New tools for understanding the local asymptotic power of panel unit root tests

Abstract Motivated by the previously documented discrepancy between actual and predicted power, the present paper provides new tools for analyzing the local asymptotic power of panel unit root tests. These tools are appropriate in general when considering panel data with a dominant autoregressive root of the form ^ρi=1+^ciN-^κT-^τ, where i=1,...,N indexes the cross-sectional units, T is the number of time periods and ^ci is a random local-to-unity parameter. A limit theory for the sample moments of such panel data is developed and is shown to involve infinite-order series expansions in the moments of ^ci, in which existing theories can be seen as mere first-order approximations. The new theory is applied to study the asymptotic local power functions of some known test statistics for a unit root. These functions can be expressed in terms of the expansions in the moments of ^ci, and include existing local power functions as special cases. Monte Carlo evidence is provided to suggest that the new results go a long way toward bridging the gap between actual and predicted power.

The local power of the CADF and CIPS panel unit root tests

Very little is known about the local power of second generation panel unit root tests that are robust to cross-section dependence. This article derives the local asymptotic power functions of the cross-section argumented Dickey–Fuller Cross-section Augmented Dickey-Fuller (CADF) and CIPS tests of Pesaran (2007), which are among the most popular tests around.

The power of PANIC

The current paper considers the asymptotic local power of second-generation panel unit root tests that are robust to the presence of cross-section dependence in the form of common factors. As a basis for our analysis, we take the PANIC approach of Bai and Ng (2004, 2010), which is one of the single most popular and general second-generation approaches around.

Rethinking the univariate approach to panel unit root testing: using covariates to resolve the incidental trend problem

In an influential article, Hansen showed that covariate augmentation can lead to substantial power gains when compared to univariate tests. In this article, we ask if this result extends also to the panel data context? The answer turns out to be yes, which is maybe not that surprising. What is surprising, however, is the extent of the power gain, which is shown to more than outweigh the well-known power loss in the presence of incidental trends. That is, the covariates have an order effect on the neighborhood around unity for which local asymptotic power is negligible.

A simple test for nonstationarity in mixed panels with incidental trends

Ng (2008) shows how the cross-sectional variance of the observed panel data can be used to construct a simple test for the proportion of non-stationary units. However, in the case with incidental trends the test is distorted. The present note shows how the distortions can be substantially reduced by the use of bias-adjustment. It also investigates the local power of the bias-adjusted test, which is shown to suffer from the same incidental trends problem previously only documented for conventional t-tests.

Pooled panel unit root tests and the effect of past initialization

This paper analyzes the role of initialization when testing for a unit root in panel data, an issue that has received surprisingly little attention in the literature. In fact, most studies assume that the initial value is either zero or bounded. As a response to this, the current paper considers a model in which the initialization is in the past, which is shown to have several distinctive features that makes it attractive, even in comparison to the common time series practice of making the initial value a draw from its unconditional distribution under the stationary alternative. The results have implications not only for theory, but also for applied work. In particular, and in contrast to the time series case, in panels the effect of the initialization need not be negative but can actually lead to improved test performance.

A simple test for nonstationarity in mixed panels: A further investigation

The test of Ng (2008) is one of the few that enables general inference regarding the proportion of non-stationary units in panel data. The current paper furthers the investigation of Ng (2008) in two directions. First, the existing sequential limit analysis is generalized to a very flexible asymptotic framework in which the number of time periods, T, can be either fixed or tending to infinity jointly with the number of cross-section units, N. Second, the test statistic is evaluated not only under the null hypothesis, but also under alternatives that can be either fixed or local.

Environmental effects of thermal and radioactive discharges from nuclear power plants in the boreal brackish-water conditions of the northern Baltic Sea

During recent decades, thermal and radioactive discharges from nuclear power plants into the aquatic environment have become the subject of lively debate as an ecological concern. The target of this thesis was to summarize the large quantity of results obtained in extensive monitoring programmes and studies carried out in recipient sea areas off the Finnish nuclear power plants at Loviisa and Olkiluoto during more than four decades. The Loviisa NPP is located on the coast of the Gulf of Finland and Olkiluoto NPP on that of the Bothnian Sea. The state of the Gulf of Finland is clearly more eutrophic; the nutrient concentrations in the surface water are about 1½ 2 times higher at Loviisa than at Olkiluoto, and the total phosphorus concentrations still increased in both areas (even doubled at Loviisa) between the early 1970s and 2000. Thus, it is a challenge to distinguish the local effects of thermal discharges from the general eutrophication process of the Gulf of Finland. The salinity is generally low in the brackish-water conditions of the northern Baltic Sea, being however about 1 higher at Olkiluoto than at Loviisa (the salinity of surface water varying at the latter from near to 0 in early spring to 4 6 in late autumn). Thus, many marine and fresh-water organisms live in the Loviisa area close to their limit of existence, which makes the biota sensitive to any additional stress. The characteristics of the discharge areas of the two sites differ from each other in many respects: the discharge area at Loviisa is a semi-enclosed bay in the inner archipelago, where the exchange of water is limited, while the discharge area at Olkiluoto is more open, and the exchange of water with the open Bothnian Sea is more effective. The effects of the cooling water discharged from the power plants on the temperatures in the sea were most obvious in winter. The formation of a permanent ice cover in the discharge areas has been delayed in early winter, and the break-up of the ice occurs earlier in spring. The prolonging of the growing season and the disturbance of the overwintering time, in conditions where the biota has adjusted to a distinct rest period in winter, have been the most significant biological effects of the thermal pollution. The soft-bottom macrofauna at Loviisa has deteriorated to the point of almost total extinction at many sampling stations during the past 40 years. A similar decline has been reported for the whole eastern Gulf of Finland. However, the local eutrophication process seems to have contributed into the decline of the zoobenthos in the discharge area at Loviisa. Thermal discharges have increased the production of organic matter, which again has led to more organic bottom deposits. These have in turn increased the tendency of the isolated deeps to a depletion of oxygen, and this has further caused strong remobilization of phosphorus from the bottom sediments. Phytoplankton primary production and primary production capacity doubled in the whole area between the late 1960s and the late 1990s, but started to decrease a little at the beginning of this century. The focus of the production shifted from spring to mid- and late summer. The general rise in the level of primary production was mainly due to the increase in nutrient concentrations over the whole Gulf of Finland, but the thermal discharge contributed to a stronger increase of production in the discharge area compared to that in the intake area. The eutrophication of littoral vegetation in the discharge area has been the most obvious, unambiguous and significant biological effect of the heated water. Myriophyllum spicatum, Potamogeton perfoliatus and Potamogeton pectinatus, and vigorous growths of numerous filamentous algae as their epiphytes have strongly increased in the vicinity of the cooling water outlet, where they have formed dense populations in the littoral zone in late summer. However, the strongest increase of phytobenthos has extended only to a distance of about 1 km from the outlet, i.e., the changes in vegetation have been largest in those areas that remain ice-free in winter. Similar trends were also discernible at Olkiluoto, but to a clearly smaller extent, which was due to the definitely weaker level of background eutrophy and nutrient concentrations in the Bothnian Sea, and the differing local hydrographical and biological factors prevailing in the Olkiluoto area. The level of primary production has also increased at Olkiluoto, but has remained at a clearly lower level than at Loviisa. In spite of the analogous changes observed in the macrozoobenthos, the benthic fauna has remained strong and diversified in the Olkiluoto area. Small amounts of local discharge nuclides were regularly detected in environmental samples taken from the discharge areas: tritium in seawater samples, and activation products, such as 60Co, 58Co, 54Mn, 110mAg, 51Cr, in suspended particulate matter, bottom sediments and in several indicator organisms (e.g., periphyton and Fucus vesiculosus) that effectively accumulate radioactive substances from the medium. The tritium discharges and the consequent detection frequency and concentrations of tritium in seawater were higher at Loviisa, but the concentrations of the activation products were higher at Olkiluoto, where traces of local discharge nuclides were also observed over a clearly wider area, due to the better exchange of water than at Loviisa, where local discharge nuclides were only detected outside Hästholmsfjärden Bay quite rarely and in smaller amounts. At the farthest, an insignificant trace amount (0.2 Bq kg-1 d.w.) of 60Co originating from Olkiluoto was detected in Fucus at a distance of 137 km from the power plant. Discharge nuclides from the local nuclear power plants were almost exclusively detected at the lower trophic levels of the ecosystems. Traces of local discharge nuclides were very seldom detected in fish, and even then only in very low quantities. As a consequence of the reduced discharges, the concentrations of local discharge nuclides in the environment have decreased noticeably in recent years at both Loviisa and Olkiluoto. Although the concentrations in environmental samples, and above all, the discharge data, are presented as seemingly large numbers, the radiation doses caused by them to the population and to the biota are very low, practically insignificant. The effects of the thermal discharges have been more significant, at least to the wildlife in the discharge areas of the cooling water, although the area of impact has been relatively small. The results show that the nutrient level and the exchange of water in the discharge area of a nuclear power plant are of crucial importance.

Topics in LIGO-related physics: interferometric speed meters and tidal work

In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors, one strategy is to monitor the relative momentum or speed of the test-mass mirrors, rather than monitoring their relative position. The most straightforward design for a speed-meter interferometer that accomplishes this is described and analyzed in Chapter 2. This design (due to Braginsky, Gorodetsky, Khalili, and Thorne) is analogous to a microwave-cavity speed meter conceived by Braginsky and Khalili. A mathematical mapping between the microwave speed meter and the optical interferometric speed meter is developed and used to show (in accord with the speed being a quantum nondemolition observable) that in principle the interferometric speed meter can beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies . However, in practice, to reach or beat the SQL, this specific speed meter requires exorbitantly high input light power. The physical reason for this is explored, along with other issues such as constraints on performance due to optical dissipation.

Chapter 3 proposes a more sophisticated version of a speed meter. This new design requires only a modest input power and appears to be a fully practical candidate for third-generation LIGO. It can beat the SQL (the approximate sensitivity of second-generation LIGO interferometers) over a broad range of frequencies (~ 10 to 100 Hz in practice) by a factor h/h_SQL ~ √W^(SQL)_(circ)/W_circ. Here W_circ is the light power circulating in the interferometer arms and W_SQL ≃ 800 kW is the circulating power required to beat the SQL at 100 Hz (the LIGO-II power). If squeezed vacuum (with a power-squeeze factor e^-2R) is injected into the interferometer's output port, the SQL can be beat with a much reduced laser power: h/h_SQL ~ √W^(SQL)_(circ)/W_circe^-2R. For realistic parameters (e^-2R ≃ 10 and W_circ ≃ 800 to 2000 kW), the SQL can be beat by a factor ~ 3 to 4 from 10 to 100 Hz. [However, as the power increases in these expressions, the speed meter becomes more narrow band; additional power and re-optimization of some parameters are required to maintain the wide band.] By performing frequency-dependent homodyne detection on the output (with the aid of two kilometer-scale filter cavities), one can markedly improve the interferometer's sensitivity at frequencies above 100 Hz.

Chapters 2 and 3 are part of an ongoing effort to develop a practical variant of an interferometric speed meter and to combine the speed meter concept with other ideas to yield a promising third- generation interferometric gravitational-wave detector that entails low laser power.

Chapter 4 is a contribution to the foundations for analyzing sources of gravitational waves for LIGO. Specifically, it presents an analysis of the tidal work done on a self-gravitating body (e.g., a neutron star or black hole) in an external tidal field (e.g., that of a binary companion). The change in the mass-energy of the body as a result of the tidal work, or "tidal heating," is analyzed using the Landau-Lifshitz pseudotensor and the local asymptotic rest frame of the body. It is shown that the work done on the body is gauge invariant, while the body-tidal-field interaction energy contained within the body's local asymptotic rest frame is gauge dependent. This is analogous to Newtonian theory, where the interaction energy is shown to depend on how one localizes gravitational energy, but the work done on the body is independent of that localization. These conclusions play a role in analyses, by others, of the dynamics and stability of the inspiraling neutron-star binaries whose gravitational waves are likely to be seen and studied by LIGO.

Secure D2D Communication in Large-Scale Cognitive Cellular Networks with Wireless Power Transfer

In this paper, we investigate secure device-to-device (D2D) communication in energy harvesting large-scale cognitive cellular networks. The energy constrained D2D transmitter harvests energy from multi-antenna equipped power beacons (PBs), and communicates with the corresponding receiver using the spectrum of the cellular base stations (BSs). We introduce a power transfer model and an information signal model to enable wireless energy harvesting and secure information transmission. In the power transfer model, we propose a new power transfer policy, namely, best power beacon (BPB) power transfer. To characterize the power transfer reliability of the proposed policy, we derive new closed-form expressions for the exact power outage probability and the asymptotic power outage probability with large antenna arrays at PBs. In the information signal model, we present a new comparative framework with two receiver selection schemes: 1) best receiver selection (BRS), and 2) nearest receiver selection (NRS). To assess the secrecy performance, we derive new expressions for the secrecy throughput considering the two receiver selection schemes using the BPB power transfer policies. We show that secrecy performance improves with increasing densities of PBs and D2D receivers because of a larger multiuser diversity gain. A pivotal conclusion is reached that BRS achieves better secrecy performance than NRS but demands more instantaneous feedback and overhead.

GLS Detrending, Efficient Unit Root Tests and Structural Change

We extend the class of M-tests for a unit root analyzed by Perron and Ng (1996) and Ng and Perron (1997) to the case where a change in the trend function is allowed to occur at an unknown time. These tests M(GLS) adopt the GLS detrending approach of Dufour and King (1991) and Elliott, Rothenberg and Stock (1996) (ERS). Following Perron (1989), we consider two models : one allowing for a change in slope and the other for both a change in intercept and slope. We derive the asymptotic distribution of the tests as well as that of the feasible point optimal tests PT(GLS) suggested by ERS. The asymptotic critical values of the tests are tabulated. Also, we compute the non-centrality parameter used for the local GLS detrending that permits the tests to have 50% asymptotic power at that value. We show that the M(GLS) and PT(GLS) tests have an asymptotic power function close to the power envelope. An extensive simulation study analyzes the size and power in finite samples under various methods to select the truncation lag for the autoregressive spectral density estimator. An empirical application is also provided.

Testing for a Unit Root in Panels with Dynamic Factors

This paper studies testing for a unit root for large n and T panels in which the cross-sectional units are correlated. To model this cross-sectional correlation, we assume that the data is generated by an unknown number of unobservable common factors. We propose unit root tests in this environment and derive their (Gaussian) asymptotic distribution under the null hypothesis of a unit root and local alternatives. We show that these tests have significant asymptotic power when the model has no incidental trends. However, when there are incidental trends in the model and it is necessary to remove heterogeneous deterministic components, we show that these tests have no power against the same local alternatives. Through Monte Carlo simulations, we provide evidence on the finite sample properties of these new tests.

Breaking Boundaries : recasting the “local” newspaper as “geo-social” news in a digital landscape

This paper reconceptualises the role of the small “local” newspaper in a new media environment and argues that definitions and concepts currently used to describe and define such publications are becoming increasingly problematic as newspapers shift into both print and online formats. The paper highlights the continued importance of geography for such newspapers at a time when there is wide academic debate on the relevance of territory and boundaries and the impact of time–space compression in a new media world. It argues, however, that a focus on a newspaper’s geographic connection must also acknowledge the increasing boundlessness and openness of the social space in which a newspaper operates. Ultimately this paper suggests the concept of “geo-social” news may be a more appropriate framework for scholars to consider such publications. I draw on the work of geography scholars, and discussions around “space” and “place” to construct the notion of “geo-social” news, highlighting some exemplars of small commercial newsroom practices in Australia, the United Kingdom and Canada and discussions with newspaper editors in Australia to demonstrate the relevance of the “geo-social” concept.