Nonparametric estimation of the characteristic triplet of a discretely observed L\'evy process

Given a discrete time sample $X_1,... X_n$ from a L\'evy process $X=(X_t)_{t\geq 0}$ of a finite jump activity, we study the problem of nonparametric estimation of the characteristic triplet $(\gamma,\sigma^2,\rho)$ corresponding to the process $X.$ Based on Fourier inversion and kernel smoothing, we propose estimators of $\gamma,\sigma^2$ and $\rho$ and study their asymptotic behaviour. The obtained results include derivation of upper bounds on the mean square error of the estimators of $\gamma$ and $\sigma^2$ and an upper bound on the mean integrated square error of an estimator of $\rho.$Comment: 29 page

Nonparametric inference for discretely sampled L\'evy processes

Given a sample from a discretely observed L\'evy process $X=(X_t)_{t\geq 0}$ of the finite jump activity, the problem of nonparametric estimation of the L\'evy density $\rho$ corresponding to the process $X$ is studied. An estimator of $\rho$ is proposed that is based on a suitable inversion of the L\'evy-Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of $\rho$ over suitable classes of L\'evy triplets. The corresponding lower bounds are also discussed.Comment: 38 page

What policies should be there for employment in urban areas of developing countries?

This paper examines employment policies in urban areas of developing world. We follow traditional economic analysis and present the urban unemployment problem as an inequality of labour supply and demand on labour markets. The effects of demand-side and supply-side policies on informal urban employment are investigated through econometrical models. One or several variables are employed as crude proxies for every policy option. The dependent variable is informal urban employment as a per cent of total urban employment, with the data on eighteen developing countries from different parts of the world.Developing countries; Urban unemployment; Employment policies

How Globalisation Shapes Public Policy? A Case of Azerbaijan

Is globalisation a conductive or destructive force for public policy development in the countries of transition? The problem is investigated through an example of oil-rich Azerbaijan. This paper first presents the current situation in the country, defines links between globalisation and public policy and describes empirical research and its main findings. The paper then explores the circumstances that have prompted such a development and concludes with the possible policy implications.Azerbaijan; Globalisation; Public Policy; Corruption

Giving the ageing of the population how can countries afford pay-as-you-go social insurance pensions?

The paper examines formation and sustainability of Pay-As-You-Go pension systems within the consequences of the ageing of population. Parametric reforms rather than institutional transformation of Pay-As-You-Go systems into funded pension schemes are advocated. Following the modern theories of family economics and contrary to the mainstream works on the issue, reciprocal causation between pension systems and ageing is stressed. The paper concludes that the World Bank’s first pillar adjustment for maintaining the Pay-As-You-Go schemes achieves its objectives only if it is focused on all elements of the Pay-As-You-Go system.Pensions; Pay-As-You-Go; Ageing

Deconvolution for an atomic distribution: rates of convergence

Let $X_1,..., X_n$ be i.i.d.\ copies of a random variable $X=Y+Z,$ where $X_i=Y_i+Z_i,$ and $Y_i$ and $Z_i$ are independent and have the same distribution as $Y$ and $Z,$ respectively. Assume that the random variables $Y_i$'s are unobservable and that $Y=AV,$ where $A$ and $V$ are independent, $A$ has a Bernoulli distribution with probability of success equal to $1-p$ and $V$ has a distribution function $F$ with density $f.$ Let the random variable $Z$ have a known distribution with density $k.$ Based on a sample $X_1,...,X_n,$ we consider the problem of nonparametric estimation of the density $f$ and the probability $p.$ Our estimators of $f$ and $p$ are constructed via Fourier inversion and kernel smoothing. We derive their convergence rates over suitable functional classes. By establishing in a number of cases the lower bounds for estimation of $f$ and $p$ we show that our estimators are rate-optimal in these cases.Comment: 27 page

Bayesian linear inverse problems in regularity scales

We obtain rates of contraction of posterior distributions in inverse problems defined by scales of smoothness classes. We derive abstract results for general priors, with contraction rates determined by Galerkin approximation. The rate depends on the amount of prior concentration near the true function and the prior mass of functions with inferior Galerkin approximation. We apply the general result to non-conjugate series priors, showing that these priors give near optimal and adaptive recovery in some generality, Gaussian priors, and mixtures of Gaussian priors, where the latter are also shown to be near optimal and adaptive. The proofs are based on general testing and approximation arguments, without explicit calculations on the posterior distribution. We are thus not restricted to priors based on the singular value decomposition of the operator. We illustrate the results with examples of inverse problems resulting from differential equations.Comment: 34 page

Georgia's Middle Class in the Making: Methods of Measurement, Trends, and Constraints

Since 2016, Georgia has been categorized as an upper middle-income economy by the World Bank. The latter corresponds to the trends from the various micro-level data sets, which suggest that the middle class has been expanding in the recent years. However, what can be referred to as 'the middle class' in the Georgian context is still largely in the making, and this process remains vulnerable to endemic problems such as high inequality, low urbanization, agricultural underdevelopment, and the existence of rather large, vulnerable social groups. Political stability, geopolitics and international economic shocks all play a role in the prospects of the middle class in Georgia