Gerogescu-Roegen versus Solow/Stiglitz and the Convergence to the Cobb-Douglas

Abstract: The value of the elasticity of substitution of capital for resources is a crucial element in the debate over whether continual growth is possible. It is generally held that the elasticity has to be at least one to permit continual growth and that there is no way of estimating this outside the range of the data. This paper presents a model in which the elasticity is determined endogenously and may converge to one. It is concluded that the general opinion is wrong: that the possibility of continual growth does not depend on the exogenously given value of the elasticity and that the value of the elasticity outside the range of the data can be studied by econometric methods.Exhaustible resources, elasticity of substitution, innovation possibility frontier

Are Core Inflation Directional Forecasts Informative?

Core inflation is under attack. Empirically, experts have become increasingly disappointed with its actual performance. Theoretically, while some claim that it is a key inflation predictor others argue that, by construction, that cannot be one of its main properties, at least in the short run. Even if true, core inflation could still be useful if it provides good directional inflation forecasts. The evidence presented here using U.S., Canadian and Brazilian data shows that this does not seem to be the case. Directional forecasts are often no better than a coin toss, especially from the level model. The gap model’s forecasts are wrong, on average, at least 20% of the time. More crucially, they are usually no better than a simple moving average of headline inflation.

Conditioning bounds for traveltime tomography in layered media

This paper revisits the problem of recovering a smooth, isotropic, layered wave speed profile from surface traveltime information. While it is classic knowledge that the diving (refracted) rays classically determine the wave speed in a weakly well-posed fashion via the Abel transform, we show in this paper that traveltimes of reflected rays do not contain enough information to recover the medium in a well-posed manner, regardless of the discretization. The counterpart of the Abel transform in the case of reflected rays is a Fredholm kernel of the first kind which is shown to have singular values that decay at least root-exponentially. Kinematically equivalent media are characterized in terms of a sequence of matching moments. This severe conditioning issue comes on top of the well-known rearrangement ambiguity due to low velocity zones. Numerical experiments in an ideal scenario show that a waveform-based model inversion code fits data accurately while converging to the wrong wave speed profile

Least-false and local misspecification methods for longitudinal data with dropout

PhD ThesisIn any longitudinal study, a dropout before the nal timepoint can rarely be avoided. The chosen dropout model is commonly one of these types: Missing Completely at Ran- dom (MCAR), Missing at Random (MAR), Missing Not at Random (MNAR) and Shared Parameter (SP). In this thesis, we present methods to estimate the longitudinal model parameters under a variety of di erent dropout models. These methods are Complete Case analysis (CC), Observed data analysis (Obs), Inverse Probability Weighted estimat- ing equations (IPW), Linear Mixed E ect models (LME), Linear Increment models (LI) and Last Observation Carried Forward (LOCF). We estimate the parameters of the longi- tudinal model under MCAR, MAR, MNAR and SP for both simulated data and real data assuming two and three timepoint examples. We show that all methods work under the MCAR model as expected. Also, the LI method give consistent estimate under the SP model. The IPW and LME give consistent estimate under MAR, while no method work under MNAR. We investigate the consequences of misspecifying the missingness mechanism by deriv- ing the so called least false values. These are the values the parameter estimates converge to, when the assumptions may be wrong. This constitutes the central part of the thesis. In order to calculate the least false values, we use the approximation to the extended skew normal distribution (ESN) as produced in Ho et al. [2012]. We give closed form expressions to calculate the least false values 3 and 4 for LI, CC and LME methods. For the IPW, we provide a closed form for 3 under SP, MAR and MNAR while for 4 we failed to nd closed form under MNAR and we use a numerical calculation instead. The knowledge of the least false values allows us to conduct sensitivity analysis which will be illustrated. This method provides an alternative to a local misspeci cation sensitivity procedure which has been developed for likelihood-based analysis. The LME method is a likelihood based method, and this idea can be also adapted for the IPW estimating equation ap- proach. We compare the results obtained by our method with the results found by using the local misspeci cation method. We show that Copas and Eguchi [2005] method and LME least false match very well. Both gave very close results. This suggests that our least false method can provide a credible alternative to Copas and Eguchi in sensitivity anal- ysis. In fact it might be preferred since there is no assumption of local misspeci cation. Moreover, we apply the local misspeci cation and least false methods to estimate the bias and sensitivity for two real data examples with two timepoint and three timepoint data. We show how the IPW method is much more sensitive to misspeci cation than the LME method