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Suppose we simply estimate a 3 variable VAR of inflation (pi), output gap (gap), and the policy interest rate (r). We impose the usual recursive error structure by ordering the variables by pi, gap and r. Now we compute impulse responses to one standard deviation policy shock. I believe the error bands in period 0 in response to the shock should be all zero (i.e., the values of upper and lower bands are the same in period 0) because (i) pi and gap do not respond to changes in r contemporaneously and (ii) the size of policy shock is @stdev(r) so that both upper and lower bands should equal to @stdev(r) in period 0. Eviews generates "zero" error bands in period 0 for pi and gap BUT NOT FOR r. Why isn't the error band for r in period 0 zero? How is it computed? Thanks.

You are correct. However, this holds if you give a shock "only" to the policy interest rate variable. By default, EViews uses Cholesky decomposition to produce the recursive error structure, which is a lower triangular matrix of impulses. When you view the impulse-responses from this factorization matrix, you'll get different (wider) error bands due to correlation between the shocks.