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Population projection and population estimation are essentially the same tool; the difference is in their application. Population estimation calculates the expected population for the present; population projection calculates the expected population for one or more periods in the future.
There are two families of techniques for projecting population, called "simple" and "composite" models. Simple projections describe changes in aggregate population; in other words, they return a single number which is the population estimate for a specified period. Simple projections operate by describing the overall direction and magnitude of past change, and applying that same trend to the recent data. Composite projections describe the direction and magnitude of the various forces that affect population change. These forces are then applied to recent data. Composite projections usually return several numbers for each period, describing the changes in the various elements of population growth or decline.
There are many types of "simple" population projection (and many of them are quite complex). The three most common models are straight-line projection, exponential projection, and Gompertz-curve projection. Straight-line projection fits a single line to the trends in past data, and applies that "trend line" to the most recent data available (Figure 3.1). You are probably familiar with this sort of projection; it underlies statements like, "The average growth rate for the past twenty years has been 10 per cent per year. At that rate, the population five years from now should be 'xxx'."
For a rough estimate, a straight-line projection is often adequate. However, it does have some problems. Notice in Figure 3.1 that the trend line sometimes under-estimates the observed population figures, and sometimes over-estimates. Over the long-run, the differences average out; but if you are estimating for only one period ahead, there is a likelihood that the estimate will be at least as inaccurate as it is in fitting past occurrences. Second, a simple model works only as long as the trend is in a single direction, as long as the past performance has been predominantly growth or decline. If the trend line is "curved," if it shifts from growth to decline (or vice-versa), none of the simple models will be accurate.
It is often possible to describe a trend line that fits the observed data more closely than a straight-line model. That is the purpose of both the exponential and the Gompertz models (Figure 3.2). In both cases, the models modify the straight-line model to take into account different dynamics of population change. The exponential model describes population growth (or decline) under unrestrained conditions. If no other forces come into play to limit population growth (forces like scarcity of land or food), population would increase slowly at first, but then the rate of increase would feed on itself and the population would increase at an ever-increasing rate. The Gompertz model (or "S-curve") describes population growth under conditions which limit the maximum size of the population (the limit could be the carrying capacity of the land, given certain assumptions about housing or food production). Population would initially increase exponentially, but as the limit was reached the rate of growth would begin to decline at an ever-increasing rate. For further discussion of simple models for population projection, see Page & Patton (1991).
Composite models for projecting population are based on the truism that population can increase in only two ways: natural increase (surplus of births over deaths) and net migration (surplus of in-migrants over out-migrants). The more sophisticated composite models provide estimates of the natural increase and net migration not just for the aggregate population, but for "cohorts," or age groups, within the population. This technique is usually called the "cohort survival method."
Composite models have several advantages. They pull out the causal dynamics underlying population change. This increased sophistication allows the model to deal with forces of change which are often working at cross-purposes. For instance, rapid gains from in-migration might foretell gains from natural increase a few years down the road. In addition, composite models make finer distinctions of which age groups are changing in the population mix. This finer-grained analysis is frequently very useful in estimating (for example) future demands for specific services.
Composite models have the advantage of providing more sophisticated analyses than simple models. Coupled with the microcomputer, composite models can be calculated almost as easily as simple models. Further, spreadsheets (which are the basis of the programs in this book) are not particularly suited for trend-line analysis. For these reasons, the remainder of this chapter will be devoted to exploring the cohort-survival method in more detail.
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