NotesECN741-page55 - ECN 741: Public Economics Fall 2008 2....

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ECN 741: Public Economics Fall 2008 2. Nature draw individual shocks θ T Θ T according to π θ ( θ T | z T ) . These draws are i.i.d across individuals conditional on z T . By law of large number, given z T , the fraction of population with shocks θ T is π θ ( θ T | z T ) . We impose the following restriction: Assumption 1 For all θ T Θ T , π θ ( θ t | z T ) = ( θ t +1 ,...,θ T ) π θ ( θ t t +1 ,...,θ T | z T ) is indepen- dent of z t +1 ,...,z T . This assumption implies that conditional on z t , ( θ t +1 ,...,θ T ) and ( z t +1 ,...,z T ) are inde- pendent. Remarks: Note that in this setup we are not imposing any restriction on time series prop- erties of θ t and z t . However, our assumption implies that by observing history of private shocks up to date t the individuals cannot infer anything about future aggregate shocks. As before, we assume that agents learn
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