The estimated percentage of all farms with liabilities (89.3 percent) had a 95 percent confidence interval of plus or minus 2.5 percentage points (Table 18). This interval is commonly called the "margin of error". Because the individual farm types had smaller sample sizes than the their total combined, their estimates had larger 95 percent confidence intervals.

Table 18 Estimated percentages of farms with liabilities

Across all farm types, as well as in the total sample, mean values of farm debt were much greater than median values. This indicates that the distribution of farm liabilities was skewed by a few farms with very large liabilities. Further, a substantial minority of farms had no liabilities. Because of the skewing and the presence of farms without liabilities, total farm liabilities were not normally distributed. One way to assess the distribution is to calculate the quartile values. The 25 percentile, the value below which 25 percent of farms lie, shows that for all but dairy and cropping farms, many farms had low liabilities (Table 19). The spread between the 25 and 75 percentiles shows that the middle 50 percent of farms occupied a very wide range of liability values.

Table 19 Estimates of total liabilities for all farms (including farms with no liabilities)

Another way to assess the distribution is by calculating the confidence interval of the mean. Farms with no debt have, by definition, total liabilities of zero. The 10 percent of farms with no liabilities constitute a second peak in the distribution, which makes estimation of the accuracy of the measures difficult. The 95 percent confidence interval for total liabilities was therefore determined only for those farms with liabilities. The confidence intervals are shown in Table 20. Because the distribution is widely spread, the confidence intervals are large.

Table 20 Estimates of total liabilities for farms with liabilities

Confidence intervals are sensitive to sample size, and to halve the confidence interval requires four times the sample size. Sheep and beef and dairy farms, with their comparatively large samples, have more precise estimates than the other farm types. The 95 percent confidence intervals for total liabilities of dairy and cropping farms sat significantly above those for all the other farm types and for the average of all farms.

Confidence intervals were also calculated for percentage equity. Because this figure is a percentage, it is more constant across farms, so we were able to calculate 95 percent confidence intervals for all farms. For all farms (weighted), mean equity was 74.6%, and the 95 percent confidence interval ranged 2.5 percent of this either way, from 72.9 percent to 76.4 percent. The 95 percent confidence interval was 2.8 percent either way for sheep and beef farms, 4.2 percent for dairy farms, 7.7 percent for horticulture farms, 7.2 percent for cropping farms, and 9.0 percent for "other" farms.

Our estimates of total farm sector debt in New Zealand rely on both our estimates of average farm debt and our count of the number of farms in New Zealand. We have already described the precision of our estimates of average farm debt. Estimation of the number of farms in New Zealand is more difficult. We cannot describe a figure for the number of farms in terms of statistical precision, as we did for farm debt. Instead we report our best estimate, along with some alternative estimates based on different counts of the number of farms in New Zealand.

In the Agribase, once farms with a predominant farm type that does not fit the survey criteria are excluded (unconfirmed farm type, no farm enterprise or farm type, blank farm type, forestry, woodlot, native bush, tourism, lifestyle, and zoological gardens), there were 78 123 farms. With this weighting of farm types, average farm debt was $274,372. With this estimate of farm numbers, total New Zealand agricultural sector debt in 1998 was $21.453 billion. We think this estimate is too high, because it includes many small farms in the estimate of farm numbers, but excludes them from the calculation of average farm debt.

As we have already indicated, the entire Agribase (with specified predominant farm types excluded) did not yield an appropriate sampling frame, and further hobby farms had to be removed. Removing the same proportion of farms from each farm type in the Agribase that we removed from the initial sample, we estimate there were 65 487 farms, and total New Zealand agricultural sector debt in 1998 was $18.726 billion. This is our best estimate.

Our lowest estimate was calculated by removing all farms outside the sampling frame from the initial sample (ceased farming, farm leased out, and duplication of respondents, as well as hobby farms with no separate farm accounts), and removing the same proportion of farms from each farm type in the Agribase that we removed from the initial sample. On this basis, we estimate there were 58 946 farms, average farm debt was $278,222, and total New Zealand agricultural sector debt in 1998 was $16.400 billion.

The only other recent estimate of the number of farms in New Zealand was calculated for 1996, a date 2 years earlier than our figures, by Statistics New Zealand (1998). Their estimate was 61 512. Using Statistics’ weighting of farm types, average farm debt was $291,464. On this basis, total New Zealand agricultural sector debt in 1998 was $17.928 billion.

A further factor could be applied to all these figures, to take account of the precision with which average farm debt was estimated. However, as we have explained, it was not possible to estimate conventional confidence intervals for average farm debt, because total farm debt was not normally distributed.

Not all farms included in the above estimates of the total number of farms were of sufficient size to be regarded as stand-alone farm businesses. For this reason the reported estimates of national farm debt from this survey does not only relate to on-farm businesses. Industry estimates suggest that New Zealand farm business debt, where the debt is serviced from the farming business, was approximately $14 billion as at June 1998. This is because the number of farm businesses is lower than the number of farms.

In the 1988 study the questionnaire "did not request information on specific loans from relatives and similar private sources so that the number of farms reporting no liabilities may be understated" (Pomeroy & Reynolds 1991, p. 6). There was a question, however, which asked for liabilities from all other lenders; we think that family loans were probably captured in this category. Thirteen percent of the individual liabilities in the 1988 survey, representing 24 percent of the total liabilities by value, were in this "all other lenders" category. By any standards, this is a very large proportion of a total to be in an "other" category. In contrast, in the present survey, only 1 percent of the liabilities, representing 1 percent by value, were in the "all other lenders" category. And 19 percent of the total liabilities by value in the present survey were in the new categories not mentioned in the 1988 survey (family members 12 percent, solicitors 6percent, and shareholders 1 percent). Therefore, we consider our belief that the 1988 survey did in fact include family loans is justified.

In addition, the sample for the 1988 survey excluded hobby farms and part-time units. This was done by ensuring that only farms contributing significantly to agricultural output, for each commodity, were included in the survey. The cut-off for selection was set such that only farms contributing the upper 95 percent of the total value of agricultural production were included in the survey. We consider that our dataset is comparable. We excluded from our sample those farms described in the Agribase as "lifestyle" farms, and although there are a number of sheep and beef farms of small size and low gross income in our sample, there are few dairy farms or cropping farms in this category. Excluding further farms, such that only farms contributing the upper 95 percent of the total value of agricultural production remain in the sample, would exclude a large number of farms that are clearly economic units.

We can therefore compare the debt per farm (weighted to reflect the proportion of farm types in New Zealand) and the estimated total debt over all farms in New Zealand, between the 1988 and 1998 surveys. After correcting for price inflation of farm inputs, average debt per farm has increased by 91 percent, while New Zealand’s total agricultural sector debt has increased by 53 percent in the same period (Table 21). The percentage increase in debt per farm is greater than the increase in the debt over the whole sector because there were fewer farms in 1998 than in 1988. This apparent reduction in the number of farms is due in part to differing definitions of a farm, so the increase in total agricultural sector debt may be different from the 53 percent reported here. We used the Producer Price Index (PPI), rather than the Consumer Price Index (CPI) to convert 1988 dollars to 1998 dollar values. The PPI increased to a much lower extent than the CPI over the 10-year period, as many farm costs have increased in price less than have consumer costs. Examples are the removal of tariffs on imported agricultural machinery and the static price of superphosphate fertiliser. Using the CPI as an index would give a larger value for 1988 dollars when converted to 1998 dollars, and thus smaller increases in debt from 1988 to 1998.

Table 21 Comparison of agricultural sector debt for 1988 and 1998