Hulton’s Theorem argues that in the presence of input-output linkages, the impact of an industry-level shock on the aggregate economy is entirely captured by the size of this industry, regardless of its position in the network. This paper proposes that the production network structure in isolation represents an essential channel in shaping GDP growth and growth volatility. First, I show evidence that as industries in the U.S. economy became sparsely connected from 1970 to 2017, that is, many more industries relied on a few central input suppliers for production, GDP growth tended to slow down and be more volatile. Motivated by these empirical facts, I embed input-output linkages into a multisector real business cycle model and provide a nonlinear characterization of the macroeconomic impact of sector-specific productivity shocks to highlight the key role of production network structures. Finally, I measure realized sector-level productivity shocks from the data, feed them into the model, and study model-implied relationships between production network structure, GDP growth, and growth volatility. Our calibrated model is able to explain about 20% of the business cycle fluctuations as observed in the data. Moreover, our results imply that network connections matter beyond industry sizes.