M Giller
email: maria.giller@kfd2.phys.uni.lodz.pl

G Wieczorek

Influence of the scattered Cherenkov light on the width of shower images as measured in the EAS fluorescence experiments

Keywords: Ultra-high energy cosmic rays, extensive air showers, fluorescence method of shower detection PACS: 96.50.sd

Influence of the scattered Cherenkov light on the width of shower images as measured in the EAS fluorescence experiments

M. Giller, G.

Introduction

Extensive Air Showers (EAS) produced in the atmosphere by cosmic ray particles cause excitation of its atoms and a subsequent isotropic emission of fluorescence light by nitrogen molecules. If the energies of cosmic particles are large enough (above ∼ 10 17 eV) this light can be detected by earth-based telescopes, so that the showers can be seen from the side from tens of kilometers away.

Another big advantage of the fluorescence technique is the possibility of registering a light image of a shower from which the shower curve -the number of particles or, strictly speaking, the energy deposit as a function of depth in the atmosphere -can be deduced. This is so because experiments show that the fluorescence light emitted by a shower path element is proportional to the energy loss of shower particles along this element [1,2].

Having determined a shower curve one can calculate the energy of the primary particle (by simply integrating the energy deposit along the track in the atmosphere) in a way (practically) independent of its mass and the actual (unknown) high energy interaction characteristics [3].

The fluorescence technique was used with success by the Fly's Eye experiment [4] and by its successors, the various set-ups of HiRes (see e.g. [5,6]).

In the recently built Pierre Auger Observatory -Southern Site in Argentina [7] this technique has also been applied, but here, apart from the optical telescopes, there are 1600 shower particle detectors covering 3000 km 2 . As the fluorescence detectors operate on clear nights only, in contrast with the particle detectors which are active all the time, the energies of showers registered by the latter (obtained by another method) can be calibrated by the sample of showers registered by both types of detectors.

The problem is that some fraction of shower particles (∼0.36 [8]) also emit Cherenkov light (ChL). Its direction is almost the same as that of the emitting particle velocity, so one might think that this light will not add to the fluorescence flux detected by a telescope situated at a large distance (more than a few km) from the shower. However, the number of Ch photons produced by a high energy particle is 5 -6 larger than its fluorescence (FL) photon count. Thus, many Ch photons accumulate as the shower develops and those scattered sideways constitute a non-negligible fraction of the total light registred by a telescope. If not properly substracted, they might mimic a larger number of electrons (and larger energy deposit) in the shower. This effect has been first aknowledged and allowed for by the Fly's Eye Collaboration [4]. Later some other methods to take it into account have been proposed [9][10][11]. In these papers, however, it was only the total number of Ch photons emitted from consecutive shower track elements that were taken into consideration. Here we are concerned with their lateral distributions (with respect to the shower axis).

A shower image (e.g. as measured in the Auger experiment ) is registered typically by a line of hit photomultipliers on a telescope camera. The closer the shower the broader the image line, because shower particles (mainly electrons of both charges) have some lateral spread, due to the Coulomb scattering in the atmosphere. The breadth of the shower image in both ChL and FL has not been investigated -although, as we shall show in this paper, an answer to this question is important. Góra et al [12] proposed that it is the FL that determines the lateral width of the shower image. In this paper we shall show that it is true only for upper parts of a shower (above its maximum). Widths of images below shower maxima are strongly affected by Ch scattered light. Thus, to correctly determine the energy deposit at a given level in the atmosphere (proportional to the FL emitted there), it is necessary to know exactly how ChL is distributed over the light image, not only along but also across the shower. Only then will one be able to subtract it properly. This is what we shall deal with in this paper (for some preliminary results, see [START_REF] Dawson | Proc. 30th ICRC[END_REF]).

It is clear that the lateral distribution of ChL (LDCh) observed at a given level of shower development depends on the angular and lateral distributions of electrons emitting ChL (we shall call them "Ch electrons") at all higher levels. We shall show that the above distributions of ChL produced at some level of the shower development depend only on the shower age and the height of this level. We shall derive how this follows from the uniquenes of various electron distributions in all large showers (the similarity of showers).

The method of calculation of the lateral distribution of ChL (LDCh)

We show here that due to the similarity of high energy showers [8,9,[START_REF] Giller | [END_REF] it is possible to calculate the lateral distribution of ChL (LDCh) without time-consuming shower simulations, but in an analytical way (with numerical calculations of integrals), using the various earlier determined electron distributions which are universal.

The general idea

The similarity of different showers is based on comparing their characteristics at levels with the same age parameter s.

The age of a particle cascade (at a given level of its development) was introduced while analytically describing developments of pure electromagnetic cascades (initiated by primary electron or photon). It was defined as

s = 3t t + 2 ln(E 0 /ε) ( 1
)
where t is the depth in cascade units, E 0 is the particle initial energy and ε is the critical energy of the medium. The spectra of high energy electrons (with energies E ≫ ε) were shown to be proportional to E -(s+1) dE [15,16].

Formula (1) was first applied by Hillas [17] to cosmic ray showers, initiated by hadrons, in the form

s = 3X (X + 2X max ) ( 2
)
where the term ln(E 0 /ε), being the depth of the cascade maximum, has been replaced by X max -the depth of the shower maximum. He also proposed a form of the energy distribution of electrons depending on s.

Following his idea we have analysed in the earlier papers of our group various electron distributions in showers simulated with the CORSIKA code [18]. We have come to the conclusion that high energy showers are similar to each other in the following sense:

-the shape of the electron energy spectrum at a given level in the atmosphere depends only on the stage of the shower development there, i.e. on the age parameter s [8]; it does not depend on primary particle mass or energy (the same conclusion was obtained by Nerling et al [10]), -the angular distribution of electrons with a fixed energy depends on this energy only -it is the same anywhere in the shower [9]; from the two statements above it follows that the angular distribution of all electrons (with any energy) depends on the shower age only, -the lateral distribution of electrons, if distances are expressed in the Molière unit r M at the level in consideration, depends on the shower age only [START_REF] Giller | [END_REF] (the same holds for electrons with a fixed energy [START_REF] Giller | Proc. 30th ICRC[END_REF]).

It has also been established that fluctuations of the above distributions from shower to shower are very small, so that these distributions can be parametrised and used to describe any individual shower. In particular, when observing a shower with a fluorescence detector and determining the position of the shower maximum, it is possible to asign age parameters to various depths along the shower track. Then the distributions of energy, angle and lateral distance of electrons, at various positions along the shower, can be predicted.

It should be noted, however, that determining shower age from X max only i.e. independently of the depth of the first interaction, X 1 , makes sense if X 1 ≪ X max . For the highest energy showers, when X 1 ≃ 50 g cm -2 for protons (and even smaller for heavier primaries) and X max > 700 g cm -2 , this condition is fulfilled. It means that in this case the actual stage of shower development is well determinied by formula (2). It is obvious that for a neutrino initiated shower the depth X in formula (2) must be measured from the first interaction rather than from the top of the atmosphere.

As we are concerned here with the Cherenkov light, emitted only by electrons with energies above some threshold energy (dependent on the atmospheric density and, therefore, on the height h in the atmosphere), the Cherenkov characteristics at a given level depend not only on the age parameter but on the height as well. However, since we have already found the angular and lateral distributions of electrons with a given energy, we can easily calculate these distributions for all electrons emitting Ch light, by integrating the former above the threshold energy E th (h).

It is convenient to assign to any electron a weight Y ch (E/E th ), proportional to the number of Ch photons it emits per unit path (in g cm -2 ). This weight equals

Y ch E E th = 1 - E th E 2 (3)
Adding up all these numbers at a given level gives what we shall call the number of Cherenkov (Ch) electrons. Multiplying this number by the amount of Ch light produced by an electron with E ≫ E th per unit path, in g cm -2 (a known constant), gives the total Ch light produced at a given level per 1 g cm -2 of shower track.

Calculations

The LDCh at a given depth of shower development s obs , being at height h obs , is a sum (integral) of lateral distributions of ChL resulting from Ch emission at all levels above the given one. It depends on the angular, G e θ (θ; s < s obs , h > h obs ), and lateral, G e x (x; s < s obs , h > h obs ), distributions of Ch electrons in the shower above this level. Here x = r/r M . As we have just discussed these distributions of Ch electrons depend on the age s of the considered level and its height h (strictly speaking -on the air density).

Angular distribution of Ch electrons, G e θ (θ; s, h)

The angular distribution G e θ (θ; s, h) (per unit angle θ) can be calculated from the known angular distributions of electrons with fixed energies, g θ (θ; E) (per unit solid angle) [9], and the energy spectrum of all electrons at level s, f (E; s) [8,10],

G e θ (θ; s, h) = 2π sin θ F (s, h) ∞ E th (h) g θ (θ; E) • f (E; s) • Y Ch E E th • dE (4)
where F (s, h) equals

F (s, h) = ∞ E th (h) f (E, s) Y Ch E E th dE (5)
The normalisation of G e θ (θ; s, h) is such that

G e θ (θ; s, h) dθ = 1 (6)
F (s, h) is the ratio of the number of Ch electrons to the total number of electrons at this level. It has been calculated in [8] that this number does not change much along the shower, being equal ∼0.36. This is a result of two competing effects: the deeper along the shower, the steeper becomes the electron energy spectrum, but at the same time the threshold for Ch emission diminishes. Once the electron energy spectra f (E; s) are known, F (s, h) can be calculated and parametrized as a function of s and h [8].

Both f (E; s) and g θ (θ; E) in ( 4) have been obtained from a sample of simulated showers with E = 10 19 eV and 10 20 eV, initiated by a primary proton or iron nucleus. Thanks to a large number of shower particles in such showers, the above distributions fluctuate very little from shower to shower so that the samples of simulated showers did not have to be large (it was ∼20 showers for each combination of E and mass).

The electron angular distributions, G e θ (θ; s, h), have been calculated as histograms for different s and h.

Angular distribution of Cherenkov light (ChL), G Ch θ (θ; s, h), emitted at level (s, h)

Having the angular distributions of electrons we can easily allow for the ChL angle of emission and calculate the angular distribution of the ChL emitted at a given level, G Ch θ (θ; s, h). This is a very small effect since the Cherenkov angle is less than 1.2 • -the emission angle at sea level by an electron with energy E ≫ E th = 21 MeV.

The idea of calculating G Ch θ (θ; s, h) is shown in Fig. 1. The radii of rings are proportional to the bins of electron angle θ. The number of electrons with angles within a given bin ∆θ equals G e θ (θ; s, h)∆θ. Each electron emits ChL at an angle θ Ch (the small ring around an electron direction). The fraction of Ch photons falling into a particular ring (θ, θ + ∆θ) equals the fraction of the Ch ring circumference within that ring (the dark parts of the Ch ring). Thus, the angular distribution of ChL equals

G Ch θ (θ i ; s, h)∆θ i = A j G e θ (θ j ; s, h) • u ji ∆θ j (7)
where u ji is the fraction of ChL emitted by an electron with angle θ j , falling into the ring (θ i ,θ + ∆θ i ) (found from simple geometric considerations); A is the normalization constant.

The results of our calculations are presented in Fig. 2 for several values of s and h. We have also shown the curves obtained by Nerling et al [10] who parametrised the results of Monte-Carlo shower simulations with CORSIKA. The agreement is very good apart from the angles 1 rad. Nevertheless, the differences are in a region where the emitted flux is more than three orders of magnitude less than that at smaller angles. What we are finally aiming at is to calculate the scattered ChL, to which the contribution of this direct light is very small at large angles. The analytical parametrizations are practically indiscernible from the numerical results. Also shown are simulation results of Nerling et al [10], which are slightly higher at large angles (dashed lines).

ACCEPTED MANUSCRIPT

Lateral distribution (LD) of Ch electrons, G e r (r; s, h), at level (s, h)

In an earlier paper of our group [START_REF] Giller | [END_REF] it was shown that LD of all electrons at a given level in the shower depended on the shower age only if the distance to the shower core was expressed in the Molière unit at this level. When one is interested in the Ch electrons only, then it is natural to examine LD(E), i.e. LD of electrons with fixed energies E, and then integrate them above the corresponding threshold energy at the level's height.

An analysis of the lateral distributions of electrons with fixed energies was done by Giller et al [START_REF] Giller | Proc. 30th ICRC[END_REF]. It was shown that if electrons with a fixed energy (in practice, from a narrow energy band) were considered, their LD depended only on the shower age s at the corresponding level.

A new distance unit was used there, r E , depending on the electron energy E and equal to

r E = X 0 • 21 MeV/E ( 8
)
where X 0 = 37 g cm -2 is the air cascade unit. Our distance unit r E differs from the Molière radius in substituting the electron energy E for the critical energy of the medium (∼80 MeV for air). By doing so the parameters describing LD(E) for different energies do not vary much and are more easily described in an analytical way.

One may wonder why LD(E), for any particular electron energy E, depends on shower age s, while the angular distribution does not. It is because the air density in the atmosphere is not uniform; in particular, it has smaller density higher up. The inhomegeneity of the medium does not affect the angular distributions. For an electron with a given energy the angles of its more energetic parents do not play any significant role, as the scattering angles add in quadrature.

The same would be for distances in a uniform medium. However, in the real atmosphere the lateral distances of the parents, as it turns out, are not negligible in comparison with those of their lower energy doughters, because of lower densities higher up.

To see whether the LD of all Ch electrons are important in calculating the LDCh (LD of Ch light) we first calculated the mean squares of LD(E), r 2 (s; E) .

LD(E) are very well described by Nishimura-Kamata-like functions of the form

g r (r; s, E) = 1 N e • dN e d log(x) = Cx α (1 + kx) -β (9)
where x = r/r E and the parameters α, β and k depend on E, and k depends also on s [START_REF] Giller | Proc. 30th ICRC[END_REF]. Thus, x 2 (s; E) can be found analytically and the result is

x 2 (s; E) = k -2 Γ(α + 2) Γ(β -(α + 2)) Γ(α) Γ(β -α) (10)
and

r 2 (s; E) = x 2 (s, E) • r 2 E ( 11
)
To calculate r 2 (s, h) of all Ch electrons at a given level (s,h) one simply needs to integrate the above mean squares over electron energies, weighted with their energy distribution f (E; s) and the Ch yield Y ch E E th (formula 3):

r ⊥ ≡ r 2 (s, h) = ∞ E th (h) r 2 (E; s, h) • f (E; s) • Y Ch E E th • dE ∞ E th (h) f (E; s) • Y Ch E E th • dE (12)
The LD of Ch electrons at level (s, h) equals

G e r (r; s, h) = 1 F (s, h) E 0 E th g r (r; s, h)f (E; s)Y Ch E E th dE ( 13
)
with the normalization

+∞ -∞ G e r (r; s, h) d log r = 1 ( 14
)
Of course, the LD of Ch light emitted by the electrons will be the same, so that

G Ch r (r; s, h) = G e r (r; s, h) (15)
The parametrization of the above distribution is presented in the Appendix.

The results of our calculations are shown in Fig. 3. The parametrization functions are also presented and it can be seen that the fit is everywhere better than 5%.

A comparison of the importance of lateral and angular distributions of electrons

To check on the influence of the two distributions (lateral and angular) on the LDCh at some level we have compared the rms radii of the ChL distribution, r rms , that would have resulted from each of these distributions alone. The situation is demonstrated in Fig. 4 where such a comparison is shown. The chosen level is at s = 1.2 (1050 g cm -2 ) for a typical proton shower with E 0 = 10 19 eV.

The curves show r rms of the LDCh contributions produced at level X (per unit path), as would have been observed if electrons had had no lateral spread, r θ , and if they had had no angular spread, r ⊥ . r θ equals the distance between the level X and that corresponding to s = 1.2 (X ≃ 1050 g cm -2 ), multiplied by the root mean square tangent of the angle of Ch electrons at level X. These two radii show effective spreads of ChL if only one distribution (lateral or angular) had been responsible for it. If both distributions were independent from each other the resulting mean square distance would be the sum of the squares of both radii. Thus, the smaller one must be comparable to the larger, to be important. We can see that it is the contributions from only the last ∼100 g cm -2 for which the lateral distribution of electrons plays a role. We have also ploted a curve proportional to the number of electrons N(X) for a typical 10 19 eV proton shower. It can be seen that the region of X where the lateral spread of electrons is important is rather small.

Final calculations of LDCh arriving at depth X obs

Not withstanding the expected small influence of the LD of Ch electrons on the LDCh arriving at some level, we do take it into account but in a somewhat simplified way. For each slant depth element ∆X where the ChL is produced and arrives at the considered level X obs , we checked which of the distributions, angular or lateral, would itself have given broader Ch lateral distribution at this level. If r θ > r ⊥ (the case for most of the shower path) then we assumed that the ChL contribution of this element has a shape following from the angular distribution of this light, but each distance r is increased by a factor 1 + (r ⊥ /r θ ) 2 . Thus, the number of Ch photons, d(∆N ch ), produced along a shower path dX at angles (θ, θ + ∆θ) equals for this case

d(∆N Ch (θ)) = k N e F (s, h) G Ch θ (θ; s, h) ∆θ dX ( 16
)
where k is the maximum number of Ch photons produced by one electron (172 photons per g cm -2 in the wave band 300 -400 nm). These photons would have arrived at the annular element of the core distance (r, r + ∆r) at level X obs , where r = y tan θ, ∆r = y ∆ tan θ and y is the distance (in length units) between the two levels X and X obs . However, to allow for the lateral distribution of the emitting electrons, we assign these photons to a larger ring (r ′ , r ′ + ∆r ′ ) where

r ′ = r • 1 + (r ⊥ /r θ ) 2 and ∆r ′ = ∆r • 1 + (r ⊥ /r θ ) 2 (17)
In the opposite case, if r ⊥ > r θ then

d(∆N Ch (r ′ )) = k N e F (s, h) G Ch r (r; s, h) ∆ log r dX ( 18
)
where G e r (r; s, h) is the LD of Ch electrons at (s, h), r ′ = r • 1 + (r θ /r ⊥ ) 2 and d(∆N ch (r ′ )) is the number of photons assigned to the annular distance element (r ′ , r ′ + ∆r ′ ). This procedure gives in any of these cases a lateral distribution of ChL for which

r 2 = r 2 θ + r 2 ⊥ ( 19
)
that would ensure the correct value of r 2 if the two distributions were independent of each other. As they are not (more distant electrons have lower energies and, what follows, larges angles) we underestimate the calculated LDCh. We think, however, that this underestimation is rather small because, as can be seen in Fig. 4, the region of X where both distributions have comparable widths (so that a correct calculation of the contribution of ChL from there to the total LDCh at level (s obs , h obs ) would be needed) is small.

To allow for extinction, the numbers of photons in ( 16) and ( 18) need to be multiplied by a transmission factor T X obs -X cos α

. It is enough to adopt that

α = arctan r 2 /y (20)
The atmospheric transmission properties change quite considerably, so that the actual LDCh depends on the particular time the shower occured. However, we shall show results of LDCh calculations for some typical atmospheric conditions in § 3.

Dependence on zenith angle

All the above considerations apply to showers with any zenith angle, i.e. the lateral and angular distributions of ChL produced at a given level in the atmosphere depend only on shower age s and height h in the atmosphere, independently of the shower zenith angle z. It does not mean, of course, that the LDCh arriving at some level and, in consequence, the LD of the Ch light scattered at this level, does not depend on the shower zenith angle z.

Let us consider how the LDCh depends on z. For each vertical shower with a given energy, with a cascade curve N(X), there is equally often (per unit solid angle, time and area) an inclined shower, at some zenith angle z, with the same N(X). It is easy to show that its maximum will be higher in the atmosphere by

∆h = -H • ln [cos(z)] ( 21
)
where H is the exponential scale height of the atmospheric density. The situation is shown in Fig. 5 where we have roughly sketched both showers and, perpendicularly to shower axes, the number of particles N(X). We can obtain N(h; z) for the inclined shower by shifting the vertical shower up by ∆h and then projecting the number of particles horizontally on the inclined axis, so Fig. 5. Illustration of a geometrical situation of two showers having the same N (X) but different zenith angles. The inclined shower can be constructed from the vertical one by shifting it by some heigth ∆h and then projecting on the inclined line.

that

N(h; z) = N(h -∆h; z = 0) (22)
The inclined shower is more elongated than the vertical one, when measured in units of length. Any shower element dX(X) has a distance y to a fixed level X obs (where we are calculating LDCh) larger by a factor 1/cos(z) than the corresponding element dX(X) in the vertical shower. If all electrons had emitted ChL then the LDCh would have been the same if lateral distances were scaled by this factor. As the Molière radius (in meters) at the level higher by ∆h increases also by 1/ cos(z), then the LDCh expressed as a function of x = r/r M would have been the same in the showers having the same N(X), independent of their zenith angles.

However, the threshold energy of the element dX of the inclined shower is higher by factor 1/ cos(z) so that there is less Ch light and the LDCh is slightly steeper. This is demonstrated in Fig. 6.

Showers, however, do fluctuate, mainly due to the fluctuations of the depth of the first interaction. Let us compare two showers, one vertical, another inclined (as before), but now with the same N(X -X max ). Assume that the inclined shower initiated deeper in the atmosphere than the vertical one, so that both maxima are at the same height above the observation level. It is easy to show then that the inclined shower will be more compressed than the vertical one, in the sense that the slant distances (in length) between levels with the same X -X max are smaller in the inclined shower that in the vertical one. This will influence the LDCh making it narrower.

In conclusion, even if the atmosphere had been ideally stable with a known dependence X(h), to calculate LDCh at some level in a shower in advance an additional parametrization of it as a function of zenith angle z and depth of shower maximum X max would be necessary (apart from that on s and h).

Results of calculations of LDCh

As we have already mentioned, to calculate the LDCh at a particular level in a shower it is necessary to know the attenuation and scattering properties of the atmosphere. As these depend on the season and may change from one night to another, or even within one hour or so, constant atmosphere monitoring is needed. This is being performed e.g. in the Auger experiment [7,[START_REF] Keilhauer | [END_REF]. However, to show what will be a typical width of a shower image in ChL and compare to it with that in fluorescence light, it is enough to adopt typical atmosphere properties.

Here we have assumed an atmosphere corresponding to the average conditions at the Pierre Auger Observatory in Argentina, with the mean free path for Rayleigh scattering λ R = 18.4 km and for aerosol (Mie) scattering λ M = 14 km at the Auger level. The exponential scale heights are correspondingly H R = 7.5 km and H M = 1.2 km.

In the experiments using the fluorescence technique the telescopes look at showers from the side (at rather large angles to shower directions). Thus, to compare both widths, in ChL and FL, of a shower image we have to calculate the ChL scattered sideways from the shower direction. As the FL is emitted isotropically from any shower element and the Rayleigh scattering is roughly isotropic (∼ 1 + cos 2 θ) we compare here numbers of Ch photons Rayleigh scattered in all directions. The proportion of the two components will be almost the same as if observed from any particular direction.

The results of calculations are presented in Fig. 6. We have chosen three levels of shower development: s = 0.9, 1.1 and 1.3 for which a comparison of the lateral spread of the scattered ChL with that of FL is shown. The curves are for typical proton and iron showers, inclined at three zenith angles: 0 • , 45 • and 60 • . The curve representing FL does not depend on zenith angle, nor on primary particle, as the lateral distribution of shower electrons depends on shower age only, if represented as a function of r/r M (as has been discussed earlier). To calculate the FL curves we have used the parametrisation of Góra et al [12].

In calculating widths of shower images these authors take into account FL only. Our results show that this is proper only for widths above (in height) shower maximum (s < 1). Fig. 6 shows that at s = 0.9 the contribution of the ChL to the FL is small. However, when s increases the ChL contribution increases also. For s = 1.1 (Fig. 6) it starts to dominate FL above one Molière radius, or so. Even deeper in the atmosphere (s = 1.3) it is the ChL which practically determines the lateral spread of the image. This corresponds to the Auger level for a 10 19 eV proton shower with z = 45 • . Thus, the LDCh can not be neglected when reconstructing the energy losses of shower particles at these levels, which are proportional to the fluorescence intensity only.

The Rayleigh (molecular) scattering is not the only process relevant. The ChL can also be scattered by aerosols present in the lower parts of the atmosphere, what is called the Mie scattering. The angular distribution of light scattered by this process depends on the size of the aerosol droplets, but for any size the distribution is rather strongly peaked forward. Thus, the Mie scattered light will contribute a little to the total light from showers observed usually at rather large angles to their axes.

However, a contribution of the Mie scattered light can be easily taken into account:

Let us denote by λ R and λ M the mean free paths for Rayleigh and Mie scatterings respectivelly, and by f R (θ) and f M (θ) the angular distributions of the scattered light for the two processes. If a shower is observed at an angle θ, then the full contribution of the scattered ChL (by both processes) can be obtained by multiplying our values from Fig. 6 by

1 + λ R f M (θ) λ M f R (θ) (23)
For example, at 2 km above the Auger level (∼ 1450 m) the mean free paths would be λ R = 24 km and λ M = 74 km, for the values given in § 3. Then the factor (23) allowing for the Mie scattering, for f M (θ) = 0.

Discussion

A proper reconstruction of the energy losses, and in consequence, of the primary energy, depends of course on how well the shower light is recovered. The data from a FL detector are in a form of the camera PMTs response in consecutive time bins (100 ns in Auger). To recover the actual signals in the consecutive time bins one looks around the direction towards the shower at a particular time (we assume that the geometry of the shower is known) and finds the total signal in the PMTs inside a viewing cone with an opening angle ζ. Summing up signals over all time bins and finding the opening angle ζ for which the signal S to noise N ratio is the largest one can hope that the signal of the whole track is within the viewing cone.

However, as ζ is the same for the whole track but the track width becomes larger when going down, it may happen that the light from lower parts of a shower will be cut out by too small an angle ζ.

This angle depends on the distance to the shower. Barbosa et al [START_REF] Barbosa | Proc. 29th ICRC[END_REF] calculated that the optimal angle ζ for a 5 km distant shower was ∼ 2.4 • . We calculate that for a 10 19 eV proton shower with z = 45 • the signal from the level s = 1.3 (just above the earth at Auger) would be collected from within r/r M < 2.1 cutting out almost half of ChL and ∼9% of Fl. (The same would happen for a 10 km distant shower and ζ = 1.2 • .) If all Ch light was subtracted from the signal this would decrease the infered FL signal from this level by ∼40%. We estimate that the primary energy of such nearby showers could be underestimated by ∼15% or so.

Summary and conclusions

We have shown that the lateral spread of the scattered Ch light has an important role in determining the width of the optical image of a shower, particularly below shower maximum. This result has been obtained without time-consuming simulations of extremely high energy showers dedicated to Cherenkov light. To do this, we have used our earlier results showing universality of the properties of large showers. We have also derived that the angular and lateral distributions of Ch electrons at some level in the atmosphere, responsible for the width of the optical image of a shower, depend on shower age and of this level only. Thus, the properties of the ChL produced at a particular level in the atmosphere depend only on the height h of this level and the stage of the shower development, measured by the age parameter s.

It is advisable to parametrize the angular distribution of ChL at this stage, as the parametrization of the image width would have to depend on another two parameters X max and z.

A full understanding of the optical shower image is nessesary to correctly infer the energy losses of shower particles along their propagation in the atmosphere. If the LDCh was broader than it is aknowledged then too much ChL could be subtracted from the total signal, leading to an underestimation of the shower primary energy.

Aknowledgments

The authors are grateful to dr. Bruce Dawson for fruitful discussions and to The Auger Collaboration where the problem of broad shower images has arisen.

The Polish Science and Higher Education is thanked for grant no 1P03 D0 1430. Having found numerically G Ch θ (θ; s, h) we have parametrized it (similarly as in [9] for all electrons) as follows

G Ch θ (θ; s, h) = 1 N Ch dN Ch dθ =              a 1 • e -(c 1 •θ+c 2 •θ 2 )
for θ < θ 0 The values of the parameters have been found by a minimization procedure, to fit best the numerical values. They are given in the table below.

p i θ 0 a 1 c 1 c 2 α p 0 6.058e+00 2.905e+00 7.320e+00 -2.754e+00 2.620e+00

Fig. 1 .

 1 Fig. 1. Illustration of the method of taking into account the Cherenkov cone: the angular distribution of Ch electrons gives the number of electrons within each annular ring (θ, θ + ∆θ). Ch light is emitted at an angle θ ch to the electron direction. The number of produced Ch photons, having angles to the shower axis within this ring, is proportional to the fraction of the circumference (2πθ ch ) lying inside this ring (the dark shaded regions).

Fig. 2 .

 2 Fig. 2. Angular distributions of Ch light, G Ch θ (θ; s, h), emitted at s=1 -two upper graphs and s=1.2, -lower graphs, left graphs -h=5 km, right graphs -h=8 km.The analytical parametrizations are practically indiscernible from the numerical results. Also shown are simulation results of Nerling et al[10], which are slightly higher at large angles (dashed lines).

Fig. 3 .

 3 Fig. 3. Lateral distributions of Ch light, G Ch r (r; s, h), emitted at s=1 -two upper graphs and s=1.2, -lower graphs, left graphs -h=5 km, right graphs -h=8 km. Points -results of calculation, lines -best fit parametrization. Error bars represent 5% of the value.

Fig. 4 .

 4 Fig.4. Root mean square (in meters) of the lateral distribution of Ch light, produced at X and observed at depth X obs = 1050 g cm -2 ; r θ -if Ch electrons had only an angular distribution (no lateral spread), r ⊥ -if Ch electrons had only a lateral distribution (no angular spread). Two curves for each case correspond to zenith angles z = 45 • , 60 • . Also shown is the shower curve N e (X) (in arbitrary units).

Fig. 6 .

 6 Fig.6. Number of Ch photons scattered at distances larger than r, (per 1 m) divided by total number of electrons, N e , compared with the fluorescence light (line marked FL) produced at distances larger than r along the same path. Three graphs correspond to values of age: s=0.8, 1.1, 1.3. Curves for proton showers are higher than those for Fe; curves for larger zenith angles are lower. The importance of ChL on the lateral width of the shower light image is evident below the shower maximum.

7. 1

 1 Parametrization of the angular distribution of the emitted Ch light, G Ch θ (θ; s, h)

a 2 •

 2 θ -α for θ > θ 0 (24) Parameters of the distribution (24) are dependent on s and h (in km, above sea level) in the following way:b(s, h) = p 0 • e p 1 •s+p 2 •h + p 3(25)where b = θ 0 , a 1 , c 1 and α, and:c 2 (s, h) = p 0 • e p 1 •s 2 +p 2 •h + (p 3 • s 2 + p 4 • s)(26)for parameter c 2 .a 2 can be obtained from the condition of continuity of the angular distribution at θ 0 .

p 1 - 1 .

 11 103e-03 -3.851e-02 -3.778e-01 -4.242e-01 6.837e-02 p 2 -2.886e-03 1.072e-01 7.202e-02 1.084e-01 -2.247e-02 p 3 -5.447e+00 1.066e+01 7.143e+00 3.344e+00 1.110e+00 p 4 -4.294e+00

The deviation of the parametrization functions from the numerically calculated values reach ∼ 10% at large angles. They are, however, a few percent for small angles. We have parametrized the lateral distribution G Ch r (r; s, h) as follows:

where C guarantees the correct normalisation, and equals:

The dependence on s and h (in km, above sea level) is as follows:

The values of the parameters are:


Dr Anthony Hoare

Dr Mark Corver

The regional geography of new graduate labour in the United Kingdom

Keywords: Participation rates Higher education capacity University catchments entwickelten Datenbank der bisherigen Wohnsitze, Universitäten und ersten Arbeitsplätze von Studenten in Großbritannien entwickeln wir in diesem Beitrag einen Rahmen zur Modellierung von Strömen zwischen diesen Standorten. Hochschulabsolventen, die von einem Arbeitsmarkt angeworben werden, werden nach vier verschiedenen Anwerbungswegen klassifiziert Auswirkungen der Abschlussklasse. Anschließend erklären wir die ausgeprägten Unterschiede bei den Ergebnissen der Regionen und schlagen politische Maßnahmen für Regionen vor, die in diesem Prozess der interregionalen Wechselwirkungen momentan potenzielle Arbeitnehmer mit Hochschulabschluss verlieren Anwerbung von Arbeitnehmern mit Hochschulabschluss Großbritannien Regionalanalyse Teilnehmerzahlen Hochschulkapazität Contratación laboral H75 -health, education

Using a newly-constructed database of UK undergraduates' previous residences, universities and first employment this paper develops a framework to model the flows between these locations. Graduates recruited by any labour market are classified into four recruitment pathways. The model is then applied to the UK regional system for four successive graduating cohorts from 1998/9. We identify clear winner and loser regions in graduate recruitment, the different roles of the four pathways and the effect of degree class. We then explain these markedly different regional outcomes and suggest the policy prescriptions for regions that currently lose potential graduate workers in this process of inter-regional interaction.

Introduction

In recent years the UK government has attached importance to more people entering higher education (HE) not just for the social benefits of wider and deeper participation but also the economic benefits of more highly educated workforce. A recent official example of this thinking is Lord Leitch's report on long-term skills needs (H.M. Treasury, 2006) which argued for a wholesale uplift in adult skills, including raising those with at least graduate skills from 29% in 2005 to 40% by 2020. Although some have questioned sending more people to university (Anon,2004;Alpin and Shackleton, 1998;Dolton and Vignoles, 2000;[START_REF] Wolf | Does Education Matter ? myths about education and economic growth[END_REF], most commentators would argue that a more university-educated population makes for a more humane, cultured, and socially-responsible citizenry and adds materially to the life-long earnings of the individual and the wealth-generating capacity of the nation [START_REF] Bynner | Revisiting the Benefits of Higher Education, Centre for Research on the Wider Benefits of Learning[END_REF].

Where the economic role of higher education has been considered at a regional level it has usually (for example, [START_REF] Boucher | Tiers of engagement by universities in their region's development[END_REF]HEFCE 2001;Kitgagaw, 2004[START_REF] Thomas | Speech at university of Bristol Enterprise Dinner, 1 st[END_REF] focussed on two lines of argument. First, that universities serve as 'basic' economic sectors, 'importing' jobs and income that cycle and recycle around the regional environments ( see [START_REF] Bleaney | What does a university add to its local economy[END_REF], [START_REF] Brownrigg | The economic impact of a new university[END_REF][START_REF] Mcnicholl | The impact of Strathclyde University on the Economy of Scotland[END_REF], Sanders, 2002); and second, through their research capacity entrepreneurial talent is 'spun off' beyond campus boundaries and into the region beyond (Deilmann, 1992;[START_REF] Forrant | Pulling together in Lowell : the university and the regional development process[END_REF][START_REF] Howells | Industry-academic links in research and innovation : a national and regional development perspective[END_REF][START_REF] Howells | Industry-academic Links in the UK[END_REF][START_REF] Keeble | High-technology industry and regional development in Britain ; the case of the Cambridge phenomenon[END_REF]Passos et al, 2004;[START_REF] Oh | Technology-based regional development policy : case study of Taedok Science Town[END_REF][START_REF] Westhead | Links between higher-education institutions and high-technology firms[END_REF]. In both respects some regions are better served with universities in proportion to their size than others. Thus pressures mount first to 'fill the gaps in the maps', exemplified in the United Kingdom by lobbies for further HE investment in Cornwall, Cumbria, Lincolnshire and the Highlands and Islands (eg Hills and Lingard, 2004 ; , 2003), and, second, to achieve critical mass in research capacity through consortia of regional (Fazackerley, 2005a[START_REF] Fazackerley | North flaunts strengths[END_REF][START_REF] Wojtas | Physicists build up critical mass[END_REF].

Our concern in this paper is with a third facet of the HE-regional economic interface -the recruitment of graduate labour -that seems less frequently considered (though Hartshorn and Sear 2005 provide a recent exception).

Here too some regions are relatively better placed than others, in ways and for reasons we focus on in the remainder of the paper. Section 2 outlines a simple model of home-university-labour-market transitions (our ' HULT' model) which Section 3 compares to current research evidence and to contemporary debates in the UK. This is also the context for our empirical exploration of the HULT model, using a novel dataset outlined in Section 4 and producing the results of Section 5. These describe the important flows and explore which component(s) of the HULT pathways might be most effectively changed to yield an increase in graduate labour. Section 6 provides a summary, some implications and extensions.

Framework for Analysis

Consider the simplest possible HULT system, with just two hypothetical regions, North and South (Figure 1a). Each is a source of undergraduates who enrol at universities in either region from where they subsequently move to graduate employment, again in either region. Four 'H-U' enrolment streams can thus be identified with an 'Hxx'-type label, thus HSN is the stream of previously-Southern (S) residents who enrol in North's (N) university.

Similarly four 'U-L' employment streams of 'Lxx'-type labels, similarly derived, link both universities' graduates to their first-job labour regional market : so We can also view these pathways from the perspective of the recruiting labour markets. North and South again have four separate pathways from which they can recruit graduates. Using the Southern labour market as the example we can classify these as follows :

• the Locals pathway (Cell 1 of Figure 1b : stream HSS + stream LSS) : these are home students from the South who also studied there before also taking a job in the South.

• the Returners pathway (Cell 2 :HSN + LNS) : those originally from the South but studying in the North, before returning South for work.

• the Stayers pathway (Cell 5 : HNS + LSS) : Northerners who decide to remain in the South after studying there.

• the Outsiders pathway (Cell 6: HNN + LNS) : these take a Southern job, despite their home and study experiences being from the North. The absolute numbers recruited through each pathway are the product of the number of graduates who are potential Southern workers multiplied by the rate at which these convert to Southern rather than Northern jobs. More formally, these 'potential' and 'conversion rate' elements are respectively defined for each pathway as follows, the first term representing the potential and the second the conversion rate: Locals = (cell 1 + cell 3) x (cell 1 /(cell 1 + cell 3)) Returners = (cell 2 + cell 4) x (cell 2 /(cell 2 + cell 4)) Stayers = (cell 5 + cell 7) x (cell 5 /(cell 5 + cell 7)) Outsiders = (cell 6 + cell 8) x (cell 6 /(cell 6 + cell 8))

Students exercise choice in where to work, and we assume that personal familiarity, either from experiences prior to, and/or while at, university should be positive factors. Assuming the locals pathway benefits from the pull on jobchoice of both 'home' and 'study' we predict its conversion rate will be the highest of the four. On similar logic, that for outsiders should be the lowest, having neither of these pulls, and those of the stayers and returners intermediate between them. We also identify as a region's 'gain rate' the graduates it attracts at the 'L' stage compared to those it generated in the same cohort at the 'H' stage. For each region this is the sum of their four graduate pathways divided by the sum of the four employment streams they attract divided by the sum of the four enrolment streams they generated, as follows:

South gain rate = ((cell 1 + cell 2 + cell 5 + cell 6) / (cell 1 + cell 2 + cell 3 + cell 4)) x 100 % North gain rate = ((cell 3 + cell 4 + cell 7 + cell 8) / (cell 5 + cell 6 + cell 7 + cell

8)) x 100%

Where the gain rate exceeds 100 the region is a graduate 'winner', recruiting more than it generates, and where below 100 a 'loser' region with the opposite characteristics.

For empirical application, of course, this two-regional model has to work in an N-regional context. However, for simplicity of analysis in the UK case to follow (where N = 12) we maintain the same 4-fold classification of recruitment pathways and conversion rates by amalgamating all regions other than the one under consideration, and ignoring the 'internal' flows among them of enrolling undergraduates and recruited labour. So for those graduates recruited by the South West region, for example, locals would be its 'home' students also studying there, returners would be its 'home' students studying in the UK anywhere outside the South West, stayers those whose home But before that, we review what we know of such HULT-type mobility thus far in the UK and beyond, and its role in current debates on regional economic growth in Britain.

: Contexts

: Academic

The key underlying principles to our investigation -that education facilitates geographical mobility which in turn is characterised by geographical disequilibria -is, of course, part of the received wisdom of the social sciences. Differential regional economic growth is far too complex to be 'explained' by just one factor (migration) let alone one sub-factor (graduate migration), but there is a case for believing the latter to have become relatively more important. A detailed overview of the geography of migration in late 20th century Britain portrays internal migration (our focus here too) as being of the young, highly educated, start-of-career or early-career professionals (Champion and Fielding, 1992). As regional specialisation has shifted to one structured on occupation rather than industrial categories so only certain locations can provide the high-flier career opportunities these migrants seek, and the training capacity for them. This reinforces the virtuous Britain's regions, a vicious one of the draining-away of human capital in others. So regional inequalities widen. Neoclassical regional theory may depict migration as a force for inter-regional equilibrium, but contemporary realities are very different.

More recent work [START_REF] Champion | Migration and Socioeconomic Change : a 2001 Census analysis of Britain's larger cities[END_REF] sharpens the focus on the 'graduate process' in such internal migration flows, and thereby on the population growth of major British cities. Analysis of longer-distance migration from the 2001 Census shows the important role here of the movement of full-time students to university, although their levels and patterns of migration after graduation cannot be traced so surely. The authors nevertheless believe their results underline the role of mobile, high-skilled graduate workers in supporting the growth points of the modern 'information economy', particularly in London. London's gain is others' loss, so these highly mobile, intending and actual graduates add further to these upwards and downwards cycles, in the HE sector (see for example, [START_REF] Hoare | UK public policy and the emergent geography of Higher Education, Being Ch[END_REF].

But this recent evidence only sheds partial light on the realities of the HULT system. The same is also true of other evidence derived from a range of other geographical contexts. Table 1 provides But as far as our present focus is concerned -continuous time-series tracking across H-U-L of the same individuals and within a national set of regionsfew precedents exist. Kodrzycki's first study from Table 1 [START_REF] Kodrzycki | New England's educational advantage : past successes and future prospects[END_REF] adopts a variety of source materials to examine New England's performance and apparent decline over time in generating, training and attracting graduate workers compared to other regions. Her second [START_REF] Kodrzycki | Migration of recent college graduates : evidence from the National Longitudinal Survey of Youth[END_REF] uses one of them, the US National Longitudinal Survey of Youth (1979Youth ( -1996)), to follow high school migrations to college and then for the first 5 years of employment.

Graduates subsequently emerge as more mobile than non-graduates.

Migration rates to college (H-U) are lower than after college (U-L), but the former also differentially encourage the latter. Clear winner and loser regions emerge in the graduate job league, rationalised by differences in their labour markets dynamism and amenity attractions.

The first UK study (Osborne et al, 1987) traces the early employment experiences of Northern Ireland students entering HE in 1979, whether there or beyond the region, noting the roles of gender, religion, academic subject and degree class. The Province emerges with a serious net loss of graduate labour from that cohort, and for our purposes it is pertinent that this is especially so for those attaining high class first degrees (upper seconds orf better). The other UK HULT-type study (Belfield and Morris, 1999) (of 1985 and 1990 ) to their first employment. These migrations again are unbalanced, and their statistical modelling and follow-up investigations suggest some of the personal and regional characteristics encouraging mobility. Interestingly, those migrating to study (ie the H-U leg) tend to be less satisfied with their courses. However, their results depend on limited samples (35% response rates from 20% of British universities) and their transitions are analysed as a set of separate legs (H-U;U-L;H-L) rather than as a continuous process. Since then the relevant datasets have improved, and the financial climate in which British students study has also changed significantly.

: Political

So have the ways in which regional labour-forces are politicised into related economic strategies. Since 1997 nine Regional Development Agencies (RDAs) have added a new and energetic component to economic analysis and policymaking in England, building on experience of equivalents in Wales and Scotland. In pursuit of their task 'to co-ordinate regional economic development and regeneration, enable the English regions to improve their relative competitiveness and reduce the imbalances that exists within and between regions ' (ODPM, 2005) a set of regional reports (appearing around 2000) were produced where the paramount activity was medium-term (usually to about 2010) regional economic strategies. And their single most prominent At the most basic level this meant upgrading literacy, numeracy and the culture for learning amongst the low and unskilled. At the 'top end' the focus was on specialist and high-level skills. Universities represented the major source of these, as some RDAs explicitly appreciated in their strategy pronouncements. Thus that for the North East region underlined the need for '[p]lacing universities and colleges at the heart of the region's economy' (ONE NorthEast, 2000), in part precisely because they are a source of training and skills among the workforce. This is the closest the RDAs have come to the symbiosis between labour market needs and the HE sector advocated by [START_REF] Goddard | Regional Development Agencies and the knowledge economy : harnessing the potential of universities[END_REF], giving them an explicit 'third role' alongside their traditional contributions to teaching and research. The neighbouring North West stressed the importance of retaining graduates for its own economic benefit in its Skills and Learning Strategy (Northwest Development Agency, 2000). And the East Midlands furthered its vision of transforming the region's educational providers into 'a dynamic strategic force for economic development' (East Midlands Development Agency, 2000a), partly through its then on-line 'Getonwithgraduates' scheme (East Midlands Development Agency, 2000b) which paired, intra-regionally, the career paths of relevant graduates with the needs of employers.

The former Department for Education and Employment's HERD (Higher Education and Regional Development) Fund also aimed 'to increase higher education's contribution to regional competitiveness by developing its responsiveness to local or regional employment markets' (DfEE, 1999).

Partners to its supported ventures included universities among other educational establishments, and private and public sector representatives (1).

But however formalised through public policy, regional stocks of skilled labour depend on significant inflows and outflows at different stages in the HULT process. In an inter-regional, zero-sum-game context, there will inevitably be regional winners and losers. However, one could be forgiven for overlooking this in the cascade of words in RDA publications and web-sites. There we find scant awareness of these inter-regional flows, let alone how well (or badly) a particular region fares from them.

Data sources

So both empirically and politically the case for a more rigorous HULT-type analysis seems clear. Our application of it to the reality of the UK experience for the first time, rests on a fundamental advance in the structure of available time-series data. The recent linking together of hitherto separate UK data sets focussing on the 'H-U' and 'U-L' segments of our model is part of a wider transformation of the scope and accuracy of HE sector statistics. The first graduate cohort to be so treated -the 1998/99 graduates -is also our starting point.

The basic approach is to use multi-stage matching across a range of personal data from individualised records to produce a matrix of links between (and within) datasets, before resolving these links into a logically consistent (HEFCE, 2005 pp 168-170). Starting with algorithms developed by one of us for determining undergraduate non-completion rates and university access statistics (HEFCE, 1999), this approach has been extended to launch studies of participation patterns (HEFCE, 2005a;[START_REF] Fazackerley | North flaunts strengths[END_REF] and undergraduate progression (HEFCE, 2003). Our analyses here take a first look at a hitherto unexplored aspect of these new data sets -the linked geographies of undergraduate origin, study and first employment.

The first two geographies derive from the HESA (Higher Education Statistics Agency) student records. This individual level data set provides course and personal details, including the postcode of the pre-admission residence. We supplement the student personal details by linking to the Universities and Colleges Admissions Service (UCAS) data sets. Whilst this linking does raise the (already high) valid postcode coverage for young entrants to around 99 per cent (HEFCE 2005b, p 179) its main advantage is in the elimination of term-time postcodes sometimes erroneously returned on the HESA record.

These residence postcodes, in combination with the location of the university attended, form the basis of a 'H-U' classification. The 'H' here really is the 'home' location, rather than that of school. The two are usually geographically close, though not necessarily so for boarding schools. Occasionally a student's term-time address will be elsewhere (notably for Home Counties, home-based students studying in London) while some universities have locations for first-degree study in other regions (HEFCE 2004), but neither should make a material difference to the broad patterns of H-U-L transitions we identify. Our first look at the data neglects these complications. A review of FDS identified some weaknesses, such as inconsistency in how and when first employment was recorded and in the practice of universities in exhorting selected recent graduates to respond. This led to improvements to the FDS for 2000 such as a common survey reference date and more data quality cross-checks by HESA. Our analyses span the pre-and post-review period, but the stability of results suggests this has not been a major break in the series. Bias may persist for our purposes if the differential energies of universities in chasing their FDS respondents and keeping sound records map onto different H-U-L profiles. It is also the case that the FDS response rates vary across groups of graduates, for example graduates who go on to postgraduate study are more likely to respond (HEFCE 2005b, pp 231-232).

It seems likely that a similar response bias would exist between, for example, Applying restrictions (a) and (b) leaves some 671,000 graduates. The further stipulation that they be young on entry reduces the total again to 525,000 graduates. The effect of these restrictions is to remove geographical compilations (such as those who have transferred between institutions, and those who are having a second chance at HE) and to focus on young full-time degree graduates. This group is the numerically dominant component of all graduates and is of particular use to us since it is likely to be especially mobile geographically, making it a sensitive testing ground for the potential spatial transitions underpinning our HULT model. These particular graduates offer interpretative and pragmatic attractions too. Their youth means that their 'home' location is likely to have been more than transient and their rapid progress through their courses (compared to part-time students) means each cohort is responding to a common national economic context. Furthermore, the participation geography of young people is better known than for other groups (HEFCE 2005a;[START_REF] Fazackerley | North flaunts strengths[END_REF]. This is not to deny the importance and interest attached to other sub-sets of graduates (or those attaining other HE qualifications, perhaps through study in Further Education Institutions, a particularly important route in Scotland), but they likely behave differently, are more difficult to measure and less responsive to the regional patterning of employment opportunities.

Our analysis requires further cuts to this population of 525,000 young graduates: d) they need to have responded to the FDS (451,000) e) and report 'full-time paid employment' as their main activity (261,000) f) and be working in the UK (250,000) g) and provide sufficient detail on their 'H', 'U' and 'L' geographies to allow the assignment of a region in each case (225,000) Clearly, we can only analyse those for whom we have FDS information. Of those, our interest is in those who go straight into full-time paid employment: the eventual employment geographies of those who go on to postgraduate study or take longer to find employment are neglected in this paper. The final 2). Although the full postcode derived 'H' and 'U' geographies could be specified in many ways this is not the case for the FDS sourced 'L' destinations which are referenced by full postcode, partial postcode or country in 24 per cent, 74 per cent and 2 per cent of cases respectively. The country level of location would be assigned where the respondent had not provided sufficient postcode information so, for example, "Bristol" would be coded to England. Since Scotland, Wales and Northern Ireland are regions in our analysis that also enjoy country status, the graduates employed there are more likely to assigned a valid 'L' geography than those in England. Almost all the 25,000 graduates removed at stage g) above are those where the 'L' location is recorded as 'England'; thus graduates working in England are under-represented slightly in our population.

Using regions for our spatial framework allows us to assign as many as possible to a valid geography and avoids the difficulties of finer-grained ones that might be readily spanned by a commute. Whilst it is easy to criticise regions for being too coarse an analytical framework, it keeps the first, largely descriptive, step in our HULT analysis, manageable. More positively, as we have seen, it is also the scale at which much sub-national policy-making over jobs, people and homes takes place. Our final population of 225,000 represents 23 per cent of all the first-degree graduates in this period, some 43 per cent of young graduates and (depending on how the FDS non- In this present, exploratory, paper we deliberately take a simplified view of this innovative dataset, distinguishing its population neither by type of degree subject nor by awarding university, although it might be argued that each may affect their quality, employability and mobility to attain employment. If we had individual university-level data (which we haven't) allowing for such interuniversity variation in degree-level training would still be problematic. But by working at the region scale we are using a framework which, in each region, amalgamates universities of very different character and 'status', hopefully smoothing over any sharp site-to-site variations in educational quality.

It is also important to stress that we are not attempting to model the flows in our HULT dataset in any optimal, distance-minimising sense. Our interest is in describing, analysing and considering some policy options based on the realworld geographical interactions that arise, for better or worse, among homes, universities and workplaces.

Analysis

The structure of the HULT system

In this first, descriptive, section we start by examining the gross outcomes of the HULT system through regional gainers and losers. Second, we quantify the recruitment pathways that underlie these broad-brush outcomes. Finally, we explore the role of degree class, to see whether quality, as well as quantity, differences characterise the UK's geography of graduate labour recruitment. Throughout, one general outcome is the uniformity of these results across the four graduating cohorts: any year-to-year differences are usually of detail rather than substance. Thus for presentational simplicity one year's results can sometimes stand for all four. Another is the reassurance, not least for policy-relevant purposes, that the contemporary geography of graduate recruitment is largely consistent over time.

: Winners and losers

We identify these based on net differences between start and end positions for any cohort : in a region with an arithmetic balance of providing undergraduates and recruiting graduates (ie gain rate = 100), substantial numbers of the former could still take jobs extra-regionally, as long as these were matched by inflows of 'stayers' and 'outsiders' to the regional labour market.

Table 2 shows an outcome clear and consistent over time and space. Only two regions -Scotland and Yorkshire and the Humber -approach this balance, each being either in modest surplus or deficit depending on the cohort concerned. The single, and emphatic, winner region is London, which recruits about twice or more first degree graduates as it provides home students to the system. There may be a hint of some relative decline over The necessary counterbalance comes in the remaining nine regions, all of which are consistently losers. Overall, the smallest such deficits are, predictably enough, in the South East: the region shares something of the economic strength of the London which partly offsets the draw of its home students to the capital's adjacent labour market. At the other extreme, Wales, Northern Ireland and the East of England are overwhelmingly loser regions in all four years, in some of which they fail to recruit the numerical equivalent of three graduates for every four they send to university.

A simple measure of consistency over time is the behaviour of the regional gain rates (defined above), which show a high degree of stability as mapped in Table 2. Its histograms cannot easily convey the rank orders of regional gain rates, but these also change little over time, as measured by the 'shift' scores shown. These record the total change in rank position for each region over three inter-cohort comparisons, the theoretical maximum being 33 and the minimum, obviously, zero for no change in rank position. The highest shift scores are only 6, in the North East, which has raised its bottom-of-the-pile 1998/9 gain rate (75%) to a 6 th ranked 90%, the recently improving East

: Catchments, conversion rates and pathways

University catchments focus on the H-U flows and determine the numbers of potential graduates on each recruitment pathway, to which their respective conversion rates apply. For present purposes we can summarise the catchments for most of the 12 regions as belonging to two broad groups (Table 3). Members of the leading group each year have larger outflows of home-residents to university places than they have opposite inflows, and these in turn exceed numbers of home students studying within the region.

For the smaller group, the first two flows are reversed in size, but the locals stream is again the smallest. The most peripheral university regions display their well-known high dependence on intra-regional student recruitment, although the inflow -outflow balance differs, while the northern English regions show relatively more balance across the three components, and some changes over time.

Turning next to the U-L flows, Table 4 displays regional conversion rates across the four pathways, taking 2001/2 as typical. As predicted earlier, locals always produce the highest conversion rates, in every region and for each cohort. This is never below 70%, and over 90% in the most peripheral regions (Scotland, Northern Ireland). At the other extreme, and again predictably, the outsiders pathways generate the lowest conversion rates, in every case. In However, the two middle categories are more clearly differentiated than our previous discussion suggested. Of the two recruitment pulls exercised by any region -that of being at home there and that of studying there -the former is the more powerful, usually by some way. So in eight cases the returners conversion rates normally exceed the stayers equivalents by over 15 percentage points, across the four cohorts. Northern Ireland is an exception, but its stayers conversion rate is based on a very small inflow of university students studying there from outside. The only other exception is in Scotland, where in three cohorts (2000/1 is the exception) the middle rates are reversed from their normal order: in-migrant students are more likely, albeit by a small amount, to be recruited to Scottish jobs than are those previously living in Scotland but now studying outside the region.

Further stability is to be found in the ranked positions of the regions on each of the four conversion rates across the survey years. Out of 48 'region x pathway' cases only four vary by more than two ranked positions across the four cohorts and one third are constant in each year. Table 5 shows what these ranked positions are, through their mean values by pathway and region. Some regions perform very differently depending on the pathway -potential locals from the South East seem to develop a preference for jobs elsewhere (probably in London) but this region has high conversion rates otherwise, London is different again: whatever the pathway, its performance is impressive against regional competitors. There seems no sign of weakness in its ability to attract newly qualified, highly qualified, labour, at least within Britain.

The absolute numbers of graduates recruited by each pathway are obviously the product of the university catchments, (generating potential recruits) , and conversion rates of 'potentials' into 'actuals' (Table 6) : their roles are sometimes conflicting and sometimes complementary. In practice, although the local pathway has universally the highest conversion rates, only four regions consistently draw their largest single volumes of graduates from itthe North East, Wales, Scotland and Northern Ireland. In the last two the percentage of home-origin students who also study in the region is particularly high, compared to those studying elsewhere or to outsiders studying in the region, so university catchments and conversion rates reinforce each other. At the other extreme, London uniquely draws its biggest volume of graduate labour from those with no prior familiarity with the region at all, as its exceptionally high 'outsiders' conversion rate is applied (inevitably) to the very large absolute number of students in that category. In the central English regions returners consistently generate the most graduate labour. Just two regions show any changes over time. Yorkshire and the Humber depends most on stayers for the first two years, but these are narrowly edged out by locals from 2000/1. The North West, also becomes reoriented towards locals in later years.

: The importance of degree class

What of the role of degree class? Over the four years between about 55% and 60% of students in the dataset were awarded first or upper second class degrees ('high' graduates) as opposed to lower seconds or below ('low' graduates). Conversion rates can be calculated separately for these two subgroups, with the outcomes shown in Table 7. Again the results are very emphatic, and again they separate the performance of the London graduate labour market from those in other regions. In all but two 'region x cohort' cases (2) the locals pathway generates a higher conversion rate for low than high graduates. So the likelihood that those who have studied in their home region will also be recruited there is greater the less well they perform in their first degree, consistent with the Osborne et al (1987) pathways -where high graduates are recruited relatively more frequently by a region -no less than nine arise in London, out of its total of 12 cases (3 pathways x 4 cohorts). Only with the outsiders (a very small conduit for graduate recruitment in absolute terms away from the capital) are regional conversion rates generally greater for high than low graduates. So when converted to absolute numbers again (Table 8) the problem for many regions of being a loser rather than a winner in graduate recruitment is compounded by their also being disproportionately dependent on those who, on the evidence of degree class, are the lower attaining and less valued segment of the graduate labour force (Owen, 2003).

So London bucks this trend, as it did earlier ones. It recruits disproportionately more high than low graduates in all but three of its 12 pathway x cohort cases over the study period, as well as enjoying higher conversion rates in general than rival regions.

Diagnosis and prescription

We now turn from description to a deeper understanding of the very different performances of the 12 regions in recruiting graduate labour, focussing on controlling factors susceptible to medium-term intervention through public policy in the education sector. HE participation rates -The participation rate of young people in higher education varies by region (HEFCE 2005). The regional participation rates for our study period varied from about 36% in Scotland to 24% in the North East. Our analysis supposes that a proportional change in a regional participation rate would bring about a similar proportional change in the number of our database population from the 'H' region. This is a reasonable approximation though the exact relationship between the two will also depend on factors including non-completion rates, course length, participation in Further Education Institutions and the share of young graduates that fall within the analysis .

ii) Regional HE capacity, in relation to the generation of undergraduates from each region -in 2001/2 universities in the East of England took in only 44% as many students as that region generated, forcing many of them to study outside its boundaries for that reason alone, whereas its neighbour, the East Midlands, had an equivalent 30% oversupply of places.

iii) University catchments -the more a region's students attend its local universities and those universities recruit local students, the more will students pack into cell 1 of our model (Figure 1b), maximising the likely graduates recruited locally.

iv)

Conversion rates -we have seen how these vary, and selfevidently the higher they are, ceteris paribus, the higher will be regional graduate recruitment.

: Diagnosis

We now estimate the contribution of each of these factors by setting them separately and in turn to appropriate national benchmarks, and observing how regional gain rates change for a given cohort. In the case of i), iii) and iv) this involved substituting the cohort national average equivalent, based on the unweighted means of the 12 regional figures, for the respective, observed region-specific values. For ii) each region's HE capacity was set to the number of students that region generated for a given cohort, so each could be self-sufficient in terms of crude demand for and supply of HE places. For iii)

and iv) these changes can be made without affecting the remainder of our HULT model, but for i) and ii) it is necessary also to allow regional HE capacity and participation rates respectively to respond subsequently, to avoid unfilled places or unsatisfied students (3).

The results again testify to the stability of the HULT system over time. To provide more realistic policy prescriptions about increasing absolute numbers of graduates in regional labour markets we now make two further modifications. First, whereas our diagnosis assumed simultaneous changes in each controlling parameter across all regions, policymaking may well prioritise individual changes by and in specific regions. Second, the scale of changes needed to raise some regions to national norms in the previous section can be unrealistically large.

So now we model the effects of each factor separately for each region (keeping the remaining 11 unchanged) in stepwise increments of 5% for :

• HE participation rates

• regional HE capacity

• conversion rates for : i) locals and returners combined ii) locals and stayers combined

• university catchments :

The last two require further explanation. The first conversion rate modification assumes that policymaking targets students from a home region, wherever The catchment modification is based on repositioning a tranche of students, numerically equivalent to 5%, 10%, 15%… of the locals cell on Figure 1b, such that a region's total undergraduate-generating and -attracting capacities are unchanged. This involves increasing cell 1 by the specified percentage, then increasing cell 4 and decreasing cells 2 and 3 by the same absolute amount. In practice, the outcomes of the conversion rate modifications are identical to some other controls, through not of course in the underlying processes -variant i) duplicates the participation rate and ii) the HE capacity effects. Results for any factor are also simple linear functions of the input changes -those for the '25% case' being five times the 5%, for instance. To summarise so far, some simple descriptive and modelling exercises have been undertaken on a uniquely compiled set of data on recent graduate employees, tying together, for the first time, their regions of pre-HE origin, of HE education and of First Destination of full-time employment (the 'HULT' system). While there are some hints of time-trends, the overwhelming impression is of a consistent geographical structure over all four cohorts. In the competition for the first destination of the young graduates the UK shows a large number of loser regions, two which break even and one dominant winner region (London). It also has a clear regional pattern of university catchments, conversion rates and pathways of graduate labour recruitment.

Almost all regions consistently show greater rates of recruiting of students with prior familiarity through home or study, and particularly both, although this does not necessarily mean that the locals pathway is the most important one for absolute graduate recruitment. At one date or another, each of these is dominant in at least one regional setting, although there is a clear geographical split between more peripheral regions most dependent on locals and more central ones on returners. The disadvantage experienced by loser regions becomes greater still once the degree class of graduates is taken into account, since these tend to recruit disproportionately more of those with lower class first degrees.

In many of these analyses London is the glaring exception. It is the overwhelming winner region for graduate recruitment, if marginally less so than it was. It enjoys high conversion rates across the pathways and is the only region to depend most on the outsider pathway for its graduate recruitment. It is also the only one which draws proportionally higher class degree students from across the pathway spectrum, and not just from outsiders, as is commonplace elsewhere.

Finally, our analysis turns to rationalising these HULT outcomes in terms of factors explicit or implicit the HE system, and the effects of policy initiatives to change these and thus effect expansion in graduate labour in particular regions. We find that the prime reasons loser regions generate more undergraduates than they recruit graduates are very varied, as is the scale of the resultant shortfalls. When we look to some simple prescriptions via more policy-realistic modelling we find that changing any loser region's HE participation rate is more effective in graduate labour changes than manipulating the other factors. We can also differentiate among regions both in terms of the size of the leverage effects of particular factors and the also relative attractiveness of different ones.

We We turn finally to the broader implications of our study. In many ways it is clear that the geography of graduate recruitment, seen quantitatively and qualitatively, reflects that of other aspects of the national HE system (Hoare 1994b[START_REF] Hoare | UK public policy and the emergent geography of Higher Education, Being Ch[END_REF], and of the UK space economy more widely, in its centreperiphery structure. London stands head and shoulders above all other regions in its powers of attraction on newly-qualified graduate labour and it is easy to see its advantages as self-reinforcing and cumulative. London dominates the geography of many graduate occupations, the further training capacity that serves sector-wide employers, and related professional institutions. All this bolsters its 'institutional thickness' and thus the external economies of scale and scope of the nation's World City economy. At first glance this seems 'bad news' for the other UK regions, but at least the unique labour opportunities of London may keep able and ambitious recent graduates who otherwise would have taken jobs abroad within the national system, with a greater chance of some subsequent internal redistribution.

In [START_REF] Massey | World City[END_REF] Nevertheless, despite its simplicity, our modelling framework demonstrates how regional outturns of young graduate recruitment can and do arise in a variety of different ways, both through the pathways that generate them and the forces relevant to HE policy that underlie these and could alter them. To change outcomes we need some indication of the relative and absolute effectiveness of alternative intervention devices. If we decide these tested here are too expensive or impractical we have to look elsewhere for solutions, perhaps to regional and sub-regional housing allocations, a revitalised regional top-jobs policy and forced decentralisation of the public sector.

Understanding a system is a pre-requisite for improving it and hitherto we've understood little about how potential and actual graduates move about the country. Our paper is intended to move things on.

F

  represents Northern graduates who remain there to work. We can pair enrolment and employment streams into 'pathways' combining their H,U and L designations. From each of the South and North home bases four such separate 'H-U-L' pathways can be traced, as recast in Figure1bin two matrices, one for each home base.

  but studying in the South West, and outsiders those with no prior South Western associations of residence or study.

  of favoured regions and, in the zero-sum-game geography of

  a summary of significant contributions. Many are international in scale -the often-called 'Brain Drain' investigations -although inter-regional examples within national confines arise as well, again highlighting the differential economic benefits and disadvantages such flows imply. Most focus on either the H-U or the U-L legs The training and practice of doctors is the single most popular research sector, as a comparatively accessible study population and one with obvious wider social consequences.

  to every such strategy, was the regional resource of labour skills.

  for the U-L leg is the HESA First Destination Survey (FDS)(HESA 2003), an annual postal survey to discover the employment status of recent full-time graduates shortly after graduation. For those reporting themselves as in full-time employment the geographical location of the employer (not the graduates' residence) is recorded. With a typical response rate of around 80% -86% for the young degree graduates that we consider in this paper -the FDS provides a comprehensive early snapshot in the evolving employment history of recent highly qualified labour. After 2001/2 the FDS was replaced by the Destination of Leavers from Higher Education (DLHE) survey(HESA 2004), so our analysis too ends with the 2001/2 graduating cohort.

  proper' graduate occupations and those in more temporary jobs, which could distort our view of the H-U-L profiles.The four cohorts of UK domiciled first degree graduates from Higher Education Institutions between1998-1999 and 2001-2002 total some 969,000 (around 1,400 EU domiciled first degree graduates are recorded as working in the UK on the FDS, but are not included in this analysis). But we are only concerned with a sub-set of these, obtained through a sequence of restrictions: a) they are full-time first degree students b) they qualify (from the same institution as they started in) three or four after starting, with no previous HE experience c) they entered their course aged 18 or 19 (defined relative to their school year : HEFCE 2005b, p 172)

  condition of allocating each qualifier into our chosen spatial framework of UK regions (Figure

  the respondents) probably around 75-80 per cent of the young graduates going directly into the labour market.

  this is a detail secondary to the capital's dominance in the geography of graduate recruitment.

  Midlands (to 5 th in 2001/2) and the South East. The last's recent downturn (to 10 th position -only Northern Ireland and the East of England being worse) might reflect the same depressurising the overheated parts of the national space economy as the possible London trend noted two paragraphs earlier. extreme, seven regions have not changed position by more than one rank (and sometimes by none) at any stage over four years.

  size, London's outsiders conversion rate is clearly exceptional,over 11%. They otherwise never breach 5%, and in four peripheral ones -Scotland, Northern Ireland, the North East and Wales -fail even to reach 1%.

  West and East of England have similar, if less extreme, tendencies. The peripheral regions, and particularly Scotland and Northern Ireland, show the opposite trend. Each is much more attractive to locals than outsiders, and more effective at retaining those who have already decided to move to the region for study than former residents who have left for university elsewhere. Finally, the very different experiences of the neighbouring North East and North West are notable in the light of the concern of the latter's RDA in raising levels of graduate recruitment, reported earlier.

  finding noted earlier. In the great majority of the returners and stayers cases the same also applies: out of 96 such cases ( 2 pathways x 12 regions x 4 cohorts) only 14 exceptions arise. And of the 16 total exceptions over all three of these

Four

  acknowledge that what we have done has its clear limitations. Within the boundaries of the datasets we have used we could (and shall) extend our HULT analysis to a range of other variables. One set would give greater attention to the nature of students -perhaps considering their age, sex, ethnicity, entry qualifications and some classification of the type of neighbourhood where they lived before entry. Another set would look more carefully at the course studied. Subject studied might be important (perhaps contrasting career-specific training degrees -lawyers and engineers -and ones) and the 12% of degree qualifiers who study parttime will presumably have tighter geographical ties prior to and during their studies. Disaggregating our regional HE data by specific universities would defuse the inevitable criticism that our analysis groups together universities very different in academic profile, wider mission and embeddedness in their local communities (eg same-city research-oriented pre-1992 universities and former polytechnics), although it would reopen questions of the inter-university comparability of academic qualifications Another attractive option, though less easy and going beyond our dataset, is to follow graduate labour geographically beyond its first destination. Our earlier supposition that the geography of first jobs influences that of subsequent ones seems reasonable but other factors are likely to also be important. With ever more mobile labourforces, both spatially and between jobs, occupations and employers, any assumption that first destinations represent jobs and labour markets for life is clearly never less tenable than now, even aside from the criticism levelled at the FDS data themselves[START_REF] Utley | Graduate jobs data deemed flawed[END_REF]. The new DLHE series which has replaced the FDS holds the promise of tracking graduate employment at two snapshot dates. Until then, Alumni records of individual universities are not only confidential but patchy, as former students show less need and interest in maintaining contact as the years pass. And while national longitudinal panel-sourced databases may seem attractive(Ruspini, 2002), none at present has the express purpose of tracking graduates into, through and beyond Higher Education. Those currently in the UK suffer from their fairly coarse data on educational its location) and/or the small number of panel respondents who have moved through the relevant pre-HE and HE stages into extended periods of post-degree employment.

  Figure captions:

  different among the regions -see below) and for each of the remainder only one cohort breaks ranks. Equally, the effect of the diagnostic changes is almost always in the same direction (upwards or downwards) for each cohort, and in the exceptions the impact is marginal.

	cohorts (although Table 9 summarises the diagnosis for the 12 regions. It identifies the factor(s)
	most responsible for their current observed recruitment status (Col. 1) when
	F o r compared to that which the application of national benchmarks would generate, those from which they would benefit most (Col 2) against current outcomes, and to some lesser extent (Col 4), if these same national norms F o r
	P were to apply. The additional graduate labour recruitment the dominant-P
	e e
	e r e r
	R R
	e e
	v i e v i e
	w w
	For O n l O n l
	eight of the 12 regions taken separately the relative effects of the four	y y
	separate estimates of graduate recruitment are consistent over all four 5.5 : Prescription
		31 32

change (Col 2) factor would generate appears in Col 3. The results are very varied, testifying to the complex ways in which a small number of controls can affect regional graduate recruitment. Consistent with what we saw before, the dominant winner (London) benefits massively from its conversion rates and suffers only modestly from being below self-sufficiency in HE capacity. In contrast, for seven regions HE capacity is their major strength while almost all would also benefit from national conversion rates. The North West would gain most from improved participation rates and Northern Ireland from a more normalised pattern of student flows and university catchments. Its potential gain here is a massive one, too, which would almost have doubled its recruitment in one cohort. Wales and the North East also have substantial benefits to reap from national conversion rates.

  and the second that the focus is the region's HE provision, irrespective of students' origins. It is less clear how it could target either more cells, or fewer (eg locals only), although our approach is adaptable to such cases.

	they study,
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y
	33

Table 10

 10 Cols 1 and 2 (shown in Col 3) gives an indication of regional variations in the relative attractiveness of these two strategies : the North East, and Northern Ireland are the best positioned to benefit from capacity expansion/conversion rate i), for example, and the East of England and South East the least so.

	automatically assume the same sequence applies in cost-effectiveness terms
	(an x% rise in participation levels/conversion rate i) may be much expensive
	than an x% increase in university places/conversion rate ii)). But the ratio of

concentrates on those regions identified earlier as in graduate deficit (ie 'losers'), and summarises the volume of factor-change necessary to effect a 10% increase in graduate labour. In every case a given (eg x%) change in participation rates is more effective than the same change in HE capacity, which in turn is considerably more so than a similar change in university catchments for constant generation and capacity levels. Of course, we cannot

The Table also identifies those regions where a given policy initiative is likely to be more or less effective. For both participation rates and HE capacity Northern Ireland, the North West, the North East and Wales are the most attractive contexts. In contrast, the leverage effects of participation rate increases are much weaker in the East Midlands, South East and South West, and, of changed HE capacity, in the West Midlands, South East and East of England. For any programme of encouraging more students to study locally and universities to recruit locally, the North East and Wales reap the greatest returns and the South East the least. Northern Ireland even produces a negative return, given its comparatively high conversion rates for stayers (4).

Table 1 Previous investigations of HULT components

 1

	Alpin, C. and Shackleton, J.R. (1998), Over-and undereducation in the UK
	graduate labour market, Studies in Higher Education, 23, 17-34.
	Alston, M (2004), 'You don't want to be a check-out chick all your life' : the
	out-migration of young people from Australia's small rural towns, Australian
	journal of Social Issues, 39, 299-313.
	Anon (2004), Social mobility ; what's it worth ? The Economist 17 th January,
	23.	r o
	Baer, L.D., Ricketts, T.C., Konrad, T.R. and Mick, S.S. (1998), Do P international medical graduates reduce rural physician shortages ? Medical e r e Care, 36, 1534-1544.
	Barnett, J.R. (1992), How long do General Practitioners remain in any one R location ? regional and urban size variations in the turnover of foreign and e new Zealand doctors in general practice, 1976-90, New Zealand Medical v e i Journal, 105, 169-171.
	w Belfield, C. and Morris, Z. (1999), Regional migration to and from Higher
	l n Education Institutions : scale, determinants and outcomes, Higher Education O Quarterly, 53, 240-263.
		y
		40

Salsberg, E.S., Wing, P., Dionne, M.G. and Jemiolo, D.J.

(1996)

, graduate medical education and physician supply in New York state, JAMA -Journal of

Table 2 Graduate labour recruitment : regional winners and losers Gain rates (100 = balance of in-and out-flows)

 2

	Status	Region
			1998/99	1999/2000	2000/01	2001/02
	Deficit	North East	75.4	79.8	85.2	90.2
		North West	86.6	88.6	92.1	94.2
		East Midlands	82.2	80.9	83.8	90.7
		West Midlands	86.4	81.8	83.8	87.3
		East of England	75.5	71.0	86.3	73.8
		South East	94.1	91.4	91.1	86.5
		South West	81.2	81.4	84.3	88.6
		Wales	79.8	75.8	81.2	88.7
		Northern Ireland	76.5	73.8	75.5	77.7
	Surplus	London	217.6	237.3	215.1	194.3
	Balanced	Yorks and Humber	100.8	97.9	101.8	110.3
		Scotland	101.3	98.5	103.8	105.6

Table 4 Graduate labour recruitment: regional conversion rates and pathways 2001/02 Conversion rates by pathways (100 = all potential graduates convert to actual recruits)

 4

	Status	Region
			Locals	Returners	Stayers	Outsiders
	Deficit	North East	85.2	44.3	17.2	0.3
		North West	89.5	54.8	26.6	1.5
		East Midlands 77.1	46.2	19.7	1.4
		West	86.8	51.5	19.5	1.4
		Midlands
		East of	76.1	45.7	19.3	2.1
		England
		South East	74.6	49.3	27.2	3.7
		South West	80.1	46.5	25.1	1.6
		Wales	90.0	41.8	22.4	0.4
		Northern	94.1	35.9	60.0	0.04
		Ireland
	Surplus	London	88.4	71.2	52.3	9.7
	Balanced	Yorks and	84.5	51.2	25.5	1.1
		Humber
		Scotland	92.1	35.9	43.2	0.4

Table 5 Rank ordering of regional recruitment pathways Average regional rank of pathways (highest = 1) 1998/99-2001/02 Status Region

 5

			Locals	Returners	Stayers	Outsiders
	Deficit	North East	6.9	9.3	12.0	10.5
		North West	4.0	2.0	5.0	5.6
		East	11.5	8.0	10.0	6.9
		Midlands
		West	5.8	3.5	9.8	5.5
		Midlands
		East of	10.3	7.0	8.3	3.0
		England
		South East	11.3	3.8	4.0	2.0
		South West 9.0	6.5	7.0	4.0
		Wales	5.0	10.8	9.3	10.4
		Northern	1.0	10.3	1.3	12.0
		Ireland
	Surplus	London	3.5	1.0	1.8	1.0
	Balanced	Yorks and	7.9	4.8	6.8	8.0
		Humber
		Scotland	2.0	11.3	3.0	9.2

Table 6 Absolute levels of regional recruitment by pathway Largest pathway (and % graduates recruited thereby)

 6

	Status	Region
			1998/99	1999/2000 2000/01	2001/02
	Deficit	North East	Locals (39) Locals (44) Locals (45) Locals (47)
		North West Returners	Locals (40) Locals (42) Locals (43)
			(38)
		East	Returners	Returners	Returners	Returners
		Midlands	(35)	(34)	(36)	(36)
		West	Returners	Returners	Returners	Returners
		Midlands	(41)	(41)	(39)	(41)
		East of	Returners	Returners	Returners	Returners
		England	(47)	(46)	(49)	(52)
		South East Returners	Returners	Returners	Returners
			(36)	(37)	(36)	(39)
		South West Returners	Returners	Returners	Returners
			(36)	(38)	(38)	(36)
		Wales	Locals (49) Locals (48) Locals (49) Locals (49)
		Northern	Locals (79) Locals (82) Locals (82) Locals (85)
		Ireland
	Surplus	London	Outsiders	Outsiders	Outsiders	Outsiders
			(49)	(55)	(49)	(45)
	Balanced	Yorks and	Stayers	Stayers	Locals	Locals (34)
		Humber	(33)	(31)	(33)
		Scotland	Locals (88) Locals (83) Locals (80) Locals (80)

Table 7 Regional conversion rates, pathways and degree class Conversion rates by pathway and degree class 2001/02

 7

	Status	Region
			Locals	Returners	Stayers	Outsiders
			High Low High Low High Low High Low
	Deficit	North East 82.3 88.8 44.2 44.5 16.6 18.4 0.3	0.3
		North West 87.7 91.3 51.2 60.7 25.5 28.1 1.6	1.4
		East	73.8 82.2 42.1 53.1 19.5 20.1 1.5	1.3
		Midlands
		West	85.4 88.9 50.4 53.4 19.0 20.5 1.5	1.2
		Midlands
		East of	72.2 82.9 43.6 49.6 18.6 20.6 2.3	1.6
		England
		South East 70.7 80.0 46.5 54.6 25.4 30.1 4.4	2.8
		South West 76.6 84.9 44.2 51.3 23.1 28.1 1.6	1.4
		Wales	90.3 89.7 37.8 46.9 22.3 22.5 0.3	0.4
		Northern	93.6 94.7 33.0 39.4 60.0 n.c	0.04 0.03
		Ireland
	Surplus	London	87.9 89.1 72.4 69.2 55.0 47.7 11.9 6.2
	Balanced Yorks and	80.4 89.5 47.6 56.5 24.5 27.2 1.3	0.9
		Humber
		Scotland	89.7 95.1 41.3 34.2 41.7 46.8 0.4	0.3
	Notes : n.c -not calculated due to zero observations
		larger conversion rate of 'high-low' pair in bold
		italics where conversion rate of high-low' is equal

outcomes for deficit regions : % changes necessary for 10% growth in total graduate recruitment

	Region	PR(a)	HE(b)	PR/HE	UC
		Col 1	Col 2	Col 3	Col 4
	North East	13.9	14.9	0.93	75.2
	North West	13.3	17.5	0.76	277.7
	East Midlands	16.4	21.4	0.77	163.9
	West Midlands	14.0	22.7	0.62	163.9
	East of England	14.7	42.7	0.34	370.3
	South East	15.1	24.2	0.62	1428.0
	South West	15.5	21.3	0.73	277.8
	Wales	13.6	14.6	0.73	69.4
	Northern Ireland	10.2	11.8	0.86	Negative effect
	Key (a) equivalent to a conversion rate i) change
	(b) equivalent to a conversion rate ii) change
	PR : participation rate
	HE : Higher Education capacity
	UC : university catchment

http://mc.manuscriptcentral.com/cres Email: regional.studies@newcastle.ac.ukRegional Studies

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