shares and changes in growth rates means that our measure is a purely statistical construct independent of currency or absolute value, which makes it internationally comparable.

From a practitioner’s perspective this categorization of spending can be useful information. Budgets are prepared as annual decisions, with changes in allocations often determined at the margin given available resources. Most budget systems don’t track spending over time, and since spending decisions over time don’t necessarily follow an orderly medium-term plan, it can be useful to let spending trend data speak for itself. Using our metric of force, spending items can be categorized by the components of force over a time period into four mutually inclusive labels: (i) relatively important or unimportant items, (ii) shrinking or steady or growing, (iii) growing faster or slower than average, and (iv) accelerating or decelerating.

What economic meaning might there be in being in these categories, or in items changing from one category to another over time? Obviously relatively important items are worth observing more closely than less important items, both because small growth in them can cause significant absolute changes in total spending, and because reforms to them can generate significant savings.

Second, significant rapid growth, persistent growth or acceleration (persistent and faster growth) in public spending items signals to the observer that something is driving expenditure. Unlike physical science, there is no assurance in public expenditures that an object (item) which has velocity (is growing) in the first period will continue to have velocity (grow) in year 2. But like physical science, an item of spending which has been stable then starts to rise, or which is rising with average spending and then starts accelerating, will have had an expenditure impulse: whether this is a policy or an increase in service coverage or quality, or simply a relative increase in price. Its growth relative to total spending and relative to inflation will give us clues as to whether there are significant cost drivers at play. For example, consider a planned scale-up in vaccination for a country. In the year of program inception, spending should accelerate with the impulse of the scale-up in persons covered. In subsequent years spending growth should stabilize according to the planned growth rate in coverage, before decelerating as coverage rates in the population reach the target level. Instead, in year two, the Ministry of Health switches to a new more virulent vaccine which costs more. If they fail to budget for this price increase, service coverage would need to drop. If they receive authorization for additional spending, the second year impetus for a further acceleration in spending would be price, not service-driven. Force would show as positive in both cases, but eventually force should rescind as program coverage peaks and the cost of vaccines stabilizes.

As this example shows, growth and acceleration in public spending as in physical science, is not necessarily a bad thing. The point is the quality of the spending, and whether it is financeable. A _sustainable_ acceleration which is associated with expansion of a basic pro-poor service can be as desirable as acceleration of a fire truck on its way to save lives, so long as it is a responsible acceleration