Joe Wolfe

John Smith

Malte Kob
email: malte.kob@hfm-detmold.de

Jithin Thilakan
email: jithin.thilakan@hfm-detmold.de

Nathalie Henrich Bernardoni

Vocal-tract impedance at the mouth -from 1995 to today A tribute to

The acoustic output signal of orators and singers contains information from the voice source as well as from the articulatory organs. The extraction of formants to achieve information about voice timbre and vocal-tract configuration is among the essential methods in speech and language processing as well as in singing-voice research. However, the validity of formant analysis is limited by voice features and analysis parameters. The measurement of the acoustic impedance of resonating structures allows one to obtain all relevant information from their resonances. The design of a method for impedance measurement at the human lips by Joe Wolfe and John Smith dates back to 1995, and since then variations of the concept have been applied in fundamental singing-voice research (high soprano and tenor voices, overtone singing), as well as for investigations in other domains such as voice rehabilitation. This review article collects methods and applications over the last 25 years, giving reference to the many colleagues and students who have contributed with theses and supporting work. The presentation is accompanied by a demonstration of the method.

INTRODUCTION

An innovative method for measuring wind-instrument and vocal-tract impedances was developed by Prof. Joe Wolfe and Prof. John Smith starting from 1995 [START_REF] Wolfe | A comparison of acoustic impedance of flutes -a preliminary study[END_REF][START_REF] Dowd | Real time non-invasive measurements of vocal tract impedance spectra and applications to speech training[END_REF]. In the case of speech and singing, it allows the measurement of vocaltract acoustical resonance properties without making any a priori assumptions about the glottal source. Earlier work of Osamu Fujimura and Jan Lindqvist has investigated the vocal tract transfer function [START_REF] Fujimura | Sweep-tone measurements of vocal-tract characteristics[END_REF] using external swept sine excitation at the larynx. This early research already revealed the significance of glottis, epiglottis and velum configuration on the resonance characteristics of the vocal-tract. In the last decade the investigation of the vocal tract acoustics using various other methods has been facilitated by the availability of MRI-based data and physical models produced with 3D printers [START_REF] Ahmadi | Measuring reso-nances of the vocal tract using frequency sweeps at the lips[END_REF][START_REF] Fleischer | How to precisely measure the volume velocity transfer function of physical vocal tract models by external excitation[END_REF]. Their results demonstrate a high comparability of resonance measurements using external excitation and formant frequencies derived from human voice signals.

The method presented here excites the vocal-tract externally with a sound wave. The development and applications of this method are detailed below.

The excitation of the vocal-tract using a broadband signal such as noise or a swept sine provides a high frequency resolution of the measurements in contrast to formant analysis methods that need to use the line spectrum of the voiced signal which -in case of high-pitched vowels -does not provide sufficient energy between the partials for an accurate formant analysis. On the other hand the determination of formants from the voice signal provides an average estimation of the vocal-tract's filter function over time which corresponds to our perception of the filtered voice signal. When the impedance at the mouth is measured during phonation the resulting signal not only contains the impedance function but also the voice signal. For a clear presentation of the impedance function the voice signal must be separated or suppressed to obtain resonance values that correspond to the formants during phonation.

Alternatively, the impedance can also be measured without phonation at all, resulting in undisturbed resonances. However, the glottal status of such measurements can be anything between open (higher resonances than average during phonation) and closed (lower resonances), resulting in a quite large variability of the impedance function and the derived resonance values [START_REF] Stoffers | Akustische Impedanzanalyse der Artikulation[END_REF]. Instructions to subjects to keep the glottis open or closed during measurements without phonation can help to define the glottal status but not necessarily provide the desired conditions. Trained subjects, however, can voluntarily open and close their glottis which provides valuable insight to the range of the vocal tract resonances for different open quotients. The position of the epiglottis can vary as well and is difficult to control voluntarily. However, the epiglottis movement would not have an equally fundamental effect on the resonance structure as the glottal status unless it is tilted back completely (as during swallowing). Further limitations of an external excitation at the lips of a speaker/singer can be the surprising sound of a noise or swept sine signal that might cause articulatory changes just before or during to the impedance measurement. To summarise, the impedance function derived at the mouth end of the vocal-tract can not provide the same information as the analysis of a voice signal but The method to measure the vocal-tract impedance was first developed for the study of musical instruments [START_REF] Wolfe | A comparison of acoustic impedance of flutes -a preliminary study[END_REF][START_REF] Wolfe | Acoustic impedance spectra of classical and modern flute[END_REF] but also soon and successfully applied to the study of vowel formants in speech [START_REF] Epps | Real time measurements of the vocal tract resonances during speech[END_REF][START_REF] Dowd | Learning to pronounce vowel sounds in a foreign language using acoustic measurements of the vocal tract as feedback in real time[END_REF] including applications to training of phonation as well as to the investigation of singing [START_REF] Joliveau | Vocal tract resonances in singing: The soprano voice[END_REF][START_REF] Vos | Resonance tuning in three girl choristers[END_REF]. We will first present the devices and their evolution in Section 2. Their application to the analysis of singing voice in different styles will then be reviewed. The nomenclature in this text follows the proposal given in [START_REF] Titze | Toward a consensus on symbolic notation of harmonics, resonances, and formants in vocalization[END_REF].

METHOD

The measurement of the acoustic impedance requires the determination of two basic properties of the sound field: acoustic pressure p(t) & acoustic velocity v(t). The acoustic impedance Z(f ) is then determined by the quotient of the RMS values of both:

Z(f ) = FFT(p(t)) FFT(ṽ(t)) . (1)
The acquisition of acoustic pressure is far easier since sensors for acoustic velocity are, due to their small size, expensive, sensitive to damage, and of limited accuracy. Despite these problems, a prototype that captures both sound pressure and velocity has been developed in 2002. The installation of the sensors in a prototype is shown in Fig. 1.

A graphic user interface for parallel evaluation of curves obtained by linear predictive coding (LPC) and vocal tract impedance at the mouth (VTMI) was developed in Matlab ( [START_REF] Katzer | Algorithmen für ein System zur akustischen Artikulationsanalyse[END_REF], Fig. 2). Within the dissertation project of Julia Stoffers [START_REF] Stoffers | Comparison of Vocal Tract Resonance Characteristics Using LPC and Impedance Measurements[END_REF] the evaluation of the impedance curves was performed with respect to several parameters which were derived from the normalised magnitude of the impedance.

Candidates for the assessment of values for amplitude and bandwidth of each resonance were the steepness and the difference between maximum and minimum. It was found that an absolute amplitude or bandwidth was difficult to obtain since these values do not seem to be constant with frequency [START_REF] Stoffers | Akustische Impedanzanalyse der Artikulation[END_REF].

One or two sensors?

Another device was developed at RWTH Aachen University in 2003 to provide both acoustic pressure and velocity values using miniature sensors in a small, portable set-up that allows mobile measurements, see Fig 3 . The KE4-211-2 capsules by Sennheiser were used for pressure, and prototypes by Microflown were used for velocity. In Fig. 4 the set-up (right) and the velocity sensor (left) are shown. By acoustic treatment of the propagation of the acoustic wave from the exciter to the exit of the measurement device, the acoustic velocity can be held approximately constant. This condition can be achieved by guiding the sound wave through a capillary wave guide or an inverse horn [START_REF] Kob | A method for measurement of the vocal tract impedance at the mouth[END_REF]. The use of a horn and additional damping material greatly reduces the feedback of an external impedance on the loudspeaker membrane. A constant sound velocity supply can be assumed. As a consequence, the relative impedance can be determined by simply measuring sound pressure p(t) instead of also measuring sound velocity v(t).

Calibration

The combined acquisition of sound pressure p(t) and velocity v(t) allows the direct calculation of the acoustic impedance by Eq. 1. If a change of the acoustic impedance is sufficient for characterisation of the resonances, and no absolute values are required, the measurement device can be calibrated against a constant impedance -such as the impedance Z 0 of the free field around the sensor, or the impedance of the closed mouth. Resonances of the vocal tract with an open mouth would then be shown as a deviation of the measured impedance from Z 0 .

Practically, the reference Z 0 is determined just prior to the measurement at the mouth and stored. After the acquisition of the sound pressure from the calibration (p 0 (t))and

Z rel (f ) = Z m Z 0 = FFT(p m (t) FFT(p 0 (t)) . (2)
Z rel (f ) is either visualised by its absolute value or phase (see Figs. 2 and 7-9).

Signal extraction

Methods for extraction of the acoustic impedance from a measurement during phonation have been developed from the beginning. Whereas early concepts used manual extraction of the resonances in the complete signal [START_REF] Epps | Real time measurements of the vocal tract resonances during speech[END_REF], signal processing was applied to separate the voice signal from the excitation signal of the measurement and the response of the vocal tract [START_REF] Delvaux | Sinesweep-based method to measure the vocal tract resonances[END_REF][START_REF] Thilakan | Acuzlite: Ultra-portable real-time estimation of vocal tract resonance[END_REF]. A new method relying on multiple chirplet transforms has recently been proposed [START_REF] Maison | Practical guidelines for implementing vocal tract resonances characterization with excitation at the lips[END_REF][START_REF] Maison | Séparation et reconstruction d'arêtes par analyse en chirplets d'ordres supérieurs[END_REF][START_REF] Maison | A new approach to measure vocal tract resonances. application to a modern singing study[END_REF] which also investigates the effect of a distant microphone position.

Miniaturisation

Portable devices have been created in two institutions, the RWTH Aachen University in 2003, and the Singapore University of Technology and Design in 2018 [START_REF] Thilakan | Acuzlite: Ultra-portable real-time estimation of vocal tract resonance[END_REF][START_REF] Thilakan | Vocal tract resonance detection at low frequencies: Improving physical and transducer configurations[END_REF]. The device developed at RWTH Aachen can be worn with a holder around the neck and contains two sensors (see Figures 3 and4). An application of the miniature device is shown in Fig. 5.

Following the successful implementation of the technique of broadband excitation at the speaker/singer's lips and the estimation of vocal tract resonances from its corresponding relative acoustic impedance spectra [START_REF] Epps | A novel instrument to measure acoustic resonances of the vocal tract during phonation[END_REF], a modified, low-cost, portable, pocket-sized, and simplified version of this technique named "ACUZ-Lite" was developed [START_REF] Thilakan | Acuzlite: Ultra-portable real-time estimation of vocal tract resonance[END_REF] for estimating the vocal tract resonances non-invasively and thereby enabling an 'ecological' way of tracking phonation gestures. Whereas the predecessor version (from [START_REF] Epps | A novel instrument to measure acoustic resonances of the vocal tract during phonation[END_REF]) required a set of dedicated and high-performance equipment and laboratory conditions to perform the measurements, the ACUZ-Lite, on the other hand, is relatively simple in terms of the hardware and software design.

This compact device (<200 grams) is constructed with a small entry-level loudspeaker and a lavalier microphone, and it is meant for performing 'quick and dirty' field measurements outside the formal laboratory environment. The device is configured in a way that the speaker/singer's lips touch the loudspeaker grill, and the loudspeaker radiates directly into the mouth opening during the measurements as shown in Fig. 6. Similar to the predecessor version, the measurement procedure of the ACUZ-Lite is a two-stage process: a calibration followed by the measurement during phonation. During the calibration process, the speaker's mouth is kept closed, the device is held in the same way shown in Fig. 6, and a broadband noise signal is iteratively modified for this configuration to attain a uniform energy distribution over the appropriate frequency range (typically from 100 Hz to 4000 Hz). Thereafter, the measurement is performed by exciting the vocal tract with the modified broadband noise signal while the speaker phonates a target vowel. Since the loudspeaker drives with considerable power at low amplitude, and also the loudspeaker cone is Figure 7. Relative acoustic impedance spectrum measured for the vowel /@/ using ACUZ-Lite [START_REF] Thilakan | Acuzlite: Ultra-portable real-time estimation of vocal tract resonance[END_REF]: magnitude (top) and phase (bottom) plots stiffer than the air, the acoustic velocity of the signal is approximated to be constant for the specified frequency range. Hence a relative acoustic impedance (Gamma) spectrum is evaluated between measured and calibrated reference loads by estimating the ratio of the corresponding pressure signals (assuming ṽ(t) = constant). When plotting the Gamma spectrum, the vocal tract resonances are reflected as 'steep negative slopes' in the magnitude plot and the 'sharp dips' in the phase plot. Figure 7 shows a typical Gamma spectrum obtained for the vowel /@/ (target word 'herd') that includes a raw (blue) and smoothed (red) version of the measurement. The first four resonance frequencies identified from both magnitude and phase spectra are highlighted.

According to a recent study on the device, tuning the physical configuration of the transducers and the implementation of acoustic foam is shown to improve the acoustic coupling between the device and the vocal tract and develop the sensitivity in low-frequency regions [START_REF] Thilakan | Vocal tract resonance detection at low frequencies: Improving physical and transducer configurations[END_REF]. In order to investigate the optimal physical configuration of transducers, new parameters from the magnitude and phase domains are established in this study for quantitatively assessing the quality and sensitivity of vocal tract resonance detection.

Although the device relies on some approximations and 'quick and dirty' measurements, the resulting relative impedance spectra are comparable in performance with previous studies made under formal laboratory conditions. Despite the absence of acoustic flow information, the device is shown to detect vocal tract resonance frequencies reliably, especially the first resonance frequency, down to 350 Hz and possibly even lower by improving its low-frequency response, and the acoustic coupling with the vocal tract. This is expected to be further enhanced by implementing a more powerful loudspeaker and larger housing, as well as a short inverse horn for acoustic coupling between the device and the vocal tract in case of small mouth openings as in the vowel /u/. Even without further modifications, the device has extended the applicability of the impedance measurement at the mouth to a wide range of vowel articulations and singing styles under 'field conditions'. Figure 8. VTMI analysis of a sequence of rising overtones [START_REF] Kob | Analysis and modelling of overtone singing in the sygyt style[END_REF] Figure 9. VTMI analysis of a morphed sound from /a:/ to an overtone sound [START_REF] Kob | Analysis and modelling of overtone singing in the sygyt style[END_REF] 3. APPLICATIONS

Analysis of overtone singing

The extraordinarily low bandwidth of the formant that occurs at the frequency of the melody pitch of singers who perform sygyt-style overtone singing, can be explained by focalisation, i.e. concentration of two resonances on one frequency [START_REF] Kob | Analysis and modelling of overtone singing in the sygyt style[END_REF]. The result from the impedance analysis of a rising overtone sequence is shown in Fig. 8 and demonstrates the presence of two resonances for some of the higher melody pitches. The impedance measurement of the vocal-tract has been used as a method to demonstrate the morphing of a sustained sound /a:/ to an overtone sound. The formant F 3 lowers its frequency from around 2 kHz to the frequency of F 2 around 1.2 kHz during the morphing process.

The resulting overtone formant has a lower bandwidth and therefore a higher selectivity than each of the formants alone. The transition of a vowel sound /a:/ to an overtone sound shown in Fig. 9 demonstrates the focalisation of two resonances that jointly create the strong overtone formant.

Resonance strategies in operatic singing

An active collaboration started in 2004 between an australian and a french research team, receiving support from a French-Australian PHC funding program for scientific and technological exchanges (FAST, 2010-2011). Resonancetuning strategies used by opera singers have been studied as a function of pitch, vocal intensity, and sung vowels. Several databases have been compiled: The analyses of these databases have revealed different resonance-tuning strategies in operatic singing. The frequencies of the first two vocal-tract acoustical resonances remained relatively constant throughout the singers' tessitura, as long as the sung note remains lower than the first-resonance frequency [START_REF] Henrich | Vocal tract resonances in singing: Strategies used by sopranos, altos, tenors, and baritones[END_REF]. These resonance frequencies can sometimes increase with an increase in fundamental frequency, reflecting a movement of jaw opening as the singer sings higher in pitch. In cases where the firstresonance frequency (f R1 ) joins the fundamental oscillatory frequency (f o ), for instance in the higher part of the tessitura or for closed vowels, a tuning [(f R1 ):f o ] is observed. This phenomenon of resonance tuning is frequent in sopranos who sing at pitches where resonance and harmonics meet, whatever the training level of the singer. It is also found in other tessituras. Alto singers demonstrate [(f R1 ):f o ] tuning for vowels with a low-frequency first resonance. In the lower part of their pitch range, they may use a [(f R1 ):2f o ] strategy. Baritones and tenors demonstrate [(f R1 ):2f o ] and [(f R1 ):3f o ] tunings in part of their pitch range, or tuning with higher harmonics in low-pitch ranges. Inter-individual differences are great, especially for low-pitch voices.

First-resonance to first-harmonic tuning may be accompanied by an additional frequency tuning to the second resonance [(f R2 ):2f o ] for some singers. To produce their highest-pitch sounds, some of the singers extend their tuning range [(f R1 ):f o ] up to 1300-1500 Hz (E6-F#6). Other singers tune the second resonance near the first harmonic [(f R2 ):f o ] to 2350 Hz (D7).

Resonance strategies in Bulgarian women's singing

If lyrical singers sometimes present a (f R1 ) resonance tuning to the second harmonic 2f o , the [(f R1 ):2f o ] tuning can be a systematic tuning strategy in other singing styles. For example, Balkan songs, and in particular traditional Bulgarian women's singing, are particularly sonorous, with a predominance of acoustic energy in the voice second harmonic as a key feature [START_REF] Messner | Die Schwebungsdiaphonie in Bistrica: Untersuchungen der mehrstimmigen Liedformen eines mittelwestbulgarischen Dorfes[END_REF][START_REF] Boersma | Spectral characteristics of three styles of croatian folk singing[END_REF]. In collaboration with Mara Kiek (ACARMP Sydney Conservatorium of Music, The University of Sydney, Australia), the vocal behavior of an Australian singer who mastered traditional Bulgarian singing techniques was explored. Two distinct vocal qualities were assessed : the teshka (heavy) quality, which corresponds to a very sonorous vocal production, and the leka (light) quality, for which vocal production is softer, approaching in timbre the register of female head voice. The analysis of vowels sung in traditional Bulgarian style has shown the search for a tuning between the first resonance and the closest harmonic, either 2f o or 1f o depending on the vowel, no matter the technique used [START_REF] Henrich | Resonance strategies used in bulgarian women's singing style: A pilot study[END_REF]. This systematic resonance-tuning strategy clearly distinguishes the vocal behavior in Bulgarian singing from the behavior in lyrical singing for the studied female singer. As shown in Figure 10, the resonance frequencies for vowels sung in head voice remain close to the resonance frequencies for the same vowels spoken.

Analysis of high tenor voices

The impedance measurement has been applied in a larger project for the analysis of potential register transitions in the high range of counter tenor singers. A comparison of the resonances during the performance of a sequence of sustained vowels allowed for grouping of the singers into one group that held the vocal tract configuration unchanged during the whole sequence, and another group that adopted vocal tract resonances to the frequencies of the first three partials. A publication of the work is pending.

CONCLUSIONS

The measurement method of vocal tract impedance, invented by Joe Wolfe and John Smith in 1995 has inspired research teams from various countries to further develop and apply it for investigations in speech and singing voice research. Different methods and their applications that had emerged from the technique of vocal tract impedance measurement at the human lips are presented in this review article. This included devices with both pressure and velocity sensors to measure the acoustic impedance, and relatively simple devices that include only a pressure sensor to estimate relative acoustic impedance. Whereas some of the devices are advanced for estimating the voice and resonance qualities for support of research on resonance phenomena in singing, a few have evolved in the direction of simple and portable use in field conditions. 25 years after the initial invention Matlab-based tool with instructions for a self-made device has been published on the UNSW web page of Joe Wolfe [START_REF] Wolfe | Vocal resonances and broad band excitation[END_REF]. Further improvement of algorithms for the resonance analysis during phonation will enable the use of such devices for singing students outside acoustic laboratories.

Figure 1 .

 1 Figure 1. VTMI device

Figure 2 .

 2 Figure 2. Applet for the VTMI device, impedance curves (top) and LPC curves (bottom) shown simultaneously for vowel /a:/

Figure 3 .

 3 Figure 3. Minature VTMI set-up

Figure 5 .Figure 6 .

 56 Figure 5. Use of the miniature VTMI device

Figure 10 .

 10 Figure 10. First-resonance frequencies for spoken vowels (horizontal black and sung vowels in bulgarian singing style (red markers) and classical female head voice (blue markers).

Acknowledgments

We acknowledge the contributions of a large number of students, co-workers and colleagues from several countries to the development of the various impedance measurement methods, namely Jer-Ming Chen, Annette Dowd, Julien Epps, Elodie Joliveau, Roman Katzer, Maëva Garnier, Timothée Maison, Luis Roca and Julia Stoffers. Dusty Eddy is thanked for proofreading the manuscript. The reviewers are acknowledged for their constructive comments that helped to improve the manuscript.


Jean-Galbert Ongono Olinga
email: jean_galbert.ongono_olinga@etu.udamail.fr

Pascale Combes Motel

José Gustavo Feres
email: jose.feres@ipea.gov.fr

Sonia Schwartz
email: sonia.schwartz@uca.fr

Protected-areas and technological progress in agriculture in the Brazilian Legal Amazon: An analysis of the Porter hypothesis

Keywords: Protected areas, efficiency, potential production frontier, Porter hypothesis C21, Q10, Q24, Q28

In this article we analyze whether environmental protection policies in Brazilian municipalities of Legal Amazon drive technical progress in agriculture, thus verifying the Porter hypothesis. Specifically, we investigate whether agricultural firms in municipalities with protected areas (PAs) are technically more performant in agriculture than firms in municipalities without protected areas. We use agricultural census data from 1995/1996 and 2005/2006 and derive estimates of potential production frontier, technical efficiency and total factor productivity as proxies of agricultural performance in a stochastic frontier framework. Next, we run estimates of a panel model with fixed effects, including difference-in-difference estimator, to assess the effect of protected-area policies on efficiency, potential production and total factor productivity changes. Results are consistent with significant changes in potential production and total factor productivity. Because the shift of the potential production across time is a result of technical progress, our estimates show that agricultural firms in municipalities with protected areas improved their technical progress more in year 2006 compared to year 1996.

Introduction

The process of designating protected areas in Brazil has evolved considerably during the past three decades. Most of the country's lands have been designated integral and sustainable protected areas over this period since 1980 in line with Brazil's goal of tackling ecological, climatic and biological diversity threats due to ongoing deforestation. Based on statistics from the National Institute for Spatial Research (INPE), ongoing deforestation is the result of agricultural activities, urbanization and human habitat evolution, which have accelerated dramatically between 1970 and 2004, causing the loss of an estimated 17% of the Amazon rainforest. In an attempt to halt this destruction, environmental policy instruments, such as protected-areas, payments for environmental services, and annual district blacklist publications, have been implemented [START_REF] Pagiola | Brazil's Experience with Payments for Environmental Services[END_REF][START_REF] Cisneros | Naming and Shaming for Conservation: Evidence from the Brazilian Amazon[END_REF][START_REF] Pfaff | Protected Areas' Impacts on Brazilian Amazon Deforestation: Examining Conservation -Development Interactions to Inform Planning[END_REF]. Among these instruments, protected areas have been the subject of particular attention by the international institutions (the World Bank) and the Brazil's federal government. Their increasing implementation in Legal Amazon has been made possible thanks to various programs, such as the "Planaforo" program financed by the World Bank, the federal government's commitment to meeting its Convention on Biological Diversity (CBD, Chart 2) targets and the Amazon's Protected Areas Program (ARPA), jointly managed by Brazil's federal and state governments. The main goal of these programs is to curtail deforestation and protect areas rich in biodiversity.

In 2010, Brazil's National System of Conservation Units statistics indicated that 22.2% of the area of Brazil had been designated as PAs [START_REF] Verissimo | Protected Areas in the Brazilian Amazon: Challenges and opportunities[END_REF], and approximately 42% of the entire area of the Legal Amazon was made up of protected-areas. They are managed according to their status, which could be local (district level), state or federal. The effectiveness of protected areas has been the subject of numerous studies, with [START_REF] Andam | Measuring the effectiveness of protected area networks in reducing deforestation[END_REF], [START_REF] Nolte | Gorvernance regime and location influence avoided deforestation succes of protected areas in the Brazilian Amazon[END_REF] and [START_REF] Pfaff | Governance, Location and Avoided Deforestation from Protected Areas: Greater Restrictions Can Have Lower Impact, Due to Differences in Location[END_REF] among the most recent contributions. Most of these studies find that protected-areas overall are helpful environmental policy instruments and effective in slowing down deforestation and conserving and protecting biological diversity. However, some shortcomings, such as weak management enforcement, failure to designate PAs on high pressure deforestation zones and some negative consequences on local development are reducing their effectiveness [START_REF] Kere | Addressing Contextual and Location Biases in the Assessment of Protected Areas Effectiveness on Deforestation in the Brazilian Amazônia[END_REF][START_REF] Chiaravalloti | Federal protected areas management strategies in Brazil: sustainable financing, staffing, and local development[END_REF][START_REF] Pfaff | Protected Areas' Impacts on Brazilian Amazon Deforestation: Examining Conservation -Development Interactions to Inform Planning[END_REF].

Other studies focus on leakages or unintended effects of protected-area policies. In fact, in some cases, the side effects of the protection, such as the displacement of deforestation to surrounding areas, have been observed [START_REF] Oliviera | Land-use Allocation Protects the Peruvian Amazon[END_REF][START_REF] Arima | Statistical confirmation of indirect land use Change the Brazilian Amazon[END_REF][START_REF] Amin | Neighborhood effects in the Brazilian Amazon: protected area and deforestation[END_REF]. The expected impact of the protection can be effectively achieved in the protected area zones but not on a global scale. Indeed, it is possible that the deforestation that would have occurred if no protection was established, happens in the surrounding areas instead [START_REF] Ewers | Estimates of reserve effectiveness are confounded by Leakage[END_REF]Rodrigues 2008, Delacote and[START_REF] Delacote | Reducing Deforestation and Forest Degradation: Leakage or Synergy?[END_REF]. Some unintended effects of protected areas are also found in local governance. [START_REF] Sauquet | Protected areas, local governments, and strategic interactions: The case of the ICMS-Ecologico in the Brazilian state of Parana[END_REF] demonstrate how reward efforts of municipalities that create protected areas in the Brazilian state of Para lead to strategic substitutability in the vicinity due to the propensity to create new protected areas. In other words, conservation units created in a municipality could discourage the creation of other protected areas in the vicinity. Other studies focus on the impact of protected areas on non-environmental targets such as poverty. They explore whether a win-win scenariothat is, a reduction of the deforestation process and the mitigation of poverty among local populations is possible [START_REF] Fearnside | Conservation Policy in Brazilian Amazonia: Understanding the Dilemmas[END_REF][START_REF] Miranda | Effects of Protected Areas on Forest Cover Change and Local Communities: Evidence from the Peruvian Amazon[END_REF][START_REF] Karki | Do protected areas and conservations incentives contribute to sustainable livelihoods? A case study of Bardia National Park, Nepal[END_REF][START_REF] Sims | Conservation and development: Evidence from Thai protected areas[END_REF][START_REF] Andam | Protected areas reduced poverty in Costa Rica and Thailand[END_REF].

In this study, we are contributing to the literature on the effectiveness of protected-area policies by studying their impact on agricultural performance. Following the insight of the Porter hypothesis which argues that environmental policies can enhance the agricultural performance of firms, we aim to explicitly check whether municipalities that welcomed protected areas in the Legal Amazon have also registered more productive practices than municipalities without protected areas. As conservation policies induce an increasing scarcity of arable land, our intuition is that this scarcity makes farmers stop practicing extensive agriculture and drives them to adopt more efficient practices. One way to understand this is to consider deforestation leakages generated by protected-area policies. The deforestation occuring from agricultural activities in surrounding conservation unit areas could happen with more efficient landuse practices because the protection delivers a signal to producers that the forest must be preserved or used with care. Thus, farmers register this information and develop new practices to increase production in their process of expanding agricultural activities outside of the protected zone. Some studies have already tested if the Porter hypothesis is verified in the case of pollution abatement policies. They highlight that pollution abatement policies trigger technological progress which improves both productivity and environmental quality. However, the productivity gains are mainly driven by the reallocation of resources across firms rather than by technological changes [START_REF] Sadeghzadeh | The Impact of environmental policies on productivity and market competition[END_REF]). In the same vein, [START_REF] Alpay | Productivity Growth and Environmental Regulation in Mexican and U.S Food Manufacturing[END_REF] also studied the Porter hypothesis focusing on food manufacturing in Mexico. They empirically showed that environmental regulation improved the competitiveness of food manufacturing firms over the long-term, resulting in significant overall changes in their productivity.

In this paper, we apply an empirical framework to demonstrate that protected-area environmental policies promote productive practices in agriculture. We hypothesize that farmers register the signal transmitted by the designation of conservation units in various areas and respond by adopting more efficient practices [START_REF] Zimmerer | Conservation Booms" with agricultural growth ? Sustainability and Shifting Environmental Governance in Latin America, 1985-2008 (Mexico, Costa Rica, Brazil, Peru, Bolivia)[END_REF]. They adopt new methods or new technologies on restricted areas in order to cover high rents. More specifically, we empirically test whether the designation of protected areas in various municipalities results in the adoption of more efficient practices by firms in these municipalities compared to firms in municipalities without protected areas.

We test this hypothesis by using 1996 and 2006 agricultural census data of Brazilian municipalities with an application of the difference-in-difference model in panel data. The diff-in-diff model compares the agricultural performance among the municipalitites. We compute the technical efficiency, the potential production and the total factor productivity as the main outcomes representing the agricultural performance, using a stochastic frontier analysis. We find that changes in terms of the potential production and total factor productivity in municipalities with protected areas compared to those without protected areas are high and significant in 2006 rather than in 1996. This leads us to a conclusion that protected-area policies drive farmers in protected zones to adopt productive practices in agriculture. The resulting intensification favors the reduction of agricultural land-use and, in fine, spare land in the edges of the forest.

The remainder of the paper is organised as follows. Section 2 provides a literature review on the relationship between environmental policies and technological innovation. The analytical framework is presented in Section 3 and our results are outlined in Section 4. Finally, a conclusion is given in Section 5.

Environmental policy and technological innovation: a literature review

The debate on the relationship between environmental policy and technical innovation stems mainly from the literature focusing on pollution abatement. In the next sub-section, we outline the traditional view of the debate and introduce insights of the Porter hypothesis. In the second sub-section, we briefly present the literature concerning factors that trigger incentives to improve technical agricultural practices. The third sub-section focuses on the Brazilian case and explores an extension of the Porter hypothesis to agriculture, substituting protected areas for environmental policies.

The traditional view and the Porter hypothesis

The traditional view of the debate on the impact of environmental policies on firm performance asserts that environmental regulation does not favor technical innovation and negatively affects the productivity, profit and competitiveness of firms [START_REF] Christainsen | The Contribution of Environmental Regulations to the Slowdown in Productivity Growth[END_REF]. As a result, the view asserts, regulated firms are not motivated to invest in new technology favorable to pollution abatement in the short term but, rather, prefer to implement end-of-pipe techniques which will decrease their polluting waste. Such solutions are less effective in terms of enhancing productivity to strenghten a firm's competitiveness than those that consist in completely changing the technological production process to one that takes environmental standards into account. Indeed, investing in new technology generates new costs, in addition to those introduced by regulations that constrain the firm in the short term [START_REF] Palmer | Tightening Environmental Standards: The Benefit-Cost or the No-Cost Paradigm[END_REF]. The traditional view of the debate supports the notion that the relationship between the regulator and regulated firms is win-lose because firm productivity cannot increase under environmental regulations. On the contrary, productivity may be negatively affected. Although empirical evidence of this argument have been demonstrated in several studies [START_REF] Hazilla | Social Costs of Environmental Quality: A General Equilibrium Analysis[END_REF][START_REF] Hazilla | Social Costs of Environmental Quality: A General Equilibrium Analysis[END_REF][START_REF] Norsworthy | The slowdown in Productivity Growth: Analysis of some Contributing Factors[END_REF], another strand of literature survey concerning this debate contradicts this notion and is based on the Porter hypothesis.

The Porter hypothesis supports the idea that stringent and properly designed environmental regulations can trigger innovations that may partially or more than fully offset the costs of complying with them (Porter and Van der Linde 1995). According to Porter and Van der Linde, environmental regulations alert firms of their inefficiencies and of the potential need for technological improvement. Regulations that address environmental targets introduce the concept that a firm's investment in environmental preservation is compatible with its primary goal of profit maximization [START_REF] Ambec | The Porter Hypothesis at 20: Can Environmental Regulation Enhance Innovation and Competitiveness?[END_REF]. In fact, they argue, the production costs of firms increase sharply in the short-term due to regulations. However, if regulations remain stringent over the long term, firms will prefer to invest in new and innovative technologies that adhere to environmental regulations rather than bearing the costs induced by them. As a result, such innovations will spark competition and spread throughout the entire economic sector. The Porter hypothesis argues that new technologies will positively impact sector productivity and simultaneously enable environmental goals to be reached. In this case, the relationship between regulator and regulated can be qualified as win-win.

Empirical and theoretical evidence supporting the positive effects of environmental regulations on technical innovation and productivity have been highlighted in the literature. According to [START_REF] Sadeghzadeh | The Impact of environmental policies on productivity and market competition[END_REF] and [START_REF] Alpay | Productivity Growth and Environmental Regulation in Mexican and U.S Food Manufacturing[END_REF], the stringency of environmental regulations can stimulate technical innovations. They argue that if regulations are more stringent, firms will invest in R&D for innovative technology that is more economically feasible for productivity improvements. Next, we present some trigger factors of the adoption of innovative practices in agriculture.

Some trigger factors of innovative practice adoption in agriculture

Different factors that trigger innovative practices in agriculture are highlighted in the literature. Among them, the consideration of environmental preservation is presented as a key factor leading to innovative agricultural practices coupled with high rents. Numerous study argue that outcomes such as an increase, both in quantity and quality, of farmers' yields, are achieved when environmental consideration is undertaken in agricultural practices [START_REF] Lanoie | Des billets verts pour des entreprises agricoles vertes[END_REF][START_REF] Lutz | Integration of Environmental Concerns into Agricultural Policies of Industrial and Developing Countries[END_REF][START_REF] Ibanez | Is Eco-Certification a Win-Win for Developing Country Agriculture? Organic Coffee Certification in Colombia[END_REF]. According to [START_REF] Ibanez | Is Eco-Certification a Win-Win for Developing Country Agriculture? Organic Coffee Certification in Colombia[END_REF] and [START_REF] Blackman | Does eco-certification have environmental benefits? Organic coffee in Costa Rica[END_REF], the adoption of ecocertification in agriculture has resulted in environmental benefits, coupled with agricultural performance, in southeastern Colombia and in Costa Rica, respectively. Adhering to environmental standards does not necessarily constrain the performance of agricultural firms. On the contrary, it can trigger the adoption of productive practices leading to larger yields for farmers.

Other studies focus on the scarcity of production factors such as land. They argue that when land scarcity increases, farmers respond by improving their practices in order to get more production in available land. Land scarcity can arise from population growth or from restrictions introduced by conservation unit policies [START_REF] Boserup | The Impact of Population Growth on Agricultural output[END_REF]and 1976[START_REF] Levi | Population Pressure and Agricultural Change in the Land-intensive Economy[END_REF][START_REF] Pingali | Population Density, Market Access and Farmer-Generated Technical Change in Sub-Saharan Africa[END_REF][START_REF] Zimmerer | Conservation Booms" with agricultural growth ? Sustainability and Shifting Environmental Governance in Latin America, 1985-2008 (Mexico, Costa Rica, Brazil, Peru, Bolivia)[END_REF]. However, [START_REF] Hertel | The Global Supply and Demand for Agricultural Land in 2050:A perfect storm in the Making[END_REF][START_REF] Hertel | Implications of Agricultural Productivity for Global Cropland Use and GHG Emissions: Borlaug vs[END_REF] argues that it is not only land scarcity that matters in the process of stimulating efficient practices' adoption. Other element such as the deficiency of various production factors (labor as an example) can result in some productive practices adoption (the replacement of workforce by machineries). Some other studies cite other factors such as commodity price booms. In fact, in order to take advantage of favorable agricultural commodity prices, farners are likely to develop innovative practices to obtain greater yields [START_REF] Barbier | Economic analysis of deforestation in Mexico[END_REF][START_REF] Barbier | Economic analysis of deforestation in Mexico[END_REF][START_REF] Elnagheeb | Extensification of agriculture and deforestation:empirical evidence from Sudan[END_REF][START_REF] Elnagheeb | Extensification of agriculture and deforestation:empirical evidence from Sudan[END_REF]. However, innovative practices resulting from commodity price booms do not necessarily favor positive environmental outcomes because they usually result in forest loss increase [START_REF] Cattaneo | A General Equilibrium Analysis of Technology, Migration and Deforestation in the Brazilian Amazon[END_REF]. Farmers investigate new areas beyond the forest frontier to achieve greater yields and profit. Among the factors presented above, others are outlined in the literature review and focused on the farm's size, the type of commodities produced (whether industrial or food crops) or the accessibility to the capital in comparison to the factor of labor avaibility (Ruff 2001 and[START_REF] Jayasuriya | Agriculture and Deforestation in Tropical Asia: An Analytical Framework[END_REF]. We focus in the next sub-section on the Brazilian Legal Amazon case.

Protected areas and agricultural performance improvement in the Brazilian Amazon

To the best of our knowledge, little work has been done to assess the effect of protected areas on agricultural performance in the Brazilian Legal Amazon. Protected areas in Brazil are considered as an effective environmental policy instrument used to reduce the deforestation process and conserve biological diversity [START_REF] Andam | Measuring the effectiveness of protected area networks in reducing deforestation[END_REF]. Given that they enforce restrictions, constraints or conditions on the use of land for agriculture, PAs often cause opposition between the regulator and farmers concerning conservation targets and the need for land for agricultural activities [START_REF] Kolk | From Conflicts to Cooperation: International Policies to Protect the Brazilian Amazon[END_REF][START_REF] Fearnside | Conservation Policy in Brazilian Amazonia: Understanding the Dilemmas[END_REF][START_REF] Brandon | Reconciling Biodiversity Conservation, People, Protected areas and Agricultural Suitability in Mexico[END_REF]). However, these constraints or restrictions can also trigger incentives for farmers to adopt more productive practices on available arable lands.

Basic statistics at the municipal level can deliver preliminary information (Tables 1 and2). On average, the overall value of agricultural production and the level of capital increased in Brazilian municipalities from 1996 to 2006 while a large portion of land has been converted into PAs. Total workers decreased during the same period (Table 1). In addition, the agricultural production was greater (on average) in municipalities with protected areas than in municipalities without protected areas, though the difference is weakly significant in 1996 (Table 2). Although land use appears higher in municipalities with protected areas, the fact that capital expanded while total workers decreased in 2006 compared to 1996, indicates that incentives from farmers to adopt productive practices were strong in these municipalities (Table 2). 5 Note that only Integral and Sustainable PAs are taken into account. The main difference between these types of protected areas involves constraints concerning their accessibility. While Integral PAs strictly prohibit human activity (except scientific research) in order to protect their natural resources, Sustainable PAs only moderately restrict human activity and 5 The fact that land use in agriculture is higher in municipalities with PAs than municipalities without PAs is explained by the PA status. We find that Sustainable PAs cover about 67 million hectares while Integral PAs only account for about 29 million hectares. Sustainable PAs enable co-activities such as agriculture. Integral and Sustainable PAs also differ in their location characteristics. [START_REF] Pfaff | Governance, Location and Avoided Deforestation from Protected Areas: Greater Restrictions Can Have Lower Impact, Due to Differences in Location[END_REF] found that in the state of Acre, Sustainable PAs are located in sites under higher clearing threat. This signals higher potential agricultural profitability. Higher agricultural profitability in municipalities with Sustainable PAs can therefore drive the extension of agricultural area.

promote the sustainable use of natural resources [START_REF] Françoso | Habitat loss and the effectiveness of protected areas in the Cerrado biodiversity Hotspot[END_REF]. 6 The total workers in agriculture refer to the number of men and women over 14 years old working in the agricultural firms in the municipality. There are 645 municipalities without missing value after the merge of the 1996 and 2006 databases. The following section focuses on the empirical strategy, developed to highlight whether the Porter hypothesis is valid with regard to protected areas.

Empirical framework

In this article, we empirically test the hypothesis that conservation units are among the factors that trigger the adoption of productive practices in Brazilian municipalities of the Legal Amazon. To do that, a two-step econometric approach is applied. We begin by estimating an oriented-output stochastic frontier model to derive the agricultural performance metrics such as technical efficiency, potential production, and productivity of the municipality. Next, we compare the agricultural performance among the municipalities with protected areas and those without the protected-areas at two different time periods. To achieve this goal, a difference -in -difference (diff -in -diff) model is applied.

The sample counts 740 municipalities. Indeed, in the Brazilian Legal Amazon, there are 772 municipalities. Because we are interested in running estimates with the Brazilian municipalities as units, we keep only those found in the Brazilian Legal Amazon in 1995 since in that year there was an agricultural census, and a few years before a large area of the Brazilian Legal Amazon had become protected [START_REF] Verissimo | Protected Areas in the Brazilian Amazon: Challenges and opportunities[END_REF]. There are exactly 750 Brazilian municipalities found in Brazilian Legal Amazon meaning that 22 municipalities are not in Brazil but belong to other surrounding countries. Ten of these 750 municipalities were subdivided during the period of 1996 to 2006. We choose to drop from the sample municipalities that changed during this period and keep only the unchanged municipalities. We also drop all of the municipalities (54) where we find only indigenous land as protected areas whose status is very specific and would add too much heterogeneity. We run estimates considering only the protected areas that were established in a municipality between 1985 and 2006. The empirical framework is organized as follows: in Sub-section 3.1 we present the data and descriptive statistics. The methodology used to compute agricultural performance with an oriented-output stochastic frontier model is given in Sub-section 3.2. In the next Subsection 3.3, the diff -in -diff econometric model is described.

Data

Protected-areas

This study is conducted focusing on the PAs that were created 10 years prior, observing the agricultural data from Brazil's 1995Brazil's /1996Brazil's and 2005Brazil's /2006 The process of designating protected areas began in Brazil in 1959 according to the National System of Conservation Units [START_REF] Verissimo | Protected Areas in the Brazilian Amazon: Challenges and opportunities[END_REF]. Up to 1985, the total area of protected areas in Brazil was approximately 124,000 square kms. Between 1990 and 1994, there was an increase in the creation of protected areas thanks to the "Planaforo" programs financed by the World Bank. The "Planaforo" programs focused on protection of areas with strong environmental characteristics [START_REF] Millikan | Politicas Publicas e Desenvolvimento Sustentavel em Rondônia: Situação atual e abordagem para um planejamento participativo de estratégias para o Estado. Governo do Estado de Rondônia[END_REF]. During 1990s, the Brazilian government engaged in a strategy of expanding protected areas in the Amazon in order to meet the biodiversity targets that it set. Several federal conservation units were created until 2002 [START_REF] Capobianco | Biodiversidade na Amazônia Brasileira: avaliação e ações prioritarias para a conservação, uso sustentavel e repartição de beneficios[END_REF].

The period spanning from 2003 to 2006 was a peak moment in the establishment of conservation units in the Brazilian Amazon. During this period, most of the conservation units found in 2010 were established [START_REF] Verissimo | Protected Areas in the Brazilian Amazon: Challenges and opportunities[END_REF]. Indeed, the collaboration of the federal and state governments to curb the deforestation process via their support to the Amazon's Protected Areas Program (ARPA) led to the creation of several protected areas. The ARPA's goals are based on the creation and management of the Brazilian Amazon Conservation Units. The ARPA performs between 2003 and 2009 by supporting the creation and the management of approximately 63 conservations units that represent an average of 340,000 square kms of the Brazilian Amazon. The conservation units established meet the classification criteria of the United Nations for Environment Program (UNEP).

Other variables

The agricultural production value variable (lnproduction_value) is available on the Instituto Brasileiro de Geografia e Estatística (IBGE) or the Instituto de Pesquisa Econômica Aplicada (IPEA) website. It lists the value in Brazilian currency (reais $) of crops, livestock, and other agricultural products. To account for the inflation effect, we deflate the agricultural production value of 2006 using the agricultural prices index computed by the Fundação Getulios Vargas institution, and which is available as IPA origem -produtos agropecuáriosíndice (ago. 1994 = 100) on the IPEA website. The capital variable (lncapital) refers to the number of materials or machinery found on the farm and used for agriculture. Precisely, we compute the capital variable, by municipality, as the sum of trucks, tractors, useful objects, planting machinery and harvest machinery of farms found in a municipality as they are specified and presented on the IBGE and IPEA websites. The land use in agriculture variable (lnagricultural_landuse) is aggregated at the municipality level. It has been computed by IBGE and is available on their website. The totalworkers variable (lntotalworkers) is the aggregate value of total workers in agriculture, by municipality. Data for this variable are also available on the IBGE website. The variables for precipitations (lnpre_mun) and temperature (lntmp_mun) have both been taken from the database CRU TS 3.22 of the University of East Anglia, which lists them for every month. A simple average of each variable is computed to obtain the annual value of precipitations and temperature. Numbers of establishments receiving technical assistance (lntechnical_assistnb) and using electrical energy (electricity_nbesth) have been taken from the IBGE website.

Agricultural performance: potential production, technical efficiency, and total factor productivity

The technical efficiency, potential production and total factor productivity are derived as the proxies of agricultural performance using an oriented-output stochastic frontier model with panel data. 7 We follow the [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] Figure 1: Inefficiency and technical progress illustration 7 The stochastic frontier model assumes that the gap between the maximum possible production (potential production) and the observed production of units is the sum of the technical inefficiency 𝐮 𝐢𝐭 and the error component 𝛆 𝐢𝐭 [START_REF] Aigner | Formulation and Estimation of Stochastic Frontier Production Function Models[END_REF][START_REF] Meeusen | Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error[END_REF]. In this study, we run two different specifications of the stochastic model: the [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] model and the Greene's (2005a) model. We retain the [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] and LL(H 1 ) are log-likelihood values of the restricted model and the unrestricted model. Indeed, the Greene (2005a) model is subject to incidental parameter. From the stochastic model of [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF], the technical inefficiency is broken out into two components: the persistent inefficiency (𝒖 𝒊 ) and the time-varying inefficiency (𝝉 𝒊𝒕 ). 8 The inefficiency is the sum between the persistent inefficiency and the variant inefficiency. The persistent inefficiency refers to the inefficiency that doesn't change over time. It's closely related to the heaviness in unit management. In contrast to the variant inefficiency, which corresponds to the inefficiency that changes with time, the persistent inefficiency explains the reason why some units' inefficiency remains unchanged although the firm is trying to improve the management of its agricultural activities. As we can observe in Figure ( 1) above, points that belong to the "frontier" are the best technical realization points representing the potential production. 9 With the stochastic frontier analysis, the "frontier" is obtained by connecting all of the best technical realization points. If the "frontier" is shifted upwards from t to t+1, then positive technological changes have been made. However, if it moves downwards, then there has been a decline in technological changes. Considering that point A is the best technical realization and point B is the observed production of a unit i, the gap between A and B is the sum of the inefficiency and the random noises. The stochastic frontier analysis assumes that the production observed is the result of the potential production, the inefficiency and the random noises occurring during the production process. [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] divide the inefficiency into the persistent inefficiency and the time-varying inefficiency. The efficiency is obtained as the exponential value of the inefficiency (exp(-𝒖 𝒊𝒕 )). 10 If individuals were perfectly efficient, that is 𝒖 𝒊𝒕 = 0, and there were no random noises, the observed production 𝒚 𝒊𝒕 would equalize the potential production, which is the combination of the inputs 𝒙 𝒊𝒕 thanks to the functional form 𝒇(. ). However, because the inefficiency exists and can arise from anywhere [START_REF] Müller | On sources of Measured Technical Efficiency: The Impact of Information[END_REF], the observed production could stay below the frontier, meaning that it is different from the combination of inputs.

Let's denote TFP ̇ as the total factor productivity changes representing the productivity changes that are unexplained by the production factor changes, so that we have:

TFP ̇ = ẏ-∑ S j x j j (2)
S j is the input j's share in the production cost, j denotes the type of inputs, ẏ and x j ̇ are the ratio of the production and the ratio of the input j's changes over the time changes. By differentiating the mathematical form of Equation (1) (we remove 𝜺 𝒊𝒕 the term that brings statistical inference), we obtain: x j ̇ and 𝜀 𝑗 is the input j's elasticity. By replacing (3) in ( 2), and arranging as:

dy it dt = ∑ ∂f(x it
9 "Frontier" refers to the representation of 𝒂 𝟎 + 𝒇(𝒙 𝒊𝒕 ; 𝜷) , the deterministic part of the stochastic frontier. 10 Kumbhakar and Heshmati (1995) use a four-step approach to estimate the persistent inefficiency and the timevarying inefficiency. Their technical inefficiency estimates are deductible after running either a standard fixed effects panel regression or a standard random effects panel regression. Persistent inefficiency is derived as the difference between the predicted value of a municipality's fixed effects and the maximum predicted fixed effects among all the municipalities. Time-varying inefficiency is derived using another application of a stochastic frontier model with the predicted errors from the first estimation of a standard fixed effects panel model as the dependant variable. In this second stochastic frontier model application, the explanative variable is a vector that contains only the numeral one as a value. The main goal in applying this is to estimate the constant term and the time-varying inefficiency. The time-varying inefficiency (or efficiency) is predicted from this second application, which is the third stage of [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] model. For further explanation, see Kumbhakar, Wang and Horncastle, (2015 pp 270-274).

TFP ̇= ∑ ε j ẋj (Kumbhakar et al. 2015 pp 286 -287). Because information concerning input prices is not available, we consider that ε j RTS = S j following Kumbhakar and Lovell (2000, p. 284). Thus, considering the gap between 1996 and 2006 as one period, the TFP change is broken down as:

TFP ̇= (RTS -1) ∑ ε j RTS ẋj j + TC -∆TE = (RTS -1) ∑ ε j RTS (𝑥 𝑗,2006 -𝑥 𝑗,1996 ) + j (f(x it , β) 2006 -f(x it , β) 1996 ) -( u i2006 -u i1996 ) (5)
Estimating the TFP requires considering the endogeneity of inputs in the production function [START_REF] Van Beveren | Total Factor productivity estimation: A practical review[END_REF][START_REF] Levinsohn | Estimating Production Functions using inputs to control for unobservables[END_REF][START_REF] Levinsohn | Estimating Production Functions using inputs to control for unobservables[END_REF]. [START_REF] Marschak | Random simultaneous equations and the theory of production[END_REF] report that inputs in the production function are not independently chosen. They are chosen depending on firm characteristics, which generates a simultaneity bias. According to [START_REF] Olley | The Dynamics of productivity in the telecommunications equipment industry[END_REF], it is a selection bias or "endogeneity of attrition" that matters because firms' decisions to enter or exit the market are motivated by the difference of their productivity in comparison to other firms, i.e., their competitors. Some studies focus on other sources of biases, such as the omitted price or the use of the same technology for multiproduct firms [START_REF] De Loecker | Product differentiation, multi-product firms and estimating the impact of trade liberalization on productivity[END_REF].

To account for the endogeneity in a stochastic frontier model, we follow [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] and Greene (2005a) who separate the heterogeneity of firms (fixed effects) from the inefficiency of firms.11 Indeed, as shown by [START_REF] Ackerberg | Econometric Tools for Analyzing Market Outcomes[END_REF], controlling for the fixed effects overcomes the simultaneity bias. The selection bias from a firm's decision to enter or exit the market, which is determined by the time invariant effect or by the firm's specific effects, is undertaken when controlling for the fixed effects in the estimation procedure. Estimated coefficients of these models are given in Table ( 4) in the sub-section 4.2 and a simple comparison of outcomes from each methodology is presented.

Comparison of agricultural performance: the difference-in-difference model

To compare the agricultural performance among the municipalities (municipalities with protected areas versus those without protected-areas), a difference-in-difference model in panel data is applied. The choice of this model is justified by the availability of the agricultural data for two points in time: 1996 and 2006. In addition to this, an increasing adoption of protected areas was observed from 1980 to 2010. In fact, the difference-in-difference estimator computes a double difference: one across time and another across units, treated and non treated (see the estimator below). The main advantage of using this estimator is that it solves the selection bias arising from the non-random units that receive the treatment, and drops all differences among units that are invariant across time (Khandker et al. 2010 pp. 71-78). Indeed, to obtain unbiased estimates when comparing two groups (treated and control group, meaning in our case municipalitities with protected areas and those without, respectively), it's important to ensure that municipalities that received the protected areas have been chosen randomly.

However, [START_REF] Andam | Measuring the effectiveness of protected area networks in reducing deforestation[END_REF] and [START_REF] Joppa | High and Far: Biaises in the Location of Protected Areas. Public Library of Science One[END_REF] have already demonstrated that some protected-area locations can be biased towards places that are unlikely to face the pressure of the deforestation process or the expansion of agricultural land-use. This is the case when protected areas are created in areas that are not suitable for agriculture. Considering this issue, if the selection bias is not solved, the estimated result of PAs is overestimated. The diffin-diff estimator then solves the selection bias by computing a double difference across time and across units. Specification of the model is as follows: for 𝐷 𝑖 = 1

𝐘 𝐢𝐭 =
The expected outcomes considering the different possible scenarios are as follows:

(a) if 𝐓 𝐭 = 𝟎 𝐚𝐧𝐝 𝐃 𝐢 = 𝟎, 𝐄(𝐘 𝐢𝐭 ) = 𝛂 + 𝛉𝐗 + 𝛍 (b) if 𝐓 𝐭 = 𝟎 𝐚𝐧𝐝 𝐃 𝐢 = 𝟏, 𝐄(𝐘 𝐢𝐭 ) = (𝛂 + 𝛄) + 𝛉𝐗 + 𝛍 (c) if 𝐓 𝐭 = 𝟏 𝐚𝐧𝐝 𝐃 𝐢 = 𝟎, 𝐄(𝐘 𝐢𝐭 ) = (𝛂 + 𝛃) + 𝛉𝐗 + 𝛍 (d) if 𝐓 𝐭 = 𝟏 𝐚𝐧𝐝 𝐃 𝐢 = 𝟏, 𝐄(𝐘 𝐢𝐭 ) = (𝛂 + 𝛃 + 𝛄 + 𝛅) + 𝛉𝐗 + 𝛍
where X is the average of 𝑿 𝒊𝒕 and 𝜇 is the average of 𝝁 𝒊 .

The diff-in-diff estimator 𝜹 is given by the difference across time (1996 and 2006) of municipalities that contain PAs (d) -(b) that is (𝜷 + 𝜹), subtracted to difference across time of municipalities that do not contain PAs (c) -(a) that is 𝜷:

Stochastic model results

Estimated coefficients of both of models are presented in Table (4). Statistical characteristics and the Likelihood Ratio test (LR test) are in favor of Greene's (2005a) model. However, in the literature, this model is subject to the incidental parameters problem (see [START_REF] Greene | Reconsidering Heterogeneity in Panel Data Estimators of the Stochastic Frontier Model[END_REF] and [START_REF] Chen | Consistent estimation of the fixed effects stochastic frontier model[END_REF]). 13 Thus, we retain the model of [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF]. We note that the coefficients of inputs in Table (3) of the frontier are statistically significant. The distribution of the variables of interest (TFP and potential production) is presented in Figure (2). We also note that the coefficient estimated for the inefficiency from [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] does not appear in the table because the authors' procedure is done in four steps and the inefficiency is derived in the second step. 13 The incidental parameters arise when the number of parameters to be estimated increase with units. The consistency of estimated parameters is not guaranteed even if the number of units is too large (N∞). In fact, the value of standard errors could depend on the ratio between units and their corresponding parameters to estimate. Related to the Greene (2005a) model, fixed effects parameters are increasing with the units. And because it's a stochastic frontier method, applying the first difference estimator to drop fixed effects doesn't solve the problem [START_REF] Greene | Reconsidering Heterogeneity in Panel Data Estimators of the Stochastic Frontier Model[END_REF]. For further information about the incidental problem, see [START_REF] Lancaster | The Incidental parameter problem since 1948[END_REF], [START_REF] Chen | Consistent estimation of the fixed effects stochastic frontier model[END_REF] or [START_REF] Greene | Reconsidering Heterogeneity in Panel Data Estimators of the Stochastic Frontier Model[END_REF]. As already explained above, to compute the inefficiency score, the authors predict the error term of the estimation of the first step (a panel model estimated with fixed effects) and apply a stochastic model with this error as the dependent variable. The independent variable is a vector (n1) with only number 1 as elements. The constant term is not considered in this step. For more information concerning the [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] procedure, see Kumbhakar, Wang and Horncastle (2015 pp 270-274). TFP [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] TFP and Frontier distributions: Greene (2005a) and [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] Table 5: The 5 best performance by year (Greene 2005a andKumbhakar and[START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] We can also observe in Figure (2) that the TFP and the potential production are higher with the [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] model. A large share of all municipalities (more than 25%) has a potential production score which stands between [6.5, 7.5] with Greene's (2005a) model, while it is [8.3, 9] with [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF]. Concerning the TFP, more than 25% of all municipalities stand in an interval of [5.7, 6.5] with Greene's (2005a) model, while it is [7.2, 7.8] with [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF]. 14 In Table ( 5), we present the 5 most productive municipalities using each methodology. We can observe that the most performant municipalities for the potential production as the outcome are always the same regardless of which of the two methodologies used. This is not the case when considering the total factor productivity (TFP). Indeed, although both methodologies separate the inefficiency to the fixed effects, they each specify the inefficiency in the model differently (see Greene 2005a and[START_REF] Kumbhakar | A Practitioner's Guide to Stochastic Frontier Analysis Using Stata[END_REF]Horncastle, 2015 pp 270-274)). 14 We note that the TFP in this case is not the total factor productivity change (TFP ̇), but the TFP at year t. 6), we present the agricultural performance distribution, by state. We can observe that Rondonia has the best performance regardless of the methodology used. This is in adequacy with results from [START_REF] Dias Avila | Agricultural Productivity in Latin America and the Caribbean and sources of growth[END_REF]. Indeed, the state Rondonia is located within the arc of deforestation. It can be assumed that recently cleared lands (i.e. land located in the arc of deforestation) are more fertile than older ones. Thus, with protection of various areas in this state, farmers develop incentives to perform agricultural practices which improve their yields.

Diff-in-diff model results

The diff-in-diff model is applied using the potential production, the technical efficiency and the TFP as the dependent variables. In Table (7), the first sub-table presents the results of the diff-in-diff model, with the maximum possible production as the main outcome. In this sub-table, the first column refers to all protected areas, the second column to protected areas with "integral protection" status and the third column to protected areas with "sustainable status." The estimated coefficient of the double difference, that is, the coefficient of variable treatment*time in the first column, is significant and positive. This means that, on average, the difference in 2006 to 1996 of the potential production of the agricultural firms in municipalities without protected areas is lower than that of the agricultural firms in municipalities with protected-areas. 15 Because changes in the potential production are the result of technological progress, these estimations suggest that, on average, productive practices in agriculture have more emerged in 2006 than in 1996 among the agricultural firms in municipalities with protected areas than the municipalities without protected-areas. In other words, municipalities with PAs technically progressed in agriculture, reaching a level of 0.201 higher score than the municipalities without PAs. Consequently, in this case the Porter hypothesis is confirmed.

The double difference coefficient is also significant in another column of municipalities with Sustainable protected-areas. Interpretation of results for this column is the same as for the first column. However, considering municipalities with areas under integral protection, the double difference coefficient is not significant, meaning that the Porter hypothesis is not verified in this case. The protection of various areas in the Legal Amazon does not only lead to forest and biodiversity conservation, as demonstrated by [START_REF] Andam | Measuring the effectiveness of protected area networks in reducing deforestation[END_REF] and [START_REF] Nolte | Gorvernance regime and location influence avoided deforestation succes of protected areas in the Brazilian Amazon[END_REF]. It also results in the adoption of more productive practices in agriculture. The same interpretation is done with results presented in the last sub-table, with the total factor productivity as the main outcome. We can observe that municipalities with PAs are more performant, with a total factor productivity change which stands at a level of 0.171 higher score than the municipalities without PAs.

Coefficients estimated in Table (7), in the first column of the second sub-table, show that the double difference coefficient of the efficiency is negative and not significant. This suggests that the difference in 2006 to 1996 of the efficiency in agricultural firms in municipalities with protected areas is not significantly different from those without protected areas. Although there are positive changes in productive practices among the municipalities with protected-areas, protection does not improve efficiency of municipalities across time.

There is an inertia in the inefficiency among the municipalities. More technically, as presented in Figure ( 1) above, municipalities tend to displace their potential production across time without significantly reducing the distance gap to the frontier. We note that the outcome referring in this second sub-table in Table ( 7) is the variant efficiency.

As a robustness check, an identical framework is applied using performance computed from Greene's (2005a) model. Results are globally the same related to the potential production changes (technical progress) but change for the total factor productivity, following the loss of data in the estimation procedure. These results are presented in Table ( 8) in the Appendix.

Table 7: Diff-in-diff model results using agricultural performance from [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF]

Concluding remarks

Protected areas in the Brazilian Legal Amazon have been expanding during the two last decades. They are considered as an important environmental policy instrument used to mitigate the deforestation process, biodiversity losses and climate change. Because the enforcement of PA restrictions constrains farmers, there is a sort of land scarcity that is increasing with the expansion of PAs. This scarcity inspires farmers to adopt technical practices that favor the intensification of agriculture and improve technical progress in the available or remaining unprotected land.

This study is applied in order to investigate the potential effect of protected areas in agriculture. The study belongs to the strand of empirical studies that focus on the effectiveness of conservation policies. We employ two-step econometric approach, the first step referring to the stochastic frontier analysis and the second to the difference-in-difference model. The empirical results show that protected areas drive farmers to practice more intense agriculture by adopting technical practices or new technologies than farmers whose land is not under protection. Because farmers want to maintain their benefits considering constraints or restrictions from protection, they are prone to develop innovative practices that help achieve both environmental and maximum agricultural production. According to the empirical strategy applied in the study, technical progress has been increasingly growing in municipalities that receive protected-area designation. Based on this result, we can verify the Porter hypothesis.

For policy-maker, these findings could be interesting and very useful. Indeed, to avoid an inverse effect of protected areas on agriculture, the government must support its environmental policy by offering technical assistance to producers in the short term. Helping them to adopt more efficient practices, machinery and new technology will increase their incentives to develop more of the same types of practices. Consequently, farmers will reach their agricultural goals and policy-makers will be satisfied with the long-term policy outcomes, achieving a win-win policy. This article does not analyze whether these changes in agricultural practices have an effect on poverty or inequality in the area of the study. The paper does not analyze whether the productive practices cause side effects such as land degradation or land pollution. Further research could consider these points.

Appendix

  )𝑥j is the allocative component, TC is the technological change and ∆TE is the technical inefficiency change

Figure 2 :

 2 Figure 2: TFP and potential production distributions

  As example: TFP 2006 = (RTS -1) ∑ ε j RTS (𝑥 𝑗,2006 ) + j f(x it , β) 2006 -( u i2006 ). Then, because the gap between 2006 and 1996 is considered as one period in the study (𝑡 2006 -𝑡 1996 = 1), the double difference presented below will deliver the TFP change as presented in Equation (5).

Table 1 :

 1 Comparison of municipalities over time IBGE and authors. (*), (**), (***) are at the 10%, 5%, and 1% significance levels.

		Mean		Mean-comparison tests
		Municipalities 1996		(Municipalities 2006 vs
	Main agricultural variables	Municipalities 2006	municipalities 1996)
	Land use in agriculture (ha)	127 944.5	125 699.5	-2 245.065
	Capital	137.0481	167.3659	30.31783***
	Total workers in agriculture	4 149.467	3 533.781	-615.6853***
	Production in value
	(1996 agricultural prices, 1000 R$)	5 758.243	8 564.237	2 805.994***
	Protected areas (ha)	35 149.01	88 179.88	53 030.87***
	Number of municipalities	645	645
	Source:

Table 2 :

 2 Protected-area versus non-protected-area municipality characteristics IBGE and authors. (*), (**), (***) are at the 10%, 5%, and 1% significance levels.

		Mean
			Municipalities	Mean-comparison tests
		Municipalities with	without	(Municipalities with PA vs
	Main agricultural variables	P.A.	P.A.	municipalities without PA)
	1996 Land use in agriculture (ha)	162 076.4	126 733	35 343.39*
	1996 Capital	127.8571	137.1252	-9.268055
	1996 Total workers in agriculture	5 435.518	4 131.469	1 304.049*
	1996 Production in value (1000 R$)	7 480.213	5 679.77	1 800.444*
	Number of municipalities	56	631
	2006 Land use in agriculture (ha)	216 549.1	119 413.9	97 135.24***
	2006 Capital	326.2143	150.1763	176.038***
	2006 Total workers in agriculture	4 665.277	3 407.293	1 257.984***
	2006 Production in value in (1000 R$)
	(1996 agricultural prices)	15 077.37	8 034.427	7 042.941***
	Number of municipalities	112	573
	Source:

  censuses. In other words, we create a dummy variable treatment that takes the value one in 1996 if a protected area was created in a municipality during the period of 1985 to 1995 and it takes the value one in 2006 if a protected area was created in a municipality during the period 1996 to 2006. This means that, considering the punctual time period of 1996 and 2006 for which agricultural data are available, the dummy variable treatment (protected-areas) takes the value one for each period if the protected areas were established between 1985 and 2006. A municipality is considered as a treated municipality if it contains a protected area. In 1996, we count 51 municipalities with PAs and 635 without PAs. In 2006, we count 95 municipalities with PAs and 589 without PAs. There are 44 municipalities that received PA designation during the period of 1996 to 2006. The study is conducted considering only the Integral and the Sustainable PAs.

  approach, as shown below: 𝒚 𝒊𝒕 = 𝒂 𝟎 + 𝒇(𝒙 𝒊𝒕 ; 𝜷, 𝒕) -𝒖 𝒊𝒕 + 𝜺 𝒊𝒕 (1) 𝒖 𝒊𝒕 = 𝒖 𝒊 + 𝝉 𝒊𝒕 𝝉 𝒊𝒕 ~ 𝒊. 𝒊. 𝒅. 𝑵 + (𝟎, 𝝈 𝝉 𝟐 ) where 𝒚 𝒊𝒕 is the output (production value in log), 𝒙 𝒊𝒕 is the vector of inputs variables (capital, workers and landuse in log), 𝒖 𝒊𝒕 is the technical inefficiency, 𝒂 𝟎 is the constant term, 𝜷 is a vector of coefficients attached to each input and 𝜺 𝒊𝒕 is the error component. The 𝒖 𝒊𝒕 term is broken down into two variables: the 𝒖 𝒊 component, representing the persistent inefficiency over time, and the 𝝉 𝒊𝒕 component, representing the residual or time-varying portion of the technical inefficiency. 8 The functional form 𝒇(. ) is a Cobb-Dougglas function without any restriction on parameters, i denotes the municipality and t is the time period. The reasoning around the stochastic frontier analysis can be summarized in Figure (1) as follows:

2*[LL(H 0 ) -LL(H 1 )], where LL(H 0 )

  stochastic model, although the LR test is in favor ofGreene's (2005a) model. The LR test statistic is given by the formula: -

  𝛂 + 𝛃𝐓 𝐭 + 𝛄𝐃 𝐢 + 𝛅𝐓 𝐭 * 𝐃 𝐢 + 𝛉𝐗 𝐢𝐭 + 𝛍 𝐢 + 𝛆 𝐢 Where 𝒀 𝒊𝒕 is the outcome, 𝑻 𝒕 is a dummy variable that equals 1 for the year 2006 and 0 for 1996 (time), 𝑫 𝒊 is a dummy variable that equals 1 if PA is found in a municipality and 0 if not (treatment), 𝑻 𝒕 * 𝑫 𝒊 is a multiplicative interaction variable of time-dummy variable 𝑻 𝒕 and treatment-dummy variable 𝑫 𝒊 , 𝑿 𝒊𝒕 is vector of control variables that explains the outcomes, 𝝁 𝒊 is vector of individual effects that measures heterogeneity among municipalities, 𝜺 𝒊 is vector of error terms, 𝛂 is a constant term, 𝛃 is the difference among municipalities with PAs and those without the PAs, 𝒊 is the municipality and t represents the years 1996 and 2006. 𝐘 𝐢𝐭 = 𝛂 + 𝛄𝐃 𝐢 + 𝛉𝐗 𝐢𝐭 + 𝛍 𝐢 + 𝛆 𝐢 for 𝑇 𝑡 = 0 (1996) (1)  𝐘 𝐢𝐭 = (𝛂 + 𝛃) + (𝛄 + 𝛅)𝐃 𝐢 + 𝛉𝐗 𝐢𝐭 + 𝛍 𝐢 + 𝛆 𝐢 for 𝑇 𝑡 = 1 (2006) (1)  𝐘 𝐢𝐭 = 𝛂 + 𝛃𝐓 𝐭 + 𝛉𝐗 𝐢𝐭 + 𝛍 𝐢 + 𝛆 𝐢 for 𝐷 𝑖 = 0 (1)  𝐘 𝐢𝐭 = (𝛂 + 𝛄) + (𝛃 + 𝛅)𝐓 𝐭 + 𝛉𝐗 𝐢𝐭 + 𝛍 𝐢 + 𝛆 𝐢

		(1)
	𝒊 = 𝟏, 𝟐, … . . , 𝒏	𝒕 = 𝟏𝟗𝟗𝟔, 𝟐𝟎𝟎𝟔

12

In Equation (1) the largest coefficient is 𝜹. We have:

(1) 

Table 3 :

 3 Descriptive statistics

	Variable	Variables definition in log	Mean	Std. Dev.	Min	Max	Observations
	lnproduction value	Production value in log (r$)	8.24	1.22	3.61	12.15	1246
		Capital = trucks + tractors +
	lncapital	planting and harvest machinery +	4.24	1.52	0	8.86	1130
		others tools
	lntotalworkers	Workers in agriculture	7.90	1.01	4.54	10.65	1246
	lnagricultural_landuse	Land use in agriculture (ha)	11.23	1.29	4.54	14.27	1245
	lntechnical_assistnb	Number of establishments technically assisted	5.25	1.85	0	9.17	1239
	lnelectricenergy_nbesth	Number of establishments using electrical energy	4.79	1.48	0	7.92	1236
	lntmp_mun	Temperature	3.28	0.03	3.15	3.33	1370
	lnpre_mun	Precipitations	5.10	0.26	4.56	5.74	1370
	lnprod_value_maize	Production value of maize (r$)	854.54
	PP_Kumbhakar&Heshmati	Potential production Kumbhakar and Heshmati (1995)	8.37	0.74	5.84	10.48	1128
	PP_Greene	Potential production Greene (2005a)	6.82	0.74	4.29	8.93	1128
	EFF_Kumbhakar&Heshmati	Efficiency Kumbhakar and Heshmati (1995)	0.85	0.04	0.59	0.95	1126
	EFF_Greene	Efficiency Greene (2005a)	0.82	0.23	0.06	1	908
	TFP_Kumbhakar&Heshmati	Total Factor Productivity Kumbhakar and Heshmati (1995)	7.30	0.62	5.17	9.13	1126
	TFP_Greene	Total Factor Productivity Greene (2005a)	5.62	0.74	2.37	7.48	908
	Source: IBGE and authors, PP = Potential Production, TFP = Total Factor Productivity, EFF = Technical Efficiency

Table 4 :

 4 Results of both stochastic frontier models

	Greene (2005a)	Kumbhakar and
		Hesmati (1995)

Greene (2005a): Potential production Kumbhakar and Heshmati (1995): Potential production

				Potential				Potential
	States	Municipality	Year	production States	Municipality	Year	production
	Para	São Félix do Xingu	2006	7.488978	Para	São Félix do Xingu	2006	8.979321
		Source: IBGE and authors

Table 6 :

 6 Agricultural firm performance by Legal Amazon states (mean of municipalities)

	states	PP_Kumbhakar & Heshmati	PP_Greene	EFF_Kumbhakar& Heshmati	EFF_Greene	TFP_Kumbhakar & Heshmati	TFP_Greene
	Acre	8.63323	7.084455	0.85933536	0.8530231	7.542431	5.94861
	Amazonia	8.166467	6.617726	0.85364564	0.7743883	7.124348	5.412025
	Amapa	7.219032	5.670324	0.85866962	0.806478	6.299547	4.728326
	Maranhao	8.332004	6.783272	0.85730487	0.8097876	7.291228	5.639527
	Matogrosso	8.708728	7.159956	0.85686028	0.8187959	7.526134	5.82642
	Para	8.487508	6.938754	0.85755436	0.8317719	7.39478	5.703878
	Rondonia	8.964354	7.415583	0.86140679	0.8800988	7.836081	6.185599
	Roraima	8.235424	6.686663	0.86018789	0.8384194	7.19927	5.565641
	Tocantin	7.953084	6.404351	0.856903	0.8238208	6.976449	5.248936
	Source: IBGE and authors
	In Table (

Table 8 :

 8 Diff-in-diff model results using agricultural performance fromGreene's (2005a) methodology Export products in Brazil's Legal Amazon (% of total production)

		PP	PP	PP	EFF	Eff	EFF	TFP	TFP	TFP
		Integral+sus	Integral_P	Sustainable_P	Integral+sus	Integral_P	Sustainable_P	Integral+sus	Integral_P	Sustainable_P
	time	-0.643***	-0.588***	-0.651***	-0.319***	-0.328***	-0.307***	-1.017***	-0.995***	-1.001***
		(0.0955)	(0.0866)	(0.0975)	(0.110)	(0.100)	(0.112)	(0.189)	(0.194)	(0.191)
	treatment	-0.0168			0.00305			-0.0241
		(0.0774)			(0.0759)			(0.141)
	Treatment*time	0.201**			-0.0288			0.0991
		(0.0804)			(0.0773)			(0.143)
	Treatment_ip		-0.0360			-0.0889			-0.242
			(0.123)			(0.112)			(0.269)
	Treatment_ip*time		0.205			0.0836			0.333
			(0.144)			(0.115)			(0.270)
	Treatment_usosus			0.00567			0.0268			0.0589
				(0.0839)			(0.0779)			(0.133)
	treatment_usosus*time			0.192**			-0.0798			-0.0193
				(0.0860)			(0.0820)			(0.139)
	lntechassist_nb	0.0577***	0.0541***	0.0567***	0.00945	0.00992	0.00933	0.0705**	0.0691**	0.0701**
		(0.0159)	(0.0156)	(0.0160)	(0.0177)	(0.0166)	(0.0182)	(0.0312)	(0.0330)	(0.0318)
	lnelectricenergy_nb	0.139***	0.134***	0.138***	0.0445*	0.0467**	0.0432*	0.194***	0.195***	0.191***
		(0.0237)	(0.0223)	(0.0238)	(0.0241)	(0.0236)	(0.0233)	(0.0451)	(0.0425)	(0.0422)
	lntmp_mun	9.989***	8.948***	10.97***	16.05***	15.99***	15.72***	31.36***	30.52***	31.44***
		(3.282)	(3.073)	(3.176)	(3.613)	(3.533)	(3.668)	(5.969)	(6.486)	(6.098)
	lnpre_mun	0.129	0.117	0.119	0.196	0.192	0.194	0.424	0.403	0.414
		(0.205)	(0.225)	(0.220)	(0.226)	(0.214)	(0.217)	(0.399)	(0.394)	(0.411)
	lnprod_value_maize	0.0517***	0.0529***	0.0529***	-0.00745	-0.00759	-0.00718	0.0451	0.0460	0.0461
		(0.0150)	(0.0148)	(0.0150)	(0.0166)	(0.0155)	(0.0158)	(0.0304)	(0.0291)	(0.0298)
	_cons	-27.59**	-24.10**	-30.76***	-53.00***	-52.76***	-51.89***	-100.7***	-97.79***	-100.9***
		(10.94)	(10.21)	(10.62)	(12.13)	(11.90)	(12.37)	(20.16)	(21.86)

Source: IBGE and authors

Table 9 :

 9 Missing data for the main export products

	Share (%) in total production of main export products in Legal Amazon
			(R$, in 2000)
	.1
	.05
	0
		Oranges	Soybeans
		Bananas	coffee
		sugar cane	maize
		Oranges	Bananas	Soybeans Coffee	Sugar	Maize
						cane
	Number of missing data	661	306	1086	1085	777	162
	(number of municipalities in
	1996 and 2006)
	Number of available data	711	1066	286	287	595	1210
	(number of municipalities in
	1996 and 2006)
	Source: IBGE and authors

The total area under integral protection (under sustainable protection) in Brazil in 1996 was approximately 5 millions hectares (respectively 19 millions hectares) while in 2006, it was approximately 22 millions hectares (respectively 47 millions hectares). Approximately 16 millions hectares were converted into Integral PAs and 28 millions hectares into Sustainable PAs between 1996 and 2006. Corresponding data was taken from Instituto Brasileiro de Meio Ambiente (2010) (IBAMA).

[START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] use a four-step approach to estimate persistent inefficiency and timevarying inefficiency, while Greene (2005a) performs a one-step approach. The inefficiency term follows a half-normal distribution in the Greene (2005a) model estimated.

Application of a diff-in-diff model as presented above requires two time periods: before and after. The time period before is from 1985 to 1995, and the time period after is from 1996 to 2006. The set of municipalities considered to have received protection in 1995 are those that received protected-areas during 1985 and 1995, both dates included. The set of municipalities considered to have received protection in 2006 are those that received protected-areas during 1996 to 2006, both dates included.

⟦𝐘 𝐢𝟐𝟎𝟎𝟔 -𝐘 𝐢𝟏𝟗𝟗𝟔 ⟧ 𝐩𝐫𝐨𝐭𝐞𝐜𝐭𝐞𝐝 > ⟦𝐘 𝐢𝟐𝟎𝟎𝟔 -𝐘 𝐢𝟏𝟗𝟗𝟔 ⟧ 𝐧𝐨𝐧-𝐩𝐫𝐨𝐭𝐞𝐜𝐭𝐞𝐝

𝛅 = ⟦𝐘 𝐢𝟐𝟎𝟎𝟔 -𝐘 𝐢𝟏𝟗𝟗𝟔 ⟧ 𝐩𝐫𝐨𝐭𝐞𝐜𝐭𝐞𝐝 -⟦𝐘 𝐢𝟐𝟎𝟎𝟔 -𝐘 𝐢𝟏𝟗𝟗𝟔 ⟧ 𝐧𝐨𝐧-𝐩𝐫𝐨𝐭𝐞𝐜𝐭𝐞𝐝

The same double difference can be obtained as follows:

In this latter form, the first difference is among municipalities without PAs and those with PAs in 2006 (d) -(c) given by (𝜸 + 𝜹). The second difference is among municiaplities without PAs and those with PAs in 1996 (b) -(a) given by 𝜸. The double difference across municipalities and across time is then given by 𝜹 , which is the difference between both the first and second differences. For this study, we use the first specification of the double difference.

Because some selective activities could partly explain the change in TFP or potential production, regardless of the presence of protected-areas, we introduce an exported agricultural product for which data are available to control for that issue. We choose maize as the control variable as it is among the main export products in Brazil and the data are more available by municipality in the Legal Amazon than for other export products (orange, soy, sugar cane, coffee, bananas), as we see in Figure (3) and Table (9) in Appendix.

Econometric results

Descriptive statistics

Descriptive statistics are presented in Table (3) below. As we can observe, the average of the potential production stands approximately at the value 8.37 for [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] model and 6.82 for Greene's (2005a) model. The largest and smallest values of the potential production are 10.48 and 5.84, respectively, for the former while they are 8.93 and 4.29, respectively, for the latter. Concerning the technical efficiency, the average is almost the same: (0.85) for the former and (0.82) for the latter. However, Greene's (2005a) methodology induces an important loss of data. There is a difference of means of the total factor productivity and the potential production. Indeed, the constant term is considered in [START_REF] Kumbhakar | Efficiency Measurement in Swedish Dairy Farms: An application of Rotating Panel Data, 1976-88[END_REF] estimated model and not in Greene's (2005a). The econometric results are presented in Table (4). Table (5) andTable (6) display information concerning the most performant municipalities and the average performance of the Legal Amazon municipalities, by state. Results and comments are presented in next section.