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.
It can be shown that a sufficient set for estimating the causal effect of 
  
    
      
        X
      
    
    {\displaystyle X}
   on 
  
    
      
        Y
      
    
    {\displaystyle Y}
   is any set of non-descendants of 
  
    
      
        X
      
    
    {\displaystyle X}
   that 
  
    
      
        d
      
    
    {\displaystyle d}
  -separate 
  
    
      
        X
      
    
    {\displaystyle X}
   from 
  
    
      
        Y
      
    
    {\displaystyle Y}
   after removing all arrows emanating from 
  
    
      
        X
      
    
    {\displaystyle X}
  .