Abstract
We study the cost efficiency of dairy farms operating under two different regulatory regimes. While neoclassical economic theory suggests that farms should maximize their efficiency regardless of their regulatory system, we find that farms operating in a more regulated environment have, on average, a lower cost efficiency. Differences in cost efficiency are primarily explained by allocative decisions—farms in the more regulated environment are overcapitalized and overly reliant on homegrown feed. Efficiency is estimated using bootstrapped data envelopment analysis and a stochastic distance function. We discuss the implications of these results for welfare and policy.
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Notes
 1.
An alternative view holds that price instability in competitive markets can reduce efficiency by forcing producers to adjust to price changes. These adjustments can lead producers to make “mistakes,” which decrease efficiency.
 2.
The Dairy Farmers of Ontario regulates the target price of fluid milk in the province of Ontario, while the Canadian Dairy Commission sets a national price for industrial milk used in processed dairy products.
 3.
Unlike Canadian dairy policies, US policies have changed substantially since 2007, most recently with the passage of the 2014 farm bill.
 4.
These assumptions are validated in the Ontario data set. Ontario farms grew significant amounts of hay forage and wheat, but only 1 farm reported sales of hay forage or purchases of wheat.
 5.
The price in New York was available from the Department of Agriculture and Markets, New York State (2010), for Ontario it was calculated using the mean annual implicit price.
 6.
 7.
In certain years there were not enough farms with <50 cows in the dataset. When this occurred additional farms were added from the next size category.
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Acknowledgments
This work was supported by the Ontario Ministry of Agriculture, Food and Rural Affairs [grant number 200222] and the Canadian Dairy Commission.
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Appendices
Appendix 1: Data
Subsampling New York producers
The procedure for subsampling was as follows:

Classify farms according to their herd size, using classes defined in Department of Agriculture and Markets, New York State (2010). These classes are: <50 cows, 50–99 cows, 100–199 cows, 200–499 cows, and 500 cows or greater.

Specify the number of farms that should be chosen from each class, each year, based on the proportion in the state population.^{Footnote 7}

Randomly select producers in each class for the first year.

Verify average herd size and average output per cow is within 1 % of the state average, if not resample.

Producers included in previous subsamples are kept in subsequent years with additional producers randomly added to satisfy the previous requirements.
Outlier detection
Data envelopment analysis is sensitive to the inclusion of producers with data errors. Detecting such data errors is typically termed “outlier detection”, though in practice one should not remove producers who are outliers due to remarkable productivity, but only those who are reasonably suspected of having errors in their data. Fortunately, we have data on most producers over multiple years and can therefore observe whether there are unreasonable changes in a producer’s data from year to year. To detect outliers we employ the following algorithm loosely based on Wilson (1995),

Calculate baseline efficiency scores as per Sect. 3.

Calculate the “superefficiency” score of each producer. The superefficiency score of a producer is estimated by removing the producer from the production possibility set and calculating their efficiency score using the remaining observations. Since the producer is not in the production possibilities set, the producer’s superefficiency score can be >100 %.

For each producer with a superefficiency score >130 % run a new DEA model without this particular producer.

Compare these new models to our baseline model by examining the mean change in efficiency and the ten largest changes in efficiency scores among other producers.
Only one producer’s removal resulted in a mean change in efficiency scores of more than 1 %. There were four other producers whose removal altered the score of ten other producers by more than 1 %. When we examined the netput of these producers in the years prior to and during our sample we did not find it them to be exceptional, and thus we left the producers in the sample. Our qualitative results do not change when these producers are removed, nor are they changed when we remove all producers with a superefficiency score >130 %.
Appendix 2: Econometric estimation of the distance function
In our estimation we assume the following Cobb–Douglas distance function,
where (\(\alpha , \beta ,\gamma\)) are parameters to be estimated, and d represents the producer’s distance from the production frontier. By homogeneity of degree one, \(\gamma _4=1\gamma _1\gamma _2\gamma _3\). Imposing this identity and rearranging Eq. 12 yields the regression equation,
Assuming that deviations from the production frontier may result from both random errors, and inefficiency, we model \(\ln (d)\) using an error components model. Similar to a stochastic frontier model we set \(\ln (d)=v+u\), where v is a random component assumed to be distributed normally with standard deviation \(\sigma _v\), and u is a nonnegative value that captures technical inefficiency. Typically, u is assumed to have a halfnormal or truncated normal distribution with standard deviation \(\sigma _u\). A likelihood ratio test does not find statistically significant differences between the halfnormal and truncated normal models (p value = 0.218), thus we employ the halfnormal model which offers an additional degree of freedom. The expected efficiency of individual producers calculated as per Battese and Coelli (1988).
Following Coelli et al. (2003), we use the duality of the input distance and the cost function to calculate cost efficiency and tabulate allocative efficiency as a residual of cost and technical efficiency. In brief, the CobbDouglas cost function is,
where (a, b, h) are parameters and w represents input prices. Using the first order conditions for cost minimization, Coelli et al. (2003) relate the parameters of the input distance and cost functions as follows, \(h_j=\gamma _j\), \(b_j=\beta _j\), \(a=\alpha \sum _{j=1}^4 \gamma _j \ln (\gamma _j)\). Using these parameters in the cost function and applying Shephard’s lemma, the cost efficient quantity of the jth input is given as \(x_j^{opt}=\frac{\partial c}{\partial w_j}=\frac{\hat{c} h_j}{w_j}\). Cost efficiency is estimated as the ratio of optimal cost to observed costs,
Table 9 presents the results of our regression equation. Feed was used as the numeraire input—implicitly the coefficient attached to feed is 0.328. As expected the inputs have a positive sign, implying the distance to the frontier is increasing in input usage. Conversely, the outputs have a negative sign, implying distance to the frontier is decreasing in production.
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Slade, P., Hailu, G. Efficiency and regulation: a comparison of dairy farms in Ontario and New York State. J Prod Anal 45, 103–115 (2016). https://doi.org/10.1007/s1112301504569
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Keywords
 Regulation
 Efficiency
 Agricultural policy
 Data envelopment analysis
 Bootstrap
 Distance function
JEL Classification
 L51
 D21
 Q18