Modelling money, price and output in India: a vector autoregressive and moving average (VARMA) approach

The present study has two purposes. First, the study examines the most substantive and debatable question: Is there any long-run relationship among money, price and output? It has been found by applying different tests of cointegration that there is no long-run relationship among these three variables in cointegration sense. Second, having ascertained that the variables under study are not cointegrated, an attempt is made to explore the short-run relationship among money, price and output exploiting the characteristics of the Vector Autoregressive and Moving Average (VARMA) model. Sub-set concept has been used to identify the best-fitted VARMA model. The paper concludes the following: (i) both money and price affect each other and there exists bi-directional causality; (ii) output affects price and there is also feedback between price and output; and (iii) money unidirectionally affects output. Various consequences of cointegration on parameter estimates of pure VAR/VARMA in difference have been discussed. Here it may be mentioned that pure VAR/VARMA in differences is not misspecified, as it could have been otherwise in the case where variables are cointegrated. However, as VARMA is more parsimonious than VAR, the VARMA model has been considered here. Attention has been paid regarding the proper transformations of the variables.