Essays on Broad Divisia Monetary Aggregates: Admissibility and Practice

Abstract

The assumption of weak separability of goods and services in the utility function is ubiquitous in macroeconomic modeling. If the goods and services are weakly separable, they can be combined into an "admissible" aggregate. This project tests the assumption of weak separability (or "admissibility") for broad Divisia monetary aggregates for the United States provided by the Center for Financial Stability; Divisia M4, Divisia M4-, and Divisia M3. These broad monetary aggregates measure the service flow of money in the macroeconomy through a share weighted index method developed by Barnett (1980), and already established as superior to simple sum aggregates in the literature collected in Barnett and Serletis (2000). The problem to be addressed is the determination of how broad a monetary aggregate should be: is the Divisia M2 level sufficient for aggregation or should other like commercial paper, overnight repurchase agreements, short term securities and large denomination time deposits be included? These components contained in broad aggregates are subject to risk that is not accounted for in the traditional user cost estimate of Barnett (1980), but can be adjusted through methods proposed in Barnett and Wu (2005). The performance of these risk adjusted aggregates is tested alongside with the risk neutral case to determine admissibility. Using microeconomic foundations in the non-parametric weak separability test literature of Varian (1982) the aggregates are examined for evidence of admissibility. Since Varian (1982) tends to over-reject weak separabiltiy, we implement methods from Barnett and de Peretti (2009) to avoid over rejection from noise in the data. Furthermore a necessary and sufficient weak separability condition is used based on the marginal rate of substitution between two goods, instead of an only sufficient condition. The results provide evidence for the use of Divisia M4 as an admissible aggregate. In the risk adjusted case several violations found in the risk neutral case dissolve, and the Divisia M4- gains support as admissible. There is less evidence to support the use of Divisia M3 as an admissible aggregate as it passes the necessary but not sufficient conditions for admissibility.