The present thesis deals with multiple econometric equations systems which might provide a useful insight into the national economy modelling. It takes into account possible pitfalls of common practices. It introduces the theory and estimation methods of multiple econometric equations systems. It also discusses the equality of savings and investment and the theory of money. Furthermore, it briefly analyses Klein's model I from a theoretical point of view and uses the three-step least squares method in order to estimate it. Partial modifications of this model are suggested and implemented. The quality of the competitive models is evaluated employing the predictive criterion. Consequently, the canonical NK DSGE model is derived and subjected to theoretical criticism. The thesis debates doubts on the relevance of the NK IS curve and argues that Lucas's critique is still valid. A generalized method of moments is used to implement the NK DSGE model. Finally, this model is briefly compared with Klein's model I.

The Priest-Klein model predicts that a decline in the plaintiff win rate might be explained by a change in stake asymmetry that favors the plaintiff; that is, the stakes for defendants increase. This lowers the plaintiff win rate because defendants increasingly look to settle cases they are less likely to win, leading them to only go to trial with cases they have a comparably higher probability of winning. We theorize a shift like this might have occurred between 1985 and 1995, as Lahav and Siegelman (2017) recently discovered that the plaintiff win rate fell from almost 70% in 1985 to just over 30% in 1995. Although they found that changing judicial caseloads and other factors represented a notable portion of the decline, they were unable to identify what drove the remaining 40%. We hypothesize that this unexplained decline was caused by increasing defendant stakes and examine two potential drivers of increasing stake asymmetry: changing judicial ideology and a rise in the number of Multi-District Litigation (MDL) cases, a type of case with higher defendant stakes. We find evidence consistent with the Priest-Klein model for MDL cases as these cases experienced lower adjudication rates, lower plaintiff win rates, and higher settlement rates. Additionally, we found that judicial ideology was substantially more important for MDL cases, suggesting that judges might make use of their greater influence in these cases to guide outcomes. Yet, while both MDL case status and judicial ideology were statistically significant predictors of plaintiff win rates, we found that neither explains a substantial portion of the decline. Thus, a large proportion of the decline found by Lahav and Siegelman remains a mystery.

If we consider ruled surfaces of the projective 3-space as a one parameter family of lines, then they appear in the well-known KLEIN-model of lines in the projective 3-space as curves of a hyperquadric in the projective 5-space. The osculating spaces of such a curve are represented in the projective 3-space by spaces of linear complexes. Those points of a generator e of the ruled surface, in which the tangent bundles are in the same time complex line bundles in the accompanying osculating line complex of the ruled surface along e, are called the LIE-points of e. The LIE-points fulfil two (real or imaginary conjugate) curves on the ruled surface called the LIE-curves. The support of the osculating-3-space of the ruled surface along a regular non-torsal generator e are two, one or zero straight lines in the osculating regulus. If thes straight lines exist, one calls them the flecnode tangents of the ruled surface. On a hyperbolic ruled surface build the points of contact of the flecnode tangents two projective distinguished curves called the flecnode curves. In this work we present the different methods of treating these curves in the history, and we give a new explicit calculation of the flecnode points and the LIE-points depending on the basis of a PLÜCKER-coordinates representation of the ruled surface. In addition we study the questions that appears by considering the LIE-curves of a ruled surface to form a pair of BERTRAND curves for which this ruled surface is the surface of common main normals. For example, the question about ruled surfaces, whose LIE-curves are orthogonal to the generators will be answered here. / Regelflächen des projektiven 3-Raums erscheinen, als (eindimensionalen) Geradenmengen aufgefasst, im bekannten KLEINschen Punktmodell der Geradenmenge vom projektiven 3-Raum als Kurven einer Hyperquadrik in einem projektiven 5-Raum. Die Schmiegräume einer solchen Kurve werden im projektiven 3-Raum durch Räume linearer Komplexe repräsentiert. Diejenigen Punkte einer Erzeugende e der Regelfläche, in denen die Tangentenbüschel gleichzeitig auch Komplexgeradenbüschel im begleitenden Schmiegkomplex von e sind, heißen LIE-Punkte von e. Die LIE-Punkte erfüllen zwei (reelle oder konjugiert imaginäre) Kurvenzüge auf der Regelfläche, die LIE-Kurven. Die Träger des Schmieg-3-Raums der Regelfläche längs einer reguläre nichttorsalen Erzeugende e sind zwei, eine oder null Geraden im Schmiegregulus. Sofern diese Geraden existieren, nennt man sie die Fleknodaltangenten der Regelfläche. Auf hyperbolischen Regelflächen bilden die Berührpunkte der Fleknodaltangenten zwei projektiv ausgezeichnete Kurven, die Fleknodalkurven. In der vorliegenden Arbeit stellen wir die unterschiedlichen Behandelungen diesen ausgezeichneten Kurven in der Geschichte dar, und geben wir eine neue explizite Berechnung von den Fleknodal- bzw. LIE-Punkte auf der Basis einer PLÜCKER-Koordinaten-Darstellung der Regelfläche. Außerdem untersuchen wir die Fragestellungen, die man bekommt, wenn man versucht, dass das paarweise auftreten der LIE-Kurven irgendwie in Analogie zum klassischen euklidischen BERTRAND-Kurvenpaar zu stellen. Z.B. lässt sich die Frage nach Regelflächen, deren LIE-Kurven Orthogonaltrajektorien der Erzeugenden sind, hier beantwortet.

If we consider ruled surfaces of the projective 3-space as a one parameter family of lines, then they appear in the well-known KLEIN-model of lines in the projective 3-space as curves of a hyperquadric in the projective 5-space. The osculating spaces of such a curve are represented in the projective 3-space by spaces of linear complexes. Those points of a generator e of the ruled surface, in which the tangent bundles are in the same time complex line bundles in the accompanying osculating line complex of the ruled surface along e, are called the LIE-points of e. The LIE-points fulfil two (real or imaginary conjugate) curves on the ruled surface called the LIE-curves. The support of the osculating-3-space of the ruled surface along a regular non-torsal generator e are two, one or zero straight lines in the osculating regulus. If thes straight lines exist, one calls them the flecnode tangents of the ruled surface. On a hyperbolic ruled surface build the points of contact of the flecnode tangents two projective distinguished curves called the flecnode curves. In this work we present the different methods of treating these curves in the history, and we give a new explicit calculation of the flecnode points and the LIE-points depending on the basis of a PLÜCKER-coordinates representation of the ruled surface. In addition we study the questions that appears by considering the LIE-curves of a ruled surface to form a pair of BERTRAND curves for which this ruled surface is the surface of common main normals. For example, the question about ruled surfaces, whose LIE-curves are orthogonal to the generators will be answered here. / Regelflächen des projektiven 3-Raums erscheinen, als (eindimensionalen) Geradenmengen aufgefasst, im bekannten KLEINschen Punktmodell der Geradenmenge vom projektiven 3-Raum als Kurven einer Hyperquadrik in einem projektiven 5-Raum. Die Schmiegräume einer solchen Kurve werden im projektiven 3-Raum durch Räume linearer Komplexe repräsentiert. Diejenigen Punkte einer Erzeugende e der Regelfläche, in denen die Tangentenbüschel gleichzeitig auch Komplexgeradenbüschel im begleitenden Schmiegkomplex von e sind, heißen LIE-Punkte von e. Die LIE-Punkte erfüllen zwei (reelle oder konjugiert imaginäre) Kurvenzüge auf der Regelfläche, die LIE-Kurven. Die Träger des Schmieg-3-Raums der Regelfläche längs einer reguläre nichttorsalen Erzeugende e sind zwei, eine oder null Geraden im Schmiegregulus. Sofern diese Geraden existieren, nennt man sie die Fleknodaltangenten der Regelfläche. Auf hyperbolischen Regelflächen bilden die Berührpunkte der Fleknodaltangenten zwei projektiv ausgezeichnete Kurven, die Fleknodalkurven. In der vorliegenden Arbeit stellen wir die unterschiedlichen Behandelungen diesen ausgezeichneten Kurven in der Geschichte dar, und geben wir eine neue explizite Berechnung von den Fleknodal- bzw. LIE-Punkte auf der Basis einer PLÜCKER-Koordinaten-Darstellung der Regelfläche. Außerdem untersuchen wir die Fragestellungen, die man bekommt, wenn man versucht, dass das paarweise auftreten der LIE-Kurven irgendwie in Analogie zum klassischen euklidischen BERTRAND-Kurvenpaar zu stellen. Z.B. lässt sich die Frage nach Regelflächen, deren LIE-Kurven Orthogonaltrajektorien der Erzeugenden sind, hier beantwortet.