---
title: "Causality"
chunk: 8/12
source: "https://en.wikipedia.org/wiki/Causality"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:43:20.686725+00:00"
instance: "kb-cron"
---

is postulated, in which 
  
    
      
        
          y
          
            i
          
        
      
    
    {\displaystyle y_{i}}
  
 is the ith observation of the dependent variable (hypothesized to be the caused variable), 
  
    
      
        
          x
          
            j
            ,
            i
          
        
      
    
    {\displaystyle 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
          
        
      
    
    {\displaystyle 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
          
        
      
    
    {\displaystyle x_{j}}
  
s is caused by y, then estimates of the coefficients 
  
    
      
        
          a
          
            j
          
        
      
    
    {\displaystyle a_{j}}
  
 are obtained. If the null hypothesis that 
  
    
      
        
          a
          
            j
          
        
        =
        0
      
    
    {\displaystyle a_{j}=0}
  
 is rejected, then the alternative hypothesis that 
  
    
      
        
          a
          
            j
          
        
        ≠
        0
      
    
    {\displaystyle a_{j}\neq 0}
  
 and equivalently that 
  
    
      
        
          x
          
            j
          
        
      
    
    {\displaystyle x_{j}}
  
 causes y cannot be rejected. On the other hand, if the null hypothesis that 
  
    
      
        
          a
          
            j
          
        
        =
        0
      
    
    {\displaystyle a_{j}=0}
  
 cannot be rejected, then equivalently the hypothesis of no causal effect of 
  
    
      
        
          x
          
            j
          
        
      
    
    {\displaystyle 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
          
        
        ≠
        0
      
    
    {\displaystyle a_{j}\neq 0}
  
, then a change in 
  
    
      
        
          x
          
            j
          
        
      
    
    {\displaystyle 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
          
        
      
    
    {\displaystyle x_{j}}
  
 is not sufficient to change y. Likewise, a change in 
  
    
      
        
          x
          
            j
          
        
      
    
    {\displaystyle 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
          
        
      
    
    {\displaystyle x_{j}}
  
. This belief can be established in one of several ways. First, the variable 
  
    
      
        
          x
          
            j
          
        
      
    
    {\displaystyle x_{j}}
  
 may be a non-economic variable: for example, if rainfall amount 
  
    
      
        
          x
          
            j
          
        
      
    
    {\displaystyle 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
          
        
      
    
    {\displaystyle x_{j+1}}
  
 induces a correlation between 
  
    
      
        
          x
          
            j
          
        
      
    
    {\displaystyle x_{j}}
  
 and 
  
    
      
        y
      
    
    {\displaystyle 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.

=== Management ===

For quality control in manufacturing in the 1960s, Kaoru Ishikawa developed a cause and effect diagram, known as an Ishikawa diagram or fishbone diagram. The diagram categorizes causes, such as into the six main categories shown here. These categories are then sub-divided. Ishikawa's method identifies "causes" in brainstorming sessions conducted among various groups involved in the manufacturing process. These groups can then be labeled as categories in the diagrams. The use of these diagrams has now spread beyond quality control, and they are used in other areas of management and in design and engineering. Ishikawa diagrams have been criticized for failing to make the distinction between necessary conditions and sufficient conditions. It seems that Ishikawa was not even aware of this distinction.

=== Humanities ===