ties; we still have rationing and the amount of rationing depends on the physician preference parameter. In physician-dense municipalities, we now have SID. In
these municipalities, the extent to which contract physicians care about their patients has no effect on whether SID takes place, but affects the amount of
inducement; the more contract physicians care about patient utility, the lower is
Ž
M D
. the amount of inducement c y c
. Consider now the policy-maker’s decision problem. In order for policy-makers
to be able to compute the physician density which maximizes social welfare for a given fee structure, they need to have information about demand and supply
functions. In practice, policy-makers have limited information about the parame- ters of the model; as mentioned in the introduction, there is not even agreement
about whether SID exists at all. However, if we accept the assumption that surveys provide information about patient utility, then the policy-maker can use surveys to
examine whether physician density is too high or too low.
Suppose that the social welfare function is equal to the utility of a representa- tive patient minus the cost of state expenditure per patient, and that consultations
are determined by the physicians. Then the policy-maker prefers the physician density which maximizes:
U yc
S
D ,c
S
D y gp
S
c
S
D
Ž . Ž .
Ž .
Ž .
where g is the marginal cost of public funds; g captures the deadweight loss of taxes as well as administrative costs. The first-order condition can be written as:
S S
S
U Ec rED s U q gp E
c rED . 4
Ž .
Ž .
Ž .
c I
Ž . Ž
. The right-hand side of Eq. 4 is the total private q public marginal cost of
physician density and can be computed from aggregate data on consultations and Ž
. other primary care services provided g is known . The left-hand side is the
marginal patient utility of physician density and can be computed from surveys provided that reported satisfaction is a valid proxy for patient utility. Thus, even
with limited information about the market for primary physician services, includ- ing whether SID takes place, the policy-maker can use surveys to examine whether
the marginal utility of physician density is higher or lower than the marginal cost of physician density and thus whether physician density is above or below the
social optimum.
3. Data and empirical specification
The rest of the paper employs a large survey data set gathered by the Norwegian Gallup Institute to study the relationship between physician density
and consumer satisfaction with primary physician services. Each year since 1993, a random sample of 15–20,000 individuals have received a questionnaire where
they were asked to rank various aspects of municipal services including primary
physician services. For the years 1993–1997, 72,186 respondents returned the questionnaire. We excluded individuals from municipalities with only employed
physicians, individuals who did not answer all questions about personal character- Ž
. istics age, gender, etc. and individuals who belonged to municipalities where
characteristics of the municipal population was missing. This left us with a sample of 55,549 individuals. The response rates for the questions on primary physician
Ž .
services were in the range 49–72 Table 1 . Since patient fees are regulated by the state, there are two potential ways that
physician density can affect consumer satisfaction. First, more physicians may imply better access to care through lower waiting time and lower travelling costs.
The questionnaire contained two questions about access to care. The exact wording of the questions is given in Table 1. Secondly, more physicians may
imply better quality of care because physicians are able to pay more attention to the problems of each patient, including spending more time with the patient. The
questionnaire contained four questions about quality of care. Finally, the question- naire contained one question about general satisfaction with primary physician
services. The respondents were asked to rank their answers on a scale from 0 to 5, where 5 is ‘ very satisfied’ and 0 is ‘ very dissatisfied’. The respondents were told
to relate the answers to their personal experience if they had seen a primary
Table 1 Ž
. Description of patient satisfaction summary statistics
Ž Variables
Question How Mean
Number of Ž
satisfiedrdissatisfied Standard
respondents .
. are you with:
deviation Access
Ž .
Waiting time waiting time to
2.63 1.65 38,110
get an appointment Ž
. Distance
travelling distance 3.79 1.19
35,472 to the physician’s
office Quality
Ž .
Communication information about
3.60 1.25 27,022
diagnoses and treatment Ž
. Friendliness
the way you were 3.70 1.26
35,016 received at the office
Ž .
Professional skills the physician’s
3.88 1.05 37,467
professional skills Ž
. Outcome
the outcome 3.66 1.21
33,588 of treatment
General satisfaction Ž
. General satisfaction
the primary 3.59 1.26
40,006 care physician
physician recently. If they had not seen a primary physician recently, they were told to report their general impression of the primary physician services within
their municipality. As the respondents’ answers are ordered discrete numbers, we estimated the
following ordered probit model for each dependent variable: SAT
s PERS b q b DENS q MUN b q ´ q ´ ,
ji t ji t
1 2
i t i t
3 i t
ji t
SAT s 0 if SAT F m ,
ji t ji t
1
SAT s 1 if m G SAT m ,
ji t 2
ji t 1
SAT s 5 if SAT m
ji t ji t
5
where SAT is the evaluation of respondent j in municipality i and year t,
ji t
PERS is a vector of personal characteristics, DENS
is physician density in
ji t i t
municipality i and year t, and MUN is a vector of municipality characteristics
i t
other than physician density which may affect demand for and supply of primary physician services. The error terms, ´
and ´ , are assumed to be independent
i t ji t
and normally distributed with constant variance; ´ captures random disturbances
i t
common to all respondents in municipality i and year t. The ms are unknown parameters to be estimated with the b s. We used LIMDEP 7.0 to estimate the
ordered probit model. Due to software limitations, the municipal error term, ´ ,
i t
was set to zero when the model was estimated on the full data set or large Ž
. subsamples Tables 3–5 . The ordered probit model with municipal error term was
Ž .
estimated for a smaller subsample Table 6 . Table 2 presents variable definitions and summary statistics of the explanatory
variables. The personal characteristics include dummy variables for age, gender, marital status, education, and family income. Physician density was defined as
primary physician person years per 10,000 inhabitants. The other municipal characteristics were similar to control variables included in earlier studies of
Ž .
satisfaction for a review see: Pascoe, 1983; Cleary and McNeil, 1988 . Firstly, they measured supply of other health services which may affect the demand for
primary physician services: person years of other personnel in primary health care, person years of personnel in care for the elderly and whether there was a hospital
in the municipality or not. The two former variables were scaled by the municipal- ity’s population and the population above 67 years of age, respectively. The
proportion of employed physicians in the municipality was also included as a control variable since employed physicians have weaker financial incentives to see
patients than fee-for-service physicians. Many rural municipalities are character- ized by a high turnover as well as considerable variability in demand for primary
physician services. These municipalities frequently use fixed salary contracts as an instrument to recruit and retain physicians. Therefore, the proportion of employed
physicians may also pick up the impact of physician turnover on consumer satisfaction.
F. Carlsen,
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Table 2 Independent variables
Independent variables Definition
Mean Ž
. Standard deviation
Variables at the leÕel of the indiÕidual Respondent’s age 1
1 if the respondent’s age is between 30 0.61
Ž .
and 59 years Reference category: - 30 years Respondent’s age 2
1 if the respondent’s age is G 60 years 0.21
Ž .
Reference category:- 30 years Respondent’s gender
1 if male 0.51
Respondent’s marital status 1 if married
0.71 Respondent’s level of education 1
1 if the respondent’s highest level of education 0.47
Ž .
is high school Reference category: primary education Respondent’s level of education 2
1 if the respondent’s highest level of education 0.30
Ž .
is college or university Reference category: primary education Ž
. Respondent’s family income
1 if respondent’s family income G NOK 300,000 £25,000 0.56
Variables at the leÕel of the municipality Ž
. Physician density
Primary care physician person years per 10,000 inhabitants 7.87 1.91
Ž .
Other personnel Person years of other personnel categories in
16.59 7.04 primary health care per 10,000 inhabitants
Ž .
Care for the elderly Input of person years in care for the elderly
0.10 0.03 per inhabitant above 67
Dummy for hospital 0.18
Ž .
Proportion of employed physicians Employed physician person years scaled
0.26 0.26 by primary care physician person years
Ž .
Population Population size
13,047 33,904 Dummy for town
1 if town with more than 10,000 inhabitants 0.28
within 30 min driving Dummy for Northern Norway
1 if municipality located in Nord-Trøndelag, 0.12
Nordland, Troms or Finnmark Ž
. Ž
. Travelling time
Mean travelling time to municipality centre in min 12.84 8.81
Ž .
Mortality Mean number of annual deaths per 100,000
913.8 111.3 inhabitants during 1990 – 1995, adjusted for variation in age
composition Ž
. Welfare clients
Number of welfare clients scaled by population above 15 0.04 0.01
Ž .
Education Number of inhabitants with completed colleger
0.10 0.03 university scaled by population above 15
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Table 3
2
Ž .
Determinants of satisfaction with primary physician services. Ordered probit regression. Wald x test statistics absolute values below the regression
coefficient The second column for each dependent variable includes only explanatory variables which are significant at p- 0.05.
Dependent variables Waiting time
Distance Communication
Variables at the leÕel of the indiÕidual Respondent’s age 1
0.19 0.19
0.16 0.16
0.30 0.30
169.2 170.1
107.8 111.4
263.2 274.2
Respondent’s age 2 0.60
0.60 0.41
0.40 0.77
0.77 1070
1108 433.5
438.7 1174
1215 Respondent’s gender
0.007 y0.08
y0.08 y0.11
y0.11 0.43
51.66 51.8
83.90 83.66
Respondent’s marital status y0.05
y0.05 y0.01
y0.002 16.80
17.68 0.71
0.03 Respondent’s level of education 1
y0.06 y0.06
y0.04 y0.04
y0.08 y0.08
18.73 18.62
9.97 9.89
23.99 24.21
Respondent’s level of education 2 y0.06
y0.06 y0.06
y0.05 y0.10
y0.10 17.65
17.60 12.56
11.58 30.15
32.22 Respondent’s family income
0.002 0.02
0.001 0.05
2.55 0.006
Variables at the leÕel of the municipality Physician density
0.059 0.059
0.026 0.026
0.022 0.022
209.4 210.7
35.13 36.07
17.81 19.62
Other personnel y0.003
y0.003 0.001
0.001 9.67
9.63 1.51
0.59 Care for the elderly
y0.70 y0.70
y0.42 y0.44
0.01 14.50
14.66 4.81
5.38 0.003
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741 Dummy for hospital
0.11 0.11
0.03 0.04
0.10 0.10
62.74 65.36
5.91 8.27
32.46 38.16
Proportion of employed physicians y0.21
y0.21 y0.04
y0.17 y0.17
59.37 59.53
2.31 24.54
28.17
y7 y7
y7 y7
y7 y7
Population 5.60=10
5.60=10 3.45=10
3.68=10 y1.71=10
y1.69=10 69.60
69.63 23.57
31.43 4.67
6.55 Dummy for town
0.11 0.11
0.08 0.08
0.09 0.09
68.40 68.77
32.46 36.14
26.17 34.36
Dummy for Northern Norway y0.17
y0.17 0.06
0.06 y0.03
91.66 91.92
13.05 14.40
1.91 Travelling time
y0.002 y0.002
y0.01 y0.01
y0.005 y0.005
12.47 12.50
189.7 201.6
41.02 45.06
Mortality y0.0008
y0.0008 y0.0004
y0.0003 y0.0005
y0.0005 114.4
115.1 27.22
25.22 33.06
41.20 Welfare clients
1.55 1.55
0.75 2.66
2.70 8.65
8.69 1.74
15.71 19.10
Education y0.83
y0.84 y0.98
y0.98 y0.09
23.30 24.97
28.88 31.61
0.20 Ž .
Mu 1 y0.84
y0.84 0.09
0.11 y0.66
y0.66 129.9
129.8 1.25
2.16 50.10
60.21 Ž .
Mu 2 y0.14
y0.14 0.96
0.99 0.26
0.26 3.80
3.64 144.0
168.6 8.14
9.74 Ž .
Mu 3 0.35
0.35 1.63
1.66 0.94
0.94 22.76
23.39 409.7
470.8 102.6
122.9 Ž .
Mu 4 0.78
0.78 2.18
2.20 1.49
1.49 112.1
114.0 718.9
819.7 255.7
306.2 Ž .
Mu 5 1.32
1.32 2.65
2.68 2.00
2.00 317.1
321.0 1044
1183 450.9
538.4 Concordant
0.60 0.60
0.58 0.58
0.61 0.61
p- 0.05. p- 0.01.
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Friendliness Professional skills
Outcome General satisfaction
0.25 0.25
0.22 0.22
0.16 0.17
0.26 0.26
255.0 254.6
209.7 227.0
105.0 114.3
316.4 333.2
0.73 0.73
0.66 0.67
0.59 0.59
0.84 0.84
1353 1399
1173 1220
866.2 892.9
2070 2132
y0.12 y0.12
y0.18 y0.18
y0.14 y0.14
y0.20 y0.20
109.9 112.4
282.7 283.1
149.7 148.3
364.6 366.1
y0.01 0.01
0.004 0.002
0.71 1.98
0.11 0.03
y0.10 y0.10
y0.10 y0.10
y0.07 y0.07
y0.15 y0.15
45.53 46.96
52.20 50.65
25.52 24.52
111.9 111.0
y0.15 y0.16
y0.20 y0.19
y0.14 y0.13
y0.22 y0.22
85.99 97.02
141.5 140.2
67.53 64.61
201.3 201.2
y0.01 y0.03
y0.02 0.01
y0.02 y0.02
1.13 7.28
5.34 2.24
6.02 5.98
0.030 0.030
0.026 0.026
0.017 0.017
0.035 0.035
45.77 48.12
39.04 40.10
15.44 15.79
74.75 76.53
0.001 y0.0007
0.0002 y0.0003
0.76 0.57
0.02 0.11
y0.01 0.07
0.14 y0.49
y0.49 0.007
0.15 0.51
7.19 7.44
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743 0.08
0.07 0.09
0.09 0.08
0.09 0.08
0.08 27.66
29.21 40.25
47.54 31.26
39.50 37.90
35.58 y0.21
y0.20 y0.19
y0.21 y0.11
y0.11 y0.21
y0.23 47.49
49.93 43.28
58.19 13.48
15.27 56.61
74.00
y7 y7
y8 y8
y8
y2.09=10 y2.19=10
y8.79=10 y8.47=10
y7.72=10 8.69
13.00 1.58
1.38 1.32
0.10 0.10
0.11 0.11
0.09 0.09
0.12 0.13
48.43 58.39
55.52 82.89
39.07 51.52
79.75 88.90
y0.03 y0.03
y0.04 y0.03
y0.03 2.59
2.93 5.64
4.23 3.57
y0.005 y0.005
y0.005 y0.006
y0.006 y0.006
y0.004 y0.005
50.66 58.48
47.52 60.75
50.07 62.21
38.62 47.77
y0.0005 y0.0005
y0.0004 y0.0003
y0.0004 y0.0003
y0.0007 y0.0007
40.00 43.98
28.74 30.84
24.34 22.70
93.06 95.08
1.71 1.85
1.03 1.15
2.42 2.12
8.91 11.75
3.61 3.91
21.12 19.16
y0.15 y0.37
y0.50 y0.41
y0.48 y0.85
y0.93 0.68
4.21 12.49
4.83 10.62
24.76 39.59
y0.32 y0.35
y0.35 y0.34
y0.32 y0.28
y0.10 y0.07
15.64 24.45
21.70 23.56
15.77 15.25
2.19 1.09
0.57 0.53
0.69 0.70
0.63 0.67
0.77 0.81
49.93 54.86
82.50 99.18
60.08 83.91
110.6 139.7
1.20 1.16
1.49 1.50
1.37 1.40
1.49 1.52
220.6 260.2
378.5 446.4
277.1 363.3
406.7 490.6
1.71 1.67
2.06 2.07
1.86 1.90
2.06 2.09
443.3 531.6
708.1 829.5
509.8 657.4
771.5 917.0
2.17 2.13
2.49 2.50
2.30 2.34
2.55 2.58
701.8 847.2
1007 1172
764.1 974.2
1161 1367
0.61 0.61
0.61 0.61
0.59 0.59
0.62 0.62
Table 4 Impact of physician density on satisfaction in lowrhigh physician density municipalities. Ordered
probit regression. Only coefficients for physician density are displayed. Wald x
2
test statistics Ž
. absolute values below the regression coefficient. High physician density area: Physician density
7.56
2
Low physician High physician
Wald x
a
density density
test statistics municipalities
municipalities Dependent Õariables
Waiting time 0.084
0.084 0.20
52.34 125.8
Distance 0.060
0.012 12.03
22.39 2.14
Communication 0.054
0.013 6.30
11.20 2.09
Friendliness 0.052
0.028 1.25
17.20 12.09
Professional skills 0.039
0.025 0.67
10.86 11.04
Outcome 0.036
0.009 1.70
7.76 1.17
General satisfaction 0.072
0.036 7.19
38.58 22.93
a 2
Ž .
Wald x test statistics absolute values refer to the interaction term between physician density
and a dummy variable for high physician density municipalities in pooled regressions. p- 0.05.
p- 0.01.
Second, the control variables measured demographic characteristics of the municipalities which may affect accessibility to primary physician services. The
following variables were included: population size, dummies for town and North- ern Norway, and the mean travelling time to the municipality centre. Third, the
control variables measured the health status of the population. The following variables were included: mortality rate, proportion of welfare clients and average
education level. All variables at the level of the municipality were obtained from the Norwegian Social Science Data Service.
4. Results and discussion
