In this paper we derive the asymptotic properties of within groups (WG), GMM, and LIML estimators for an autoregressive model with random effects when both T and N tend to infinity. GMM and LIML are consistent and asymptotically equivalent to the WG estimator. When T /N → 0 the fixed T results for GMM and LIML remain valid, but WG, although consistent, has an asymptotic bias in its asymptotic distribution. When T /N tends to a positive constant, the WG, GMM, and LIML estimators exhibit negative asymptotic biases of order 1/T , 1/N , and 1/ 2N − T , respectively. In addition, the crude GMM estimator that neglects the autocorrelation in first differenced errors is inconsistent as T /N → c > 0, despite being consistent for fixed T . Finally, we discuss the properties of a random effects pseudo MLE with unrestricted initial conditions when both T and N tend to infinity.

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We model earnings processes allowing for lots of heterogeneity across agents. We also introduce an extension to the linear ARMA model which allows the initial convergence in the long run to be different from that implied by the conventional ARMA model. This is particularly important for unit root tests, which are actually tests of a composite of two independent hypotheses. We fit to a variety of statistics including most of those considered by previous investigators. We use a sample drawn from the Panel Study of Income Dynamics (PSID), and focus on white males with a high‐school degree. Despite this observable homogeneity, we find more latent heterogeneity than previous investigators. We show that allowance for heterogeneity makes substantial differences to estimates of model parameters and to outcomes of interest. Additionally, we find strong evidence against the hypothesis that any worker has a unit root.

Nowadays, one of the most popular ways to get a more sustainable cement industry is using additions as cement replacement. However, there are many civil engineering applications in which the use of sustainable cements is not extended yet, such as special foundations, and particularly micropiles, even though the standards do not restrict the cement type to use. These elements are frequently exposed to the sulphates present in soils. The purpose of this research is to study the effects in the very long-term (until 600 days) of sulphate attack in the microstructure of micropiles grouts, prepared with ordinary Portland cement, fly ash and slag commercial cements, continuing a previous work, in which these effects were studied in the short-term. The microstructure changes have been analysed with the non-destructive impedance spectroscopy technique, mercury intrusion porosimetry and the “Wenner” resistivity test. The mass variation and the compressive strength have also been studied. The impedance spectroscopy has been the most sensitive technique for following the sulphate attack process. Considering the results obtained, micropiles grouts with slag and fly ash, exposed to an aggressive medium with high content of sulphates, have shown good behaviour in the very long-term (600 days) compared to grouts made with OPC.