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A useful strategy to examine serial correlation in panel regression models is to adopt serially correlated error terms. The random effect is also present to address the individual-specific heterogeneity. Familiar transformations can restructure the AR(1) process into a serially uncorrelated dynamic model. It may result in unfitting estimation results once the statistical inference is carried on the conditional likelihood. We discuss in the article the consequence of this action. In particular, in the case of large cross-section units and short time-sequences, we provide analytical expressions for the asymptotic bias of maximum likelihood estimates when the analyst naïvely neglects the initial conditions problem. Under several conditions, we compute the size of biases and measure the mean squared errors to illustrate this violation. We also construct a joint regression model of the initial and subsequent responses to handle the initial conditions. Then, we conduct simulation studies to determine the asymptotic behavior. [ABSTRACT FROM AUTHOR]

Stratospheric variability may affect tropospheric weather on time scales between a few weeks and a few months, thus providing great potential for sub‐seasonal to seasonal weather forecasts of extremes. Unlike standard linear regression, which is based on the conditional mean of the response variable, lagged quantile regression is used here, which enables modeling the response variable's complete conditional distribution. Using the ERA5 reanalysis, we explore the relation of prominent teleconnection indices and gridded tropospheric fields to the stratosphere during boreal winter for various quantiles and lags. Significant differences in duration, strength, and direction of the stratosphere‐troposphere connection in outer quantiles compared to the median are identified. In particular, tropospheric extremes and their relation to the polar vortex strength are discussed, and an outlook is given. Plain Language Summary: Variations in stratospheric wind and temperature may affect surface weather for a few weeks to a few months. Sub‐seasonal to seasonal weather forecasts of extreme events, highly sought after by various industrial sectors, make use of this connection. Standard linear regression (LR) models base the prediction on the conditional mean of the tropospheric response variable while assuming constant variance of corresponding residuals which is often not the case. As an alternative, we use lagged quantile regression (QR), enabling us to model the response variable's complete conditional distribution. Thereby, using ERA5 reanalysis we explore the relation of prominent teleconnections and tropospheric fields to the boreal winter stratosphere for various quantiles. We find significant differences in duration, strength, and direction of the stratosphere‐troposphere connection in outer quantiles compared to the median. Thus, the QR framework offers straightforward access to valuable, supplementary information, not derivable from LR. Key Points: Straightforward access to invaluable, supplementary information, not derivable from ordinary linear regressionAsymmetric response of teleconnection indices and mid‐tropospheric gridded fields to stratospheric variability across quantilesDistinct extreme event characteristics in for example, persistence and strength and clear lagged effect compared to the median quantile regression [ABSTRACT FROM AUTHOR]

We investigate the spatio-temporal characteristics of the austral spring Ross Ice Shelf Polynya (RISP) and its relationship with atmospheric circulation anomalies based on the sea ice concentration data from the National Snow and Ice Data Center (NSIDC) and the ERA5 reanalysis data. The RISP area series is derived by choosing 25% sea ice concentration as the threshold. Then the principal spatial patterns of the RISP are acquired by using the empirical orthogonal function (EOF) analysis. The leading EOF (EOF1) has a spatial distribution of a strong negative core in the northeastern RISP with a weak positive core near the Cape Adare, explaining 48.1% of the variance. This mode matches the wind pattern of the northwesterly on the western Ross Sea while southwesterly on the eastern Ross Sea, which reflects the zonal variation of the RISP. There is also a strong positive correlation between the RISP area and the PC1. The EOF2 explains 27.4% of the variance, and is mainly characterized by a large region of low values in the northwestern Ross Sea with a small region of high value near Cape Colbeck. Matching the strong southerly over the western Ross Sea, the EOF2 partly depicts the meridional variation of the RISP. We further explored the connections between the RISP and sea level pressure, and found that a deeper and more eastward Amundsen Sea Low (ASL) in November often coincides with a larger and more eastward RISP in December. This lagged response is partly generated through the influence of the ASL on the RISP in November. [ABSTRACT FROM AUTHOR]

• For the past 40 years, theBeijing-Tianjin sand source region has been a carbon sink. • As drought intensifies, the negative impact of drought on Net Ecosystem Exchange becomes more pronounced. • In this region, grassland Net Ecosystem Exchange is most affected by and sensitive to drought. • Moisture limitation is the main driver of carbon source/sink change in this region. In the context of global change, the carbon budget in arid and semi-arid regions have changed significantly. Understanding these dynamic features and their response to climate change is essential for regional carbon cycle assessments. The Beijing-Tianjin Sand Source Region (BTSSR), a significant ecological project in China, is central to studies on carbon budget dynamics. While global change intensifies, understanding its carbon budget response to drought is crucial. By integrating data from the Net Ecosystem Exchange (NEE) and the Standardized Precipitation Evapotranspiration Index (SPEI), we analyzed the spatiotemporal attributes of NEE in this region and its response to drought. The BTSSR is currently in a carbon sink state, with the mean NEE being −45.13 gCm−2 and a rate of change at −0.005 gCm−2a-1. The maximum carbon sink occurs during the summer, whereas the winter is characterized by a net release of carbon to the atmosphere. In terms of spatial variation, the NEE shifts from positive to negative from southeast to northwest across the region. The impact of drought on summer NEE is notably significant, with the correlation and sensitivity being −0.717 (p < 0.05) and −3.911, respectively. As drought intensity increases, NEE changes from negative to positive, transforming BTSSR into a carbon source. NEE responded most significantly to strong drought and was less affected by light drought. The NEE of BTSSR showed a significant short-term response to drought, with a lag of 1–4 months. Considering different vegetation types, the temperate desert's NEE is most significantly affected by drought and is the most sensitive, with correlation and sensitivity values of −0.841 (p < 0.05) and −12.570, respectively. In contrast, the warm temperate deciduous broadleaf forest shows stronger resistance to drought. This study elucidates how the carbon budget of different vegetation types in a typical ecological engineering area changes under the background of climate change and human activities, and contributes to the understanding of the impacts of drought events on the carbon cycle of different vegetation types, as well as the response of the latter to the former, especially the lagged response. It provides different perspectives for the subsequent ecological engineering construction. [ABSTRACT FROM AUTHOR]

Vegetation growth is interactively controlled by hydrothermal conditions and the associated biophysiological changes. These factors have experienced dramatic changes over the past decades in Central Asia, where vegetation growth is primarily constrained by soil water availability. However, we have limited understanding of the time scales and the underlying drivers for the responses of vegetation growth to variations in soil water availability between wet and dry periods. Here, we explored the response of vegetation growth to decadal‐scale hydroclimatic variations in wet versus dry periods, during 1992–2015, using remote sensing retrievals of normalized difference vegetation index and multiple climate factors. We discovered divergent responses of vegetation growth to soil water availability, measured by soil moisture content (SM), between wet and dry periods, with spatiotemporally intensified correlation to SM in the dry period. We revealed a unanimous 1‐month time lag in the response of vegetation growth to SM in the dry period, contrary to much longer time lags and a more spatially heterogeneous response in the wet period. The divergent vegetation responses to SM can be largely explained by the variations in hydroclimatic conditions and spring phenology. The intensified vegetation growth‐SM response in the dry period was strongly associated with increased temperature and vapor pressure deficit. Earlier spring phenology exerts a crucial role in mediating the relationship between vegetation growth and SM in the dry period. The complicated interactions between vegetation phenology and hydroclimatic variations should be explicitly considered in predicting regional vegetation growth under a warmer and drier climate regime in water‐stressed regions. Key Points: Vegetation growth responds to soil water availability at much shorter time scales in the dry than in the wet periodsIntensified growth response to soil water availability in the dry period was strongly associated with increased temperature and vapor pressure deficit (VPD)Earlier spring phenology plays a crucial role in mediating the vegetation response to soil water availability during the dry period [ABSTRACT FROM AUTHOR]

Abstract Ecosystems continuously adapt to interacting environmental drivers that change over time. Consequently, the carbon balance of terrestrial ecosystem may presently still be affected by past anthropogenic disturbances (e.g., deforestation) and other environmental changes (e.g., climate change). However, even though such so‐called “legacy effects” are implicitly included in many carbon cycle modeling studies, they are typically not explicitly quantified and therefore scientists might not be aware of their long‐term importance. Here, we use the ecosystem model LPJ‐GUESS to quantify legacy effects for the 21st century and the respective contributions of the following environmental drivers: climate change, CO2 fertilization, land use change, wood harvest, nitrogen deposition, and nitrogen fertilization. According to our simulations, the combined legacy effects of historical (1850–2015) environmental changes result in a land carbon uptake of +126 Gt C over the future (2015–2099) period. This by far exceeds the impacts of future environmental changes (range −53 Gt C to +16 Gt C for three scenarios) and is comparable in magnitude to historical carbon losses (−154 Gt C). Legacy effects can mainly be attributed to ecosystems still adapting to historical increases in atmospheric CO2 (+65 Gt C) and nitrogen deposition (+33 Gt C), but long‐term vegetation regrowth following agricultural abandonment (+8 Gt C) and wood harvest (+19 Gt C) also play a role. The response of the biosphere to historical environmental changes dominates future terrestrial carbon cycling at least until midcentury. Legacy effects persist many decades after environmental changes occurred and need to be considered when interpreting changes and estimating terrestrial carbon uptake potentials.

As result of ocean warming, marine boreal species have shifted their distribution poleward, with increases in abundance at higher latitudes, and declines in abundance at lower latitudes. A key to predict future changes in fish communities is to understand how fish stocks respond to climate variability. Scattered field observations in the first half of the 20th century suggested that boreal fish may coherently invade Greenland waters when temperatures rise, but this hypothesis has remained untested. Therefore, we studied how local temperature variability and the dynamics of the subpolar gyre, a large‐scale driver of oceanic conditions in the North Atlantic, affect abundance of boreal fishes in a region that sharply defines their lower thermal boundary. We analysed information from demersal trawl surveys from 1981 to 2017, for species distributed from shallow shelf to depths of 1,500 m, collected at over 10,000 stations along ~3,000 km of Greenland. Our results show that local temperature and variability of Labrador and Irminger Sea water in the subpolar gyre region drive interdecadal variability of boreal fish abundance in Greenland waters. Although temperature fluctuations were higher in shallow than deep regions, fish abundance changed as quickly in great depths as in shallow depths. This link between physics and biology provides an opportunity for prediction of future trends, which is of utility in Greenland, where fisheries constitute more than 90% of the national export value. [ABSTRACT FROM AUTHOR]

Ecosystems continuously adapt to interacting environmental drivers that change over time. Consequently, the carbon balance of terrestrial ecosystem may presently still be affected by past anthropogenic disturbances (e.g., deforestation) and other environmental changes (e.g., climate change). However, even though such so‐called "legacy effects" are implicitly included in many carbon cycle modeling studies, they are typically not explicitly quantified and therefore scientists might not be aware of their long‐term importance. Here, we use the ecosystem model LPJ‐GUESS to quantify legacy effects for the 21st century and the respective contributions of the following environmental drivers: climate change, CO2 fertilization, land use change, wood harvest, nitrogen deposition, and nitrogen fertilization. According to our simulations, the combined legacy effects of historical (1850–2015) environmental changes result in a land carbon uptake of +126 Gt C over the future (2015–2099) period. This by far exceeds the impacts of future environmental changes (range −53 Gt C to +16 Gt C for three scenarios) and is comparable in magnitude to historical carbon losses (−154 Gt C). Legacy effects can mainly be attributed to ecosystems still adapting to historical increases in atmospheric CO2 (+65 Gt C) and nitrogen deposition (+33 Gt C), but long‐term vegetation regrowth following agricultural abandonment (+8 Gt C) and wood harvest (+19 Gt C) also play a role. The response of the biosphere to historical environmental changes dominates future terrestrial carbon cycling at least until midcentury. Legacy effects persist many decades after environmental changes occurred and need to be considered when interpreting changes and estimating terrestrial carbon uptake potentials. Key Points: Terrestrial ecosystems only slowly adapt to environmental changesMost of the modeled future (2015–2099) carbon uptake can be attributed to historical (1850–2015) rather than future environmental changesLegacy effects are mostly a result of CO2 fertilization and also due to historical nitrogen deposition, land use change, and wood harvest [ABSTRACT FROM AUTHOR]

Understanding the responses of organisms to different environmental drivers is critical for improving ecosystem management and conservation. Estuarine ecosystems are under pressure from multiple anthropogenic stressors (e.g. increasing sediment and nutrient loads, pollution, climate change) that are affecting the functions and services these ecosystems provide. Here, we used long-term estuarine benthic invertebrate monitoring data (∼30 year time-series) to evaluate the responses of macrobenthic invertebrate communities and indicator species to climatic, oceanic, freshwater, and local environmental drivers in New Zealand estuaries. We aimed to improve our ability to predict ecosystem change and understand the effects of multiple environment drivers on benthic communities. Our analyses showed that the abundance and richness of macrobenthic fauna and four indicator taxa (bivalves known to have differing tolerances to sediment mud content: Austrovenus stutchburyi , Macomona liliana , Theora lubrica , and Arthritica bifurca) responded to unique combinations of multiple environmental drivers across sites and times. Macrobenthic responses were highly mixed (i.e., positive and negative) and site-dependent. We also show that responses of macrobenthic fauna were lagged and most strongly related to climatic and oceanic drivers. The way the macrobenthos responded has implications for predicting and understanding the ecological consequences of a rapidly changing environment and how we conserve and manage coastal ecosystems. • Long-term estuarine monitoring data (∼30 yrs) was used to evaluate the responses of macrofauna to environmental drivers. • Macrofauna responded to unique combinations of multiple environmental drivers. • Macrofaunal responses to environmental drivers were idiosyncratic and site-mediated. • Macrofaunal responses were mostly related to lagged permutations of climatic and oceanic drivers. • We highlight the complexity of predicting macrofauna responses to environmental change. [ABSTRACT FROM AUTHOR]

Recent studies suggest a response in the North Atlantic winter circulation which lags by a couple of years with respect to sunspot maximum. This has been explained by two different top‐down mechanisms: a solar wind driven particle effect in the polar atmosphere during the declining phase of the solar cycle, and the re‐emergence and amplification of heat anomalies in the Atlantic Ocean produced by enhanced solar ultraviolet (UV). Here we study how December to February climate is affected by two solar‐related drivers: geomagnetic activity (proxy of particle precipitation) and sunspot activity (proxy of solar UV) during 1948–2017. We use reanalysis data of sea‐level pressure (SLP) and zonal wind (U) to show that both geomagnetic activity and sunspot activity independently and simultaneously produce atmospheric circulation responses in the North Atlantic whose evolutions clearly differ from each other. Geomagnetic activity produces a strengthening of the polar vortex and a negative poleward SLP gradient between mid‐ and high latitudes, resembling a positive NAO‐type circulation pattern during December to February. Solar UV produces a positive U anomaly in the low‐latitude stratosphere during December, which moves poleward and downward during the winter resulting in a negative poleward SLP gradient between mid‐ and high latitudes during February. We find the lagged sunspot activity responses in SLP to form zonal pressure patterns (wave‐train structure) resembling the Eurasian pattern. Geomagnetic activity responses remain essentially the same when we introduce the lag with respect to sunspot activity supporting its independency as a driving mechanism. Our results suggest that solar wind related particle precipitation and (lagged) solar UV mechanism provide independent, significant circulation signals in the North Atlantic winter. [ABSTRACT FROM AUTHOR]

Abstract Relation of decadal variations of the North Atlantic Oscillation index (NAOI) to the 11-year solar cycle in the sunspot number is analyzed for almost 200-year observational period with the use of cross-spectral and cross-wavelet techniques. Based on wavelet transforms of a pair of time series, local cross characteristics such as the local coherency and local correlation are used to study time evolution of the solar–NAOI relationship. The analysis of the NAOI is supplemented and confirmed by similar analysis of more than 300-year long data of Central England temperature (CET). Both the solar cycle–NAOI and solar cycle–CET relationships exhibit a quasi-periodic oscillation with the mean period of about 50 years, which includes a subinterval with positive coherency and a subinterval with negative coherency between the solar cycle and the 11-year modes of the NAOI and CET. The same multidecadal modulation of the solar–NAOI relationship is manifested in the temporal structure of the local correlation between the 11-year modes of the NAOI and the sunspot number at specific time lags of the NAOI relative to the sunspot number. It is distinct in the local correlations for the extended winter period (November–March) NAOI lagging by 7 years after the sunspot number. At this lag, the NAOI anticorrelates in general with the sunspot number and the local anticorrelation reinforces periodically with the aforementioned ∼50 year period. At the 1-year lag, which differs from the 7-year lag by a half solar cycle, the 11-year mode of the winter NAOI correlates in general with the solar cycle but the correlation is mainly associated with the last 70-year time interval. The change in the sign of the solar–NAOI relationship is also the case for the extended summer periods of the year (May–September). For this period, the approximately mirror image of the local correlations is observed at the 7-year and 1-year lags. The multidecadal modulation is likely associated with periods of enhanced solar impact on the NAO. Highlights • Relation of the North Atlantic Oscillation index to the solar cycle is modulated. • The mean period of the modulation is about 50 years. • The effect is clearly seen in the 7-year lagged response to the solar cycle. • The modulation is likely associated with multidecadal variations in solar activity. [ABSTRACT FROM AUTHOR]

Abstract: A robust impact of El Niño on the Northern Hemisphere (NH) polar stratosphere has been demonstrated by previous studies, although whether this applies to extreme El Niño is uncertain. The time evolution of the response of the NH stratospheric vortex to extreme El Niño, compared with that to moderate eastern Pacific El Niño, is addressed by means of composite analysis using the National Centers for Environmental Prediction/Department of Energy reanalysis data set from 1980 to 2016. Lead‐lag analysis indicates that the El Niño signal actually leads the stratospheric response by ~2 months. Considering the time lag, the signal of December‐January‐February El Niño in the NH stratospheric vortex should mature in the February‐March‐April season (late winter/early spring). The patterns of circulation and temperature for late winter/early spring during extreme and moderate El Niño events are significant, exhibiting similar structure. The results are confirmed with the Whole Atmosphere Community Climate Model version 4 model, which is forced with observed SSTs of extreme and moderate El Niño in winter (December‐January‐February) to analyze the day‐to‐day propagation of their signals. Note that the magnitudes of the stratospheric responses are much larger in the case of extreme El Niño, as stronger upward propagation of planetary waves leads to a weaker northern polar vortex than during moderate El Niño events. [ABSTRACT FROM AUTHOR]

Agricultural productivity depends critically on investments in research and development (R&D), but there is a long lag in this response. Failing to invest today in improvements of agricultural productivity cannot be simply corrected a few decades later if the world finds itself short of food at that point in time. This fundamental irreversibility is particularly problematic in light of uncertain future population, income, and climate change, as portrayed in the IPCC’s Shared Socio-Economic Pathways (SSPs). This paper finds the optimal path of agricultural R&D spending over the 21st century for each SSP, along with valuation of those regrets associated with investment decisions later revealed to be in error. The maximum regret is minimized to find a robust optimal R&D pathway that factors in key uncertainties and the lag in productivity response to R&D. Results indicate that the whole of uncertainty’s impact on R&D is greater than the sum of its individual parts. Uncertainty in future population has the dominant impact on the optimal R&D expenditure path. The robust solution suggests that the optimal R&D spending strategy is very close to the one that will increase agricultural productivity fast enough to feed the World under the most populous scenario. It also suggests that society should accelerate R&D spending up to mid-century, thereafter moderating this growth rate. [ABSTRACT FROM AUTHOR]

Wildfire area is predicted to increase with global warming. Empirical statistical models and process-based simulations agree almost universally. The key relationship for this unanimity, observed at multiple spatial and temporal scales, is between drought and fire. Predictive models often focus on ecosystems in which this relationship appears to be particularly strong, such as mesic and arid forests and shrublands with substantial biomass such as chaparral. We examine the drought-fire relationship, specifically the correlations between water-balance deficit and annual area burned, across the full gradient of deficit in the western USA, from temperate rainforest to desert. In the middle of this gradient, conditional on vegetation (fuels), correlations are strong, but outside this range the equivalence hotter and drier equals more fire either breaks down or is contingent on other factors such as previous-year climate. This suggests that the regional drought-fire dynamic will not be stationary in future climate, nor will other more complex contingencies associated with the variation in fire extent. Predictions of future wildfire area therefore need to consider not only vegetation changes, as some dynamic vegetation models now do, but also potential changes in the drought-fire dynamic that will ensue in a warming climate. [ABSTRACT FROM AUTHOR]

Our knowledge on tree responses to drought is mainly based on short-term manipulation experiments which do not capture any possible long-term adjustments in this response. Therefore, historical water channels in inner-Alpine dry valleys were used as century-long irrigation experiments to investigate adjustments in tree growth to contrasting water supply. This involved quantifying the tree-ring growth of irrigated and non-irrigated (control) Scots pine ( Pinus sylvestris L.) in Valais (Switzerland), as well as European larch ( Larix decidua Mill.) and black pine ( Pinus nigra Arnold) in Vinschgau (Italy). Furthermore, the adjustments in radial growth of Scots pine and European larch to an abrupt stop in irrigation were analyzed. Irrigation promoted the radial growth of all tree species investigated compared to the control: (1) directly through increased soil water availability, and (2) indirectly through increased soil nutrients and humus contents in the irrigated plots. Irrigation led to a full elimination of growth responses to climate for European larch and black pine, but not for Scots pine, which might become more sensitive to drought with increasing tree size in Valais. For the control trees, the response of the latewood increment to water availability in July/August has decreased in recent decades for all species, but increased in May for Scots pine only. The sudden irrigation stop caused a drop in radial growth to a lower level for Scots pine or similar level for larch compared to the control for up to ten years. However, both tree species were then able to adjust to the new conditions and subsequently grew with similar (Scots pine) or even higher growth rates (larch) than the control. To estimate the impact of climate change on future forest development, the duration of manipulation experiments should be on longer time scales in order to capture adjustment processes and feedback mechanisms of forest ecosystems. [ABSTRACT FROM AUTHOR]

Background: Climate manipulation experiments have found lagged responses in biomass and community composition. Aims: To look for lagged responses of flowering phenology and effects on duration of reproductive phases. Methods: Treatment and post-treatment year phenological data from 12 species in a 1-year step warming and double precipitation experiment was examined. Results: Changes in phenology due to the previous year's warming were in the opposite direction to those observed during the treatment year. Six species responded to warming in 2004, delaying flowering 6.2 days and fruiting 7.9 days. Unlike 2003, no species advanced flowering phenology in 2004. Delays resulted from a soil moisture deficit in formerly warmed plots that lasted 3 months or more after warming ended. Increased precipitation altered phenology in one species but did not affect duration of reproductive phases. While 10 of 11 responsive species entered bud phase earlier under warming than in controls in 2003, in only two species showed a phenological delay at the beginning of the bud phase in 2004. Warming tended to shorten flowering and fruiting stages and total duration in spring annuals. Conclusions: Together, these results suggest that climate anomalies can influence phenology in the following year, here due to a lag in soil moisture recharge. [ABSTRACT FROM AUTHOR]

Numerous studies have suggested an impact of the 11 year solar cycle on the winter North Atlantic Oscillation (NAO), with an increased tendency for positive (negative) NAO signals to occur at maxima (minima) of the solar cycle. Climate models have successfully reproduced this solar cycle modulation of the NAO, although the magnitude of the effect is often considerably weaker than implied by observations. A leading candidate for the mechanism of solar influence is via the impact of ultraviolet radiation variability on heating rates in the tropical upper stratosphere, and consequently on the meridional temperature gradient and zonal winds. Model simulations show a zonal mean wind anomaly that migrates polewards and downwards through wave–mean flow interaction. On reaching the troposphere this produces a response similar to the winter NAO. Recent analyses of observations have shown that solar cycle–NAO link becomes clearer approximately three years after solar maximum and minimum. Previous modelling studies have been unable to reproduce a lagged response of the observed magnitude. In this study, the impact of solar cycle on the NAO is investigated using an atmosphere–ocean coupled climate model. Simulations that include climate forcings are performed over the period 1960–2009 for two solar forcing scenarios: constant solar irradiance, and time-varying solar irradiance. We show that the model produces significant NAO responses peaking several years after extrema of the solar cycle, persisting even when the solar forcing becomes neutral. This confirms suggestions of a further component to the solar influence on the NAO beyond direct atmospheric heating and its dynamical response. Analysis of simulated upper ocean temperature anomalies confirms that the North Atlantic Ocean provides the memory of the solar forcing required to produce the lagged NAO response. These results have implications for improving skill in decadal predictions of the European and North American winter climate.

Alperovich G. (1983) Lagged response in intra-urban migration of home owners, Reg. Studies 17, 297–304. Interregional migration found in several studies to be characterized by lag structure. This paper investigates the lag structure hypothesis on data pertraining to intra-urban migration. The results of the analysis point to two important conclusions. First, there is evidence to support the hypothesis that it takes no less than ten years before the system converges to equilibrium. Second, estimating model for shorter time periods does not result in major distortions. [ABSTRACT FROM PUBLISHER]