Aspekte der linearen Minimax-Schätzung

Es werde das lineare Regressionsmodell y = X b + e mit den ueblichen Bedingungen betrachtet. Weiter werde angenommen, dass der Parametervektor aus einem Ellipsoid stammt. Ein optimaler Schaetzer fuer den Parametervektor ist durch den Minimax-Schaetzer gegeben. Nach der entscheidungstheoretischen Formulierung des Minimax-Schaetzproblems werden mit dem Bayesschen Ansatz, Spektralen Methoden und der Darstellung von Hoffmann und Laeuter Wege zur Bestimmung des Minimax- Schaetzers dargestellt und in Beziehung gebracht. Eine Betrachtung von Modellen mit drei Einflussgroeßen und gemeinsamen Eigenvektor fuehrt zu einer Strukturierung des Problems nach der Vielfachheit des maximalen Eigenwerts. Die Bestimmung des Minimax-Schaetzers in einem noch nicht geloesten Fall kann auf die Bestimmung einer Nullstelle einer nichtlinearen reellwertigen Funktion gefuehrt werden. Es wird ein Beispiel gefunden, in dem die Nullstelle nicht durch Radikale angegeben werden kann. Durch das Intervallschachtelungs-Prinzip oder Newton-Verfahren ist die numerische Bestimmung der Nullstelle moeglich. Durch Entwicklung einer Fixpunktgleichung aus der Darstellung von Hoffmann und Laeuter war es in einer Simulation moeglich die angestrebten Loesungen zu finden.

Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.

Design, implementation and application of a generic framework for integrated regional land-use modeling

Land use is a crucial link between human activities and the natural environment and one of the main driving forces of global environmental change. Large parts of the terrestrial land surface are used for agriculture, forestry, settlements and infrastructure. Given the importance of land use, it is essential to understand the multitude of influential factors and resulting land use patterns. An essential methodology to study and quantify such interactions is provided by the adoption of land-use models. By the application of land-use models, it is possible to analyze the complex structure of linkages and feedbacks and to also determine the relevance of driving forces. Modeling land use and land use changes has a long-term tradition. In particular on the regional scale, a variety of models for different regions and research questions has been created. Modeling capabilities grow with steady advances in computer technology, which on the one hand are driven by increasing computing power on the other hand by new methods in software development, e.g. object- and component-oriented architectures. In this thesis, SITE (Simulation of Terrestrial Environments), a novel framework for integrated regional sland-use modeling, will be introduced and discussed. Particular features of SITE are the notably extended capability to integrate models and the strict separation of application and implementation. These features enable efficient development, test and usage of integrated land-use models. On its system side, SITE provides generic data structures (grid, grid cells, attributes etc.) and takes over the responsibility for their administration. By means of a scripting language (Python) that has been extended by language features specific for land-use modeling, these data structures can be utilized and manipulated by modeling applications. The scripting language interpreter is embedded in SITE. The integration of sub models can be achieved via the scripting language or by usage of a generic interface provided by SITE. Furthermore, functionalities important for land-use modeling like model calibration, model tests and analysis support of simulation results have been integrated into the generic framework. During the implementation of SITE, specific emphasis was laid on expandability, maintainability and usability. Along with the modeling framework a land use model for the analysis of the stability of tropical rainforest margins was developed in the context of the collaborative research project STORMA (SFB 552). In a research area in Central Sulawesi, Indonesia, socio-environmental impacts of land-use changes were examined. SITE was used to simulate land-use dynamics in the historical period of 1981 to 2002. Analogous to that, a scenario that did not consider migration in the population dynamics, was analyzed. For the calculation of crop yields and trace gas emissions, the DAYCENT agro-ecosystem model was integrated. In this case study, it could be shown that land-use changes in the Indonesian research area could mainly be characterized by the expansion of agricultural areas at the expense of natural forest. For this reason, the situation had to be interpreted as unsustainable even though increased agricultural use implied economic improvements and higher farmers' incomes. Due to the importance of model calibration, it was explicitly addressed in the SITE architecture through the introduction of a specific component. The calibration functionality can be used by all SITE applications and enables largely automated model calibration. Calibration in SITE is understood as a process that finds an optimal or at least adequate solution for a set of arbitrarily selectable model parameters with respect to an objective function. In SITE, an objective function typically is a map comparison algorithm capable of comparing a simulation result to a reference map. Several map optimization and map comparison methodologies are available and can be combined. The STORMA land-use model was calibrated using a genetic algorithm for optimization and the figure of merit map comparison measure as objective function. The time period for the calibration ranged from 1981 to 2002. For this period, respective reference land-use maps were compiled. It could be shown, that an efficient automated model calibration with SITE is possible. Nevertheless, the selection of the calibration parameters required detailed knowledge about the underlying land-use model and cannot be automated. In another case study decreases in crop yields and resulting losses in income from coffee cultivation were analyzed and quantified under the assumption of four different deforestation scenarios. For this task, an empirical model, describing the dependence of bee pollination and resulting coffee fruit set from the distance to the closest natural forest, was integrated. Land-use simulations showed, that depending on the magnitude and location of ongoing forest conversion, pollination services are expected to decline continuously. This results in a reduction of coffee yields of up to 18% and a loss of net revenues per hectare of up to 14%. However, the study also showed that ecological and economic values can be preserved if patches of natural vegetation are conservated in the agricultural landscape. -----------------------------------------------------------------------

The role of ligneous vegetation for livestock nutrition in the sub-Sahelian and Sudanian zones of West Africa: Potential effects of climate change

Climate change and variability in sub-Saharan West Africa is expected to have negative consequences for crop and livestock farming due to the strong dependence of these sectors on rainfall and natural resources, and the low adaptive capacity of crops farmers, agro-pastoralist and pastoralists in the region. The objective of this PhD research was to investigate the anticipated impacts of expected future climate change and variability on nutrition and grazing management of livestock in the prevailing extensive agro-pastoral and pastoral systems of the Sahelian and Sudanian zones of Burkina Faso. To achieve this, three studies were undertaken in selected village territories (100 km² each) in the southern Sahelian (Taffogo), northern Sudanian (Nobere, Safane) and southern Sudanian (Sokouraba) zone of the country during 2009 and 2010. The choice of two villages in the northern Sudanian zone was guided by the dichotomy between intense agricultural land use and high population density near Safane, and lower agricultural land use in the tampon zone between the village of Nobere and the National Park Kaboré Tambi of Pô. Using global positioning and geographical information systems tools, the spatio-temporal variation in the use of grazing areas by cattle, sheep and goats, and in their foraging behaviour in the four villages was assessed by monitoring three herds each per species during a one-year cycle (Chapter 2). Maximum itinerary lengths (km/d) were observed in the hot dry season (March-May); they were longer for sheep (18.8) and cattle (17.4) than for goats (10.5, p<0.05). Daily total grazing time spent on pasture ranged from 6 - 11 h with cattle staying longer on pasture than small ruminants (p<0.05). Feeding time accounted for 52% - 72% of daily time on pasture, irrespective of species. Herds spent longer time on pasture and walked farther distances in the southern Sahelian than the two Sudanian zones (p<0.01), while daily feeding time was longer in the southern Sudanian than in the other two zones (p>0.05). Proportional time spent resting decreased from the rainy (June - October) to the cool (November - February) and hot dry season (p<0.05), while in parallel the proportion of walking time increased. Feeding time of all species was to a significantly high proportion spent on wooded land (tree crown cover 5-10%, or shrub cover >10%) in the southern Sahelian zone, and on forest land (tree crown cover >10%) in the two Sudanian zones, irrespective of season. It is concluded that with the expansion of cropland in the whole region, remaining islands of wooded land, including also fields fallowed for three or more years with their considerable shrub cover, are particularly valuable pasturing areas for ruminant stock. Measures must be taken that counteract the shrinking of wooded land and forests across the whole region, including also active protection and (re)establishment of drought-tolerant fodder trees. Observation of the selection behaviour of the above herds of cattle and small ruminant as far as browse species were concerned, and interviews with 75 of Fulani livestock keepers on use of browse as feed by their ruminant stock and as remedies for animal disease treatment was undertaken (Chapter 3) in order to evaluate the consequence of climate change for the contribution of browse to livestock nutrition and animal health in the extensive grazing-based livestock systems. The results indicated that grazing cattle and small ruminants do make considerable use of browse species on pasture across the studied agro-ecological zones. Goats spent more time (p<0.01) feeding on browse species than sheep and cattle, which spent a low to moderate proportion of their feeding time on browsing in any of the study sites. As far as the agro-ecological zones were concerned, the contribution of browse species to livestock nutrition was more important in the southern Sahelian and northern Sudanian zone than the southern Sudanian zone, and this contribution is higher during the cold and hot dry season than during the rainy season. A total of 75 browse species were selected on pasture year around, whereby cattle strongly preferred Afzelia africana, Pterocarpus erinaceus and Piliostigma sp., while sheep and goats primarily fed on Balanites aegyptiaca, Ziziphus mauritiana and Acacia sp. Crude protein concentration (in DM) of pods or fruits of the most important browse species selected by goats, sheep and cattle ranged from 7% to 13% for pods, and from 10% to 18% for foliage. The concentration of digestible organic matter of preferred browse species mostly ranged from 40% to 60%, and the concentrations of total phenols, condensed tannins and acid detergent lignin were low. Linear regression analyses showed that browse preference on pasture is strongly related to its contents (% of DM) of CP, ADF, NDF and OM digestibility. Interviewed livestock keepers reported that browse species are increasingly use by their grazing animals, while for animal health care use of tree- and shrub-based remedies decreased over the last two decades. It is concluded that due to climate change with expected negative impact on the productivity of the herbaceous layer of communal pastures browse fodder will gain in importance for animal nutrition. Therefore re-establishment and dissemination of locally adapted browse species preferred by ruminants is needed to increase the nutritional situation of ruminant stock in the region and contribute to species diversity and soil fertility restoration in degraded pasture areas. In Chapter 4 a combination of household surveys and participatory research approaches was used in the four villages, and additionally in the village of Zogoré (southern Sahelian zone) and of Karangasso Vigué (northern Sudanian zone) to investigate pastoralists’ (n= 76) and agro-pastoralists’ (n= 83) perception of climate change, and their adaptation strategies in crop and livestock production at farm level. Across the three agro-ecological zones, the majority of the interviewees perceived an increase in maximum day temperatures and decrease of total annual rainfall over the last two decades. Perceptions of change in climate patterns were in line with meteorological data for increased temperatures while for total rainfall farmers’ views contrasted the rainfall records which showed a slight increase of precipitation. According to all interviewees climate change and variability have negative impacts on their crop and animal husbandry, and most of them already adopted some coping and adaptation strategies at farm level to secure their livelihoods and reduce negative impacts on their farming system. Although these strategies are valuable and can help crop and livestock farmers to cope with the recurrent droughts and climate variability, they are not effective against expected extreme climate events. Governmental and non-governmental organisations should develop effective policies and strategies at local, regional and national level to support farmers in their endeavours to cope with climate change phenomena; measures should be site-specific and take into account farmers’ experiences and strategies already in place.

Individual Decision-Making and Inflation Persistence

The traditional task of a central bank is to preserve price stability and, in doing so, not to impair the real economy more than necessary. To meet this challenge, it is of great relevance whether inflation is only driven by inflation expectations and the current output gap or whether it is, in addition, influenced by past inflation. In the former case, as described by the New Keynesian Phillips curve, the central bank can immediately and simultaneously achieve price stability and equilibrium output, the so-called ‘divine coincidence’ (Blanchard and Galí 2007). In the latter case, the achievement of price stability is costly in terms of output and will be pursued over several periods. Similarly, it is important to distinguish this latter case, which describes ‘intrinsic’ inflation persistence, from that of ‘extrinsic’ inflation persistence, where the sluggishness of inflation is not a ‘structural’ feature of the economy but merely ‘inherited’ from the sluggishness of the other driving forces, inflation expectations and output. ‘Extrinsic’ inflation persistence is usually considered to be the less challenging case, as policy-makers are supposed to fight against the persistence in the driving forces, especially to reduce the stickiness of inflation expectations by a credible monetary policy, in order to reestablish the ‘divine coincidence’. The scope of this dissertation is to contribute to the vast literature and ongoing discussion on inflation persistence: Chapter 1 describes the policy consequences of inflation persistence and summarizes the empirical and theoretical literature. Chapter 2 compares two models of staggered price setting, one with a fixed two-period duration and the other with a stochastic duration of prices. I show that in an economy with a timeless optimizing central bank the model with the two-period alternating price-setting (for most parameter values) leads to more persistent inflation than the model with stochastic price duration. This result amends earlier work by Kiley (2002) who found that the model with stochastic price duration generates more persistent inflation in response to an exogenous monetary shock. Chapter 3 extends the two-period alternating price-setting model to the case of 3- and 4-period price durations. This results in a more complex Phillips curve with a negative impact of past inflation on current inflation. As simulations show, this multi-period Phillips curve generates a too low degree of autocorrelation and too early turnings points of inflation and is outperformed by a simple Hybrid Phillips curve. Chapter 4 starts from the critique of Driscoll and Holden (2003) on the relative real-wage model of Fuhrer and Moore (1995). While taking the critique seriously that Fuhrer and Moore’s model will collapse to a much simpler one without intrinsic inflation persistence if one takes their arguments literally, I extend the model by a term for inequality aversion. This model extension is not only in line with experimental evidence but results in a Hybrid Phillips curve with inflation persistence that is observably equivalent to that presented by Fuhrer and Moore (1995). In chapter 5, I present a model that especially allows to study the relationship between fairness attitudes and time preference (impatience). In the model, two individuals take decisions in two subsequent periods. In period 1, both individuals are endowed with resources and are able to donate a share of their resources to the other individual. In period 2, the two individuals might join in a common production after having bargained on the split of its output. The size of the production output depends on the relative share of resources at the end of period 1 as the human capital of the individuals, which is built by means of their resources, cannot fully be substituted one against each other. Therefore, it might be rational for a well-endowed individual in period 1 to act in a seemingly ‘fair’ manner and to donate own resources to its poorer counterpart. This decision also depends on the individuals’ impatience which is induced by the small but positive probability that production is not possible in period 2. As a general result, the individuals in the model economy are more likely to behave in a ‘fair’ manner, i.e., to donate resources to the other individual, the lower their own impatience and the higher the productivity of the other individual. As the (seemingly) ‘fair’ behavior is modelled as an endogenous outcome and as it is related to the aspect of time preference, the presented framework might help to further integrate behavioral economics and macroeconomics.