# **1: Introduction**

Sir Isaac Newton’s second law of motion tells us that the net force on an object (of constant mass) is equal to the rate of change of its linear momentum over a period of time. In other words, if an object of a given mass is accelerating over time, there is force acting on it. We do not know from observing the dynamics of the object while it is in motion what _caused_ the initial impulse for the object to increase or decrease velocity. But monitoring the rate of change of velocity (the object’s acceleration) over time tells us about the direction of the force operating on it, whether it persists through time, and given its direction, size and speed, whether it is likely to cause a collision unless its path is corrected. This paper applies these concepts to public spending analysis to provide new signaling tools for fiscal economists.

Acceleration is not a new concept to macro economists or financial analysts. Monetary economists have long since learned that acceleration in the growth of the money supply or in the rate of price inflation is destabilizing. Growth economists have characterized sudden and sustained increases in the rate of growth of an economy as `growth accelerations’, and have set about trying to explain what drives them. The old investment accelerator theory in macro economics suggests that as demand or income increases in an economy, so does the investment made by firms, which in turn increases demand. This growth attracts more investors, which accelerates growth - the upshot being that investment in the economy accelerates until the economy reaches a new equilibrium. The more recent `financial accelerator mechanism’ describes a situation where lower asset prices spur lower credit and lower credit in turn leads to a reduction in investment. This in turn leads to further reductions in asset prices due to their procyclicality, which in the end will lead to a self-reinforced pro-cyclical drop in domestic absorption and output, asset prices and credit. Finally, short-term asset traders have long observed the signaling effects of stock price oscillations, and so they track short-term fluctuations in price `velocity’ and price `acceleration’ before looking into the drivers of these.

The economic concept of acceleration is as straightforward as the arithmetic. But to our knowledge there has been no previous attempt to apply measures of acceleration to public expenditure analysis, which at the macro level typically analyzes sector shares of spending and growth rates over time. Part of the reason for this may have been the lack – up until now - of organized and detailed micro data for public spending in countries. This data constraint is changing as the World Bank’s BOOST public expenditure analysis tool is making new micro spending data sets available.<sup>2</sup> Drawing from the concepts of velocity, acceleration, momentum and force from physical science and financial analysis, we devise in section 2 a measure of “force” for the ` _dismal science_ ’ of public finance economics. We use shares and growth rates in our measure of force, but by adding acceleration, we provide more information to the analyst in a standardized and globally comparable metric.

> 2 See Kheyfets, Mastruzzi, Merotto and Sondergaard (2010), “A New Data Tool to Boost Public Spending Efficiency”, World Bank Europe and Central Asia Knowledge Brief#43, September 2011.