The impact of health insurance on out of pocket payments in the mekong river delta

UNIVERSITY OF ECONOMICS ERASMUS UNVERSITY ROTTERDAM HO CHI MINH CITY INSTITUTE OF SOCIAL STUDIES VIETNAM - NETHERLANDS PROGRAMME FOR M.A IN DEVELOPMENT ECONOMICS THE IMPACT OF HEALTH IN

UNIVERSITY OF ECONOMICS ERASMUS UNVERSITY ROTTERDAM

HO CHI MINH CITY INSTITUTE OF SOCIAL STUDIES

VIETNAM - NETHERLANDS PROGRAMME FOR M.A IN DEVELOPMENT ECONOMICS

THE IMPACT OF HEALTH INSURANCE ON OUT-OF-POCKET PAYMENTS IN THE

MEKONG RIVER DELTA

BY

TA THI HONG NGOC

MASTER OF ARTS IN DEVELOPMENT ECONOMICS

HO CHI MINH CITY - DECEMBER, 2017

UNIVERSITY OF ECONOMICS INSTITUTE OF SOCIAL STUDIES

HO CHI MINH CITY THE HAGUE

VIETNAM THE NETHERLANDS

VIETNAM - NETHERLANDS PROGRAMME FOR M.A IN DEVELOPMENT ECONOMICS

THE IMPACT OF HEALTH INSURANCE ON

OUT-OF-POCKET PAYMENTS IN THE MEKONG RIVER DELTA

A thesis submitted in partial fulfilment of the requirements for the degree of

MASTER OF ARTS IN DEVELOPMENT ECONOMICS

DECLARATION

“I certify that this material is my own work, containing my independent research results, have not been published I assure that all sources of information in the thesis, including data sets, are clearly acknowledged

I pledge to take responsibility for my research.”

Signature

Ta Thi Hong Ngoc Date: December, 2017

ACKNOWLEDGEMENT

Firstly, I would like to express my appreciation to my supervisor Dr Tu Van Binh who provided me motivation, patience, and knowledge to complete my thesis I am very grateful for his sympathy and his kind encouragement to me last year when my mother was deeply sick His friendly guidance in all the time of research helped me overcome a hard time

of writing this thesis

Besides my supervisor, I am grateful to Dr Truong Dang Thuy and Dr Pham Khanh Nam who have provided the theoretical background and econometrics methodology, which strongly supported my thesis

My sincere thanks to tutor Nguyen Van Dung who support me data and kindly encourage me during my thesis

I would thank all lecturers, administrators and my VNP 22 classmate in the Vietnam – The Netherlands Program for giving me a loyal sympathy, for the memorable moments we were working together before deadlines of assignments and exams during the course

Finally, I would like to give a special thanks to my family who has encouraged me not only in thesis period but also in my life

ABSTRACT

The study uses the Vietnam Household Living Standard Survey in the year of 2012 and 2014 in 13 provinces in the Mekong River Delta (MRD) to evaluate the impact of health insurance on out-of-pocket payments in the MRD Three models including Pool OLS, Random Effects and Fixed Effects are applied and the regression result shows that health insurance is statistically significant and has the negative relationship with out-of-pocket expenses per visit to outpatient service and inpatient service The study indicates that health insurance has a positive impact on reducing out-of-pocket expenses, meaning that people who have health insurance spend less than those who do not have health insurance Heath insurance benefits the society by reducing the monetary cost of using the health services and therefore is potentially advantageous for poor and underprivileged people in approaching healthcare resources The policy implication insists that it is essential to increase health insurance coverage, especially for the poor and near poor In addition, policy makers could consider reducing or eliminating co-payments for the poor and policy beneficiaries such as ethnic minorities in the MRD Moreover, the authority needs to concern about awareness raising in the health insurance of people living in this area

Key words: Health Insurance, Out-of-pocket expenses, Mekong River Delta

JEL Classification: I13.

2.3 Empirical studies about the impact of health insurance on out-of-pocket payments 8

3.3 Model specification 17

4.1.1 Background of health insurance in Vietnam and the MRD 21 4.1.2 Overview of out-of-pocket health expenditure in Vietnam 24

LIST OF TABLES

Table 3 1: Variable description and sources 18

Table 4 1: Descriptive statistics 26 Table 4 2: The correlation coefficient between the variables 27 Table 4 3: Number of observations and proportion of people having health insurance28 Table 4 4: Proportion of people having health insurance in 13 provinces in the MRD29 Table 4 5: Statistical coverage of health insurance by age 30 Table 4 6: Statistics on the share of health insurance participation by gender 30 Table 4 7: Statistics on the share of health insurance participation by marital status 31 Table 4 8: Statistics on health insurance participation by ethnics 31 Table 4 9: Statistics on health insurance coverage by level of education 32 Table 4 10: Statistics on health insurance coverage by rural, urban area 33 Table 4 11: The panel data regression result with Out-of-pocket expenses per visit to outpatient service (OOV) 34 Table 4 12: The panel data regression result with Out-of-pocket expenses per visit to inpatient service (OIV) 37

LIST OF FIGURES

Figure 1 Analytical framework 13

LIST OF ACRONYMS

OIV Out-of-pocket expenses per visit to inpatient service

OOV Out-of-pocket expenses per visit to outpatient

VHLSS Vietnam Household Living Standard Survey

CHAPTER 1: INTRODUCTION

1.1 The practical problem

Out-of-pocket expenses are popular in health care study According to WHO (2005), results of 108 surveys conducting in 86 countries showed that catastrophic expenses for health care services lead 5% of households into poverty To address the problem of reducing out-of-pocket payments due to illnesses, health insurance is expected as a good measure for its important role in health care and financial protection It facilitates insured people to approach health care services better and protects them from financial burdens resulting from health problems As people in the Mekong River Delta (MRD) do not have a long tradition of using health insurance, an interesting question is “to what extent does health insurance affect out-of-pocket expenses in this region?”

There are currently several problems with the health care system in Vietnam, where using health insurance is normally linked with a poor service In spite of the fact that there is

an improvement in the coverage of health insurance, it is reported that only 52% of annual outpatient contacts use health insurance and up to 40% of the insured people did not use health insurances when having health care treatments in 2006 (Nguyen, 2012) It is also the case of in the MRD Therefore, understanding the impact of health insurance on out-of-pocket payments can contribute some ideas to the government so that health insurance scheme may increase its effectiveness

1.2 The research problem

Within the context of Vietnam, there have been some researches on the impact of health insurance on out-of-pocket expenses Nevertheless, the effects of health insurance on out-of-pocket expenses are not homogeneous

Some studies confirm the positive effects of health insurance on reducing pocket expenses (Jowett et al., 2003, Wagstaff & Pradhan, 2005, Sepehri et al., 2006) However, Wagstaff (2010) and Nguyen (2012) found that voluntary health insurance does not have an impact on out-of-pocket expenditures Moreover, to the best of my knowledge, there has not been any studies on this issue in the context of the MRD

out-of-Therefore, this research may contribute to filling the literature gap in the context of the MRD, which is still considered a poor region in Vietnam Moreover, this study reexamines the impact of health insurance on out-of-pocket payments with updated data

1.3 Research Objectives

The study has the following objectives:

(i) to estimate the impacts of health insurance on out-of-pocket payments

(ii) to propose feasible policies to better manage health insurance program

This study employs the Vietnam Household Living Standard Survey (VHLSS) in the year of 2012 and 2014 are used in the research to approach the research objectives The data set covers 13 provinces/city (Long An, Tien Giang, Ben Tre, Tra Vinh, Vinh Long, Dongs Thap, An Giang, Kien Giang, Can Tho, Hau Giang, Soc Trang, Bac Lieu, Ca Mau) with approximately 7,000 observations/wave This thesis utilized Pool OLS, Fixed Effect, Random Effect regressions to test the impact of health insurance on out – of – pocket payments

1.4 Contribution of the Study

This study makes a major contribution in two aspects as follows First, there have been many empirical studies on the impact of health insurance on out-of-pocket expenses However, most of these studies mainly focus on the case of developed countries There are still few studies about this issue for developing countries where using health insurance is normally linked with a poor service In the case of the MRD, the rural area of Vietnam, there

is still no published studies on this topic Therefore, this paper contributes to the literature as one of the first comprehensive analysis of this issue in the Vietnamese case Second, the research results are an important and reliable source of information for policy makers to better manage the health insurance service in the MRD in particular and in Vietnam in general

1.5 Organization of the Study

The organization of the study is structured as follows

Chapter 1 introduce the practical problem, the research problem as well as research objectives

Chapter 2 gives a review of the definition, core concepts of health insurance and pocket payments In addition, theories and empirical studies are also presented

out-of-Chapter 3 presents the analytical framework, the research methodology, model specification and data

Chapter 4 gives a general review of background of health insurance in Vietnam and the MRD,

an overview of out-of-pocket health expenditure in Vietnam, the descriptive statistics of variables used in the study and the findings and discussion

Chapter 5 presents the conclusion, suggests some practical policy implications, and discusses the limitation and direction for further studies

CHAPTER 2: LITERATURE REVIEW

2.1 Core concepts

2.1.1 Health insurance

It is important to understand clearly the concept “health insurance” before going further with the study The concept of “health insurance” is popular in health economics

Health insurance is defined as “coverage that provides for the payments of benefits as a result

of sickness or injury It includes insurance for losses from accident, medical expense, disability, or accidental death and dismemberment” (Health Insurance Association of

America, 2010)

According to the Vietnamese Health Insurance Law No 25/2008/QH12, “Health

insurance is a form of services that is applied in the field of health care, not for profit purposes, organized by the State and those who are responsible for participating in provisions of law.” The health insurance fund is made up of contributions from the insured's

income, managed centrally and transparently, ensuring a balance between revenue and state protection Thus, although health insurance is a service, the activity must be based on risk-sharing, shared financial burdens on sickness and illness, and health insurance is not for the purpose of profit, but for the purpose of providing health care for people participating in the purchase of health insurance is regulated by the state Health insurance is also a form of undertaking socialization of the health sector as it helps to mobilize the contribution of the society When the budget for health is limited, the health insurance fund is also a way to share the medical burden for many patients, especially those with limited income and dependents Assistance between healthy people and the sick, between the young and the elderly, between the rich and the poor has contributed to the reduction of injustice

Under the Vietnamese Health Insurance Law No 25/2008/QH12, there are 25 groups including policy beneficiaries and target groups The law stipulates that workers with a contract of 3 months or more, indefinite labor, the staff at agencies, public service units, pensioners, etc belong to the group of buyers of compulsory health insurance Health insurance premiums will also be set for each beneficiary under which certain policy beneficiaries will be paid by third parties, while employees and employers pay premiums according to the income level of workers Voluntary health insurance applies to those who wish to volunteer to participate in health insurance, including those who have participated in compulsory health insurance but who wish to participate in voluntary health insurance in order to qualify for higher health insurance services This type of insurance is not for profit but only for the purpose of encouraging all people to participate in health insurance In the

context that Vietnam has not yet implemented the form of universal health insurance, in order

to avoid moral hazard and budget deficit, voluntary health insurance sets a number of rules to limit the status of people who have high risk buy new health insurance According to the Circular 06/2007/TTLT-BYT-BTC, the rules for the issuance of voluntary health insurance cards are as follows:

For household members, they will buy voluntary health insurance according to the place of their residence and must ensure that 100% of their members participate in each issuance, at least 10% in the area For students, voluntary school-based health insurance is compulsory for at least 10% of the participating students

Thus, the voluntary insurance scheme to expand the coverage of health insurance coverage and to implement this group of people requires deep and broad dissemination to help people understand the meaning of health insurance operation

2.1.2 Out-of-pocket payments

The concept of “out-of-pocket payments” is a widely used concept in health

economics It is defined as: “cost-sharing, self-medication and other expenditure paid

directly by private households, irrespective of whether the contact with the health care system was established on referral or on the patient’s own initiative” (OECD, 2003) According to

World Bank (2016), “out-of-pocket payments” is “any direct outlay by households, including

gratuities and in-kind payments, to health practitioners and suppliers of pharmaceuticals, therapeutic appliances, and other goods and services whose primary intent is to contribute to the restoration or enhancement of the health status of individuals or population groups It is a part of private health expenditure.” According to Hoang et al (2013), “out-of-pocket

payments” refer to “the payments made by households at the point they receive health

services Typically these include doctor’s consultation fees, purchases of medication and hospital bills Although spending on alternative and/or traditional medicine is included in out

of pocket payments, expenditure on health-related transportation and special nutrition are excluded Out-of-pocket payments are net of insurance reimbursement.”

2.2 Theoretical background

Assuming that health is a productive asset, creating health can be considered as an investment to compensate for the capital spent on age and lifestyle Creating health is an increase in “health capital” This investment is achieved through the use of medical treatments and personal efforts in preventing illness The benefit from health capital is the reduction of

time spent in a “sick” health state Over time, the increase in the utility towards health services is linked to the increase in income and consumption Therefore, the maximization of utility among rational individuals is in line with the optimal amount of money they invest in health services Grossman's study (1972) analyzes this optimization problem with optimal control theory

Consider an individual with a two-stage plan In each period, he or she has to spend a lot of time sick 𝑡𝑠, if the health capital is larger, this time less In other words, healthy times are the health benefits (non-exchangeable) of health capital The individual receives a positive level of enjoyment from consumer goods X and negative levels of utility from time of illness

𝑡𝑠 (𝐻) Such conditions create the independence of the utility function overtime, that is, the marginal rate between time and consumption is unchanged The utility then is discounted by

an element, β≤1, in the future As a result, this individual maximizes the discounted µ

The constraint is set in this equation for the optimal utility of individuals This equation shows that individuals’ health, wealth, and knowledge varies across time The

savings of individual in the first stage will be used in the second stage The interest rate is R =

1 + r The equation indicates that individuals just invest in health services at the first stage

As for health insurance, the individual property and income are considered as a source

for healthcare expenditures p is the price of healthcare services, and 𝑤0 is the salary in the

first stage In this case, both the first and the second stage must have positive consumption, and the sum of time is 1 Establish those things together, we have the budget constraints after the discount as follows:

Taking the derivative with the variables μ and λ is to ensure that the constraints in the above equations occur, we do not present them here Considering 𝐻0 is a given constant value, we have:

𝜕𝑈/𝜕𝑋0

𝜕𝑈/𝜕𝑋 1 = 𝛽𝑅 (2.11) Solve the equation (2.9), find 𝜆

𝑅 then substituting into equation (2.5) we obtain:

Substitute μ in equation (2.13) into equation (2.12) we have

Under the above condition, there is the equality between the marginal utility and the marginal cost for healthcare services

The effectiveness of the investment is measured through prerequisites The reduction

in the illness time of an individual will result in the positive investment The combination of both the negative derivative of 𝜕𝑡

𝑠

𝜕𝐻 1 and the positive value of the function causes the left side of condition (2.14) to be positive, for example, the margin of positive right-hand margin

Consider health as consumer goods The decrease in the duration of sickness (as well

as the increased health benefit) increases the utility directly because 𝜕𝑈

𝜕𝑡 𝑠 <0 If discounted, the benefit from the utility level is 𝛽 𝜕

𝜕𝑡 𝑠 If condition (14) is only the first factor in the investment and well-being state’s marginal utility, the consumption model is pure

When health investment is considered as investing in a certain item, the decrease in sickness has an immediate impact on an individual's well-being through −𝛽 𝜕𝑡𝑠

𝜕𝐻 1 and real wage

𝑤1

𝑐 This value depends on 𝜕𝑈

𝜕𝑋 1 (marginal margin of consumption of an additional commodity)

So, even if the sickness time is not denied because of the discomfort itself, health investment brings benefits to the increase in labor income and individual wealth In this situation when health is considered as goods, its assessment should be examined together with its influence

on wealth The condition (2.14) is an individual’s pure investment

The marginal cost of an additional health investment is on the right-hand side of the equation (2.14)

Marginal utility level 𝜕𝑈

𝜕𝑋 0 represents what is lost from skipping a part of consumption

beneficiary when p is at a high rate Similarly, the level of utility actually lost from abandoning a particular consumption needs to be adjusted by the consumer price because if 𝑐

is high, only a few units of 𝑋0 are abandoned

To sum up, the Grossman model shows the interrelation between healthcare investment and the health status of individuals The value is adjusted to reach the optimal level across time for each individual The increase in consumption and investment is explained by the increase in the marginal utility of an additional health unit The total marginal utility has to be the same as the marginal cost of health investment

2.3 Empirical studies about the impact of health insurance on out-of-pocket payments 2.3.1 Out-of-pocket payments definition and measurements

Out-of-pocket payments have been used as the main variable in a number of studies by many researchers around the world Based on such a huge amount of research, a variety of definitions and measurements for this variable is drawn In the study with the sample of three provinces in Vietnam in 1999, Jowett et al (2003) suggest that this variable can be measured

by adding up both official and unofficial payments to achieve the total expenditure on healthcare Sephri et al (2006) did not mention official or unofficial payments but just consider out-of-pocket payments as the household expenditure on health during the past 12 months Ekman (2007) has a quite different point of view that the difference between the income of a patient and the expense of the household on heath is the out-of-pocket payments Fan et al (2012) divide healthcare services into two elements, inpatient and outpatient services Each element is also the combination of different indicators at the household level Out-of-pocket payments are the sum of these two elements This variable is adjusted to the monthly scale and is divided by the household size to have the spending per capita Using the Indonesia’s Family Life Survey in four years, Aji et al (2013) show that out-of-pocket payments include all medical costs such as hospitalization, clinic, physicians, traditional cures, and medicines except transportation costs due to the unavailability of the data The effects of inflation on household expenditures on health are eliminated by instilling the Consumer Price Index (CPI) in 2007 Similar to Fan et al (2012), the adjustment of the variable based on the household size is added to get payments per capita Van Minh et al (2013) also hold that payments on health services should take into account consultation, medication, hospitalization, and medicine costs but not costs related to transportation and nutrition

2.3.2 Estimation method

A wide range of methods has been used by different authors to test the relationship between out-of-pocket payments and a certain factor To estimate the effects of health insurance on health expenditures, Jowett et al (2003) use Ordinary Least Squares (OLS) for the regression models However, this method is limited due to the assumption that there is no relationship between health expenditures and unobservable factors Ekman (2007) also analyzes the impact of health insurance on health expenditures in Zambia, a low-income country, in 1998 only by multivariate regressions Compared with these two cross-sectional studies, Sepehri et al (2011) expand the study scope to the panel data of VHLSS 2004-2006 with the use of Fixed Effects (FE) and Random Effects (RE) for the insured and uninsured group With a variety of methods for panel data regression like Pooled Ordinary Least Squares (POLS) and Fixed Effects (FE) for models without endogeneity as well as Two-stage Least Squares (2SLS) for models with instrumental variables (IV), Aji et al (2013) discover a significantly negative relation between out-of-pocket payments and health insurance programs According to the paper, household participation in the communal gatherings, women’s groups, and co-operation are considered as the three instrumental variables in the research

Besides, some other studies provide researchers with different kinds of regression methods Sepehri et al (2006) apply Tobit and truncated regression models to interpret the relationship between health insurance and health expenditures In these two models, Fixed Effects and Random Effects for the panel data of VLSS are included in the regression Van Minh et al (2013) approach the research with the logistic model to examine whether the catastrophe and poverty will decide the probability of having an out-of-pocket expenditure of

a household

Other methods commonly used by several researchers is Propensity Score Matching (PSM) and Difference-in-Difference (DID) While Wagstaff and Pradhan (2005) just apply double difference for their research, Wagstaff (2010) later extend this method, ranging from single difference, double difference, and triple difference, together with the matching method Nguyen (2012) combines OLS, IV, PSM, and DID in his research to measure the impact of voluntary insurance on health expenditures for VHLSS 2004 – 2006 Fan et al (2012) also use DID analysis for their study in Southern India with the clear division of data into the treated and control group Recently, the paper of Alkenbrack and Lindelow (2015) employs propensity score matching for 3000 households in Laos and then double treatment effects to examine the influence of out-of-pocket payments

2.3.3 Control variables

A great number of control variables have been defined and listed in some studies related to out-of-pocket expenditures In general, control variables are composed of two types, demographic and attitude variables

Demographic variables include the characteristics of the household head (gender, age, education, marital status, occupation, ethnicity, health status), the characteristics of the household (size, income, expenditure, distance to healthcare providers, location, the elderly, children), and the feature of healthcare services (insurance types, health facilities, outpatient visits, outpatient contacts) (Jowett et al, 2003; Sepehri et al, 2006; Ekman, 2007; Sepehri et al, 2011; Fan et al, 2012; Nguyen, 2012; Aji et al, 2013; Van Minh et al, 2013)

Attitude variables are mention recently in the research of Alkenbrack and Lindelow (2015) In this paper, aside from the demographic variables presented in the previous papers, they take into account risk preferences of the household head and attitudes of households toward insurance

2.3.4 Results

The results on the impacts of health insurance on out-of-pocket payments show a distinct polarization, making this relationship interesting for researchers across the globe to pay their attention to Health insurance may have no, positive, or negative effects on out-of-pocket payments

King et al (2009) indicate the insignificant impact of health insurance on healthcare service expenditures for the case of households in Mexico However, he says that this insignificance may be due to the fact that the health insurance program is only distributed to the poor and it lasts just for a short period of ten months Nguyen (2012) points out the similar finding that the voluntary health insurance has no impact on out-of-pocket expenditures His explanation is that health insurance only pays for the costs of healthcare and drugs, while he defines this variable as the total of treatment and other related treatment costs Another problem may be due to measurement errors in measuring out-of-pocket expenditures for the research data

Ekman (2007) researches households in Zambia and shows that health insurance has

no role to play in the protection of household members from the catastrophe He finds that this influence of health insurance is mainly guided by the quality and the provision of the insurance The research suggests that the higher income a household has, the lower risks of disasters it incurs, and the further a house is, compared to the healthcare service providers, the

higher spending on catastrophe a household suffers In addition, those who are employed or are farmers confront smaller risks of disasters than other groups

On the contrary, Fan et al (2012) found the negative relationship between health insurance and out-of-pocket payments The research shows that during the first nine months after the introduction of health insurance, both inpatient and outpatient expenses reduce at the state of Andhra Pradesh in Southern India This result is proved to be robust after the use of quantile regression and the matching method Aji et al (2013) give the same results when doing research in Indonesia They suggest that the two largest health insurance programs are the main cause leading to the decrease in households’ out-of-pocket payments Van Minh et

al (2013) identifying the determinants of health spending on catastrophe show that the enrollment of households in health insurance helps them lower the expenditures on catastrophe and impoverishment Alkenbrack and Lindelow (2015) say that those who are insured have more opportunities to lower their out-of-pocket payments and disaster rates than those who are not They show a surprising result that the health insurance program protects the rich better than the poor since the poor are unlikely to pay out-of-pocket costs

The context of Vietnam rises some highlighted studies on the impacts of health insurance on out-of-pocket payments Jowett et al (2003) indicate that both voluntary health and student insurance make out-of-pocket payments decrease Especially, health insurance helps reduce out-of-pocket payments for Vietnamese households up to 200% This effect is clearly observed through the expenditures of the poor rather than the rich Using the VLSS in

1993 and 1998, Wagstaff and Pradhan (2005) find that health insurance is positively linked to the adoption of healthcare services and is the reason for the increase in the households’ visits

to hospitals Finally, their study holds that health insurance is proved to cause out-of-pocket expenditures to fall In the further study, Wagstaff (2010) discovers that although Vietnam’s Health Care Fund for the poor truly does not have any effect on the use of healthcare services,

it has, in effect, reduced out-of-pocket expenditures Sepehri et al (2006), like Wagstaff and Pradhan (2005), use the panel data of VLSS in 1993 and 1998 to measure the effects of health insurance They then come to the same conclusion that health insurance decreases out-of-pocket payments after controlling unobserved heterogeneity They show that health insurance lowers out-of-pocket expenditures from 16% to 18% and that the decrease in expenditure is larger for the high than the low-income households Later research of Sepehri et al (2011) again supports the decrease in out-of-pocket expenditures by 24% if patients have either compulsory or voluntary health insurance As for the poor, the use of health insurance helps them reduce their out-of-pocket payments by approximately 15% The study proves that if

patients visit healthcare centers at the district or higher level instead of the communal level, they can lower their expenditures on health services Both the compulsory and voluntary health insurance have no effects at the commune health facilitates In addition, compared with those who are uninsured, those who are insured can decrease their out-of-pocket payments by 32% to 40%

CHAPTER 3: RESEARCH METHODOLOGY

AND DATA

3.1 Analytical framework

Based on empirical studies on the impacts of health insurance on out-of-pocket payments mentioned above, the analytical framework analyzes the factors that affect out-of-pocket payments for this study include three groups of factors: (i) Socio-Economic and Demographic Characteristics, (ii) Health insurance participation and medical service usage, and (iii) Living Environment characteristics

Figure 1 Analytical framework

Health insurance Inpatient

Outpatient

Out-of-pocket expenses per visit

Living Environment characteristics

Urban area Rural area

3.2.1 Fixed Effects Estimation

In the fixed effects estimation, the unobserved effects 𝛼𝑖 is eliminated by using the transformation So do the time constant explanatory variables together with 𝛼𝑖

The transformation of the function by using the first difference is one of the methods that help to put away the fixed effects (Woolridge, 2003) Another effective way is the transformation of fixed effects The method can be explained through the consideration of these below functions

For each 𝑖,

𝑦𝑖𝑡 = 𝛽1𝑥𝑖𝑡+ 𝛼𝑖 + 𝜇𝑖𝑡, 𝑡 = 1,2, … 𝑇 (3.1) Now, for each 𝑖, average this equation over time We get

𝑦̅𝑖 = 𝛽1𝑥̅𝑖 + 𝛼𝑖 + 𝜇̅𝑖, (3.2) Where 𝑦̅𝑖 = 𝑇−1∑𝑇𝑡=1𝑦𝑖𝑡 , and so on 𝛼𝑖 is unchanged over time; therefore, it is the same in these two above functions Then, the two are subjected from each other to gain this following function

𝑦𝑖𝑡− 𝑦̅𝑖 = 𝛽1(𝑥𝑖𝑡− 𝑥̅𝑖) + 𝜇𝑖𝑡− 𝜇̅𝑖, 𝑡 = 1,2, … 𝑇,

Or

𝑦̈𝑖𝑡 = 𝛽1𝑥̈𝑖𝑡+ 𝜇̈𝑖𝑡, 𝑡 = 1,2, … 𝑇, (3.3) Where 𝑦̈𝑖𝑡 = 𝑦𝑖𝑡 − 𝑦̅𝑖 is the difference between the real value and the average value of the dependent variable It is similar to the case of 𝑥̈𝑖𝑡, the independent variables, and 𝜇̈𝑖𝑡, the error terms Besides the name of fixed effects transformation, this method is also named the within transformation In the equation (3.3), the unobserved effects 𝛼𝑖 is removed, proposing the use of Pooled OLS estimation for this equation When Pooled OLS estimation is used under this transformation, this estimator has the name of fixed effects or within estimator According to this estimator, y and x variate in time within cross-sectional observations

After the addition of explanatory variables to the equation (3.3), we gain the model for unobserved effects at first

𝑦𝑖𝑡 = 𝛽1𝑥𝑖𝑡1+ 𝛽2𝑥𝑖𝑡2+ ⋯ + 𝛽𝑘𝑥𝑖𝑡𝑘+ 𝛼𝑖 + 𝜇𝑖𝑡, 𝑡 = 1,2, … 𝑇 (3.4) Then, the application of the fixed effects method with time dummies and Pooled OLS estimation as what is explained in advance is included to get the general equation demeaning

in time for each 𝑖

𝑦̈𝑖𝑡 = 𝛽1𝑥̈𝑖𝑡1+ 𝛽2𝑥̈𝑖𝑡2+ 𝛽𝑘𝑥̈𝑖𝑡𝑘+ 𝜇̈𝑖𝑡, 𝑡 = 1,2, … 𝑇 (3.5) This equation is estimated with Pooled OLS regression

The fixed effects method will be biased if the strict assumption of the exogenous problem is broken The assumption is that the error term 𝜇𝑖𝑡 is not allowed to correlate with

independent variables across time, but the cross sectional difference can have the correlation with the explanatory variables The transformation helps eliminate any explanatory variable unchanged through time: 𝑥̈𝑖𝑡 = 0 for all 𝑖 and 𝑡, if 𝑥𝑖𝑡 is constant across 𝑡

The degrees of freedom for this estimation is easy to incorrectly identify In the equation (3.5) calculated through Pooled OLS, NT is the total observations and k is the number of independent variables Therefore, the degrees of freedom can be inferred by taking subjection of k from NT However, this calculation creates a misleading result because, through each cross-sectional observation, the degrees of freedom will reduce by one due to the demeaning of time In short, the true degrees of freedom should be 𝑑𝑓 = 𝑁𝑇 − 𝑁 − 𝑘 =𝑁(𝑇 − 1) − 𝑘 Fortunately, the regression in the fixed effects package of statistics software compute the degrees of freedom correctly However, there is still work to be done, that is, the correction of the standard errors and the statistical tests after the estimation of Pooled OLS

3.2.2 Fixed Effects with Unbalanced Panels

When the data have missing values for individuals across years, the data set is called unbalanced panel data Different kinds of panels will have different estimations Compared with balanced panel data, the method of fixed effects estimation for unbalanced panel data is far more difficult In the equation, 𝑇𝑖 is denoted as the number of time periods for each individual 𝑖 Based on this, 𝑇1+ 𝑇2+ ⋯ + 𝑇𝑁 is considered as the total number of observations As mentioned above, in the balanced panel data, the demeaning of time reduces the degrees of freedom by one for each cross sectional individual The package for this regression method always shows the result of the degrees of freedom at the end of the regression to adjust the degrees of freedom The degrees of freedom are similarly calculated

as for the case of dummy variable regression

When the observed individual has only a single time period, it has no effect on the fixed effects estimation Such kind of individual has zero time demeaning and is not included

in the estimation What is considered difficult here is how to determine the panel data is unbalanced If the independent variables in the unbalanced panel data with missing value have

no correlation with the error terms 𝜇𝑖𝑡, the unbalanced panel does not matter at all

3.2.3 Random Effects Models

Similar to fixed effects method, the random effects method starts with the unobserved effects equation,

𝑦𝑖𝑡= 𝛽0+ 𝛽1𝑥𝑖𝑡1+ ⋯ + 𝛽𝑘𝑥𝑖𝑡𝑘+ 𝛼𝑖+ 𝜇𝑖𝑡 (3.7)

The constant is added to the equation, the unobserved effect 𝛼𝑖 is assumed to have zero mean, and the dummies of time is included in the explanatory variables The use of fixed effects requires the unobserved effects 𝛼𝑖 to be removed from the equation because of its correlation with the independent variables 𝑥𝑖𝑡𝑗 However, if the unobserved effect is not correlated with the explanatory variable across time, the elimination of this effect will cause inefficient estimation

The situation that the unobserved effect has no correlation with the independent variables turns the equation (3.7) into a random effects model

𝐶𝑜𝑣(𝑥𝑖𝑡𝑗, 𝛼𝑖) = 0, 𝑡 = 1,2, … 𝑇; 𝑗 = 1,2, … , 𝑘 (3.8) The assumptions in the random effects model combine the assumptions of fixed effects model and the assumptions that the unobserved variables are not correlated with the independent variables If the latter assumption is true, the single cross section is enough to estimate the coefficient of independent variables 𝛽𝑗, and the panel data should not be employed Nevertheless, the method of a single cross section cannot be used because of its lack of essential information over time If it truly happens, the use Pooled OLS with time dummies is enough to get the consistent coefficients for the random effects model The equation (3.7) can be rewritten when error terms are decomposed by 𝛼𝑖 and 𝜇𝑖𝑡; 𝑣𝑖𝑡 = 𝛼𝑖 +

𝜇𝑖𝑡

𝑦𝑖𝑡 = 𝛽0+ 𝛽1𝑥𝑖𝑡1+ ⋯ 𝛽𝑘𝑥𝑖𝑡𝑘+ 𝑣𝑖𝑡 (3.9)

In this function, the error term 𝛼𝑖 is defined for the time period; therefore, the total error terms will be serially correlated over time Based on the random effects model, covariance is computed

3.2.4 Random Effects or Fixed Effects

Fixed effects estimation is considered to be better than random effects estimation because it takes the correlation between the differences between 𝑥𝑖𝑡𝑗 and 𝛼𝑖 into consideration On the other hand, in certain situation, random effects estimation is still used