On Whitney type inequalities for local anisotropic polynomial approximation

We prove a multivariate Whitney type theorem for the local anisotropic polynomial approximation in $L_p(Q)$ with $1\leq p\leq \infty$. Here $Q$ is a $d$-parallelepiped in \RR^d with sides parallel to the coordinate axes. We consider the error of best approximation of a function $f$ by algebraic polynomials of fixed degree at most $r_i - 1$ in variable $x_i,\ i=1,...,d$, and relate it to a so-called total mixed modulus of smoothness appropriate to characterizing the convergence rate of the approximation error. This theorem is derived from a Johnen type theorem on equivalence between a certain K-functional and the total mixed modulus of smoothness which is proved in the present paper.Comment: 12 pages; the proofs of Theorems 1.2 and 2.2 and Lemma 3.1 are revised; typos are corrected; Acknowledgments are added; the results are unchange

Fiscal solvency and sustainability in economic management

Fiscal policy is central to a country's economic and social objectives, from macroeconomic stability to sustainable growth and poverty reduction. But evaluations of a country's fiscal performance, over time or relative to other countries, are often conducted independent of other development objectives, disregarding the links between fiscal, monetary, and exchange rate policies. A budget deficit of 4 percent of GDP, for example, may be acceptable in one country but not in another, because of different initial conditions and policy priorities. In the same country, a level of fiscal deficit may be acceptable one year but not the next, depending on developments and changes in policy objectives. The author argues for assessing fiscal performance (1) as part of the entire framework of economic policy, (2) against a policy objective, (3) by taking into account both short- and long-term considerations, and (4) with an eye to the quality of adjustment (whether there are income inequalities or other social issues, for example) as well as its magnitude. The approach he proposes for assessing country fiscal performance requires a minimum of data and takes into account flow and stock variables on internal and external debt. The approach addresses the shortcomings of conventional analysis by incorporating the debt dynamics and other macroeconomic targets of growth, inflation, and external and internal debt. While its theoretical foundation is well known in the literature, this approach has not been adapted for assessing fiscal performance either over time or across countries, and he discusses practical issues arising from this adaptation. The author proposes two indicators to measure fiscal adjustment efforts: Fiscal solvency adjustment, which measures how far additional fiscal efforts must be taken to restore solvency to the fiscal sector. Fiscal sustainability adjustment, which measures how far additional fiscal efforts must be taken to maintain the ratios of internal and external debt to output. The author applies the proposed framework to evaluate recent fiscal performance in three countries-Argentina, India, and Zambia-each with a different income level and located on a different continent. The countries were selected on the basis of recent World Bank economic work using the proposed approach or an equivalent. The author finds the proposed approach useful for identifying key fiscal issues, for assessing the adequacy and pace of fiscal adjustment consistent with the overall economic and social objectives, and for highlighting the tradeoffs between policy initiatives. Sound fiscal policy is crucial for macroeconomic stability. When fiscal issues are under control, it is easier to coordinate other policies. When fiscal issues are part of the problem, the tradeoffs between policy outcomes become pronounced, and economic management, including the management of capital flows, becomes much more difficult.Strategic Debt Management,Economic Theory&Research,Payment Systems&Infrastructure,Banks&Banking Reform,Environmental Economics&Policies,Economic Stabilization,National Governance,Economic Theory&Research,Strategic Debt Management,Banks&Banking Reform

Inflation tax and deficit financing in Egypt

Although Egypt's budget deficit is far above the level found in other low-middle-income countries, the inflation rate in Egypt has never been very high. This is because the country has managed to finance these budget deficits by resorting to an inflation tax that, at 11 percent of GDP in 1987, constitutes a large share of total tax revenues. By contrast, conventional tax revenues come to only 17 percent of GDP. The authors report a large, underlying inflation-tax base - from which the Egyptian government has collected substantial revenues which exist because of money balances held by the private sector. The authors find that the private business sector, with anet borrowing position of 14 percent of GDP, has benefited from the inflation tax. Households, on the other hand, pay more of the inflation tax than other sectors, turning over 8 percent of GDP to the government. This compares with 0.5 percent of GDP that households pay in income tax. Although income tax in Egypt is fairly progressive, the greater reliance on the inflation tax makes Egypt's overall tax structure fairly regressive. The authors argue that : i) understanding the role and size of the inflation tax will help in determining the sequencing and equity aspects of any future reform program; and ii) the financial side cannot continue to bear the burden for the real side; Egypt must move swiftly to cut its budget deficit, the underlying cause of its dependence on the inflation tax.Economic Theory&Research,Public Sector Economics&Finance,Banks&Banking Reform,Environmental Economics&Policies,Macroeconomic Management

Money, inflation, and deficit in Egypt

Egypt has been able to escape high inflation by depleting its stocks of creditworthiness, money illusion, and enforceable foreign-exchange controls. These nonrecoverable assets are quickly becoming extinct and the economy is on an unsustainable path. The authors present a short- and medium-term dynamic model of the Egyptian economy and use it to simulate the effects on output and inflation of a stabilization-cum-adjustment program. Their conclusion is to make the public sector live within its means, and to do so at once. This is a demanding prescription; political and social pressure can become intolerable under adjustment. The authors show that both a slowdown in output and the initial rise in inflation associated with a tough reform program will be short-lived. And a do-nothing strategy will soon push the country into a serious crisis, the correction of which will certainly be more painful.Economic Theory&Research,Economic Stabilization,Environmental Economics&Policies,Banks&Banking Reform,Public Sector Economics&Finance

Linear degree growth in lattice equations

We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth and hence are linearizable