APPENDIX

A PRELIMINARY EXAMINATION OF THE ASSOCIATION BETWEEN MALNUTRITION AND SELECTED ECONOMIC INDICATORS: LESOTHO (1981-1985)

Introduction

The prevalence of malnutrition data (clinic-based) for a number of countries has already been discussed in the main body of the report. The availability of these data for several years offers an opportunity to look in greater depth at the changing prevalence in terms of trend and seasonal components. In addition, it is clearly of interest-having regard to the human implications of economic adjustment - to investigate the association between prevalence and one or more economic indicators. In this appendix we report on one approach to these issues which appears to hold some promise. Data from Lesotho (see Sections 2.1 and 4.6) has been chosen for this study, as it has been established that variation in clinic-coverage has had no statistically discernible effect on prevalence estimates.¹³

¹³ Test, K., J. Mason, P. Bertolin and R. Sarnoff (1987). Trends in Prevalences of Malnutrition in Five African Countries from Clinic Data: 1982-1985. Submitted for publication.

It is important to stress that this is a preliminary note, and that further work will be needed to develop the technique and to extend the analysis to other countries.

Data and Methods

A cursory examination of the original series (fig. A1) indicates a strong seasonal component, coupled with trend and irregular effects. An initial decomposition based on the assumption that trend and seasonal components remain constant over the span of the Series proved unsatisfactory. Inspection of the latter model shoved that the magnitude of the seasonal effects differed substantially from year to year, and the overall fit was poor. An alternative approach based on an adaptive model - one which allows both components to change with time, i.e. a model which is locally constant only - proved adequate. Specifically, the method adopted is discussed by Abraham and Ledolter¹⁴, and is based on a discounted least squares technique. The model is expressed as:

Z_n = T_n X S_n + e_n

where Z_n is the original series; T_n is the trend estimate; S_n is the seasonal effect; and e_n represents the residual or irregular component. The trend component is linear and may be further decomposed into:-

T_n = (mu_n + b)

i.e. the level of the series mu, and the slope b. These components are re-estimated as each new observation becomes available.

¹⁴ Abraham, B. and J. Ledolter (1983). Statistical Methods for Forecasting (Chpt. 4). Wiley, New York.

Results

Estimation requires the application of three smoothing constants a_i (i=1,3), associated with the level, slope and seasonal effects, respectively. Each lies between 0 and 1. For these data the overall sums of squared errors (SSE) was minimized with a_i (for all i) = 0.18, producing an SSE = 70.7. The 1-step ahead forecasts are shown superimposed on the original series in figure A1. The estimated seasonal factors and the fluctuating level of prevalence (adjusted for seasonality) are depicted in figures A2 and A3. For comparison purposes the latter figure is repeated on the following page. In addition, the estimated slope is shown in figure A4, while the two selected economic indicators¹⁵ (Rate of Exchange and Consumer Price Index) are plotted in figure A5. Forecasts for the first half of 1986, are:

¹⁵ IMF, 1987. International Financial Statistics: Bureau of Statistics of the International Monetary Fund, Vol XL, No. 3. Washington D.C.

Discussion

In spite of the apparent complexity of the raw series, the above model provides a readily interpretable decomposition. The fit to the original series is evidently very good (fig. A1). The seasonal factors are pronounced and regular over the span of the series, with a slight tapering in amplitude towards 1985. The annual average is 1.0. Peaks reaching 110% occur in January through March of each year - which is immediately prior to the annual harvest (April/May), and troughs of around 90% follow the harvest in June/July. The level of prevalence (figure A3), corrected for seasonality and trend, was apparently falling slightly between 1981 and mid 1983. This is followed by a sharp upturn which continues for the remaining years. From figure A4 it will be observed that the slope also shows this pronounced increase from mid 1983. (It should be noted that during 1983/84, Lesotho suffered a drought and a national emergency was declared.) Of the two economic series chosen, the exchange rate suffers a much sharper decline after mid 1983, and, slightly later in the year, the rate of increase in CPI also rises somewhat. Regression analysis (results not included here) indicates that the prevalence level is strongly dependent on the exchange rate in particular. Naturally, this is not to imply that the relationship between these series is necessarily causal. Nevertheless, this exploratory exercise is clearly encouraging, and is certainly suggestive. It remains to extend the analysis by looking at other countries and additional economic indicators.

Figure A1 - Observed and Predicted % Prevalence

Figure A2 -Multiplicative Seasonal Factor

Figure A3 - Estimated Prevalence Level

Figure A3 (repeated) - Estimated Prevalence Level

Figure A4 - Estimated Slope of Prevalence Series

Figure A5 - Economic Series