The potential growth of the Belgian economy and its determinants

The potential growth path of the economy is at the centre of various fundamental economic questions, particularly in connection with the conduct of monetary policy and the management of public finances. It also determines the progress of living standards, so that the adverse population prospects confronting the European economies have rekindled interest in the subject. The first chapter of the article reports on the developments recorded over the past twenty years, using a method derived from the one adopted by the EC and based on the use of a production function. The role played by the three determinants – labour, capital and total factor productivity – is discussed, focusing on the case of the Belgian economy while comparing the results with those recorded in the EU-15. With potential growth averaging 2.2 p.c. for the private sector and 2.1 p.c. in the whole economy, Belgium is in the middle group of European countries. A growth breakdown between labour volume and labour productivity is proposed in chapter 2. Belgium’s advantages and disadvantages are assessed, not only in comparison with the EU-15 average but also in relation to the United States. Particular attention is drawn to the divergent picture in terms of productivity on the two continents. The improving performance in the United States in this respect contrasts with the deceleration recorded in Europe. The slowdown was also experienced in Belgium although, in the past ten years, the weaker growth in labour productivity here was due essentially to a slower increase in capital intensity. Having diminished between 1985 and 1995, the growth of total factor productivity, which in principle measures the overall productive capacity of the economy, stabilised at a level above the European average and close to that of the United States. This relatively good performance could be due to the fairly widespread use of ICT, as Belgium’s investment expenditure on this item is greater than that of the majority of European countries. The highly skilled labour force provides additional support for total factor productivity, although its impact has not been quantified in the case of Belgium. Expenditure on research and development could also yield substantial productivity returns. Particular efforts in these three fields, in a context within which market forces provide appropriate incentives to the economic agents, could hold possibilities for enhancing productivity growth. This could contribute to stimulate growth in view of the anticipated adverse demographic developments in the coming decades, that will also require raising the rates of participation in the labour market.potential output, labour productivity, growth accounting, total factor productivity

A note on syndeticity, recognizable sets and Cobham's theorem

In this note, we give an alternative proof of the following result. Let p, q >= 2 be two multiplicatively independent integers. If an infinite set of integers is both p- and q-recognizable, then it is syndetic. Notice that this result is needed in the classical proof of the celebrated Cobham?s theorem. Therefore the aim of this paper is to complete [13] and [1] to obtain an accessible proof of Cobham?s theorem

A conditional 0-1 law for the symmetric sigma-field

Let (\Omega,\mathcal{B},P) be a probability space, \mathcal{A} a sub-sigma-field of \mathcal{B}, and \mu a regular conditional distribution for P given \mathcal{A}. For various, classically interesting, choices of \mathcal{A} (including tail and symmetric) the following 0-1 law is proved: There is a set A_0 in \mathcal{A} such that P(A_0)=1 and \mu(\omega)(A) is 0 or 1 for all A in \mathcal{A} and \omega in A_0. Provided \mathcal{B} is countably generated (and certain regular conditional distributions exist), the result applies whatever P is.Comment: 9 page

Multidimensional extension of the Morse--Hedlund theorem

A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence $x$ over a finite alphabet is ultimately periodic if and only if, for some $n$, the number of different factors of length $n$ appearing in $x$ is less than $n+1$. Attempts to extend this fundamental result, for example, to higher dimensions, have been considered during the last fifteen years. Let $d\ge 2$. A legitimate extension to a multidimensional setting of the notion of periodicity is to consider sets of \ZZ^d definable by a first order formula in the Presburger arithmetic . With this latter notion and using a powerful criterion due to Muchnik, we exhibit a complete extension of the Morse--Hedlund theorem to an arbitrary dimension $d$ and characterize sets of $\ZZ^d$ definable in in terms of some functions counting recurrent blocks, that is, blocks occurring infinitely often

Avoiding 2-binomial squares and cubes

Two finite words $u,v$ are 2-binomially equivalent if, for all words $x$ of length at most 2, the number of occurrences of $x$ as a (scattered) subword of $u$ is equal to the number of occurrences of $x$ in $v$. This notion is a refinement of the usual abelian equivalence. A 2-binomial square is a word $uv$ where $u$ and $v$ are 2-binomially equivalent. In this paper, considering pure morphic words, we prove that 2-binomial squares (resp. cubes) are avoidable over a 3-letter (resp. 2-letter) alphabet. The sizes of the alphabets are optimal