The 'Reverse Square Root' Shape of Recessions

Milton Friedman’s plucking model of business cycles hypothesizes that deeper recessions forecast larger booms while stronger booms do not necessarily forecast deeper recessions. This paper tests the plucking model using Maddison Project growth data for 169 countries across several centuries. We find 56.9% of the per capita GDP growth magnitude in the last year of a downturn forecasts the per capita GDP growth magnitude of the subsequent first recovery year while only 16.2% of the last boom year per capita GDP growth magnitude forecasts the per capita GDP growth magnitude of the first year in the subsequent downturn, suggesting that the plucking model holds up relatively well. Combining our finding that first post-recession boom year per capita GDP growth rate is typically is 0.7% higher than later boom years suggests that recoveries generally exhibit “reverse square root” shapes.米尔顿·弗里德曼（Milton Friedman）提出的商业周期拉扯模型（plucking model）假设：程度更深的衰退可预示更强的复苏，而强劲的复苏却未必能预示更严重的衰退。本文采用跨越数个世纪的169个国家的麦迪森项目（Maddison Project）增长数据，对该模型开展检验。研究结果显示：衰退末期的人均国内生产总值（per capita GDP）增长幅度中，有56.9%可预示后续首个复苏年份的人均国内生产总值增长幅度；而繁荣末期的人均国内生产总值增长幅度中，仅有16.2%可预示后续首个衰退年份的人均国内生产总值增长幅度，这表明拉扯模型的拟合效果相对良好。结合“衰退后首个繁荣年份的人均国内生产总值增长率通常较后续繁荣年份高出0.7个百分点”这一发现，可知经济复苏整体呈现“反平方根”（reverse square root）形态。