Do tobacco taxes reduce lung cancer mortality?* by José Julián Escario** José Alberto Molina¹** DOCUMENTO DE TRABAJO 2000-17

September, 2000

* This paper was partially written while José Alberto Molina was Visiting Researcher at the Foundation for Applied Economic Studies-FEDEA (Madrid, Spain). He is very grateful for the hospitality and facilities provided by this institution. The authors would also like to express their thanks for the financial support provided by the Spanish Ministry of Education-CICYT and the European Commission (Project 2FD97-2057).

** Department of Economic Analysis, University of Zaragoza.

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¹ Corresponding author: Dr. José Alberto Molina. Departamento de Análisis Económico. Facultad de Ciencias Económicas y Empresariales. Gran Vía, 2. 50005 Zaragoza. Spain. Tfo: 34-976-761818. Fax: 34-976-761996. E-mail: jamolina@posta.unizar.es

In this paper we have carried out a quantitative evaluation of the effects of special tobacco tax policies on smokers' health. Specifically, the results show that tobacco taxes would appear to be a useful tool for reducing long cancer mortality related to tobacco consumption. Thus, a 10% increase in tax will reduce tobacco consumption by 3.8% in the first year, which will give rise to a 1.12% reduction in the lung cancer mortality rate, a reduction which, in the long term, will be in the order of 8.81%. For the twelve European Union countries being considered, this means that 1,707 deaths will be avoided in the first year, 4,491 in the fifth year and 12,366 after the smoking population has been completely renewed.

JEL classification: I18, I12

Keyords: Tobacco taxes; Lung cancer; Avoidable mortality.

1. Introduction

After the appearance in 1964 of the first official report in the United States to recognise the harmful effects of tobacco consumption on smokers, entitled The Surgeon General's Report on Smoking and Health, practically every Western government began its own battle against such consumption. This is a battle which has been growing in intensity over the years and which has been especially stimulated by the proposals made by a series of social collectives demanding ever-greater government intervention against tobacco. These groups have requested a series of policies aimed at reducing tobacco consumption, and therefore its harmful effects by, for example, limiting advertising or the number of places in which smoking is permitted. At the same time, governments have promoted information campaigns warning of the harmful effects of tobacco consumption, or have established a series of special taxes which have raised the price of tobacco.

If we concentrate on the fiscal aspect, it is well known that special taxes on consumer goods should only be applied when the benefits deriving from them make-up for the negative effects they generate in terms of the overall efficiency of the economy. Therefore, the principal argument justifying the levying of this type of specific tax on tobacco consumption is the need to internalise the external costs arising from such consumption. This means, in fact, charging smokers for the external costs that they impose on nonsmokers. Thus, given that tobacco consumption is an obvious determining factor in the appearance of different diseases (bronchitis, cardio-vascular disorders, emphysemas, malignant tumours in the lung, trachea, larynx, oesophagus, etc.), such consumption is accompanied by the use of medical and health services by smokers, whose cost obviously constitutes an external cost which tobacco consumers impose on non-smokers. This justification for special taxes has given rise to a relatively extensive empirical literature on the subject, which has traditionally concentrated on analysing the effects of these taxes on consumption (Lewit and Coate, 1982; Kao and Tremblay, 1988; Chaloupka, 1991; Becker et al., 1994; Chaloupka and Wechsler, 1997), but has ignored the study of the effects of these levying policies on smokers' health.

Thus, if we consider that the governments in different countries can limit their populations' health problems by proposing economic measures to reduce tobacco consumption, the objective of this paper is to make a quantitative evaluation of the effects of special tobacco tax policies on smokers' health. As a measure of the harmful effects on health arising from tobacco consumption, we chose the mortality rate from malignant tumours of the lung, trachea and bronchi (hereafter mortality rate from lung cancer), since this is an objective indicator, exempt from potential measurement errors. In fact, our aim is to determine whether special tobacco taxes are a useful tool for reducing the lung cancer mortality rate and, therefore, an appropriate instrument for improving the population's health.

Against this background, we first formulate a theoretical model which relates tobacco consumption with the probability of death as a consequence of such consumption. This will enable us to analyse the effects of variations in consumption on the lung cancer mortality rate. Additionally, we specify two econometric models. In the first of these, we make empirically explicit the theoretical functional relationship obtained between tobacco consumption and the lung cancer mortality rate, while in the second, we quantify the relationship between this consumption and special tobacco taxes. Joint consideration of these two econometric specifications will enable us to finally meet the objective of this study, which is to evaluate the effects of special tobacco taxes on smokers' health. The statistical information used includes a pool of observations for twelve European Union countries covering eleven years, from 1983 to 1993. The two econometric specifications will then be estimated by ordinary least squares, by introducing into the first case a simultaneous correction by heteroscedasticity and autocorrelation, while in the second econometric relationship we shall introduce a correction due solely to the temporal nature of the set of observations. Finally, after obtaining all the empirical results, and also using the implications of the theoretical model, we simulate the avoidable mortality for the sample countries in a tax scenario which supposes an increase of 10% in tobacco taxes.

Following this introduction, in the next section we develop the theoretical model which shows the relationship, both short and long term, between tobacco consumption and lung cancer mortality. In Section 3 we describe the statistical information used in the empirical analyses. Section 4 includes the specification, estimation and results of the econometric models that show the relationship between tobacco consumption, mortality rate and taxes. In Section 5 we use the theoretical and econometric results to simulate avoidable mortalities in response to tax increases. Finally, Section 6 closes the paper with a summary of the principal conclusions.

2. The theoretical model

It is well known that tobacco consumption is a determining factor in the appearance of lung cancer, and therefore has a significant influence on mortality from this illness. Thus, the more tobacco a smoker has consumed during his/her life, the greater the probability of suffering lung cancer. We also know that similar levels of consumption do not cause the same effects on the health of all smokers, since each individual has a maximum value or threshold which indicates the maximum amount of tobacco consumption that may be undertaken before the said smoker dies.

The threshold of individual consumption, u, depends firstly on the physical characteristics of the person, in the form of the initial state of health that he/she was born with, and secondly, on his/her life style, e.g. eating habits, sporting activities, living with smokers, etc. Thus, given that this threshold is different for each individual, and although it cannot be known a priori, what we can assume is that it adjusts to a particular probability distribution, , with x being the accumulated consumption from birth up to the present. Therefore, indicates the probability of a smoker exceeding his/her threshold, and consequently dying from lung cancer. If we assume that individuals, with a life span of T periods, consume at a constant annual rate, c, then at any given moment of their lives, t, the accumulated consumption will be Consequently, the probability will enable us to calculate the number of people in a generation who die from lung cancer, and thus, if we assume that N individuals are born each year, the total number of persons, of those born t years ago, who have died for this reason will be

We can also calculate the rate of individuals in one generation who reach the threshold, and therefore die, at a particular moment in time. To that end, we first take the derivative of the number of people who die with regard to time, thereby obtaining the number of individuals who reach the threshold at a given moment, and we then divide this value by the number of people in that generation; in other words, , where is the function of the distribution density. Next, we can calculate the average rate of individuals who reach the threshold for all generations from period 0 up to that is to say, the whole population, by integrating between these two limits and dividing by T:

\[T _ {p} = \frac {1}{T} \int_ {0} ^ {T} T _ {g} (t) d t = c \frac {1}{T} \int_ {0} ^ {T} f (c t) d t\tag{1}\]

Taking this initial proposal as a basis, we then analyse the effect of a variation in tobacco consumption on the lung cancer mortality rate. We note, firstly, that a variation in the current rate of consumption will immediately produce a change in the mortality rate in the same proportion. Thus, let us assume that the mortality rate changes from to a lower rate that is to say, . When one period has passed after the rate variation, we shall have to distinguish between individuals who have been smoking for less than a year and those who have been longer-term smokers. The former, given that they began their consumption after the rate variation, have been consuming the whole time at the new rate d. However, the latter have been consuming at two rates, the latter period at rate d and all previous periods at the rate c. Consequently, the total tobacco consumption for a person of generation t will be shown by if he/she has always consumed at the new rate, or by , if the consumption has been at the two rates. Therefore, the number of people who have reached the threshold in each of the two cases will be and . Deriving these expressions with regard to time and dividing by the number of individuals making up each generation, we obtain the mortality rate corresponding to each generation for each of the two previous cases, i.e. for individuals who have been smoking for less than one year and for the remaining smokers. Thus, we can obtain the mortality rate of the population as a weighted average of the mortality rates of all generations:

\[T _ {p} = \frac {1}{T} \int_ {0} ^ {T} T _ {g} (t) d t = \frac {1}{T} \left[ d \int_ {0} ^ {T} f (c t - c \delta t) d t + d \int_ {1} ^ {T} f (c t - c \delta) d t \right]\tag{2}\]

Given that the two density functions may be expressed generically as , we can rewrite the mortality rate of the population as:

\[T _ {p} = \frac {1}{T} \int_ {0} ^ {T} T _ {g} (t) d t = \frac {d}{T} \int_ {0} ^ {T} f [ c t - c \delta \min (t, 1) ] d t = \frac {d}{T} \int_ {0} ^ {T} f (c t) d t\tag{3}\]

showing that the lung cancer mortality rate varies immediately in the same proportion as the consumption variation. In other words, if tobacco consumption manages to be reduced by a certain percentage, the number of people dying from cancer is reduced in the same proportion.

Now, in the long term, in other words, once the whole population has undergone a renewal, if the variation in consumption rate from c to d continues, then the rate at which the population reaches the threshold will be changing. Therefore, after the population has undergone a complete renewal (T generations), the population rate will be obtained using equation (1) as a basis, substituting c for d:

\[T _ {p} = \frac {1}{T} \int_ {0} ^ {T} T _ {g} (t) d t = \frac {d}{T} \int_ {0} ^ {T} f (d t) d t\tag{4}\]

We can see that the density function argument in (4) is different to that of the density function in (1), unlike the situation in (3), and so the comparison between the two population rates, which calls for evaluating the two integrals, will depend on the density function used.

We assume a defined lineal density function for tobacco consumption from 0 up to a maximum of , so that, in the lower limit, the probability of going beyond the threshold implied by lung cancer death is zero, but as the consumption increases, so does the accumulated probability, in line with the increasing section of a parabola with a minimum. This seems to be a reasonable supposition, since reduced tobacco consumption will probably not produce cancer, although this probability of death will grow more than proportionally as consumption increases. Therefore, if the population has consumed at a rate c per period, the rate of population dying from lung cancer in one period will be:

\[T _ {p} = \frac {1}{T} \int_ {0} ^ {T} T _ {g} (t) d t = \frac {c}{T} \int_ {0} ^ {T} B c t d t = \frac {B c ^ {2} T}{2}\tag{5}\]

If the consumption rate varies from c to , then the consumption of a t-year-old person, h years after this variation will be min(t,h), and therefore, after one year, , the new mortality rate will be:

\[T _ {p} = \frac {1}{T} \int_ {0} ^ {T} T _ {g} (t) d t = \frac {d}{T} \int_ {0} ^ {T} B c (t, 1) d t \cong \frac {d}{T} \int_ {0} ^ {T} B c t d t = \frac {B c d T}{2}\tag{6}\]

The comparison between these two rates shows that , in other words, the rate of people going beyond the threshold is reduced in one period by approximately the same proportion as the tobacco consumption.

Once the whole population has been regenerated, the generations will have consumed tobacco at a rate per period, and so the rate of the population reaching the threshold will be:

\[T _ {p} = \frac {1}{T} \int_ {0} ^ {T} T _ {\mathrm{g}} (t) d t = \frac {d}{T} \int_ {0} ^ {T} B d t d t = \frac {B d ^ {2} T}{2} = \frac {B c ^ {2} T}{2} (1 - \delta) ^ {2}\tag{7}\]

Therefore, comparing (5) and (7), we can see that the population rate going beyond the threshold has reduced by a percentage equal to Thus, we have obtained a relation which indicates the long-term variation of the rate at which the population is afflicted by lung cancer. Table 1 shows the percentage variation in population mortality with regard to different percentage reductions in consumption, and here we can see that small reductions in lower than , mean reductions of roughly two times. However, as the variation in consumption increases, the mortality rate also gets further away from given that the reduction in the longterm mortality for a rate of consumption is given by

Table 1

In summary, this model enables us to conclude, as a generality, that a reduction in the rate of consumption by a given percentage reduces the rate at which the population reaches the threshold by approximately the same amount in the said period, independant of the density function chosen. However, after T periods, in other words, in the long term, this reduction is duplicated, taking on a lineal density function with a positive slope.

Finally, the mortality rate, given a modification in the consumption rate, will follow the following temporal adjustment until a complete renovation of the population has taken place. Knowing that the mortality rate varies immediately in the same proportion as consumption, this mortality rate will adjust in accordance with:

\[\begin{array}{l} T _ {p} = \frac {d}{T} \int_ {0} ^ {T} B d t d t + \frac {d}{T} \int_ {0} ^ {T} B (c t - c \delta h) d t = \\ = \frac {1}{T} \left[ \frac {B c d T ^ {2}}{2} - \frac {B c d h ^ {2} \delta}{2} - b c d h (T - h) \delta \right] = \frac {B c d T}{2} + \frac {B c d \delta}{T} \left[ \frac {h ^ {2}}{2} - T h \right] \end{array}\]

\[\forall h > 0, h \leq T\tag{8}\]

with h showing the number of periods that have passed since the current consumption rate c was modified to d.

This equation shows us that immediately following the change in consumption rate, i.e. , the mortality rate will be , a result obtained previously, in line with which the population mortality rate varies immediately in the same proportion as consumption. In addition, T periods after the change in consumption rate, , the population mortality rate will be

This equation (8) also shows us the path being followed by the population mortality rate as the number of periods since modification in consumption increases. This evolution is reflected in Figure 1, in which we see that, up to period j, the population mortality rate is , with c being the annual consumption per head. Now, if consumption falls to d in this period, the mortality rate will immediately fall to , and from this point on the rate will evolve, adding to itself the second addend in (8), i.e. , which is a convex and decreasing function with respect to h.

3. Data

The data used in this study form a homogeneous pool for twelve European Union countries, namely Austria, Belgium, Denmark, Finland, France, Greece, Holland, Ireland, Italy, Spain, Sweden and the United Kingdom over eleven years, 1983-1993.

Tobacco consumption for each country was obtained from Tabacalera, S.A., the per capita values being calculated by dividing amongst the population over 15 and under 65, with this data being taken from the OECD "Labour Force Statistics". The tax rate on tobacco has been calculated by dividing the amount collected, taken from the "Revenue Statistics of OECD Member Countries" and "Impôts et Cotisations Sociales" of the OECD and EEC respectively, by the number of cigarettes. This tax rate has been deflated with a 1993 tobacco prices index obtained by dividing the nominal and real cost series of the OECD's "National Accounts Vol. II". Both the tax rate and the income have been converted to US dollars using purchasing power parities. The cancer mortality rate has been calculated as the weighted average of standardised mortality rates of men and women from cancer of the lung, bronchi and trachea calculated by the WHO. Finally, we have obtained the consumption of alcohol from the Eurostat Yearbooks

Table 2 shows the typical averages and deviations for all variables of the observations pool, while Tables 3 and 4 show the same statistical indicators by country and by year, respectively. In the first instance, if we compare the total values with figures corresponding to the different countries, we can observe the following. Belgium, Holland and the United Kingdom show the highest mean values of standardised mortality rate (per 100,000 inhabitants), 40.85, 40.59 and 39.97, respectively, well above the average figure for the observations pool, 30.9. On the other hand, the countries presenting the lowest values of this variable are Sweden and Spain, 16.55 and 23.2, respectively. With regard to cigarette consumption per head, we can see that the overall average figure, 2,663.5 is easily surpassed by the highest average values corresponding to Greece, 4,313.6 and Spain, 3,084.3, whilst Holland and Sweden are the countries with the lowest consumption figures, 2,043.3 and 2,076.3, respectively. With regard to per capita income, France, Austria and Belgium show the highest values, 25,627.5, 25,401.4 and 25,239.2, respectively, whilst the lowest figures are to be found in Greece and Ireland, 11,663.1 and 17,136.1, respectively. The highest taxes on cigarettes appear in Belgium, 0.0840 and the United Kingdom, 0.0801, a long way above the average value for the observations pool, 0.0581; whilst Spain and France are the countries with the lowest taxes, 0.0200 and 0.0443, respectively. Finally, the highest per capita consumption of alcohol appears in France and Spain, 15.94 and 14.36, respectively, whilst the lowest values are to be found in Sweden, 6.60 and Finland, 8.74.

Table 4 shows the temporal evolution of the variables considered in the analysis. Here, we can see that the standardised mortality rate has fallen regularly, from the highest values, around 31.5 in the first sample years, down to the lowest figure, 30.21 in the final year. A similar observation may be made with respect to the per capita consumption of cigarettes, which has decreased regularly from the highest value in the first sample year, 2,780.8, to the lowest figure of the final year, 2,551.1. On the other hand, per capita income has been clearly rising, with the lowest figure in the first year, 19,715.7, and the highest in the final period, 23,260.7. With regard to cigarette taxes, we can note a decreasing trend, although with oscillations, given that the highest values appear in the earlier sample years and the lowest in the final period. Finally, per capita alcohol consumption, as with cigarettes, has shown a clear downward trend, from the highest value in the first sample year, 11.74, to the lowest in the final period, 10.78.

Table 3

4. Models and empirical results

The causal relationship between tobacco consumption and cancer is clearly empirically acknowledged by the scientific community. In this respect, Bartechi et al. (1994) note that passive smoking is the cause of 17% of lung cancers in non-smokers; Yuan et al. (1996) state that the possibility of a smoker suffering cancer is nine times higher than that of a non-smoker and, finally, Moore (1995) observes that the lung cancer mortality rate is between 2 and 14 times greater among smokers than nonsmokers.

With regard to the effects of a reduction of consumption on health, studies confirm that health benefits are produced over a period of several years, sometimes more than a decade, although the benefits begin to appear fairly soon. In the case of lung cancer, studies confirm that current consumption and that of the immediately preceding year are significant variables in the explanation of lung cancer mortality. In fact, although the effects of tobacco consumption last many years, and the mortality rate caused by tobacco is the result of consumption exercised during the entire life of an individual, the mortality rate will be sensitive to recent changes in consumption, due to the fact that there will always be people who find themselves one, two, three or more periods away from their consumption threshold. Thus, a reduction in consumption will modify the mortality rate, which will reflect the improvement in health, with this observed reduction in the mortality rate mainly affecting older people. Thus, let us now go on to empirically illustrate the results of the theoretical model mentioned in Section 2, in accordance with which the mortality rate is sensitive to the recent changes in tobacco consumption (see Cook and Tauchen, 1982).

When evaluating empirically the relation between tobacco consumption and the mortality rate, we take as our basis the equation which suggests that, taking the logarithm of the mortality rate as a dependent variable in the econometric specification, tobacco consumption must also appear in logarithms, since it is then feasible to disaggregate the right hand side of the equation thus: log However, given that statistical information on lung cancer mortality also includes mortality cases that cannot be attributed to tobacco, we need to add other variables to the right hand side in order to explain this proportion of the total mortality rate. In fact, to explain the expected value of the logarithm of the standardised mortality rate, we use as exogenous variables the per capita income, the current consumption of alcohol, the proportion of the total population with regard to the population between 15 and 64 years old, and finally, a set of dummy variables which include specific fixed effects for each country and year. The per capita income will aim to include effects derived from each country's economic growth. The alcohol consumption will try to capture the probable accumulation of risk arising from the simultaneous consumption of two substances that are harmful to health, namely tobacco and alcohol. In line with these variables, the functional form of the standardised mortality rate to be estimated will be:

\[\log T _ {p i t} = \beta_ {0} + \beta_ {1} \log c _ {i t} + \beta_ {2} \log y _ {i t} + \beta_ {3} \log a _ {i t} + \beta_ {4} p p _ {i t} + v _ {i} + \lambda_ {t} + e _ {i t}\tag{9}\]

where is the mortality rate in country i in the period is the per capita consumption of tobacco, is the per capita income, is the per capita consumption of alcohol, is the proportion of the population, is invariant over time for the country is the specific effect of the general period t for all countries and, finally, is the error term.

\[\sigma_ {v} ^ {2}\]

In the specification of the stochastic properties of the error term, we assume that death from lung cancer is an independent event for each person, and therefore the probabilities of different people dying from this illness are independent. Thus, if we call this probability , the number of people dying from lung cancer will follow a binomial distribution and so a country's mortality rate will have a mean and variance with N being the population of the country. This distribution may be approximated by another lognormal distribution, which involves , with v being distributed in accordance with a normal distribution. The mean and variance of the log-normal distribution are shown by and , and therefore, by equalising these moments with their corresponding binomial distribution, we can determine the variance of the heteroscedastic component of the error term, . In addition, assuming that the expected value of the mortality rate logarithm has an inertia comportment, we must include an autocorrelation adjustment, which we shall assume to have a unitary order. Thus we specify an error term, e, which will include two components, that is to say, v exhibiting heteroscedasticity, and u presenting autocorrelation. The variance and covariance matrix of the complete error term, e, will be:

\[V a r (e) = \Omega = \left[ \begin{array}{c c c c} \Sigma_ {1} & 0 & & 0 \\ 0 & \Sigma_ {2} & & 0 \\ \dots & \dots & \dots & \dots \\ 0 & 0 & & \Sigma_ {n} \end{array} \right]\tag{10}\]

with being a diagonal block matrix, one for each of the sample countries, where each component of the diagonal is shown by:

\[V a r (e _ {i}) = \Sigma_ {i} = \left[ \begin{array}{c c c c} ^ 2 _ {v i 1} & 0 & & 0 \\ 0 & \sigma_ {v i 2 _ {2}} ^ {2} & & 0 \\ \dots & \dots & \dots & \dots \\ 0 & 0 & & \sigma_ {v i T} ^ {2} \end{array} \right] + \sigma_ {u} ^ {2} \left[ \begin{array}{c c c c} 1 & \rho & & \rho^ {T - 1} \\ \rho & 1 & & \rho^ {T - 2} \\ \rho^ {T - 1} & \rho^ {T - 2} & & 1 \end{array} \right]\tag{11}\]

with T being the number of temporal observations for each country. Thus, the individual covariance matrix is the sum of two matrices. The first includes the heteroscedastic component which depends on the population, while the second includes the autoregressive part of the error.

Given this error term structure, we shall estimate by generalised least squares. For this, we first need to obtain an estimation of the diagonal matrix, which means deriving estimations of and . In line with the supposed independence of the error terms, we estimate the regression by non-linear least squares, with the estimated value of being the estimation of while the estimated value of enables us to obtain the estimation of the heteroscedastic component log of each observation. Finally, to obtain an estimation of the parameter we use the property of independence between the heteroscedastic component and the autoregressive component of the error term, whereby Thus, the estimation of this covariance, together with the estimation of gives us an estimation of

One important question to be considered before going on to the estimation of the previous functional form is the exogenous nature of the explanatory variables, given that it is well known that the majority of estimation techniques for models with lag distribution are only valid if the causality between the variables operates in just one direction, specifically, if the independent variables cause the dependent variable, and not the other way round (Sims, 1972). Therefore, for the estimations of this type of model to be valid, consumption must be exogenous with regard to the mortality rate; in other words, there must be no a feedback effect whereby smokers modify their consumption in response to variations in the observed mortality rate.

Thus, to test whether there is unidirectional causality, one possibility is to carry out a regression of the exogenous variable on its past values and on the past values of the endogenous variable, so that if the past coefficients of the endogenous variable are statistically null, then we can conclude that the endogenous variable does not cause the exogenous variable (Granger, 1969). Another alternative would be to carry out a regression of the supposed endogenous variable on the past, present and future values of the supposedly exogenous variables, so that if the endogenous variable does not cause the exogenous variables, the coefficients of the latter with regard to the future must be statistically null (Sims, 1972). In spite of their different specification, the Granger and Sims tests are valid for practically the same hypothesis (Chamberlain, 1982), and the suitability of these tests for detecting possible feedback processes is confirmed by two Monte Carlo studies (Geweke et al., 1979; Guilkey and Salemi, 1982).

Thus, we test the directional causality hypothesis in model (9), with the results appearing in Table 5. We can see that the coefficient accompanying the previous mortality rate is non-significant, which indicates that the past values of the endogenous variable do not explain the part of the exogenous variable that is not explained by its own past, and consequently we have no problem in accepting the exogenous nature of the consumption.

Therefore, having shown the exogenous nature of the taxes, we can now go on to the estimation of the model. The main result is that current consumption has a positive and significant effect on the lung cancer mortality rate. With regard to the specific estimations in Table 6, we find that the elasticity of the mortality rate with regard to current consumption, i.e. the coefficient of cigarette consumption, varies between 0.326 and 0.34 for the two sets of explanatory variables. Thus, we see that this elasticity remains stable for the different values of obtained in each of the estimations. In other words, the results are not especially sensitive to possible bias in the estimation of Furthermore, we must bear in mind that the estimated value of must be positive. In fact, the elasticity of the population mortality rate with regard to the per capita consumption will be in the region of 0.33, so that a 10% fall in tobacco consumption, remembering that only 85% of the total mortality rate is due to such consumption, will generate a 3.88% reduction in the mortality rate.

Another important result is that the income level appears with a positive and significant coefficient, so that aspects inherent to economic growth, such as higher pollution or a more sedentary lifestyle, may increase the harmful effects of tobacco consumption. Finally, the parameter corresponding to alcohol consumption is also positive, although nonsignificant.

Table 6

Asymptotic t-statistics in parentheses * Indicates individual significance at the 5% level

Next, we go on to analyse how demand for tobacco evolves. For this, we consider the reduced form of a model in which we directly relate the logarithm of per capita tobacco consumption with the present and future values of the taxes and per capita income:

\[\log c _ {i t} = \Sigma_ {j} \alpha_ {j} t _ {i} t _ {- j} + \Sigma_ {j} \beta_ {j} y _ {i} t _ {- j} + a _ {i t} + v _ {i} + \lambda_ {t} + e _ {i t}\tag{12}\]

where is the per capita tobacco consumption in country i in period t, is the tax per packet, yit is the per capita income, is the per capita consumption of alcohol, is invariant over time for country is the specific effect of the general period t for all countries and, finally, is the error term. Given the temporal component of the observations, it is to be expected that the error term will show autocorrelation, so that if we assume a first order autoregression process, we have , with being white noise.

The variance and covariance matrix of the error term may be expressed as:

\[V a r (e) = \Omega = \left[ \begin{array}{c c c c} \Sigma_ {1} & 0 & & 0 \\ 0 & \Sigma_ {2} & & 0 \\ \dots & \dots & \dots & \dots \\ 0 & 0 & & \Sigma_ {n} \end{array} \right]\tag{13}\]

with being a block diagonal matrix, one for each of the sample countries, where each component of the diagonal is shown by:

\[V a r (e _ {i}) = \Sigma_ {i} = \sigma_ {u} ^ {2} \left[ \begin{array}{c c c c} 1 & \rho & & \rho^ {T - 1} \\ \rho & 1 & & \rho^ {T - 2} \\ \dots & \dots & \dots & \dots \\ \rho^ {T - 1} & \rho^ {T - 2} & & 1 \end{array} \right]\tag{14}\]

Once again,, the estimations of model (12) will only be valid if the explanatory variables are exogenous with regard to consumption, which means the non-existence of a feedback process to modify, for example, taxes in response to variations in consumption. In other words, the causality must operate in a single direction, i.e. the exogenous variables cause the endogenous variable, and not the other way around. Thus, to test the existence, or otherwise of bi-directional causality, we use Granger's test (1969), which consists of carrying out a regression of the exogenous variable on its lagged values, as well as on the lagged value of the endogenous variable, so that there is no bi-directional causality, i.e. the endogenous variable does not cause the exogenous variable if the lagged coefficients of the endogenous variable are statistically null. The results presented in Table 7 confirm that the coefficient which accompanies the logarithm of the delayed mortality rate is not individually significant, indicating that the past values of the endogenous variable do not explain the part of the exogenous variable that is not explained by its own past, and therefore we may discard the hypothesis of bi-directional causality. In other words, we accept the exogenous nature of the taxes.

Table 8 shows the results of model (12). The per capita income exercises a negative effect, although not significant at the 5% level. This is in line with the fact that in recent years the richest countries have managed to stabilise, or even reduce, tobacco consumption, thus obtaining negative, although non-significant income elasticity (Wasserman et al., 1991). Another interesting result is the complementary nature detected between tobacco and alcohol consumption, which implies that tobacco taxes also reduce alcohol consumption. Finally, we can note that tobacco taxes exert an immediate effect on consumption, given that current elasticity, measured in mean values, varies between -0.372 and -0.394. In addition, the elasticity with regard to the lagged tax is between -0.161 and -0.149, while in the long term it varies between -0.521 and -0.549.

Once we have obtained the effects of taxes on consumption and, in turn, of consumption on the mortality rate, we can now combine these effects in order to calculate the final effect of taxes on the mortality rate. Thus, the one period lagged elasticity of the mortality rate with regard to taxes, obtained by multiplying the elasticity of the mortality rate with regard to consumption by the elasticity of consumption with regard to taxes, will equal -0.169, a value very similar to those obtained in the empirical literature (Moore, 1996).

Asymptotic t-statistics in parentheses * Indicates individual significance at the 5% level

5. Avoidable mortality

The results obtained up to now may finally be used to forecasts the impact of economic and public healh policies aimed at reducing tobacco consumption and thus the lung cancer mortality rate. Specitically, we conclude this section by carrying out a simulation exercise which will enable us to calculate the avoidable mortality arising from a given increase in taxes.

Thus, if we initially consider a 10% increase in tobacco tax, there will be a 3.8% decrease in consumption in the first year, while in the long term, consumption will fall by 5.3%. The short term reduction in consumption will mean, in line with the theoretical model, an identical fall in the mortality rate, which, taking into account that tobacco mortality represents 85% of the total, will be a fall of 3.23%. However, according to the estimations carried out, the mortality rate should fall by 1.21%, as a result of multiplying the fall in consumption, 3.8%, by the elasticity of the mortality rate with regard to consumption, 0.32. The simple explanation for this divergence is that it comes about because some smokers do not die in the year in which they have reached their threshold, but in later years. In fact, some epidemiological studies have shown that the risk of death may persist for several years, up to a decade, after giving up smoking. Thus, we may assume that, once consumption has been modified, the mortality rate will reach the same variation after a certain number of years. Therefore, bearing in mind that for every 100 deaths from lung cancer, only 85 are caused by tobacco, the reduction in the mortality rate will be 3.8% of these 85 deaths after this certain number of years, and this will mean a 3.23% reduction with regard to the total mortality.

In the long term, the empirical results enable us to confirm that a 10% increase in tobacco tax will mean a 5.3% reduction in consumption in the long term, and that this, in line with the tobacco mortality figures, will imply a 4.5% reduction in the mortality rate. This decrease will practically double, in line with the theoretical model, reaching a value of 8.81% after two generations, the first to reduce consumption by 5.3% and the second for mortality to be adjusted in the long term. Thus, once the smoking population has been renewed, so that everyone is consuming at the new rate, mortality will have fallen by approximately 8.81%.

The above discussion enables us to calculate the deaths that may be avoided or delayed by a 10% increase in tax. Thus, Table 9 shows that this increase will reduce mortality by 1.21% in the first year, 3.2% in the fifth and 8.81% in the long term, once the smoking population has been renewed.

To calculate the number of avoided lung cancer deaths, we use the values of the gross mortality rate and of the population for 1993. Thus, the results show that a 10% increase in the tax, ceteris paribus, would avoid some 1,707 deaths in the twelve countries making up the sample during the first period, 4,491 in the fifth year and some 12,366 in the long term, i.e. the year in which the smoking population will have been totally renewed. Specifically, for the case of Spain, we find that 183 deaths would be avoided in the first year, 482 in the fifth year and 1,327 deaths after the generation of smokers has been totally renewed.

Tabla 9 Avoidable mortality

6. Summary and conclusions

In this paper, we have carried out an analysis of whether tobacco taxes may be used as an efficient tool to reduce lung cancer mortality. The theoretical model has enabled us to show that if individuals die for this reason after reaching their threshold, the variations in per capita consumption will be transposed in similar variations in the mortality rate in the same period, while in the long term, i.e. once the population has been completely renewed, the reduction in the mortality rate will practically double.

However, the short-term empirical evidence has revealed that, given the existence of a temporal lapse between the moment of exceeding the threshold and the moment of death, this theoretical similarity partially disappears. The results obtained show an elasticity of the mortality rate with regard to per capita current consumption of 0.32. However, a 10% reduction in consumption, which should give rise to the same percentage reduction in the mortality rate, only means a reduction of approximately one third, which will be completed once all those who have exceeded the threshold before the variation in consumption have died.

To obtain the effect that taxes have on tobacco consumption, we directly estimate the reduced form of the demand equation. We find evidence that taxes exert a significant negative effect on tobacco consumption, an effect which is immediately evident in the current and subsequent period. Once we accept that tobacco taxes may be considered as exogenous, we find that the elasticity of consumption with regard to the current tax is approximately -0.38, while the long term elasticity is around 0.53. These values are possibly over-biased due to the fact that the figures refer to declared or legal tobacco consumption, and therefore the proportion of consumption not included in official statistics has been ignored.

In accordance with the above figures, a 10% increase in tax will reduce consumption by 3.8% in the first year, which will give rise to a 1.12% reduction in the lung cancer mortality rate, a reduction which, in the long term, will be in the order of 8.81%. For the twelve countries being considered, this means that 1,707 deaths will be avoided in the first year, 4,491 in the fifth year and 12,366 after the smoking population has been completely renewed.

In summary, tobacco taxes would appear to be a useful tool for reducing long cancer mortality related to tobacco consumption. In addition, and given the complementary nature of tobacco and alcohol consumption, health improvements will also flow from reducing the consumption of the latter. Finally, per capita income has a negative, although non-significant effect on tobacco consumption.

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