Inflation and GDP Dynamics in Production Networks : A Sufficient Statistics Approach

We provide closed-form solutions for inflation and GDP dynamics in multi-sector New Keynesian economies with arbitrary input-output linkages. In particular, we show that a sufficient statistic for dynamics of sectoral prices is the principal square root of the Leontief matrix that is appropriately adjusted for the sectoral frequencies of price adjustments. We measure this sufficient statistic for the U.S. and find a significant quantitative role for production networks in the propagation of monetary and sectoral supply shocks. In response to monetary shocks, input-output linkages significantly increase the persistence of inflation and lead to a GDP response that is more than three times the response in an economy with a horizontal production network. In response to a negative supply shock in the “computers and electronics industry,” input-output linkages propagate this shock by increasing the cost of downstream sectors, which acts like a markup shock to these sectors. These spillover effects generate a bigger and more persistent increase in aggregate inflation relative to an economy with a horizontal production network, which leads to about a three times bigger contraction in aggregate GDP. We show that a monetary policy response that fully offsets the inflationary effect of this negative sectoral supply shock on impact generates an aggregate GDP contraction that is more than twice as large as the case with no such policy response