In response to some readers’ questions prompted by my post on “The New Stability and Growth Pact: A view from Italy”, I wish to provide a more detailed exemplification of my points that a) the SGP indicators are growth-sensitive, and b) there is a viable alternative to a fixed deficit/GDP ceiling for all. The premise, shared by many economists if not the majority, is that the truly important fiscal issue in a monetary union is debt stability (for low-debt countries) or debt reduction (for high-debt countries). Fiscal accounting implies that the debt/GDP ratio and the deficit/GDP ratio cannot be controlled independently. Once a government is targeting the former, the latter is given according to the implied primary balance, the real interest rate and the GDP growth rate. Thus there is no need to attach symbolic figures to the deficit/GDP ratio. Some simple algebra may help. The debt/GDP ratio d(t) changes over time (approximately) according to the following formula: d(t) - d(t-1) = (i(t) – n(t))d(t-1) – b'(t) where i(t) is the nominal interest rate, n(t) is the nominal growth rate of GDP and b'(t) is the primary balance over GDP (a positive sign denotes a surplus). The nominal growth rate can be conveniently split into the inflation rate p(t) and the real growth rate g(t), n(t) = g(t) + p(t). The same can be done with the nominal interest rate, i(t) = r(t) + p(t), where r(t) is the real interest rate. Hence it is easy to see that, given the initial stock of debt, the real interest rate and the growth rate, the instrument that actually controls the debt/GDP ratio is the primary balance. Typically, a country in the EMU may be required to keep its d(t) constant or make it fall steadily over time, i.e. [d(t) - d(t-1)] = x(t)* __<__ 0. Therefore, the implied primary balance/GDP ratio is b’*(t) = -x*(t) + d(t-1)(r* – g*) where r* and g* are, respectively, the *expected values* of the real interest rate and the potential growth rate over the time horizon of the fiscal plan. Hence a country that plans to reduce its debt/GDP ratio by say 1 point each year has to develop a primary surplus worth 1 point of GDP per year. This target has to be increased (decreased) in proportion to outstanding debt if the real interest rate is larger (smaller) than the potential growth rate. These corrections are more important, the higher is the initial stock of debt. Thus a central issue in the debt-control approach is that high-debt, slow-growth countries should have *primary *budget targets more “ambitious” than those of countries with low initial debt and high real growth. This circumstance may by itself incentivate reduction of high debt and promotion of growth, thus making sense of a Pact for *Stability* *and* *Growth*. The picture may become more complicated if structural fiscal variables happen to affect g* (r*, p* might also be affected, but this is less likely for a single country in a monetary union). Economists disagree on this point, but if a relationship turns out to exist, it is possible to take it into account in the determination of the optimal budget path (the new SGP in fact includes a list of pro-growth fiscal instruments that can be waived from the excess deficit procedure). We can now see why the total-balance ratio to GDP, b(t), cannot be determined independently of the debt target. In fact (approximately) b(t) = b'(t) – i(t)d(t-1) and therefore, given b’*(t), it follows that b*(t) = -x*(t) – d(t-1)(g* + p*) The budget target turns out to depend on the planned change in the debt/GDP ratio corrected for potential growth and the target inflation rate (as fixed by the ECB). It is true that the Maastricht Treaty parameters are consistent with this arithmetic: if d(t-1) = 60%, so that x*(t) = 0, and if g* = 3%, p* = 2%, then b*(t) = -3%. But this does not mean that such a number may come out from any possible fiscal plan in any possible country-specific situation. As just a back-of-the-envelope calculation, let us consider again the case of the 2007-11 plan presented by the Italian government, where t=2007, d(t-1) = 107%, and x* = -2% per year. With g* = 2%, and p* = 2%, we obtain b’*(t) = 2.5% roughly constant for the whole period, and b*(t) = -2.3% with further cuts of about 0.8% per year. Italy, a high-debt, low-growth country, needs budget targets stricter than 3%, and its plan is consistently in line with these figures. On the other hand, it is conceivable that countries with lower debt and higher growth might well keep their debt stable even with deficits exceeding 3% of GDP. In this connection, it is worth paying some attention to the Commission’s view that the 3% deficit/GDP ratio is to be taken as the *upper limit* during recessions, wheres the true target, or “structural”, budget should be “close to balance or in surplus”. Leaving aside that it is doubtful whether such a specific commitment is in the spirit and letter of the Treaty of Maastricht, the previous relationships reveal that it has a strong implication as to debt dynamics. Let us start from b*(t) = 0. Then it must be that b’*(t) = i(t)d(t-1), and, going backwards to debt, x(t) = – n(t)d(t-1). This means that a country keeping its budget in balance obtains a constant debt stock while its ratio to GDP falls at a rate equal to the nominal growth of GDP. Hence, the balanced-budget recommendation is, *implicitly*, a way to induce a particular rate of debt consolidation. What is its rationale? Is it necessarily good always and everywhere? For instance, balanced-growth models maintain that *all* stocks should *grow* at the same rate as GDP. As a matter of fact, one might observe that in the very long run, if wealth increases with GDP, the stock of risk-free debt will become negligible relative to other stocks, which may be somewhat problematic for the liquidity of asset markets and the conduct of monetary policy. Finally, and more importantly, we can see how actual fiscal aggregates can evolve, *and deviate from the plan*, owing to exogenous shocks to growth, say u(t), and to interest rates, say v(t). Suppose that g(t) = g* + u(t) and r(t) = r* + v(t), whereas the ECB keeps inflation at p*. Then, if the government complies with the planned primary balance ratio, b’*(t), it happens that d(t) = d*(t) + d(t-1)(v(t) – u(t)) and b(t) = b*(t) – d(t-1)v(t) Clearly, a growth shortage (u(t) < 0) or an upsurge in the real interest rate (v(t) > 0) worsen the debt/GDP ratio as well as the deficit/GDP ratio with respect to their targets by mere accounting effects, with no direct responsbility of the government. The reason is that the planned rate of primary balance b’*(t) is no longer sufficient to keep b(t) and d(t) on track. In addition, behind accounting relationships there are also macroeconomic relationships. Growth gaps are likely to affect the primary balance adversely by way of automatic stabilizers, so that it may be harder, or counterproductive, for a government to keep up even with b’*(t) in the face of a growth gap. With due care, these unfavourable events can, and should, be discounted in the year by year assessment of the country’s fiscal stance in order to avoid procyclical fiscal policy as well as negative demand spillovers across countries during cyclical swings. These simple relationships give an idea of how the SGP might work without the 3% deficit ceiling taboo. It may be noted that the relevant figures throughout most of the euro-area would yield budget targets rarely above and quite often below 3% of GDP. Yet the key point is that Governments would have the right indication and incentive to concentrate on debt control in the medium-long term while allowing fiscal stabilization to unfold as much as necessary in the short run. As I argued in my previous posting, some elements of a viable reform of the SGP are already in place. Yet the glass is still half empty. First, the new approach based on “growth gaps” has not yet been fully applied and translated into appropriate measures of cyclically adjusted budgets. Second, shocks to the euro-area real interest rate should be considered as well. The euro-area as a whole is an open economy, and as such it is exposed to international shocks of all sorts, as shown by recent experiences. If the ECB wants a totally free hand in its tight interest-rate policy, the consequences cannot simply be off-loaded onto the shoulders of silent governments. In addition, more often than not, interest-rate spikes and growth gaps go hand in hand, at least in the short-to-medium run. Finally, as indicated by the exchange of views between the Commission and the Italian government, besides technicalities the SGP needs some finer institutional tuning as regards its ultimate ends as well as the means and scope of intervention by the Commission.