0.0190*** (0.00245)
Drink alcohol daily or more often	−0.0303** (0.0115)	-	−0.01838** (0.00711)	−0.0227*** (0.00654)	-	−0.0214*** (0.00473)	-	−0.0132** (0.00408)	−0.0149*** (0.00300)

Notes: Standard errors in parentheses. *p < 0.05, **p < 0.01, ***p < 0.001.

Abbreviations: TPM, two-part model; RE, random effect; GSEM, generalized structural equation model; GLM, generalized linear model; PHI, private health insurance.