Statistical and Econometric Foundations of Causal Economics

3.1 Introduction to Statistical Foundations of Causality

Statistics is a very important part of causal reasoning since it gives formal mechanisms to measure the relationship, estimate uncertainty, and examine evidence in economic analysis. Whereas descriptive statistics summarize observed statistics, predictive statistics are concerned with predicting future developments and causal statistics with cause-effect relationships explaining how and why economic developments change with interventions of different kinds. This means that correlation does not suffice economic decisions, which are statistically associated variables due to the possibility of confounding variables, reverse causation, or spurious relationship, which can make wrong policy inferences [41]. In recognition of these shortcomings, the discipline has developed out of classical statistical tools based on association and hypothesis testing to contemporary causal inference models that explicitly reflect assumptions, counterfactual logic and identification procedures to be able to make plausible causal assertions in economics.

3.2 Probability Theory and Causal Interpretation

Causal inference in economics is based on probability theory to provide a strict mathematical framework used to measure uncertainty and model the fluctuation of economic results amongst either individuals, firms, or markets. Fundamentally, probability theory brings on board the concept of random variables, which are economic quantities whose value is not deterministic but may have various outcomes with respect to some probability distribution [42]. The discrete and continuous forms of this distributions enable the researcher to specify the probability of different events to occur as well as to calculate the expectations, variances, and other measures of central tendencies, and dispersion of economic events [43]. In making uncertainty formal in such a manner, probability theory offers the language and the tools to be able to get off the simple observation of correlation that can be made to a more accurate view of causation relations. What is especially important to causal reasoning is conditional probability, a measure of the probability of an event given that another event has occurred, and conditional expectation, a measure of the expected value of a variable, given that a sequence of explanatory events has occurred. An example of this is when testing the impact of a policy intervention on household consumption or labor supply, conditional probability will allow economists to control the impact of the treatment by other factors that may also have the same effect, thus giving an approximation to the concept of a counterfactual situation in which the intervention does not take place [44]. It is also vital that there is a difference between independence and conditional independence. Though seeming to be correlated in isolation, by considering confounding factors, two variables that seem to be correlated may turn out to be actually not correlated after conditioning confounding factors is done, hence the need to condition in causal inferences. This is the core difference between the contemporary econometric techniques, such as matching, regression adjustment, and instrumental variables, all of which are based on the assumptions of conditional independence to determine the unbiased effects of causality. The Bayesian theory also advances the analysis of causality with a methodical approach to updating beliefs on the basis of the novel information. In economics, it enables researchers to improve estimates of causal effects as more data is received and combine previous knowledge in conjunction with the observed data in order to come up with probabilistic statements regarding the cause-effect relationships. As an example, Bayesian techniques can be applied by policymakers to revise the forecasts of the effects of a tax reform on investment behavior as additional quarters of economic data become known, and better information is available to aid decision-making under uncertainty. These probabilistic ideas are the basis of the concept of probabilistic causation, a concept that is inherently different than deterministic causation by admitting that causes do not always result in a given outcome with certainty but instead tend to increase or decrease the probability of that outcome or its distribution. Applied to the economy, this is a manifestation of the complexity and heterogeneity of human behavior, market interactions and institutional environments, where the same intervention can produce diverse outcomes in different people or different places at different times. More complex causal models, including structural equation modeling, potential outcomes analysis and graphical models, are also based on probability theory, in which individuals can express their causal assumptions and causal expectations in terms of random variables, conditional probabilities and expectations [45]. With these mathematical instruments combined with empirical data, economists can no longer achieve the tasks of description and prediction, but they can build models that give some approximation to what they believe are the causal processes that underlie the observed phenomena. Also, the sensitivity analysis, robustness, and quantification of uncertainty surrounding the causal estimates, which are essential to academic research and policy evaluation, are easier to perform through probabilistic reasoning. In general, probability theory allows entrepreneurs to formulate, test, and develop causal hypotheses in a rigorous and systematic way, closing the gap between abstract economic theory and the results of research, and having become the mathematical foundation of causal inference in economics today. As Figure 3.1 shows, probability theory can be used to cause a causal interpretation, which points the assumptions and counterfactual reasoning as well as the identification strategies used to establish credible cause-effect relationships in economics.