Modelling the heterogeneous effects of stocking rate on dairy production: an application of unconditional quantile regression with fixed effects

ABSTRACT

This article analyses the effects of stocking rate on dairy production, using New Zealand dairy farm business data for the period 2005–2014. Unlike previous studies that assume a homogenous relationship between stocking rate and dairy production, we contribute to the literature by investigating the heterogeneous effects of stocking rate on milksolids production and applying an unconditional quantile regression model with fixed effects to control for unobserved farm-specific traits that are time invariant. The empirical results show that stocking rate exerts significant heterogeneous effects on milksolids production at different quantiles. In particular, we find that an additional increase in stocking rate (i.e. one cow/ha increase) increases milksolids production per hectare by between 17% and 25% but decreases milksolids production per cow by between 5% and 12%. In addition, we find that milking interval, dairy breed, farm labour, access to irrigation and farm location are important factors that increase milksolids production.

KEYWORDS:

• Stocking rate
• milksolids production
• unconditional quantile regression
• fixed effects
• New Zealand

JEL CLASSIFICATION:

• C32
• D13
• D22

Acknowledgements

This research is one of a series of analyses in the Marginal Imperative Project funded by New Zealand dairy farmers through DairyNZ and the Ministry for Primary Industries in the Transforming the Dairy Value Chain Primary Growth Partnership programme.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Stocking rate is generally defined as the number of milking cows per unit of effective land area (cows/ha).

² Globally, milk is usually valued in two ways to reflect a milk component market price: milksolids price (i.e. the globally traded value of fat and protein products) and milk price (i.e. a fluid market milk price where milk composition is not considered). In the context of New Zealand, milksolids price is used in milk transaction markets.

³ DairyBase® is owned and managed by DairyNZ on behalf of the dairy farmers of New Zealand.

⁴ In the North Island these are Northland, Waikato, Bay of Plenty, Taranaki and Lower North Island and in the South Island, these are West Coast-Tasman, Marlborough–Canterbury and Otago–Southland.

⁵ The number of cows is calculated as the highest number of cows used for production during the season.

⁶ A fixed effects model assumes that the individual specific effect is correlated to the independent variable, while a random effects model assumes that the individual-specific effects are uncorrelated with the independent variables.

⁷ The CQR model measures $\frac{\mathrm{\partial }Y\left(q^{th}|S,X\right)}{\mathrm{\partial }S}$, while the UQR model measures $\frac{\mathrm{\partial }Y\left(q^{th}\right)}{\mathrm{\partial }S}$.

⁸ The UQR fixed effects model can be implemented by ‘xtrifreg’ in STATA.

⁹ In New Zealand, dairy farmers are usually price-takers and there exist small variations in milk prices among dairy farms. Thus, milk price is not the main indicator that determines dairy profitability in New Zealand, and this is supported by the findings in Ma, Renwick, and Bicknell (2018).