Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities

Traditionally, it is assumed that the population size of cities in a country follows a Pareto distribution. This assumption is typically supported by nding evidence of Zipf's Law. Recent studies question this nding, highlighting that, while the Pareto distribution may t reasonably well when the data is truncated at the upper tail, i.e. for the largest cities of a country, the log-normal distribution may apply when all cities are considered. Moreover, conclusions may be sensitive to the choice of a particular truncation threshold, a yet overlooked issue in the literature. In this paper, then, we reassess the city size distribution in relation to its sensitivity to the choice of truncation point. In particular, we look at US Census data and apply a recursive-truncation approach to estimate Zipf's Law and a non-parametric alternative test where we consider each possible truncation point of the distribution of all cities. Results con rm the sensitivity of results to the truncation point. Moreover, repeating the analysis over simulated data con rms the di culty of distinguishing a Pareto tail from the tail of a log-normal and, in turn, identifying the city size distribution as a false or a weak Pareto law.

Flying High and Laying Low in the Public and Private Sectors: A Comparison of Pay Differentials for Full-Time Male Employees in Britain

Using new linked employee-employer data for Britain in 2004, this paper shows that, on average, full-time male public sector employees earn 11.7 log wage points more than their private sector counterparts. Decomposition analysis reveals that the majority of this pay premium is associated with public sector employees having individual characteristics associated with higher pay and to their working in higher paid occupations. Further focussing analysis on the highly skilled and unskilled occupations in both sectors, reveals evidence of workplace segregation positively impacting on earnings in the private sector for the highly skilled, and in the public sector for the unskilled. Substantial earnings gaps between the highly skilled and unskilled are found, and the unexplained components in these gaps are very similar regardless of sector.

Growth and Survival Determinants of Chinese Private Firms: Fieldwork evidence and econometric estimates

This paper reports on one of the first empirical attempts to investigate small firm growth and survival, and their determinants, in the Peoples’ Republic of China. The work is based on field work evidence gathered from a sample of 83 Chinese private firms (mainly SMEs) collected initially by face-to-face interviews, and subsequently by follow-up telephone interviews a year later. We extend the models of Gibrat (1931) and Jovanovic (1982), which traditionally focus on size and age alone (e.g. Brock and Evans, 1986), to a ‘comprehensive’ growth model with two types of additional explanatory variables: firm-specific (e.g. business planning); and environmental (e.g. choice of location). We estimate two econometric models: a ‘basic’ age-size-growth model; and a ‘comprehensive’ growth model, using Heckman’s two-step regression procedure. Estimation is by log-linear regression on cross-section data, with corrections for sample selection bias and heteroskedasticity. Our results refute a pure Gibrat model (but support a more general variant) and support the learning model, as regards the consequences of size and age for growth; and our extension to a comprehensive model highlights the importance of location choice and customer orientation for the growth of Chinese private firms. In the latter model, growth is explained by variables like planning, R&D orientation, market competition, elasticity of demand etc. as well as by control variables. Our work on small firm growth achieves two things. First, it upholds the validity of ‘basic’ size-age-growth models, and successfully applies them to the Chinese economy. Second, it extends the compass of such models to a ‘comprehensive’ growth model incorporating firm-specific and environmental variables.

Growth Rate Estimation in the presence of Unit Roots

This study addresses the issue of the presence of a unit root on the growth rate estimation by the least-squares approach. We argue that when the log of a variable contains a unit root, i.e., it is not stationary then the growth rate estimate from the log-linear trend model is not a valid representation of the actual growth of the series. In fact, under such a situation, we show that the growth of the series is the cumulative impact of a stochastic process. As such the growth estimate from such a model is just a spurious representation of the actual growth of the series, which we refer to as a “pseudo growth rate”. Hence such an estimate should be interpreted with caution. On the other hand, we highlight that the statistical representation of a series as containing a unit root is not easy to separate from an alternative description which represents the series as fundamentally deterministic (no unit root) but containing a structural break. In search of a way around this, our study presents a survey of both the theoretical and empirical literature on unit root tests that takes into account possible structural breaks. We show that when a series is trendstationary with breaks, it is possible to use the log-linear trend model to obtain well defined estimates of growth rates for sub-periods which are valid representations of the actual growth of the series. Finally, to highlight the above issues, we carry out an empirical application whereby we estimate meaningful growth rates of real wages per worker for 51 industries from the organised manufacturing sector in India for the period 1973-2003, which are not only unbiased but also asymptotically efficient. We use these growth rate estimates to highlight the evolving inter-industry wage structure in India.

Regional productivity variation and the impact of public capital stock: an analysis with spatial interaction, with reference to Spain

In this paper we examine whether variations in the level of public capital across Spain‟s Provinces affected productivity levels over the period 1996-2005. The analysis is motivated by contemporary urban economics theory, involving a production function for the competitive sector of the economy („industry‟) which includes the level of composite services derived from „service‟ firms under monopolistic competition. The outcome is potentially increasing returns to scale resulting from pecuniary externalities deriving from internal increasing returns in the monopolistic competition sector. We extend the production function by also making (log) labour efficiency a function of (log) total public capital stock and (log) human capital stock, leading to a simple and empirically tractable reduced form linking productivity level to density of employment, human capital and public capital stock. The model is further extended to include technological externalities or spillovers across provinces. Using panel data methodology, we find significant elasticities for total capital stock and for human capital stock, and a significant impact for employment density. The finding that the effect of public capital is significantly different from zero, indicating that it has a direct effect even after controlling for employment density, is contrary to some of the earlier research findings which leave the question of the impact of public capital unresolved.

Growth and Survival Determinants of Chinese Private Firms: Fieldwork evidence and econometric estimates

This paper reports on one of the first empirical attempts to investigate small firm growth and survival, and their determinants, in the Peoples’ Republic of China. The work is based on field work evidence gathered from a sample of 83 Chinese private firms (mainly SMEs) collected initially by face-to-face interviews, and subsequently by follow-up telephone interviews a year later. We extend the models of Gibrat (1931) and Jovanovic (1982), which traditionally focus on size and age alone (e.g. Brock and Evans, 1986), to a ‘comprehensive’ growth model with two types of additional explanatory variables: firm-specific (e.g. business planning); and environmental (e.g. choice of location). We estimate two econometric models: a ‘basic’ age-size-growth model; and a ‘comprehensive’ growth model, using Heckman’s two-step regression procedure. Estimation is by log-linear regression on cross-section data, with corrections for sample selection bias and heteroskedasticity. Our results refute a pure Gibrat model (but support a more general variant) and support the learning model, as regards the consequences of size and age for growth; and our extension to a comprehensive model highlights the importance of location choice and customer orientation for the growth of Chinese private firms. In the latter model, growth is explained by variables like planning, R&D orientation, market competition, elasticity of demand etc. as well as by control variables. Our work on small firm growth achieves two things. First, it upholds the validity of ‘basic’ size-age-growth models, and successfully applies them to the Chinese economy. Second, it extends the compass of such models to a ‘comprehensive’ growth model incorporating firm-specific and environmental variables.

UK House Prices: Convergence Clubs and Spillovers

This paper uses the log t test to analyse the convergence of house prices across UK regions and the presence of spillovers e ects. We nd that UK house prices can be grouped into four clusters. Moreover we document the dynamics of the house price spillovers across regions.

The convenient calculation of some test statistics in models of discrete choice

The paper considers the use of artificial regression in calculating different types of score test when the log

A test of long memory hypothesis based on self-similarity

This paper develops a new test of true versus spurious long memory, based on log-periodogram estimation of the long memory parameter using skip-sampled data. A correction factor is derived to overcome the bias in this estimator due to aliasing. The procedure is designed to be used in the context of a conventional test of significance of the long memory parameter, and composite test procedure described that has the properties of known asymptotic size and consistency. The test is implemented using the bootstrap, with the distribution under the null hypothesis being approximated using a dependent-sample bootstrap technique to approximate short-run dependence following fractional differencing. The properties of the test are investigated in a set of Monte Carlo experiments. The procedure is illustrated by applications to exchange rate volatility and dividend growth series.