Assessing the Impacts of Pillar 1 and 2 Subsidies on TFP in French Crop Farms

Abstract

This article analyses the impact of common agricultural policy (CAP) subsidies on total factor productivity using a FADN dataset of French crop farms between 1996 and 2003. We first estimate a production function using a system GMM approach and then recover farm-level total factor productivity (TFP). Further, the impact of Pillar 1 and 2 subsidies on TFP is investigated and results show that several subsidies have a negative impact on productivity during the period covered in the dataset. CAP reforms have also had an impact on the relationship between subsidies and productivity.

1. Introduction

Since the 1990s, the European Union has progressively and structurally reformed the common agricultural policy (CAP), which today includes two Pillars with specific objectives and instruments. In 1992, the MacSharry reforms made radical changes to the CAP, replacing a system of protection through prices with a system of compensatory income support. The reform was phased in from 1993 onwards, but only applied to certain products: crops such as cereals, oilseeds, and proteins. In particular, reductions in the level of support prices in the cereals sector were compensated by area payments provided that farmers would adhere to certain restrictions on input use, such as set-aside for arable producers. Moreover, a number of additional instruments were created, especially agri-environmental and less favoured areas (LFA) payments, with a focus on rural development and environmental risks, the maintenance of rural farming, and the promotion and preservation of countryside and landscapes.

The current objective of the CAP, according to the ‘EU 2020’ strategy, is that agriculture should contribute to smart (knowledge and innovation based), sustainable and inclusive growth (European Commission, 2010). Therefore, to support policy design towards meeting this objective, assessment of the CAP and its impacts on farm behaviour and performance is needed. The aim of this study is to assess the impacts of CAP subsidies on productivity at the farm level and to provide insights on the debate regarding the evolution, the role, and weight of the various payments within Pillars 1 and 2.

There is an extensive empirical and theoretical literature that examines the impacts of agricultural payments on farm output (e.g. Goodwin and Mishra, 2006), investment (e.g. Sckokai and Moro, 2009), and land (e.g. Féménia et al., 2010) decisions among many other topics and highlights several transmission channels (e.g. Henessy, 1998) suggesting that CAP subsidies are likely to affect farm performance. However, it is impossible to deduce the nature and the amplitude of the relationship between subsidies and productivity from theoretical considerations. As we can expect CAP subsidies to have simultaneously both positive and negative impacts on farm performance, the effect of CAP subsidies on productivity remains an empirical question.

Most of the empirical literature has reported that subsidies have negative impacts on efficiency and/or productivity (e.g. Zhu and Oude Lansink, 2010; see Latruffe, 2010). However, because these studies consider only the total amount of subsidies, they cannot provide evidence on the impact of specific CAP schemes. In contrast, this study examines the impact of various CAP instruments, that is, investment subsidies, crop area payments, set-aside premiums, agri-environmental, and LFA payments, at the farm level, with an application to French crop farms over the period between 1996 and 2003.

Several methods have been applied to measure farm performance via efficiency or productivity measurements. In this study, we use a parametric approach to the direct estimation of a production function, that is, the generalised method of moments (GMM) system (Blundell and Bond, 2000). Unlike the non-parametric deterministic Data Envelope Analysis (DEA) approach, this technique accounts for random shocks, which strongly impact on the production process of crop farmers (e.g. weather conditions affecting yields). Moreover, the system GMM has the advantage over the Stochastic Frontier Analysis (SFA) approach of taking into account the problems induced by the simultaneity/endogeneity of independent variables (Bokusheva et al., 2012), that is, the fact that inputs are likely to be correlated with productivity shocks. As has been acknowledged in a seminal article by Marshak and Andrews (1944), this will result in biased estimates of the production function, and consequently a spurious measure of productivity. Similarly, the SFA suffers from this identification problem (Shee and Stefanou, 2011). Finally, the system GMM has several advantages over two-step approaches (Wooldridge, 2009),² which assume that the unobserved productivity terms can be adequately controlled by using investment (Olley and Pakes, 1996) or intermediary inputs (Levinsohn and Petrin, 2003). Consequently, system GMM has now become the estimator of choice in many dynamic panel settings.

The next section describes the model. Section 3 presents the data and variables. Results are discussed in sections 4 and 5 concludes.

2. Model

The model is based on the framework proposed by Blundell and Bond (2000), which assumes that serially correlated shocks allow a dynamic representation of the production function. We consider a Cobb–Douglas³ production function without imposing constant returns to scale:

• 

where farms are indexed by i and time is indexed by t, Y_it is production output of farm i at period t, K_it represents capital stock, N_it is the labour, L_it is land, and Z_it is a productivity shock. Taking logarithms we obtain:

• (1)

where y_it = ln(Y_it), k_it = ln(K_it), n_it = ln(N_it), l_it = ln(L_it), and u_it = ln(Z_it). We specify the following structure for the productivity shock:

• (2)

where G_t is an effect common to all farms, η_i is a time-invariant farm-specific effect, v_it is an autoregressive of order one (AR(1)) idiosyncratic shock, and m_it are uncorrelated measurement errors, that is, follow a moving average of order 0 (m_it ∼ MA(0)). ξ_it are independently distributed with zero mean and variance .

To estimate the parameters (β_K, β_N, β_L, ρ), we formulate the dynamic representation⁴ of (1):

• (3)

or

• (4)

subject to three nonlinear restrictions: π₂ = −π₁π₇, π₄ = −π₃π₇, and π₆ = −π₅π₇, and where and . Given consistent estimates of the unrestricted parameter vector π = (π₁, π₂, π₃, π₄, π₅, π₆, π₇)′ and its variance–covariance, the restrictions can be tested and imposed by minimum distance to obtain estimates for the restricted parameter vector (β_K, β_N, β_L, ρ)′. e_it follow a MA(0) process if there are no measurement errors (i.e. e_it = ξ_it) and a MA(1) otherwise (i.e. e_it = ξ_it + m_it − ρm_i,t−1).

3. Data and Variables

The dataset used in this study is drawn from the French Farm Business Surveys (Farm Accountancy Data Network, European Commission). The data are farm level with the samples of farms chosen so as to be representative of French agriculture, with detailed data provided on farm output, on farm labour supply, farm investment, etc. The sample is defined according to a set of criteria, which are given in the appendix. There are 1,529 crop farms, observed for 8 years, between 1996 and 2003, satisfying these conditions for a total number of 7,479 observations. Labour inputs are represented by time worked in hours by total labour input on holding. Capital stock is a value of machinery and equipment at closing valuation. Land is the total used agricultural area. Further details are provided in Appendix 1.

The presence of unit roots may affect the estimation. Indeed, if the dependent variable is not stationary, then the introduction of a lagged dependent variable to model dynamics will lead to spurious regressions. Moreover, the presence of unit root is closely related to the identification of parameters of interest in micro panels. Thus, evidence on the time series properties of the data can be crucial for the choice of estimator to be considered (Bond et al., 2005).

Following Maddala and Wu (1999), which assume that all series are non-stationary under the null hypothesis against the alternative that at least one series in the panel is stationary, the stationarity for an unbalanced panel is tested using Fisher’s tests. Both Phillips–Perron and Augmented Dickey–Fuller tests are implemented.⁵ Finally, two t-tests based on least squares estimators that have been suggested by Bond et al. (2005) are considered. We conclude that there is no unit root in the panel (Tables 1 and 2).⁶

Table 1.    Unit root tests, Maddala and Wu (1999)

Dependent variable	Augmented Dickey–Fuller	Phillips–Perron	Conclusion
n t	Prob. > χ^2 = 0.000	Prob. > χ^2 = 0.000	Reject a unit root
l t	Prob. > χ^2 = 0.000	Prob. > χ^2 = 0.000	Reject a unit root
y t	Prob. > χ^2 = 0.000	Prob. > χ^2 = 0.000	Reject a unit root
k t	Prob. > χ^2 = 0.000	Prob. > χ^2 = 0.000	Reject a unit root

Table 2.    Persistence, unit root tests for capital variables

	k t
Note: *t-test: H0 : α = 1 and H1 : α < 1. See Bond et al. (2005) for a detailed description of these two t-tests.
Lagged variable	0.973 (0.009)
OLS t-test* conclusion	Reject unit root (1%)
	k t−1
Lagged variable	0.928 (0.010)
Breitung–Meyer t-test* conclusion	Reject unit root (1%)

4. Estimation Results

The system GMM applied to the estimation of production functions has been found to greatly improve the performance of the first-differenced GMM estimator (Blundell and Bond, 2000). In this application, the two-step system GMM estimator (Windmeijer, 2005) is our preferred estimator because it is more efficient (in terms of mean squared error) than the first-step estimator. In addition, the corrected two-step Wald test has similar size properties to the standard one-step Wald test and can improve on the power of the standard one-step Wald test. Inference based on corrected two-step GMM estimators is also found more reliable than approaches to bootstrapping in the context of GMM estimators for dynamic panel data models (Bond and Windmeijer, 2005).

4.1. Production function estimates

Results for the production function are reported for both one-step and two-step system GMM estimators in Table 3, which provides the estimates for the unrestricted model (4).

Table 3.    Production function estimates†

y t	One-step		Two-step
	SYS–GMM t − 2	SYS–GMM t − 3	SYS–GMM t − 2	SYS–GMM t − 3
Notes: Asymptotic standard errors in parentheses. Windmeijer correction applied for GMM estimation. Year dummies included in all models. ***significant at 1%, **significant at 5%, and *significant at 10%. †m1 and m2 are tests for first-order and second-order serial correlation, asymptotically N(0, 1). First-differenced residuals are tested in all columns. Comfac is a minimum distance test of the nonlinear common factor restrictions imposed in the restricted models. P-values are reported.
n t	0.245**	0.145	0.188*	0.123
	(0.103)	(0.117)	(0.097)	(0.119)
n t−1	−0.022	0.124	0.047	0.145
	(0.101)	(0.116)	(0.100)	(0.134)
k t	0.131***	0.263***	0.086*	0.185***
	(0.048)	(0.062)	(0.044)	(0.063)
k t−1	0.000	−0.022	0.003	−0.004
	(0.045)	(0.043)	(0.042)	(0.046)
l t	0.319	0.360	0.257	0.643
	(0.346)	(0.364)	(0.328)	(0.412)
l t−1	−0.024	−0.143	0.187	−0.378
	(0.345)	(0.358)	(0.322)	(0.391)
y t−1	0.203***	0.329***	0.169***	0.343**
	(0.048)	(0.106)	(0.061)	(0.164)
m1 (P-value)	−8.17 (0.000)	−5.33 (0.000)	−6.87 (0.000)	−4.02 (0.000)
m2 (P-value)	1.52 (0.128)	0.46 (0.644)	1.74 (0.081)	0.86 (0.391)
Sargan (d.f.)	0.004 (91)	0.069 (67)	0.004 (91)	0.069 (67)
Instruments in the first-differenced equations	Lagged levels t − 2	Lagged levels t − 3	Lagged levels t − 2	Lagged levels t − 3
Instruments in the levels equations	Lagged first-differences	Lagged first-differences t − 2	Lagged first-differences	Lagged first-differences t − 2
Comfac	0.886	0.062	0.547	0.063

The validity of lagged levels dated t − 2 as instruments in the first-differenced equations is clearly rejected by the Sargan test of over-identifying restrictions. This is consistent with the presence of measurement errors. Instruments dated t − 3 (and earlier) are not rejected.⁷ This is true for both one-step and two-step estimations. Coefficients of capital and of the lagged dependent variable are of positive sign and significant at 1% and 5%, respectively. However, the coefficient of capital is much higher in the one-step estimation (0.263 against 0.185 in the two-step estimation). Further, coefficients for labour and land also have positive signs, but are not significant,⁸ in both one-step and two-step estimations. The test of common factors is not rejected in all configurations confirming the dynamic representation of the model.

In Table 4, the technological parameters are recovered by means of a minimum distance estimator⁹ that exploits the constraints associated with the technological parameters. All parameters are significantly positive for both one-step and two-step system GMM estimations. In fact, the parameters of labour and land are extremely close in both estimations; there is only one difference regarding the coefficient of capital, which is much higher in the one-step estimation. Constant returns to scale are not rejected in all estimations.

Table 4.    Technological parameters

	One-step	Two-step
	SYS–GMM t − 3	SYS–GMM t − 3
Note: ***significant at 1%, **significant at 5%, and *significant at 10%.CRS is a Wald test of the constant returns to scale hypothesis in the restricted models. P-values are reported.
β n	0.234** (0.090)	0.234*** (0.088)
β k	0.288*** (0.060)	0.181*** (0.056)
β l	0.331** (0.140)	0.321* (0.175)
CRS	0.380	0.184

4.2. Total factor productivity change in the French crop sector

We now use the two-step production parameters from Table 4 (second column) to construct a measure of farm-level productivity and analyse changes that occurred between 1996 and 2003. Following Olley and Pakes (1996), farm-level productivity p_it is calculated as follows:

• 

Aggregate productivity in the French crop sector is then calculated annually as the share-weighted average of the farm-level productivity measure, using output shares as weights. Table 5 presents the annual productivity growth rates and the sectoral TFP index.

Table 5.    TFP change in the French crop sector

	TFP sectoral index	TFP change (%)
1997	0.79	–
1998	0.85	7.36
1999	0.84	−1.45
2000	0.86	3.13
2001	0.97	12.19
2002	0.89	−8.10
2003	0.91	2.54
Average annual growth rate		2.06

The annual growth rate of TFP per year (as the geometric mean over the period) is estimated at 2.06%. This is consistent with previous studies (Coelli and Rao, 2005), but much higher than the estimate of 0.4% found by Fogarasi and Latruffe (2009) using a sample of French crop farms between 2001 and 2004. However, their results are based on the DEA approach, which does not include the effect of random shocks. The rate of TFP growth varies substantially from one year to another. For example, in 2001, TFP increased by 12%, whereas it decreased by 8% the following year. This can be partly explained by the impact that climatic variables had on crop producers during these years. However, the changes in EU agricultural policy also potentially played a role in explaining the development of TFP in French crop farms. The next section thus investigates the impacts of CAP subsidies on TFP.

4.3. The impacts of CAP subsidies on TFP

To obtain estimates of the impact of CAP subsidies on farm productivity, one has to account for potential biases when implementing such analysis. Indeed, structural differences between farms, which may result from their geographical location (e.g. LFA¹⁰), from the agro-ecological environment in which they operate or from the amount and/or type of CAP subsidies they receive, may lead to biased estimates and in turn incorrect policy implications. In particular, with respect to the latter, the different nature of CAP subsidies implies that subsidies are endogenous variables reflecting characteristics of national (or regional) CAP implementation (e.g. animal or crop payments are linked to regional productivity or yield references) as well as farmer’s behaviour/participation in specific schemes (e.g. investment support measures require the submission of a project, which is not automatically accepted, and some farms may decide not to take part in such schemes because they are not certain to receive any subsidies). To account for such endogeneity issues, we use the system GMM estimation method. As explained earlier, this method accounts for the endogeneity of independent variables. Moreover, tests for the presence of unit roots in CAP subsidies also highlight the fact that some payments display relatively high persistence. The system GMM also allows accounting for subsidy autocorrelation.

Table 6 presents the results of two-step system GMM regressions, which estimates the impacts of various farm payments on TFP growth¹¹ over the whole period covered by the dataset. All amounts of subsidies are per 1,000 euros. Estimation results over the whole period show that several farm subsidies negatively affect TFP in French crop farms. Set-aside premiums, LFA payments, and livestock subsidies have a significant negative impact on productivity with respective coefficients of −0.00019, −0.00016, and −0.00003. This means, for example, that an increase of 100 euros in set-aside premiums would decrease farm-level TFP by 0.019%. Such results are in line with the literature, which traditionally reports negative impacts on farm performance when considering the total amount of subsidies (e.g. Zhu and Oude Lansink, 2010). No significant effect is found for environmental payments, other crop subsidies, crop area payments, and investment subsidies.

Table 6.    Impacts of farm subsidies on TFP

	1996–2003
Note: ***significant at 1%, **significant at 5%, and *significant at 10%.
Economic size (ESU)	0.00002***
Investment subsidies	−0.00003
Set-aside premiums	−0.00019***
LFA payments	−0.00016*
Agri-environmental payments	−0.00001
Livestock subsidies	−0.00003**
Crop area payments	−0.00001
Other crop subsidies	−0.00002
CAP Reform dummy	0.00148***
m1 (P-value)	−8.13 (0.000)
m2 (P-value)	1.65 (0.100)
Sargan (d.f.)	0.057 (148)

As explained above, each CAP payment differs, especially when comparing payments from both Pillars, as their characteristics can be fundamentally diverse. However, among all, farmers are likely to distinguish between CAP subsidies that are automatic and those that are selective. The latter are typically some rural development measures that are subject to the judgement and approval of LEADER Action Groups (or expert committees) and are only granted to selected applicants (i.e. investment or environmental measures). Automatic subsidies are paid per hectare or per head (e.g. livestock subsidies), provided that farmers meet the requirements specified in the scheme regulations (e.g. set-aside, quality of agricultural land), and whose amount can be expected by farmers with (quasi-) full certainty. With respect to this dichotomy based on the design of the payment, it is interesting to note that the CAP payments with a negative impact on productivity are all automatic (i.e. set-aside premiums, LFA payments, and livestock subsidies). In contrast, selective (targeted) subsidies, such as investment and environmental measures, have been found to have no significant impact on TFP.

Furthermore, we introduce a dummy variable as an explanatory variable to capture the Agenda 2000 reform as has been already done in the literature (e.g. Carroll et al., 2009), to examine the impact of CAP reforms on farm-level TFP, to confirm whether the redistribution of instruments within the CAP resulting from the reforming process has affected farm performance in the French crop sector. The parameter associated with the dummy variable is significant and of positive sign, suggesting that CAP reforms introduced by Agenda 2000 have had a positive impact on TFP in French crop farms. This is in line with Fogarasi and Latruffe (2009), who report a positive impact of the total amount of subsidies on a productivity change index between 2001 and 2004 in French crops agriculture. However, caution is required when interpreting our result because Latruffe (2010) argues that the use of period dummies may also capture economic and institutional changes unrelated to the policy change.¹²

5. Summary and Conclusions

This study estimates Cobb–Douglas production functions using panel data covering a large FADN sample of French crop farms observed between 1996 and 2003, through system GMM estimation, so as to calculate a measure of farm-level total factor productivity. We then investigate the impacts of CAP Pillar 1 and 2 payments on farm performance. First, we find that the annual average TFP change in the French crop sector is 2%, in line with commonly reported estimates for developed economies (e.g. Coelli and Rao, 2005). However, this is much higher than the estimate of 0.4% found by Fogarasi and Latruffe (2009) using a sample of French crop farms between 2001 and 2004.

Second, we confirm that several CAP subsidies have a negative effect on TFP, as suggested in the literature. However, in contrast with previous studies, we are able to show that not all CAP payments have significantly negative impacts. More specifically, we show that the farm subsidies which have negative impacts on TFP during the period are those which are effectively automatic. Selective (targeted) subsidies are found to have no significant impact on productivity. These results have clear implications for the design of future policy instruments and deserve attention from both policy-makers and economists.

We also find that the impacts of LFA payments are significantly negative. LFA payments, according to these results, end up having effects on farm productivity which partially prevent the fulfilment of their initial objectives, aiming particularly towards the viability of farming in these areas.

Furthermore, we show that the impacts of Pillar 1 and 2 payments have evolved over time with CAP reforms. CAP reforms through Agenda 2000 seem to have affected farm performance, as the dummy variable accounting for CAP reforms is significantly positive. This is different from Coelli et al. (2006), who find no discernable effect of CAP reforms on TFP trends in Belgian arable agriculture, but somewhat similar to the results of Fogarasi and Latruffe (2009), who confirm a positive impact of the total amount of subsidies on a productivity change index between 2001 and 2004 in French crop agriculture. However, as explained above, this result should be interpreted with care.

Footnotes

• 2

   First, Ackerberg et al. (2006) show that there are potentially serious collinearity problems with two-step estimations, which can generate problems with the identification of the parameters. Second, bootstrapping is not required to obtain fully robust, relatively simple standard errors when using GMM estimation. Finally, over-identification assumptions implied by the economic theory can be easily tested without bootstrapping.

• 3

   Despite restricted assumptions, the Cobb–Douglas production function provides a rather simple framework that is the most commonly used form of production functions in economics research mainly for its ease of manipulation and interpretation. In addition, less restrictive functional forms have not produced significantly better estimates (Mundlak, 2000).

• 4

   Because we assume labour, land, and capital to be potentially correlated with the farm-specific effects, the productivity shocks, and/or the measurement errors, there are no valid moment conditions for the static specification (1) if the disturbances v_it are indeed autoregressive. However, the model has a dynamic representation (Bond, 2002).

• 5

   The reported statistics and conclusions are obtained using one lagged first difference terms (ADF test) and one periods of serial correlation (PP test). ADF and PP test the null hypothesis of existence of unit root.

• 6

   We also run a series of auto-regressions for all our variables, thus examining the size of the coefficient of the lagged variables.

• 7

   Evidence of second-order correlation in the first-differenced residuals (i.e. a MA(1) component in the error term in levels) explains why instruments dated t − 2 are invalid, and instruments dated t − 3 are valid (Bond and Meghir, 1994).

• 8

   The coefficient of land is significant at 12%.

• 9

   The minimum distance estimator uses the information contained within the variance–covariance matrix of parameters estimated in Table 3. It is not surprising that coefficients, which are not significant at conventional levels in Table 3, are now significant in Table 4. This is because covariances of y_t and k_t (both significant at high levels in Table 3) with other coefficients (in particular labour) are extremely small and positively penalise the significance of both labour and (to a lesser extent) land coefficients.

• 10

   In the sample, only 69 crop specialist farms receive LFA payments from 2000 onwards.

• 11

   The logarithm of TFP is regressed over subsidies in levels.

• 12

   This result also implicitly assumes a single period response in productivity to the policy reform, which ignores the possibility for farmers to progressively adjust to the new policy environment, by phasing in different patterns of input or output allocation. Yet, it allows capturing the change in farm behaviour in face of expected policy changes.

Appendix

Appendix 1: Description of Data and Variables

The data are farm-level data with the samples of farms chosen so as to be representative of French agriculture, with detailed data provided on farm output, on farm labour supply, farm investment, assets and debts, etc. However, neither consumption data nor off-farm labour information is available in the data. The sample used for study is defined according the following criteria, starting with an original sample of 1,575 farms observed for 8 years, between 1996 and 2003, for a total number of 8,685 observations. As the panel is incomplete, some farms are only present in the database for 1, 2 or 3 years. The sample consists of all the farms that have been surveyed for at least 4 years. This rule of thumb ensures that the sample used for this study only includes farms which have provided data for at least half of the study period, and avoids including observations that could come from exceptional events such as weather disasters. During the years covered by the dataset, mergers and acquisitions by some farms has potentially led to the removal of the newly acquired farms from the database, although the remaining farms have kept the same identifying number. However, their capital or land allocations are likely to have grown in an exceptional manner, which could potentially bias the estimations. The following criterion is then used to identify and to remove those farms. All observations, where the log difference of the capital stock variable between two consecutive years exceeds three in absolute value have been dropped. Finally, the sample has been further reduced by eliminating farms that present ‘outliers’ in output quantities. The aim is to eliminate those observations that are likely to generate what amount to measurement errors. The log difference of the output variable between two consecutive years is computed, and values which exceed three in absolute value are considered outliers. Thus, there are 1,529 crop farms, observed for a minimum number of 4 years, between 1996 and 2003, satisfying these conditions for a total number of 7,479 observations.

Output: Total output is used. Each specific part of total output is divided by the appropriate specific price index. The cereals’ output is divided by the cereals’ price index and so on. Prices are taken from the Eurostat Prices indexes.

Capital: Constructed using values for machinery and equipment. Buildings are not included. An overall deflator for machinery and equipment is used as farm-level prices are not available in our dataset.

Labour: Labour consists of the total number of hours (including full time and part time labour and owner/occupiers’ own labour).

Land: Land is the total utilised agricultural area. It does not include areas used for mushrooms, land rented for less than a year on an occasional basis, and woodland and other farm areas. It consists of land in owner occupation, rented land, and land in share-cropping. It includes agricultural land temporarily not under cultivation for agricultural reasons or being withdrawn from production as part of agricultural policy measures. The price deflator of land uses the land rental price series from the French Ministry of Agriculture.