A Neural Phillips Curve and a Deep Output Gap

Many problems plague empirical Phillips curves (PCs). Among them is the hurdle that the two key components, inflation expectations and the output gap, are both unobserved. Traditional remedies include proxying for the absentees or extracting them via assumptions-heavy filtering procedures. I propose an alternative route: a Hemisphere Neural Network (HNN) whose architecture yields a final layer where components can be interpreted as latent states within a Neural PC. First, HNN conducts the supervised estimation of nonlinearities that arise when translating a high-dimensional set of observed regressors into latent states. Second, forecasts are economically interpretable. Among other findings, the contribution of real activity to inflation appears understated in traditional PCs. In contrast, HNN captures the 2021 upswing in inflation and attributes it to a large positive output gap starting from late 2020. The unique path of HNN’s gap comes from dispensing with unemployment and GDP in favor of an amalgam of nonlinearly processed alternative tightness indicators.经验菲利普斯曲线（Phillips Curves，以下简称PCs）面临诸多严峻挑战。其中一大核心障碍在于，其两大关键组成部分——通胀预期与产出缺口——均为不可观测变量。传统解决方案包括为这类缺失变量选取代理变量，或是通过依赖大量先验假设的滤波流程对其进行提取。本文提出一种替代方案：半球神经网络（Hemisphere Neural Network，以下简称HNN），其架构的最终输出层各组成部分可被解释为神经菲利普斯曲线（Neural PC）中的潜在状态变量。首先，HNN可对高维观测回归变量转化为潜在状态过程中产生的非线性关系开展有监督估计；其次，模型生成的预测结果具备良好的经济学可解释性。在各类研究发现中，传统PCs对实体经济活动向通胀的贡献度的估计存在明显低估。与之形成鲜明对比的是，HNN能够精准捕捉2021年的通胀上行趋势，并将其归因自2020年末起出现的大幅正向产出缺口。HNN所得到的缺口序列具备独特演进路径，这是因为其摒弃了失业率与GDP两类传统指标，转而采用经过非线性处理的多维度替代松紧度指标的整合集。