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The straightforward answer is if you have no lags, you have no VAR and no Granger Causality. By definition both methods require at least one lag. Respective definitions at Wikipedia are pretty helpful and clear on the concept. The Present can be associated with the Present. That relationship may not have a determined direction (correlation, linear ...


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There could be reasons for including only lag but it’s hard to say from your description. For example, if there is endogeneity between employment and number of children then you could justify using only lagged number of children, as lags can often serve as instruments for contemporaneous variables and you can interpret including only lag as reduced form of ...


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