Indeterminacy in a Matching Model of Money with Productive Government Expenditure

This study explores the effects of inflation on economic growth in a two-sector monetary search-and-matching model with productive government expenditure. We find that when labor intensity of production in the centralized market is below a threshold, the economy features a unique balanced growth path along which inflation reduces growth so long as capital intensity of production in the decentralized market is positive. When labor intensity in the centralized market is above the threshold however, the economy may feature multiple balanced growth paths. Multiple equilibria arise when the matching probability in the decentralized market is above a threshold. In this case, the high-growth equilibrium features a negative effect of inflation on economic growth whereas the low-growth equilibrium may feature a negative, positive or non-monotonic effect of inflation on growth. When the matching probability is above the threshold but not too high, the low-growth equilibrium is locally determinate whereas the high-growth equilibrium is locally indeterminate and subject to sunspot-driven business cycles around it. Finally, when the matching probability is sufficiently high, both equilibria are locally determinate, and hence, either equilibrium may emerge in the economy