Common knowledge and quantification

Summary. The paper consists of two parts. The first one is a concise introduction to epistemic (both propositional and predicate) logic with common knowledge operator. As the full predicate logics of common knowledge are not even recursively enumerable, in the second part we introduce and investigate the monodic fragment of these logics which allows applications of the epistemic operators to formulas with at most one free variable. We provide the monodic fragments of the most important common knowledge predicate logics with finite Hilbert-style axiomatizations, prove their completeness, and single out a number of decidable subfragments. On the other hand, we show that the addition of equality to the monodic fragment makes it not recursively enumerable. Received: March 7, 2001; revised version: April 4, 2001     

Regional Coronavirus Hotspots During the COVID-19 Outbreak in the Netherlands

De Economist - We explore the impact of COVID-19 hotspots and regional lockdowns on the Dutch labour market during the outbreak of COVID-19. Using weekly administrative panel microdata for 50 per...     

Multiple Glass Ceilings

Both vertical (between job levels) and horizontal (within job levels) mobility can be sources of wage growth. We find that the glass ceiling operates at both margins. The unexplained part of the wage gap grows across job levels (glass ceiling at the vertical margin) and across the deciles of the intra‐job‐level wage distribution (glass ceiling at the horizontal margin). This implies that women face many glass ceilings, one for each job level above the second, and that the glass ceiling is a pervasive phenomenon. In the Netherlands it affects about 88 percent of jobs, and 81 percent of Dutch women in employment work in job levels where a glass ceiling is present.     

Der zusammenhang zwischen produktionsstruktur und entwicklungsniveau

Summary The Relation between the Structure of Production and the Stage of Economic Development. — The paper attempts to identify the regularities that characterize the process of sectoral change and to test their prognostic values. The central hypothesis is that the share of the various sectors of production in GNP depends essentially on the per capita income and the population size. First, the implications of this hypothesis are discussed along with the conditions under which the past structural patterns may be used for future forecasts. Secondly, the hypothesis is tested by means of international cross-section data and the time series data for the German Federal Republic. The endogenous variables are made up of the contributions (in percent) of 11 sectors to the total national product and the value-added per capita of 13 (sometimes 20) industries. The exogenous variables considered are: per capita income, population size, degree of industrialization, foreign trade and consumption ratios. The function types underlying the estimates take into account not only variable elasticity coefficients but also the maxima and minima. The estimates show that in most cases there is a significant correlation between a sector’s contribution to the national product and the per capita income. The result is very often improved when additional exogenous variables are introduced. On the basis of the structural patterns so arrived, an attempt has been made to work out a structure-forecast, up to 1980, for 11 sectors and 13 manufacturing branches of the West German economy. Time series functions have been used for forecasting those sectors for which the cross sectional functions yielded unsatisfactory results in ex-post-forecasts. On plausibility grounds, in case of some industries the forecasted values had to be adjusted intuitively. The present study differs from Chenery’s and the United Nations’ in so far as it considers a greater number of sectors and industries, is based on more recent data, uses a different type of function and to the extent that its purpose is to test the prognostic value of development patterns.

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Résumé La relation entre structure de production et niveau de développement. — L’article traite les régularités qui caractérisent le processus de changement structurel, et examine ces régularités au point de vue de leur utilité pour la prévision économique. L’hypothèse centrale de cette étude prétend que l’importance relative des différents secteurs de production d’un pays dépend d’une fa?on décisive du revenu par tête de sa population. Sont discutées d’abord les implications de cette hypothèse et les conditions sous lesquelles on peut utiliser les schémas de développement structurels, trouvés pour le passé, pour la prévision. Puis, l’hypothèse est mise à l’épreuve à l’aide de données obtenues par analyse de section transversale internationale et par analyse de séries temporelles pour la République Fédérale Allemande. Les variables endogènes sont: les contributions (en pour-cent) au produit national de 11 secteurs et le valeur ajouté par tête de 13 (parfois 20) industries; comme variables exogènes sont prises en considération: le revenu par tête, la population totale, le degré d’industrialisation et les quoteparts du commerce extérieur et de la consommation. Le type de fonction, qui est à la base des estimations, n’admet pas seulement des coefficients d’élasticité variables, mais aussi des maxima et minima. Les estimations démontrent qu’il y a, dans la plupart des cas, un rapport significatif entre la contribution au produit national et le revenu par tête. Souvent, le résultat est amélioré si l’on introduit des variables exogènes additionnelles. A l’aide des schémas de développement structurels ainsi trouvés, on a essayé d’élaborer des prévisions de structure, jusqu’à 1980, pour onze secteurs et treize industries de l’économie allemande fédérale. Pour les secteurs où les fonctions basées sur des données obtenues par analyse de section transversale s’ajustaient mal aux prévisions ex post, on a basé les prévisions sur les fonctions basées sur des données obtenues par analyse de séries temporelles. Pour quelques industries, les valeurs de prévision à cause des raisons de plausibilité, devaient être ajusté de manière intui tive. L’étude présente diffère de celle de Chenery et celle des Nations Unies en ceci: elle tient compte d’un plus grand nombre de secteurs et d’industries, elle se base sur des données plus actuelles et sur un autre type de fonction, et elle a pour but de tester la valeur de prévision des schémas de développement structurels élaborés dans cette étude.

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Resumen La relación entre la estructura de producción y el grado de desarrollo. — El articulo se propone analizar las regularidades que caracterizan el proceso del cambio estructural entre los sectores económicos, y examinar hasta qué punto se prestan a la realization de un prognóstico de los nivelés sectoriales de productión. La hipótesis central de este estudio es que la importancia relativa de los sectores productivos en un pais dado depende de su ingreso per cápita. En primer lugar, los autores discuten las implicaciones de esta hipótesis y se?alan las condiciones que deben regir, para que el módulo de desarrollo, encontrado para el pasado, pueda servir para hacer un prognóstico sectoral. A continuatión, se examina dicha hipótesis para el caso de la República Federal Alemana, sobre la base de los parámétros obtenidos a través de regresiones múltiples de corte traversai internacional y de regresiones múltiples de una série de tiempo. Se consideran como variables endógenas en un caso las participaciones de 11 sectores productivos en el producto nacional, en otro caso el valor a?adido per cápita de 13 (y hasta 20) ramas industriales; como variables exógenas figuran, además de la renta real por habitante, la población, una medida para el grado relativo de industrializatión y los porcentajes del comercio exterior y del consumo privado con relación al producto nacional. El tipo de función elegido permite no sólo que los coeficientes de elasticidad de la variable endógena con respecto a las exógenas tomen valores variables (según se muevan los valores observados de las variables explicatorias) sino también valores máximos y mínimos. Las estimaciones demuestran, que en la mayoría de los casos existe una asociación significativa entre la participación de los sectores productivos en el producto nacional (y de las ramas industriales en el valor a?adido del sector fabril) y la renta real per cápita; en varios casos el coeficiente de determinación mejora si se introducen otras variables exógenas. Por medio del módulo de desarrollo, así estimado, los autores intentan proyectar la evolución de 11 sectores productivos y de 13 ramas industriales de la economía alemana hasta 1980. Para aquellos sectores en los que resulta que las predicciones ex post, hechas por medio de las funciones de regresión de corte traversal, se realizan en exceso o en defecto no tolerable de los valores observados, el análisis de proyección fue basado en funciones de regresión de una serie de tiempo. Los valores de predicción correspondientes a varias ramas industriales tuvieron que ser ajustados intuitivamente, en base a reflexiones de plausibilidad. El presente trabajo se diferencia de los estudios de Chenery y las Naciones Unidas en que incluye un mayor número de actividades, en que recurre a datos más actualizados, en que se utilizan ecuaciones definidas en otra forma, y en que tiene por finalidad apreciar la fiabilidad que un análisis regresivo del módulo de desarrollo merece como herramienta de prognósticos sectoriales.

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Riassunto La connessione tra struttura della produzione e livello dello sviluppo.-L’articolo si occupa di questo, di mostrare le regolarità che contraddistinguono il processo del cambiamento della struttura settoriale e verificare la loro capacità di prognosi. L’ipotesi centrale della ricerca è che il significato relativo dei singoli settori délla produzione in un Paese dipende in modo decisivo dal reddito pro capite di questo. Dapprima vengono discusse le implicazione di questa ipotesi come anche le condizioni che devono essere rispettate perché si possa far uso del modello di sviluppo rinvenuto per il passato per prognosi di struttura. L’ipotesi è poi verificata per la Repubblica federale sulla base di dati trasversali internazionali e dati di serie cronologici. Variabili endogene sono i contributi, in percentuale, del prodotto sociale di 11 settori e i valori aggiunti pro capite di 13 (in parte anche 20) rami dell’industria; come variabili esogene sono utilizzati, accanto al reddito pro capite, il numero della popolazione, il grado di industrializzazione come anche le quote del commercio estero e di consumo. Il tipo di funzione che è, in generale, alla base delle stime permette non soltanto coefficienti variabili di elasticità ma anche massimi e minimi. Le stime mostrano che nella maggior parte dei casi esiste una connessione significante tra contribute del prodotto sociale e reddito pro capite; sovente il risultato della regressione migliora ancora se vengono introdotte variabili esogene supplementari. Con l’aiuto del modello di sviluppo così stimato, si è tentato di elaborare una prognosi della struttura fino al 1980 per 11 settori e 13 rami dell’industria del l’economia tedesca occidentale. Per settori in cui funzioni trasversali in ex-post-prognosi mostrarono un cattivo adattamento, è stato previsto sulla base di funzioni di serie cronologiche. I valori di prognosi per i diversi rami dell’industria dovettero essere aggiustati intuitivamente sulla base di considerazioni di plausibilità. Lo studio qui presentato diverge dalle ricerche di Chenery e delle Nazioni Unite per il fatto che esso comprende un cerchio piú grande di settori e di rami, si basa su dati piú attuali, pone alla base un altro tipo di funzione e per il fatto che il suo obiettivo consiste nell’esaminare le qualità di prognosi di modelli di sviluppo.

     

The Part-Time Wage Gap: a Career Perspective

Summary  Because promotions are an important source of wage growth, we argue that the low incidence of promotions among part-time workers will contribute to the emergence of the part-time wage gap. We test this claim using Dutch employer–employee matched data. We find that the part-time wage gap is absent among young school leavers, but that it is well established among more mature workers. Moreover, we find that promotions account for a wage growth of about eight log points. Finally, workers in part-time jobs experience a lower rate of promotion relative to workers in full-time jobs. We are grateful to the Dutch Ministry of Social Affairs and Employment for granting access to the data. The paper greatly benefited from comments by Daniel Hamermesh, Jonathan Wadsworth, and seminar participants at ZEW in Mannheim, at WPEG conference at York University and Tilburg University. We are also indebted to two anonymous referees for helpful suggestions that substantially improved the quality of the paper. The usual disclaimer applies.