Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

Nuclear accumulation of the phytochrome A photoreceptor requires FHY1.

The phytochrome family of red/far-red (R/FR)-responsive photoreceptors plays a key role throughout the life cycle of plants . Arabidopsis has five phytochromes, phyA-phyE, among which phyA and phyB play the most predominant functions . Light-regulated nuclear accumulation of the phytochromes is an important regulatory step of this pathway, but to this date no factor specifically required for this event has been identified . Among all phyA signaling mutants, fhy1 and fhy3 (far-red elongated hypocotyl 1 and 3) have the most severe hyposensitive phenotype, indicating that they play particularly important roles . FHY1 is a small plant-specific protein of unknown function localized both in the nucleus and the cytoplasm . Here we show that FHY1 is specifically required for the light-regulated nuclear accumulation of phyA but not phyB. Moreover, phyA accumulation is only slightly affected in fhy3, indicating that the diminished nuclear accumulation of phyA observed in fhy1 seedlings is not simply a general consequence of reduced phyA signaling. By in vitro pull-down and yeast two-hybrid analyses, we demonstrate that FHY1 physically interacts with phyA, preferentially in its active Pfr form. Furthermore, FHY1 and phyA colocalize in planta. We therefore identify the first component required for light-regulated phytochrome nuclear accumulation.

Unstable equilibrium: young adult women in family and career formation in Southern Europe

The paper examines the relationship between family formation (i.e., living with a partner and having children) and women’s occupational career in southern Europe (i.e., Greece, Italy, Portugal and Spain). The relationship is explored by analysing the impact that different family structures and male [nvolvement in caring activities have on women’s early occupational trajectories (i.e., remaining in the same occupational status, experiencing downward or upward mobility, or withdrawing from paid work). This research shows that male involvement in caring activities does not really push women ahead in their career, but the absolute lack of male support seems to negatively affect women’s permanence in paid work. These results apply to all southern European countries except Portugal, where the absolute absence of the partners’ support in caring activities does not seem to alter women’s determination to remain in paid work. The methodology applied consists of the estimation of multinomial logit regression models and the analysis is based on eight waves (1994-2001) of the European Community Household Panel (ECHP).

Pessoas com úlceras vasculogênicas em atendimento ambulatorial de enfermagem: estudo das variáveis clínicas e sociodemográficas

Objetivou-se analisar características sociodemográficas e clínicas de pessoas com úlceras vasculogênicas e investigar a associação entre estas variáveis. Realizou-se um estudo clínico observacional transversal, em salas de curativo de serviços municipais de saúde, de fevereiro a agosto de 2009. Realizou-se entrevista, exame clínico, aplicação da escala Pressure Ulcer Scale Healing (PUSH) e registro fotográfico das lesões. Participaram 42 indivíduos, com média de 60 anos (± 12), 73,8% do sexo masculino, com lesões únicas (66,7%), decorrentes de alteração da circulação venosa (90,5%), duração de até um ano (55,5%). Houve associação entre o escore da PUSH (p=0,019) e profundidade da lesão (p=0,027) com exercício de atividade ocupacional na atualidade, assim como entre o histórico de tabagismo e o gênero (p=0,049). As características sociodemográficas evidenciadas são semelhantes às de outros, com exceção do gênero masculino, o que indica a necessidade de maiores investigações na população goianiense.

Kaupungin ja maaseudun vuorovaikutus alueellisessa kehittämispolitiikassa

In Finland, European Union membership and economic globalisation have changed the position of regions from closed territorial systems to nodes of open international networks. The increasing complexity of cities as globalised knowledge centres and functionally specialised and diversified rural areas, and on the other hand growing disparities between prosperous urban cores and lagging peripheral areas are also essential features in contemporary regional development. These trends have produced new needs to promote mutual dialogue between cities and the countryside in western market economies. Urban-rural interaction is an idea which was developed in the late 1990s within regional policy to pull together these new challenges to regional development and handle cities and the countryside as a whole. The aim of my study is to conceptualise the idea of urban-rural interaction, explain the phenomenon theoretically, clarify past and present urban and rural development and analyse regional policies from the interaction angle. The ultimate purpose is to illustrate the existence and nature of particular interaction policy in a globalising society. The general method is discourse analysis, which I use in three cases: Central Finland, South-Ostrobothnia and South-West Finland. Theoretically I have a two-dimensional approach. On the first hand I use World-System theory to explain how the global economy is moulding urban and rural structures at the regional level. On the other hand I use regime theory to explain local political actions and practises between cities and the countryside under the overlapping pressures deriving from reformulated regional structures and policies.

Adaptation to globalisation in Finland has been carried out by strengthening urban centres. The stress in regional policy has been in urban development. The development of the countryside has mostly been implemented by a separate rural policy. At the end of the 1990s and early 2000s Finnish cities have actually shown themselves to be competitive in global markets. The drawbacks of the new growth centre policy have been the sparse network of prosperous cities and their weak spreading effects, which have hindered comprehensive regional development. Tensions between urban and rural areas have also deepened. In this situation the interaction policy is used as a way of balancing development and moderate conflicts within the regions. From this point of view urban-rural interaction can be seen as a way of tackling the challenges of globalisation.

On the other hand the results emphasise that actors involved in regional development still believe, although the hegemonic discourse is on urban policy, that there are opportunities to stimulate progress in the countryside as well. In the situation where regional authorities control development resources, rural development can be successful only if rural actors manage to establish fruitful relationships with their urban partners. This is also the weakness of the programme-based regional policy. If rural municipalities or other actors are for any reason incapable of building development regimes with cities, the offers of interaction policy will be useless.

The problem of the interaction policy is that the focus and methods of it have so far been rather underdeveloped. In order to improve the efficiency of the interaction policy, further research should concentrate on the social processes which define the position of cities and the countryside as partners of interaction, and practises which promote or prohibit the possibilities of developing the interaction policy. The efforts to define different contents of urban-rural interaction or promote interaction projects should not have such an important role in the future as they have had so far. Instead, the focus of interaction policy should be on questions such as how to manage the political tensions between town and country and how to create a positive atmosphere for regional policy where the needs of urban and rural development are promoted equally.

Financial Markets and Real Ecinomy: Four Essays in International Trade

Financial markets play an important role in an economy performing various functions like mobilizing and pooling savings, producing information about investment opportunities, screening and monitoring investments, implementation of corporate governance, diversification and management of risk. These functions influence saving rates, investment decisions, technological innovation and, therefore, have important implications for welfare. In my PhD dissertation I examine the interplay of financial and product markets by looking at different channels through which financial markets may influence an economy.My dissertation consists of four chapters. The first chapter is a co-authored work with Martin Strieborny, a PhD student from the University of Lausanne. The second chapter is a co-authored work with Melise Jaud, a PhD student from the Paris School of Economics. The third chapter is co-authored with both Melise Jaud and Martin Strieborny. The last chapter of my PhD dissertation is a single author paper.Chapter 1 of my PhD thesis analyzes the effect of financial development on growth of contract intensive industries. These industries intensively use intermediate inputs that neither can be sold on organized exchange, nor are reference-priced (Levchenko, 2007; Nunn, 2007). A typical example of a contract intensive industry would be an industry where an upstream supplier has to make investments in order to customize a product for needs of a downstream buyer. After the investment is made and the product is adjusted, the buyer may refuse to meet a commitment and trigger ex post renegotiation. Since the product is customized to the buyer's needs, the supplier cannot sell the product to a different buyer at the original price. This is referred in the literature as the holdup problem. As a consequence, the individually rational suppliers will underinvest into relationship-specific assets, hurting the downstream firms with negative consequences for aggregate growth. The standard way to mitigate the hold up problem is to write a binding contract and to rely on the legal enforcement by the state. However, even the most effective contract enforcement might fail to protect the supplier in tough times when the buyer lacks a reliable source of external financing. This suggests the potential role of financial intermediaries, banks in particular, in mitigating the incomplete contract problem. First, financial products like letters of credit and letters of guarantee can substantially decrease a risk and transaction costs of parties. Second, a bank loan can serve as a signal about a buyer's true financial situation, an upstream firm will be more willing undertake relationship-specific investment knowing that the business partner is creditworthy and will abstain from myopic behavior (Fama, 1985; von Thadden, 1995). Therefore, a well-developed financial (especially banking) system should disproportionately benefit contract intensive industries.The empirical test confirms this hypothesis. Indeed, contract intensive industries seem to grow faster in countries with a well developed financial system. Furthermore, this effect comes from a more developed banking sector rather than from a deeper stock market. These results are reaffirmed examining the effect of US bank deregulation on the growth of contract intensive industries in different states. Beyond an overall pro-growth effect, the bank deregulation seems to disproportionately benefit the industries requiring relationship-specific investments from their suppliers.Chapter 2 of my PhD focuses on the role of the financial sector in promoting exports of developing countries. In particular, it investigates how credit constraints affect the ability of firms operating in agri-food sectors of developing countries to keep exporting to foreign markets.Trade in high-value agri-food products from developing countries has expanded enormously over the last two decades offering opportunities for development. However, trade in agri-food is governed by a growing array of standards. Sanitary and Phytosanitary standards (SPS) and technical regulations impose additional sunk, fixed and operating costs along the firms' export life. Such costs may be detrimental to firms' survival, "pricing out" producers that cannot comply. The existence of these costs suggests a potential role of credit constraints in shaping the duration of trade relationships on foreign markets. A well-developed financial system provides the funds to exporters necessary to adjust production processes in order to meet quality and quantity requirements in foreign markets and to maintain long-standing trade relationships. The products with higher needs for financing should benefit the most from a well functioning financial system. This differential effect calls for a difference-in-difference approach initially proposed by Rajan and Zingales (1998). As a proxy for demand for financing of agri-food products, the sanitary risk index developed by Jaud et al. (2009) is used. The empirical literature on standards and norms show high costs of compliance, both variable and fixed, for high-value food products (Garcia-Martinez and Poole, 2004; Maskus et al., 2005). The sanitary risk index reflects the propensity of products to fail health and safety controls on the European Union (EU) market. Given the high costs of compliance, the sanitary risk index captures the demand for external financing to comply with such regulations.The prediction is empirically tested examining the export survival of different agri-food products from firms operating in Ghana, Mali, Malawi, Senegal and Tanzania. The results suggest that agri-food products that require more financing to keep up with food safety regulation of the destination market, indeed sustain longer in foreign market, when they are exported from countries with better developed financial markets.Chapter 3 analyzes the link between financial markets and efficiency of resource allocation in an economy. Producing and exporting products inconsistent with a country's factor endowments constitutes a serious misallocation of funds, which undermines competitiveness of the economy and inhibits its long term growth. In this chapter, inefficient exporting patterns are analyzed through the lens of the agency theories from the corporate finance literature. Managers may pursue projects with negative net present values because their perquisites or even their job might depend on them. Exporting activities are particularly prone to this problem. Business related to foreign markets involves both high levels of additional spending and strong incentives for managers to overinvest. Rational managers might have incentives to push for exports that use country's scarce factors which is suboptimal from a social point of view. Export subsidies might further skew the incentives towards inefficient exporting. Management can divert the export subsidies into investments promoting inefficient exporting.Corporate finance literature stresses the disciplining role of outside debt in counteracting the internal pressures to divert such "free cash flow" into unprofitable investments. Managers can lose both their reputation and the control of "their" firm if the unpaid external debt triggers a bankruptcy procedure. The threat of possible failure to satisfy debt service payments pushes the managers toward an efficient use of available resources (Jensen, 1986; Stulz, 1990; Hart and Moore, 1995). The main sources of debt financing in the most countries are banks. The disciplining role of banks might be especially important in the countries suffering from insufficient judicial quality. Banks, in pursuing their rights, rely on comparatively simple legal interventions that can be implemented even by mediocre courts. In addition to their disciplining role, banks can promote efficient exporting patterns in a more direct way by relaxing credit constraints of producers, through screening, identifying and investing in the most profitable investment projects. Therefore, a well-developed domestic financial system, and particular banking system, would help to push a country's exports towards products congruent with its comparative advantage.This prediction is tested looking at the survival of different product categories exported to US market. Products are identified according to the Euclidian distance between their revealed factor intensity and the country's factor endowments. The results suggest that products suffering from a comparative disadvantage (labour-intensive products from capital-abundant countries) survive less on the competitive US market. This pattern is stronger if the exporting country has a well-developed banking system. Thus, a strong banking sector promotes exports consistent with a country comparative advantage.Chapter 4 of my PhD thesis further examines the role of financial markets in fostering efficient resource allocation in an economy. In particular, the allocative efficiency hypothesis is investigated in the context of equity market liberalization.Many empirical studies document a positive and significant effect of financial liberalization on growth (Levchenko et al. 2009; Quinn and Toyoda 2009; Bekaert et al., 2005). However, the decrease in the cost of capital and the associated growth in investment appears rather modest in comparison to the large GDP growth effect (Bekaert and Harvey, 2005; Henry, 2000, 2003). Therefore, financial liberalization may have a positive impact on growth through its effect on the allocation of funds across firms and sectors.Free access to international capital markets allows the largest and most profitable domestic firms to borrow funds in foreign markets (Rajan and Zingales, 2003). As domestic banks loose some of their best clients, they reoptimize their lending practices seeking new clients among small and younger industrial firms. These firms are likely to be more risky than large and established companies. Screening of customers becomes prevalent as the return to screening rises. Banks, ceteris paribus, tend to focus on firms operating in comparative-advantage sectors because they are better risks. Firms in comparative-disadvantage sectors finding it harder to finance their entry into or survival in export markets either exit or refrain from entering export markets. On aggregate, one should therefore expect to see less entry, more exit, and shorter survival on export markets in those sectors after financial liberalization.The paper investigates the effect of financial liberalization on a country's export pattern by comparing the dynamics of entry and exit of different products in a country export portfolio before and after financial liberalization.The results suggest that products that lie far from the country's comparative advantage set tend to disappear relatively faster from the country's export portfolio following the liberalization of financial markets. In other words, financial liberalization tends to rebalance the composition of a country's export portfolio towards the products that intensively use the economy's abundant factors.

Structural development of the Tso Morari ultra-high pressure nappe of the Ladakh Himalaya

A continental subduction-related and multistage exhumation process for the Tso Morari ultra-high pressure nappe is proposed. The model is constrained by published thermo-barometry and age data, combined with new geological and tectonic maps. Additionally, observations on the structural and metamorphic evolution of the Tso Morari area and the North Himalayan nappes are presented. The northern margin of the Indian continental crust was subducted to a depth of >90 km below Asia after continental collision some 55 Ma ago. The underthrusting was accompanied by the detachment and accretion of Late Proterozoic to Early Eocene sediments, creating the North Himalayan accretionary wedge, in front of the active Asian margin and the 103-50 Ma Ladakh arc batholith. The basic dikes in the Ordovician Tso Morari granite were transformed to eclogites with crystallization of coesite, some 53 Ma ago at a depth of >90 kin (>27 kbar) and temperatures of 500 to 600 degrees C. The detachment and extrusion of the low density Tso Morari nappe, composed of 70% of the Tso Morari granite and 30% of graywackes with some eclogitic dikes, occurred by ductile pure and simple shear deformation. It was pushed by buoyancy forces and by squeezing between the underthrusted Indian lithosphere and the Asian mantle wedge. The extruding Tso Morari nappe reached a depth of 35 km at the base of the North Himalayan accretionary wedge some 48 Ma ago. There the whole nappe stack recrystallized under amphibolite facies conditions of a Barrovian regional metamorphism with a metamorphic field gradient of 20 degrees C/km. An intense schistosity with a W-E oriented stretching lineation L, and top-to-the E shear criteria and crystallization of oriented sillimanite needles after kyanite, testify to the Tso Morari nappe extrusion and pressure drop. The whole nappe stack, comprising from the base to top the Tso Morari, Tetraogal, Karzok and Mata-Nyimaling-Tsarap nappes, was overprinted by new schistosities with a first N-directed and a second NE-directed stretching lineation L-2 and L-3 reaching the base of the North Himalayan accretionary wedge. They are characterized by top-to-the S and SW shear criteria. This structural overprint was related to an early N- and a younger NE-directed underthrusting of the Indian plate below Asia that was accompanied by anticlockwise rotation of India. The warping of the Tso Morari dome started already some 48 Ma ago with the formation of an extruding nappe at depth. The Tso Morari dome reached a depth of 15 km about 40 Ma ago in the eastern Kiagar La region and 30 Ma ago in the western Nuruchan region. The extrusion rate was of about 3 cm/yr between 53 and 48 Ma, followed by an uplift rate of 1.2 mm/yr between 48 and 30 Ma and of only 0.5 mm/yr after 30 Ma. Geomorphology observations show that the Tso Morari dome is still affected by faults, open regional dome, and basin and pull-apart structures, in a zone of active dextral transpression parallel to the Indus Suture zone.

Kermit interacts with gαo, vang, and motor proteins in Drosophila planar cell polarity.

In addition to the ubiquitous apical-basal polarity, epithelial cells are often polarized within the plane of the tissue - the phenomenon known as planar cell polarity (PCP). In Drosophila, manifestations of PCP are visible in the eye, wing, and cuticle. Several components of the PCP signaling have been characterized in flies and vertebrates, including the heterotrimeric Go protein. However, Go signaling partners in PCP remain largely unknown. Using a genetic screen we uncover Kermit, previously implicated in G protein and PCP signaling, as a novel binding partner of Go. Through pull-down and genetic interaction studies, we find that Kermit interacts with Go and another PCP component Vang, known to undergo intracellular relocalization during PCP establishment. We further demonstrate that the activity of Kermit in PCP differentially relies on the motor proteins: the microtubule-based dynein and kinesin motors and the actin-based myosin VI. Our results place Kermit as a potential transducer of Go, linking Vang with motor proteins for its delivery to dedicated cellular compartments during PCP establishment.

Laser therapy in pressure ulcers: evaluation by the Pressure Ulcer Scale for Healing and Nursing Outcomes Classification

AbstractOBJECTIVETo describe the pressure ulcer healing process in critically ill patients treated with conventional dressing therapy plus low-intensity laser therapy evaluated by the Pressure Ulcer Scale for Healing (PUSH) and the result of Wound Healing: Secondary Intention, according to the Nursing Outcomes Classification (NOC).METHODCase report study according to nursing process conducted with an Intensive Care Unit patient. Data were collected with an instrument containing the PUSH and the result of the NOC. In the analysis we used descriptive statistics, considering the scores obtained on the instrument.RESULTSA reduction in the size of lesions of 7cm to 1.5cm of length and 6cm to 1.1cm width, in addition to the increase of epithelial tissue and granulation, decreased secretion and odor.CONCLUSIONThere was improvement in the healing process of the lesion treated with adjuvant therapy and the use of NOC allowed a more detailed and accurate assessment than the PUSH.

Off-resonance angiography: a new method to depict vessels--phantom and rabbit studies.

PURPOSE: To evaluate the utility of inversion recovery with on-resonant water suppression (IRON) in combination with injection of the long-circulating monocrystalline iron oxide nanoparticle (MION)-47 for contrast material-enhanced magnetic resonance (MR) angiography. MATERIALS AND METhods: Experiments were approved by the institutional animal care committee. Eleven rabbits were imaged at baseline before injection of a contrast agent and then serially 5-30 minutes, 2 hours, 1 day, and 3 days after a single intravenous bolus injection of 80 micromol of MION-47 per kilogram of body weight (n = 6) or 250 micromol/kg MION-47 (n = 5). Conventional T1-weighted MR angiography and IRON MR angiography were performed on a clinical 3.0-T imager. Signal-to-noise and contrast-to-noise ratios were measured in the aorta of rabbits in vivo. Venous blood was obtained from the rabbits before and after MION-47 injection for use in phantom studies. RESULTS: In vitro blood that contained MION-47 appeared signal attenuated on T1-weighted angiograms, while characteristic signal-enhanced dipolar fields were observed on IRON angiograms. In vivo, the vessel lumen was signal attenuated on T1-weighted MR angiograms after MION-47 injection, while IRON supported high intravascular contrast by simultaneously providing positive signal within the vessels and suppressing background tissue (mean contrast-to-noise ratio, 61.9 +/- 12.4 [standard deviation] after injection vs 1.1 +/- 0.4 at baseline, P < .001). Contrast-to-noise ratio was higher on IRON MR angiograms than on conventional T1-weighted MR angiograms (9.0 +/- 2.5, P < .001 vs IRON MR angiography) and persisted up to 24 hours after MION-47 injection (76.2 +/- 15.9, P < .001 vs baseline). CONCLUSION: IRON MR angiography in conjunction with superparamagnetic nanoparticle administration provides high intravascular contrast over a long time and without the need for image subtraction.

Changes in spring-mass model characteristics during repeated running sprints.

This study investigated fatigue-induced changes in spring-mass model characteristics during repeated running sprints. Sixteen active subjects performed 12 × 40 m sprints interspersed with 30 s of passive recovery. Vertical and anterior-posterior ground reaction forces were measured at 5-10 m and 30-35 m and used to determine spring-mass model characteristics. Contact (P &lt; 0.001), flight (P &lt; 0.05) and swing times (P &lt; 0.001) together with braking, push-off and total stride durations (P &lt; 0.001) lengthened across repetitions. Stride frequency (P &lt; 0.001) and push-off forces (P &lt; 0.05) decreased with fatigue, whereas stride length (P = 0.06), braking (P = 0.08) and peak vertical forces (P = 0.17) changes approached significance. Center of mass vertical displacement (P &lt; 0.001) but not leg compression (P &gt; 0.05) increased with time. As a result, vertical stiffness decreased (P &lt; 0.001) from the first to the last repetition, whereas leg stiffness changes across sprint trials were not significant (P &gt; 0.05). Changes in vertical stiffness were correlated (r &gt; 0.7; P &lt; 0.001) with changes in stride frequency. When compared to 5-10 m, most of ground reaction force-related parameters were higher (P &lt; 0.05) at 30-35 m, whereas contact time, stride frequency, vertical and leg stiffness were lower (P &lt; 0.05). Vertical stiffness deteriorates when 40 m run-based sprints are repeated, which alters impact parameters. Maintaining faster stride frequencies through retaining higher vertical stiffness is a prerequisite to improve performance during repeated sprinting.

Honey, I shrunk the sample covariance matrix

The central message of this paper is that nobody should be using the samplecovariance matrix for the purpose of portfolio optimization. It containsestimation error of the kind most likely to perturb a mean-varianceoptimizer. In its place, we suggest using the matrix obtained from thesample covariance matrix through a transformation called shrinkage. Thistends to pull the most extreme coefficients towards more central values,thereby systematically reducing estimation error where it matters most.Statistically, the challenge is to know the optimal shrinkage intensity,and we give the formula for that. Without changing any other step in theportfolio optimization process, we show on actual stock market data thatshrinkage reduces tracking error relative to a benchmark index, andsubstantially increases the realized information ratio of the activeportfolio manager.

Why England? Demand, growth and inequality during the Industrial Revolution

Why was England first? And why Europe? We present a probabilistic model that builds on big-push models by Murphy, Shleifer and Vishny (1989), combined with hierarchical preferences. The interaction of exogenous demographic factors (in particular the English low-pressure variant of the European marriage pattern)and redistributive institutions such as the old Poor Law combined to make an Industrial Revolution more likely. Essentially, industrialization is the result of having a critical mass of consumers that is rich enough to afford (potentially) mass-produced goods. Our model is then calibrated to match the main characteristics of the English economy in 1750 and the observed transition until 1850.This allows us to address explicitly one of the key features of the British IndustrialRevolution unearthed by economic historians over the last three decades the slowness of productivity and output change. In our calibration, we find that the probability of Britain industrializing is 5 times larger than France s. Contrary to the recent argument by Pomeranz, China in the 18th century had essentially no chance to industrialize at all. This difference is decomposed into a demographic and a policy component, with the former being far more important than the latter.

On the timing of balance of payments crises: Disaggregated information and interest rate policy

This paper proposes a dynamic framework to study the timing of balance of paymentscrises. The model incorporates two main ingredients: (i) investors have private information; (ii)investors interact in a dynamic setting, weighing the high returns on domestic assets against the incentives to pull out before the devaluation. The model shows that the presence of disaggregated information delays the onset of BOP crises, giving rise to discrete devaluations. It also shows that high interest rates can be eective in delaying and possibly avoiding the abandonment of the peg. The optimal policy is to raise interest rates sharply as fundamentals become very weak. However, this policy is time inconsistent, suggesting a role for commitment devices such as currency boards or IMF pressure.