causality

Causality is an influence by which one event, process, state, or subject (i.e., a cause) contributes to the production of another event, process, state, or object (i.e., an effect) where the cause is at least partly responsible for the effect, and the effect is at least partly dependent on the cause. The cause of something may also be described as the reason behind the event or process. In general, a process can have multiple causes, which are also said to be causal factors for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future. Thus, the distinction between cause and effect either follows from or else provides the distinction between past and future. While the former viewpoint is more prevalent in physics, some writers have held that causality is metaphysically prior to notions of time and space. Causality is an abstraction that indicates how the world progresses. As such, it is a basic concept, and one might expect it to be more apt as an explanation of other concepts of progression than as something to be explained by yet more fundamental ideas. The concept is like those of agency and efficacy. For this reason, a leap of intuition may be needed to grasp it.…

Causality is an influence by which one event, process, state, or subject (i.e., a cause) contributes to the production of another event, process, state, or object (i.e., an effect) where the cause is at least partly responsible for the effect, and the effect is at least partly dependent on the cause. The cause of something may also be described as the reason behind the event or process. In general, a process can have multiple causes, which are also said to be causal factors for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future. Thus, the distinction between cause and effect either follows from or else provides the distinction between past and future. While the former viewpoint is more prevalent in physics, some writers have held that causality is metaphysically prior to notions of time and space. Causality is an abstraction that indicates how the world progresses. As such, it is a basic concept, and one might expect it to be more apt as an explanation of other concepts of progression than as something to be explained by yet more fundamental ideas. The concept is like those of agency and efficacy. For this reason, a leap of intuition may be needed to grasp it. Accordingly, causality is implicit in the structure of ordinary language, as well as explicit in the language of scientific causal notation. In English studies of Aristotelian philosophy, the word "cause" is used as a specialized technical term, the translation of Aristotle's term , by which Aristotle meant "explanation" or "answer to a 'why' question". Aristotle categorized the four types of answers as material, formal, efficient, and final "causes". In this case, the "cause" is the explanans for the explanandum, and failure to recognize that different kinds of "cause" are being considered can lead to futile debate. Of Aristotle's four explanatory modes, the one nearest to the concerns of the present article is the "efficient" one. David Hume, as part of his opposition to rationalism, argued that pure reason alone cannot prove the reality of efficient causality; instead, he appealed to custom and mental habit, observing that all human knowledge derives solely from experience. The topic of causality remains a staple in contemporary philosophy. We have to be very careful with causality in physics and engineering. Cellier, Elmqvist, and Otter describe causality forming the basis of physics as a misconception, because physics is essentially acausal. In their article they cite a simple example: "The relationship between voltage across and current through an electrical resistor can be described by Ohm's law: V = IR, yet, whether it is the current flowing through the resistor that causes a voltage drop, or whether it is the difference between the electrical potentials on the two wires that causes current to flow is, from a physical perspective, a meaningless question". In fact, if we explain cause-effect using the law, we need two explanations to describe an electrical resistor: as a voltage-drop-causer or as a current-flow-causer. There is no physical experiment in the world that can distinguish between action and reaction. y_i = a_0 + a_1x_{1,i} + a_2x_{2,i} + \dots + a_kx_{k,i} + e_i is postulated, in which y_i is the ith observation of the dependent variable (hypothesized to be the caused variable), x_{j,i} for j=1,...,k is the ith observation on the jth independent variable (hypothesized to be a causative variable), and e_i is the error term for the ith observation (containing the combined effects of all other causative variables, which must be uncorrelated with the included independent variables). If there is reason to believe that none of the x_j s is caused by y, then estimates of the coefficients a_j are obtained. If the null hypothesis that a_j=0 is rejected, then the alternative hypothesis that a_{j} \ne 0 and equivalently that x_j causes y cannot be rejected. On the other hand, if the null hypothesis that a_j=0 cannot be rejected, then equivalently the hypothesis of no causal effect of x_j on y cannot be rejected. Here the notion of causality is one of contributory causality as discussed above: If the true value a_j \ne 0 , then a change in x_j will result in a change in y unless some other causative variable(s), either included in the regression or implicit in the error term, change in such a way as to exactly offset its effect; thus a change in x_j is not sufficient to change y. Likewise, a change in x_j is not necessary to change y, because a change in y could be caused by something implicit in the error term (or by some other causative explanatory variable included in the model). The above way of testing for causality requires belief that there is no reverse causation, in which y would cause x_j . This belief can be established in one of several ways. First, the variable x_j may be a non-economic variable: for example, if rainfall amount x_j is hypothesized to affect the futures price y of some agricultural commodity, it is impossible that in fact the futures price affects rainfall amount (provided that cloud seeding is never attempted). Second, the instrumental variables technique may be employed to remove any reverse causation by introducing a role for other variables (instruments) that are known to be unaffected by the dependent variable. Third, the principle that effects cannot precede causes can be invoked, by including on the right side of the regression only variables that precede in time the dependent variable; this principle is invoked, for example, in testing for Granger causality and in its multivariate analog, vector autoregression, both of which control for lagged values of the dependent variable while testing for causal effects of lagged independent variables. Regression analysis controls for other relevant variables by including them as regressors (explanatory variables). This helps to avoid false inferences of causality due to the presence of a third, underlying, variable that influences both the potentially causative variable and the potentially caused variable: its effect on the potentially caused variable is captured by directly including it in the regression, so that effect will not be picked up as an indirect effect through the potentially causative variable of interest. Given the above procedures, coincidental (as opposed to causal) correlation can be probabilistically rejected if data samples are large and if regression results pass cross-validation tests showing that the correlations hold even for data that were not used in the regression. Asserting with certitude that a common-cause is absent and the regression represents the true causal structure is in principle impossible. The problem of omitted variable bias, however, has to be balanced against the risk of inserting Causal colliders, in which the addition of a new variable x_{j+1} induces a correlation between x_j and y via Berkson's paradox. Apart from constructing statistical models of observational and experimental data, economists use axiomatic (mathematical) models to infer and represent causal mechanisms. Highly abstract theoretical models that isolate and idealize one mechanism dominate microeconomics. In macroeconomics, economists use broad mathematical models that are calibrated on historical data. A subgroup of calibrated models, dynamic stochastic general equilibrium (DSGE) models are employed to represent (in a simplified way) the whole economy and simulate changes in fiscal and monetary policy. Statistical and economic analyses often rely on regression methods applied to observational or pre‑existing data to infer causal relationships. Experimental designs, in contrast, establish causality by systematically manipulating independent variables under controlled conditions. Experiments therefore provide stronger internal validity because causal mechanisms are demonstrated directly rather than inferred from patterns in observational data.

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