Using Signal Processing Tools for Regulation Analysis and Implementation

Regulators often face the challenge of designing and implementing rules that both, respond to the policy objectives and that can be clearly referred to the day-to-day operations and practices in the marketplace. In many cases, the actual codes end up being a cumbersome collection of conditions that are very difficult to evaluate and re-design. This paper suggests that some of the most commonly used tools in Signal Processing could offer a convenient vehicle for tackling these difficulties. By starting from a SIMULINKr model of the regulation of Banco de Mexico on the foreign exchange transactions of commercial banks, this papers offers an example of how those tools could be used in this context. Introduction Regulators often face the challenge of designing and implementing rules that both, respond to their policy objectives and that can be clearly referred Instituto Tecnologico Autonomo de Mexico First draft. Comments welcome 1 to the day-to-day operations and practices in the marketplace. In many cases, specially in the areas of taxation, payment systems and regulation of financial intermediaries, the actual codes end up being a cumbersome collection of definitions, conditions, restrictions and cross-references that, ex post, are very difficult to evaluate and fine tune. One way of tackling this problem would be to try to write down every equation implied by the existing regulation in order to get to a closed form solution that could help in assessing its effects. The problem with this approach is that most regulations include various forms of discontinuities and non-linearities that rarely have a closed form solution. An alternative would be to use the structural form to run simulations and from there work through some optimization method to improve the rules, i.e. by sequentially excluding equations or by recursively calibrating some of the parameters. This approach has the disadvantage of presenting the policy maker with too many parameters to look at, leaving him not very sure about the final outcome of any ulterior regulatory reform. From this perspective, I believe that the tools that economists commonly use for designing optimal policies offer little relief to practitioners, specially when dealing with regulatory design. In fact, taking this on a practical stand, one thing is to deal with a abstract maximization exercise where the idea is to find the best path or reaction function for a control variable it; and a very different one, when the government sets specific rules for the way in which individual agents interact among them and with its agencies. In the first situation, one could comfortably rely on dynamic programming techniques, whereas the complexity of the second is more analogous to the design of complex dynamic systems where a series of inputs come together, are added, lagged, or combined to get an output.. In fact, the alluded tools have some noteworthy advantages: They have been thought for large and complex dynamic systems They are commonly used improving the design of complex devices running from microprocessors to automobiles or aircrafts. Robust visualization tools Resources such as periodograms, zero-pole plots, frequency response, system response and impulse response functions, Notwithstanding, for many commonly used dynamic programming models in Economics, one could find a direct relationship between the Euler equations and Linear Time Invariant Filters. Some examples can be found in Reynoso [12]