Health Selection vs. Social Causation - The Issue of Causality

4.1.1. The Counterfactual Model of Causality

In this thesis, I propose different theoretical explanations of how health selection processes can generate health inequalities. I apply the theory to health differences between incumbents of high status and of regular jobs. The theory makes clear statements about causal mechanisms.

The question is now, which methods are adequate for testing these causal relationships?

I will address this question in two steps. First, I will define the concept of causality I am using and describe what problems arise when testing causal claims based on this notion of causality.

Second, I will describe which specific problems apply to my empirical example of high status job attainment on the German labor market using SOEP data. I will show caveats and how I will deal with them. Finally, I will sum up and discuss in what sense “effects” from the statistical models should be understood as causal in this thesis.

Discussing causality is important, because sociologists have changed their way of treating the matter of causation (Bernert 1983). In my thesis I use the model often referred to as the counterfactual model of causality. In economics it is clearly the dominant framework of causality (Angrist & Pischke 2010). A similar trend can be observed for sociology (Gangl 2010). Another term for the model is the Rubin causal model (RCM) after Rubin (1974) who introduced it to non-experimental data. Rubin calls the model potential outcomes. I will use the terms counterfactual model or counterfactual argument throughout the thesis.

I chose the counterfactual model for two reasons. First, it reflects the current state of the art regarding causality in (quantitative) social sciences (e.g. Angrist & Pischke 2010, Gangl 2010).

Second, it has a clear theoretical definition of causality and is able to transfer this definition unambiguously into statistical models which can be applied to quantitative data analysis.

4.1.2. The Counterfactual Argument

When talking about treatment and outcome in this section the most basic criterion which needs to be fulfilled is the temporal relationship. The treatment has to come before the outcome, otherwise it cannot have a causal effect on the outcome (Ward 2009). Following the counterfactual model of causality researchers ask the “what if” question. The interest lies in the effect Y of a certain treatment X on a particular unit i. To answer the question if X causes Y one asks “what would have happened to unit i if it had (not) been treated with X?”. The actual outcome, that is the outcome that really happened, is compared with the counterfactual outcome that would have happened if the treatment had been withheld - all other things being equal. One thus tries to compare two different versions of reality which vary only in regard to whether unit i is given the treatment or not (Kaufman & Poole 2000, 102). This is done for every unit under observation. The difference between the actual and the counterfactual effect is called unit effect (Winship & Sobel 2001, 14).

For the purpose of my study one would ask for example: What would happen to a certain worker’s job status if he was not in poor health, but was in good health? The difference in job status between the actual outcome (poor health) and the potential outcome (good health) is the unit effect.

Due to the fact that one of the outcomes is unobservable, the unit effect is by nature not measurable. If one unit has been treated it cannot be compared with its untreated status since it has already been treated. This problem is known as the “Fundamental Problem of Causality”

(Holland 1986, 947).

The good news is that compared to others sciences (like e.g. medicine) in social sciences the single unit effect is rarely of high interest. The focus lies on theaverage treatment effect (ATE) which is the average of all unit effects. This means that social scientist do not ask: What happens to the career prospects of a specific worker if his or her health changes? Rather they ask: What happens on average to the career prospects of workers if his or her health changes by a certain degree? The equation to calculate the ATE is (Winship & Sobel 2001, 18):

δ¯=E[Y_t−Y_c] =E[Y_t]−E[Y_c] =

i∈P

(Y_ti−Y_ci)

N (4.1)

where P denotes the population under observation, the index t stands for treatment while c stands for non-treatment or control. δ can only be estimated, never measured or calculated directly. For the calculation the unobserable counterfactual outcomes are needed. To make a consistent estimate of δ a sufficient assumption is that the treatment effect on the treated (ATT) is the same as the treatment effect on the untreated (ATU) and that the non-treatment effect is the same for the treated and the untreated:

E[Y_t|X =t] =E[Y_t|X =c];E[Y_c|X =t] =E[Y_c|X =c] (4.2) The assumption implies that for example the job status of those workers who are actually in poor health is affected in the same way as would the job status of those workers who are actually in good health if they were in a different health state.

The assumption of equation 4.2 can be achieved through randomized assignment of the treatment as done in experiments (Winship & Sobel 2001, 22). If equation 4.2 holds true, the ATE can be calculated as:

δ¯=E[Yt|X =t]−E[Yc|X =c] (4.3)

This means that if health status were assigned to workers randomly, the difference in job status between the groups of the treated (good health) and the untreated (bad health) would be equal to the ATE of health on job status.

If random assignment cannot be guaranteed¹ this estimation might be biased for two possible reasons:

1. The baseline difference in the outcomeY is unequal to zero.

2. There is a difference in the treatment effect between the treated and the controls.

Bias 1 means that the treatment group has a higher level of the outcome variableY (e.g. job status) than the non-treatment group before the treatment. So the difference in Y measured after treatment cannot be attributed to the treatment, but to some other causes prior to the treatment. For example, workers in good health might for different reasons be in better jobs before they experience a change in health than those workers who are in bad health. The difference then does not stem from the treatment, but from some other cause (e.g. difference in education as a common cause for job status and health).

Bias 2 states that the ATE is estimated incorrectly if the treatment has a different effect for the treated than for the untreated. This is often the case in processes of self selection into the treatment². The second bias does not have to be a problem for a researcher. It depends if one seeks to estimate the average treatment effect on the whole population or if one is interested in the treatment effect on the actually treated (ATT). In the latter case bias 2 can be admitted freely, but ignored as the conclusion which is drawn is limited to the group of the treated (Winship & Sobel 2001, 23-24). For this study it means that I could state for example that a change of health status (treatment) does have a negative causal effect on workers’ job

1As it is certainly the case with health due to practical and ethical reasons.

2Those who benefit more are more likely to choose the treatment.

status. But I can only say that it has this effect for those workers who actually experience a change in health. I do not know if a change in health would have the same effect on those who were not treated (and did not change their health status).

A weaker form than random assignment to overcome bias 1 is ignorability. It relaxes the assumption that the treatment is independent of all variables. It only states, that the treatment is at least independent of the potential outcomes (Winship & Sobel 2001, 26-27):

(Y_t, Y_c)⊥X (4.4)

Unfortunatelyignorability is rarely given in social sciences and, as will be shown later, is not given in this study. Rather the probability is dependent on other variables Z. But it can be argued that given the probability to get the treatment (P(Z)), ignorability holds:

(Y_t, Y_c)⊥X|P(Z) (4.5)

This is also called theconditional independence assumption (Dawid 2000, 419). It would mean for example that health (the treatment) is not independent of job status (the outcome). Due to some other factors the workers in regular jobs have worse health than workers in high status jobs. At the same time these factors (e.g. education) influence the chance of being a regular worker. Therefore regular jobs and health are not independent.

However, one can estimate the probability to be in a certain health state dependent on these factors, which link job status and health. Given this probability³, health can be seen as if it were randomly assigned with regard to job status.

The model to estimate P(Z) has to be complete for the ignorability assumption to hold.

This will be a problem if there are important unmeasured variables which can bias P(Z).

As Rubin (2005, 324) states: In the end “[...] causal inference is impossible without assumptions.” Consequently, I will make an effort to guarantee that the conditional independence assumption holds true, so that causal inference is possible from the estimates in my thesis.