RESEARCH

In this paper, I propose a non-linear time-series model incorporating a particular neural network algorithm, a recurrent neural network. The construction of neural network algorithms shows the models approximate the data process by taking advantage of latent hidden units. A proposed model combines an economic model-based restriction with the recurrent neural network algorithm, where serial correlation is considered and the results are interpretable in terms of economics. Identification issues of model parameters are discussed, and the relations of observationally equivalent sets of parameters of the neural network algorithm are formalized. I illustrate the usefulness of my method by revisiting the Phillips curve. In particular, I examine the stability of a correlation between the inflation rate and labor market conditions. I find evidence that the Phillips curve has flattened since the 1990s and that the curve has reverted after the Great Recession and COVID-19, showing that the inflation rate has been more sensitive to labor market conditions in recent years. Furthermore, I find evidence that inflation expectations have become more important after COVID-19. A model-based forecast of the inflation rate is also studied, and the model is useful to forecast atypical changes in the inflation rate.

we propose a state space model for panel data, which is useful to analyze the non-constant influences of latent characteristics on economic outcome variables without proxy variables. We show the similarity transform of model parameters and identify the model parameters from the first and second moments of the data. We consider two specific situations: an assumption for the initial condition of a latent characteristic, and an assumption for the conditional variance of idiosyncratic shock. We obtain rank conditions for local identification from the similarity transformation relations of model parameters.