Sources of productivity growth using the Färe-Primont decomposition. An empirical application to the Irish beef sector

ABSTRACT

Several competing methodologies for TFP estimation have been developed in the past decades. A popular approach in the literature is index number computation. The most widely implemented TFP indices face however several important limitations. For example, Fisher, Tornqvist or Malmquist TFP indices do not satisfy the transitivity test, precluding reliable direct inter-temporal comparisons. The recently developed Färe-Primont TFP index satisfies this property, and therefore it is applied to analyse the evolution of TFP in the Irish beef sector between 2010 and 2016. Moreover, this index is multiplicatively complete, allowing a consistent decomposition of TFP growth in different sources. The sample of Irish beef farms used in the analysis is clustered to account for differences in production technology in the sector. The cluster-specific TFP changes computed were found to present important differences across the seven clusters identified. Significant TFP growth was identified in five of the classes, while TFP declined for the other two. Dispersion and mobility of the TFP levels indicate a lack of structural changes in the sector regardless of the cluster considered.

KEYWORDS:

• Total factor productivity
• DEA
• Färe-Primont index
• beef production
• latent class cluster model
• technical change

JEL CLASSIFICATION:

• Q18
• Q12

Acknowledgments

The authors gratefully acknowledge the useful comments provided by Hervé Dakpo regarding the estimation of the Färe-Primont indices using R.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Modelled using a multinomial logit function: p_r(Z_i; β) = $\frac{exp\left({\mathrm{Z}}_{\mathrm{i}}{\beta }_{\mathrm{r}}\right)}{{\sum }_{\mathrm{r}=1}^{\mathrm{R}}exp\left({\mathrm{Z}}_{\mathrm{i}}{\beta }_{\mathrm{r}}\right)}$(Linzer and Lewis 2011). In addition, ${\sum }_r{p}_r=1$.

² AIC = −2 LL + 2 P and BIC = −2 LL + P lnN, where LL denotes the log-likelihood of the model, P is the number of parameters and N is the number of observations.

³ This notation has been chosen based on the inter-temporal comparison performed in this empirical application; however, reliable cross-firm comparisons are also possible with transitive indices.

⁴ The literature recommends defining the representative output and input quantities as sample means (O’Donnell 2011; Dakpo 2016).

⁵ Where OSME_it = TFPE_it/OTE_it; and TFPE_it = TFP_it/TFP_t*.

⁶ https://ec.europa.eu/eurostat/statistics-explained/index.php/Glossary:Standard_output_%28SO%29.

⁷ It is also possible to estimate LC cluster models using continuous variables; however, categorical variables were built to simplify the clustering process.

⁸ This is achieved by specifying all variables included in the LC model as farm-specific time-invariant averages for the period in which each farm appears in the panel (Alvarez and Del Corral 2010). This imposes the assumption that farms do not switch classes with time. This assumption is not deemed too strong in this case, since no evidence of significant structural change has been uncovered for Irish beef farms in the period analysed.

⁹ The outlier detection method proposed in Hadi (1992, 1994) and of Hadi and Simonoff (1993) for multivariate data is used.

¹⁰ Note however that the direct interpretation of the effects is complicated because all variables (categorical Y_i and concomitant Z_i variables) enter the likelihood function (see Equations (1) and (2)), and therefore they all affect the partition of the sample.

¹¹ We use the package productivity in the statistical program R (Dakpo, Desjeux, and Latruffe 2017). Since we use an unbalanced panel, the observations for farms which did not appear every year in the panel were filled in using 2-year moving averages.

¹² Note that in the Färe-Primont decomposition technical change estimates are computed based on the assumption that all observations in the sample experience the same set of production possibilities; therefore it is assumed constant for observations in each time period T (O’Donnell 2011). The partition of the sample in differentiated sub-samples of farms using comparable production technologies is however expected to mitigate the effects of this assumption.

¹³ Taking the transition matrix for class 7 as an example, the percentages in each cell is interpreted as follows. Farms that were classified in group 1 in 2010 remained in that group in 2016. Most farms what were classified in TFP group 2 in 2010 (70%) remained in that category in 2016, while 10% moved to the higher TFP group 3, and 20% moved down to the lower TFP group 1. All the farms that were classified in group 3 in 2010 moved to lower TFP group 2 in 2016.

Additional information

Funding

This research has been funded by the Irish Department of Agriculture under project number REG6654.