Master’s Thesis
The determinants of health care utilisation
Stijn Louca
Student number: 10789499
Date of final version: December 20, 2018
Master’s programme: Econometrics
Specialisation: Econometrics
Supervisor: dr. J. C. M. van Ophem
Second reader: dr. E. Aristodemou
Faculty of Economics and Business
Abstract
In this thesis the determinants of health care utilisation, measured in terms of physician visits, are studied based on data provided by the Medical Expenditure Panel Survey. In particular, the EPET-Poisson model is used to take account of both the possible endogeneity in choice of health insurance coverage and endogenous participation. Demographics and health related characteristics appear to be more important in determining health care use than socioeconomic characteristics. However, estimates based on di↵erent population groups show some di↵erences.
i Statement of Originality
This document is written by Student Stijn Louca who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Contents
1 Introduction 1
2 Literature Review 3
3 Model and method 5
4 Data 8 5 Results 11 6 Conclusion 20 A 21 Bibliography 23 ii
Chapter 1
Introduction
Health care expenditures have increased in the United States (U.S.) by staggering amounts over the past decades. In fact, health care expenditures totalled approximately 74.6 billion dollars in 1970. In 2016 that amount increased to 3300 billion dollars, i.e on a per capita basis, health care expenditures increased from 355 dollars per person in 1970 to 10348 dollars in 2016 (Kamal and Cox, 2017). The average amount spent on health care per person in comparable countries totalled approximatly 5198 dollars in 2016, which is almost half that of the U.S. (Kamal and Cox, 2018). Two important factors in the development of health care expenditures are health care prices paid to providers or for drugs and the volume of health care services used (i.e. demand for health care). In essence, total health spending is the product of these two factors. The increase in health care prices can partly explain the high level of health care expenditures (Claxton et al., 2018) and compared to other coutries the U.S. has higher prices for most health care services (Kamal and Cox, 2018). In constrast, health care use of several services, including physician consultations and hospital stays, is lower compared to similar countries, whereas the amount of surgeries are typically higher Kamal and Cox (2017). To obtain a better assessment of the two forces that have caused the increase in health care expenditures, it is essential to understand their underlying processes. The aim of this thesis is to gain an insight into the determinants of health care utilisation.
Some features of the process underlying health care utilisation have to be addressed. Health insurance coverage may be an important factor in determining health care service use. However, in the U.S. health insurance coverage is a choice for many people and therefore possibly endogenous with respect to health care utilisation. The cause of this endogeneity could be adverse selection, which arises when there is asymmetric information in the market place (Rothschild and Stiglitz, 1976). To illustrate, people with greater need for health care may have more incentives to purchase health insurance coverage. In addition, moral hazard may also cause endogeneity issues. Because people with health insurance coverage may use health care services more than their uninsured counterparts (Arrow, 1963). In other words, individuals may have unobserved behavioural idiosyncrasies that a↵ect both the choice of health insurance coverage and health care utilisation, such as the propensity to seek health care. Not taking account of
CHAPTER 1. INTRODUCTION 2 this issue can result in biased estimates. Another feature concerns the two-part character of the decision making process of health care utilisation. For example, an individual has an own choice to visit the physician (i.e. contact decision), whereas the intensity of the treatment is determined in consultation with the physician (i.e frequency decision) (Pohlmeier and Ulrich, 1995). Therefore, health care utilisation may be generated by two distinct processes. However, it is unrealistic to assume that the decision to visit the physician and the subsequent amount of treatment are uncorrelated. A person may only visit the physician if he or she is ill and the intensity of the treatment may depend on the severity of the illness. Moreover, people with a high propensity to seek healthcare are perhaps more likely to visit the physician and to visit a high number of times. This induces another endogeneity issue, which is potentially caused by the same unobserved behavioural idiosyncrasie that a↵ects the health insurance coverage decision. The last feature concerns the character of the dependent variable. In this thesis health care utilisation is measured as the number of visits to the physician. Undoubtedly, this variable is a discrete nonnegative dependent variable. For example, some people may have visited the physician zero times during a year, whereas others had single or multiple visits. Hence, application of a count data model would be appropriate.
In this thesis the endogenous participation endogenous treatment (EPET) - Poisson model, proposed by Bratti and Miranda (2011), is used, which incorporates all aforementioned aspects. In general, this model allows for an endogenous binary treatment (e.g. health insurance coverage) that a↵ects a count outcome among other covariates in the presence of endogenous participation (e.g. correlation between contact and frequency decision). Not only does application of this model give an insight into the process of health care utilisation but also in the choice of health insurance coverage. Estimates are based on data of the Medical Expenditure Panel Survey (MEPS) of 2016. The remainder of this thesis is as follows. Chapter 2 gives an overview of some econometric literature on health care utilisation and an overview of some previous findings. Chapter 3 explains the EPET - Poisson model and discusses the estimation method. Chapter 4 describes the data. Chapter 5 reports the estimation results, together with the results of several robustness checks. Chapter 6 concludes with a brief discussion of the results and suggestions for future research.
Chapter 2
Literature Review
Empirical studies on health care utilisation are well-established in the econometric literature. What follows is a discussion of some of these papers and an overview of their findings.
Cameron et al. (1988) models the demand of several health care services, including the number of consultations with a doctor or specialists, using a cross-sectional data set from the Australian Health Survey. They apply the negative binomial model to allow for unobserved heterogeneity. The Maximum likelihood (ML) method is used for estimation. Furthermore, they acknowledge the possible endogeneity in choice of health insurance coverage. Therefore, they also consider a linear version of the model, thus ignoring the discrete nature of the dependent variable, such that instrumental variables can be applied. Pohlmeier and Ulrich (1995) estimate a model of the two-part decisionmaking process concerning general practitioners and specialists visits. Their estimates are based on data from the German Socioeconomic Panel. They use a negative binomial hurdle model to distinguish between the contact and frequency decision and apply the ML method for estimation. Windmeijer and Santos Silva (1997) estimate a model for the number of visits to doctors based on data from the British Health and Lifestyle Survey, with as a possible endogenous regressor a self-reported binary health index. They propose a generalised method of moments strategy, that only requires the specification of the conditional mean of the dependent variable, to correct for endogenous regressors. Riphahn et al. (2002) estimate a model for the number of physician and hospital visits based on panel data from the German Socioeconomic Panel. They use a bivariate lognormal Poisson distribution to allow for possible correlation between physician and hospital visits. Furthermore, they numerically calculate the likelihood function and apply the ML method to estimate the model. Shen (2013) studies the whole process of health insurance choice, health care utilisation and health care expenditures for the obese population using data from the MEPS. The model takes care of the endogeneity in health insurance coverage and of the two-part decisionmaking process. The model is estimated by both a parametric and semi-parametric approach.
The approach used in this thesis di↵ers from the other papers in the joint analysis of endogenous treatment and endogenous participation by applying the EPET-Poisson model, proposed by Bratti and Miranda (2011). In particular, a hurdle specification is used to model
CHAPTER 2. LITERATURE REVIEW 4 physician visits with as a possible endogenous regressor a binary health insurance coverage variable. In addition, the model allows for a correlation between the contact and frequency decision. Furthermore, maximum simulated likelihood is used to estimate the model, since this method is appropriate to deal with endogenous treatment and endogenous participation. Bratti and Miranda (2011) use the EPET-Poisson model to investigate the e↵ect of physician advice on the amount of alcohol consumption, where both the likelihood of receiving physician advice and of drinking alcohol are determined by a common unobservable variable.
Commonly, micro-level information on demographics, socioeconomic status and health related characteristics are used to examine health care utilisation. Regarding demographics, most studies find that age has a quadratic e↵ect on health care use, however Shen (2013) finds that age has no e↵ect after the insurance decision is made. Furthermore, all the studies find that males are less likely to use health care than females. In addition, Pohlmeier and Ulrich (1995) find that this result only holds for the contact decision. As soon as contact is made gender appears to have no e↵ect on the frequency decision. Di↵erent results are found for the e↵ect of marital status. Windmeijer and Santos Silva (1997) and Riphahn et al. (2002) find no significant e↵ect, Cameron et al. (1988) did not include this variable in their model and Pohlmeier and Ulrich (1995) find that this e↵ect only holds for the contact decision. Socioeconomic characteristics are generally less important in determining health care use. In fact, Shen (2013) shows that income has no e↵ect at all, Riphahn et al. (2002) only finds a significant e↵ect for female hospital visits, Pohlmeier and Ulrich (1995) only find a significant e↵ect of a high income for the contact decision and no e↵ect for the frequency decision, Windmeijer and Santos Silva (1997) find a slightly non-linear e↵ect of income and Cameron et al. (1988) shows that income is quite unresponsive to utilisation of most health care services, besides consultations with non-doctor health specialists and prescribed medicines. Di↵erent results are found for the e↵ect of education. Shen (2013) finds that years of schooling has a positive e↵ect on health care utilisation, whereas Riphahn et al. (2002) finds a negative e↵ect of years of schooling for males and no e↵ect at all for females. Pohlmeier and Ulrich (1995) finds a negative e↵ect of education only for the contact decision and Cameron et al. (1988) did not include education in their model. Furthermore, all studies find a substantial positive e↵ect for health related characteristics.
Chapter 3
Model and method
The EPET - Poisson model, proposed by Bratti and Miranda (2011), allows for endogenous participation and endogenous treatment at the same time. In particular the model consists of three interrelated parts. The first part deals with the potential endogenous treatment. In the context of this paper the treatment indicates whether the respondent has a health insurance coverage. Let Ti denote individual’s i health insurance status, with Ti= 0 if he or she does not
have health insurance coverage and Ti = 1 if he or she does have coverage. A health insurance
coverage is chosen if Ti⇤ is greater than zero. Where Ti⇤ is an unobserved continuous latent variable. Hence, the model of health insurance coverage is as follows
Ti = I{Ti⇤> 0}, where Ti⇤= z|i + vi (3.1)
with I{·} a binary indicator function, zi a KT ⇥ 1 vector of explanatory variables, a Kz⇥ 1
vector of coefficients and vi an error term. The second part explains the participation desicion
(i.e. contact decision). Let Pidenote individual’s i participation status, with Pi = 0 if he or she
has not visited the physician in the past year and Pi= 1 if he or she has visited the physician.
Therefore, participants are defined as those who have made a visit to the physician at least one time in the past year. As with the health insurance equation, the contact desicion is generated according to a continuous latent variable model
Pi= I{Pi⇤ > 0}, where Pi⇤ = r|i✓ + Ti+ qi (3.2)
with ri a KP ⇥ 1 vector of explanatory variables, ✓ a KP ⇥ 1 vector of coefficients, Ti the
endogenous treatment e↵ect and qi an error term. The third part of the model describes the
outcome, thus the number of visits to the physician (i.e frequency desicion). Let yi denote the
number of visits to the physician. Moreover, it assumed that yi is generated according to the
following distribution function
f (yi|µi) = 8 > < > : — if Pi= 0 µyii exp( µi) 1 exp( µi) yi! if Pi= 1 (3.3) 5
CHAPTER 3. MODEL AND METHOD 6 with yi = 8 < : 0 if Pi = 0 1, 2, 3, . . . if Pi = 1. (3.4) and where µi is the intensity rate of yi. Hence, yi follows a zero-truncated Poisson distribution
if Pi = 1 and is equal to zero if Pi = 0. A log-linear specification is used to model the intensity
rate
log(µi) = x|i + Ti+ ⌘i, (3.5)
with xia Ky⇥1 vector of explanatory variables, a Ky⇥1 vector of coefficients, the coefficient
on the endogenous treatment e↵ect and ⌘iis unobserved heterogeneity that captures behavioural
idiosyncracies.
Interrelation among the aforementioned equations is possible through the error terms of equations (3.1) and (3.2) as follows
vi= 1⌘i+ ✏1i
qi= 2⌘i+ ✏2i
(3.6) with 1 and 2 free factor loadings, which are estimated among the other parameters, and
✏1i and ✏2i are error terms. Hence, the endogeneity of both treatment and participation are
determined by a common unobservable variable. Furthermore, it is assumed that ⌘i⇠ N (0, ⌘)
and that both ✏1iand ✏2iare distributed according to a standard normal distribution. Therefore,
unoberserved heterogeneity is assumed to behave in a systematic way and the assumptions made on ✏1iand ✏2iimply that both Ti and Piare probit models. If ⌘ = 0 then there is no unobserved
heterogeneity.
The EPET-Poisson model implies the following correlations between the error terms
⇢⌘,v= 1 2 ⌘ q 2 ⌘( 21 2⌘+ 1) ⇢⌘,q= 2 ⌘2 q 2 ⌘( 22 ⌘2+ 1) ⇢v,q= 1 2 ⌘2 q ( 21 2 ⌘+ 1)( 22 ⌘2+ 1) (3.7)
The treatment e↵ect Ti is exogenous with respect to Pi and yi if ⇢v,q = 0 and ⇢⌘,v = 0,
respectively. Similarly, participation Pi is exogenous with respect to yi if ⇢⌘,q= 0.
LetPPi(0|⌘i) denote the conditional probability of Pi= 0 given ⌘iandPPi(1|⌘) the conditional
probability of Pi = 1 given ⌘i. Similarly,PT(⌧i|⌘i) is the conditional probability of Ti = ⌧i given
⌘i, with ⌧i = {0, 1}. In fact, these probabilities follow from the probit model specification,
hence PPi(0|⌘i) = ( (r | i✓ + Ti+ 2⌘i)) PTi(0|⌘i) = ( (z | i + 1⌘i)) PPi(1|⌘i) = (r | i✓ + Ti+ 2⌘i) PTi(1|⌘i) = (z | i + 1⌘i) (3.8)
CHAPTER 3. MODEL AND METHOD 7 with (·) the cumulative distribution function of a standard normal distribution. Subsequently, the log-likelihood function can be written as follows
log(L(⌦)) = X P =0 X ⌧ !⌧log ⇣ Z +1 1 PP (0|⌘)PT(⌧|⌘)'(⌘)d⌘ ⌘ +X P =1 X ⌧ !⌧log ⇣ Z +1 1 PP (1|⌘)PT(⌧|⌘)f(y|⌘)'(⌘)d⌘ ⌘ (3.9)
with ⌦ a vector containing the parameters to be estimated, !0 = I(T = 0) and !1 = I(T = 1)
and '(·) is the density of a normal distribution with zero mean and variance 2⌘. To simplify notation, the subscript i is omitted in the log-likelihood function.
Analytical solutions of the integrals are difficult if not impossible to find and hence straightforward estimation of the parameters by means of maximum likelihood is not possible. One way to solve this issue is to use maximum simulated likelihood (MSL). In general, the MSL estimator maximizes the log-likelihood function based on a simulated estimate of the density. More accurate, the integrands in equation (3.9) can be considered as functions of ⌘, say
h⌧(⌘) =PP(0|⌘)PT(⌧|⌘)
g⌧(⌘) =PP(1|⌘)PT(⌧|⌘)f(y|⌘)
(3.10)
and the integrals as expected values of these functions, thus E(h⌧(⌘)) = Z 1 1 h⌧(⌘)'(⌘)d⌘ E(g⌧(⌘)) = Z 1 1 g⌧(⌘)'(⌘)d⌘ (3.11)
Therefore, it is possible to estimate the integrals by taking the average of a sample based on draws from the density of ⌘. However, drawing pseudo-random numbers directly from the density of ⌘ is not possible, since ⌘ is unknown. Therefore, draws are from a standard normal
distribution and ⌘ is estimated among the parameters. Hence, the log-likelihood function to
be maximized with respect to the parameters is log( ˆL(⌦)) = X P =0 X ⌧ !⌧log⇣ 1 S X s PP(0|zs)PT(⌧|zs) ⌘ +X P =1 X ⌧ !⌧log⇣ 1 S X s PP(1|zs)PT(⌧|zs)f (y|zs) ⌘ (3.12)
where zs, s = 1, 2, ..., S are S pseudo-random number draws from the standard normal distribution.
For a more thorough discussion on MSL see for example (Cameron and Trivedi, 2005). Furthermore, the log-likelihood function in equation (3.12) is numerically maximised1 by using the BHHH method, proposed by Berndt et al. (1974). The gradient and hessian of the log-likelihood function are calculated numerically.
1All estimates are calculated with R (free software environment for statistical computing). In particular, the
Chapter 4
Data
The data used in this thesis is taken from the Medical Expenditure Panel Survey (MEPS). Since 1996 the MEPS is a repeated cross-section on a yearly base. Information of health care use, expenditures, sources of payments and health insurance coverage, among demographic and socioeconomic characteristics for the U.S. civilian noninstitutionalized population are provided. This thesis uses a cross-sectional data set of 2016. The sample is restricted to individuals aged 23 through 64 year. Following (Shen, 2013), individuals who are unemployed are excluded from the data set, because private health insurance is typically related to employment in the U.S. Furthermore, individuals with public health insurance are not included in the sample, because public health insurance is most likely not a choice for working adults. After exclusion of missing values of the other variables, the final sample consists of 8273 observations.
Health care utilisation is examined in terms of the number of visits to the physician in the past year and a binary index variable indicates the private health insurance coverage status of an individual. Other explanatory variables are categorised in demographics, socioeconomic status and health related characteristics. Age, gender, race, ethnicity, marital status, family size and region are included among demographics. The age variable is measured in whole years. The binary gender variable indicates whether the respondent is a male or a female, where a one represents a male. Furthermore, race categories in the U.S. are defined as white, black or African American, American Indian or Alaska native, Asian, Native Hawaiian or other Pacific Islander and multiple races. However, the majority of the U.S. population is either white and black or African American, therefore all the race categories besides white and black or African American are grouped together and considered as other races. Ethnicity is categorised into hispanic and non-hispanic by definition. Marital status indicates whether the respondent is married or not married, where not married could mean widowed, divorced, separated or never married. Family size is a measure of the number of persons living together in the same household who are related by blood, marriage, adoption or as foster children. In addition, unmarried persons living together who recognise themselves as a family unit are also defined as a family by the MEPS. Region is categorised into 4 dummy variables, namely northeast, midwest, south and west. Regarding socioeconomic status, education, income and occupation
CHAPTER 4. DATA 9 class are included. Education is measured as the total years of schooling. Income is measured as the total income in thousands of U.S. dollars of the past year. Occupation class indicates whether the respondent has a white-collar job. Where a white-collar job is defined as work concerning management, business, financial operation and professional and related occupation. Health related characteristics are smoke status, mental health and physical health. Obviously age can also be considered as a health related characteristics. Smoke status is included as a binary variable that indicates whether the respondent currently smokes. Various studies have shown that smoking has major health consequences and that it is associated with a numerous of diseases, see for example (US Department of Health and Human Services and others, 2014). Other lifestyle habits, such as alcohol consumption and cannabis use, also have an a↵ect on health. For example, Klatsky et al. (1977) show that regular alcohol consumption is associated with an increase in the probability of having high blood pressure and van Ours and Williams (2011) show that using cannabis increases the likelihood of mental health problems. However, information on alcohol consumption, cannabis use or other lifestyle habits are not available in the MEPS. Furthermore, information of diagnosis on specific mental health diseases are not available in the MEPS data. Therefore, mental health is measured by the Kessler Psychological Distress Scale (K6) proposed by Kessler et al. (2002). The K6 index measures the score on a questionnaire consisting of 6 questions. An example of a question on the questionnaire is “During the past 30 days, about how often did you feel nervous?”, to which the respondent could answer “None of the time”, “A little of the time”, “Some of the time”, “Most of the time” or “All of the time”, where the score to each answer is respectively 0, 1, 2, 3 and 4. The sum of the 6 individual scores is defined as the Kessler index. The higher the value of the Kessler index, the greater the respondents tendency towards mental illness. Physical health is measured by the number of comorbidities and weight status. In particular, respondents of the MEPS were asked whether they had any of the following health conditions: High blood pressure, heart disease, stroke, emphysema, chronic bronchitis, high cholesterol, cancer, diabetes, joint pain, arthritis and asthma. The total number of comorbidities counts the aforementioned health conditions for each respondent, which gives an indication of the physical health status. Although it is difficult to measure mental and physical health directly, the kessler index and number of comorbidities are believed to be good proxies and have been used in (van Ours and Williams, 2011) and (Shen, 2013), respectively. The body mass index (BMI) is typically used as a screening method for overweight or obesity. In particular BMI is a measure of the proportion of height and weight. The centres for disease control and prevention considers the following weight status categories associated with BMI: below 18.5 is regarded as underweight, between 18.5 and 24.9 is a normal weight or healthy weight, between 25.0 and 29.9 is overweight and above or equal to 30 is obese. Bratti and Miranda (2011) recommend inclusion of equation specific covariates to ensure the empirical identification of the parameters of the EPET - Poisson model. Shen (2013) proposes the following exclusion restrictions in a similar context. Occupation is excluded from both the participation and outcome equation and marital status and region are excluded only from
CHAPTER 4. DATA 10 the outcome equation. In addition, for each dummy variable one category is dropped from the model to avoid multicollinearity. In particular, female, white, not married, northeast, not white collar, not currently smoking and normal weight are excluded from the model. Table 4.1 summarises the variables together with some descriptive statistics.
Table 4.1: Descriptive statistics
Variable Mean St. Dev. Min 25% 75% Max
Visits to physician 2.090 3.569 0 0 3 54
Private health insurance 0.798 0.402 0 1 1 1
Age 42.648 11.271 23 33 52 64
Male 0.526 0.499 0 0 1 1
White 0.717 0.450 0 0 1 1
Black or African American 0.158 0.365 0 0 0 1
Other race 0.125 0.330 0 0 0 1 Hispanic 0.280 0.449 0 0 1 1 Marital status 0.574 0.494 0 0 1 1 Family size 2.994 1.528 1 2 4 10 Northeast 0.141 0.348 0 0 0 1 Midwest 0.213 0.410 0 0 0 1 South 0.392 0.488 0 0 1 1 West 0.253 0.435 0 0 1 1 Years of schooling 13.557 2.945 0 12 16 17 Income 51.614 41.194 0.067 25.000 64.000 269.424 White collar 0.400 0.490 0 0 1 1 Current smoker 0.125 0.331 0 0 0 1 Kessler index 2.143 3.134 0 0 3 24 Number of comorbidities 0.349 0.575 0 0 1 4 Underweight 0.008 0.089 0 0 0 1 Normal weight 0.282 0.450 0 0 1 1 Overweight 0.369 0.482 0 0 1 1 Obesity 0.342 0.474 0 0 1 1
Chapter 5
Results
Estimates are calculated by means of MSL, where 1500 pseudo-random number draws were used. Table 5.1 presents the estimation results of the EPET-Poisson model. What follows is a discussion of the estimates of the contact and frequency decision. Thereafter, the estimates of the health insurance equation and the results of the remaining parameters are discussed. At last, the estimation results of several robustness checks are presented.
Suprisingly, both age variables show no significant e↵ect for both the contact and frequency decision. In contrast, a significant e↵ect at a level of 1 percent for gender is found for the contact and frequency decision. Males appear to be less likely to visit the physician than females. In addition, they also appear to visit the physician less a year than females. Furthermore, the results show that Black or African American people are less likely than white people to visit the physician and the number of visits per year by Black or African American people is lower. Other races show a similar behaviour. Both race variables are significant at a 1 percent level. Furthermore, the ethnicity variable has a significant e↵ect at a 1 percent level on the contact decision. However, the frequency decision appears to be unresponsive to ethnicity. This suggests that Hispanic people are less likely to contact a physician than non Hispanic people. But as soon as a contact has taken place, their behaviour is no longer di↵erent. Marital status is one of the exclusion restrictions and hence only results for the contact decision are observerd. In particular. a marriage appears to increase the probability to contact a physician. The family size variable has a significant negative e↵ect at 1 percent for both the contact and frequency decision. Hence, families with many children may have to be more carefull with spending money and thus are less likely to contact the physician and at the same time visit the physician less a year. Region, one of the exclusion restrictions, has a significant e↵ect on the probability of visiting a physician. In particular, the results show that people from the midwest, northeast and west are less likely to contact the physician than people from the northeast. All three region indicators are significant at a level of 1 percent. Years of schooling has a positive significant e↵ect at 1 percent for the contact decision and at 10 percent for the frequency decision. Therefore, people with a higher education appear to be more likely to contact the physican and also visit the physician more often a year. The income variable has a positive significant e↵ect on the contact
CHAPTER 5. RESULTS 12 decision, whereas the frequency decision appears to be unresponsive to income. Hence, people with high income are more likely to contact a physician. But as soon as a contact has taken place, income appears to have no e↵ect on the subsequent visits. Smoke status is significant for the contact decision at a level of 1 percent. In particular, current smokers are on average less likely to visit a physician than non-smokers. However, after a contact has taken place, smoke status has no significant e↵ect for the frequency decision. The two proxies for physical and mental health show for both the contact and frequency decision a positive significant e↵ect at a 1 percent level. Hence, people with a greater tendency towards mental health problems are more likely to visit a physician and at the same time visit a physician more often. Furthermore, an additional physical disease increases the probability of visiting a physician and also increases the number of subsequent visits. Furthermore, both the underweight and overweigth variables are insignificant for the contact and frequency decision. However, obesity shows a significant e↵ect for both the contact decision and frequency decision at a level of 5 percent. In particular, people with obesity are more likely to visit the physician and also visit the physician more often. Both the contact and frequency decision are highly responsive to the private health insurance variable. In particular, people with a private health insurance coverage are more likely to visit the physician than people with no health insurance and they also visit the physician more often. With respect to the health insurance equation, age has a significant e↵ect at 5 percent on whether a person has a private health insurance coverage and age2 is significant at 1 percent. Moreover, the probability of having health insurance appears to decreases as age increases up until the age of approximately 34, thereupon the probability of having health insurance increases as age increases. Furthermore, males are less likely to have private health insurance coverage than females at a significance level of 1 percent. Regarding race, both the Black or African American and other race variables show a negative significant e↵ect at a 5 and 1 percent level, respectively. Hence, white people appear to be more likely to have a private health insurance coverage than non-white people. The ethnicity variable has the biggest negative e↵ect on the health insurance coverage decision and is significant at a 1 percent level. Therefore, Hispanic people are less likely to have private health insurance coverge than non-Hispanic people. Furthermore, marital status is significant at 1 percent and has a relative big e↵ect on the insurance decision. Married people appear to be more likely of have a private health insurance coverage than non-married people. Family size is also signifacant at 1 percent and has a negative e↵ect on the health insurance decision. Region is partly significant, with the south indicator significant at a level of 1 percent. People in the south region are less likely than people in the northeast to have health insurance coverage. In contrast, both the midwest and west variables are not significant. Years of schooling is significant at a 1 percent level and has a positive e↵ect on the probability of having private health insurance coverage. Hence, people with a higher education are more likely to have private health insurance coverage than people with a lower education. Income also has a positive e↵ect on the probability of having private health insurance and is significant at 1 percent. Occupation class is significant at 1 percent and has
CHAPTER 5. RESULTS 13 a positive e↵ect on the insurance decision. Therefore, people with a white collared job are more likely to have health insurance coverage than people with a job from another occupation class. Smoke status has a negative e↵ect on the probability to have private health insurance coverage and is significant at 1 percent. In particular, current smokers are less likely to have private health insurance coverage than non-smokers. Interestingly, mental and physical health are both insignificant at a level of 10 percent. Weight status is partly significant, with the obesity indicator significant at a 5 percent level. In particular, obese people are more likely to have private health insurance coverage than people with a normal weight.
The estimate of the standard deviation of unobserved heterogeneity and the factor loadings are also presented in table 5.1. First note that ⌘ is significantly di↵erent from zero. Therefore,
unobserved heterogeneity is present. Furthermore, both 1and 2are negative and significant at
10 and 1 percent, respectively. Therefore, unobserved heterogeneity appears to have a negative e↵ect on both the health insurance coverage and contact decision. The correlations between the error terms can also be found in table 5.1. The estimate of ⇢⌘,vis negative and significant at a 10
percent level and ⇢v,q is insignificant. Hence, it is possible to consider private health insurance
coverage as exogenous with respect to health care utilisation. Furthermore, the estimate of ⇢⌘,q
is negative and significant at 1 percent. This implies a negative correlation between the errors of the contact and the frequency decision.
Several robusness checks are performed by estimating the model on di↵erent population groups. In particular, samples of males, females, people aged 23 through 43, people aged 44 through 64, people with a high school degree or less and people with a college degree or higher are considered. In addition, the ET-Poisson and EP-Poisson model are estimated, where either endogenous treatment or endogenous participation is neglected. In particular, the ET-Poisson model takes account of the potential endogenous treatment and neglects endogenous participation, whereas the EP-Poisson neglects endogenous treatment and takes account of endogenous participation1. In discussing the results of these robustness checks presented in tables 5.2 to 5.5, the main focus lies on the di↵erences compared to the results of the main sample.
The estimates of the contact decision, presented in table 5.2 show some di↵erences when estimated on the di↵erent population groups. The other race variable is insignificant based on the male sample. The estimates based on the female sample are robust, since no substantial changes occur. Region becomes insignificant if estimated on the sample with people aged 23 through 43. For people aged 44 through 64 the variables other race, Hispanic and obesity become insignificant. When estimated on the sample of people with a lower education, other race, years of schooling and region become insignificant. For the higher educated people, black or African American and obesity become insignificant. Estimates of the frequency decision, presented in table 5.3 also show some di↵erences. In particular, years of schooling, obesity and private health
1Both the ET-Poisson and the EP-Poisson are estimated by means of MSL, where 1500 pseudo random
number draws are used. A more detailed discussion of the ET-Poisson and EP-Poisson model can be found in the appendix.
CHAPTER 5. RESULTS 14 insurance coverage become insignificant for males. For females, only years of schooling becomes insignificant. Age and overweight become significant if estimated on the sample of people aged 23 through 43, whereas private health insurance coverage becomes insignificant. Years of schooling, obesity and private health insurance coverage become insignificant for people aged 44 through 64. Other race, obesity and private health insurance coverage become insignificant if estimated on a sample with lower educated people. For higher educated people, years of schooling and private health insurance coverage become insignificant. The estimates of the health insurance model, presented in table 5.4 seem to be more sensitive to only some population groups. The estimates based on the male sample show no substantial di↵erences. The variables, Black or African American, family size and smoke status become insignificant if estimated on the female sample. For people aged 23 through 43 only obesity becomes insignificant. For people aged 44 through 64, age, black or African American and family size become insignificant. No substantial changes occur if estimtated on people with a lower education. Most changes occur if estimated on the high education sample. In fact, almost all variables become insignificant besides, other race, Hispanic, married, income, white collar and smoke status. Furthermore, the estimates of
1, 2and ⌘ based on di↵erent population groups are similar compared to the estimates based
on the main sample.
The estimates based on the ET-Poisson and EP-Poisson model are presented in table 5.5. The results of the frequency decision of the ET-Poisson model are similar to the estimates of the contact decision based on the EPET-Poisson model, whereas they di↵er more in compirason with estimates of the frequency decision of the EPET-Poisson model. Hence, the estimates of the ET-Poisson model are likely to be dominated by the contact decision. Thus, neglecting the hurdle specification can lead to biased estimates and to misinterpretation. As expected, the results of the EP and EPET-Poisson model are quite similar. This is because health insurance coverage is found to be weakly endogenous and thus there is only a small bias in the estimates of the EP-Poisson model.
CHAPTER 5. RESULTS 15
Table 5.1: Estimation results of the EPET-Poisson model
Parameters Health insurance Contact Frequency Constant -0.057 (0.285) -0.789 (0.251)*** 0.347 (0.289) Age -0.033 (0.013)** 0.009 (0.011) -0.003 (0.013) Age2 4.860E-04 (1.497E-04)*** 3.744E-05 (1.313E-04) 9.629E-05 (1.418E-04) Male -0.238 (0.039)*** -0.470 (0.033)*** -0.367 (0.042)*** Black or African American -0.127 (0.055)** -0.160 (0.047)*** -0.222 (0.052)*** Other race -0.169 (0.061)*** -0.168 (0.048)*** -0.147 (0.050)*** Hispanic -0.589 (0.047)*** -0.128 (0.042)*** -0.074 (0.054) Married 0.368 (0.041)*** 0.206 (0.037)*** Family size -0.041 (0.013)*** -0.080 (0.012)*** -0.045 (0.013)*** Midwest 0.029 (0.068) -0.184 (0.053)*** South -0.190 (0.060)*** -0.145 (0.049)*** West 0.050 (0.065) -0.165 (0.051)*** Years of schooling 0.091 (0.007)*** 0.034 (0.006)*** 0.016 (0.009)* Income 0.011 (5.493E-04)*** 0.002 (4.274E-04)*** -6.707E-06 (4.702E-04) White collar 0.199 (0.046)*** Current smoker -0.208 (0.052)*** -0.239 (0.048)*** -0.005 (0.058) Kessler index -0.006 (0.006) 0.045 (0.005)*** 0.033 (0.005)*** Number of comorbidities 0.028 (0.035) 0.420 (0.031)*** 0.138 (0.033)*** Underweight -0.171 (0.183) -0.165 (0.176) 0.158 (0.262) Overweight 0.038 (0.047) 0.033 (0.039) 0.060 (0.043) Obesity 0.118 (0.048)** 0.098 (0.041)** 0.094 (0.044)** Private health insurance 0.379 (0.060)*** 0.472 (0.141)***
1 -0.179 (0.102)* 2 -0.299 (0.078)*** ⌘ 0.889 (0.016)*** ⇢⌘,v -0.157 (0.088)* ⇢⌘,q -0.257 (0.064)*** ⇢v,q 0.040 (0.027)
*** Significant at 1%, **significant at 5% and *significant at 10%. Standard errors are reported in parentheses, where the estimate of the asymptotic variance is used and for ⇢⌘,v, ⇢⌘,qand ⇢v,qthe delta method is used. The Wald test statistic is used
to test ⇢⌘,v= 0, ⇢⌘,q= 0 and ⇢v,q= 0, where W = h( ˆ⌦)|(var(h( ˆ⌦))) 1h( ˆ⌦)⇠ 2(1), with h( ˆ⌦) the estimated correlation
C HAP T E R 5. R E S UL T S 16
Table 5.2: Robustness checks on the contact decision
Main sample Male Female 23 Age 43 44 Age 64 High school or less College or higher
Sample size 8273 4355 3918 4333 3940 4542 3731
Constant -0.789 (0.251)*** -1.424 (0.349)*** -0.737 (0.393)* -1.118 (0.663)* -2.984 (1.691)* -0.462 (0.342) -1.484 (0.553)*** Age 0.009 (0.011) 0.007 (0.016) 0.018 (0.018) 0.025 (0.039) 0.102 (0.063) -0.004 (0.015) 0.020 (0.019) Age2 3.744E-05 (1.131E-04) 1.067E-04 (1.827E-04) 1.106E-04 (2.040E-04) -3.061E-04 (5.847E-04) -8.751E-04 (5.874E-04) 1.983E-04 (1.740E-04) -8.707E-05 (2.168E-04)
Male -0.470 (0.033)*** -0.576 (0.046)*** -0.379 (0.063)*** -0.465 (0.047)*** -0.489 (0.061)*** Black or African American -0.160 (0.047)*** -0.136 (0.068) ** -0.190 (0.071) *** -0.132 (0.067)** -0.216 (0.077)*** -0.174 (0.062)*** -0.066 (0.076) Other race -0.168 (0.048)*** -0.096 (0.067) -0.248 (0.077)*** -0.221 (0.063)*** -0.110 (0.087) -0.075 (0.079) -0.243 (0.067)*** Hispanic -0.128 (0.042)*** -0.133 (0.059)** -0.127 (0.067)* -0.123 (0.057)** -0.117 (0.075) -0.122 (0.057)** -0.175 (0.072)** Married 0.210 (0.037)*** 0.147 (0.053)*** 0.259 (0.055) *** 0.214 (0.049)*** 0.200 (0.066)*** 0.197 (0.049)*** 0.205 (0.061)*** Family size -0.080 (0.012)*** -0.049 (0.016)*** -0.129 (0.020) *** -0.079 (0.016)*** -0.086 (0.022)*** -0.071 (0.016)*** -0.097 (0.022)*** Midwest -0.184 (0.053)*** -0.202 (0.073) *** -0.181 (0.084)** -0.038 (0.075) -0.402 (0.091)*** -0.072 (0.076) -0.293 (0.080)*** South -0.145 (0.049)*** -0.152 (0.066)** -0.143 (0.077)* -0.044 (0.069) -0.273 (0.080)*** -0.073 (0.068) -0.181 (0.074)** West -0.165 (0.051)*** -0.141 (0.069)** -0.197 (0.082)** -0.053 (0.071) -0.303 (0.085)*** -5.504E-04 (0.073) -0.313 (0.078)*** Years of schooling 0.034 (0.006)*** 0.029 (0.009) *** 0.041 (0.011)*** 0.036 (0.010)*** 0.032 (0.011)*** 0.005 (0.010) 0.076 (0.025)*** Income 0.002 (4.274E-04)*** 0.002 (5.683E-04) *** 0.002 (7.158E-04)** 0.003 (6.591E-04)*** 0.001 (6.742E-04)** 0.003 (8.535E-04)*** 0.001 (5.527E-04)* Current smoker -0.239 (0.048)*** -0.238 (0.063) *** -0.263 (0.083)*** -0.192 (0.068)*** -0.319 (0.083)*** -0.202 (0.058)*** -0.202 (0.097)** Kessler index 0.045 (0.005)*** 0.046 (0.007) *** 0.047 (0.008) *** 0.057 (0.007)*** 0.032 (0.009)*** 0.043 (0.006)*** 0.049 (0.009)*** Number of comorbidities 0.420 (0.031)*** 0.490 (0.044) *** 0.353 (0.052)*** 0.350 (0.051)*** 0.515 (0.063)*** 0.479 (0.041)*** 0.356 (0.056)*** Underweight -0.165 (0.176) 0.045 (0.409) -0.273 (0.209) -0.098 (0.226) -0.326 (0.338) -0.252 (0.264) -0.068 (0.257) Overweight 0.033 (0.039) 0.028 (0.054) 0.047 (0.061) 0.076 (0.053) -0.025 (0.067) 0.042 (0.056) 0.045 (0.058) Obesity 0.098 (0.041)** 0.100 (0.059)* 0.098 (0.061) 0.103 (0.055)* 0.088 (0.071) 0.141 (0.057)** 0.076 (0.064) Private health insurance 0.379 (0.060)*** 0.486 (0.096) *** 0.323 (0.097)*** 0.444 (0.078)*** 0.528 (0.197)*** 0.415 (0.105)*** 0.469 (0.162)***
2 -0.299 (0.078)*** -0.347 (0.159)** -0.482 (0.126)*** -0.304 (0.102)*** -0.661 (0.208)*** -0.343 (0.109)*** -0.407 (0.256) *** Significant at 1%, **significant at 5% and *significant at 10%. Standard errors are reported in parentheses, where the estimate of the asymptotic variance is used.
C HAP T E R 5. R E S UL T S 17
Table 5.3: Robustness checks on the frequency decision
Main sample Male Female 23 Age 43 44 Age 64 High school or less College or higher
Sample size 8273 4355 3918 4333 3940 4542 3731
Constant 0.346 (0.289) -0.116 (0.510) 0.851 (0.373)** -1.265 (0.924) 0.097 (1.527) 0.313 (0.471) 1.102 (0.637)* Age -0.003 (0.013) 0.005 (0.020) -0.014 (0.017) 0.102 (0.053)* 0.010 (0.055) 0.009 (0.018) -0.017 (0.018) Age2 9.628E-05 (1.418E-04) 1.388E-04 (2.257E-04) 1.304E-04 (1.891E-04) -0.001 (7.895E-04)* 3.082E-05 (5.120E-04) -2.441E-05 (2.064E-04) 2.644E-04 (2.092E-04)
Male -0.367 (0.040)*** -0.613 (0.068)*** -0.164 (0.054)*** -0.284 (0.056)*** -0.382 (0.065)*** Black or African American -0.221 (0.052)*** -0.176 (0.093)* -0.240 (0.063)*** -0.290 (0.081)*** -0.170 (0.068)** -0.217 (0.078)*** -0.238 (0.073)*** Other race -0.147 (0.050)*** -0.143 (0.085)* -0.132 (0.073)* -0.220 (0.085)*** -0.125 (0.074)* -0.005 (0.085) -0.226 (0.076)*** Hispanic -0.074 (0.054) -0.140 (0.084)* -0.054 (0.065) -0.153 (0.084)* -0.075 (0.077) -0.125 (0.079) -0.105 (0.083) Family size -0.045 (0.013)*** -0.047 (0.019)** -0.044 (0.018)** -0.062 (0.020)*** -0.040 (0.019)** -0.043 (0.019)** -0.034 (0.019)* Years of schooling 0.016 (0.009)* 0.015 (0.013) 0.012 (0.010) 0.041 (0.017)** 0.015 (0.010) 0.002 (0.015) 0.017 (0.025) Income -6.707E-06 (4.702E-04) 3.567E-04 (6.845E-04) 1.181E-04 (7.232E-05) 2.751E-04 (8.952E-04) 1.668E-04 (6.072E-04) -0.001 (0.001) 5.726E-04 (5.938E-04) Current smoker -0.005 (0.058) 0.041 (0.088) -0.047 (0.082) 0.027 (0.097) -0.012 (0.078) 0.026 (0.076) -0.053 (0.099) Kessler index 0.033 (0.005)*** 0.042 (0.010)*** 0.028 (0.006)*** 0.028 (0.008)*** 0.032 (0.007)*** 0.024 (0.007)*** 0.038 (0.009)*** Number of comorbidities 0.138 (0.033)*** 0.094 (0.055)* 0.131 (0.043)*** 0.103 (0.062)* 0.095 (0.048)** 0.149 (0.042)*** 0.126 (0.054)** Underweight 0.158 (0.262) -0.109 (0.640) 0.256 (0.293) 0.065 (0.383) 0.342 (0.392) 0.295 (0.492) 0.053 (0.314) Overweight 0.059 (0.043) 0.033 (0.070) 0.085 (0.056) 0.119 (0.067)* 0.032 (0.057) 0.065 (0.068) 0.074 (0.055) Obesity 0.094 (0.044)** 0.103 (0.074) 0.127 (0.058)** 0.159 (0.070)** 0.063 (0.060) 0.099 (0.068) 0.127 (0.060)** Private health insurance 0.472 (0.141)*** 0.126 (0.254) 0.514 (0.132)*** -0.072 (0.211) 0.241 (0.292) 0.425 (0.279) -0.036 (0.320)
⌘ 0.889 (0.016)*** 0.897 (0.031)*** 0.910 (0.023)*** 0.946 (0.025)*** 0.897 (0.043)*** 0.912 (0.025)*** 0.878 (0.038)*** *** Significant at 1%, **significant at 5% and *significant at 10%. Standard errors are reported in parentheses, where the estimate of the asymptotic variance is used.
C HAP T E R 5. R E S UL T S 18
Table 5.4: Robustness checks on the health insurance coverage decision
Main sample Male Female 23 Age 43 44 Age 64 High school or less College or higher Sample size 8273 4355 3918 4333 3940 4542 3731 Constant -0.057 (0.285) -0.177 (0.371) -0.104 (0.443) 0.204 (0.764) -1.296 (1.857) 0.209 (0.343) 0.027 (0.685) Age -0.033 (0.013)** -0.041 (0.017)** -0.025 (0.020) -0.095 (0.047)** 0.038 (0.070) -0.050 (0.015)*** 0.004 (0.024) Age2 4.860E-04 (1.497E-04)*** 5.926E-04 (1.997E-04)*** 3.947E-04 (2.291E-04)* 0.001 (7.031E-04)** -2.375E-04 (6.493E-04) 7.357E-04 (1.784E-04)*** -6.052E-05 (2.826E-04)
Male -0.238 (0.039)*** -0.228 (0.054)*** -0.264 (0.058)*** -0.301 (0.047)*** -0.081 (0.070) Black or African American -0.127 (0.055)** -0.158 (0.077)** -0.085 (0.082) -0.181 (0.076)** -0.054 (0.082) -0.139 (0.065)** -0.118 (0.107) Other race -0.169 (0.061)*** -0.166 (0.082)** -0.183 (0.093)* -0.146 (0.084)* -0.265 (0.096)*** -0.148 (0.082)* -0.201 (0.096)** Hispanic -0.589 (0.047)*** -0.622 (0.063)*** -0.543 (0.071)*** -0.571 (0.065)*** -0.623 (0.072)*** -0.581 (0.057)*** -0.554 (0.085)*** Married 0.368 (0.041)*** 0.367 (0.056)*** 0.373 (0.061)*** 0.280 (0.056)*** 0.457 (0.064)*** 0.361 (0.049)*** 0.299 (0.079)*** Family size -0.041 (0.013)*** -0.049 (0.017)*** -0.028 (0.021) -0.041 (0.017)** -0.023 (0.022) -0.045 (0.015)*** -0.008 (0.028) Midwest 0.029 (0.068) 0.032 (0.088) 0.011 (0.111) 0.027 (0.095) 0.029 (0.103) -0.026 (0.086) 0.141 (0.117) South -0.190 (0.060)*** -0.153 (0.079)* -0.236 (0.095)** -0.177 (0.085)** -0.220 (0.089)** -0.265 (0.076)*** -0.048 (0.105) West 0.050 (0.065) 0.058 (0.083) 0.031 (0.105) 0.045 (0.090) 0.020 (0.097) 0.048 (0.082) 0.032 (0.111) Years of schooling 0.091 (0.007)*** 0.100 (0.009)*** 0.072 (0.011)*** 0.145 (0.012)*** 0.049 (0.010)*** 0.092 (0.010)*** 0.043 (0.033) Income 0.011 (5.493E-04)*** 0.009 (6.493E-04)*** 0.016 (0.001)*** 0.012 (8.839E-04)*** 0.010 (8.369E-04)*** 0.012 (7.126E-04)*** 0.011 (9.113E-04)*** White collar 0.197 (0.046)*** 0.185 (0.064)*** 0.213 (0.067)*** 0.197 (0.063)*** 0.138 (0.069)** 0.161 (0.062)*** 0.238 (0.073)*** Current smoker -0.208 (0.052)*** -0.239 (0.064)*** -0.150 (0.092) -0.211 (0.070)*** -0.167 (0.080)** -0.177 (0.059)*** 0.287 (0.117)** Kessler index -0.006 (0.006) -0.005 (0.008) -0.006 (0.008) -0.007 (0.008) -0.006 (0.009) -0.006 (0.006) -0.008 (0.012) Number of comorbidities 0.028 (0.035) 0.010 (0.045) 0.047 (0.055) -0.007 (0.058) 0.047 (0.044) 0.051 (0.042) -0.013 (0.064) Underweight -0.171 (0.183) -0.008 (0.348) -0.235 (0.222) -0.129 (0.231) -0.241 (0.335) -0.028 (0.255) -0.353 (0.302) Overweight 0.038 (0.047) 0.079 (0.062) 0.008 (0.072) 0.015 (0.063) 0.096 (0.073) 0.039 (0.057) 0.049 (0.082) Obesity 0.118 (0.048)** 0.201 (0.066) *** 0.030 (0.070) 0.073 (0.063) 0.192 (0.076)** 0.163 (0.058)*** 0.003 (0.086) 1 -0.179 (0.102)* 0.021 (0.160) -0.200 (0.099)** 0.205 (0.146) -0.111 (0.197) -0.105 (0.193) 0.062 (0.220)
CHAPTER 5. RESULTS 19
Table 5.5: Estimation results of the ET-Poisson and EP-Poisson model
ET-Poisson EP-Poisson
Health insurance Frequency Contact Frequency Constant -0.022 (-0.284) -1.797 (0.266)*** -0.816 (0.251)*** 0.398 (0.284) Age -0.033 (0.013)*** 0.019 (0.012) 0.009 (0.011) -0.001 (0.012) Age2 4.943E-04 (1.485E-04)*** -1.961E-05 (1.410E-04) 3.403E-05 (1.315E-04) 9.287E-05 (1.397E-04)
Male -0.241 (0.039)*** -0.651 (-0.035)*** -0.468 (0.032)*** -0.374 (0.037)*** Black or African American -0.123 (0.055)*** -0.297 (0.052)*** -0.158 (0.047)*** -0.236 (0.051)*** Other race -0.167 (0.061)*** -0.215 (0.047)*** -0.166 (0.048)*** -0.157 (0.049)*** Hispanic -0.585 (0.047)*** -0.144 (0.050)*** -0.116 (0.042)*** -0.113 (0.047)** Married 0.380 (0.041)*** 0.202 (0.036)*** Family size -0.043 (0.013)*** -0.079 (0.012)*** -0.080 (0.012)*** -0.046 (0.012)*** Midwest 0.024 (0.068) -0.190 (0.053)*** South -0.199 (0.060)*** -0.143 (0.049)*** West 0.042 (0.064) -0.166 (0.051)*** Years of schooling 0.089 (0.007)*** 0.041 (0.007)*** 0.032 (0.006)*** 0.024 (0.007)*** Income 0.011 (5.343E-04)*** -0.001 (4.922E-04)*** 0.002 (4.220E-04)*** 1.826E-04 (4.500E-04) White collar 0.206 (0.045)*** Current smoker -0.208 (0.052)*** -0.238 (0.053)*** -0.236 (0.048)*** -0.012 (0.057) Kessler index -0.006 (0.006) 0.063 (0.005)*** 0.045 (0.005)*** 0.031 (0.005)*** Number of comorbidities 0.344 (0.035) 0.411 (0.033)*** 0.421 (0.031)*** 0.135 (0.031)*** Underweight -0.169 (0.182) -0.065 (0.210) -0.164 (0.174) 0.158 (0.260 Overweight 0.039 (0.047) 0.047 (0.041) 0.032 (0.039) 0.067 (0.042) Obesity 0.133 (0.042)*** 0.096 (0.041)** 0.099 (0.044)**
Private health insurance 0.119 (0.047)** 0.882 (0.111)*** 0.451 (0.042)*** 0.224 (0.053)***
1 -0.125 (0.052)**
2 -0.316 (0.065)***
⌘ 1.160 (0.016)*** 0.884 (0.015)***
*** Significant at 1%, **significant at 5% and *significant at 10%. Standard errors are reported in parentheses, where the estimate of the asymptotic variance is used.
Chapter 6
Conclusion
In this thesis the determinants of health care utilisation, measured in terms of physician visits, are studied based on data provided by the Medical Expenditure Panel Survey. In particular, the EPET-Poisson model is used to take account of both the possible endogeneity in choice of health insurance coverage and endogenous participation. Maximum simulated likelihood is used to estimate the model.
Demographics appear to be important in determining health care use. In fact, both the contact and frequency decision are responsive to most demographics. However, age appears to have only an e↵ect on the insurance decision. Furthermore, the results suggest that socioeconomic variables are less important in determining health care use than health insurance choice. Moreover, after the first visit to the physician, the subsequent visits appear to be unresponsive to socioeconomic variables. Health status appears to be more important in determining health care use than health insurance choice and health insurance coverage has a substantial e↵ect on both the contact and frequency decision. These results are broadly in line with those found in previous studies. However, estimates based on di↵erent population groups show some di↵erences. Furthermore, health insurance coverage is found to be weakly endogenous with respect to health care utilisation and a negative correlation is found between the contact and frequency decision. Hence, estimation results based on a model that only takes account of endogenous participation shows no substantial di↵erences, whereas estimates based on a model that only takes endogenous treatment into account shows more substantial di↵erences.
There are some limitations in the approach used in this thesis. The endogeneity in choice of health insurance coverage and participation are assumed to be determined by the same unobservable variable. In reality this might not be the case. Instead there might be more unobservables that cause endogeneity issues. In addition, health care use is only measured in terms of physician visits. Therefore, it would be useful to distinguish between di↵erent type of health care services. Furthermore, a fully parametric approach is used. However, the assumptions made on the error terms may be to restrictive and can lead to biased estimates. Therefore, it could be better to use a semi-parametric approach. Finally, a cross-sectional data set is used. Therefore, it is not possible to capture temporal e↵ects.
Appendix A
EP - Poisson model
The EP - Poisson takes account of endogenous participation and neglects endogenous treatment. Therefore, the EP-Poisson model is similar to the EPET-Poisson model.
The participation equation is modelled as
Pi ={Pi⇤ > 0} where Pi⇤ = r|i✓ + Ti+ qi, (A.1)
with ria KPx1 vector of explanatory variables, ✓ a KPx1 vector of coefficients, Tithe endogenous
treatment e↵ect and qi an error term.
The count yi is generated according to the following distribution
f (yi|µi) = 8 < : — if Pi = 0 µiexp( µi) (1 exp( µi))yi! if Pi = 1 (A.2) with yi = 8 < : 0 if Pi = 0 1, 2, 3, . . . if Pi = 1 (A.3) and µi is the intensity rate of yi. A log-linear model is used to generate the intensity rate
log(µi) = x|i + T + ⌘i (A.4)
with xi a Kyx1 vector of explanatory variables, a Kyx1 vector of coefficients, the coefficient
on the endogenous treatment e↵ect and ⌘i is unobserved heterogeneity.
Interrelation between Pi and yi is possible through their error terms as follows
qi= 2⌘i+ ✏i (A.5)
with 2 a free factor loading, which is estimated among the other parameters, and ✏i is an
error term. Furthermore it is assumed that ⌘i ⇠ N (0, ⌘) and that ✏i|⌘i follows a standard
normal distribution. ⌘ is another additional parameter needed to be estimated among the
other parameters.
LetPPi(0|⌘i) denote the conditional probability of Pi= 0 given ⌘iandPPi(1|⌘) the conditional
probability of Pi= 1 given ⌘i. Subsequently the log-likelihood function can be written as
log(L(⌦)) = X
P =0
log⇣ Z P(0|⌘)'(⌘)d⌘⌘+X
P =1
log⇣ Z P(1|⌘)f(y|⌘)'(⌘)d⌘⌘ (A.6)
APPENDIX A. 22
ET - Poisson model
The ET - Poisson model takes account of endogenous treatment and neglects both endogenous participation and the two-part character of the count.
The treatment is modelled as
Ti = I{Ti⇤ > 0} where Ti⇤ = z|i + vi (A.7)
with I{·} an indicator function, zi a KTx1 vector of explanatory variables, a Kzx1 vector of
coefficients and vi an error term.
The count yi is generated according to a Poisson model
f (yi|µi) =
exp( µi)µyii
yi!
, where y = 0, 1, 2, . . . (A.8)
with µi the intensity rate of yi. A log-linear model is used to generate the intensity rate
log(µi) = x|i + T + ⌘i (A.9)
with xi a Kyx1 vector of explanatory variables, a Kyx1 vector of coefficients, the coefficient
on the endogenous treatment e↵ect and ⌘i unobserved heterogeneity. Interrelation among Ti
and yi is possible through their error terms
vi = 1⌘i+ ✏i (A.10)
with 1 a free factor loading, which is estimated among the other parameters, and ✏i is an error
term. Furthermore it is assumed that ⌘i ⇠ N (0, ⌘) and that ✏i|⌘i follows a standard normal
distribution. ⌘ is an additional parameter that needs to be estimated.
LetPTi(0|⌘i) denote the conditional probability of Ti = 0 given ⌘iandPTi(1|⌘) the conditional
probability of Ti= 1 given ⌘i. Subsequently, the log-likelihood function can be written as.
log(L(⌦)) = X T =0 log⇣ Z PT(0|⌘)f(y|⌘)'(⌘)d⌘ ⌘ +X T =1 log Z PT(1|⌘)f(y|⌘)'(⌘)d⌘ ⌘ (A.11)
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