Health Is care really a luxury?
By A.G. Blomqvist, R.A.L. Carter Department of Economics, University of Western Ontario,London, Ont.N6A5C2,Canada Journal of Health Economics 16 (1997) 207-229. Presented by: Rubin Luniku April 19 2004 Eco 7550
Introduction
Much of previous work based on international cross-section data or on pooled cross-sections and time series has led to a view that the income elasticity of health care spending exceeds one. Here this hypothesis is re-examined in the contest of long-run relationships between non-stationary time series, including autonomous trends. Results cast doubt upon the notion of income elasticity above one (luxury good). A puzzling fact from aggregative c-s data is that income elasticity of the demand for health care is bigger than one. If so, then the health care falls into the luxury good category. In most cases health care spending grew faster than real income. Health care services based on "needs" or a luxury concept? The discrepancy between income elasticities estimated from individual and family data (well below unity) and from aggregative c-section or time series data is not easy to explain. The existence of public-sector insurance programmes (U.S. Medicare and Medicaid) weaken the link between income and health spending and might explain some of the discrepancy.
Once we aggregate the data the health care spending behaves as a luxury good, why is this? Possible explanation: Suggestion that the per-unit cost of health care (a labor-intensive commodity) tends to rise, relative to that of the other goods and services, as income rises. Work done by Parkin et al.(1987) in a c-section data of 18 countries with an elasticity of aggregate health care on real GDP equal to 0.90 support this idea. Instead, work by Gerdtham and Jonsson (1991 and 1992, henceforth GSJA) gave an estimated income elasticity of 1.43 and found no significant effect of the health care relative price variable. Both studies were based on a two-variable regressions of health care spending on GDP. There are substantial differences among the countries regarding the financing, monitoring the cost, and organization of health care services. GSJA used three c-sections of 19 countries each, some 6 or 7 years apart, including dummy variables to separate the three c-sections. Long enough time series were not available for all countries by that time and this was the reason for three c-sections estimates.
The GSJA equations produce estimates of the income elasticity about 1.3 and remain significantly above unity, also statistically significant upward shifts in health spending over time were found. Per capita health care spending has grown at a little above 1.5% per year in real terms after controlling for the per capita income effect. Deterministic trend. In this paper's model to capture this effect, which partially represent the technological change related to a strong cost-increasing effect in health care, a linear time trend is included. In this paper the sample of data consist of 32 annual observations for 18 countries, time series analysis is adopted when investigating the GSJA results regarding the health care-income relationship shifting over time. Testing for the presence of an independent time trend in health care spending series and also focusing on the long-run relationship between health care spending and income. To construct comparable time series for all countries, a country specific dummy variables is used to make up for omitted institutional and demographic variables considered in GSJA. The purposes of this paper are: - Test for the presence of unit roots in these series and for co integration, or the existence of long-run relationship between these two series; - distinguish between the impact upon the real health care spending of deterministic linear trends, and of real per capita income; - discover whether pooling of time series and c-section data to be more precise about the income elasticity if it is >1 or not.
The Data
The model: a simple log- linear relationship between per capita health care spending and per capita income, both in real terms. The data spanning from 1960 to 1991 for 18 countries, in PPP terms, real values were obtained by deflating nominal values by US GDP deflator. hit and yit as the natural logarithms of real US dollar per capita values of health care spending and income in country i in year t, and ait the percentage of the population 65 years or older in each of countries. Replicating previous results: Using the OLS to csections of data on 18 countries to investigate whether the income elasticity for the health care spending was above one. The model used to test this was:
Year
a0 s.e. () -4.52 (.425) -4.44 (.364) -5.75 (.425) -5.92 (.54) -5.1 (.51)
a1 s.e. () 1.36 (.12) 1.37 (.08) 1.65 (.08) 1.71 (.10) 1.59 (.12)
a2 s.e. () -.0183 (.020) -.014 (.014) .0047 (.008) -.002 (.014) -.026 (.01)
R
2
DW
Reset
1960
.908
2.37
.431
1967
.907
1.70
.325
1975
.937
1.98
.617
1983
.914
2.17
.462
hit = 0 + 1 yit + 2 ait + uit for i = 1...18.
The OLS estimates were: see table1. The results seem to support the view that the income elasticity of demand for health care is >1.
1991
.837
1.97
.068
However, if we look carefully the point estimates and intercepts become larger in later years, implying a MA process and probably non-stationary time series over time. Also the non expected negative signs of the a2 in 4 out 5 years cast doubt upon the role of people aged 65 and over in health care spending. Analysis if individual country series: Since per capita health care spending and income are non-stationary series, perhaps around a linear trend, it suggest that conventional methods used in estimating the long-run relationship between them may have yielded misleading results. If a variable is not stationary, it is described as being I(1), integrated of order one, and then we have to check whether the first differences are stationary, so I(0). So the first stage of econometric analysis in this paper was to see whether both series hit and yit are I(1) for each country. This is done by investigating the autocorrelation and PAF for each series and its first difference. By applying the Phillips-Perron technique to test the null hypothesis of a unit root existence against the alternative on the regression: xt = 0 + 1 * t + 2 * xt -1 + u t (2)
Where xt is either hit or yit or their first difference. Like Dickey-Fuller procedure it produces two test statistics, a Z-statistic and a t-ratio. The results are given in table 2 for both levels and first differences.
Table 2. Phillips-Perron test statistics.
Statistic hi"
Yi,t
Level
1 st diff.
Level
1 st diff.
Australia
t Z
- 0.95290 - 2.6889 - 24.549
-4.5100
- 0.69246 - 1.8547 - 25.452
- 4.4567
Austria
t Z
- 0.97920 -3.0605
- 4.4206 -24.116
-0.72726 -1.4041 - 32.348
- 5.4923
Belgium
t Z
- 0.79604 -2.1179
:- 3: 7614 -18.068
-2.0897 - 3.5250 -29.503
- 5.5812
Canada.
t Z
-2.0025 -6.1443
-4.9884 - 27.858
- 1.1763 - 5.3470 - 24.459
-4.0166
Denmark
t Z
-4.0767 -5.6726
-6.2843
-3.4624 -12.123
-6.0769 - 30.240
- 26.988
Finland
t Z
- 2.1290
-3.7341 - 20.934
- 4.0830 -23.354
- 3.0443
- 3.9952 - 35.398
France
t
-
-6.1580
2.9619
- 2.2068
-4.4763
Z
- 2.8858
-29.977
- 3.0197
- 22.022
Levin and Lin in (1993) developed a test of the null hypothesis that there is a unit root, in addition to an intercept and a linear trend, in every series of a pooled set. This test was conducted for all the hit and yit series jointly. The values of test statistics, asymptotically N(0,1), were -.326 for hit set and -.360 for yit set, both not rejecting the null (2 = 0), and concluding that hit and yit are I(1) around a linear trend. The next stage is to check whether the pairs hit and yit are cointegrated for each country. This is done following the Engle and Granger procedure. Test for root unit test in the residuals from the least squares fit of hit on yit. Also in order to reduce the least squares biases due to a short finite sample, the residuals are taken from dynamic regressions like: (3)
h = + * y +
it 0 ,i i ,1 i ,t
i,2
*y
i ,t - 1
+ * y
i ,3
i ,t - 2
+ * hi ,t -1 + * hi ,t - 2 + * t + i ,t
i,4 i ,5 i ,6
^ In test regressions: t = * - + t ^t 1 u
(4)
Then a test of Ho: =0, a unit root test so that the series is I(1), is a test for the failure of cointegration. The results of such a test are in table 3.
Table 3 , Cointegration t-ratios using Phillips-Perron procedure.
country Australia Austria Belgium Canada Denmark Finland France Germany Greece Iceland Italy
T-ratio -5.4885
Japan
-5.3878
Netherlands -5.662 -5.7648 -4.748 -5.7588 -5.4424 -5.7 -5.244 -5.158 -6.847 -6.195 USA Switzerland Norway
-5.329
-5.346
Sweden
-4.930
-5.240
UK
-5.678
-6.869
Estimated critical values:
1%, -4.9: 5%, -4.12: 10% , -3.749
As we can see from the table 3 results we reject the null Ho:(=0) of no cointegration at 5% level for all
countries. Even though the dynamic eq.(3) is an improvement over a static regression still the OLS estimators are not asymptotically efficient and unbiased.
h
i ,t
= 0,i + 1,i * t + 2,i * y + wi ,t
i ,t
(5)
The tests for cointegration are repeated using the residuals from the equation (5) and getting consistent estimates of the autonomous growth and elasticity for country i. Still the estimators on elasticity are asymptotically biased and inefficient as T. Two other steps are required to avoid these pitfalls: -First, to eliminate the serial correlation between wit and yit leads and lags of yit must be added to the right side of eq.(5). -Second, adjustment accounting for the weak dependence of wit, in order to make the remaining error serially uncorrelated to independent variables, and then apply least squares. The model for the long-run equilibrium for country i was: J K (6) hi ,t = 0,i + 1,i * t + 2,i * y + * y + wi ,t - j + vi ,t
2
i ,t
k =- K 1
k ,i
i ,t -k
j =1
j ,i
The equation(6) is nonlinear. High values of K1 and K2 uses up the degrees of freedom and it becomes relevant here cause the sample is small and in this sense a compromise was to set K1=K2=2. The value of J is related to having white noise residuals.
Adding the logit transform of age variable in the eq.(6) showed not to be significant for all countries. The results for this equation show that none of the DW (Durbin-Watson under null is N(2,4/T) or BL (Box-Ljung under null is with five d. of freedom ) statistics values is large enough to reject the null hypothesis that of an independent errors.
2
The conclusion from table 3 that the cointegration holds for each country is confirmed even if the Shin (1994) test on cointegration is used instead of the Phillips-Perron test. The estimates of the deterministic trend coefficient 1,i and elasticity estimates 2,i are imprecise and vary widely in magnitude among the countries. In response to this imprecision and to increase the sample size the pooling of the time series across countries was studied. Pooling Cointegrated Series : For each country the pair hit and yit are cointegrated, with a deterministic trend, and then each country's error is: wi ,t =hi ,t -.i -,i * t - ,i * yi ,t 0 1 2 (7) By stacking the wi vectors on top of one another we get a 576X1 vector w eq.(9) . Pooling involves imposing restrictions (10) and (11) that all 1,i and 2,i for i=1...18, are the same for each country. If these restrictions are correct then the final equation (7) can be written as (12): (12)
h = 0 ,i * d i + 1 * s + 2 * y + w
1
18
Where: di are dummy variables, y is 576x1 vector of stacked yi vectors, and s is formed by stacking 18 versions of si. If the restrictions (10) and (11) are correct then w will be I(0), and a test for cointegration in a pooled regression is also a test of the validity of the pooling restriction. The first step in pooled estimation is to estimate all parameters of eq.(9) without imposing the pooling restrictions. From the values of DW and BL statistics we have no indication of autocorrelated errors and also the null hypothesis of cointegration could not been rejected. The estimates are now more precise, but still exists considerable variation among the results for different countries. Now by including both restrictions (10) and (11), with single variables s and y for each country, implying that all parameters from (12) should be the same across all equations. The result of pooled estimation was:
(13)
h = 0,i * d i + 0.0203 * s + .976 * y + w
1
18
The intercepts were left unrestricted in the hope of estimating the country-specific effects, last line of table 6. The r...