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I would like to thank Bernardin Akitoby, Anton Belyakov, Ray Brooks, Reda Cherif, Julio Escolano, Matthew Gaertner, Vitor Gaspar, Mikhail Krastanov, Jun Kim, Ines Lopes, Paulo Medas, Marialuz Moreno Badia, Andrea Schaechter, Abdelhak Senhadji, Vladimir Veliov and the participants in the IMF FAD Seminar for valuable comments and suggestions. All remaining errors are my own.
For instance, Mody et al. (2012), have attributed a significant part of the increase in savings rates in the aftermath of the financial crisis to the precautionary motive. Their result is explained with the heightened uncertainty about labor income and investment returns.
October 2015 Fiscal Monitor data base.
Some authors find a negative impact of high public debt on growth (e.g., Kumar and Woo, 2010). The effect becomes pronounced only after a certain threshold of the debt-to-GDP ratio is reached. This threshold varies by country and depends on a number of factors, such as level of development and investors base.
The concept of certainty equivalence was introduced by Simon (1956) in the one-dimensional case and later generalized by Theil (1957). Most results related to certainty equivalence are obtained for LQ problems with additive Gaussian disturbances. Deviations from this framework may cause the principle to fail (see Chapter 10 in Chow (1986)).
The approach of Arrow and Hurwicz (1972) is in spirit closer to the non-probabilistic frame-work proposed by Shackle than the decision theory based on subjective probability developed by Savage (see Zappia (2014) for an extensive account of Shackles work.)
Gilboa and Schmeidler (1989), p. 142.
It is interesting to note that two decades before Gilboa and Schmeidler, Witsenhausen discussed the expected minimax utility criterion. He argued that the minimax decision rule, or ”guaranteed performance evaluator” in his terminology, is a special case of an ”expected guaranteed performance evaluator” which essentially combines expectations with the minimax.
In practice, the primary balance may not be fully controllable given its endogeneity to growth and implementation lags. Since we are primarily concerned with annual observations, we can assume that most of the effects of fiscal measures will take place within the year.
Admitting the possibility that fiscal policy can influence
Suppose we are given a model with Gaussian errors where the variables of interest have been estimated statistically and are known to be distributed normally with mean μ and covariance matrix Σ. The level sets of the normal distribution, or the surfaces of constant probability density, are the sets of points x such that
One possible extension of the fiscal consolidation model is to consider two control variables - taxes and expenditure- to calculate both the optimal pace and composition of adjustment. However, if the revenue and spending multipliers differ significantly, it may be necessary to modify the solution so as to constrain the controls. Otherwise, the model might suggest unrealistically large swings in the tax and expenditure ratios.
In fact, one could argue that the proposed approach is more appealing for countries with poor data availability or a track record of erratic fiscal behavior, given that in such cases the probabilistic framework would be difficult to apply.
Potential nominal GDP is calculated based on the output gap shown in Table 1 of IMF (2011). Stock-flow adjustments are obtained as the difference between actual debt in the current period and the sum of the debt in the previous period, interest payments and the primary deficit. It is important to note that the actual fiscal adjustment path (as well as growth and debt) were different from the ones envisaged in 2011.
The authors find that the average first-year spending multiplier is about 0.75 and the revenue multiplier is about 0.25.
As discussed in Appendix A.4, an ellipsoid in R2 with a diagonal shape matrix is contained in a rectangle with sides equal to two times the square root of the main diagonal entries. In this case, this is a rectangle centered at (-1,1) with sides
The disturbance ellipsoids were calibrated based on past data just for illustrative purposes and the median absolute deviation was chosen as a robust measure of variability. Of course, if more detailed and forward-looking information is available to the decision maker, it would be natural to incorporate it and possibly specify different ellipsoidal bounds for each period.
The plots are generated using the Matlab Ellipsoidal Toolbox by Alex Kurzhanskiy.
Empirical evidence, based on a model where the feedback of debt introduces non-linearity, can be found in Cherif and Hasanov (2012).
Boltyanskii and Cebotaru (1974) have proved such a maximum principle for both discrete and continuous time problems but in their set-up the uncertainty features in the criterion, not in the dynamics.
The system of difference equation as stated above is implicit. In principle, it is possible to solve the second equation for pt+1 to derive an explicit system.
For convex sets, possessing the central symmetry property the approximation can be improved substantially: E(0, Q) ⊂ D ⊂ E(0, nQ).