Estimating the Willingness-to-Pay for Attributes of General Practitioners: A Travel Cost Approach GEIR GODAGER Institute of Health Management and Health Economics, University of Oslo, P.O. Box 1089 Blindern, 0317 Oslo, Norway E-mail: g.c.godager@medisin.uio.no Incomplete draft. Not for circulation, citation, or quotation. Version of April 30, 2007 Abstract: The aim of this paper is to estimate the consumers willingness to pay for certain attributes of GPs such as whether or not the physician has fulfilled a post-graduate education programme and achieved status as specialist in general medicine. The individual consumer s choice of general practitioner is modelled within the random utility framework. Data are from the regular general practitioner scheme organized as a list patient system introduced in Norwegian general practice in June 2001. Prior to the reform the health authorities asked all the inhabitants to submit a form ranking their three most preferred general practitioners (GPs). Interpreting the most preferred GP as the chosen alternative, choice probabilities are estimated by means of conditional logit regression. Having information on Zip codes of patients residential addresses as well as zip codes of addresses at which practices are located, we are able to study how patients balance travel costs and attributes of GPs. Since travelling when healthy may not be the same as travelling when ill, travel costs associated with different modes of travel are considered, and discussed. At the time our data was collected GPs who are specialists in general medicine received an additional fee of 51 NOK per consultation from the National Insurance Scheme, while the patients out of pocket fee for consulting a specialist in general medicine was the same as for consulting a non-specialist. The results indicate that patients willingness to pay for consulting a specialist is considerably lower than the additional fee specialists receive from the National Insurance Scheme. Keywords: GP services. Discrete choice. Travel cost method. Willingness-to-pay. Health care demand. Norway.
1 Introduction An important feature of the market for general practitioners service is that the doctor-patient relationship is often long term and likely to be characterized by repeated transactions. Patients consult their GPs more frequently than they use more specialized health care services. A durable doctor-patient relationship results in two-way information transmission between doctor and patient. From the doctor the patient receives information about health problems and the options available for treatment, and the doctor receives information from the patient about symptoms, social background, and how the patient values alternative health care services. It has been argued that increasing the frequency of transactions between parties reduces the costs of information transmission and may also reduce monitoring costs (Williamson, 1993). Several studies report that patients who see the same GP at each visit both prefer and are more compliant with treatment recommendations (Dietrich and Marton, 1982, Hjortdahl and Laerum, 1992). Several studies provide evidence suggesting that physicians who are trained in communication skills have patients who are more satisfied, more compliant with recommended treatment, and have better health status (Ong et al., 1995, Kaplan et al., 1989, Wartman et al., 1983, Stewart, 1995). In this paper we argue that communication and information transmission between doctors and patients are important input in the GPs production function. The rational consumer and potential patient would thus prefer to be listed in a practice of a GP such that the transmission of information is unstrained. An auxiliary hypothesis is that the transmission of information is easier between physicians and patients that resemble one another on observable characteristics. We model the patient s choice of GP within the framework of the random utility model (RUM), and expect that the consumer s utility associated with a given GP is higher the more similar the GP is to the decision maker. Most earlier studies on matching of GPs and patients consist of analysis of individuals stated preferences with regard to hypothetical GPs. (Examples of such studies are Vick and Scott (1998), Scott and Vick (1999) and Veale, (1995)). In June 2001 a regular GP scheme was introduced in Norwegian general practice, making the GPs responsible for the provision of primary care services to the persons listed at their practice. Prior to the reform the health authorities gathered the 1
information needed to assign one GP to each Norwegian inhabitant. All inhabitants were asked to rank their three most preferred GPs in a form, and all GPs were asked to report the maximum number of patients they would like to take care of. The health authorities designed an algorithm merging this information in order to obtain a one-to-one match between inhabitants and GPs. This reform gave opportunities to study the revealed preferences of consumers with regard to choice of GP. Applying data from this natural experiment, Hilde Lurås (2003) studied the consumers ranking of GPs and estimated choice probabilities by means of a Luce model of ranking. Lurås found that individuals preferred GPs that were specialists in general medicine compared to GPs who had not engaged in further education in order to get specialist status. The consumer also preferred a GP with the same gender, and Lurås found that the choice probabilities were declining in the age difference between the GP and the patient. In this paper we utilize a part of the data set applied in Lurås (2003) that was not used in that study, namely observations of choice made by consumers living in Oslo, the capital of Norway. This part of the data set was presumably dropped due to difficulties imposed by vast size of the data set. The large size of the sample necessitates the use of a random sample of the observations in order to estimate choice probabilities by means of available computer resources. The study of the behaviour of inhabitants of Oslo thus comes at cost, but there are also potential benefits of studying the choices made in Oslo. The availability of information on the zip-code of the residential address of consumers as well as zip-codes of the addresses at which practices are located give us the opportunity to study how consumers trade off attributes of the GP with something that we can relate to: travel distance. Further, if it is possible to attach monetary value to travel distances within Oslo, we are able to derive a monetary value of GP attributes, such as GPs engaging in training and education to become a specialist in general medicine.description of difference between being a specialist and not being a specialist to be entered! 2 Random utility and the logit model We denote by U ij the utility consumer i obtains when selecting GP j. The utility is decomposed into a part that is a function of variables that are observable to us, 2
and a part that is unobservable. We denote the observable or deterministic part of utility by V ij. The random part of the utility is denoted by ε ij. The logit model is obtained by assuming that ε ij is independently, identically distributed extreme value type 1. The utility consumer i obtains when selecting GP j is stochastic and equal to the sum of the deterministic and stochastic part of utility: U ij = V ij + ε ij In this paper we specify V ij as a linear function of observable variables: V ij = X ij β + Z j γ where X ij and Z j are vectors of explanatory variables and β and γ are vectors of the unknown parameters to be estimated. X ij are explanatory variables interacting characteristics of the alternative j with characteristics of consumer i, and Z j are explanatory variables describing characteristics or attributes of alternative j. In contrast with X ij, Z j does not show any variation between decision makers, or in other words, there are no within alternative variation in Z j. Examples of variables in the X ij vector are dummies indicating travel distance between decision maker and the alternative GP, and dummies indicating whether or not the decision maker and the alternative GP have the same gender. Examples of variables in the Z j vector are dummies indicating whether or not the GP is married, and whether or not the GP is born in Norway. The probability that consumer i choose GP j can be expressed as: P ij = P rob(v ij + ε ij > V ik + ε ik ; j k) = P rob(ε ik < ε ij + V ij V ik +; j k) A property of the logit model is that we get closed form expressions for P ij. It can be shown that the logit probabilities are given by: P ij = ev ij k e V ik We now let y ij = 1 if individual i chose alternative j, and zero otherwise. Assuming that the choice of GP made by consumer i is independent of choices made by other consumers, we may express the likelihood function by: L(β, γ) = i (P ij ) y ij j This is an application of McFaddens (1973, 1974) choice model, and by means of a conditional logistic regression model, we will estimate the parameters β and γ. 3
The estimation method applied is the maximum likelihood method available in the software STATA version 9.1. 3 Matching of GPs and consumers Consumers visit their GP in events of illness. The first of the GP s important tasks is to reveal what is the cause of illness, i.e. what is the diagnosis. A second important task is to recommend an appropriate treatment, and ensure that the patient is compliant with the treatment. Communication between the GP and the patient is an important input in both these processes. If the information transmission is unstrained and the GP and the patient are able to communicate easily and understand each other, than the GP may be more likely to succeed in setting the correct diagnosis than if the converse was true. One may also argue that unstrained communication may cause the treatment to be more effective, since patients may be more likely to be compliant with treatment if the patient receives and understand the information given with regard to the treatment. One might expect that communicative skills vary both between patients and between physicians. Further it seems reasonable that all patients do not communicate equally well with all types of physicians. Correspondingly, a particular GP may communicate better with a patient having certain characteristics. If conversation is an important input in the GPs health production function, then, matching a GP with patients which with whom the GP are able to communicate with ease may improve the GP s productivity compared to the converse case where a GP is matched with patients such that communication is more difficult. In the Norwegian regular general practitioner scheme the consumer and potential patient revealed their preferences for GP by means of returning an entry form ranking their three most preferred GPs in descending order. A large share of the inhabitants only filled in the most preferred GP. 1 In this paper we refer to the most preferred GP as the selected GP, and we assume that the consumer selected the GP that maximized utility. We assume that the consumers when selecting their GP appreciate that communication is an important input in general practice and that the consumer thus preferred GPs with 1 In the next version of the paper we shall state the proportion of inhabitants who only filled in the most preferred GP. 4
attributes such that the communication was expected to be unstrained. In this paper we apply the idea that people that have similar characteristics communicate better than people that are different. We thus apply the old saying that birds of a feather flock together, and state our main hypothesis that patients preferred GPs that resemble them selves on observable characteristics such as gender and age. We construct a dummy variable, SAMEGENDER, equal to one if the GP and patients are of the same gender and zero otherwise. We expect SAMEGENDER to have a positive effect on choice probabilities. Further we compute the absolute value of the age difference between the patient and the GP, AGEDIFF. Since an increase in AGEDIFF implies that that the patient and GP are more unlike, we expect the effect of AGEDIFF on choice probabilities to be negative. We also take account of the possibility that the consumers may not be indifferent to whether the GP is older or younger than oneself by including the GPs age, AGEGP, as an explanatory variable. Since travel is costly, we expect that GPs with practices that are located close to the consumer s residential address are preferred to GPs located further away. The Norwegian Mail Service has given every address in the country a four digit zip code. We have information on the zip code of both the GPs practices, and the residential address of consumers. We have access to a matrix containing travel distance in kilometers and and travel time in hours between all Norwegian zipcodes. We expect the choice probabilities to be decreasing in travel time and travel distance. By applying information on travel times and travel distances we will also calculate different travel costs associated with different modes of travel. 2 The GPs accessibility in terms of opening hours is an important attribute of the GP. We expect that GPs who have many office hours during the week are preferred to GPs that are working part time. Unfortunately we do not have information on the number of weekly business hours. Prior to the implementation of the regular general practitioner scheme the GPs was asked to state the maximum number of patients they would like to take care of. This number was to constitute an upper limit on the number of patients that the health authorities would allocate 2 The company Infomap Norway has collected actual travel distances and travel times associated with travel by means of a light truck on public roads between centers of the zip-code areas. 5
to the GPs, and this number has often been interpreted as the GPs preferred list size (Iversen and Lurås 2000, Iversen and Lurås 2002, Iversen 2004). It seems reasonable that GPs who were planning to have a part time practice on average reported a lower preferred list size compared to GPs that were planning to have a full time practice. We thus apply the GPs preferred list size, PREFLIST, as an indicator of the GPs accessibility, and we expect this variable to have a positive effect on the choice probabilities. After receiving a medical licence, GPs may undertake further medical training and become a specialist in general medicine. We expect that GPs who are specialists in general medicine is preferred to GPs who are not specialists, ceteris paribus. We thus include a dummy, SPECIALIST, equal to one if the GP is a specialist in general medicine and zero otherwise. Our data contain information on the birth country of the GP. Most inhabitants of Oslo are born in Norway. By following the reasoning that consumers prefer GPs that resemble themselves on observable characteristics, we expect consumers to prefer GPs that are born in Norway. We introduce a dummy, FOREIGNGP, that equals one if the GP was born outside Norway and zero otherwise. We expect FOREIGNGP to have a negative effect on the choice probabilities. One may argue that persons with unfavorable personal characteristics are less likely to be married. Therefore people with unfavorable characteristics are likely to be underrepresented among people who are married. We include a dummy (MARRIEDGP) equal to one if the GP is married. We expect MARRIEDGP to have a positive effect on the choice probabilities. 4 Data Our data set is provided by the Norwegian Social Science Data Services. The observation unit is the individual inhabitant. All inhabitants in 14 selected Norwegian municipalities are included. The sample is stratified according to Statistics Norway s measure of the centrality of Norwegian municipalities. In this paper we will only use observations from inhabitants and GPs in Oslo. One of the reasons for this is that the data from Oslo render the possibility of including indicators of travel distance to the GP in the analysis by utilizing information on zip codes. 6
After taking out inhabitants that is registered to be living in municipalities outside Oslo, our data set has 457 080 unique observations. Not all inhabitants returned the entry form revealing their preferences for GP, and consequently information on the preferred GPs is missing for some of the inhabitants. We note that inhabitants who refrained from returning the entry form most likely differ from inhabitants who returned the form on both observable and unobservable characteristics. We will not address this issue in this version of the paper. We note however that the representativety of our sample have implications for how we interpret the results. This issue will receive more attention in the next version of this paper. When we take out all inhabitants that are not registered with a first choice GP, 164 818 observations disappear, and we are left with 292 262 observations. Not everyone who disappears refrained from returning the entry form. 26 583 observations disappear despite the fact that they actually returned the entry form. Among these 26 583 persons, 7 776 have been assigned GPs that have practices outside of the 14 municipalities included in our sample. Most likely the number of inhabitants who preferred a GP outside of these 14 municipalities is even higher. If an inhabitant requested a GP outside of the 14 municipalities, this could explain the fact that information on the first choice GP is missing. When the inhabitants returned the entry form, the inhabitants had the opportunity of refraining from participating in the regular general practitioner scheme all together. 4 170 who disappeared when removing inhabitants without a registered first choice GP have requested not to participate in the regular general practitioner scheme. The rest of the inhabitants that disappear despite the fact that they returned the entry form might be due to problems with registration, such as problems with optic reading of paper forms. We are planning to use the zip code regions in Oslo in our analysis. The zip code starting with 00 are reserved for special addresses such as H.M. The King, the Royal Castle, the National Hospital, The Norwegian Mail Service and the Norwegian Parliament. When we take out observations with zip code codes starting with 00, 34 observations disappear and we are left with 292 228 observations. We are interested in studying the choice of sovereign consumers. Since parents are likely to choose the GP for their children we exclude observations of consumers younger than 18 years old. When we do this 38 738 observations disappear, and we are left with 253 490 observations. Last we take out observations of inhabitants 7
who selected a GP with a practice address outside of Oslo. When we do this 95 inhabitants disappear and we are left with a sample of 253 395 observations. In this large sample there are 437 alternative GPs, meaning that 437 GPs have been ranked as the most preferred GP by at least one inhabitant. This sample is still too big to be used by means of the available computer resources. 3 We thus need to perform our estimation on a sub sample. Since zip code regions play an important role in the analysis we draw our sample from within each of the twelve zip code regions. When stratifying the sample according to zip code regions we also reduce the risk of alternatives falling out of the sample. We ask the program SPSS to draw a random sample of 10 % of the observations from within each of the zip code regions. This sub sample consists of 25 345 unique observations. We check whether the construction of a sub sample has resulted in some of the alternatives falling out of the sample. It turns out that there are still 437 alternatives in the sub sample. In table 1 we present some descriptive statistics on variables at the patient level and compare the whole sample with sub sample. 3 The most important constraint seems to be the amount of memory (RAM) the computer can provide to the STATA program. The computer used for estimation is able to provide at most 938 MB of memory to the program. Even when variables are compressed to the minimum, the available memory impose a binding constraint on both the size of the estimation sample and the number of explanatory variables that can be included. 8
Table 1: Variables describing the consumer. Variable Sample N Mean Std. Dev. Min Max AGE Gross sample 253395 48.63 18.46 18 106 FEMALE 0.58 0.49 0 1 AGE Sub sample 25345 48.56 18.54 18 106 FEMALE 0.58 0.49 0 1 We see that the average age of consumers within the sample is 48 years, and that 58 % of the consumers in the sample are females. The high proportion of females might seem a bit surprising. One of the reasons for this is that a higher proportion of females returned the entry form compared to what was the case among male inhabitants. Another possible explanation is that females have higher life expectancy. We have excluded persons younger than 18 from the sample, contributing to inflating the proportion of females. The high proportion of females can also be caused by a higher proportion of females moving from rural areas to the city. In tables 2a and 2b we describe variables where consumer and GP characteristics are interacted. In table 2a we de describe the variables interacting the characteristics of consumers and GPs across all combinations of consumers and alternative GPs. We se that the average age difference between consumer and the selected GP is 16 years. We see that the average traveltime across alternatives is 0.14 hours or about 8 minutes, and that the average travel distance across alternatives is 8.55 kilometers. Table 2A: Variables interacting the characteristics of consumers and GPs. No of obs=11075765 Variable Mean Std. Dev. Min Max AGEDIFF 16.47 11.40 0.00 78.00 SAMEGENDER 0.48 0.50 0.00 1.00 TRAVELTIME (hrs) 0.14 0.07 0.00 0.52 TRAVELDISTANCE (km) 8.55 4.72 0.00 29.80 In table 2B we de describe the variables interacting the characteristics of consumers and the chosen GP. Comparing with table 2A we see that the age difference 9
between consumer and chosen GP is smaller than the average across all alternatives. We see that 59 % of the sample selected a GP with the same gender. We also see that the travel distance measured in both time and kilometers between consumers and the chosen altarnative is considerably shorter. While the average traveltime across all alternatives is 0.14 hours the average traveltime across chosen alternatives is 0.04 hours or 3.4 minutes. We also see that average travel distance across the chosen alternatives is only 2.58 kilometers. Table 2B: Descriptive statistics of variables interacting the characteristics of consumers and the chosen alternative. No of obs=25345 Variable Mean Std. Dev. Min Max AGEDIFF 15.64 10.87 0.00 61.00 SAMEGENDER 0.59 0.49 0.00 1.00 TRAVELTIME (hrs) 0.04 0.05 0.00 0.40 TRAVELDISTANCE (km) 2.58 3.09 0.00 24.10 The Norwegian Mail Service refers to the two first digits in this code as the zip code region. In Oslo there are 12 different zip code regions 4 : 01, 02, 03,..., 12. For a consumer living in zip code region 2, it is an important attribute of the GP whether the GPs practice is located in zip code region 2 or in an other zip code region such as zip code region 10. In table 3 we present a cross tabulation of the zip code region of the practice address and the zip code region of the consumers residential address. We have highlighted the elements on the main diagonal. We see that the proportion of consumers that have selected a GP located in the same zip code region as the residential address is high across all the zip code regions. We also see that very few of the cells are empty. The fact that few consumers selected a GP located outside of the zip code region is somewhat surprising knowing that many of the zip code regions are within walking distance to each other. 4 if we ignore the zip code region 00 which is reserved for special addresses 10
Table 3: Cross tabulation of Zip-codes of residential address of consumer and address of the selected GP. Zip consumers 1 2 3 4 5 6 7 8 9 10 11 12 total Zip GPs 1 621 121 155 275 349 403 64 58 121 114 97 86 2464 2 60 1250 445 110 95 107 172 37 46 33 62 40 2457 3 138 423 1324 237 108 130 312 107 46 24 67 27 2943 4 36 18 32 1667 273 77 15 95 40 35 22 19 2329 5 63 26 28 126 1799 158 22 18 114 45 40 27 2466 6 41 11 21 34 150 3175 14 8 76 96 198 65 3889 7 13 37 151 18 13 28 1119 17 7 6 4 1 1414 8 16 37 58 96 46 34 27 692 27 12 11 12 1068 9 5 4 5 12 49 19 2 2 1592 57 5 5 1757 10 3 1 2 3 3 15 0 0 35 852 3 3 920 11 68 10 13 18 20 138 10 4 15 10 2084 136 2526 12 2 0 1 3 4 15 0 2 3 2 27 1053 1112 total 1066 1938 2235 2599 2909 4299 1757 1040 2122 1286 2620 1474 25345 In table 4 we describe variables at the level of the GP. We see that 20 % of GPs in Oslo are born in a country other than Norway. Further we see that the average size of the GPs preferred list size is 1403. We also see that 38 % of the GPs are females, and that the average age of GPs in Oslo is 47 years. The mean of SPECIALIST indicate that 53% of the GPs in Oslo are specialists in general medicine. We also see that 66 % of the GPs are married. Table 4: Descriptive statistics of variables at the level of the GP. No of obs=437 Variable Mean Std. Dev. Min Max SPECIALIST 0.53 0.50 0.00 1.00 PREFLIST 1403.02 651.13 200.00 5000.00 AGEGEP 46.92 7.40 28.00 70.00 FEMALEGP 0.38 0.49 0.00 1.00 FOREIGNGP 0.20 0.40 0.00 1.00 MARRIEDGP 0.66 0.47 0.00 1.00 11
5 Estimation and results In table 5 we present the results from conditional logistic regression where the dependent variable indicate the GP ranked as the consumers first choice of GP. We present the results from two different models, correspondingly with travel indicated by the distance in kilometers and travel indicated by the travel time measured in hours. We see that all the estimated coefficients are statistically significant. If we look at the estimated effect of SPECIALIST in model 1, we see that being a specialist in general medicine has a positive effect on the choice probability. Further we see that GPs that was born in a country other than Norway ceteris paribus have lower choice probabilities compared to GPs that were born in Norway. We see that our results indicate that marital status of the GP also affect the choice probabilities and the effect seems to be of simmilar magnitude as the effect of specialist status. We see that our results also seem to indicate that individuals prefer GPs of the same gender. We see that if the consumer is a female (male), the probability of selecting a GP that is also a female (male) is higher than the probability of selecting a male (female) GP. given that all the other attributes are the same. We see that the coefficient on AGEDIFF is negative. Our results indicate that choice probabilities are declining in the age difference between the consumer and the GP. We see however that our results indicate that choice probabilities, when controlling for the age difference, are increasing in the GPs age. An interpretation of the joint result that choice probabilities are declining in age difference and increasing in the age of the GP is that consumer prefer GPs that are of approximately the same age, but a GP that is older than themselves are preferred to a GP that is younger then themselves. We see that the estimated coefficient on the indicator of accessibility, PREFLIST is positive as expected. Our interpretation is that a longer weekly opening hours as indicated by a longer preferred list, is a positive attribute of the GP. We see that the effect of increasing travel distance by a marginal kilometer is sizable compared to the other coefficients. We see that the consumer values specialist status in general medicine to the equivalent of avoiding 300 meters of travel. Calculating the marginal rate of substitution between travel time and specialist status in general medicine we find that the consumer values a specialist to the equivalent of avoiding approximately twenty seconds of travel time. 12
Table 5: Results from conditional logistic regression. No of obs=11075765 Distance model Traveltime model CHOICE Coef. Std. Err. Coef. Std. Err. SPECIALIST 0.2098 0.0141** 0.2325 0.0141** PREFLIST 0.0002 0.0000** 0.0002 0.0000** AGEGP 0.0153 0.0010** 0.0154 0.0010** AGEDIFF -0.0200 0.0010** -0.0202 0.0010** SAMEGENDER 0.5055 0.0135** 0.5083 0.0136** FOREIGNGP -0.4108 0.0183** -0.4064 0.0183** MARRIEDGP 0.2098 0.0144** 0.2188 0.0144** TRAVELDISTANCE -0.6969 0.0036** TRAVELTIME -40.8259 0.2017** OSLO1 1.0492 0.0660** 0.7362 0.0613** OSLO2 1.6121 0.0690** 1.3318 0.0642** OSLO3 1.1381 0.0680** 0.7906 0.0633** OSLO4 1.0374 0.0669** 0.7854 0.0624** OSLO5 0.6796 0.0653** 0.4107 0.0612** OSLO6 0.8601 0.0596** 0.6983 0.0561** OSLO7 1.5324 0.0747** 1.2210 0.0703** OSLO8 1.6474 0.0724** 1.2515 0.0681** OSLO9 0.1639 0.0745* 0.2725 0.0704** OSLO10 0.1588 0.0791* 0.3240 0.0751** OSLO11 0.5735 0.0500** 0.4254 0.0485** Loglikelihood -113199.24-113449.83 Pseudo R2 0.2654 0.2638 LR chi2(19) 81793.34 81292.15 P-value 0.000 0.000 Willingnes to pay for attributes of the GP Since travel distance is an attribute that may be easier to measure in monetary units than other attributes, a lot of studies within the field of environmental economics apply recreation demand models and the so called travel cost method as an alternative to contingent valuation methods when the aim is to get estimates on 13
the willingness to pay for for example changes in attributes of public goods. A survey on recreation demand models in environmental economics is given in Phaneuf and Smith (2005) while a survey on applications of travel cost methods is given in Parsons (2003). We are now ready to estimate the willingness-to pay for attributes of the GP. Remembering that the ratio of two coefficients has the interpretation of marginal rate of substitution between the two attributes, all we need in order to get a meassure of the WTP for the various attributes is a measure of the travel costs. There are a lot of difficulties with this procedure. One of the difficulties is that traveling when healthy and traveling when ill may not be the same. It is not obvious whether traveling costs are higher when ill due to the discomfort associated with traveling in the event of illness, or whether it is lower because the marginal utility of leisure is lower when the consumer is on sick-leave. Never the less travel involves both the use of time, as well as travel expenses. In the following the value of the consumers time use is set to 100 NOK per hour. We now suggest two different travel modes corresponding to one low-cost and one high-cost alternative. High cost: Taxi One suggestion on how to measure the cost of travel within an urban area in a way that incorporates both the cost of time use and cost related to distance is to measure travel costs by means of taxi fares. Taxi fares are calculated as a linear combination of time- and distance rates. In this version of the paper we apply the Taxi rate fee schedule from 2005, and discount the rates by 21.2% as indicated by the Taxi cost index provided by the the Norwegian Association of Taxi Drivers. This results in the following travel cost function: Taxi= 28 nok + 9.5 nok*kilometers + [254.50 nok + 100 nok]*hours Low cost: Private Car Another suggestion is to apply the compensation rate of 3.20 NOK per kilometers that is paid to public employees when they use their private car in work related activities. This results in the following travel cost function: 14
Private car = 3.2 nok*kilometers + 100 nok*hours In table 6A and 6B we present a description of the two travelcost variables associated with correspondingly the chosen alternative and all alternatives. Table 6A: Travelcosts associated with the chosen alternative. No of obs=25345 Variable Obs Mean Std. Dev. Min Max PRIVATE CAR 25345 12.55 14.87 0.00 112.00 TAXI 25345 67.71 47.05 28.00 383.55 Table 6B: Travelcosts across all alternatives. No of obs=11075765 Variable Obs Mean Std. Dev. Min Max PRIVATE CAR 11075765 40.87 22.25 0.00 143.84 TAXI 11075765 157.14 70.21 28.00 484.99 The results from conditional logistic regression with the two suggested travel costs variables are given in table 7. 15
Table 7: Results from conditional logistic regression with travel costs. No of obs=11075765 Private car model Taxi model choice Coef. Std. Err. Coef. Std. Err. SPECIALIST 0.2184 0.0141** 0.2194 0.0141** PREFLIST 0.0002 0.0000** 0.0002 0.0000** AGEGP 0.0153 0.0010** 0.0153 0.0010** AGEDIFF -0.0201 0.0010** -0.0201 0.0010** SAMEGENDER 0.5066 0.0136** 0.5067 0.0136** FOREIGNGP -0.4085 0.0183** -0.4083 0.0183** MARRIEDGP 0.2124 0.0144** 0.2127 0.0144** PRIVATE CAR -0.1435 0.0007** TAXI -0.0453 0.0002** oslo1 0.9851 0.0650** 0.9736 0.0649** oslo2 1.5621 0.0681** 1.5522 0.0679** oslo3 1.0616 0.0671** 1.0487 0.0669** oslo4 0.9861 0.0660** 0.9768 0.0659** oslo5 0.6185 0.0646** 0.6084 0.0644** oslo6 0.8289 0.0590** 0.8229 0.0589** oslo7 1.4548 0.0739** 1.4428 0.0738** oslo8 1.5528 0.0716** 1.5378 0.0714** oslo9 0.2209 0.0739** 0.2259 0.0737** oslo10 0.2186 0.0785** 0.2252 0.0783** oslo11 0.5333 0.0498** 0.5273 0.0498** Log likelihood -112942.2-112936.01 Pseudo R2 0.2671 0.2671 LR chi2(19) 82307.41 82319.79 P-value 0.0000 0.0000 From the estimated coefficients in table 7 we are able to calculate the representative consumer s willingnes-to-pay for partial changes in the attributes of GPs. The results from these calculations are given in table 8. 16
Table 8: Estimates of willingness-to-pay for partial changes in GP attributes (Norwegian kroner). Travel costs Low (Private car) High (Taxi) SPECIALIST 1.52 4.84 PREFLIST 0.00 0.00 AGEGP 0.11 0.34 AGEDIFF -0.14-0.44 SAMEGENDER 3.53 11.19 FOREIGNGP -2.85-9.02 MARRIEDGP 1.48 4.70 If the suggested travel costs are representative for a representative consumer travelling to the GP, the willingness to pay for consulting a specialist is in the range between 1.52nok to 4.84NOK per visit. We note that when the general practitioner scheme was implemented the patients paid the same out of pocket fee when consulting a specialist in general medicine as when consulting a GP that is not a specialist. From July 2005 the patients needed to pay 25 kroner extra per consultation when seeing a GP with specialization compared to a GP without the specialization. Our results indicate that a representative individual s willingness-to-pay for consulting a GP with specialist status might be considerably lower than the new out of pocket fee introduced. We see that an estimate of the willingness to pay for not having to go to a non-norwegian GP is within the range 2.85nok to 9.02NOK. We see that the consumer has a higher willingness to pay for consulting a GP that has the same gender as the consumer as compared to the willingness to pay for consulting a specialist in general practice. We see that the estimated willingness to pay for consulting a a GP with the same gender is within the range 3.53nok to 11.19NOK. 6 Discussion and conclusion The value or importance that decision makers place on each attribute of the alternatives will in general show variation over decision makers. A weakness of the 17
logit model is that it can not handle random taste variation. The logit model can however represent taste variation of decision makers as long as tastes variation is related to observable characteristics (Train, 2003). In this paper we have handled some taste variation, by taking account of the possibility that attributes of a GP such as the GPs gender does not affect a male decision maker in the same way as a female decision maker. Most likely however there is a lot of taste variation that is not taken account of in this paper. For instance the taste for GPs that are specialists in general medicine is likely to vary across decision makers with different income levels and different levels of education. In the data set applied in this paper, we are fortunate to have information on the decision makers income, wealth and education available. Unfortunately, these variables can not be compressed as much as dummy variables, and in this version of the paper we had to delete these variables due to limits on the available computer resources. In the next version of the paper, heterogeneity in taste that relates to income, wealth and education of decision makers will be given more attention. In this paper we have devoted little attention to the fact that it was voluntary to return the entry form ranking the three most preferred GPs. If the set of decision makers who returned the entry form differs systematically from those who refrained from returning the entry form, we must be careful with interpreting the effect on the choice probabilities as effects on market demand. If there are heterogeneity in tastes such that the inhabitants who refrained from returning the entry form are indifferent to for instance the GPs birth country, our approach would exaggerate the effect of birth country on the market demand facing the GP. In the next version of the paper, the aim is to also estimate the effect of inhabitants characteristics on the probability of submitting the entry form and thus the probability of entering the estimation sample applied in this version of the paper. Our results confirm all the results by Lurås (2003). Lurås found that choice probabilities are higher when the GP is a specialist in general medicine and when the GP and patients have the same gender. Lurås also found a positive effect of the GPs preferred list size and of the GPs age, while the effect of age difference between patient and GP was found to be negative. It seems reasonable to conclude that consumer s choice of GP was not random. Further there is evidence in the data suggesting that consumers prefer GPs that 18
resemble themselves on observable characteristics. Our somewhat rough calculation of the willingness to pay for consulting a specialist in general medicine seems to indicate that the willingness to pay is lower than the extra fee introduced in 2005. From welfare theory we know that if the marginal income of the suppliers exceeds the consumers willingness to pay, we are in a sub optimal equilibrium with excess supply. An implication of the results in this study may thus be that the supply of specialists in general medicine now and in the future is likely to be higher than what is socially optimal. 19
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