Estimating Policy-Invariant Deep Parameters in the Financial Sector When Risk and Growth Matter
Barnett, William A., Kirova, Milka, Pasupathy, Meenakshi, Cecchetti, Stephen G., Marshall, David A., Journal of Money, Credit & Banking
THIS PAPER provides and illustrates an approach to the estimation of technology parameters in the financial sector. The relevant technologies are those of the financial intermediaries that produce inside money as output services and the nonfinancial firms that demand financial services as inputs to production technology. We also display analogous results for consumer demand, but without the modeling and econometric details, which are available elsewhere. The problems that we seek to solve through our approach to modeling and Euler equation estimation are the "Lucas Critique" and what Chrystal and MacDonald (1994, p. 76) recently have called the "Barnett Critique." We also explore the tracking ability of the Divisia monetary aggregate and simple sum monetary aggregate relative to the GMM estimated exact rational expectations monetary aggregate for each type of economic agent.
In this paper, we produce and estimate Euler equations for firms that demand or supply financial services as an illustration of the available approach, first advocated forcefully and convincingly for the financial sector by Poterba and Rotemberg (1987) with respect to consumer demand for financial services. We do not seek to integrate the three sectors into a complete economy, in which aggregation blockings would have to conform across sectors. In addition, we do not explore in detail the implications of our parameter estimates for the elasticities and other properties of technology, although the approach clearly is relevant to the creation of a small-scale macroeconomic model based upon the estimation of deep parameters, and is relevant to the investigation of demand and supply elasticities, economies of scale, and technological change. However, those objectives are beyond the scope of the current paper, which is an illustration of the available methodology, rather than a final modeling result.(1)
The Lucas Critique
According to the Lucas critique, private sector parameters and the parameters of central bank policy rules are confounded together within the demand and supply solution functions that typically are estimated in macroeconometric models. When modeled dynamically, those demand and supply functions are the feedback rules or contingency plans that comprise the solution functions to dynamic programming or optimal control decisions of consumers and firms. However, the central bank's policy process is among the laws of motion serving as constraints in the private sector's dynamic decision. Hence the feedback rules that solve the private sector's decision depend upon the parameters of those processes as well of the private sector's own taste and technology parameters. Shifts in the parameters of the central bank's policy process will shift the private sector's solution feedback rules.
The source of this confounding is the solution of the first-order conditions (Euler equations) of the private sector's decision, since that solution cannot be acquired without augmenting the private sector's Euler equations with the government's policy rules. In particular, the central bank's policy rule, interest rate, processes, and other governmentally influenced stochastic processes for variables that are in the private agent's decision, but are not under the control of that private decision maker, must be adjoined to private decision maker's Euler equations, before the solution for the feedback rules (demand and supply functions) can be found. But if the Euler equations of the private sector are estimated directly, the confounding problem is avoided. Hence in macroeconomics, there is wide acceptance of the idea that Euler equations should be estimated, rather than the demand and supply functions that are the solution to the augmented system. See, for example, Sims and Leeper (1994).
Despite the influence of Euler equation estimation and the Lucas critique in macroeconomics, a substantial portion of the literature on monetary economics has continued to use estimated money demand and money supply functions, which are vulnerable to the Lucas critique. …