4. Results for the Agricultural Sector

The volume of real net output (real factor income) has increased steadily over the period from1972 to 1998 with little growth in total labour employed and gross capital stock employed (Figure 2). The labour force has been in decline since 1982 and the capital stock employed has been in decline since 1987; the latter due to the slowdown of reinvestment. The broad trends in the agriculture sector are set out in Table 1.

Table 1: The agriculture sector of New Zealand (1982-83 prices)

Attribute		1972	1998	Growth rate
Labour force	FTEs	132,000	118,900	-0.5%
Capital employed	$million	$16,850	$18,638	0.3%
Real value added	$million	$1,650	$3,230	3.0%
Labour productivity	$/FTE	$12,490	$127,165	3.6%
Capital productivity	$/$1000 cap	$97.8	$173.3	2.5%
TFP ave factor share	Index	1000	2029	3.3%
TFP Laspeyre	Index	1000	2445	4.1%
TFP Tornqvist	Index	1000	3100	3.5%

Figure 2: Indices of real income, labour units and capital value

Figure 3 shows the trends in labour and capital productivity and the weighted mean of the two. Fluctuations in productivity are caused by changes in national income from agriculture rather than from the input series.

Figure 3: Agricultural productivity

The rates of change shown in Table 1 are derived from regression estimates of the rate of change over the whole period. Table 2 shows the goodness of fit statistics for the regressions for the variables entering into the total productivity and the factor productivity estimates. Where the Durbin-Watson (DW) test was poor, a first difference transformation was explored. The different specification does not change the growth rate estimates by a great margin. The equation for estimating growth rates is:

(13)	my	=	a + βt
where	my	=	log to the base e of index,
	a	=	constant,
	β	=	an estimated coefficient,
	t	=	time.

We read β as the multiplicative annual rate of change averaged over the period concerned.

Table 2: Goodness of fit for whole period (1972-98)

	Original data			First differences
	β	R²	DW	β	R²	DW
Tornqvist
Output	1.016	.90	1.41	1.016	.91	2.01
All inputs	1.007	.02	1.54	-
TIP	1.015	.86	1.27	1.016	.85	2.16
Factor income	1.034	.88	1.86	-
Factor inputs	0.998	.12	0.24	0.994	.24	2.33
TFP	1.035	.87	1.52	-
Laspeyre
Output	1.018	.92	1.15	1.019	.87	2.04
All inputs	1.009	.03	1.67	-
TIP	1.017	.89	1.15	1.018	.86	2.06
Factor income	1.040	.91	1.66	-
Factor inputs	0.999	.05	0.21	0.995	23	2.37
TFP	1.041	.89	1.38	1.044	.90	1.99

Table 3 shows total input productivity (TIP) growth rates estimated from Laspeyre base-weighted index numbers and from Tornqvist geometric weighted index numbers. The latter weights are derived from average value shares between the current year nominal factor shares and the base year factor shares. If an input or an output mix is changing in a systematic way the geometric method makes the appropriate adjustment.

Table 3: Total input productivity by weighting method and periods (annual growth rates)

	Tornqvist			Laspeyre
	Output	Input	TIP	Output	Input	TIP
1972-84	1.1	0.5	0.6	1.0	0.3	0.7
1985-98	1.8	0.0	1.8	2.2	0.3	1.9
1972-98	1.6	0.7	1.5	1.8	0.9	1.7

Figure 4 shows a comparison of the two weighting methods for gross output of the agricultural sector, Figure 5 shows the comparison for total inputs employed, and Figure 6 shows the comparison for the total input productivity index.

Figure 4: Comparison of agricultural gross output

Figure 5: Comparison of agricultural total input indexes

Figure 6: Comparison of total input productivity indexes

Total input productivity tends to be over-stated by base-weighted indexes particularly since 1985. Thus the better estimate of long run total productivity is 1.5 percent per year since 1972. Both methods suggest that the rate of growth has improved since 1985 compared with the earlier period 1972-84.

Table 4 shows the results for total factor productivity and Figure 7 shows a comparison of the two weighting methods for the total factor productivity (TFP) index.

Table 4: Total factor productivity by periods (growth rates)

	Tornqvist			Laspeyre
	Output	Input	TIP	Output	Input	TIP
1972-84	2.6	0.8	1.8	3.1	0.9	2.2
1985-98	3.2	-0.8	4.0	3.7	-0.6	4.3
1972-98	3.4	-0.2	3.5	4.0	-0.1	4.1

Again Tornqvist indexes tend to lower the factor income increase and the factor input increase (slightly) with the resulting effect on the productivity growth rate. Thus the best estimate for factor productivity growth for the period since 1972 is more likely 3.5 percent per year rather than 4.1 percent per year as might have been indicated by the Laspeyre index.