# Discussion Papers

All of the Department Discussion Papers are submitted to RePEc. The EconPapers or IDEAS sites allow you to search by author, title, keyword, JEL category and abstract contents.

Papers from 1998 onwards are available on-line as .PDF files.

## 10 Most Recent Papers

### 14/11 Ali al-Nowaihi and Sanjit Dhami

14/11 Foundations and Properties of Time Discount Functions

A critical element in all discounted utility models is the specification of a discount function. We introduce three functions: the delay, speedup and generating functions. Each can be uniquely elicited from behaviour. The delay function determines stationary and the common difference effect. The speedup function determines impatience. Additivity is jointly determined by the delay and speedup functions. The speedup and generating functions jointly determine a unique discount function. Conversely, a continuous discount function determines unique speedup and generating functions.** **

### 14/10 Eleni Stathopoulou

14/10 Environmental campaigns and endogenous technology choice under international oligopoly

In an international duopoly context, where two goods are produced by two firms located in two separate countries, F and NF, we study the issue of firms' environmental technology choice. When consumers in country F are environmentally aware, in the sense that they care about emissions in their own country, it is shown that the firm in country F adopts a cleaner technology compared to the firm in country NF. Moreover, leakage appears, as the demand by consumers in country F shifts to the good produced by the firm in country NF. This, in turn, provides a rationale for raising awareness among consumers in country F about the effects of their consumption on pollution in country NF. Thereby, this paper adds to the existing literature by analysing how this increased awareness may affect consumers' demand for the domestic and the foreign good and, therefore,firms' endogenous technology choice. Also, changes in each country's and aggregate pollution are examined in order to assess whether having domestic consumers aware of foreign emissions could be considered as an option for tackling leakage.

### 14/09 Martin Kaae Jensen and Alexandros Rigos

14/09 Evoluntionary Games with Group Selection*

This paper introduces two new concepts in evolutionary game theory: Nash equilibrium with Group Selection (NEGS) and Evolutionarily Stable Strategy with Group Selection (ESSGS). These concepts generalize Maynard Smith and Price (1973) to settings with arbitrary matching rules, in particular they reduce, respectively, to Nash equilibrium and ESS when matching is random. NEGS and ESSGS are to the canonical group selection model of evolutionary theory what Nash Equilibrium and ESS are to the standard replicator dynamics: any NEGS is a steady state, any stable steady state is a NEGS, and any ESSGS is asymptotically stable. We exploit this to prove what may be called “the second welfare theorem of evolution”: Any evolutionary optimum will be a NEGS under some matching rule. Our results are illustrated in Hawk-Dove, Prisoners’ dilemma, and Stag Hunt games.

### 14/08 Deborah Gefang and Geraint Johnes

Asymmetric volatility spillovers between UK regional worker flows and vacancies

This paper investigates volatility spillovers between UK regional job finding, job separation and vacancy rates. Employing a logistic smooth transition vector autoregression (VAR) to model the large nonlinear dynamic system, we use the methods of Diebold and Yilmaz (2012) to decompose the forecast error variances. Our approach is Bayesian. More specifically, we extend doubly adaptive elastic-net Lasso (DAELasso) methods for VAR parameter shrinkage into a nonlinear framework to allow for the possible regime changes. We find that for each variable, both the volatility spillovers to and from other variables are high, providing clear evidence for the close interdependence between UK regional labour markets. The pivotal role of London in generating and spreading changes in volatility is highlighted. Analysis of net spillovers shows that, in general, shocks to job separation rates tend to spread into job finding and vacancy rates. By contrast, vacancy rates are usually at the receiving ends of shocks transmitted from the job separation and finding rates. We further examine the shock propagation mechanism in more detail, such as the differences in spillovers between regions within the same regime, and that of the same region but in different regimes. Finally, we draw inferences that are of economic and policy importance.

### 14/07 Stephen Pollock

A variety of filters that are commonly employed by econometricians are analysed with a view to determining their effectiveness in extracting well-defined components of economic data sequences. These components can be defined in terms of their spectral structures—i.e. their frequency content—and it is argued that the process of econometric signal extraction should be guided by a careful appraisal of the periodogram of the detrended data sequence.

A preliminary estimate of the trend can often be obtained by fitting a polynomial function to the data. This can provide a firm benchmark against which the deviations of the business cycle and the fluctuations of seasonal activities can be measured. The trend-cycle component may be estimated by adding the business cycle estimate to the trend function. In cases where there are evident structural breaks in the data, other means are suggested for estimating the underlying trajectory of the data.

Whereas it is true that many annual and quarterly economic data sequences are amenable to relatively unsophisticated filtering techniques, it is often the case that monthly data that exhibit strong seasonal fluctuations require a far more delicate approach. In such cases, it may be appropriate to use filters that work directly in the frequency domain by selecting or modifying the spectral ordinates of a Fourier decomposition of data that have been subject to a preliminary detrending.

### 14/06 Heather D. Gibson, Stephen G. Hall and George S. Tavlas

Are All Sovereigns Equal? A Test of the Common Determination of Sovereign Spreads in the Euro Area

With the outbreak of the Greek financial crisis in late 2009, spreads on Greek (and other) sovereigns reached unprecedented levels. Using a panel data of euro-area countries, we test whether the markets treated all euro-area countries in an equal manner over the period 1998:m1 to 2012:m6. In a F-test of the pooling assumptions suggests that Greece, Ireland and Portugal were not part of the overall pool. In a separate test on the individual coefficients we find that the coefficients on these three countries moved in a similar direction away from the pool, suggesting that markets treated these three countries more acutely than the rest of the pool.

### 14/05 Stephen Pollock

Econometrics: An Historical Guide for the Uninitiated

This essay was written to accompany a lecture to beginning students of the course of Economic Analytics, which is taught in the Institute of Econometrics of the University of Lodz in Poland. It provides, within a few pages, a broad historical account the development of econometrics. It begins by describing the origin of regression analysis and it concludes with an account of cointegration analysis. The purpose of the essay is to provide a context in which the students can locate various aspects of econometric analysis. A distinction must be made between the means by which new ideas were propagated and the manner and the circumstances in which they have originated. This account is concerned primarily with the propagation of the ideas.

### 14/04 Stephen Pollock

Trends Cycles and Seasons: Econometric Methods of Signal Extraction

Alternative methods of trend extraction and of seasonal adjustment are described that operate in the time domain and in the frequency domain. The time-domain methods that are implemented in the TRAMO–SEATS and the STAMP programs are described and compared. An abbreviated time-domain method of seasonal adjustment that is implemented in the IDEOLOG program is also described. Finite-sample versions of the Wiener–Kolmogorov filter are described that can be used to implement the methods in a common way. The frequency-domain method, which is also implemented in the IDEOLOG program, employs a ideal frequency selective filter that depends on identifying the ordinates of the Fourier transform of a detrended data sequence that should lie in the pass band of the filter and those that should lie in its stop band. Filters of this nature can be used both for extracting a low-frequency cyclical component of the data and for extracting the seasonal component.

### 14/03 Stephen Pollock

Cycles, Syllogisms and Semantics: Examining the Idea of Spurious Cycles

The claim that linear filters are liable to induce spurious fluctuations has been repeated many times of late. However, there are good reasons for asserting that this cannot be the case for the filters that, nowadays, are commonly employed by econometricians. If these filters cannot have the effects that have been attributed to them, then one must ask what effects the filters do have that could have led to the aspersions that have been made against them.

### 14/02 Stephen Pollock

On Kronecker Products, Tensor Products and Matrix Differential Calculus

The algebra of the Kronecker products of matrices is recapitulated using a notation that reveals the tensor structures of the matrices. It is claimed that many of the difficulties that are encountered in working with the algebra can be alleviated by paying close attention to the indices that are concealed beneath the conventional matrix notation. The vectorisation operations and the commutation transformations that are common in multivariate statistical analysis alter the positional relationship of the matrix elements. These elements correspond to numbers that are liable to be stored in contiguous memory cells of a computer, which should remain undisturbed. It is suggested that, in the absence of an adequate index notation that enables the manipulations to be performed without disturbing the data, even the most clear-headed of computer programmers is liable to perform wholly unnecessary and time-wasting operations that shift data between memory cells.