Non-projectability of polytope skeleta

We investigate necessary conditions for the existence of projections of polytopes that preserve full k-skeleta. More precisely, given the combinatorics of a polytope and the dimension e of the target space, what are obstructions to the existence of a geometric realization of a polytope with the given combinatorial type such that a linear projection to e-space strictly preserves the k-skeleton. Building on the work of Sanyal (2009), we develop a general framework to calculate obstructions to the existence of such realizations using topological combinatorics. Our obstructions take the form of graph colorings and linear integer programs. We focus on polytopes of product type and calculate the obstructions for products of polygons, products of simplices, and wedge products of polytopes. Our results show the limitations of constructions for the deformed products of polygons of Sanyal & Ziegler (2009) and the wedge product surfaces of R\"orig & Ziegler (2009) and complement their results.Comment: 18 pages, 2 figure

Essays in Macroeconomics and Heterogeneity

This thesis contains four chapters, addressing two separate but equally prominent research areas in macroeconomics. The first two chapters focus on the effects of firm heterogeneity and firm dynamics on macroeconomic outcomes, particularly how the transmission of macroeconomic shocks is impacted by strategic behaviour and the distribution of financially constrained firms. The last two chapters address the topic of identification in macroeconomics with the last chapter focusing on the measurement of heterogeneous dynamic effects after a macroeconomic policy shock. The first chapter examines how oligopolistic competition, firm heterogeneity and entry of firms alter the transmission of monetary policy through the lens of a New Keynesian model. The standard textbook New Keynesian model relies on counter-cyclical profits for monetary policy to have an effect as recently pointed out by Broer et al. (2020). This paper first tests this hypothesis by adding oligopolistic competition and static free entry to an otherwise standard NK model. Including search and matching frictions to the labour market, breaks the result of money neutrality despite free entry of firms. Beyond that the model is further augmented to accommodate firm heterogeneity and dynamic entry to investigate how the market structure affects the propagation of monetary policy shocks. The findings are threefold: First, through the channel of oligopolistic competition, heterogeneity in firms’ productivity leads to pro-cyclical profits for lower levels of wage rigidity compared to the homogeneous case. Second, firm heterogeneity increases the response in aggregate output which is in line with Mongey (2017). Third, dynamic entry is further enhancing this effect, yet the strengthening of competition has a negative impact on firms’ profits. Local projections using Compustat firm-level data and Romer & Romer (2004) monetary policy shocks support the predictions of the theoretical model. The second chapter, which is co-authored with Miguel H. Ferreira and Timo Haber, investigates how distributional properties of financially constrained firms shape macroeconomic outcomes. Using a unique dataset covering the universe of Portuguese firms and their credit situation we revisit the relation between firm size, their financial situation, and sensitivity to the cycle. First, we provide two stylized facts: (1) Financially constrained firms react more to the business cycle and this mechanism is orthogonal to the size channel proposed by Crouzet & Mehrotra (2020). (2) Constrained firms are found across the entire size distribution, also in the top percentiles, which is in contrast to what standard financial friction models would predict. We then show that ex-ante heterogeneity of firms, a possible explanatory factor, persists over the firms’ life cycle and affects constrained and unconstrained firms differently. Incorporating this ex-ante heterogeneity into an otherwise standard financial frictions model simultaneously accounts for the stylized facts, gives rise to large constrained firms, and leads to larger aggregate fluctuations and capital misallocation. In the third chapter, together with my supervisor Pontus Rendahl, we investigate the effect of saving shocks on business cycle fluctuations. A common modeling tool – and a popular narrative – used to explain the financial crisis of 2008-2010 is a sudden increase in the desire to save. Such “marginal propensity to save” (MPS) shocks can be triggered by, for instance, a rise in uncertainty surrounding the economic climate, and depress interest rates, inflation, and generally cause an economic contraction. This paper uses the long-run properties arising from MPS shocks in both exogenous- and endogenous growth models with sticky prices in order to identify their causal effect on output. We find that time series data from the United States is strongly supportive of the notion that MPS shocks indeed have a causal, and contractionary, effect on economic activity, lending support to the most common approach of studying the financial crisis. The fourth chapter is co-authored with Adrian Ochs and aims to improve and facilitate the measurement of heterogeneous macroeconomic policy effects by using machine learning techniques. Specifically, the paper proposes a flexible framework to identify state-dependent effects of macroeconomic policies. In the literature it is common to either estimate constant policy effects or introduce state-dependency in a parametric fashion. This, however, demands prior assumptions about the functional form. Our new method allows to identify state-dependent effects and possible interactions in a datadriven way. Specifically, we estimate heterogeneous policy effects using semi-parametric varying-coefficient models in an otherwise standard VAR structure. While keeping a parametric reduced form for interpretability and efficiency, we estimate the coefficients as functions of modifying macroeconomic variables, using random forests as the underlying non-parametric estimator. Simulation studies show that this method correctly identifies multiple states even for relatively small sample sizes. To further illustrate our method, we apply the semi-parametric framework to the historical data set by Ramey & Zubairy (2018) and offer a more granular perspective on the dependence of the fiscal policy efficacy on unemployment and interest rates.Cambridge Trust & INE

'Hygiene im Äther' oder die verpaßte Realität : Karl-Eduard von Schnitzler und der 'Der Schwarze Kanal'

Als sich Karl-Eduard von Schnitzler am 30.10.1989 mit seiner Sendung ‚Der Schwarze Kanal‘ nach fast dreißig Jahren vom Bildschirm verabschiedete, ging eine Ära des DDR-Fernsehens zu Ende. Wohl kaum ein zweiter Journalist der DDR erreichte jenen Bekanntheitsgrad, wohl kaum eine andere offizielle Stimme sorgte dauerhaft für ähnlich erhitzte Gemüter, wie die polemisch-aggressiven Haßtiraden von Schnitzlers. Trotz dieser Begebenheiten ist das ‘Phänomen’ dieser Wochenschau ins westliche Fernsehen bisher nur ungenügend ergründet, was sich auch daran zeigt, welches Interesse immer noch an der Person von Schnitzlers und seiner journalistischen Denkart besteht. Obwohl mittlerweile in Rente und keine offizielle Meinung mehr verkündend, wird Karl-Eduard von Schnitzler mit seinen mittlerweile 80 Jahren nicht müde, seine sozialistischen Gedanken weiter zu verbreiten