The method of detection and localization of configuration defects in geodetic networks by means of Tikhonov regularization

In adjusted geodetic networks, cases of local configuration defects (defects in the geometric structure of the network due to missing data or errors in point numbering) can be encountered, which lead to the singularity of the normal equation system in the least-squares procedure. Numbering errors in observation sets cause the computer program to define the network geometry incorrectly. Another cause of a defect may be accidental omission of certain data records, causing local indeterminacy or lowering of local reliability rates in a network. Obviously, the problem of a configuration defect may be easily detectable in networks with a small number of points. However, it becomes a real problem in large networks, where manual checking of all data becomes a very expensive task. The paper presents a new strategy for the detection of configuration defects with the use of the Tikhonov regularization method. The method was implemented in 1992 in the GEONET system (www.geonet.net.pl).

PROGRESSIVE TAXATION AND MACROECONOMICS (IN)STABILITY UNDER HOUSEHOLD HETEROGENEITY

It has been shown that progressive income taxation may stabilize an otherwise standard representative-agent real business cycle model with an indeterminate steady state against aggregate fluctuations caused by agents’ animal spirits. By contrast, within an identical model that allows for sustained economic growth, progressive taxation could lead to equilibrium indeterminacy and sunspot-driven fluctuations. In the context of household heterogeneity that gives rise to income and asset inequality, the fiscal authority has (at least) two options of setting the baseline level of taxable income: (i) the economy-wide average level of income and (ii) the economy’s steady-state level of per capita income. I show that the adoption of a fiscal rule (i) invalidates the effects that a progressive tax can exert on the model’s local stability properties. Progressive income taxation thus no longer operates as an automatic stabilizer that mitigates belief-driven cyclical fluctuations in a no-growth economy, nor as an automatic destabilizer that leads to local indeterminacy in a sustained-growth economy. If a tax policy rule (ii) is instead adopted, then the existing literature’s findings of the (de)stabilizing roles of progressive taxation are robust to the inclusion of household heterogeneity.

A NOTE ON BALANCED-BUDGET INCOME TAXES AND AGGREGATE (IN)STABILITY IN MULTI-SECTOR ECONOMIES

We examine the impact of balanced-budget labor income taxes on the existence of expectation-driven business cycles in a two-sector version of the Schmitt-Grohé and Uribe (SGU) [(1997) Journal of Political Economy 105, 976–1000] model with constant government expenditures and counter-cyclical taxes. Our results show that the destabilizing impact of labor income taxes strongly depends on the capital intensity difference across sectors. Local indeterminacy is indeed more likely when the consumption good sector is capital intensive, as the minimal tax rate decreases, and less likely when the investment good sector is capital intensive, as the minimal tax rate increases. The implication of this result can be quantitatively significant. Indeed, when compared to SGU, local indeterminacy can be either completely ruled out for all OECD countries when the investment good is sufficiently capital intensive or drastically improved, delivering indeterminacy for a larger set of OECD countries, if the consumption good is sufficiently capital intensive. Focusing however on recent estimates of the sectoral capital shares corresponding to the empirically plausible case of a capital intensive consumption good, we find that there is a significant increase of the range of economically relevant labor tax rates (from a minimum tax rate of 30% to 24.7% for which local indeterminacy arises with respect to the aggregate formulation of SGU.

Macroeconomic (in)stability and endogenous market structure with productive government expenditure

We consider the congestion effect of productive government spending in a monopolistic competition model with endogenous entry, and analyze the possibility of local indeterminacy. Some main findings emerge from the analysis. First, the indeterminacy condition is independent of the monopoly power. Second, productive government expenditure can be a source of local indeterminacy, while a higher degree of public goods congestion lessens the beneficial effect of productive government expenditure, and therefore reduces the possibility of indeterminacy. Third, a higher degree of internal returns to scale is associated with a lower possibility for the emergence of indeterminacy when production externalities are present.

Complementarity between signaling and local indeterminacy

The correlations that violate the CHSH inequality are known to have complementary contributions from signaling and local indeterminacy. This complementarity is shown to represent a strengthening of Bell's theorem, and can be used to certify randomness in a device-independent way, assuming neither the validity of quantum mechanics nor even no-signaling. We obtain general nonlocal resources that can simulate the statistics of the singlet state, encompassing existing results. We prove a conjecture due to Hall (2010) and Kar et al. (2011) on the complementarity for such resources.

TARIFF AND EQUILIBRIUM INDETERMINACY: A GLOBAL ANALYSIS

Zhang [Tariff and Equilibrium Indeterminacy, available at http://mpra.ub.uni-muenchen.de/13099/ (2009)] shows that endogenous tariffs (or energy taxes) and endogenous labor income taxes are equivalent in generating local indeterminacy. Using methods developed by Stockman [Journal of Economic Theory 145 (2010), 1060–1085], we extend Zhang's analysis to prove that endogenous tariffs and endogenous labor income taxes are also equivalent in generating global indeterminacy (chaotic equilibria) under a balanced-budget rule. More precisely, we show that the existence of Euler equation branching in an arbitrarily small neighborhood of a steady state can imply topological chaos in the sense of Devaney. In addition, Euler equation branching occurs regardless of the local uniqueness of the equilibrium around the steady state.

LOCAL INDETERMINACY IN CONTINUOUS-TIME MODELS: THE ROLE OF RETURNS TO SCALE

The aim of this paper is to discuss the effect on returns to scale on the local determinacy properties of the steady state in a continuous-time two-sector economy with endogenous labor supply and sector-specific externalities. First we show that when labor is inelastic and the elasticity of intertemporal substitution in consumption is large enough, for any configuration of the returns to scale, local indeterminacy is obtained if there is a capital intensity reversal between the private and the social levels. Second, we prove that when labor is infinitely elastic, saddlepoint stability is obtained if the investment good sector has constant social returns, whereas local indeterminacy arises if the investment good sector has increasing social returns and the elasticity of intertemporal substitution in consumption admits intermediate values. Finally, our main conclusion shows that local indeterminacy requires a low elasticity of labor when the investment good has constant social returns, but requires either a low enough or a large enough elasticity of labor when the investment good has increasing social returns.