# The Effect of Health Information on Cigarette Consumption: Evidence from British Panel Data

Andrew E. Clark, Fabrice Etilé

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Andrew E. Clark, Fabrice Etilé. The Effect of Health Information on Cigarette Consumption: Evidence from British Panel Data. 1999. halshs-03592627

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UNIVERSITÉ PARIS 1
-PANTHÉON - SORBONNE -

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Cahiers
de la
MSE

The Effect of Health Information
on Cigarette Consumption :
Evidence From British Panel Data

Andrew CLARK

Fabrice ETILE

1999.90

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CENTRE NATIONAL
DE LA RECHERCHE
SCIENTIFIQUE

Maison des Sciences Économiques, 106-112 boulevard de L'Hôpital, 75647 Paris Cedex 13

ISSN : 1624-0340
THE EFFECT OF HEALTH INFORMATION ON CIGARETTE CONSUMPTION:
EVIDENCE FROM BRITISH PANEL DATA

Andrew Clark<fnref n="1" />, CNRS and LEO-CRESEP, University of Orléans

Fabrice Etilé<fnref n="2" />, TEAM, University of Paris-1 Panthéon-Sorbonne

October 1999

<footnote n="1">¹ LEO-CRESEP, Université d'Orléans, Rue de Blois - B.P. 6739, 45067 Orléans cedex 2,
France. Tel: (33)-2-38-41-73-65. E-mail: Andrew.Clark@univ-orleans.fr</footnote>

<footnote n="2">² TEAM, Université Paris-1 Panthéon-Sorbonne, 106-112 Boulevard de l'Hôpital, 75647 Paris cedex 13, France. Tel: (33)-1-55-43-42-48. E-mail: etile@univ-paris1.fr</footnote>
THE EFFECT OF HEALTH INFORMATION ON CIGARETTE CONSUMPTION:
EVIDENCE FROM BRITISH PANEL DATA*

Andrew Clark

Fabrice Etilé

October 1999

Abstract

This paper presents and tests a model of cigarette consumption which mixes two types of intertemporal dependencies: habit-formation and learning about the health consequences of smoking. This latter is argued to result from the observation of health developments, both one's own and those of other smokers in the same household. Using seven waves of British Household Panel Survey data, we present results consistent with habit-formation, but joint with learning about smoking's health risks. We find some effect from the individual's own health developments, but little effect from health developments amongst other smokers. Public health policy may therefore have a greater impact on smokers' behaviour through the delivery of personalised health information, for example through the medical profession, than through impersonal information provision, such as advertising campaigns.

Résumé

Afin d'étudier l'impact sur la consommation de cigarettes d'informations concernant les dangers du tabagisme, nous complétons le modèle d'addiction rationnelle par une hypothèse d'incertitude quant au risque sanitaire individuel. Utilisant des données de panel du British Household Panel Survey, nous trouvons que les processus de formation d'habitude et d'apprentissage du risque déterminent simultanément la consommation des fumeurs et leur choix d'arrêter. Les fumeurs tiennent compte, pour fixer leur niveau de consommation, d'aléas de santé personnels corrélés à leur consommation passée, mais pas des problèmes survenus aux autres fumeurs de leur foyer. Il semble que les politiques d'information des fumeurs sont plus efficaces lorsqu'elles apportent une information personnalisée sur les risques du tabac, par exemple par l'intermédiaire de l'institution médicale.

JEL classification: C33, D83, I12, I18.

Keywords: Smoking, Health, Information, Learning, Public Health Policy.

Mots-clés: Cigarettes, Santé, Information, Apprentissage, Politique publique de santé.

Corresponding author: Fabrice Etilé, TEAM, 106-112 Boulevard de l'Hôpital, 75647 Paris cedex 13, France. Tel: (33)-1-55-43-42-48. E-mail: etile@univ-paris1.fr.
# THE EFFECT OF HEALTH INFORMATION ON CIGARETTE CONSUMPTION: EVIDENCE FROM BRITISH PANEL DATA

Andrew Clark and Fabrice Etilé

## 1. Introduction

This paper asks whether health information influences smoking behaviour, either by reducing the average number of cigarettes smoked per day, or by encouraging individuals to stop smoking altogether. Public health policy aimed at tobacco often makes use of information regarding the health consequences of smoking. To evaluate its effectiveness, it is essential to understand the role of such health information in determining behaviour. In the absence of good disaggregated data regarding such policies, one way of approaching this question is to consider interdependencies between members of a group. One might, in particular, consider that one's own health developments, and those amongst individuals (and especially smokers) with whom the individual lives, provide credible information about the possible dangers of smoking¹.

Interdependence is often modelled via relative utility, whereby an individual's utility from the consumption of a good depends in part on the consumption of his or her reference group, as it is the relative level of consumption which yields rank or status (see Kapteyn *et al.*, 1997). In this set up, individual preferences are endogenous. This is also the case if there is habit formation, except that now it is one's own past consumption (rather than that of others) which helps to determine the marginal utility (and thus the level) of current consumption. This latter hypothesis is often appealed to in the light of the strong autocorrelation in consumption for certain goods. Although demand equations including such interdependencies have been estimated with some success (Alessie and Kapteyn, 1991), it is possible that other phenomena are behind the intertemporal structure of demand².
Duesenberry (1949) is often evoked as one of the key texts with respect to relative utility. It is, however, worth remembering that he equally developed the idea of demonstration effects (Chapter 3, Section 4), whereby persistence in consumption may be dampened if others' consumption reveals information about the good in question. We are here in a world of uncertainty, as opposed to theories of rational addiction which are typically presented under the assumption of perfect information. In this paper, we develop a model of both habit-formation and learning, based on that of Grossman (1972), where health is considered as a stock, the level of which is affected by the consumption of certain goods and services, amongst which are cigarettes. The individual does not know the health consequences of smoking with certainty, and may infer them from what happens to herself and others³. Demonstration effects arise if observation of others reveals information hitherto unincorporated into the individual's perception of the health consequences of smoking⁴.

This model is tested on the first seven waves of the British Household Panel Survey (BHPS). This general survey covers roughly ten thousand people in five thousand different households per year, and includes information on cigarette consumption, as well as a wide range of information regarding demographics, health, employment and income. As all adults in the same household are interviewed, we can directly match health information from other individuals in the same household to an individual's smoking behaviour. In addition, as we use panel data, we can calculate *changes* in various measures of health, both for the individual and for the other individuals in the same household. It is these developments which will be argued to provide information in the sense of the model outlined above.

Much of the empirical literature on smoking in economics has used either double-hurdle (Jones, 1989) or rational addiction models (Becker, Grossman and Murphy, 1994, and Chaloupka, 1991). Although the first is an excellent way of modelling participation, its combination with our model seems too complicated. We therefore estimate our model on
samples of "confirmed" smokers (those who are observed to smoke over three consecutive
waves). We do, however, complement this analysis with probit estimation of the decision to
stop smoking. The rational addiction approach requires good instruments for past and future
consumption (typically prices). The lack of such instruments in our data⁵ precludes the
estimation of a fully-fledged rational addiction model.

The paper is organised as follows. Section two presents our theoretical model, and section
three the demand equations which result from it. Section four discusses the data, and the
estimation results, with their interpretation, follow in section five. The last section concludes
with some implications for public health policy.

2. <u>Theoretical Model</u>

Consider an individual, *i*, belonging to household *f*. The instantaneous utility function (anticipated at *t*=0) at time *t* is $U_{it}=U(x_{it}, y_{it}; S_{it})$, where $x_{it}$ is the number of cigarettes consumed, and $y_{it}$ is the numeraire good. $S_{it}$ is the stock of cigarette capital, as in Becker and Murphy (1988). The individual's discount rate is represented by $\beta$, and $A_i$ is individual wealth.

We consider that individual preferences are additive and intertemporally separable. As in El-Safty (1976), the endogenous modification of preferences can be modelled by the introduction of a taste parameter, $S_{it}$, in the utility function. In the rational addiction model of Becker and Murphy (1988), $U_{it}=U(f(x_{it}; S_{it}), y_{it})$, where $f(x_{it}; S_{it})$ is the euphoria produced by smoking, which depends on $S_{it}$. A common formulation is $f(x_{it}; S_{it})=x_{it}-S_{it}$, where $S_{it}=\lambda x_{i0}$ in models of myopic habit formation⁶ (Pollak, 1970), $S_{it}=\lambda x_{it-1}$ in models of rational addiction (Spinnewyn, 1981, Iannaccone, 1986, Becker and Murphy, 1988), and $S_{it}=\Lambda X_{t-1}$, where $X_{t-1}$ is a vector of the reference group's past consumption in models of interdependence (Alessie and Kapteyn, 1991). In the rational addiction model, the complementarity of past and present consumption in
the utility function (greater consumption at t-1 increases the marginal utility of consumption at t) reflects the phenomenon of reinforcement.

Cigarettes have three different types of negative effects: the first is associated with tolerance, modelled in Becker and Murphy (1988) as $\frac{\partial U}{\partial S} \le 0$, $\frac{\partial^2 U}{\partial S^2} < 0$; the second comes from any adjustment costs associated with reducing consumption (which do not typically appear in rational addiction models), as in Jones (1999) and Suranovic et al. (1999); and the third results from the detrimental health effects of smoking⁷. In Becker and Murphy (1988) this latter is modelled as a negative correlation between past consumption and current marginal productivity, and thus expected wealth.

We consider an individual whose utility depends only on the current consumption of cigarettes, $x_{it}$, on the stock of consumption capital, and on health, $H_{it}$. This latter is determined by the current consumption of both cigarettes (negatively) and the numeraire good (positively). The rate of depreciation of health between periods is $1-\delta<1$. The health impact of cigarettes is captured by an individual health risk factor, $r_i$, considered exogenous and fixed for the moment. The health equation is thus

$$H_{it} = \delta H_{it-1} - r_i x_{it-1} + y_{it-1}, \quad (1)$$

and utility, which is separable over cigarette consumption and health, is

$$U(x_{it}, S_{it}, H_{it}) = v(x_{it}, S_{it}) + w(H_{it} - \tau H_{it-1}), \quad (2)$$

where $\frac{\partial v}{\partial x}$, $\frac{\partial^2 v}{\partial x \partial S} > 0$, $\frac{\partial v}{\partial S}$, $\frac{\partial^2 v}{\partial S^2}$, $\frac{\partial^2 v}{\partial x^2} < 0$, $w'>0$, $w''<0$. Utility thus depends on a measure of the change in health from one period to another, with a coefficient of habit formation of $\tau$. If $\tau=0$ then utility depends only on the level of health; if $\tau=1$ then utility depends only on the change in health; last, if $\tau=\delta$ then utility depends on the depreciated value of health.
The above holds in the case of certainty. Now imagine that the individual is not sure about the health consequences of smoking. We consider that the parameter $r_i$ is distributed normally with unknown mean, $\bar{r}_i$, but a known variance of $\sigma_i^2$: $r_i \rightarrow N(\bar{r}_i, \sigma_i^2)$. We assume that the stock, $S_{it}$, is captured by last period's consumption, $x_{it-1}$, and that the individual discount factor, $\beta$, equals the interest rate. The price of cigarettes is denoted by $p_t$, and $E_{i0}$ is the expectations operator conditional on the information available at time zero. Expected utility maximisation (with infinitely-lived individuals) is described by the following program:

$$ \begin{array}{l} \displaystyle \max_{\{x_{it}, y_{it}\}_{t=0,...,\infty}} E_{i0} \left[ \sum_{t=0}^{\infty} \beta^t [v(x_{it}, S_{it}) + w((\delta - \tau)H_{it-1} - r_{it}x_{it-1} + y_{it-1})] \right] \\ \left| \sum_{t=0}^{\infty} \beta^t [p_t x_{it} + y_{it}] \right| = A_i \\ S_{it} = x_{it-1} \end{array} \quad (3) $$

Of prime importance here is the information that the individual uses to estimate $r_{it}$, the health risks from smoking. This information may come either from the individual's own experience, or from the observation of others. We use the following adaptive learning process:

$$ E_{it}(r_{it}) = \lambda E_{it-1}(r_{it-1}) + (1-\lambda)(\alpha \tilde{r}_{it-1} + \gamma \tilde{r}_{ft-1}) \quad (4) $$

with $0<\lambda<1$.

The expectation of $r_{it}$ is thus a weighted average of the previous expectation and a term reflecting information revealed at time $t$. The variable $\tilde{r}_{ft-1}$ describes the information from external sources, identified here with other individuals in the same household, whereas $\tilde{r}_{it-1}$ is the individual's own experience of the health consequences of smoking at time $t-1$. These two health information sources are not given equal weight in the learning process, and we might well imagine that $\alpha > \gamma$.

The expected value of the utility stream in equation (3) is
$$E_{i0} \left[ \sum_{t=0}^{\infty} \beta^t [v(x_{it}, S_{it}) + w((\delta - \tau)H_{it-1} - r_{it}x_{it-1} + y_{it-1})] \right] = \sum_{t=0}^{\infty} \beta^t [v(x_{it}, S_{it}) + E_{i0}w((\delta - \tau)H_{it-1} - r_{it}x_{it-1} + y_{it-1})].$$

We make the assumption that $\delta=\tau$, i.e. that utility depends on the depreciated value of health. This assumption is not essential, but facilitates the derivation of a solution to equation (3). We consider a quadratic form for the utility function:

$$v(x, S) = \frac{a_{xx}}{2} x^2 + a_x x + \frac{a_{ss}}{2} S^2 + a_S S + a_{xS} x S, \text{ and}$$

$$w(z) = \frac{b_{HH}}{2} z^2 + b_H z \Rightarrow E_{i0} w((\delta - \tau)H_{it-1} - r_{it-1}x_{it-1} + y_{it-1}) = w(y_{it-1} - E_{i0}(r_{it-1})x_{it-1}) + \frac{b_{HH}}{2} \sigma_i^2 x_{it-1}^2$$

The first-order conditions from the maximisation of (3) at time t are thus

$$\begin{cases} x_t : \frac{\partial v}{\partial x}(x_{it}, x_{it-1}) + \beta \frac{\partial v}{\partial S}(x_{it+1}, x_{it}) = \theta p_t + \beta E_{it}(r_{it}) w'[y_{it} - E_{it}(r_{it})x_{it}] - \beta b_{HH} \sigma_i^2 x_{it} \\ y_t : w'[y_{it} - E_{it}(r_{it})x_{it}] = \theta \end{cases} \quad (5)$$

where $\theta$ is the marginal utility of wealth. From equation (5) we can derive

$$a_{xx}x_{it} + a_x + a_{xS}x_{it-1} + \beta a_{SS}x_{it} + \beta a_S + \beta a_{CS}x_{it+1} = \theta p_t + \beta E_{it}(r_{it})\theta - \beta b_{HH}\sigma_i^2 x_{it} \quad (6)$$

The interpretation of (6) is straightforward. The marginal utility of an extra cigarette today (including the effect through the stock, S) equals the full price: price times the marginal utility of wealth, plus a term reflecting the expected health implications. From (6),

$$x_{it} = \frac{\theta}{(a_{xx} + \beta a_{SS} + \beta b_{HH} \sigma_i^2)} p_t + \frac{\beta \theta}{(a_{xx} + \beta a_{SS} + \beta b_{HH} \sigma_i^2)} E_{it}(r_{it}) - \frac{b_H + a_C + \beta a_S}{(a_{xx} + \beta a_{SS} + \beta b_{HH} \sigma_i^2)} \quad (7) \\ - \frac{a_{CS}}{(a_{xx} + \beta a_{SS} + \beta b_{HH} \sigma_i^2)} x_{it-1} - \frac{\beta a_{CS}}{(a_{xx} + \beta a_{SS} + \beta b_{HH} \sigma_i^2)} x_{it+1}$$

Hence demand at date t can be written as

$$x_{it} = a_0 + a_1 p_t + a_2 E_{it}(r_{it}) + a_3 x_{it-1} + \beta a_3 x_{it+1} \quad (8)$$

The relation between cigarette demand and the (expectation of the) individual's risk factor, $r_{it}$, is captured by the parameter $a_2$. This is negative ($\theta>0$), and the denominator is negative by
concavity)⁸. Equation (8) implies, as in all rational addiction models, that current consumption is a function of future consumption. Our contribution to this class of models is to add the variable E<sub>it</sub>(r<sub>it</sub>), which captures the individual's perception of smoking's risks.

### 3. Empirical Specification

A key variable in equation (8) is the individual's perception of smoking's health risks, E<sub>it</sub>(r<sub>it</sub>). This perception is not measured in our data (although questions aimed at its revelation can be envisaged, see Viscusi, 1992). Our approach consists in finding a specification of cigarette demand, from equations (4) and (8), which will allow us to derive an estimate of λ, the speed of learning.

Using (4) to substitute out E<sub>it</sub>(r<sub>it</sub>) in equation (8), we obtain:

$$x_{it} = a_0 + a_1 p_t + a_2 \lambda E_{it-1}(r_{it-1}) + a_3 (1-\lambda)(\alpha \tilde{r}_{it-1} + \gamma \tilde{r}_{ft-1}) + a_3 x_{it-1} + \beta a_3 x_{it+1} \quad (9)$$

We now turn our attention to the specification of the terms in (9) representing information about the health risks of smoking. We use the following specifications.

• $\tilde{r}_{it-1} = (\psi_2 \Delta H_{it-1} + \delta_i + \tilde{\varepsilon}_{it}) / a_2 (1-\lambda) \alpha$, where $\Delta H_{it-1}$ is a vector of individual health events at time t-1, which he or she might consider to be connected to cigarettes. The term $\delta_i$ reflects possible unobserved individual and $\tilde{\varepsilon}_{it}$ is a normally-distributed error with zero mean.

• $\tilde{r}_{ft-1} = \psi_3 \Delta H_{ft-1} / a_2 (1-\lambda) \gamma$. The individual observes health outcomes for other household members (but not any heterogeneity associated with their risk factors)⁹.

Equation (9) thus becomes

$$x_{it} = a_0 + a_1 p_t + a_2 \lambda E_{it-1}(r_{it-1}) + a_3 x_{it-1} + \beta a_3 x_{it+1} + \psi_2 \Delta H_{it-1} + \psi_3 \Delta H_{ft-1} + \delta_i + \tilde{\varepsilon}_{it} \quad (10)$$

To eliminate E<sub>it-1</sub>(r<sub>it-1</sub>), we can rewrite (8) for consumption lagged one period, which, substituted in (10), gives
$$x_{it} - \lambda x_{it-1} = a_0(1-\lambda) + a_1(1-\lambda)p_t + a_1\lambda dp_t - \lambda a_3 x_{it-2} + a_3 x_{it-1} - \lambda\beta a_3 x_{it} \\ + \beta a_3 x_{it+1} + \psi_2\Delta H_{it-1} + \psi_3\Delta H_{ft-1} + \delta_i + \tilde{\varepsilon}_{it} \quad (11)$$

where d is the first difference operator. Adding a vector $Y_{it}$ of socio-demographic variables to (11), to account for heterogeneity in consumption, the consumption equation becomes:

$$x_{it} = \frac{(\lambda + a_3)}{1 + \lambda \beta a_3} x_{it-1} - \frac{\lambda a_3}{1 + \lambda \beta a_3} x_{it-2} + \frac{a_0(1-\lambda)}{1 + \lambda \beta a_3} + \frac{(1-\lambda)a_1}{1 + \lambda \beta a_3} p_t + \frac{\lambda a_1}{1 + \lambda \beta a_3} dp_t + \frac{\beta a_3}{1 + \lambda \beta a_3} x_{it+1} \\ + \frac{\psi_1}{1 + \lambda \beta a_3} Y_{it} + \frac{\psi_2}{1 + \lambda \beta a_3} \Delta H_{it-1} + \frac{\psi_3}{1 + \lambda \beta a_3} \Delta H_{ft-1} + \delta_i + \tilde{\varepsilon}_{it} \quad (12)$$

As the error term is autocorrelated, the estimation of rational addiction models requires that future and past consumption, which are endogenous, be instrumented in equation (12); this is typically carried out using prices as instruments (as in Chaloupka, 1991). In addition, had we not made the assumption that $\delta=\tau$, current demand would depend on all past and future demands, which equally requires suitable instruments for lagged and leading consumption.

In our data, we are able to instrument $x_{t+1}$, $x_{t-1}$ and $x_{t-2}$ on consumption lagged three periods and more, as well as socio-demographic variables. This instrumentation turns out to be weak (as only $x_{t-3}$ is a strong instrument), and the results are not reliable (Bound, Jaeger and Baker, 1995). In the absence of sufficient instruments, such as prices, we omit future consumption and estimate a model in which $x_{t-1}$ and $x_{t-2}$ only are instrumented. Last, in the absence of price information, our estimating equation will drop the price terms, and assume that they are picked up by region and year dummies. The final consumption equation we estimate is as follows:

$$x_{it} = (\lambda + a_3)x_{it-1} - \lambda a_3 x_{it-2} + a_0(1-\lambda) + \psi_1 Y_{it} + \psi_2 \Delta H_{it-1} + \psi_3 \Delta H_{ft-1} + \delta_i + \tilde{\varepsilon}_{it} \quad (13)$$

We thus have a fixed-effect dynamic model with heteroscedastic autocorrelated errors.

If there is no habit-formation in cigarette consumption, i.e. if $a_3$ is small or zero, two-period lagged consumption will likely be insignificant in equation (13). Equally, if learning (with respect to the health effects of smoking) is rapid (i.e. $\lambda$ is close to zero, and $1-\lambda$ is thus close to
one), the coefficient on $x_{it-2}$ will be close to zero, but we would expect significant estimates on the health development variables. Hence insignificant health information effects, but a significant estimate on two-period lagged consumption signifies an absence of learning through information interdependencies (although all conclusions are conditional on our modelling of myopic, rather than rational, habit formation).

## 4. Smoking Data in the BHPS

The British Household Panel Survey is an annual panel of roughly 10 000 individuals in around 5 000 different households in Great Britain. We use here the first seven waves (1991-1997). All adults in the household are interviewed separately with respect to their socio-demographic characteristics, their income, their employment, and their health. Further details of this survey are available in Buck *et al.* (1994). With respect to cigarettes, individuals are first asked whether they smoke, and then how many cigarettes they smoke per day. This data is summarised in Table 1.

Of the 10 264 individuals interviewed at wave one, 6 608 are present for all seven waves. There are a total of 67 250 observations on 14 026 different individuals, giving an average number of interviews per respondent of just under 5. As can be seen from equation (13), the estimation of our model requires that individuals be observed continuously over three waves, which reduces the number of observations which we can use. In our estimations, we use only individuals who are observed to smoke over three consecutive waves, due to issues of selection bias relating to stopping and starting decisions. The distribution of this sample over the different waves is reported in Appendix A.

Self-reported data on the consumption of cigarettes, tobacco and illegal drugs likely contain errors (Hoyt and Chaloupka, 1994). In the case of cigarettes, there is first the difficulty of producing an accurate figure with regard to daily consumption, and, second, the possibility that
the presence of other household members during the interview may bias the reported figure (a
bias which we typically imagine to be negative). The first bias appears clearly when we look at
the distribution of daily cigarette consumption in BHPS data, as shown in Table 2. These
figures refer to individuals who are observed to smoke over three consecutive waves.

Smokers seem to have difficulty in evaluating precisely their daily consumption, and base
their replies on the obvious fractions and multiples of a packet, a phenomenon reminiscent to
that of "heaping" in self-reported job tenure data. This bias is equally found in year-to-year
changes in cigarette consumption, as shown in Table 3. This noisy first difference data renders
difficult the estimation of a model with individual fixed effects.

The second bias, due to the presence of others when the interview is taking place, is
potentially more easy to deal with. The dataset used contains information on which other
household members (if any) were present during the respondent's interview, from which
dummy variables can be created for the regression analysis of self-reported cigarette
consumption. In practice, we find that these variables are insignificant, suggesting that, over
the whole sample, this bias is not too important.

Our main interest in this paper is to explain cigarette consumption as a function of health
information (both own and others'), which is argued to inform the individual's evaluation of the
health consequences of smoking. The list of BHPS health variables used in our analysis is given
below; the descriptive statistics of all variables are presented in Appendix A. Note that, as we
are interested in health information, we use the change in these variables between *t*-1 and *t* as
explanatory variables in our regressions¹⁰.

> *Mobility problems*. Here we have two variables, difficulty in climbing stairs and difficulty in walking for more than a few minutes. The variable LIMACT counts the number of these two problems reported by the individual, and so takes on the values 0, 1 or 2. We equally have the same variable at the household level, defined as the number of
smokers having these problems, LIMACTH. These variables have little variability in level
terms, and even less in first difference, which may explain their insignificance in the
regression analysis. They are also linked in a natural way to the respondent's age, although
specifications with interactions between age and mobility problems did not yield significant
coefficients either.

> **Specific health problems.** Here we consider two types of health problems which are often thought to be linked with smoking: Chest/Breathing and Heart/Blood Pressure. A cardinal variable, HLTHPRB, counts the number of these problems (they are individually insignificant in our regression specification). HLTHPRBH is similarly defined as the number of these health problems reported by other smokers in the same household. An alternative specification of these two measures (which are entered as first differences in the regressions) is to define a dummy variable equal to 1 if the number of health problems increased between t-1 and t.

> **Subjective Health Status.** Individuals also reply to the following question: *Please think back over the last 12 months about how your health has been. Compared to people of your own age, would you say that your health has on the whole been..., with the possible replies Excellent, Good, Fair, Poor, and Very poor. The last two categories are regrouped, due to the small number of people who report the worst level of health. At the household level, we construct four variables measuring the number of other smokers in the household reporting health in each of these four different categories.*

> **Check-ups.** We are particularly interested here in check-ups regarding two parts of the body which are affected by smoking: the heart and the lungs, check-ups being indicated by dummy variables. In addition to information gleaned from his/her own and others' health developments, as described in the previous variables, individuals may also learn about the health consequences of smoking as a result of interaction with the medical profession.
Region and wave dummies are included in the vector of Y variables as partial controls for price differences. We also include dummies for labour force status (10 levels), education (3), sex, ethnic origin (4), marital status (6), number of children (4), household size (6), and membership of organisations or social activities (14). These last dummies are introduced in response to Lee and Davis (1993), who show that individuals learn about smoking norms as a function of their social activities. Last, we control for the respondent's age.

## 5. Regression Results

The sample for the estimation of equation (13) consists of smokers observed over three years of cigarette consumption. The rate of entry and exit into this sample of the BHPS data is non-negligible, either due to attrition or entry into the panel, or due to starting or stopping smoking¹¹. As a result, our panel is unbalanced. Balanced panel data has the disadvantage of reducing the sample size, but the advantage of likely improving the performance of any statistical tests (Jimenez-Martin, 1998)¹². We carry out most of our estimation on the unbalanced panel, but report some results on balanced data.

In order to get consistent estimates of the parameters in (13), we first difference the equation to eliminate the individual fixed effects. The estimated equation is thus:

$$dx_{it} = (\lambda + a_3)dx_{it-1} - \lambda a_3 dx_{it-2} + \psi_1 dY_{it} + \psi_2 d\Delta H_{it-1} + \psi_3 d\Delta H_{ft-1} + d\tilde{\varepsilon}_{it} \quad (14)$$

Anderson and Hsiao (1982) suggest lagged consumption as an instrument, hence $dx_{it-1}$ and $dx_{it-2}$ can be instrumented by $x_{it-2}$, $x_{it-3}$, and so on. This choice of instruments is particularly apt for cigarette consumption, as a large part of current consumption is explained by the dependence effects, and therefore by past consumption. This strategy is most suitable if $d\tilde{\varepsilon}_{it}$ is not autocorrelated of order greater than one, as the consistency of GMM estimators of (14) hinges upon the assumption that, after instrumentation, $E(d\tilde{\varepsilon}_{it} d\tilde{\varepsilon}_{it-2})=0$. Following Arellano and Bond (1991), we use the $m_2$ specification tests to reveal the presence of second-order
serial correlation. Instrument validity is also tested using Hansen's test of over-identification.
Using both of these tests we can determine the best set of instruments. More details on the
estimation techniques are provided in Appendix B.

Estimation results may, however, be misleading if the instruments are weak, and neither the
$m_2$ nor the Hansen statistics allow us to judge instrument relevance. To evaluate instrument
power, we analyse the first stage regressions of the endogenous regressors on the instruments.
These estimations often yield a low adjusted R$^2$, and a number of instruments, although
significant, seem to be weak; this is specifically the case for consumption lagged of order
greater than 3. This weakness could explain the sensitivity of our results to the instruments
used (as will be shown below in Tables 4 and 5).

Exogenous regressors capturing socio-demographic effects are mostly time-variant dummy variables. However, relatively few people are observed to change status from one period to another, which leads to imprecise estimates. In addition, as our health variables are qualitative, not quantitative, it is difficult to construct easily-interpretable measures of their second differences. Estimation of the fixed effects equation, (14), yields poor results, as the first difference in consumption is very noisy, and it is not possible to model the change in health information correctly (as health is qualitative, not quantitative). We therefore also estimate the following demand equation, under the assumption of no unobserved individual heterogeneity:

$$x_{it} = (\lambda + a_3)x_{it-1} - \lambda a_3 x_{it-2} + a_0(1-\lambda) + \psi_1 Y_{it} + \psi_2 \Delta H_{it-1} + \psi_3 \Delta H_{ft-1} + \tilde{\varepsilon}_{it} \quad (15)$$

It is well known that estimates with this specification will produce biased results. The coefficient of the one-period lagged consumption is biased upward, but we cannot assert *a priori* the biases on the other coefficients. We can, however, estimate health information effects in this specification. As we omit the individual fixed effects, the residuals are likely to be autocorrelated, so that both $x_{it-1}$ and $x_{it-2}$ are endogenous. Past consumption lagged of order
greater than two should are therefore not totally valid instruments. But, as we have no other viable instruments available, we are constrained to use them, checking their validity with a Sargan test¹³.

The biases in the estimates of health effects depend on the covariances between the health information variables and the individual effects. To evaluate the sign of these biases, we first obtain the individual effects from first-difference regression, where we control for all time-variant socio-demographic and health effects. In the second stage, we regress these estimated individual effects, adjusted by their estimated variances, on the instrumented variables of the model without fixed effects. This indicates the sign of the biases, even if the results should be interpreted with caution, due to the low intertemporal dimension of the data.

Table 4 contains the results of GMM estimation of the fixed-effects model. Current cigarette consumption is modelled as a function of one- and two-period lagged consumption, region and year dummies, unbalanced panel controls (as suggested in Verbeek and Nijman, 1992). The first three columns report results without any of the health variables and with different instrument sets. The last two columns show the estimates for a specification including exogenous regressors, with two different types of instruments. The instruments used are displayed in the last row, with A-B indicating the Arellano-Bond method of instrumentation.

In Table 4, one-period lagged consumption has a positive, not always significant, coefficient. Two-period lagged consumption is never significant (this is important for our estimates of λ, the speed of learning). Income is also insignificant, but we find a positive effect of managerial status. Stressful events, such as divorce and separation, also attract positive significant coefficients. Despite the problems of variable construction mentioned above, we also added health variables in second differences in the last two columns. A small number of the results are presented. A change in personal health status from excellent to poor reduces smoking, as expected. However, worsening health problems amongst other household smokers
attracts a small positive, but significant, coefficient, contrary to that implied by demonstration effects.

Table 5 shows regression results for the model without the individual effects, where health information effects can be constructed more satisfactorily. In the first column, $x_{it-2}$ is not instrumented, whereas it is in the second and third columns. The final column reproduces the first column's GMM estimates on the balanced panel. Although biased, these regressions explain a non-negligible part of the variance of current cigarette consumption (conditional on being a smoker observed over a three-year period).

Of primary importance here are the estimated coefficients on one- and two-period lagged consumption, $\lambda+a_3$ and $-\lambda a_3$ respectively. The variable $a_3$ reflects habit formation (through the role of the consumption stock, $S$, in the utility function), while $\lambda$ shows the speed of learning. From (4), if $\lambda$ is close to zero then learning is very fast; if, on the other hand, $\lambda$ is close to 1 then health information has little impact on individual evaluations of smoking's health risks.

Tables 4 and 5 show, in all columns, a positive coefficient for $x_{it-1}$, and, in some estimates, a negative coefficient for $x_{it-2}$, as expected. The parameters $\lambda$ and $a_3$ can thus be identified by solving a second order equation, despite the fact that they play a symmetric role in our model. The two possible solutions are either a high value of $\lambda$ close to 1 (persistence in beliefs), but a small value of $a_3$ (little habit-formation), or a low value of $\lambda$ (close to zero which means rapid learning), and a larger value of $a_3$ (habit-formation). In light of the large literature on nicotine dependence, we prefer the latter interpretation. There are thus two, opposing, effects at work here: a pharmacological or psychological process of dependence, together with a learning process about the long-run health effects of smoking. We can estimate $\lambda$ and $a_3$, using the delta method for the variances¹⁴, as shown below.

## Estimates of habit-formation and learning

Table 4

Table 5
<table><thead><tr><th>Estimate</th><th>FD1</th><th>FD2</th><th>FD3</th><th>FD4</th><th>L1</th><th>L2</th><th>L3</th></tr></thead><tbody><tr><td>a<sub>3</sub></td><td>0.159</td><td>0.445</td><td>0.119</td><td>N.S.</td><td>0.980***</td><td>0.973***</td><td>0.980***</td></tr><tr><td>λ</td><td>-0.079</td><td>0.147</td><td>-0.059</td><td>N.S.</td><td>0.057</td><td>-0.406***</td><td>-0.078</td></tr></tbody></table>

***=significant at the 1% level, N.S.=No solution

Except for the estimate in the second column of Table 5, we cannot reject the hypothesis that $\lambda=0$. The data thus indicate that there is a learning process at work. The coefficient of habit-formation is estimated to be close to one in the level estimations, but much smaller in the fixed effect estimates

A number of socio-demographic variables have little or no effect in the regressions in Table 5, particularly sex, a number of the labour force status dummies, marital status and ethnic origin. Income has a negative effect on cigarette consumption, but this becomes insignificant in the estimates on balanced data. Some regional and year dummies are significant, which could capture price or public health effects. Cigarette consumption falls with age (but there is a negative bias) and is lower for those who are active in community organisations.

A number of health information variables are significant. Health effects often appear in these regressions for certain demographic groups only, which could reflect differing marginal utilities of health across groups, or different proclivities in inferring risk from health developments. Mobility problems do not play a significant role, partly due to the lack of variation, as discussed in section 4. However, some significant results are obtained when we examine developments in subjective health status. As this variable is ordinal, we create dummy variables for all possible movements between the four categories.

We find a negative effect from moving from excellent to poor health, as in the fixed effect estimates. We also have a negative effect from staying in fair or poor health (if the individual has children and is aged over 25). However, for men, a worsening in health status from good is associated with increased smoking, and an improvement in health from fair to good with reduced smoking. Some of these effects disappear in the balanced panel results.
A lung check-up over the past year is associated with a somewhat *higher* current consumption of cigarettes, while heart check-ups are associated with reduced consumption (for men, but not for women). With respect to heart or lung problems, we find that an increase in such problems for older men reduces smoking. The last two health variables provide some evidence of interdependencies at the household level, but in the opposite direction to that expected (although both become insignificant in column 4's balanced panel estimates). A rise in the number of individual heart or lung problems is associated with reduced consumption, as is an improvement in other smokers' subjective health (contrary to demonstration effects).

As discussed above, we can use a multi-stage technique to obtain a rough idea of the biases in these level estimates without fixed effects. Table 6 shows the estimated sign of these biases for the estimates in columns 1 and 3 of Table 5. The estimate on one-period lagged consumption is biased upwards, as expected. There is, however, no bias in the estimate on two-period lagged consumption. As it is the latter which is behind our estimate of $\lambda$, we feel confident that the conclusion regarding speed of learning is robust. Also important are the biases associated with the health information variables. A number of significant biases are identified. However, only for three out of the eleven health variables do we find that the bias may have led us to an erroneous conclusion regarding the sign and significance of the effect.

Overall, the estimates on the lagged consumption variables suggest the presence of both habit-formation and learning. We have, however, not been totally successful in identifying an impact of health development variables on cigarette consumption. In particular, we are not able to satisfactorily calculate health information variables in the first-difference equations. One important point (about which we can do very little) is that the variables we have used to try to model explicitly this process measure only imperfectly the information that the individual receives and, perhaps more importantly, believes and acts upon. Another important point which we have not hitherto raised is that of adjustment costs (Suranovic et al., 1999), thought
to be associated with reductions in cigarette consumption, but not necessarily with increases.
In the face of such costs, an individual's response to health information may be muted, even
though a process of learning about health consequences is present. The relation between
adjustment costs (which we have not attempted to model) and the effect of health information
on cigarette consumption will depend in a natural way on the individual's subjective discount
rate, β.

The presence of adjustment costs leads to selection bias. One interpretation of the health
results in Table 5, is that, as health changes, some smokers quit altogether. As quitting is
generally negatively correlated with past consumption, we may observe greater than average
consumption amongst those who continue smoking after a health development, due to non-
random quitting. In the light of the somewhat mitigated results for the health variables in
explaining cigarette consumption in Table 5, we thus consider whether health developments
are correlated with the decision to stop smoking.

We estimate a probit quit equation (between *t* and *t+1*), as a function of health
developments between *t*-1 and *t*. We include one-period lagged consumption as a proxy for the
adjustment costs associated with stopping smoking. It is obviously difficult to distinguish
adjustment costs from habit formation, as both are assumed to be captured by past
consumption. The finding that past consumption is negatively correlated with quit probability
(as we find below) is consistent with both hypotheses. As one-period lagged consumption is
endogenous, it is instrumented by consumption lagged two or more periods, plus socio-
demographic variables. We use heteroscedastic probit techniques, whereby individual
heteroscedasticity is modelled as a function of a vector of explanatory variables, *X*ᵢ. Chi-
squared tests show that the hypothesis of no heteroscedasticity is rejected by the data
(although very similar results are obtained in a standard probit model).

The results are presented in Table 7. There are five main points to note.
(a) Lagged consumption is negatively correlated with the quit probability, as in Jones (1994).

(b) Social activity, income and education are all positively correlated with quitting.

(c) Six out of the eight health variables enter with the expected sign. Staying in excellent (good or fair) health reduces (increases) the quit probability. A change in health status from good to poor increases quit probability for the young. Those with a heart check-up are more likely to quit.

(d) An improvement in the health of other household smokers reduces quitting, as demonstration effects would predict.

(e) There are, however, two health variables which are incorrectly signed. An increase in the number of heart or lung problems for 35-45 year olds reduces quitting, as does a change in health status from excellent to poor.

These quit equations are generally more in line with the predictions of the theoretical model regarding the effect of health information than are the consumption equations in Table 5. It remains true, however, that a number of health variables are "misbehaved" in our regressions. One point is that our health variables may be inadequate proxies for an individual's true health developments, or that many of smokers' health developments may be perceived by them to have nothing to do with smoking.

An alternative hypothesis emphasises the role of cigarettes in relieving stress, while declining health is in itself stressful. Without developing a full empirical model (involving the joint modelling of stress and cigarette consumption, as a function of health developments), we carried out a simple test using one measure of stress available in the BHPS, the GHQ-12 (developed by Goldberg, 1972). This battery of twelve questions in a self-completion questionnaire covers feelings of helplessness, depression, happiness, problems sleeping, and so on¹⁵. We use the caseness measure of GHQ as our stress indicator, which counts the number of
questions that are answered "negatively". This index thus runs from 0 to 12. We estimate a
simple ordered probit of the caseness GHQ score using all of Table 5's health variables as
regressors.

There are six "wrongly-signed" health variables in Table 5 (whereby improving health is associated with a rise in cigarette consumption, for example). Our GHQ regression reproduces the signs of all six of these variables: a health development associated with more (less) smoking is also associated with greater (lower) stress. Five out of the six estimates are significant, the exceptions being the household health development variables (which is, however, insignificant in Table 5's balanced panel estimates). Although these results are only suggestive, there seems to be a case for explicitly considering stress when modelling cigarette consumption; and in the data examined here, worsening health is associated with higher stress.

6. Conclusion

One of the major objectives of public health policy over recent years has been to reduce tobacco consumption. One widely-used policy is the provision of health information. It is in this perspective that we have modelled learning about smoking's health risks, using changes in various health variables as proxies for the revelation of this information. Taking advantage of the household aspect of our data, we have distinguished between information revealed by the respondent's own health outcomes, and that coming from the health outcomes of other smokers in the household (often called demonstration effects). We believe this to be one of the first papers to model explicitly the impact of different sources of health information on smoking behaviour.

Our data cover around 10 000 individuals per year over a seven-year period. We develop an explicit model of cigarette consumption including both habit-formation and learning. We consider lung and heart problems, lung and heart check-ups, and subjective health status as our
health variables. Our main results are consistent with the joint existence of habit formation and
a process of learning about the health impact of smoking from health developments.

The cigarette consumption equations reveal a number of significant correlations with health
development variables. Although some of these are "correctly" signed, showing that worsening
health reduces consumption, others attract coefficients with the opposite sign to that expected.
We offer two explanations. The first involves explicitly modelling quit decisions. If quit
probability is negatively correlated with consumption (as is usually found), then the sample of
remaining smokers will be non-random. Our quit equations reveal mostly correctly-signed
coefficients on the health development variables. This conclusion is consistent with that of
Lanoie and Leclair (1998), who use Canadian panel data from 1980 to 1995 to show that
public health information does not influence cigarette demand by smokers, but is significantly
correlated with the participation decision. The second explanation involves the perceived
stress-reducing role of smoking. Using a psychological health variable, we show that most of
the health development variables that paradoxically increase smoking also increase stress.

Although we have been able to identify some significant correlations between individual
health developments and smoking behaviour, by and large we have been less successful in
finding evidence of demonstration effects, whereby health developments of other smokers in
the same household influence smoking. One of our conclusions is therefore that health
information largely matters only when it is personalised: public health policy aimed at
providing general information about the health consequences of smoking may have only a
limited impact on both the number of cigarettes smoked and on the decision to stop smoking.
A second conclusion for policy purposes is that health information may increase stress, which
is in itself positively correlated with cigarette consumption. A health program combining health
information with personalised counselling may therefore have a greater impact than one based
only on the revelation of smoking's harmful health consequences.
We obviously have not been able to cover all of the pertinent issues regarding health information and smoking. In particular, we have not jointly modelled the participation decision and the level of cigarette consumption, and, in general, we have not estimated starting to smoke equations. We have modelled quitting, but without distinguishing between successful and unsuccessful quits (which will likely require more waves of panel data than we currently have available). In addition, measurement errors in self-reported cigarette consumption and the qualitative nature of most of our health variables have rendered the estimation of fixed-effects models problematic. Last, our health variables are only imperfect proxies of the information that the individual receives regarding smoking. Future work may well find better measures.

Models of habit-formation have been very popular in both theoretical and empirical work on the demand for certain types of goods. Perhaps the most general conclusion of this paper is that the combination of habit-formation with models of learning under uncertainty may prove to be a profitable way of analysing a variety of individual behaviours.
* We are grateful to Brigitte Dormont, Daniele Fabbri, Louis Lévy-Garboua, Salah Ghabri, David Margolis, Georges Ménahem, Claude Montmarquette, Jean-Marc Robin and seminar participants at CREST, the 8th European Workshop on Econometrics and Health Economics (Catania), and the 16th Journées de Micro-économie Appliquée (Lyon) for comments. The BHPS data were made available through the ESRC Data Archive. The data were originally collected by the ESRC Research Centre on Micro-social Change at the University of Essex. Neither the original collectors of the data nor the Archive bear any responsibility for the analyses or interpretations presented here.

<footnote n="1">¹ Viscusi (1992) examines the impact of publicly-provided health information on individuals' perception of the risks from smoking, and on the prevalence of smoking.</footnote>

<footnote n="2">² An alternative approach is to show that others' income, or one's own past income, enters negatively and significantly in proxy utility equations; see Clark and Oswald (1996) and Clark (1999).</footnote>

<footnote n="3">³ Public health campaigns are also important here, although we do not have the necessary information to analyse their effect empirically.</footnote>

<footnote n="4">⁴ This is reminiscent of the literature on "social learning" (Banerjee, 1993, Bikhchandani et al., 1992, Ellison and Fudenberg, 1993 and 1995, Bala and Goyal, 1998), although it is not clear exactly how the transmission mechanism should be specified in an empirical model.</footnote>

<footnote n="5">⁵ For prices to be a useful instrument, there must be sufficient variation in them. This is far more likely to be true in the US (due to state taxes) than in the UK.</footnote>

<footnote n="6">⁶ Myopic habit-formation implies that the individual takes into account past consumption when deciding current consumption, but ignores the effect of current consumption on future consumption decisions. This yields additively separable intertemporal preferences, which is not the case in the rational addiction model.</footnote>

<footnote n="7">⁷ See the web site http://www.nida.nih.gov/Infofax/tobacco.html, or Roques (1999).</footnote>

<footnote n="8">⁸ The effect of health information in reducing consumption is often modelled using time series aggregate data: a fall over time in the intercept of a consumption equation being interpreted as resulting from the public provision of health information (see Gallet and Agarwal, 1999).</footnote>

<footnote n="9">⁹ We cannot match households across waves, so estimates are restricted to an individual correlation structure.</footnote>

<footnote n="10">¹⁰ All health information previous to *t-1* will be incorporated in $E_{it-1}(r_{it-1})$, which has been explicitly substituted out of our equation (which in fact explains the presence of two-period lagged consumption).</footnote>

<footnote n="11">¹¹ We do not address the endogeneity of starting (see Douglas and Hariharan, 1994) or stopping decisions. Given the complexity of estimating even consumption equations in our model, and the likely correlations between the decision to start and stop and previous consumption levels (both one's own and of others), the careful estimation of such a system remains a subject for future work.</footnote>

<footnote n="12">¹² In addition, corrections for autocorrelation will be less efficient on unbalanced panels, in which the proportion of observations containing no information about this autocorrelation is larger.</footnote>

<footnote n="13">¹³ The estimated value of the autocorrelation coefficient is relatively low, which somewhat reduces our worries about instrumenting using lagged consumption. An alternative method, using lagged changes in consumption as instruments (Blundell and Bond, 1998) did not yield usable results, likely due to the noise in consumption changes (see Table 3).</footnote>

<footnote n="14">¹⁴ This is a large-sample method to test the hypothesis that $r(\hat{\theta})=0$, $r$ being a function of the coefficients $\hat{\theta}$, of which we have an estimate $\hat{\theta}$. Asymptotically, $W=r(\hat{\theta})(\text{var}(r(\hat{\theta})))^{-1}r(\hat{\theta})\rightarrow\chi^2(1)$, and $\text{var}(r(\hat{\theta}))=C\text{var}(\hat{\theta})C$, where $C = \frac{\partial r(\hat{\theta})}{\partial \hat{\theta}}$.</footnote>

<footnote n="15">¹⁵ Individuals are asked whether they have recently "been able to concentrate on whatever you're doing ?", "lost much sleep over worry ?", "felt constantly under strain ?", "felt you couldn't overcome your difficulties ?", "been feeling unhappy or depressed ?", "been losing confidence in yourself ?", "been thinking of yourself as a worthless person ?", felt that you were playing a useful part in things ?", "felt capable of making decisions about things ?", "been able to enjoy your normal day-to-day activities ?", "been able to face up to problems ?" and "been feeling reasonably happy, all things considered ?". All questions are answered on a four-point</footnote>
response scale, with two "negative" and two "positive" answers. Clark and Oswald (1994) use the GHQ to
examine the well-being effects of unemployment.
# Appendix A. Description of Sample.

The sample consists of all individuals with positive cigarette consumption over waves t, t-1 and t-2. It thus covers five waves only (3 to 7) with 8557 observations on 2537 individuals. The following table summarises the "smoking trajectories" of these individuals ("X" indicating smoking at the current wave plus the two previous waves, "0" indicating other trajectories).

<table><caption>Table A1.</caption><thead><tr><th>Number of individuals</th><th>%</th><th>Cumulative %</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th></tr></thead><tbody><tr><td>1102</td><td>43.44</td><td>43.44</td><td>X</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>224</td><td>8.83</td><td>52.27</td><td>O</td><td>O</td><td>O</td><td>O</td><td>X</td></tr><tr><td>207</td><td>8.16</td><td>60.43</td><td>O</td><td>O</td><td>O</td><td>X</td><td>X</td></tr><tr><td>192</td><td>7.57</td><td>67.99</td><td>X</td><td>O</td><td>O</td><td>O</td><td>O</td></tr><tr><td>174</td><td>6.86</td><td>74.85</td><td>X</td><td>X</td><td>O</td><td>O</td><td>O</td></tr><tr><td>143</td><td>5.64</td><td>80.49</td><td>O</td><td>O</td><td>X</td><td>X</td><td>X</td></tr><tr><td>111</td><td>4.38</td><td>84.86</td><td>X</td><td>X</td><td>X</td><td>X</td><td>O</td></tr><tr><td>109</td><td>4.30</td><td>89.16</td><td>O</td><td>X</td><td>X</td><td>X</td><td>X</td></tr><tr><td>103</td><td>4.06</td><td>93.22</td><td>X</td><td>X</td><td>X</td><td>O</td><td>O</td></tr><tr><td>40</td><td>1.58</td><td>94.80</td><td>O</td><td>O</td><td>O</td><td>X</td><td>O</td></tr><tr><td>38</td><td>1.50</td><td>96.29</td><td>O</td><td>X</td><td>O</td><td>O</td><td>O</td></tr><tr><td>35</td><td>1.38</td><td>97.67</td><td>O</td><td>O</td><td>X</td><td>O</td><td>O</td></tr><tr><td>25</td><td>0.99</td><td>98.66</td><td>O</td><td>O</td><td>X</td><td>X</td><td>O</td></tr><tr><td>20</td><td>0.79</td><td>99.45</td><td>O</td><td>X</td><td>X</td><td>X</td><td>O</td></tr><tr><td>14</td><td>0.55</td><td>100.00</td><td>O</td><td>X</td><td>X</td><td>O</td><td>O</td></tr><tr><td>2537</td><td>100</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<table><caption>Table A2. Descriptive Statistics</caption><thead><tr><th>Variables</th><th>No. Obs</th><th>Mean</th><th>Standard Deviation</th><th>Min.</th><th>Max.</th></tr></thead><tbody><tr><td colspan="6"><strong>DEPENDENT VARIABLE</strong></td></tr><tr><td>Cigarette Consumption</td><td>8557</td><td>16.49</td><td>8.09</td><td>1</td><td>81</td></tr><tr><td>One-period lagged consumption</td><td>8557</td><td>16.43</td><td>8.03</td><td>1</td><td>81</td></tr><tr><td>Two-period lagged consumption</td><td>8557</td><td>16.29</td><td>8.13</td><td>1</td><td>81</td></tr><tr><td colspan="6"><strong>INSTRUMENTAL VARIABLES</strong></td></tr><tr><td>Max(x<sub>t-2</sub>:0)</td><td>8557</td><td>16.29</td><td>8.13</td><td>1</td><td>81</td></tr><tr><td>Max(x<sub>t-3</sub>:0)</td><td>8112</td><td>12.27</td><td>10.03</td><td>0</td><td>81</td></tr><tr><td>Max(x<sub>t-4</sub>:0)</td><td>8141</td><td>8.59</td><td>10.14</td><td>0</td><td>81</td></tr><tr><td>Max(x<sub>t-5</sub>:0)</td><td>8258</td><td>5.41</td><td>9.09</td><td>0</td><td>60</td></tr><tr><td>Max(x<sub>t-6</sub>:0)</td><td>8415</td><td>2.57</td><td>6.87</td><td>0</td><td>60</td></tr><tr><td colspan="6"><strong>SOCIO-DEMOGRAPHIC VARIABLES</strong></td></tr><tr><td>Age</td><td>8557</td><td>43.33</td><td>15.94</td><td>17</td><td>92</td></tr><tr><td>Sex</td><td>8557</td><td>0.45</td><td>0.50</td><td>0</td><td>1</td></tr><tr><td>Log monthly income (£1000's)</td><td>8412</td><td>8.68</td><td>0.93</td><td>-0.73</td><td>12.20</td></tr><tr><td>Household Size = 1</td><td>8557</td><td>0.16</td><td>0.36</td><td>0</td><td>1</td></tr><tr><td>Household Size = 2</td><td>8557</td><td>0.32</td><td>0.47</td><td>0</td><td>1</td></tr><tr><td>Household Size = 3</td><td>8557</td><td>0.21</td><td>0.41</td><td>0</td><td>1</td></tr><tr><td>Household Size = 4</td><td>8557</td><td>0.19</td><td>0.39</td><td>0</td><td>1</td></tr><tr><td>Household Size = 5</td><td>8557</td><td>0.09</td><td>0.29</td><td>0</td><td>1</td></tr></tbody></table>
<table><tr><td>Household Size > 5</td><td>8557</td><td>0.03</td><td>0.18</td><td>0</td><td>1</td></tr><tr><td>Spouse present at interview</td><td>8557</td><td>0.28</td><td>0.45</td><td>0</td><td>1</td></tr><tr><td>Child present at interview</td><td>8557</td><td>0.11</td><td>0.32</td><td>0</td><td>1</td></tr><tr><td>Other adult present at interview</td><td>8557</td><td>0.12</td><td>0.33</td><td>0</td><td>1</td></tr><tr><td>Married</td><td>8557</td><td>0.53</td><td>0.50</td><td>0</td><td>1</td></tr><tr><td>Single</td><td>8557</td><td>0.11</td><td>0.32</td><td>0</td><td>1</td></tr><tr><td>Widowed</td><td>8557</td><td>0.07</td><td>0.25</td><td>0</td><td>1</td></tr><tr><td>Divorced</td><td>8557</td><td>0.08</td><td>0.28</td><td>0</td><td>1</td></tr><tr><td>Separated</td><td>8557</td><td>0.03</td><td>0.16</td><td>0</td><td>1</td></tr><tr><td>Living together</td><td>8557</td><td>0.17</td><td>0.38</td><td>0</td><td>1</td></tr><tr><td>Belongs to another community group</td><td>8474</td><td>0.01</td><td>0.10</td><td>0</td><td>1</td></tr><tr><td>Active in religious organisation</td><td>8474</td><td>0.05</td><td>0.21</td><td>0</td><td>1</td></tr><tr><td>Active in Sports</td><td>8474</td><td>0.13</td><td>0.34</td><td>0</td><td>1</td></tr><tr><td>Active in other organisation</td><td>8474</td><td>0.04</td><td>0.19</td><td>0</td><td>1</td></tr><tr><td>Manager (permanent)</td><td>8550</td><td>0.08</td><td>0.27</td><td>0</td><td>1</td></tr><tr><td>Supervisor (permanent)</td><td>8550</td><td>0.08</td><td>0.28</td><td>0</td><td>1</td></tr><tr><td>No responsibilities (permanent)</td><td>8550</td><td>0.31</td><td>0.46</td><td>0</td><td>1</td></tr><tr><td>No responsibilities (temporary)</td><td>8550</td><td>0.20</td><td>0.40</td><td>0</td><td>1</td></tr><tr><td>Self-employed</td><td>8550</td><td>0.07</td><td>0.25</td><td>0</td><td>1</td></tr><tr><td>Unemployed</td><td>8550</td><td>0.08</td><td>0.27</td><td>0</td><td>1</td></tr><tr><td>Retired</td><td>8550</td><td>0.14</td><td>0.35</td><td>0</td><td>1</td></tr><tr><td>Housewife</td><td>8550</td><td>0.11</td><td>0.31</td><td>0</td><td>1</td></tr><tr><td>Studying or Training</td><td>8550</td><td>0.02</td><td>0.15</td><td>0</td><td>1</td></tr><tr><td>Other</td><td>8550</td><td>0.07</td><td>0.26</td><td>0</td><td>1</td></tr><tr><td>Education &lt;A-level</td><td>8524</td><td>0.47</td><td>0.50</td><td>0</td><td>1</td></tr><tr><td>Education = A-Level</td><td>8524</td><td>0.33</td><td>0.47</td><td>0</td><td>1</td></tr><tr><td>Education &gt; A-level</td><td>8524</td><td>0.20</td><td>0.40</td><td>0</td><td>1</td></tr><tr><td>Present three waves</td><td>8557</td><td>0.06</td><td>0.23</td><td>0</td><td>1</td></tr><tr><td>Present four waves</td><td>8557</td><td>0.10</td><td>0.31</td><td>0</td><td>1</td></tr><tr><td>Present five waves</td><td>8557</td><td>0.09</td><td>0.29</td><td>0</td><td>1</td></tr><tr><td>Present six waves</td><td>8557</td><td>0.10</td><td>0.30</td><td>0</td><td>1</td></tr><tr><td>Present seven waves</td><td>8557</td><td>0.64</td><td>0.48</td><td>0</td><td>1</td></tr></table>

## HEALTH VARIABLES

<table><tr><td>Health hinders climbing the stairs</td><td>8557</td><td>0.08</td><td>0.27</td><td>0</td><td>1</td></tr><tr><td>Health hinders walking more than 10mn</td><td>8557</td><td>0.08</td><td>0.28</td><td>0</td><td>1</td></tr><tr><td>LIMACT</td><td>8557</td><td>0.16</td><td>0.50</td><td>0</td><td>2</td></tr><tr><td>LIMACTH</td><td>8557</td><td>0.05</td><td>0.29</td><td>0</td><td>4</td></tr><tr><td>Lung problem</td><td>8557</td><td>0.15</td><td>0.36</td><td>0</td><td>1</td></tr><tr><td>Heart problem</td><td>8557</td><td>0.11</td><td>0.32</td><td>0</td><td>1</td></tr><tr><td>HLTHPRB</td><td>8557</td><td>0.26</td><td>0.50</td><td>0</td><td>2</td></tr><tr><td>HLTHPRBH</td><td>8557</td><td>0.09</td><td>0.33</td><td>0</td><td>4</td></tr><tr><td>Health status is excellent</td><td>8557</td><td>0.18</td><td>0.38</td><td>0</td><td>1</td></tr><tr><td>Health status is good</td><td>8557</td><td>0.46</td><td>0.50</td><td>0</td><td>1</td></tr><tr><td>Health status is fair</td><td>8557</td><td>0.25</td><td>0.43</td><td>0</td><td>1</td></tr><tr><td>Health status is bad or poor</td><td>8557</td><td>0.12</td><td>0.33</td><td>0</td><td>1</td></tr><tr><td>Number of other household smokers in excellent health</td><td>8557</td><td>-0.01</td><td>0.33</td><td>-2</td><td>2</td></tr><tr><td>Number of other household smokers in good health</td><td>8557</td><td>-0.01</td><td>0.51</td><td>-4</td><td>3</td></tr><tr><td>Number of other household smokers in fair health</td><td>8557</td><td>0.00</td><td>0.38</td><td>-3</td><td>3</td></tr><tr><td>Number of other household smokers in excellent health</td><td>8557</td><td>0.00</td><td>0.24</td><td>-3</td><td>2</td></tr></table>
bad/poor health

<table><tr><td>Male, 55 or over, heart or lung problems increased</td><td>8557</td><td>0.01</td><td>0.11</td><td>0</td><td>1</td></tr><tr><td>35-45, heart or lung problems increased</td><td>8557</td><td>0.012</td><td>0.110</td><td>0</td><td>1</td></tr><tr><td>Health status changed from excellent to fair</td><td>8536</td><td>0.014</td><td>0.116</td><td>0</td><td>1</td></tr><tr><td>Health status changed from excellent to poor</td><td>8536</td><td>0.292</td><td>0.455</td><td>0</td><td>1</td></tr><tr><td>Health status stays good</td><td>8536</td><td>0.111</td><td>0.315</td><td>0</td><td>1</td></tr><tr><td>Health status stays fair</td><td>8557</td><td>0.025</td><td>0.157</td><td>0</td><td>1</td></tr><tr><td>35-45, health status stays excellent</td><td>8557</td><td>0.001</td><td>0.036</td><td>0</td><td>1</td></tr><tr><td>25-35, health status changed from good to poor</td><td>8557</td><td>0.045</td><td>0.207</td><td>0</td><td>1</td></tr><tr><td>Male, health status worsened from good</td><td>8557</td><td>0.034</td><td>0.181</td><td>0</td><td>1</td></tr><tr><td>Male, health status changed from fair to good</td><td>8557</td><td>0.028</td><td>0.165</td><td>0</td><td>1</td></tr><tr><td>Has children, over 25, health status stays fair</td><td>8557</td><td>0.018</td><td>0.131</td><td>0</td><td>1</td></tr><tr><td>Has children, over 25, health status stays poor</td><td>8557</td><td>0.007</td><td>0.081</td><td>0</td><td>1</td></tr><tr><td>Male, under 45, lung check-up, lung problems at t-1</td><td>8557</td><td>0.044</td><td>0.204</td><td>0</td><td>1</td></tr><tr><td>45 or over, lung check-up</td><td>8557</td><td>0.021</td><td>0.142</td><td>0</td><td>1</td></tr><tr><td>Male, under 65, heart check-up, heart problems at t-1</td><td>8557</td><td>0.030</td><td>0.172</td><td>0</td><td>1</td></tr><tr><td>Female, 65 or over, heart check-up</td><td>8557</td><td>0.362</td><td>0.480</td><td>0</td><td>1</td></tr><tr><td>Heart check-up, no heart problem at t-1</td><td>8557</td><td>0.012</td><td>0.109</td><td>0</td><td>1</td></tr><tr><td>Female, 35 or over heart or lung problems of other household smokers increased</td><td>8557</td><td>0.019</td><td>0.138</td><td>0</td><td>1</td></tr><tr><td>Other households smokers' health status changed from good to excellent</td><td>8557</td><td>0.019</td><td>0.138</td><td>0</td><td>1</td></tr><tr><td>Number of other household smokers in excellent health rises</td><td>8557</td><td>0.043</td><td>0.203</td><td>0</td><td>1</td></tr></table>

Note: Except for age, the distribution of these variables is very similar in this sample and the whole population of smokers.
Appendix B. Estimation Methods

In equations (13) and (15), dx<sub>it-1</sub> and dx<sub>it-2</sub> (respectively x<sub>it-1</sub> and x<sub>it-2</sub>) have to be instrumented, due to the form of the error term (respectively its autocorrelation). We correct for this endogeneity using traditional instrumentation techniques. We can write the equations as

$$
X = Z\beta + \tilde{\alpha} \tag{16}
$$

where Z is the matrix of explanatory variables. Let W be the matrix of instruments, then the
GMM estimator of β results from the maximisation of the following quadratic equation:

$$
(X - Z\beta)' WAW' (X - Z\beta) \tag{17}
$$

where the weighting matrix A equals (WW')^{-1} for the first-stage IV estimation, and
[Var(\frac{1}{\sqrt{N}}W'(X - Z\beta))]^{-1} for the second-stage GMM estimation (N being the number of
individuals). For the GMM estimates, a first estimate of β is required, for example using the IV
method, in order to calculate the inverse of the variance-covariance matrix of moments,
\hat{A} = [Var(\frac{1}{\sqrt{N}}W'(X - Z\hat{\beta}))]^{-1}. We can then re-estimate β using the GMM method and re-
iterate the process until convergence is reached<fnref n="3" />. We thus obtain the following estimate:
\hat{\beta}_{GMM} = (Z^T W \hat{A} X)^{-1} X^T W \hat{A} W^T X, to be compared with \hat{\beta}_{IV} = (Z^T P_w Z)^{-1} Z^T P_w X. The variance-
covariance matrix of the coefficients for the GMM method is: \hat{V}(\hat{\beta}_{GMM}) = N(Z^T W \hat{A} W^T Z)^{-1}.

This method is typically more efficient than that of instrumental variables (Davidson and MacKinnon, 1993, p.612). It nevertheless requires an asymptotically convergent estimate of the variance of the moments. Let $\beta_{\text{IV}}$ be the IV estimate, then we have to construct $\hat{A} = [\text{Var}(W'(X - Z\hat{\beta}_{\text{IV}}))]^{-1}$, using $\hat{\alpha} = X - Z\hat{\beta}_{\text{IV}}$, the vector of estimated residuals. The main difficulty in these estimations comes from the matrix of weights, $A$, which may not be strictly positive definite. In this case, it is necessary to reduce the number of instruments, or to increase the size of the sample. Hansen's test of over-identifying restrictions considers the validity of the $J$ moment conditions, corresponding to the instruments used: the instruments should be as orthogonal as possible to the residuals. It is also a test of the exogeneity of the instruments. Under this latter hypothesis we have: $N\hat{\alpha}W^T\hat{A}W\hat{\alpha} \to \chi^2(J-K)$, where $K$ is the number of explanatory variables. $m_2$ test is a statistic proposed by Arellano and Bond (1991) to detect the presence of serially correlated error terms in the first-differenced equation. In case of rejection of this assumption, we have to adjust the instrument set.

An alternative approach mixes IV and GMM, using "standard" OLS techniques with instrumental variables to derive the estimated coefficients, but the method of moments to estimate the associated standard errors In this method (IV/GMM), the variance-covariance matrix is estimated by

$$
\hat{V}(\hat{\beta}_{\text{IV/GMM}}) = (Z^T P_w Z)^{-1} Z^T W (W^T W)^{-1} [\text{Var}(W'(X - Z\hat{\beta}_{\text{IV}}))] (W^T W)^{-1} W^T Z (Z^T P_w Z)^{-1}, \text{ where}
P_w \text{ is the orthogonal projection in the space of the instrumental variables. The re-estimation of}
\text{Table 4 and 5's specifications using this method did not yield any additional insights.}
$$

<footnote n="3"><sup>3</sup> In our data, convergence was reached after only one iteration.</footnote>
We sometimes use a matrix of instruments of the form suggested by Arellano-Bond (1991) in our estimations (denoted A-B). When some of these A-B instruments are too weak, we preferred to use a simpler but more robust intrumentation method. In this case the individual matrix of instruments is of the following type:

$$ \begin{bmatrix} x_{i2} & x_{i1} & 0 & 0 \\ x_{i3} & x_{i2} & x_{i1} & 0 \\ x_{i4} & x_{i3} & x_{i2} & x_{i1} \\ x_{i7} & x_{i4} & x_{i3} & x_{i2} \end{bmatrix} $$

The bias in the estimates when we omit the fixed effects, is $(Z' P_W Z)^{-1} Z' P_W D$, where D is the vector of individual fixed effects. This is exactly the coefficients vector of the regression of D on P_W Z. We thus first obtain a consistent estimate of D, $\hat{d}$, from the estimation of the model in first difference. Then regressing, by IV or GMM, $\hat{d}$ on Z reveals the sign of the bias.
<table><caption>Table 1. Smoking Data in the BHPS</caption><thead><tr><th>Wave</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th></tr></thead><tbody><tr><td>Number of individuals</td><td>10264</td><td>9845</td><td>9600</td><td>9481</td><td>9249</td><td>9438</td><td>9373</td></tr><tr><td>% non-response to smoking questions</td><td>1.68%</td><td>1.96%</td><td>6.65%</td><td>5.09%</td><td>5.04%</td><td>3.76%</td><td>3.38%</td></tr><tr><td>Number of smokers</td><td>2900</td><td>2638</td><td>2429</td><td>2455</td><td>2413</td><td>2522</td><td>2490</td></tr><tr><td>% of smokers</td><td>28.25%</td><td>26.80%</td><td>25.30%</td><td>25.89%</td><td>26.09%</td><td>26.72%</td><td>26.57%</td></tr><tr><td>% stopping smoking</td><td>9.83%</td><td>8.61%</td><td>8.11%</td><td>5.62%</td><td>7.09%</td><td>7.18%</td><td></td></tr><tr><td>% starting smoking</td><td></td><td>5.76%</td><td>7.12%</td><td>7.54%</td><td>8.45%</td><td>6.34%</td><td>7.03%</td></tr></tbody></table>

<table><caption>Table 2. Number of Cigarettes Smoked</caption><thead><tr><th>Number of cigarettes smoked per day</th><th>Frequency</th><th>%</th><th>Cumulative %</th></tr></thead><tbody><tr><td>Between 1 and 4</td><td>351</td><td>4.11%</td><td>4.11%</td></tr><tr><td>5 cigarettes</td><td>377</td><td>4.42%</td><td>8.53%</td></tr><tr><td>Between 6 and 9</td><td>474</td><td>5.55%</td><td>14.08%</td></tr><tr><td>10 cigarettes</td><td>1454</td><td>17.03%</td><td>31.11%</td></tr><tr><td>Between 11 and 14</td><td>383</td><td>4.49%</td><td>35.60%</td></tr><tr><td>15 cigarettes</td><td>1402</td><td>16.42%</td><td>52.02%</td></tr><tr><td>Between 16 and 19</td><td>204</td><td>2.39%</td><td>54.41%</td></tr><tr><td>20 cigarettes</td><td>2602</td><td>30.48%</td><td>84.89%</td></tr><tr><td>Between 21 and 24</td><td>52</td><td>0.61%</td><td>85.50%</td></tr><tr><td>25 cigarettes</td><td>474</td><td>5.55%</td><td>91.05%</td></tr><tr><td>Between 26 and 29</td><td>19</td><td>0.22%</td><td>91.27%</td></tr><tr><td>30 cigarettes</td><td>494</td><td>5.79%</td><td>97.06%</td></tr><tr><td>Between 30 and 40</td><td>50</td><td>0.59%</td><td>97.65%</td></tr><tr><td>40 cigarettes</td><td>167</td><td>1.96%</td><td>99.60%</td></tr><tr><td>Over 40</td><td>34</td><td>0.40%</td><td>100.00%</td></tr><tr><td>Total</td><td>8557</td><td>100.00%</td><td></td></tr></tbody></table>

<table><caption>Table 3. Yearly Change in Number of Cigarettes Smoked</caption><thead><tr><th>Year-to-year change in number of cigarettes smoked per day</th><th>Frequency</th><th>%</th><th>Cumulative %</th></tr></thead><tbody><tr><td>Reduction of more than 10 cigarettes per day</td><td>138</td><td>1.62%</td><td>1.62%</td></tr><tr><td>10 cigarettes less per day</td><td>334</td><td>3.91%</td><td>5.53%</td></tr><tr><td>Between 9 and 6 less cigarettes per day</td><td>134</td><td>1.57%</td><td>7.10%</td></tr><tr><td>5 cigarettes less per day</td><td>892</td><td>10.45%</td><td>17.55%</td></tr><tr><td>Between 4 and 1 less cigarettes per day</td><td>811</td><td>9.50%</td><td>27.05%</td></tr><tr><td>No change</td><td>3793</td><td>44.43%</td><td>71.48%</td></tr><tr><td>Between 1 and 4 more cigarettes per day</td><td>843</td><td>9.87%</td><td>81.35%</td></tr><tr><td>5 cigarettes more per day</td><td>972</td><td>11.39%</td><td>92.74%</td></tr><tr><td>Between 6 and 9 more cigarettes per day</td><td>143</td><td>1.68%</td><td>94.41%</td></tr><tr><td>10 cigarettes more per day</td><td>342</td><td>4.01%</td><td>98.42%</td></tr><tr><td>Increase of more than 10 cigarettes per day</td><td>135</td><td>1.58%</td><td>100.00%</td></tr><tr><td>Total</td><td>8557</td><td>100.00%</td><td></td></tr></tbody></table>
<table><caption>Table 4. Estimation of Cigarette Consumption in First Differences (equation (14))</caption><caption>dx<sub>it</sub> = (λ + a<sub>3</sub>)dx<sub>it-1</sub> - λa<sub>3</sub>dx<sub>it-2</sub> + ψ<sub>1</sub>dY<sub>it</sub> + ψ<sub>2</sub>dΔH<sub>it-1</sub> + ψ<sub>3</sub>dΔH<sub>ft-1</sub> + dξ<sub>it</sub></caption><thead><tr><th>Method</th><th>GMM<br>(FD1)</th><th>GMM<br>(FD1')</th><th>GMM<br>(FD2)</th><th>GMM<br>(FD3)</th><th>GMM<br>(FD4)</th></tr></thead><tbody><tr><td>One-period lagged consumption</td><td>0.080*<br>(0.052)</td><td>0.089*<br>(0.059)</td><td>0.570<br>(0.433)</td><td>0.061<br>(0.063)</td><td>0.333*<br>(0.192)</td></tr><tr><td>Two-period lagged consumption</td><td>0.013<br>(0.026)</td><td>0.008<br>(0.028)</td><td>-0.062<br>(0.080)</td><td>0.009<br>(0.030)</td><td>-0.029<br>(0.044)</td></tr><tr><td>Logarithm real income</td><td>No</td><td>No</td><td>No</td><td>0.025<br>(0.165)</td><td>0.019<br>(0.179)</td></tr><tr><td>Labour force status: manager, permanent</td><td>No</td><td>No</td><td>No</td><td>significant,<br>positive***</td><td>significant,<br>positive***</td></tr><tr><td>Health status changed from excellent to poor</td><td>No</td><td>No</td><td>No</td><td>-2.178*<br>(1.140)</td><td>-2.346*<br>(1.308)</td></tr><tr><td>Divorced</td><td>No</td><td>No</td><td>No</td><td>significant,<br>positive***</td><td>significant,<br>positive***</td></tr><tr><td>Separated</td><td>No</td><td>No</td><td>No</td><td>significant,<br>positive**</td><td>significant,<br>positive**</td></tr><tr><td>Active in community group</td><td>No</td><td>No</td><td>No</td><td>significant,<br>negative**</td><td>significant,<br>negative**</td></tr><tr><td>Variation of the number of household smokers<br>heart/lung problems</td><td>No</td><td>No</td><td>No</td><td>0.340*<br>(0.176)</td><td>0.393*<br>(0.200)</td></tr><tr><td>Controls for time-variant socio-demographic &<br>health effects</td><td>No</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td>Controls for unbalanced panel (4 dummies),<br>waves (4 dummies), regions (18 dummies)</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>Number of observations</td><td>5753</td><td>5723</td><td>5753</td><td>5324</td><td>5324</td></tr><tr><td>m<sub>2</sub> statistic (critical value at 10% level = ±1.65)</td><td>-0.707</td><td>-0.491</td><td>0.964</td><td>-0.360</td><td>1.07</td></tr><tr><td>Hansen Statistic (critical value at 10% level)</td><td>16.92 (14.7)</td><td>4.34 (6.3)</td><td>5.27 (9.2)</td><td>5.43(6.3)</td><td>7.97 (13.3)</td></tr><tr><td>Instruments</td><td>x<sub>it-2</sub>,x<sub>it-3</sub>,x<sub>it-4</sub><br>(A-B)</td><td>x<sub>it-2</sub> to x<sub>it-6</sub></td><td>x<sub>it-3</sub>,x<sub>it-4</sub><br>(A-B)</td><td>x<sub>it-2</sub> to x<sub>it-6</sub></td><td>x<sub>it-3</sub> to x<sub>it-6</sub><br>(A-B)</td></tr></tbody></table>

Standard errors in parentheses. \*=significant at the 10% level, \*\*=significant at the 5% level, \*\*\*=significant at the 1% level, N.S.=insignificant at the 10% level.
<caption>Table 5. Estimation of Current Cigarette Consumption (equation (15))</caption>

$$x_{it} = (\lambda + a_3)x_{it-1} - \lambda a_3 x_{it-2} + a_0(1-\lambda) + \psi_1 Y_{it} + \psi_2 \Delta H_{it-1} + \psi_3 \Delta H_{it-2} + \tilde{\varepsilon}_{it}$$

<table><thead><tr><th>Method</th><th>GMM (L1)</th><th>GMM (L2)</th><th>GMM (L3)</th><th>GMM (Balanced)</th></tr></thead><tbody><tr><td>One-period lagged consumption</td><td>1.037***<br>(.070)</td><td>0.567*<br>(0.295)</td><td>0.902***<br>(0.216)</td><td>1.031***<br>(0.050)</td></tr><tr><td>Two-period lagged consumption</td><td>-0.056<br>(.057)</td><td>0.395<br>(0.279)</td><td>0.076<br>(0.204)</td><td>-0.058<br>(0.043)</td></tr><tr><td>Health status changed from excellent to poor</td><td>-2.357**<br>(1.140)</td><td>-2.584***<br>(0.996)</td><td>-2.765***<br>(1.042)</td><td>-2.555*<br>(1.344)</td></tr><tr><td>Has children, Over 25, Health status stays fair</td><td>-0.666**<br>(.308)</td><td>-0.554*<br>(0.348)</td><td>-0.802***<br>(0.304)</td><td>-.410<br>(.340)</td></tr><tr><td>Has children, Over 25, Health status stays poor</td><td>-0.897**<br>(.420)</td><td>-0.808*<br>(0.427)</td><td>-0.898**<br>(0.403)</td><td>-.668<br>(.441)</td></tr><tr><td>Male, Health status worsened from good</td><td>1.246***<br>(.358)</td><td>0.928**<br>(0.410)</td><td>1.193***<br>(0.375)</td><td>1.356***<br>(.420)</td></tr><tr><td>Male, Health status changed from fair to good</td><td>-0.755**<br>(.358)</td><td>-0.398<br>(0.466)</td><td>-0.750*<br>(0.401)</td><td>-0.994**<br>(.436)</td></tr><tr><td>Male, under 45, lung check-up, lung problems at t-1</td><td>1.974**<br>(0.954)</td><td>1.659*<br>(0.982)</td><td>2.062**<br>(0.934)</td><td>1.358<br>(1.213)</td></tr><tr><td>45 or over, lung check-up</td><td>1.478***<br>(0.365)</td><td>0.999**<br>(0.454)</td><td>1.377***<br>(0.393)</td><td>1.439***<br>(.396)</td></tr><tr><td>Male, under 65, heart check-up, heart problems at t-1</td><td>-1.042**<br>(0.488)</td><td>-0.718*<br>(0.472)</td><td>-0.975**<br>(0.453)</td><td>-1.102**<br>(.531)</td></tr><tr><td>Female, 65 or over, heart check-up</td><td>0.470*<br>(0.283)</td><td>0.207<br>(0.282)</td><td>0.311<br>(0.264)</td><td>-.033<br>(.210)</td></tr><tr><td>Male, 55 or over, heart or lung problems increased</td><td>-1.295**<br>(0.609)</td><td>-1.210**<br>(0.507)</td><td>-1.142*<br>(0.533)</td><td>-.984<br>(.677)</td></tr><tr><td>Other household smokers' health status changed from good to excellent</td><td>-1.182**<br>(0.536)</td><td>-0.897**<br>(0.448)</td><td>-0.972**<br>(0.476)</td><td>-1.047<br>(.661)</td></tr><tr><td>Logarithm real income</td><td>-0.137*<br>(0.065)</td><td>-0.139**<br>(0.065)</td><td>-0.147**<br>(0.061)</td><td>-0.058<br>(0.075)</td></tr><tr><td>Age</td><td>-0.014***<br>(0.003)</td><td>-0.017***<br>(0.005)</td><td>-0.013***<br>(0.004)</td><td>-.008**<br>(.004)</td></tr><tr><td>Active in community group</td><td>-1.481***<br>(0.529)</td><td>-1.090***<br>(0.477)</td><td>-1.225**<br>(0.469)</td><td>-1.344**<br>(.50)</td></tr><tr><td>Active in other organisation</td><td>0.428*<br>(0.237)</td><td>0.479**<br>(0.236)</td><td>0.459**<br>(0.218)</td><td>0.593**<br>(0.252)</td></tr><tr><td>Other social or community activities (political parties, trade unions, sports clubs, ...)</td><td>N.S.</td><td>No</td><td>No</td><td>No</td></tr><tr><td>Living alone (not divorced, widowed or separated)</td><td>-0.373**<br>(0.156)</td><td>-0.392**<br>(0.184)</td><td>-0.368**<br>(0.162)</td><td>-0.300*<br>(0.191)</td></tr><tr><td>Has one or more children (all under 16)</td><td>0.396***<br>(0.110)</td><td>0.427***<br>(0.130)</td><td>0.426***<br>(0.113)</td><td>.493***<br>(.120)</td></tr><tr><td>Labour force status: mother at home</td><td>-0.484***<br>(0.165)</td><td>-0.334*<br>(0.178)</td><td>-0.368**<br>(0.162)</td><td>-.257<br>(.176)</td></tr><tr><td>Other variables for labour force status, marital status, sex and education</td><td>No</td><td>No</td><td>No</td><td>No</td></tr><tr><td>Child present at interview</td><td>N.S.</td><td>N.S.</td><td>N.S.</td><td>N.S.</td></tr><tr><td>Spouse present at interview</td><td>N.S.</td><td>N.S.</td><td>N.S.</td><td>N.S.</td></tr><tr><td>Other adult present at interview</td><td>N.S.</td><td>N.S.</td><td>N.S.</td><td>N.S.</td></tr><tr><td>Controls for unbalanced panel (5 dummies)</td><td>N.S.</td><td>N.S.</td><td>N.S.</td><td>N.S.</td></tr><tr><td>Dummies for waves and regions (4+18: in level)</td><td>Yes</td><td>Yes</td><td>Yes</td><td>No</td></tr></tbody></table>
<table><tr><td>Constant</td><td>1.790**<br>(0.667)</td><td>2.076***<br>(0.685)</td><td>1.840***<br>(0.639)</td><td>0.962<br>(0.760)</td></tr><tr><td>Number of observations</td><td>7427</td><td>7427</td><td>7116</td><td>5383</td></tr><tr><td>Hansen Statistic (critical value at 10% level)</td><td>3.160 (7.8)</td><td>3.087 (4.6)</td><td>9.274 (15.5)</td><td>7.144 (7.8)</td></tr><tr><td>Instruments</td><td>x<sub>it-2</sub> to x<sub>it-6</sub></td><td>x<sub>it-3</sub> to x<sub>it-6</sub></td><td>x<sub>it-3</sub> to x<sub>it-6</sub><br>(A-B)</td><td>x<sub>it-2</sub> to x<sub>it-6</sub></td></tr></table>

Standard errors in parentheses. \*=significant at the 10% level, \*\*=significant at the 5% level, \*\*\*=significant at the 1% level, N.S.=insignificant at the 10% level.

<table><caption>Table 6. Biases in the Estimation of Current Cigarette Consumption (equation (15))</caption><thead><tr><th>Method</th><th>GMM<br>(L1)</th><th>GMM<br>(Bias)</th><th>GMM<br>(L3)</th><th>GMM<br>(Bias)</th></tr></thead><tbody><tr><td>One-period lagged consumption</td><td>1.037***<br>(.070)</td><td>+***</td><td>0.902***<br>(0.216)</td><td>+**</td></tr><tr><td>Two-period lagged consumption</td><td>-0.056<br>(.057)</td><td>-</td><td>0.076<br>(0.204)</td><td>+</td></tr><tr><td>Health status changed from excellent to poor</td><td>-2.357**<br>(1.140)</td><td>-</td><td>-2.765***<br>(1.042)</td><td>-</td></tr><tr><td>Has children, Over 25, Health status stays fair</td><td>-0.666**<br>(.308)</td><td>+***</td><td>-0.802***<br>(0.304)</td><td>+</td></tr><tr><td>Has children, Over 25, Health status stays poor</td><td>-0.897**<br>(.420)</td><td>+</td><td>-0.898**<br>(0.403)</td><td>-</td></tr><tr><td>Male, Health status worsened from good</td><td>1.246***<br>(.358)</td><td>-</td><td>1.193***<br>(0.375)</td><td>-**</td></tr><tr><td>Male, Health status changed from fair to good</td><td>-0.755**<br>(.358)</td><td>-***</td><td>-0.750*<br>(0.401)</td><td>-***</td></tr><tr><td>Male, under 45, lung check-up, lung problems at t-1</td><td>1.974**<br>(0.954)</td><td>-</td><td>2.062**<br>(0.934)</td><td>-</td></tr><tr><td>45 or over, lung check-up</td><td>1.478***<br>(0.365)</td><td>+**</td><td>1.377***<br>(0.393)</td><td>+</td></tr><tr><td>Male, under 65, heart check-up, heart problems at t-1</td><td>-1.042**<br>(0.488)</td><td>-</td><td>-0.975**<br>(0.453)</td><td>-</td></tr><tr><td>Female, 65 or over, heart check-up</td><td>0.470*<br>(0.283)</td><td>-</td><td>0.311<br>(0.264)</td><td>-</td></tr><tr><td>Male, 55 or over, heart or lung problems increased</td><td>-1.295**<br>(0.609)</td><td>-***</td><td>-1.142*<br>(0.533)</td><td>-</td></tr><tr><td>Other household smokers' health status changed from good to excellent</td><td>-1.182**<br>(0.536)</td><td>-</td><td>-0.972**<br>(0.476)</td><td>-</td></tr><tr><td>Logarithm real income</td><td>-0.137*<br>(0.065)</td><td>-**</td><td>-0.147**<br>(0.061)</td><td>-</td></tr><tr><td>Age</td><td>-0.014***<br>(0.003)</td><td>-***</td><td>-0.013***<br>(0.004)</td><td>-**</td></tr><tr><td>Active in community group</td><td>-1.481***<br>(0.529)</td><td>+***</td><td>-1.225**<br>(0.469)</td><td>+**</td></tr><tr><td>Active in other organisation</td><td>0.428*<br>(0.237)</td><td>+</td><td>0.459**<br>(0.218)</td><td>-</td></tr><tr><td>Other social or community activities (political parties, trade unions, sports clubs, ...)</td><td>N.S.</td><td>No</td><td>No</td><td>No</td></tr><tr><td>Living alone (not divorced, widowed or separated)</td><td>-0.373**<br>(0.156)</td><td>+</td><td>-0.368**<br>(0.162)</td><td>+</td></tr><tr><td>Has one or more children (all under 16)</td><td>0.396***<br>(0.110)</td><td>+</td><td>0.426***<br>(0.113)</td><td>-</td></tr><tr><td>Labour force status: mother at home</td><td>-0.484***<br>(0.165)</td><td>+</td><td>-0.368**<br>(0.162)</td><td>-</td></tr></tbody></table>
<table><thead><tr><th>Other variables for labour force status, marital status, sex and education</th><th>No</th><th>No</th><th>No</th><th>No</th></tr></thead><tbody><tr><td>Child present at interview</td><td>N.S.</td><td>-</td><td>N.S</td><td>+</td></tr><tr><td>Spouse present at interview</td><td>N.S.</td><td>+</td><td>N.S.</td><td>-</td></tr><tr><td>Other adult present at interview</td><td>N.S.</td><td>-</td><td>N.S.</td><td>-</td></tr><tr><td>Controls for unbalanced panel (5 dummies)</td><td>N.S.</td><td>N.S.</td><td>N.S.</td><td>N.S.</td></tr><tr><td>Dummies for waves and regions (5+18)</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Constant</td><td>1.790**<br>(0.667)</td><td>-</td><td>1.840***<br>(0.639)</td><td>-*</td></tr><tr><td>Number of observations</td><td>7427</td><td>4952</td><td>7116</td><td>4952</td></tr><tr><td>Hansen Statistic (critical value at 10% level)</td><td>3.16 (7.8)</td><td>1.38 (6.3)</td><td>9.27 (15.5)</td><td>11.36 (13.8)</td></tr><tr><td>Instruments</td><td>x<sub>it-2</sub> to x<sub>it-6</sub></td><td>x<sub>it-2</sub> to x<sub>it-5</sub></td><td>x<sub>it-3</sub> to x<sub>it-6</sub><br>(A-B)</td><td>x<sub>it-3</sub> to x<sub>it-6</sub><br>(A-B)</td></tr></tbody></table>

Standard errors in parentheses. *=significant at the 10% level, **=significant at the 5% level, ***=significant at the 1% level, N.S.=insignificant at the 10% level.
<caption>**Table 7. Heteroscedastic Probit Stop Smoking Equation**</caption>

*Dependent variable: stopped smoking between t and t+1*

<table><tr><td>One-period lagged consumption (predicted value)</td><td>-0.023*** (.005)</td></tr><tr><td>Two person household</td><td>0.076* (0.045)</td></tr><tr><td>Divorced</td><td>-0.335*** (0.103)</td></tr><tr><td>Member of a religious organisation</td><td>0.276*** (0.083)</td></tr><tr><td>Member of a sport club</td><td>0.316** (0.125)</td></tr><tr><td>Education > A-levels</td><td>0.134** (0.053)</td></tr><tr><td>Logarithm real income</td><td>0.056** (0.027)</td></tr><tr><td>Region = East Anglia</td><td>0.276** (.113)</td></tr><tr><td>Region = West Mid. Conurbation</td><td>0.316*** (0.099)</td></tr><tr><td>35-45, heart or lung problems increased</td><td>-.454* (.273)</td></tr><tr><td>Heart check-up, no health problems at t-1</td><td>0.090** (0.045)</td></tr><tr><td>35-45, health status stays excellent</td><td>-.354** (.172)</td></tr><tr><td>Health status changed from excellent to fair</td><td>-.415* (.234)</td></tr><tr><td>Health status stays good</td><td>.089* (0.048)</td></tr><tr><td>25-35, health status changed from good to poor</td><td>.525** (.234)</td></tr><tr><td>Health status stays fair</td><td>.164** (0.068)</td></tr><tr><td>Number of other household smokers in excellent health rises</td><td>-.316*** (.112)</td></tr><tr><td>Constant</td><td>-1.709*** (.236)</td></tr><tr><td>Log-likelihood</td><td>Initial: -5756; without information variables: -1864<br>Final:-1845</td></tr><tr><td>Wald Chi-squared statistic</td><td>125.4***</td></tr><tr><td>Number of observations</td><td>8304</td></tr><tr><td>Number of individuals stopping smoking</td><td>517</td></tr><tr><td>Number of individuals continuing to smoke</td><td>7787</td></tr><tr><td colspan="2">Variables (X<sub>i</sub>) used to model heteroscedasticity: ln(&sigma;<sub>i</sub><sup>2</sup>)=&beta;X<sub>i</sub></td></tr><tr><td>Male</td><td>0.067**(0.033)</td></tr><tr><td>Year = 1994</td><td>-0.190*** (0.040)</td></tr><tr><td>Year = 1995</td><td>-0.194*** (0.040)</td></tr><tr><td>Year = 1996</td><td>-0.123*** (0.040)</td></tr></table>

Standard errors in parentheses. \*=significant at the 10% level, \*=significant at the 5% level, \*=significant at the 1% level, N.S.=insignificant at the 10% level.
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