Economic Planning in Rural Areas 41 ANNINIZ,Fpundation OP ABRICULJ K

AGRICULTURAL:ADJUSTMENT UNIT -!- LINIVERSITV-'0F NEWCASTLE UPON TYNE

AVIodells of Population and income: Economic Planning in Rural Areas 41 ANNINIZ,FPUNDATiON OP ABRICULJ K. G. Willis Li "

E., ECONOMICiit THE AGRICULTURAL ADJUSTMENT UNIT THE UNIVERSITY OF NEWCASTLE UPON TYNE

In recent years the forces of change have been reshaping the whole economy and, in the process, the economic framework of our society has been subject to pressures from which the agricultural sector of the economy is not insulated. The rate of technical advance and innovation in agriculture has increased, generating inescapable economic forces. The organisation of production and marketing, as well as the social structure, come inevitably under stress. In February 1966 the Agricultural Adjustment Unit was established within the Department of Agricultural Economics at the University of Newcastle upon Tyne. This was facilitated by a grant from the W.K. Kellogg Foundation at Battle Creek, Michigan, U.S.A. The purpose of the Unit is to collect and disseminate information concerning the changing role of agriculture in the British and Irish economies, in the belief that a better understanding of the problems and processes ofchange can lead to a smoother, less painful and more efficient adaptation to new conditions.

Publications To achieve its major aim of disseminating information the Unit will be publishing a series of pamphlets, bulletins and books covering various aspects of agricultural adjustment. These publications will arise in a number of ways. They may report on special studies carried out by individuals; they may be the result ofjoint studies; they may be the reproduction of papers prepared in a particular context, but thought to be of more general interest. The Unit would welcome comments on its publications and suggestions for future work. The Unit would also welcome approaches from other organisations and groups interested in the subject of agricultural adjustment. All such enquiries should be addressed to the Director of the Unit.

Unit Staff Director: Professor J. Ashton, M.A., B.Litt, M.S. Head of Unit: S. J. Rogers, B.Sc.(Econ) Administrative Officer: B. H. Davey, B.Sc.(Agric), M.Econ

The Agricultural Adjustment Unit, Department of Agricultural Economics, The University, Newcastle upon Tyne, NE1 7RU. MODELS OF POPULATION AND INCOME: ECONOMIC PLANNING IN RURAL AREAS

K. G. WILLIS

Research Monograph No. 1

AGRICULTURAL ADJUSTMENT UNIT UNIVERSITY OF NEWCASTLE UPON TYNE 1971 PREFACE

This paper is the first of a new series of research monographs. In the course of its programme on policy questions affecting U.K. agriculture the Agricultural Adjustment Unit has moved into several areas of research where it has judged additional work to be necessary. As a result of these activities points of methodo- logical interest are emerging, which, although they are intended to bear on policy questions, are theoretical. This series ofresearch monographs is intended to improve analytical tools to handle the complex problems of agricultural and rural policies. It has become increasingly apparent that, on some issues, agriculture and agri- cultural policy are only contributory elements in the complex of rural affairs. This is particularly the case when considering some ofthe remoter areas ofthe U.K. These are areas where any move to a more efficient agriculture can result in accelerating depopulation and where long-term viability of the whole rural community is in question. In these cases it is appropriate to re-state the adjustment problem in terms of rural societies rather than agricultural communities and in terms of the rural economy as a whole in which agriculture, although important, is not the sole industry. In an enlarged E.E.C. the subject of rural communities and regional development will loom even larger in the thinking of those concerned with agricultural matters. In practice, the solution to the problems of remote areas is often likely to be beyond the capacity of any agricultural policy and will involve other economic and social measures. It was with these thoughts in mind that the Agricultural Adjustment Unit mounted a Conference at Aviemore in October 1969, the proceedings of which are being published for the Unit by Oliver and Boyd early in 1972 under the title 'The Remoter Rural Areas of Britain'. This conference demonstrated that there was widespread interest in the problems of remoter areas, and led the Adjustment Unit into research programmes in this general field. One factor, apparent from the beginning, was that although the remote areas have some similarities they also have profound differences. Consequently the combination of policies which may be appropriate for one region may be in- appropriate for others. As a starting point it is therefore necessary to classify remote areas by some means. Key factors in such an analysis are likely to be the expected changes in population and the levels ofincome within the geographical area being considered. Dr. K. G. Willis has been working on these problems since April 1970 and this monograph represents the first results of his work. Dr. Willis explores the methods of population projection and the measurement of income and concludes broadly that, although published statistical sources may be indicative, there is not 3 sufficient information available to enable accurate diagnosis of problems to be made. In consequence, interest in this monograph should focus on the methodo- logical aspects, rather than the results generated for the North of England, which can only be regarded as first approximations. Two further stages are currently envisaged for research in this field. Firstly, there is need to refme the methods of projecting population and measuring rural income. Secondly, there is a need to examine the objectives applicable to rural areas and the range of policies which could be implemented to achieve them. This monograph can be regarded as the Agricultural Adjustment Unit's first effort in what may prove to be a long research programme. In the course of its preparation assistance was received from Mr. M. C. Whitby, who is generally responsible for this field of research in the Unit and to whom acknowledgement is made. Finally, since this monograph hopes to stimulate discussion, the Agricultural Adjustment Unit would welcome the views of readers on any of the matters discussed. J. ASHTON November 1971 MODELS OF POPULATION AND INCOME: ECONOMIC PLANNING IN RURAL AREAS

CONTENTS Page 1. Introduction .. • • • • • • • • • • • • • • • • 7

2. Methods of Population Projection and Income Estimation .. • • 12 Methods of population projection .. • • • • • • • • 12 Population projection—applicability to rural areas .. • • • • 13 Assumptions .. • • • • • • • • • • • • • • 18 Methods of estimating income • • • • • • • • • • 20

3. Population Projections and Income Estimates in the Northern Pennines 24 Population trends • • • • • • • • • • • • 24 Income estimates, earnings and Inland Revenue data • • • • 27

4. Problem Area Identification • • • • • • • • • • • • 31

5. An Econometric Study ofIncome and Labour .. • • • • • • 36

6. Summary and Conclusions.. • • • • • • • • • • • • 43

Appendix 1. Cohort-survival formulae in population projections • • 47

Appendix 2. Population projection as a stochastic process .. .. • • 49

Appendix 3. Population projection, 1991, by local authority area and quinary age and sex groups .. • • • • • • • • 50

Appendix 4. Estimates of earnings and incomes by parish .. 54

Appendix 5. Classification of parishes by type of problem area • • • • 60

References and Notes .• • • • • • • • • •. • • • • 62

5 1. INTRODUCTION

The object of this monograph is to develop information and techniques of analysis which can be used to make a better evaluation ofthe regional economy in remoter rural areas, with the aim of making policy formulation and direction more effective and efficient. It focuses initially on two areas currently of great interest to planners and policy makers concerned with rural areas: population and income. The remote upland areas of Britain have felt and continue to feel the chilly winds of economic pressure. The economies of such marginal areas continue to decline despite the injection of large amounts of capital to aid farming, industry and the social environment. The greatest capital flow into sectors directly concerned with the production ofeconomic goods has been to farmers in these hill and upland areas. The present grants to agriculture in upland areas comprise: hill cows(13.7 million for 1970-71); hill sheep (k8.5 million); winter keep ( 4-.19 million); beef cows(5.8 million) and hill land improvement(k2.2 million). In addition, million was paid in 1970-71 under the old Livestock Rearing Act grants. These grants, in total, amount to well over 30 million. Upland farmers also benefit from such other schemes as the Farm Improvement Scheme and drainage grants but the payments cannot be separately identified. However, Bulletin 13 of the Agricultural Adjustment Unit on Hill Sheep Farming* looked at government support measures in 1967-68 and estimated the share of other support to hill and upland areas to be equal to direct recorded support. Under the objectives of the 1947 Agriculture Act,' this investment is designed to promote an efficient agri- cultural industry with proper renumeration for workers in agriculture. However, the question should be asked, could this money be better utilised in alternative investment projects in these remote rural areas ? How effective is the agricultural policy in stimulating income growth in such areas; in meeting population policy objectives(such as a minimum population); in creating employment and promoting economic development? Should rural development not be looked at as a whole rather than in terms of agriculture as distinct from other sectors ? • Planning proceeds by bringing together a knowledge of the operating charac- teristics of a system and a set of aims which the system is expected to serve. The combination of these two different elements can be carried out 'by hand': a group ofindividuals studying, formulating and discussing, and in this way finally arriving at a policy. This was the procedure at a conference on The Changing Uplands in 1970 organised by the Northern Pennines Rural Development Board and the Country Land Owners' Association.2 Alternatively, an attempt can be made to formalise the process and to incorporate some, if not all, of it in a model. This

*Agricultural Adjustment Unit, Bulletin 13, 'Hill Sheep Farming Today and Tomorrow'. Table 11, page 19. 7 study follows the latter approach. But in both cases the need for comprehensiveness in looking at problems and deriving solutions should be emphasised. This report describes a means of co-ordinating within a single framework a great variety of information and techniques and shows how this information can be used analytically to evaluate aspects of the rural economy. The framework proposed and the methods associated with it are designed to serve two aims, one general and one specific. It has aimed specifically at two topics of interest to planners,(a) population and methods of projection, and (b) income with methods of estimation. It has aimed generally at incorporating these variables into an integrated system to identify the types of analysis that seem desirable in rural development studies. This study was originally initiated when the Northern Pennines Rural Development Board was in existence, and it seemed appropriate to use the R.D.B. area in the four northern counties ofDurham, Northumberland, Cumberland and Westmorland (Fig. 1) to apply the techniques developed. It is in such remote rural areas that economic problems are most acutely felt. A comprehensive survey of demographic estimation and projection techniques is beyond the scope of this monograph yet no book covers this subject (which is regrettable), and the limits of the field are undefined. Literature on population projection is fragmented rather than scarce, with articles investigating specific problems in various journals. This bulletin reviews some major methods of population projection with specific reference to rural areas and discusses the implications for regional planning of the difficulties of making accurate long-term projections. There is a need for accurate forecasts offuture population distribution. Develop- ment policy is essentially long-term and planning decisions have to be based on expected requirements several decades ahead. The provision of social capital, the provision of health and social services, the requirements of public transport, roads and communications are all closely related to population. However, size and structure of population only partly determine what provisions are made for the future. Development programmes should be set against estimates of income, for in the short run, demand for, and provision of housing, amenities, public transport etc., is affected by income level and financial arrangements. An analysis of income is also the starting point for a wider field of study in regional economic research. It provides a frame of reference for the distribution of investment, for gauging the average rate of growth in per capita income, and in establishing the relationship between rural emigration and income. Workers in other fields and disciplines have become aware of the initial importance of income; for example, transportation studies have noted that household income is an important variable in determining travel demand. Planning goals provide important reasons for estimating regional income and drawing up social accounts. A frequent planning objective is the maintenance of a minimum population in a 8 LOCAL AUTHORITIES AND NORTHERN PENNINES RURAL DEVELOPMENT BOARD AREAS depressed agricultural region. This means that migration from agriculture, as opposed to demographic increase, has to be absorbed within the industrial and service sectors by the creation of employment opportunities within the region. This raises the question of employment multipliers* either basic or refined to be based on regional accounting and an input-output matrix. There are three primary determinants of the economic welfare of an area: (i) the demand for goods produced within it, or services rendered by residents, (ii) the technical efficiency of these economic operations, (iii) distribution of welfare or income. A low demand for goods and services relative to other areas will depress job opportunities and profits. Even if a high demand exists technical inefficiency (inferior land and inadequate capital resources) will render the area less competitive. Earnings and incomes of an area are related to each of these factors, i.e. after the basic industrial and occupational structure it provides a good measure of the economic health of an area. In Great Britain national economic planning operates within the constraints of regional objectives. Two of these are important as far as rural areas are concerned. The first is the maintenance of an unspecified minimum population in remoter agricultural regions, already mentioned. The second constraint is the prevention of relative decline in regional per capita income. This is a difficult objective, since the poorest regions are most often those growing at the lowest rate. Considerable attention is therefore devoted to population and income in this study. In the latter half of the monograph, however, the field of study is widened to include a cursory review of some rural development and planning issues. Planning in its broadest sense is an ordered sequence of operations, designed to lead to the achievement of either a single goal or to a balance between several goals. The whole process is not described in this study—objectives are not defined, alternative approaches and policy solutions are not evaluated. Nevertheless two important aspects of the planning process are discussed. First of all, it is necessary to define a problem area, in terms of problems and areas affected by common problems. Variables such as population decline and income are included here and a procedure was used to group these and other variables into common problem area types and identify these on the ground. Secondly, to improve intervention and effectiveness of policies it is necessary to have a greater knowledge of the sim- ultaneous interactions between economic variables, that is to assess the importance of predetermined variables which affect income and the proportion of population in the labour force. An elementary econometric model is therefore proposed to estimate the relationships among the variables. An employment multiplier is the relationship between increasing investment or income and subsequent employment this generates. The concept was originally formulated by Kahn.3 10 This approach to rural development has great potential for further research. For example, a whole series of simultaneous equation models could be developed to explain how the rural economy functions and to estimate such endogenous variables as total income, service income, employment, unemployment, migration, total population size etc. The third aspect of the development problem—deter- mining the types of aid to match the varying problems has not been discussed here. But from the econometric model exogenous variables related to policy goals can be identified and their importance quantified in promoting a given goal. An important issue is to help aspiring areas to decide which route or policy (industrial development, recreation, or agricultural development) is most feasible for them in terms of a greater probability of success. It is hoped that this will provide the substance of a subsequent monograph.

11 2. METHODS OF POPULATION PROJECTION AND INCOME ESTIMATION

Methods of Population Projection There are a number of major methods for projecting population. These differ in concept, orientation and operation and can be broadly classified as either direct or indirect. Direct methods are based on current and past data on population numbers. Indirect methods relate to other economic, social and political indices, such as statistics on employment, investment, income, exports, or school enrolments and are based primarily on regression and correlation analysis.4 This monograph is concerned with direct methods of population analysis. Included among traditional direct methods are cohort-survival models, which focus principally on the age-sex distribution of a population at a given time. Data are analysed in terms of appropriate age-sex specific rates offertility, mortality and mobility in order to project the age-sex distribution ofthe survivors and descendants of the original population over successive intervals of time. Another set of direct methods are components-of-change models which analyse each major factor in population change. Methods such as inflow-outflow analysis and natural increase analysis, take each major factor in population change—births, deaths and mi- gration—and combine this information with population data of a base year to estimate future population. The cohort-survival method has provided the conceptual framework for a number of studies of population redistribution such as that by House and Knight5 'Migrants of North East England' analysed by age and sex. Several local authorities in the North-East have used cohort-survival models on a sub-regional basis in urban areas, but have tended to concentrate on the housing unit method6 in preparing population estimates. Population estimates and projections are obtained by the housing unit method from the product of the estimated number of houses (or households) multiplied by an estimate of the average size of households. The short-comings of all these methods in a planning context have already been documented.7 Cohort-survival and components-of-change models are manifestly dynamic but have an aspatial structure. Spatial differences are measured only in so far as the analysis is repeated for each of the geographical units in the study area. But space and time should be considered simultaneously to explain the processes of population systems. Moreover, only by considering such an integrated system in space as well as time can the effects of rural depopulation and county planning decisions on regrouping of population on the demographic structure of neigh- bouring areas be assessed. Cohort-survival models provide no evidence on the repercussions of any change in migration associated with one area on the demo- graphic events in surrounding geographical areas. 12 Markov chain theory has been use& to construct a probabilistic migration model, in which interaction between specific areas occurs, to project future populations of local authority areas in urban North-East England. The spatial effects of policy decisions were assessed by introducing policy constraints into the model. The inadequacies ofshort term planning and population projections were demonstrated, through considerable oscillations in the proportional distribution of population between areas particularly in the immediate 20 to 40 years. The population of an area as a proportion of the national total can vary substantially over time, and in some areas increase over the immediate 20 year period only to decline below its initial base population in 1961. Since economic investment in schools etc., is essentially long term, the possible long run consequences of population processes should be borne in mind in planning proposals.

Population Projection—applicability to rural areas Many of the techniques described have been applied to national populations of Britain and particularly of the United States of America. In practice, however, there are great differences between local and national projections. The chief problem in population projection in local rural areas is the small total population. Even with complete statistical information, calculation of, say, a birth rate in an area is subject to stochastic fluctutations through time and has a 95 per cent chance of being in between

)1±2 where n is the population and p is the mean rate of birth. Thus n has to be great if sufficient approximation is required. Random fluctuations can, therefore, become important at this level of disaggregation. Experience has confirmed the theory that estimates and forecasts are generally more accurate the larger the population or the geographic extent of the area and the more varied its economic activities. In contrast to rural areas, large industrial areas or cities have shown a capacity to generate new growth in alternative activities even when their major industries are declining. Such urban areas, therefore, exhibit a stability in their population trends despite unpredicted variations in economic conditions. Population trends in agricultural areas have exhibited a. constant tendency towards rural depopulation; but in rural industrial and com- mercial areas such as Haltwhistle,9 population trends are less predictable." Linked to the problem of a small statistical population is the greater scarcity of published data for local areas, particularly rural areas. Population figures by sex, age etc., are available only for census dates. Annual births, deaths and marriages are not available by age and sex, the former two being indicated in terms of crude rates for the whole population." In local areas with small populations, the difference 13 between enumerated and resident population, and the location of non-civilians assumes greater importance. The enumerated or de facto population includes all persons (visitors etc.) in an area at the time of the census. County volumes of the Census of Population give only enumerated population by age, sex, marital condition etc., for each administrative area. The resident or de jure population comprises those normally resident in an area at the time of the census and it is this 'population' which should be considered as a base for any projections. Demographic rates are characteristic of the area in which a person normally resides. The greatest difficulties involved in the population projections of local areas undertaken by the General Register Office for the former Ministry of Housing and Local Government—now the Department of the Environment—are caused by three special population groups: residents in institutions, visitors from outside England and Wales and non-civilians.12 The Registrar General's estimates are the only national projections for all local authority areas, yet for practical purposes they are severely defective since no account is taken of migration. Amendments to the projections to account for migration are left for regional MHLG offices, to bring more local knowledge to bear, but estimates of migration in such organ- isations are intuitive guesses. As one proceeds from a relatively closed national population to the analysis of essentially open areas within multiregional systems, the importance of migration as a contributor to population change increases rapidly. At a local community level, migration assumes primary importance and becomes the fundamental explanatory variable in population change and growth. Unfortunately, data is scantiest and guesses of the future course of events most hazardous for this variable. Demographically, rural areas, especially remote rural areas, are quite distinct from urban areas in age structure and sex ratio. Many of the problems of rural areas are centred on the greater preponderance of old people and the predominance of males.'3 The more unbalanced structure of the population in rural than urban areas creates planning problems in the provision of services where both fertility and the proportion of older people are higher than the national average. Conse- quently there exists a need to project not only total population but also its age and sex structure. Traditional direct methods ofprojecting total population alone are not sufficiently informative of social processes and rural population trends. Moreover, the housing unit method is known to yield estimates on the high side for cities (average error plus 5 per cent); with the error in the estimate of the number of households the greater contributor to error than the estimate of the average size of household.14 This particular method seems beset with a number of hazards when applied to rural areas. Building permits and plans indicate intent to build, but not all are completed and time lag patterns between plan and completion vary from area to 14 area. Vacancy rates* are particularly important in rural areas where there is often no pressure of demand; and average size of household may differ if young single adults migrate upon leaving school to seek job opportunities. A second home population comprising weekend cottages may also indicate a higher estimated population than actual. The use of electricity accounts and electoral rolls to check the number of households may not overcome these difficulties. The use of a matrix projection operator t to develop an inter-area population system forward through time allows one to focus on the projection process itself, its application to another population and its long-term implications. More- over, the insights yielded by such an analysis are not attainable by conventional techniques of population analysis, especially in problems of estimation, stability, intervention and migration. This method of population projection has been used successfully on a regional basis15 and for local authority areas in urban North-East England.16 On current data available, it proved unsuccessful for rural areas through both the small number of observations recorded (10 per cent sample) and the under-enumeration t in the 1966 Census." Under-enumeration particularly affected urban areas," resulting in a probable true estimation of in-migration to rural areas and an under-estimation of out-migration to urban areas, but not necessarily other rural areas. The Markov migration model takes the form =(P+B—D)x o where B = diag. .. . pn) = birth rate D = diag.(pr. .. . pn)== death rate xo = initial population at time t x,= population at year 0-1 P = stochastic migration matrix with elements pij0 &Epij=1.

Since P exhibited bias from sampling, the model when applied to the North Pennines rural area, resulted in considerable population growth in some remote areas contrary to expectations. This type of model, which is preferable to all other types, for population projection in rural areas, will become feasible with the 1971 Census, if 100 per cent counts ofin and out migration are obtained. For immediate

*Length of time between a dwelling becoming vacant and next family moving in. tA matrix growth operator for projection purposes is defined as(P+B —D)where B and D are diagonal matrices whose non-zero elements denote birth and death rates, and P is a migration transition matrix. For a more realistic application of birth, death and migration rates, demographers have turned to the definition of more homogeneous population groups for projection purposes. rThe population. of England and Wales on census day 1966 is officially estimated at 48,005,000 but the number of people enumerated in the sample census when multiplied by 10 is 47,135,510 about 1.8 per cent below the estimate. 15 purposes the feasibility of an alternative method of population projection needs to be assessed. Resort must be made, therefore, to one of the traditional direct methods. The need to project the structure as well as the total population leads to the recon- sideration of cohort-survival models. Cohort-survival projection method The cohort-survival method of population projection gives rise to two funda- mental problems in time and space. These will become obvious in the description of the two major variants of this residual method, which are (i) vital statistics method, which employs actual birth and death statistics of each area to allow for natural increase or decrease (ii) survival rate method which, as it is generally applied, employs national life table survival rates to allow for mortality and national birth rates to allow for natality. Net migration is the difference between the total number of persons entering an area during the inter-censual interval (decade or quinquennium), and the total number of persons leaving the area during the period (decade or quinquennium). Siegel and Hamilton" have demonstrated how the vital statistics formula makes allowance for those migrants both in and out, who die after migrating (see Ap- pendix 1). In Britain the requisite vital birth and death statistics for each of the local authority areas are not available on a cohort basis. But even if individual returns on births and deaths could be obtained, the vital statistics method requires that the rates are calculated for each local authority area, which is cumbersome. Where vital statistics for local areas are not used accuracy is lost, but by the use of survival rate methods painstaking work is avoided. Survival rate methods present a number of problems. Do survival rates and birth rates (usually national rates) reflect accurately the mortality and fertility of the population of a local area Do the survival rates, even if correct, really measure the number of deaths in an area because of the occurrence of migration ?20 Two survival rate methods lend themselves to population projection: (i) forward survival rate (ii) average survival rate. The formulae for these are given in Appendix 1. The distinction between the vital statistics method (recording exact population change) and the forward survival rate method is the difference between the deaths of in-migrants and out-migrants. This difference may not be negligible and for each rural area will depend on the distribution of its in and out migration to other areas. In-migrants to a rural area may originate mainly from a conurbation and have a higher death rate than out- migrants from the rural area. For example in 1950-52, ratios of actual to expected 16 deaths, in density aggregates, based on national experience in England and Wales were as follows: Density aggregate Men Women

Conurbations 1•065 1•026 Urban areas > 100,000 population 1•065 1037 Urban areas 50,000-100,000 population 0-989 0.966 Urban areas <50,000 population 0•981 0998 Rural areas 0.876 0.941 Depending, therefore, on the distribution of migration to and from each area and its occupational structure there could be considerable differences in death rates between in- and out-migrants. According to the forward survival method, the population at a given age at the beginning of a decade is multiplied by an appropriate survival rate to obtain an estimate of the population 10 years older that would be present at the end of the decade ifno migration occurs. This number ofexpected survivors is then compared with the actual population in the age group at the end of the decade to determine the amount ofnet migration. The forward method, therefore, assumes all migration takes place at the end of each cycle over which the projection is carried forward. This gives rise to errors in 'time'. If all migration occurred instantaneously at the beginning of the decade and all out-migration instantaneously at the end of the decade, or, vice versa, the maximum possible migration estimate error in using , the forward survival rate is the total number of deaths among in-migrants or deaths among out-migrants, according to when migration occurs in time. Much mi- gration is related to economic fluctuations in the economy, although different areas are often subject to different economic conditions or varying intensities of similar economic problems. It would seem, therefore, that an average method could be applied more generally throughout all areas since the maximum possible error is the average of deaths among in-migrants and deaths among out-migrants. The algebraic formula for the average method is also given in Appendix 1. The average survival method gives the same results as the vital statistics method if one-half of the implied net number of deaths among migrating cohorts occurs after migration. This method implies an even flow, or an approximately even flow, of migrants during a given time period. Obviously this method is superior to the forward method in that mortality is allowed to affect migrants between the base year and every interval (decade or quinquennium) for which a projection is given. This is the method adopted in practice. Under extreme conditions, and particularly at ages subject to high mortality, errors in using these census survival rate formulae could in some cases exceed considerably the difference between the two estimates and provide inaccurate results. This is especially likely in rural areas which have an unbalanced age structure. 17 Given perfectly enumerated data the vital statistics method provides an exact measurement of demographic change in local areas. Census survival rate methods, in contrast, suffer from census errors and from the inability of survival rates and fertility rates to measure deaths and births occurring in the area exactly. Price21 called attention to the fact that neglect of considering the difference between national, regional, and local survival rates could lead to large absolute and also relative errors. Some adjustment of rates is necessary to allow for variations between local and national mortality and fertility rates. This traditional type of cohort analysis is not very elegant and at first sight conveys little about the demographic processes in the area concerned. An aspatial situation, recording a demographic process, can be treated with insight as a stoch- astic process (see Appendix 2). This type of analysis is satisfactory where the entire population is treated as one group, since one equation can describe the major demographic processes and their relative importance in an area. When disaggre- gated into cohorts, with interaction between cohort groups, such a stochastic scheme needs to be evaluated in matrix terms and reduces to the matrix repre- sentation of the traditional cohort type analysis.

Assumptions Local adjustments Craig22 has considered several possible indicators of the variation of local to national mortality rates, in terms of frequency of collection and publication, areas covered, and age-sex breakdown. Craig's procedure was adopted in this study to adjust mortality rates in estimating net migration over the period 1951-61. Standardised mortality ratios are produced decennially, covering counties sub- divided into County Boroughs, urban areas and rural areas (aggregates).23 Age-sex breakdown is not in all cases by quinary groups.* Where the quinary breakdown was not given the rates were averaged and smoothed before being used to adjust the national mortality rates to comparable local rates. Adjustment for spatial variations in birth rates is more difficult, with figures available only for Tyneside and the rest of the Northern Region as a whole. To assess migration from 1951 to 1961, the Northern Region birth rate was used. This was found to underestimate the number of children born in some localities, with a consequent increased estimate of in-migration at young ages. For example the local birth rate, after adjusting for age-sex structure, was 20 per cent above the national rate in Bellingham R.D. 1951-61, and 10 per cent above in Rothbury R.D. There is much more variation in birth than death rates between rural local authority areas. An allowance can be made for spatial differences in birth rates by applying total population (age corrected) differentials to all fertility data for

*Quinary groups are five year cohort age groups. 18 female birth-producing cohorts 15-45.21 This is admittedly crude but no other measure for local areas is feasible. Cohort birth rates 1951-61 were adjusted by the ratio of local and national rates. However, it proved impossible to project these local authority differential birth rates by any mathematical function, due to large stochastic variations between individual years. Recently the differential between rural and national rates has narrowed; local rates appear to be converging to the national rate. It has been assumed that for births after 1961, the base year of the projection, national rates reflect adequately the fertility processes in local areas. For similar reasons, such as the small number of observations, the standardised mortality ratios produced decennially, could not be projected. Recent trends indicate that in many of the rural areas under study, the local birth rate is approaching the national rate (when the local rate is adjusted for age and sex). A similar observation relating to the greater equalisation of rural and urban mortality rates was made in 1964 by Glass.25 While migration rates between 1951 and 1961 were calculated on the basis of adjusting for local differences in fertility and mortality rates, the predictions from 1961 onwards assume national rates. Such an equalisation of vital statistics between different types of areas would go some way to meeting one ofthe objections to the forward survival rate method, although migrants may not be representative of the total population and hence the prob- ability of dying may still differ as between in and out migrants. Nationalfertility and mortality rates Past national male and female birth rates can be derived for quinary female child- bearing cohorts, and past male and female mortality rates for all cohorts from the Registrar General's annual Statistical Review.26 Estimates of future fertility and mortality rates for England and Wales are provided by the Government Actuary's, Department. The most recent assumptions underlying future estimates of vital statistic rates, used by the Government Actuary's Department to project the U.K. population are given in 'Economic Trends' 1965.27 Basically fertility rates, for women married once only, were estimated from fertility rates by marriage age and duration since marriage. These are, in essence, a projection of the series of Tables QQ (a) in the Registrar General's Statistical Review ofEngland and Wales Part 11.28 Adjustments are made to the resulting births to allow for children of second marriages and for illegitimate births. These estimates offuture births and deaths made by the Govern- ment Actuary's Department, on assumptions about future trends indicated in 'Economic Trends'29 were used for the present projections. Migration Using an average survival rate method, and data from the G.R.O. Statistical Review adjusted for local areas, net migration rates for 1951-61 were calculated 19 for each quinary group. These compared favourably, in total for all ages, with unpublished estimates of net migration made by the Office of Population Censuses and Surveys for 1951-61. It is necessary next to consider possible future migration— some results are given in the following section. Migration is the most important factor in estimating future populations of local areas and the one that is most uncertain. Knowledge of the social forces underlying changes in fertility, nuptiality, migration and mortality is very incomplete, and the precise effects of suspected causes cannot be ascertained at present. Many political and economic events in the future cannot be foreseen, yet these influence demographic trends. Methods of Estimating Income There are a number of basic sources of data relating to income or forms ofincome. These are the Inland Revenue, earnings data of the Department of Employment and Productivity, material from the Family Expenditure Survey and Ministry of Social Security data. Published data from these sources relate to the county, regional and national level. In 1966 the Family Expenditure Survey(F.E.S.) began tabulating data by regions; previously only national estimates of income and expenditure were given. The F.E.S. suffers from both a small sample size and bias in non-response rates and cannot be applied directly to local areas. Nevertheless, F.E.S. data and earnings data lend themselves to estimation procedures ofincomes if combined with census data. Social Security data have been used by MacLeod and Watkin3° to estimate regional earnings by matching tax deduction cards with employment insurance cards used in administering the graduated pension scheme. The small sample size did not permit a breakdown below regional level; self employed persons are not included and no allowance is made for income other than that from employment, i.e. pensions, profits, interest and rents are excluded. These statistics also omit all employment for less than 48 weeks per year, i.e. temporary and cyclic work; this amounts to 10 per cent of male and 30 per cent offemale employees.'3 The only direct source ofincome data is the Board ofInland Revenue's compre- hensive series, theoretically applying to the whole population of taxable income receivers.32 These large comprehensive surveys are published quinquennially. Inland Revenue data identify tax units as tax districts. Where detailed area break- down is required, the limitations of this source become pronounced; data refer to area of employment and not of residence. The lack of official information on income and expenditure for areas smaller than regions or counties has resulted in estimates based on proxy variables.* Such

*Substitute variables which are known to be highly correlated with income and expenditure at a national level, and capable of being used to estimate income. 20 variables have ranged from four independent variables—the reciprocal of the infant mortality rate for a town, the logarithm of the rateable value per head, illegitimacy rate, and the logarithm of the number of private motor cars per head—giving a multiple correlation coefficient of +0.91 with income designated as the dependent variable.33 Variables such as infant mortality rate are known to vary with levels of living. The proportion ofjurors in an administrative area34 and the ratio of car licences to households35 have also been used. However, the latter proxy variable is very difficult to obtain from official British sources. In 1966, the Institute of Practitioners in Advertising related six social grades to income, the major criterion used in assessing the social level of each household being the occupation of the head of the household.36 Lewis37 used this latter procedure in the estimation of income distributions for small areas in Glamorgan, by undertaking a postal questionnaire and classifying respondents into socio-economic groups and noting their income. These estimates were matched against ward data, from the 1966 census, of socio- economic groups of economically active males; a correction was made for house- holds with multiple wage earners. Apart from the necessity to undertake a large postal survey, this technique raises a number of problems such as the proportion of heads of households to economically active males in each socio-economic group, the transition from head of household income to total household income which must be calibrated from national data through unavailability of local information, variations in local conditions, such as economic activity variations, and variations in the proportion of unemployed. Cox38 has applied a proposed method of income estimation to a number of London boroughs and Lancashire towns and the remainder of this section is an attempt to extend Cox's methods to smaller units, namely parishes, in the remoter rural areas of Northern England. Cox's method is dependent upon two pairs of empirical statistical relationships: (1) from the Family Expenditure Survey (1961), a close relationship was found to exist (r---= +0.94) between the average number of persons per household and the weekly income of households. Larger families with greater opportunity and need for multiple wage earners have higher incomes than smaller families. Mogridge has shown the inherent stability over time ofhousehold composition at each separate relative income leve1.39 (2) from the 1961 Census, a high inverse relationship (r= —0.81) was found between the percentage of occupied and retired males in the professional and managerial category and the average number of persons per household in the area. Households in which the occupied and retired males are in the professional and managerial category tend to be smaller households, with fewer multiple wage earners. Willmott,4° however, has shown that this correlation may prove to be unstable. 21 In order to produce a single measure of the household characteristics of an area a 'household index' is derived based on the percentage of occupied and retired males in the professional and managerial categories in comparison with the England and Wales average and the number of persons per household in comparison with the national norm. The combined index is based on the assignment of equal weights to the two factors. Table 2.1 shows the 'household indices' for a number of rural parishes in Northern England. TABLE 2.1 HOUSEHOLD INDEX 1966 Socio-economic Persons per Household Area classification Household* index 1966

Alston with Garrigill 94.6 84-4 89.5 Askerton 82.8 98.9 90.9 Bewcastle 101.9 761 89.0 Brampton 184.0 84-7 134.2 Burtholme 264.9 1111 188.0 Stanhope 48.3 88.9 68.6 Kirkoswald 23.7 80.0 51.8 Kirkby Stephen 79.5 95.0 87-2

*Persons per household corrected for parish economic activity rate-see page 27. This household index is then linked with data in the Family Expenditure Survey and an income index developed by Cox from the F.E.S. This income index is a two factor index using average number of persons per household as one factor and occupational classification (occupations equivalent to socio-economic groups form- ing the household index) as the other. Table 2.2 shows the relationship between the F.E.S. index and weekly household income groups. TABLE 2.2 FAMILY EXPENDITURE SURVEY (F.E.S.) INDEX 1966 Weekly income Occupation Persons per F.E.S. Average of household classification household index income (22.1% = 100) (3.03 .---- 100) k

Under k6 0 34 17 (0-28) 5-02 6 and under li) 25 52 39 (29-51) 7-95 k1.0 and under J15 52 72 62 (52-65) 12.47 J15 and under J,20 43 94 69 (66-75) 17.60 k20 and under k25 54 110 82 (76-85) 22.50 25 and under 3() 63 114 89 (86-104) 27.47 34.35 7C30 and under £40 121 115 118 (105-131) £40 and under £50 169 121 145 (132-148) 44.69 £50 and more 171 132 152 (149 & over) 69.27

22 The Household Index is matched against the F.E.S. index and the average household income group of each area read off. For example, Alston with Garrigill with a Household Index of 89-5 when matched against the F.E.S. index gives an estimated weekly household income of 25 and under 3O. Brampton with a Household Index of 134-2 has an estimated PO and under 51:) per household per week from the F.E.S. index. From Table 2 in the 1966 Family Expenditure Survey, the average household income in each ofthe income ranges(groups) can be obtained, and this multiplied by the total number of households in the area, gives an estimate of the weekly total area income. The above method of estimating income is based entirely on published official government data. An alternative approach, again based on published data, may be considered by way of a cross check. The 1966 Census ward data provide infor- mation on the industrial structure of the resident population in each parish by sex. This can be combined with information from the 1968 New Earnings Survey41 to estimate total earnings and earnings generated in each of the major industrial activities. Earnings by industry group are given for each region by sex for full-time manual and full-time non-manual adult workers. Census parish data, while split into males and females by industry, are not divided between manual and non-manual workers. An arbitrary division was made for each industry, by using the ratio of the number in the professional and managerial category to the totally economically active. Pensioners living in one- or two-person households were included with an allow- ance above the standard pension rate for other income from social security, rent, etc. Unemployed persons were treated similarly to pensioners. This type of exercise relates to earnings and thus makes no allowance for other income. This may be partly offset by the fact that earnings relate to 1968 and not 1966, and include the effect of two years inflation. Income from sources other than wages and salaries varies according to weekly income ofhousehold. 42 Households with weekly incomes ofless than 15 or more than 5(:1 have a smaller percentage of their weekly income from wages and salaries than households with weekly incomes between these two ranges.43 Thus parishes which have either low or high average weekly household incomes may have their total income considerably underestimated by the earnings method, perhaps by as much as one-third or more. Nevertheless, the earnings method allows the individual contributions to the local economy made by agriculture, mining, manufacturing and construction, transport, distribution and civilian services, national and local government and pensioners to be assessed.

23 3. POPULATION PROJECTIONS AND INCOME ESTIMATES IN THE NORTHERN PENNINES

Population Trends An attempt was made to define by multiple regression the factors which would be important with regard to gross in- and out-migration in rural areas of Northumber- land and in the areas ofDurham, Cumberland and Westmorland formally covered by the North Pennines Rural Development Board (Fig. 1). The technique also forms a predictive tool by which migration rates in future years can be predicted from changes in the socio-economic character of the areas. This is a deductive analysis, drawing on previous theoretical work, to build up a hypothesis to test. The logical consequences are tested here and the model predictions are compared with actual migration rates 1961-66, by local authority areas. The model explaining most variance in out-migration 1961-66 took the form Y=366.134+0.178(X i,)+2.206(X 3)+0.012(X 5) —0-652(X,) —0.191(X 9)+0.075 (X 13) This had a multiple correlation coefficient of 0.915 explaining 83.7 per cent of variance. Coefficients of all variables in the equation were significant at the 95 per cent level. The variables used in the model were: X1 size of area in square kilometres X, total population X3 density of population X, percentage males in socio-economic groups 1, 2, 3, 4(per 1000 males) X5 percentage males in socio-economic groups 13, 14, 15 (per 1000 males) X6 percentage of population (males and females) in 15-24 age group X, percentage of population (males and females) in 25-44 age group X8 percentage of population (males and females) in over 65 age group X9 percentage of population 25 years or over with 15 years or less as terminal school leaving age X„ distance to nearest urban district in kilometres Xn distance to nearest County Borough in kilometres X12 percentage of standard man days devoted to sheep X13 percentage of resident population in employment working outside area X14 employment in area as a percentage of residents in employment X15 percentage of population in owner occupied housing in 1961 X16 percentage of population in local authority housing 1961 X17 percentage of population in housing held by virtue of employment X18 percentage of population in private rented housing. 24 The model explaining most variance in in-migration 1961-66 took the form Y=310.638-0.869(X 18)+0.086 (X 4)-0.082(X 11) —0.203(X") This had a multiple correlation coefficient of 0.879, explaining 77.3 per cent of variance. The variables included were all significant at the 95 per cent level. Both models, while explaining a relatively high percentage of variance, still have low predictive value. This arises from the fact that the error term associated with each equation is greater than the net migration rate which is critical in determining population growth or decline. Also the models are cross-sectional, as time series information on in and out migration is lacking. Time series analysis on net migra- tion is difficult to justify since net migration is not a single phenomenon related to a single set offactors, but a complex result oftwo opposing flows, each represented by their own sets offactors associated with each origin and destination of migrants. The average of the estimates of age-sex net migration 1951-61 for each area were therefore assumed to continue. These provide reasonable estimates of total net migration for local authority areas compared with General Register Office un- published estimates of net migration 1961-6844. In proceeding from national to local area populations the importance of migration as an element in population change increases dramatically. Migration becomes the critical factor in population projections oflocal areas. This is shown by a sensitivity analysis(Table 3.1) in which assumed birth, death and migration rates are each altered by a constant proportion, holding the other two rates constant, so that the effect of each variable on the system may be assessed. TABLE 3.1 SENSITIVITY ANALYSIS POPULATION ESTIMATES 1991 WITH CHANGES IN DEMOGRAPHIC RATES

Population projection assuming Assuming 10% Assuming 10% Assuming 10% current birth decrease in births increase in deaths increase in net and death rates out-migration

M F M F M F M F Bellingham 2,577 2,657 2,391 2,508 2,552 2,635 1,321 1,373 Glendale 2,648 2,634 2,501 2,498 2,614 2,602 1,369 1,364 South Westmorland 10,544 10,015 9,931 9,504 10,421 9,885 5,442 5,187

A 10 per cent change in migration rates can result in radically different population projections compared with a similar proportional change in birth and death rates. 25 Table 3.1 shows that any error in projecting mortality is not serious in its effect on population projections since it only advances or delays by a few years the time at which the deaths will occur. An error in fertility is more serious and persists for a long time. Migration is the most difficult to project, which is unfortunate since it is the crucial variable in future population projections. The chief influence on migration is economic which is difficult to assess; the second influence is social characteristics and these vary and are impossible to measure for thousands of potential migrants. Housing is of great importance in some instances, and since house building plans are often what population projections are wanted for, the procedure becomes partially circular.'" It might be thought that demographers could do rather better, but there is little foundation for hopes of improvement in projections.

TABLE 3.2 PRESENT AND PROJECTED POPULATION WITH PERCENTAGE AGE GROUP BREAKDOWN

Percentage in Age Groups Total Pop. Actual Proj. 0-4 15-34 35-64 65+ 1961 1991 1961 1991 1961 1991 1961 1991 1961 1991

Alston with Garrigill 2,105 1,164 22.7 19.0 20.8 23.3 41.3 37.2 15.2 20.5 Border 29,644 26,972 23.2 25.6 25.9 28.0 38.6 33.5 12.3 12.9 Penrith 11,658 10,498 24.0 23.8 26.4 29.8 371 35-2 12.5 1F2 Barnard Castle 17,027 12,529 24.7 29.6 24.6 28.0 38.4 29.4 12-3 13.0 Lanchester 14,612 11,450 23.7 23.8 27.0 28.0 37-5 34.0 11.8 14.2 Weardale 8,457 6,224 21.3 25.6 23-2 27.6 40.4 321 151 14.7 Bellingham 5,287 5,234 28.2 32.5 22.0 34.7 38.6 27.8 11.2 9.7 Glendale 6,031 5,282 23.8 25.2 23.0 27.4 39.5 33.8 13.7 13.6 Haltwhistle 6,879 4,895 21.2 23.0 22.3 26.9 42.3 34.9 141 15-3 Hexham 20,248 16,842 21.9 23.4 231 28.0 40.6 34.0 14.4 14.6 Rothbury 5,498 4,313 23.6 22.7 21.8 25.9 38.2 34.8 16.4 16.6 Appleby 1,755 1,926 19.7 20.8 26.8 30.0 40.3 39.0 13.2 10.2 North Westmorland 15,354 9,777 23.8 24-0 24.8 27.0 381 36-3 13.3 12-7 South Westmorland 18,849 20,546 231 25-0 23.5 28.6 38.2 33.2 15-2 13.2

Table 3.2 records the age-sex characteristics of the population in each local authority area in 1961 and provides estimates for 1991 based on the assumptions outlined. The chief feature of this table is the widespread population decline likely to occur throughout the area in 1961-91 and particularly in Alston with Garrigill (-45 per cent decline in 1991 population compared with 1961), Border 26 (-9 per cent), Penrith (-10 per cent), North -Westmorland (-36 per cent), Glendale( —25 per cent), Haltwhistle (-29 per cent), Hexham (-17 per cent), Rothbury( —22 per cent), Barnard Castle (-21 per cent), Lanchester (-22 per cent)and Weardale(-26 per cent). It is probable that some population growth will take place in South Westmorland, a minor increase in Appleby, with stability in population size in Bellingham. Within areas of population decline, some parishes are obviously growing in size as a result of redistribution and relocation of population, while within South Westmorland and Bellingham a number of parishes are declining in population size. Projection of current demographic processes results in a much younger age structure of population in 1991 compared with 1961 in all the local authority areas, with the exception of Lanchester. This is coupled with a sharp drop in the per- centage of the population over 65 in Westmorland,but a sharp increase in this age group may be expected in Alston with Garrigill and Lanchester. The large number offemales compared with males in this age group in 1961, a feature also in 1991, is notable. The proportion of children (0-14) in the population increases in all areas except Rothbury, Lanchester, Alston with Garrigill and Penrith. This probably reflects an increase in birth rate between now and the end of the century. The increase in birth rate affects later age cohorts with time, resulting in all areas in an increased proportion of young male and female workers and married women between 15-34. Older workers(35-64) show a numerical and proportional decline. Projections of absolute numbers by quinary age groups are given in Appendix 3. Summary If current migration trends continue, the remoter rural areas of the North Pennines will suffer a substantial population loss, not only from agricultural areas but also from towns such as Haltwhisde. An additional significant feature will be a change in the age structure of the population. This has important implications for the provision of services in these areas, and any planning proposals should be justified economically on the expected population to be served through the life of the project and not on the present population alone.

Income Estimates, Earnings and Inland Revenue Data The degree of correspondence between estimates of the income and earnings was good for a number of parishes such as Alston with Garrigill and Bellingham (see Appendix 4). In general, however, the F.E.S. method tended to produce much higher estimates of income than the earnings method; this was particularly so in parishes where the average household income group was greater than k40, since much unearned income was not being included in the earnings method. However, a part of this difference is undoubtedly due to the lower economic activity rates in rural areas," i.e. there are not on average so many income earners per household 27 members of working age. For this reason it is doubtful whether Cox's method should be applied direct to rural areas without modification. The 'Household Index' was therefore adjusted according to the difference between the national economic activity rate in 1966 and the parish activity rate calculated from the 1966 Population Census parish data. This adjustment had the effect of reducing the income group to which some of the higher average income parishes had been classified. In local areas, with very small populations, both methods suffer severely from the small sample size (10 per cent). This is particularly true of Cox's F.E.S. method. Parishes such as Bavington, Greystead, Akeld, Earle, Ilderton, Kilham and Roddam in Northumberland have an estimated income one half or one third of estimated earnings. This is entirely due to the fact that no persons were recorded in these areas in the critical socio-economic groups which go to form half of the 'house- hold index'. TABLE 3.3 AGGREGATE INCOME ESTIMATES FOR FIVE NORTHERN COUNTIES

Income per week

Cumberland Estimate by Cox method* 2,504,201 Inland Revenue Estimate 1,813,461 Cox's method with activity correction rate* 2,368,226 Westmorland Cox method* 638,858 Inland Revenue 448,076 Cox method with activity correction rates* 614,838 North Riding Cox method* 4,686,610 Inland Revenue 3,063,462 Cox method with activity correction rates* 4,259,784 Durham Cox method* 11,136,782 Inland Revenue 8,496,154 Cox method with activity correction rates* 10,003,422 Northumberland Cox method* 7,133,564 Inland Revenue 5,575,000 Cox method with activity correction rates* 7,004,289

*Estimates derived by aggregating all local authority area estimates in each county.

Table 3.3 indicates that the derived estimates of income corrected for economic activity rates have reasonable accordance with Inland Revenue survey estimates for the five Northern Counties in 1964-5.47 The Inland Revenue figures represent 28 income as computed for tax purposes and are themselves under-estimates since they fail to cover: (i) some employees of farmers for whom there are no tax deduction cards and some domestic servants and members of the Forces with incomes above the deduction card limit but not liable to tax and for whom, by special concession, no deduction cards are issued (ii) deficiency in total income reported from investments estimated to be some- what over 4 per cent ofinvestment income (unearned income) (iii) wives earning less than 5.25 per week (iv) the first 15 of Savings Bank interest (v) certain National Insurance Benefits. Differences arising from: (i) inflation—Inland Revenue figures refer to 1964-5 but the derived estimates are for 1966 (ii) pensions and other non-taxable income (iii) earned and unearned income which is not declared must also be taken into account. Cox's method appears to overestimate the income ofareas on a parish and county basis compared with the earnings estimate and Inland Revenue data. When the method was corrected for economic activity rates in areas to which it was applied, better estimates resulted. Deviations between the two estimates at a parish level can probably be explained by census sampling error. On a local authority and county basis, income estimates were higher than Inland Revenue figures but the latter are known to be under-estimates. Table 3.4 shows income and earnings per week for local authorities and parts of local authorities in the former North Pennines Rural Development Board area. A more detailed breakdown by parishes is given in Appendix 4. Local authority areas in the more remote and upland areas, e.g. Alston with Garrigill, Weardale, Bellingham, Glendale, Rothbury and North Westmorland have lower average household incomes than the less remote and more agriculturally productive areas such as Border, Penrith, Lanchester, Hexham and South Westmorland. Even Haltwhistle in the Tyne Valley, a town with some industry, but nevertheless remote, has a relatively low household income. Bellingham and Penrith are heavily dependent upon agriculture with about 40 per cent of earnings derived from this source. Commuting and residential areas with greater proportions of professional workers, e.g. Humshaugh and Brampton, have very high household incomes. Service centres have greater total incomes with a smaller percentage of earnings from agriculture; these include Middleton in Teesdale, Lanchester, Stanhope, Wolsingham, Bellingham and Rothbury (Appendix 4). Parishes with some 29 industry, such as Haltwhistle and Shap, have substantially higher total earnings and income than surrounding parishes or others in the same local authority. North Westmorland is characterised by areas with a great dispersion of average household income from very high to very low, but is on average a poorer area per capita than South Westmorland. This may be partly explained by the location of more profitable types of farming in the south. Relatively prosperous agricultural areas such as Allendale have emerged with average household incomes of 40 per week. TABLE 3.4 INCOME AND EARNINGS ESTIMATES** PER WEEK

Earnings 1966 Income 1966*** Authority Local %earningsfrom Total Average Total agriculture earnings household income income

Alston with Garrigill 1F4 17,871 25—<30 18,130 Border* 23-9 97,136 30—C40 127,041 Penrith* 41.6 28,887 30—C40 34,703 Barnard Castle* 18-4 68,110 15—<20 45,680 Lanchester* 7-9 55,810 30—<40 60,981 Weardale* 30.2 41,330 20—<25 56,588 Bellingham* 38.3 43,706 25—<30 46,152 Glendale* 23.6 28,584 25—c30 29,456 Haltwhistle 11-5 64,765 20—<25 48,287 Hexham* 32-3 77,186 30—<40 91,460 Rothbury* 29.4 31,582 25—<30 34,917 Appleby 5.4 7,038 30—<40 8,244 North Westmorland* 27.5 111,897 25—<30 103,986 South Westmorland* 25.7 51,682 30—<40 62,605

*Estimates only for parts of areas within the former North Pennines Rural Development Board area. **Compiled from parish data in Appendix 4. ***Cox method corrected for activity rates.

Summary Considerable variations exist in the degree of prosperity or poverty over the Northern Pennines. Income estimates of this type would seem to be useful for assessing variations in the demand for goods and services in different areas, and are also useful in the planning of social welfare services following the recognition of the areas of greatest social need. Earnings and incomes provide a good measure of the economic health of an area and as such are used in the following section which deals with identification of economic problem areas. 30 4. PROBLEM AREA IDENTIFICATION

In the previous section, it was shown that many remote rural areas had low incomes and were likely to suffer from population decline over the next 20 years. However, great variety was seen to exist over the North Pennines with areas of high income interspersed with areas oflow income, and areas of population growth adjacent to areas of population decline. The problems of high rates of unemployment and relatively low family incomes in many rural areas in the Northern Pennines are by no means recent. Government has the power to formulate comprehensive develop- ment programmes for improving incomes and levels of living, so it is important to determine not only whether a small area is economically viable in terms of sufficient size and with adequate resources, but also to identify types of aid which are appropriate to the particular problems. In regional economic planning it is necessary, first of all, to define a problem area. There is little need to plan unless a problem is specified. Rarely can a single problem be identified, rather a whole complex of problems exist with inter- relationships between them. Because the combination of factors that cause low income and restrict opportunity vary among areas, no one standard treatment can be prescribed for all situations. In recent years, more than ever before, the agricul- tural sector is being recognised as only one of many interacting problem sectors of the rural economy. Low incomes, high unemployment, low economic activity rates and population decline have also to be considered in any remedial planning proposals. In the present study five variables have been chosen as characteristic of some of the problems facing remote rural areas today. This list is by no means a comprehensive coverage of all problems, being merely broadly indicative. These variables are (1) percentage population decline 1951-61, (2) average household income 1966, (3) unemployment rate 1966, (4) proportion of the population economically non-active, (5) the percentage of S.M.D.'s devoted to sheep 1966. Farm Management Survey figures for the Northern Region show Livestock Mostly Sheep farms as the poorest income generators. Variable (5) is therefore included as symptomatic of agricultural problems. Many other variables from the agricultural census, such as a measure of farm structure could be used but corre- sponding detailed and reliable socio-economic variables are lacking until 1971 Census data become available. Inter-relationships between these five 'problem' variables are not explored, but usually it will be possible to identify certain constraints and limitations to action which will determine the range of possible solutions. When there are multipl objectives the problem becomes more complex. One could conceive of a pro- gramme to increase average income for an area which resulted in more unemploy- ment, a lower economic activity rate, or a more unequal distribution of income. 31 This is a question of selecting the most feasible of the range of rural development strategies that an area might pursue. The immediate concern, and that to which the rest of this section is devoted, is to identify homogeneous areas in respect of common economic problems. In economic planning, a homogeneous region is a clear starting point. Economic planning regions may be defined in terms of type (agricultural, industrial, rec- reational etc.) and also the degree of economic development within each type. To analyse the character of various areas, an attempt must be made to discover the homogeneity of the development mechanism and problems or, better still, the homogeneity discernible from the various possible types of development, taking into account not only all the usual characteristic economic factors but also possibly the population's similarity of behaviour (cultural and social) with regard to develop- ment, provided the latter information is available. Multivariate statistics have now made it possible to analyse objectively certain statistical variations among areas, and group those criteria where the patterns of variation show the most similarity. - In order to establish different area types exhibiting differing problems here regarded as characterised by only five variables and to identify these problems within broad groups of areas, before applying varying treatments, a grouping procedure based on Ward's" method was followed. The objective was 'co relate a number of variables—percentage population decline 1951-61, average household income, percentage unemployed, percentage of labour force not economically active, and the percentage S.M.D.'s in sheep,—in each parish to such variables in other parishes in such a way that linked groups of variables and parishes may be built up in an orderly sequence to form a complete linkage tree. Each pair ofitems or observations, and subsequent groups, are joined so that the least possible incre- ment in the error sum of squares is made (or the minimum amount of within- group variability relative to the total data matrix variation) at each step in the sequence." Ward's grouping procedure is based on the premise that the greatest amount of information is available when a set of n members is ungrouped. The first step is to group two parishes, which, when united, will reduce by one the number of sub-sets while producing the least increase in the error sum of squares from the within group variance. The number of subsets is systematically reduced (n, n-1,....1) and a 'hierarchical grouping' results. Hierarchical groupings are particularly useful for classification purposes and identifying 'types' of prob- lems and associated areas. The significance of differences between aggregate groups of items or observations should refer to that stage in the linkage tree or hierarchical grouping where between group variability exceeds the overall within group variabilities. However, for the sake of interpretation of the underlying trends a cut-offpoint was taken at eight cluster groups. This number is small enough to allow generalisation and large enough to reveal the considerable differences in economic needs among parishes. 32 The five variables used to measure the relative economic health of each parish represent distinct and different aspects of the economic problem. This can be seen from Table 4.1 which shows the inter-correlations between the variables, and from the eigenvalues* and cumulative variance explained. The economic factors characteristic of each of homogeneous group or cluster of parishes are summarized in Table 4.2. The table shows general positive or negative relationships of each criteria with each cluster.

TABLE 4.1 CORRELATION MATRIX OF CRITERIA

(1) (2) (3) (4) (5) Population change (1) 1.000 , Income (2) 0.057 1.000 Unemployment(3) 0.037 0.051 1.000 Economically not active (4) —0.036 —0151 —0.007 1.000 S.M.D.'s sheep (5) —0.088 —0130 —0.012 —0.063 1.000 Eigenvalues 1-23 1.08 0.99 0.94 0.76 Cumulative variance 24.64 4615 65.95 84-80 100.00

TABLE 4.2 RELATIONSHIPS OF CRITERIA (PROBLEMS) TO CLUSTERS (PARISHES)

CRITERIA

Cluster Population Economically S.M.D.'s in Number change Income Unemployment Not-Active sheep

1. + S+ 2. — + + + 3. + + — 4. — — + 5. — — 6. ± — — 7. + — 8. — +

The identity of parishes in each cluster is given in Appendix 5. These groups identify common factors in economic health or deprivation covering a number of parishes as follows: 1. Parishes such as Alston, Kingwater, Bellingham, Kielder, Wark etc., exhibit population growth or stability, with a high percentage of S.M.D's in sheep. *Eigenvalues are the characteristic roots of a square matrix, and may be thought of, in this case, as 'stretchability coefficients' in each dimension of the problem. These coefficients are similar in value, indicating that the five variables measure independent aspects of the general problem in rural areas. 33 2. Bewcastle, Cumrew, Midgeholme, Allendale etc., have no distinct single common factor, but have average to high household income, high per- centage S.M.D's in sheep, but a low economic activity rate and population decline. 3. Brampton, Lanchester, Wolsingham, Wooler, Haydon, Appleby (mostly settlement parishes) are characterised by low percentage S.M.D's in sheep, with average to high household incomes and population growth. 4. Kirkandrews, Nicholforest, Woodland, Healeyfield, Hartleyburn etc., exhibit very low average household incomes, a very low economic activity rate, and high population decline. 5. Hayton, Kirkoswald, Lynesack and Softley, Haltwhistle, Rothbury etc., are characterised primarily by very low household income and also by a low percentage of S.M.D's in sheep. 6. Irthington, Walton, Plenmeller with Whitfield, Casterton, Greyrigg etc., are mainly characterised by two variables namely high household income and high percentage of economically active population. This category is the complete reverse of group 4. 7. Only five parishes fall into this cluster which remains distinct until only three clusters remain. Stapleton,He)diamshire Low Quarter,Nateby, Dillicar, Whitwell and Selside exhibit very high unemployment rates coupled with very high economic activity rates; they also show moderately high incomes. 8. Forest and Frith, Stanhope, Bavington, Corsenside, Falstone, Greystead, Otterbum etc., form a group not well distinguished by one criterion but exhibiting a moderately high economic activity rate, a high percentage of S.M.D's in sheep but with low income, population decline and unemploy- ment. Within any regional planning strategy covering overall development, sub- regional structure plans must exist. These will probably vary considerably in policy terms, for example in the objectives to be pursued, and in which areas are designated for growth, defensive or anchorage points, and areas to be abandoned or written off. Cluster analysis provides a convenient method by which such areas might be identified, and the general types of policy which might be applicable to different areas. It strongly reinforces the argument against having one standard policy for all rural areas irrespective of each sub-area's particular problems. The analysis shows that problems vary between areas to a great extent, and suggests that blanket support to agriculture, industry or recreation should not be spread over the whole area. The rate of return on investment in agriculture or industry would be much higher in some areas than others in terms of existing potential in agricultural type and structure and for industry in terms of labour supply. 34 Groups (I), (3), and (6) exhibit considerable economic health while group (7) requires measures to deal with unemployment. Groups (4), (5), (8) and (2) have more diverse problems requiring varying economic policies. The criteria used mean there are numerous goals and tables of value. The multiplicity of goals to be attained and problems to be solved and the preference functions of the areas may be so different that no coherent ordering will appear at the regional level. In current economic policy it may not be possible to take account of every possible aim or some aims may conflict so that a limited set must be chosen constituting the objective function of a programme. For example, a regional development pro- gramme may bring economic growth but not increase per capita income. It might increase the volume of output but might involve expanding low paying primary industries and so reduce aggregate regional income in relation to average national regional income. From a complexity of objectives a policy must be chosen. To determine this, each goal has to be expressed as a function of other goals, i.e. goals must be weighted in an evaluation matrix.50 This is the second step in building a regional operational model. The first step implies the choice of regional criteria and identification of problems. This division of space may be thought of as the establishment of programming regions. Cluster analysis provides an admirable tool for the first step: the division of space into homogeneous units for future programming and modelling. The following section explores the possibility of building an elementary model ofthe income and labour sector of the rural economy, with the object of evaluating methods and policies of improving agricultural and non-agricultural income and labour participation.

35 5. AN ECONOMETRIC STUDY OF INCOME AND LABOUR

Introduction To mitigate the undesirable effects of unemployment or underemployment or to avoid low and extreme income differentials within an area, it is often necessary to introduce regional planning and thereby attain better co-ordination ofeconomic and social activities within and among regions. Such a regional plan must be based on estimates and forecasts of social and economic conditions in the area of study. Methods of projecting population and estimating income have been discussed. A frequently quoted objective or goal in regional planning is the achievement of higher incomes, but this must be done in terms of a whole set offactors considered together in their inter-relationships. Only in this way will certain constraints and limitations to action be identified which will determine the range of possible solutions. In this section tools will be considered which can be used to isolate in a realistic manner the operation of the key indicators in determining income and labour force employment. Secondly and relatedly, the effect of changes in these indices and their inter-relationship which would arise through positive action devoted to the achievement of stated goals (e.g. increasing agricultural income, raising the proportion of the population employed), either singly or in combina- tion, is considered. The primary purpose of this section is the construction of a small area econo- metric model sufficiently accurate to be helpful in policy determination. Until more data are available, regional models will continue to be relatively simple, but an attempt is made here to undertake a quantitative analysis, by parish, ofearnings from agriculture and non-agricultural pursuits(based on earnings estimates derived from census data) and of labour participation* (as recorded by the 1966 census). A simultaneous equation model was employed to estimate the relative import- ance ofvariables thought to be involved in determining farm and non-farm income and labour participation in the work force. The essence of much economics is the interdependence between variables: it is often impossible to discover situations in which one variable may be taken as given and then observe the effect on the other. In a simultaneous equation system, the restriction of the multivariate regression model that one and only one dependent variable of the related set of dependent variables appears in the regression equation is relaxed, allowing the explicit specifi- cation ofthe dependence relation of one dependent variable on one or more ofthe other jointly dependent variables. It is assumed that income depends on labour participation and that labour participation is influenced by income levels. In an equation of a simultaneous equation system, it is generally assumed that statistical

*Labour participation: the population who are economically active (employed and unemployed) as proportion of those eligible to work (population between 15 and 64 years of age). 36 dependence exists between the jointly dependent variables appearing in the right- hand side of the equation and the disturbance term of that equation. Two stage least squares (2SLS) estimation procedure was therefore used. The important property of this estimation method is that it avoids the simple one-stage least- squares bias and lack of consistency which appears if Y2(t) was simply regressed on Yl(t). By using 2SLS that part of the variation in variable Y1 due to the disturbance is eliminated. This removes inconsistency, and the method is unbiased asympto- tically. The model is intended to account for variations in the following endogenous variables: Yl=income per capita from agriculture Y2=income per capita from all non-agricultural economic activities (excludes pensions etc.) Y3=labour participation rate (total labour force with jobs/total population eligible to work, i.e. males and females 15-64). The predetermined variables included were: X2=percentage of labour force in agriculture X3=percentage of labour force unemployed X4=median age X5=percentage of population in each parish in higher socio-economic groups (1, 2, 3, 4, 13) X6=1 if parish is service centre, 0 otherwise X7=percentage of S.M.D's devoted to sheep.

On the basis of these a formal economic model was postulated. The structural equations of the model of income and labour differences took the form: Ylt = ni+PlaYat4-Yi2X2t4-Yi4X4t+Yi6X6t -FYi7X7t Y2t = Y214 -P23Y3t Y22X2t Y24X4t Y25X5t Y26X6t

Y3t = Y31+fl32 Y2 t Y32X2t+Y33X3t + Y35 X5 t Y36 X6 t or in matrix notation

1 0 —Pm] [Y11 .V12 0 Y14 0 Y16 Y171 [0 1 --/323 1172 = ,V21 Y22 0 Y24 Y25 Y26 0 —f332 1 Y3 Y31 Y32 Y33 Y35 Y36

37 The model hypothesises that farm income or income derived from agriculture is determined by labour participation, the percentage of the labour force in agri- culture, the median age of the population, the degree of service facilities in the area, and the percentage of S.M.D's devoted to sheep. Income from non-agri- cultural economic activities is determined by labour participation, the percentage of labour force in agriculture, the median age of population, the percentage of the population in higher socio-economic groups, and the degree ofservice provision in the area. In turn, non-farm income is postulated as influencing labour par- ticipation, together with the percentage of labour force in agriculture, the per- centage of the labour force unemployed, the percentage of population in higher socio-economic groups, and the degree of service facilities in the area as a measure of increased employment opportunities. Estimates of structural parameters. All the equations of the model are over-identified.* In order to avoid the weaknesses and inconsistencies of ordinary least squares(OLS) methods, two stage least squares (2SLS) estimation method was employed. This method not only uses over-identifying restrictions but is asymptotically efficient compared with other estimators using the same a priori information. A limited information maximum likelihood estimator is also consistent and uses over-identifying restrictions and ranks as a substitute for 2SLS. However, 2SLS is less influenced by multi- collinearity than the limited information method and is therefore preferred. The data consisted of 165 observations, that is all parishes in Cumberland, Westmorland, Northumberland and Durham wholly or partly within the former Northern Pennines Rural Development Board area. Multicollinearity among the predetermined variables was low as can be seen from Table 5.1. TABLE 5.1 CORRELATION MATRIX OF PREDETERMINED VARIABLES ,

Xx6 X X2 X3 X4 7

X2 1 •00 X —045 1.00 X34 —0.03 0.03 1.00 X5 0.03 0.02 —0.01 1.00 X6 —0.34 0.07 0.14 —0.02 1.00 X7 0.18 —0.01 0.02 —0.13 —0.08 1.00 ,

*A necessary condition for over-identification of an equation is that the number ofendogenous variables in the equation is less than or equal to the number of predetermined variables in the system but not in the equation.

38 The 2SLS estimates of the structural parameters together with t values* are = —33.433 + 0 .564 0.072X 2,—0 .0524 (7.995) (5.920) (-7.866) —1-120X 6 —0.016X„ (-6.877) (-5.906) Y2,= — 1.426+0-113173,-0.1534+0.0234 (0.448) (-3.380) (0.960) +0 .0014+ 0 .350X„ (0.028) (0.540)

Y3,= 61.474+0.317Y 2,-1-0'220X2,-1-0•1654 (0.192) (0.943) (0.284) +0.0364+2.2494 (0.314) (0.697) In single equation systems there are regression coefficients which measure systematic relationships between the variable to be explained and the explanatory variables and there are also correlation coefficients which measure the extent to which these systematic relationships do, in fact, explain the fluctutations in the dependent variable. For simultaneous equations, only the former aspect has been widely developed and the regression coefficients associated with the present simultaneous equations of income and labour are given above. It is not possible to derive a statistic to estimate the goodness offit ofeach equation in a simultaneous system.t However it is useful to have a generalised correlation coefficient which measures the extent to which the systematic relationships explain the fluctuations in the set of all jointly dependent variables. Hooper52 has proposed a statistic, which he calls the trace correlation, to measure the proportion of the total variance ofthe jointly dependent variables as a group that is explained by the predetermined variables as a group in a structural model. Hooper shows that his trace correlation 1.2 is equal to the simple average of the canonical correlationst between the

*For structural equations with two or more jointly dependent variables, results must be regarded as approximate because the normal distribution is only approximately appropriate. tA statistic analogous to the squared multiple correlation coefficient R2 might be thought of such as 1 —.Ette/gYit —i71)2 Basmannsi, however, has pointed out that this statistic can be negative because 22 (residuals) can exceed gyit ---hr and this can happen even when the correct model is being used. IThe maximum correlation (least-squares optimum) between a set of criteria variables and a set of predictor variables such that the combined sum of the criteria variables correlate maximally with the combined sum of the predictor variables fl(Y1, Y2 • • • • YP)= f2 (Xlt X2 'CO These are simply two batteries which must be weighted so that the residual variance is as small as possible. Hotelling" termed this technique 'canonical correlation'. Canonical correlation can be regarded as a measure of the extent to which individuals occupy the same relative positions in the p-dimensional space as they do in the q-dimensional space. 39 dependent variables and the predetermined variables. From the econometric model of income and labour 2 is equal to 0.961 Thus approximately all the generalised variance of the set of jointly dependent variables has been accounted for by the regression relationship and approximately 5 per cent remains =explained. The structural model in matrix notation is of the form = yX from which the reduced form coefficients can be derived by determining Y = 13-1yX The influence of the predetermined variables on agricultural income, non-farm income and labour participation can be seen from the reduced form coefficients in Table 5.2. These record the change in income and labour participation rates as a TABLE 5.2 REDUCED FORM COEFFICIENTS OF PREDETERMINED VARIABLES IN INCOME-LABOUR MODEL

Predetermined Percentage variables— of Parish population subject to Percentage Percentage 1 service Percentage in each policy of of Median centre S.M.D's influence labour labour age of parish in 0 not devoted force in force population higher service to sheep Dependent agriculture unemployed socio- centre variable to economic be explained groups

X2 X3 X4 X5 X6 X7 Y,t Agricultural ' income per head +0168 +0.096 —0.048 +0.021 +0.209 —0.016 Y2t Non farm income per head —0.133 +0.019 +0.024 +0.005 +0.626 ___. Y,1 Labour participation rate +0.278 +0171 +0.007 +0.037 +2.445 ___ result of a change, perhaps induced by a policy change, in the predetermined variables. For example a decrease of one unit in S.M.D's devoted to sheep pro- duction would raise agricultural income per head by 0.016 units; a one percentage rise of the share of the labour force in agriculture would increase agricultural 40 income by 0468. These reduced form coefficients have allowed for the effects on other predetermined variables and their influence on the dependent variable as a result of the change. It should be noted that the coefficients in the structural equations are not necessarily of the same sign or magnitude as the reduced form coefficients.

Results Agricultural and non-agricultural income were well accounted for by the model. Agricultural income per capita is positively related to the labour activity rate; but while the percentage of the labour force in agriculture is positively related to income, and median age and percentage S.M.D's devoted to sheep are negatively related to income, and all highly significant, their coefficients are small. A unit increase in the percentage of the labour force in agriculture would only raise agricultural income by a small amount, as would any decrease in median age of population and S.M.D's devoted to sheep. The service centre variable indicates that agricultural per capita income is higher nearer to or at service centres and lower in the rural hinterland as would be expected. This latter variable, together with labour activity rates for the total working population (Y,), are highly sig- nificant determinants of agricultural income; and any change in these variables (Y3 and X6)will result in radical changes in agricultural income per capita, compared with results from any other changes in the remaining variables in the model. This analysis suggests that the direct effects of increasing activity rates would more than offset the downward pressure on agricultural income resulting from the older age structure in rural areas and the greater concentration on sheep production. Non-agricultural income per capita was found to be negatively related to the percentage of the labour force in agriculture in rural areas. Other variables were not related significantly to non-farm income with labour participation unexpectedly proving insignificant with a small structural coefficient. It might be hypothesised that activity rates would have been greater in areas where non-farm incomes were high with more people being persuaded to enter the labour market. Presumably this would have been especially likely to happen in service centres. The third structural equation, while recording a large coefficient, indicative of a large in- crease in activity rates within service areas, has a non-significant t value. Equation 2 records that there is a relationship between service provision and the level of non-agricultural income, but that it is non-significant. Median age is more sig- nificantly related but has less effect on non-agricultural income; the proportion of the population in higher socio-economic groups is not related to non-agri- cultural income in this rural area. The third structural equation is included in the model primarily for statistical reasons. That is, the direction of causation between labour participation and other endogenous variables should run both ways, and this must be recognised by a 41 separate equation in order to obtain consistent estimates of the parameters of Equations 1 and 2, namely agricultural and non-agricultural income per capita. Equation 3 reveals no variables significantly correlated with economic activity rates but that such rates are probably related positively both to the agricultural and service sectors. It is conceivable that in remote rural areas with a large proportion of the population in agriculture, labour participation may rise somewhat as wives and relatives are engaged in farm work; at the opposite end ofthe scale, equally and with more effect, the greater the degree ofurbanisation the greater the employment opportunities giving rise to greater economic activity rates. In seeking higher agricultural income levels in rural areas more attention should probably be given to increasing labour force participation by stimulating additional employment and facilitating movement from rural areas. The provision of more labour market information in these areas might serve the same goal as well as prompting greater participation in the local labour force. Reducing dependence upon sheep would improve income levels, but in general by only a small amount. These are policy decisions but they must be reached. The problems of rural areas are complex, with effects interwoven in different economic spheres and finding expression in a variety of economic indices. The primary purpose of this section, the construction of a small area econometric model of income, has been successfully achieved. The analysis is based on cross- section data. This is a weakness in any policy model but as more data become available time-series models will be built. Time-series models assume that the equation will apply without change (i.e. the a and 13 parameters will not change) from year to year at least for a certain period of years. Data constraints limit the sophistication of the present model but it should be sufficiently accurate to be helpful in policy determination. Until more data are available regional models will continue to be relatively simple. In future research more attention should be paid to the important sectors of local economies, for instance to equations relating the region's key industries and to equations relating these and income to employment and other significant variables. It is hoped that this section has shown the usefulness and great potential of econometric techniques in regional analysis in Britain.

42 6. SUMMARY AND CONCLUSIONS This monograph has attempted to co-ordinate in an analytical context economic and social information from different sources. The general aim has been to give numerical definition to the pattern and make-up of society and to changes in this pattern through time. It has aimed specifically at providing a consistent and repeatable basis of analysis and research upon which to base policy and planning. It has thus served related aims of integrating in a feasible way social, economic and other statistics and providing a systematic framework for the analysis of many aspects of social change such as variations in quantity and types of demographic, income and labour outputs following changes in the structure ofthe socio-economic environment. The results obtained show that a start can usefully be made with existing official statistics, but gaps and inadequacies in the material soon become apparent. When results of projections made in the past are compared with population changes that have actually taken place, it is sometimes, and perhaps not surprisingly, found that the projections have not been accurate. Demographers therefore avoid using words such as 'forecast' or 'predict' and use less ambitious verbs, for example 'estimate' or 'project'. A 'projection' ranges further into the future than an 'esti- mate'; it depicts what would happen if certain assumptions as to fertility, mortality and migration were borne out, but little claim is made that in fact these assumptions will be borne out in practice. Moreover, the conditions of human life are complex and it is questionable whether one could adequately express socio-economic trends over a long period even if data were available. The population projections pre- sented here are based on current information about growth, direction offlow, etc.; under these assumptions, which reflect the current economic state of rural areas and existing policies towards them, population decline will be widespread through- out the Northern Pennines. No attempt has been made to adjust rates for future time periods on the basis of changes (such as possible policy changes) thought likely to occur. • The assumptions upon which income estimates were based are also likely to change over a long period. This will not affect the 1966 income estimates in Appendix 4, but future estimates based on the method outlined should make allowance for possible changes in professional and managerial households with respect to the number of wage earners and the recent reduction in selective employment tax (July 1971). The latter change may give rise to more part-time employment and result in changes in activity rates especially among the female population. The population projections indicate further widespread population decline in rural areas based on the assumptions outlined. For the area as a whole (comprising the local authority areas in Cumberland, Westmorland, Northumberland and 43 Durham wholly or partly within the former Northern Pennines Rural Develop- ment Board area) the population may be summarised as follows:

POPULATION CHANGE 1961-91

Male Female Total

1961 81,675 82,729 164,404 1991 67,800 70,852 138,652 Percentage change —170 , —144 —157...

This conflicts directly with the published planning goals for the maintenance of an acceptable level of population in agricultural regions. Even though concern may be expressed on making the best use of capital investment,'The over-riding matter for concern of a rural policy for Northumberland, however, is to devise a plan that will enable the run down of the rural community to be halted'. 'The population trends in Northumberland.. , have been on a dramatic scale and go beyond the point where one could regard the process in a tolerant way'.54 No a priori social objectives are stated to justify such a conclusion which takes no account of economic costs. Since no philosophy is proposed to justify the maintenance of the rural community it can always be asked whether the run down of population is necessarily bad and then attempt to assess its effects and ramifications. Depopulation has the effect oflowering many communities towards critical social and economic thresholds. Thresholds relate to the size of population served which justifies the provision of an economic or social service within the area. Social thresholds relate to the numbers required to maintain community institutions etc. in life, and economic thresholds the numbers required to maintain economic services such as public transport, distributive and personal services. Many rural communities are already below a population size which justify banking and legal services or consumer durable shops. Others are tending downwards to a level where public transport and food distribution services are in danger of being withdrawn. Rural districts are known to have diseconomies in the provision of a wide range of local government services because of their small size.55 Yet the econometric study of income and labour suggests that agricultural income per head would rise if more out movement of population occurred, although real income could presumably fall. Depopulation will not be uniformly distributed so that in some areas such as Alston with Garrigill, North Westmorland and Weardale it is likely to be in- creasingly difficult to maintain services. Not unexpectedly, the situation is likely to be more serious in the uplands and upper dales than lower down the valleys in the Hexham, Border and Penrith areas. Many areas such as North Westmorland 44 already have low incomes which are inhibiting tertiary (service) development. It is clear that over a large section of the North Pennines there will be insufficient people to maintain vigorous, efficient and viable communities. The present situation is likely to deteriorate, rapidly and drastically in some areas. This is likely to have far reaching effects on the type of society to be found in rural areas in the future. Further cuts in distributive and transport services will be inevitable and greater dependence on towns and service centres outside the area will ensue, with demands for private transport. If depopulation is to be influenced and money incomes improved relative to existing higher urban incomes, positive rural policies are needed. It may be ques- tioned whether incomes can be effectively raised by transferring resources out of sheep production and concentrating on other types of agriculture or by the restructuring of agriculture in remoter areas. The analysis here suggests the over- riding need is to increase labour activity rates; the most obvious way to do this is to provide more employment outside agriculture. There is at present a lack of variety in rural employment. To retain as many people as possible in agriculture is contrary to the aim of achieving equality ofincome and standard ofliving for those engaged in agriculture with those in other occupations. The largest coefficient influencing farm income, non-farm income and labour participation, was that associated with the urban hierarchy (see Table 5.2): whether a settlement was classified as a service centre or not. Moreover, higher returns on investment in service provision (roads etc.) are to be expected in places with a higher concentration of population. Farm income could be raised by intensifying agriculture in favourable locations near service centres and abandoning the remoter and poorer agricultural areas to farming. Rural upland areas can best be helped if the available resources are concentrated into a few well-chosen locations, rather than dispersed over wide areas. These should be chosen on the basis of their inherent ability to grow, rather than the needs of an area to be served by a centre. There will never be enough funds to satisfy all the objectives throughout the entire rural area, and it is usually better to do a few things well than a lot badly. By concentration in selected areas labour participation and non-farm income could be raised in a suitable way (see Table 5.2). The first aim of a planning proposal must be to state the problem and to define the objectives: in terms of the level and distribution of income in society etc. This study has been concerned with statements of fact and trends; little has been said on objectives. Clearly population, income and other socio-economic variables can be influenced to a given end. A method ofgrouping areas with similar problems or possibilities has been proposed so that once policies are proposed for given objectives suitable areas for each type of policy can be identified. A simultaneous equation model of the rural economy will identify difficulties and constraints in the solution and also the range of possible solutions. It is intended that a subsequent 45 monograph will indicate the techniques which will make it possible to distinguish which of the various types of agricultural enterprises, recreational enterprises and industry groups the region possesses the greatest comparative advantage for, and hence to assist in deciding the optimum policy to pursue to attain given objectives in a given part of the country.

46 APPENDIX 1

Cohort-Survival Formulae in Population Projections

The equation widely used as model in estimating population has the form EPod-EB—ED+EM = EP, (1) where EB and ED, respectively, symbolise the total number of births and deaths occurring to residents in the area, EM the balance of all movements into and out of the area, and EA,and EP, respectively, the total population at the beginning and end of the period. This vital statistics formula applies to the total population of all ages; hence the need for including births and the population age groups representing their survivors at the end of the decade. For age cohorts born during the projection period: P,= B—D+M For age cohorts born before the base year of the projection: = Po—D+M Total net migration equals surviving in-migrants and in-migrants who die minus surviving out-migrants and out-migrants who die. The 'vital statistics' formula makes proper allowance for those migrants, both in and out, who die after migrating. From EM (P1—EP0)—(B—ED) Siegel and Hamilton have shown M = Mi—M0 = Li+Dia—Lo—Doa and that D = Dn-I-Dia+Dob where M = Mi+Mo = exact net migration = in-migrant sub-cohort Mo = out-migrant sub-cohort = in-migrant sub-cohort enumerated final population within area Dia = in-migrant sub-cohort deaths within area Lo = out-migrant sub-cohort enumerated final population outside area Doa= out-migrant sub-cohort deaths outside area = non-migrant sub-cohort deaths within area Dob = out-migrant sub-cohort deaths within area. While not important Dob is included for the sake of completeness. 47 The 'forward survival rate' formula has the form: Po—(1 — r)Pod-M (2) for an ageing cohort. Where r represents the survival rate, (1—r) the mortality rate which is the complement of the survival rate. For new born cohorts the equation would also include a birth rate, estimated from fertility rates of women by age groups, and a survival rate applied to the number of births. Equation (2) is similar to equation (1)for ageing cohorts(births are excluded here since they make the argument more complex) in that(1-0P 0 has been substituted for D. But this substitution is not a valid one. The number of deaths in an ageing cohort Po is represented by (1—r)Po, and this is equal to: D.+D oa+D ob and not D.+Dia+Dob as the substitution assumes. The difference, Doa—Dia, is the difference between the deaths of in-migrants and out-migrants. The forward survival method implies that no persons who die during the period (including those who move and then die) have migrated. Alternative methods of computing net migration are the 'reverse survival' rate, which has the form: (1—r)P1 M and the 'average survival' rate (an average of the forward and reverse methods) expressed as (1 -I- r) 2r (P1— rPo The forward survival rate method implies that no persons who die during the period (including those who move and then die) have migrated. The reverse formula implies that all in the migrating cohorts who die during the period (including those who die without actually moving) have migrated. The average survival formula (1-1-0/31 (1+OrP0 M = 2r 2r may be used as a projection equation in the form: 2M = (r -1+r + 130)

48 APPENDIX 2

Population Projection as a Stochastic Process Let the population at time t be P(t), net migration be m(persons/time period), death rate p, and birth rate p. Then considering a very short time period (t, t+At) P(t-I-At) = P(t)—pAtP(t)-kflAtP(t)-ErnAt dPt at- = for which the solution is m 6—(p-P)t m P(t) = (P(0)— (p —/3) This assumes migrants have the same fertility and mortality patterns as others, but other assumptions are feasible. Migration is added as a constant irrespective of P(t); if migration is assessed proportionally dependent upon P(t)(as gravity and intervening opportunity models predict56) then it may be treated as part of the birth process. Rates may be substituted for p; 13 and m and the demographic consequences assessed.

49 APPENDIX 3 Population Projection, 1991, by Local Authority Area and Quinary Age-Sex Groups

Alston & Garrigill R.D. Border R.D. 1961 1991 1961 1991 M F M F M F M F 0-4 89 79 35 34 1,200 1,098 1,112 1,107 5-9 63 79 38 36 1,063 1,060 1,150 1,104 10-14 100 67 42 36 1,301 1,162 1,355 1,088 15-19 78 69 38 31 1,756 898 1,345 1,002 20-24 44 43 34 26 800 806 957 909 25-29 45 57 35 27 821 782 752 919 30-34 52 49 48 32 937 882 739 921 35-39 65 71 34 33 1,015 1,035 616 905 40-44 84 69 53 30 1,014 960 626 1,021 45-49 75 89 48 38 985 995 819 855 50-54 83 78 30 28 1,065 1,003 482 820 55-59 76 72 29 42 860 912 597 784 60-64 37 70 30 38 713 875 669 825 65-69 44 73 31 53 594 734 591 840 70-74 31 45 28 40 437 608 395 588 75+ 58 71 25 63 500 773 329 749 1,024 1,081 577 587 15,061 14,583 12,536 14,436

Penrith R.D. Weardale R.D. 1961 1991 1961 1991 M F M F M F M F 0-4 468 468 420 398 296 272 262 244 5-9 483 427 431 400 227 251 288 248 10-14 497 450 461 392 414 343 304 248 15-19 539 400 461 362 283 267 264 229 20-24 315 299 431 335 257 221 228 209 25-29 369 355 436 337 227 226 220 207 30-34 402 398 421 346 250 227 183 179 35-39 383 388 412 314 245 249 117 160 40 11 417 339 378 329 266 306 193 218 45-49 398 349 384 309 316 296 150 188 50-54 373 401 221 243 297 303 149 171 55-59 338 362 252 285 301 329 136 179 60-64 278 294 263 302 245 264 155 179 65-69 251 283 211 261 211 248 133 180 70-74 187 221 157 178 155 213 93 177 75+ 228 298 126 242 173 279 84 248 5,926 5,732 5,464 5,034 4,163 4,294 2,960 3,264 50 Barnard Castle R.D. Lanchester R.D.

1961 1991 1961 1991 M F M F M F M F

0-4 692 689 678 626 616 494 465 428 5-9 631 614 714 629 548 498 480 417 10-14 859 724 738 613 694 610 518 416 15-19 551 559 642 564 678 492 505 404 20-24 502 510 435 521 507 434 434 385 25-29 494 446 314 525 478 431 400 385 30-34 556 573 256 525 460 472 368 321 35-39 589 597 208 451 508 498 297 326 40 44 545 565 252 515 473 452 347 402 45-49 552 536 171 412 503 479 352 339 50-54 569 575 212 390 457 465 290 313 55-59 550 533 280 339 436 464 292 316 60-64 416 509 334 426 341 399 277 347 65-69 344 453 300 407 263 338 259 340 70-74 250 322 196 305 189 273 171 259 75+ 317 405 182 370 273 389 171 426 8,417 8,610 5,911 7,618 7,424 7,188 5,627 5,823

Bellingham R.D. Glendale R.D.

1961 1991 1961 1991 M F M F M F M F

0-4 232 245 268 235 306 252 231 218 5-9 239 231 331 260 269 239 237 221 10-14 279 263 357 250 314 293 223 201 15-19 145 131 290 204 230 204 197 175 20-24 147 115 206 169 162 173 179 168 25-29 142 144 169 163 217 200 188 180 30-34 192 149 159 206 216 214 199 163 35-39 191 189 130 185 241 244 165 143 4044 187 170 130 211 227 200 198 184 45-49 172 162 70 113 238 234 159 143 50-54 195 176 79 103 239 234 115 123 55-59 169 163 81 127 238 274 144 137 60-64 119 146 108 120 190 219 129 145 65-69 98 121 89 126 130 220 120 155 70-74 73 87 60 85 123 145 81 104 75+ 90 125 51 98 148 198 81 173 2,670 2,617 2,577 2,657 3,488 3,543 2,648 2,634

51 D* Haltwhistle R.D. Hexham R.D.

1961 1991 1961 • 1991 M'. F M • F M F M:. F

0-4 216. 230 - 198 177 • 815 705 684 628 5-9 - 255 200 202 175 704 644 693 609 10-14 307 252 . 204 168 829 735 700 605, 15-19 235 216 198 158. 667 653 660 . 596 20-24 177 169 183 154 510 589 614 569 25-29 166 183 181 158 522 536 • 631 555 30-34 198 191 138 146 607 602 632 503 35-39 208 250 156 128 . 633 678 . 527 464 . 40-44 250 236 189 169 643 692 . 607 522 45-49 242 254 150 160 711. 640 513 462 50-54 266 275 116 129 693 814 413 431 55-59 237 257 106 140 701 775 418 418 60-64 204 228 121 145 534 693 464 479 65-69 159 195 106 170 442 608 411 488 70-74 119 145 87 124 356 • 443 290 398 . 75+ 158 201 81 179 419 655 284. 572 3,397 3,482 2,415 2,480 9,786 10,462 8,542 8,300

Rothbury R.D. South Westmorland R.D.

1961 1991 1961 - 1991 M F M F M F M F

0-4 227 226 165 160 704 619 859 773 5-9 212 215 172 164 681 639 934 780 10-14 209 208 169 , 150 967 737 994 794 15-19 186 142 152 129 . 753 620 904 749 20-24 142 143 139 117' 518 434 804 662 25-29 140 137 144 124 514 447 801 638 30-34 148 161 164 146 580 555 ' 756 577 35-39 168 . 180 154 142 563 594 642 569 40-44 167 174 152 150 564 549 823 645 45-49 174 198 139 111 584 688 675 578 50-54 170 , 199 104 117 577 713 476 432 55-59 155 191 98 111 608 649 447 465 60-64 154 171 101 123 . 481.. 644 471 592 65-69 115. 165 103 129 385 543 389 594 70-74 112 158 81 108 297 492 282 434 • 75-F. 154 197 94 200 433 717 286 729 . • 2,633 2,865 2,132 2,181 9,209 • 9,640' 10,544 10,002

52 Appleby M.B. North Westmorland R.D.

1961 1991 1961 1991 M F. M F M F • M F

0—.4 64 ' 41 70 70 659 . 617 393 383 5-9 48 59 64 . 66 558 594 401 396 10-14 • 70 64 66 67 '630 - 594 ' 395 381 15-19 77 .54.. 75 70 540 497 360 333 20-24 80 62 81 64 460 391 324 308 25-29 47 . '39 93 63 454 . 449 321 316 30-34 58 ''''53 94 37 "'-‘ '532' 491 347 328 35-39 55 60 . . 74. 52 516 449 288 312 40 11 51 . 44 102 54 488 482 331 329 45-49 71 81 100 45 498 503 . 304 . 307 :... 50-54. 69 60 91 54 525 513 • :271 • 251 55-59 48 64 47 35 • 513 497 264 285 60-64 47 57 49 48 - 386 . 476 296 310 65-69 • 28 57 35 .. . 51 342 403 241 _255 70-74 25 52 18 28 264 342 145 ..- 209 75+ 23 47 16 48 , 251 440 112. 283 861 894 1,075 - 851 7,616 7,738 4,792 4,985

53 APPENDIX 4

Estimates of Earnings and Incomes by Parish per week

Cox method correctedfor activity rates Local Authority Parish Earnings 1966 Income 1966 & Parish % earnings Average from Total household Total agriculture earnings income income

Cumberland- Alston & Garrigifi R.D. & C.P. 11.4 17,871 25-30 18,130 Border R.D. Askerton 52.5 1,563 25-30 1,373 Bewcastle 71.2 2,853 25-30 3,571 Brampton 3•6 35,988 40-50 58,097 Burtholme 59.7 2,549 >50 4,848 Castle Carrock 24.0 2,590 30-40 3,091 Cumrew 50.6 649 40-50 1,341 Farham 19•6 4,743 20-25 5,768 Geltsdale Hayton* 19•3 12,913 10-15 4,988 Hethersgill 41•7 2,146 >50 8,312 Irthington 45.6 7,631 >50 14,550 Kingwater 59.5 1,873 25-30 1,374 Kirkandrews 27.3 6,316 25-30 5,494 Midgeholme 0.0 750 30-40 1,031 Nether Denton 27.4 2.965 20-25 2,250 Nicholforest* 35.9 2,845 6-10 954 Solport 944 1,465 30-40 1,718 Stapleton 27-0 2,226 30-40 2,061 Upper Denton 71.0 840 30-40 1,031 Walton 18.3 1,452 40-50 3,128 Waterhead 46.7 2,779 30-40 2,061 Penrith R.D. Ainstable 55•2 3,794 40-50 5,810 Culgaith 33.9 5,525 20-25 4,725 Glassonby 78.4 1,591 15-20 1,760 Hunsonby 31.7 3,464 25-30 3,296

*Parishes in which no persons were recorded in socia-economic groups forming (with people per household) the 'Household Index'. 54 APPENDIX 4-continued

Cox method correctedfor activity rates Local Authority Parish Earnings 1966 Income 1966 & Parish % earnings Average from Total household Total agriculture earnings income income k k k Kirkoswald 45.2 5,804 6-10 1,829 Langwathby 29.6 6,065 >50 13,161 Ousby 48.4 2,644 30-40 4,122 Durham- Barnard Castle R.D. Eggleston 35.7 3,621 20-25 3,375 Evenwood & Barony 6.3 25,732 10-15 12,594 Forest & Frith 57.2 2,232 25-30 2,472 Langleydale & Shotton* 64.3 243 <6 100 Lynesack & Softley 20.2 14,023 15-20 9,856 Marwood 54.0 5,057 30-40 5,496 Middleton in Teesdale 10-7 12,797 15-20 9,328 Newbiggin* 36.8 1,273 6-10 477 South Bedburn* 44-7 1,334 6-10 398 Woodland 10.3 1,798 15-20 1,584 Lanchester Healeyfield 5.7 10,770 20-25 9,900 Lanchester 6.7 41,407 30-40 47,060 Muggleswick 33.7 2,182 >50 3,464 Satley* 21.5 1,451 6-10 557 Weardale Edmondbyers 81.0 1,338 25-30 1,374 Hunstanworth 25•1 1,472 25-30 1,374 Stanhope 13.6 4,800 15-20 29,392 Wolsingham 13.4 33,720 25-30 24,448 Northumberland- Bellingham R.D. Bavington* 78.3 399 6-10 159 Bellingham 13.8 8,864 25-30 9,065

*Parishes in which no persons were recorded in socio-economic groups forming (with people per household) the 'Household Index'. 55 APPENDIX •4-continued

Cox method correctedfor activity rates Local Authority Parish Earnings 1966 Income 1966 & Parish % earnings Average from Total household Total agriculture earnings income income Z 4 4 Birtley 691 1,238 40-50 2,234 Corsenside 26.5 4,184 20-25 3,825 Falstone 51-6 3,320 25-30 2,198 Greystead* 37.7 828 6-10 318 Kielder 87.0 3,621 25-30 3,296 Kirkwhelpington 59.0 3,298 >50 7,620 Otterburn 25.9 5,139 25-30 4,395 Rochester 48.0 3,673 25-30 3,845 Tarset 45.6 3,083 40-50 4,022 Wark 26.5 6,059 20-25 5,175

Glendale R.D. Akeld* 18.6 1,069 6-10 239 Earle* 49.9 1,156 15-20 528 Ilderton* 41.2 1,515 10-15 624 Ingram 23.0 1,239 30-40 1,374 Kilham 6F5 1,238 10-15 499 Kirknewton 84.9 1,807 25-30 1,648 Roddam* 79.5 922 10-15 499 Wooler 10-3 19,638 30-40 24,045 , Haltwhistle R.D. Bardon Mill 22.7 3,573 30-40 4,809 Coanwood* 38.8 2,051 6-10 716 Featherstone 48.3 1,271 40-50 2,681 Greenhead 8.8 4,115 15-20 2,640 Haltwhistle 1.8 37,244 15-20 22,528 Hardeyburn* 33.5 1,258 6-10 636 Henshaw 181 4,900 15-20 3,520 Melkridge 0.0 1,962 30-40 2,061 Plenmeller & Whitfield 43.3 3,437 >50 6,234 Slaggyford* 43.6 1,788 6-10 716 Thirlwall 19.7 3,166 10-15 1,746

people per *Parishes in which no persons were recorded in socio-economic groups forming (with household) the 'Household Index'. 56 APPENDIX 4-continued

Cox method correctedfor activity rates Local Authority Parish Earnings 1966 Income 1966 & Parish % earnings Average from Total household Total agriculture earnings income income

Hexham R.D. Allendale 30.0 12,747 30-40 18,893 Blanchland 62.2 2,410 30-40 2,061 Chollerton 41.8 7,765 30-40 9,618 Haydon 15.8 18,594 25-30 17,581 Healey 57.0 1,337 30-40 1,374 Hexhamshire 86.2 2,632 40-50 4,022 Hexhamshire Low Quarter 35.1 1,826 30-40 2,748 Humshaugh 27.2 7,430 >50 13,161 Newbrough 16.4 5,592 20-25 4,275 Shotley Low Quarter 60.6 4,071 15-20 2,816 Simonburn 62.9 1,976 25-30 1,923 Slaley 33.9 5,624 40-50 7,150 Warden 17.1 4,360 20-25 4,050 West Allen 51.9 822 40-50 1,788

Rothbury R.D. Alnham 100.0 968 >50 2,771 Alwin.ton 70.0 1,256 30-40 1,718 Biddlestone* 100.0 577 15-20 352 Elsdon 0.0 2,397 25-30 2,198 Harbottle 48.5 1,608 15-20 1,408 Hepple 27.1 788 40-50 1,788 Hesleyhurst* 28.2 554 6-10 159 Hollinghill* 100.0 468 6-10 239 Nunnykirk* 62.7 746 6-10 398 Rothbury 6.2 16,167 15-20 10,736 Rothley 100.0 952 30-40 1,374 Tosson 52.1 1,259 >50 2,771 Whitdngham 56.4 3,842 >50 9,005 Westmorland Appleby M.B. 5.4 7,038 30-40 8,244 *Parishes in which no persons were recorded in socio-economic groups forming (with people per household) the 'Household Index'. 57 APPENDIX 4-continued

Cox method correctedfor activity rates Local Authority Parish Earnings 1966 Income 1966 & Parish % earnings Average from Total household Total agriculture earnings income income

North Westmorland Asby 75.7 3,412 >50 6,927 Bolton 42.3 2,509 25-30 2,198 Brough 15.1 5,437 30-4-0 6,870 Brough Sowerby* 41.1 380 <6 151 Colby* 100.0 624 6-10 239 Crackenthorpe* 31.0 504 10-15 249 Crosby Garrett* 0.0 1,053 <6 201 Crosby Ravensworth 50.0 4,358 >50 11,083 Dufton 54.2 1,877 25-30 1,648 Hartley 25.4 1,122 30-40 1,374 Hillbeck Hoff 21•0 1,687 30-40 1,718 Kaber 62-3 958 >50 1,385 King's Meaburn* 18.7 833 6-10 318 Kirkby Stephen 6.9 14,054 25-30 12,362 Kirky Thore 22.0 4,522 20-25 3,600 Long Marton 37.7 6,392 30-40 7,214 Mallerstang 78.7 911 30-40 1,374 Milburn 31•5 1,426 25-30 1,648 Morland* 0.0 1,742 6-10 716 Murton 34.6 2,951 10-15 1,372 Musgrave* 50•3 1,240 6-10 398 Nateby* 0•0 806 15-20 528 Newbiggin 917 1,039 40-50 2,234 Newby 72•4 1,052 30-40 1,374 Ormside 79.0 1,112 30-40 1,031 Orton 42.4 3,377 6-10 1,431 Ravenstonedale 41.7 4,291 25-30 3,846 Shap 2•8 13,358 25-30 10,164 Shap Rural* 64.3 243 <6 100 Sleagill 702 1,481 >50 2,078 Soulby 69.1 1,938 40-50 1,788

*Parishes in which no persons were recorded in socio-economic groups forming (with people per household) the 'Household Index'. 58 APPENDIX 4- continued

Cox method correctedfor activity rates Local Authority Parish Earnings 1966 Income 1966 & Parish % earnings Average from Total household Total agriculture earnings income income Z k Z Stainmore* 31.2 999 <6 301 Tebay 21.5 6,797 20-50 4,950 Temple Sowerby 20.0 3,887 25-30 3,296 Thrimby 100.0 968 >50 1,385 Waitby* 100.0 156 6-10 80 Waroop 19.8 11,327 25-30 4,121 Wharton - - - - Winton 39.7 1,074 40-50 2,234

South Westmorland Barton 27.3 2,255 40-50 4,022 Casterton 29.6 3,160 >50 5,541 Dillicar 40.7 1,270 >50 2,078 Docker* 100.0 312 15-20 176 Fawcett Forest* 100.0 265 15-20 176 Firbank* 82.8 565 6-10 239 Grayrigg 41.2 1,760 >50 3,464 Killington* 0.0 848 <6 201 Kirkby Lonsdale 7.0 14,558 40-50 21,004 Lambrigg* 0.0 1,042 10-15 249 Lupton* 34.0 917 <6 251 Mansergh* 68.0 1,376 20-25 900 Middleton* 70.9 1,010 15-20 352 New Hutton 58.3 2,273 25-30 1,923 Old Hutton & Holmescales 13.4 1,417 25-30 1,923 Patton* 19.6 796 25-30 549 Preston Patrick 53.7 3,398 30-40 4,122 Preston Richard 14.4 7,152 25-30 7,142 Scalthwaiterigg 36.4 1,792 40-50 1,788 Skelsmergh 14.9 3,137 40-50 4,022 Whinfell* 100.0 468 10-15 249 Whitwell & Selside 18.3 1,911 40-50 2,234

*Parishes in which no persons were recorded in socio-eeonomic groups forming (with people per household) the 'Household Index'. 59 APPENDIX 5

Classification of Parishes by Type of Problem Area

CLUSTER 1 CLUSTER 3 Alston with Garrigill Brampton Kingwater Burtholme Upper Denton Castle Carrock Waterhead Hethersgill Marwood Nether Denton Edmondbyers Ainstable Bellingham Calgaith Kielder Hunsonby Rochester Langwathby Wark Ousby Henshaw Lanchester Newbrough Wolsingham Nunnyldrk Wooler Fawcett Forest Haydon Whinfell Humshaugh Slaley CLUSTER 2 Appleby Askerton Bolton Bewcastle Brough Cumrew Crackenthorpe Midgeholme Crosby Ravensworth Muggleswick Hoff Birtley Long Marton Kirkwhelpington Newbiggin Ingram Newby Kirknewton Soulby Bardon Mill Thrimby Featherstone Winton Allendale Kirkby Lonsdale Chollerton New Hutton Haley Old Hutton & Holmescales Hexhamshire Preston Patrick West Allen Preston Richard Alnham Skelsmergh Alwinton Hepple CLUSTER 4 Rothley Farlam Tosson Kirkandrews Whittingham Nicholforest Asby Glassonby Mallerstang Langleydale & Shotton. Milburn Middleton in Teesdale Scalthwaiterigg Newbiggin 60 APPENDIX 5—continued

CLUSTER 4 continued Temple Sowerby Woodland Warcop Healeyfield Barbon Coanwood Casterton Hartleyburn Grayrigg Slaggyford Patton Thirlwall Warden CLUSTER 7 Hollinghill Stapleton Brough Sowerby Hexhamshire Low Quarter Crosby Garrett Nateby Orton Dillicar Shap Rural Whitwell & Selside Stainmore Waitby CLUSTER 8 Firbank Forest & Frith Killington Hunstanworth Stanhope CLUSTER 5 Bavington Hayton Corsenside Kirkoswald Falstone Eggleston Greystead Evenwood & Barony Otterburn Lynesack & Softley Tarset South Bedbum Akeld Satley Earle Haltwhistle Ilderton Shotley Low Quarter ICilham Rothbury Roddam Colby Greenhead King's Meaburn Melkridge Kirky Thore Blanchland Morland Simonbum Musgrave Biddlestone Docker Elsdon Lambrigg Harbottle Lupton Hesleyhurst Dufton CLUSTER 6 Hartley Irthington Kirkby Stephen Solport Murton Walton Ravenstonedale Plenmeller with Whitfield Shap Kaber Tebay Ormside Mansergh Sleagill Middleton 61 REFERENCES AND NOTES 1. Section 1 of the Agriculture Act 1947. 2. Northern Pennines Rural Development Board and Country Landowners' Association (1970), 'The Changing Uplands'. C.L.A., London. 3. Kahn, R. F.(1931) 'The Relation of Home Investment to Unemployment'. Economic Journal 41, 173-198. 4. An explanation of all such early regression and components-of-change models is contained in W. Isard (1960), 'Methods of Regional Analysis: an Introduction to Regional Science'. Massachusetts Institute of Technology Press. Indirect methods have become largely redundant as more demographic data is now available. 5. House, J. W. and Knight, E. M.(1965), 'Migrants of North-East England, 1951-1961: Character, Age and Sex'. Papers on Migration and Mobility in Northern England No. 2, Department of Geography, University of Newcastle upon Tyne. 6. For an account of this method see D. E. Starsinic & M. Zitter (1968),'Accuracy of the Housing Unit Method in Preparing Population Estimates for Cities'. Demography 5, 475-484. 7. Rogers, A.(1966), 'A Markovian Policy Model of Interregional Migration'. Regional Science Association Papers 17, 204-224. 8. Willis, K. G. (1970), 'Migration and Future Population on Tyneside: an analysis of census data'. Paper presented to British Association for the Advancement of Science, Annual Meeting, Durham 1970. 9. House, J. W. & Knight, E. M.(1966), 'People on the Move. The South Tyne in the Sixties'. Papers on Migration and Mobility in North-East England No. 3, University of Newcastle upon Tyne. 10. Thomas, D. S. (1941), 'Social and Economic Aspects of Swedish Population Movements 1750-1933'. Macmillan, New York. 11. See the Registrar General's Statistical Review of England & Wales. Annual, Part II, Tables, Civil Population. H.M.S.O. The crude rate can be corrected for age distribution but whether older or younger women have children is not given. This is important since fertility rates depend on marriage rates, age and duration since marriage. 12. Schneider, J. R. L. (1956),'Local Population Projections in England and Wales' Popu- lation Studies 10, 95-114. 13. This affects such services as demand for public transport, health centres, etc. See H.E. Bracy(1970), 'People and the Countryside', Routledge and Kegan Paul, London. For the influence on and choices facing the individual see W. M. Williams(1956), 'The Sociology ofan English Village: Gosforth', Routledge and Kegan Paul, London. J. S. N. Nalson (1968), 'Mobility of Farm Families Manchester University Press. 14. Starsinic, D. E. & Zitter, M.(1968) op. cit. 15. Rogers, A.(1965) 'Projected Population Growth in California Regions: 1960-1980'. Centre for Planning and Development Research, University of California, Berkeley. 62 16. Willis, K. G.(1970), op. cit.

17. General Register Office,'The Registrar General's Statistical Review ofEngland and Wales for the year 1966. Part III. Commentary. London H.M.S.O. 1970. 18. General Register Office, 'Sample Census 1966, England & Wales County Report, Greater London, Appendix D' London, H.M.S.O. 1967. Defects in the sampling frame (list of occupied and vacant dwellings) resulted in errors which were most likely to occur in areas with relatively high proportions of large houses occupied by several households, i.e. in urban areas, particularly the central areas of towns. 19. Siegel, J. S. & Hamilton, C. H. (1952), 'Some Considerations in the Use of the Residual Method of Estimating Net Migration'.Journal ofAmerican Statistical Association 47, 475-500.

20. U.S. Bureau of the Census (1951), 'Handbook of Statistical Methods for Demographers'. U.S. Government Printing Office, Washington, D.C. 21. Price, D. 0.(1955), 'Examination of Two Sources of Error in the Estimation of Net Internal Migration',Journal of the American Statistical Association 50, 689-700. 22. Craig, J. (1970), 'Estimating the Age and Sex Structure of Net Migration for a Sub.. Region'. Regional Studies 4, 333-347. 23. The Registrar General (1967), 'Decennial Supplement, England and Wales 1961 Area Mortality Tables', H.M.S.O. London.

24. The Registrar General (annual) 'Statistical Review of England and Wales. Part 2 Tables Population'. H.M.S.O., London. 25. Glass, D. V.(1964), 'Some Indicators of Differences between Urban and Rural Mor- tality in England and Wales and Scotland', Population Studies 17, 263-267. 26. Registrar General, 'Statistical Review' op. cit. 27. Economic Trends, May 1965, iii-x. 28. General Register Office. 'The Registrar General's Statistical Review ofEngland and Wales Part II. Annual, H.M.S.O. London. Table QQ(a) Legitimate fertility rates, for women married once only, at integral marriage durations, by age at marriage and year of marriage. 29. Economic Trends, May 1965, op. cit. 30. Macleod, K. W., & Watkin, E. E.(1969), 'Regional Earnings and Regional Develop- ment'. Centre for Environmental Studies, University Working Paper, 1, London. 31. Mogridge, M.J. H.(1969), 'An Analysis of Household Income in Great Britain and its Relationship with Employment Income'. Centre for Environmental Studies. Working Paper 48, London. 32. Board of Inland Revenue,(1967), '109th Report'—including Quinquennial Survey of Personal Incomes, 1964-65, H.M.S.O., London. 33. Wilkins,L. T., (1952), 'Estimating the Social Class of Towns'. Applied Statistics 1, 27-33. 63 34. Gray, P. G., Corlett, T., & Jones, P.(1951), 'The Proportion ofJurors as an Index of the Economic Status ofa District'. The Social Survey, Central Office of Information, London. 35. George, K. D.(1966), 'Productivity in Distribution', Cambridge University Press. 36. Institute of Practitioners in Advertising (1966). 'IPA National Readership Surveys, January—December 1965; London, The Institute of Practitioners in Advertising. 37. Lewis, R. J., 'The Use of Census Data in the Estimation of Income Distributions for Small Areas', in Papers from the Seminar on the Use of Census Data in the Estimation of Income Distributions for Small Areas, Centre for Environmental Studies, Information Paper 17, London, 1970. 38. Cox, W.E. (1968), 'The Estimation of Incomes and Expenditures in British Towns'. Applied Statistics 17, 252-259. 39. Mogridge, M.J. H.(1969), 'Household Income and Household Composition'. Centre for Environmental Studies, Working Paper 29. London. 40. Willmott, P.(1969), 'Some Social Trends', Urban Studies 6, 286-308. 41. Department of Employment and Productivity (1970), 'New Earnings Survey, 1968', H.M.S.O. London. 42. Department of Employment and Productivity (annually) 'Family Expenditure Survey Reports',(formerly Ministry of Labour), H.M.S.O. 43. Mogridge, M.J. H.(1969), op. cit. C.E.S. Working Paper 48. 44. Unpublished estimates of past net migration for the total population from the Office of Population Censuses and Surveys. 45. Hollingsworth, T. H.(1969), 'Population', in 'Regional & Urban Studies', S. C. Orr & J. B. Cullingworth (eds), Allen & Unwin, London. 46. See for example, I. R. Gordan (1970), 'Activity Rates: Regional and sub-regional Differentials'. Regional Studies 4, 411-424. Shows the wide variations in activity rates between areas. 47. Board ofInland Revenue (1967), op. cit. 48. Ward,J. H.(1963), 'Hierarchical Grouping to Optimize an Objective Function',Journal ofthe American Statistical Association 58, 236-244. 49. Fisher, L. & Van Ness,J. W.(1971), 'Admissible Clustering Procedures', Biornetrika 58, 91-104. 50. See for example M. Hill (1968),'A Goals-Achievement Matrix for Evaluating Alter- native Plans',Journal ofAmerican Institute ofPlanners 33, 19-29. 51. Basmann, R. L.(1962) 'Letter to the Editor', Econometrica 30, 824-826. 52. Hooper, J. W. (1959),. 'Simultaneous Equations and Canonical Correlation Theory', Econometrica 27, 245-256. 53. Hotelling, H.(1936), 'Relations Between Two Sets of Variates', Biometrika 28, 321-377. 64 54. Northumberland County Council (1969), 'Rural Northumberland, Report 2—Policy for Growth and Concentration'. 55. Gupta, S. P. & Hutton, J. P.(1968), 'Economies of Scale in Local Government Services'. Research Studies 3, Royal Commission on Local Government in England. The Institute of Social & Economic Research, University of York & H.M.S.O., London. 56. See G. A. P. Carrothers (1956), An Historical Review of the Gravity and Potential Concepts ofHuman Interaction'.journal ofAmerican Institute ofPlanners 22, 94-102 and S. A. Stouffer (1940), 'Intervening Opportunities: A Theory Relating Mobility and Distance', American Sociological Review 5, 845-867.

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Monograph

1. Models of Population and Inc9me: Economic Planning in Rural Areas • • • • •• •• • • • • 50p 5p Books Postage & Price Packing Economic Change and Agriculture • • • • • • 2.1.0 22-ip Edited by J. Ashton and S. J. Rogers (Oliver and Boyd 1967) Research, Education and Extensions in Agriculture .. 1..50 15p Edited by J. Ashton and R. F. Lord (Oliver and Boyd 1968) The Economic Prospects for Horticulture • • • • 1..50 15p Edited by E. D. Sargent and S. J. Rogers (Oliver and Boyd 1970)

Technical Papers TP1A. Organisational Possibilities in Farming and Types of Business Organisation • • • • • • • • 15p 3p by M. A. Gregory and I. S. Stephenson TP2. Life Assurance in the Farming Business .. 15p 3p by Leo Menage TP3. Management Techniques for Reducing Costs or Increasing Revenues .. .. • • • • 15p 3p by R. W. Helme TP4A.Current Taxation and Some Future Possibilities .. 15p 3p by R. L. Herdman and I. Weir TP5. Insurance in Agriculture .. • • • • 15p 3p by C. T.Jameson and J. Rawlings TP6. Budgeting and Budgetary Control 15p 3p by J. C. Cole TP7A.Estate Duty and Capital Gains Tax in Agriculture .. 15p 3p by C. Townsend TP8. Modern Management • • • • 15p 3p by J. R. Gemmell TP9. Agricultural Co-operative Activities and Case Histories of Co-operatives ...... 15p 3p by D. G. Bailey and E. T. Gibbons TP10. Human Factors in Agriculture .. • • 15p 3p by Dr.J. D. G. Troup TP11. The Role of Ergonomics in the Efficient Utilisation of Agricultural Labour • • • • • • • • 15p 3p by J. Matthews TP12. Efficient Labour Organisation • • 15p 3p by N. W. Dilke TP13. Labour Relations in Farming • • • • • • 15p 3p by D. Hodsdon and J. N. Merridew

Details of the publication programme and a subscription scheme can be obtained from the Administrative Officer of the Unit. November 1971