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\begin{document}

\title[Article Title]{Gravity with agricultural data: Estimating the impacts of deep trade agreements}

\author[1]{\fnm{Xin} \sur{Lin}}

\author[2]{\fnm{Donglin} \sur{Li}}

\author[3]{\fnm{Huimin} \sur{Xie}}

\author[4]{\fnm{Wei} \sur{Jia}}

\affil[1]{\orgdiv{Institute of Agricultural Economics and Information}, \orgname{Anhui Academy of Agricultural Sciences}, \orgaddress{\street{No.40 Nongke South Road, Luyang District}, \city{Hefei}, \postcode{230041}, \state{Anhui}, \country{China}}}

\affil[2]{\orgdiv{Institute of Industrial Economics}, \orgname{Chinese Academy of Social Sciences}, \orgaddress{\street{No.1 Dongchang Hutong, Dongcheng District}, \city{Beijing}, \postcode{100006}, \country{China}}}

\affil[3]{\orgdiv{Institute of World Economics and Politics}, \orgname{Chinese Academy of Social Sciences}, \orgaddress{\street{No.5 Jianguomennei Street, Dongcheng District}, \city{Beijing}, \postcode{100732}, \country{China}}}

\affil[4]{\orgdiv{Institute of Agricultural Economics and Development}, \orgname{Chinese Academy of Agricultural Sciences}, \orgaddress{\street{No.12 Zhongguancun South Street, Haidian District}, \city{Beijing}, \postcode{100081}, \country{China}}}


\abstract{Modern Preferential Trade Agreements (PTAs) extend beyond simple tariff reductions, incorporating a range of provisions that emphasize deeper commitments related to non-tariff barriers and behind-the-border policies. This complexity complicates the assessment of their impacts on agricultural trade. By integrating data from the Deep Trade Agreements (DTAs) database and the UN Comtrade database, our study investigates the effects of deepening agricultural provisions in DTAs on agricultural trade. The analysis utilizes an extended three-way structural gravity model with a panel dataset covering 225 countries. Compared to ``shallow'' PTAs, DTAs with detailed provisions significantly boost agricultural trade, with the average effect varying according to the income levels of partner countries and aggregated product levels. However, the capacity of DTAs to promote trade is not fully leveraged in the post-pandemic period due to heightened market uncertainty. The findings highlight the roles of behind-the-border provisions in agricultural trade integration.}

\keywords{Deep trade agreements, Preferential trade agreements, Agricultural trade, Structural gravity model}

\pacs[JEL Classification]{F13, F14, Q17, C23}

\maketitle

\section{Introduction}\label{sec1}

As global value chains evolve and production networks develop, trade barriers significantly hinder international specialization \citep{Pahl2020}. Consequently, PTAs become essential, serving as crucial mechanisms for establishing trade regulations\footnote{We use the term PTAs to broadly refer to trade agreements between two or more countries, encompassing free trade agreements, customs unions, common markets, economic unions, and regional trade agreements.}. A growing number of PTAs, especially those with comprehensive commitments known as DTAs, are built on a multilateral framework and extend beyond basic economic cooperation. They encompass a broader range of provisions and integrative measures, thereby strengthening trade connectivity. Compared to the manufacturing industry, which has experienced many rounds of liberalization, the agriculture sector is often viewed as sensitive in terms of trade policy disciplines \citep{Fulponi2015}. While the GATT/WTO has not made substantial strides in agriculture, PTAs have provided countries with opportunities to liberalize and boost agricultural trade among members. Furthermore, the expansion of the PTA's scope appears to support the agricultural sector by applying broader provisions to relevant issues \citep{Thompson2019}. In the agricultural sector, trade commitments have undergone substantial evolution. Analyzing these changes is essential to assess the impact of DTAs as they progress towards trade liberalization in this sector. Moreover, it's important to ascetain whether DTAs are becoming more effective at eliminating distortions in the global agricultural market. Such evaluations are key to fully understanding the evolution of agricultural trade and pinpointing potential future policy directions. \\
Since \cite{Viner1950book} pioneering exploration into the impact of PTAs on international trade, the economic literature has extensively examined this topic (\citealp{Fugazza2013}; \citealp{Baier2019}; \citealp{Adams2024}). While Vinerian analyses mainly focus on tariff liberalization, specifically regarding trade creation versus trade diversion. The emergence of more overlapping and deeper PTAs introduces new challenges, goning beyond simple tariff reductions to cover a wider array of policy areas such as services, intellectual property, and environmental concerns \citep{Hofmann2017}. The depth of a DTA is typically gauged by the number and scope of policy areas it covers, along with the degree of commitment and enforcement mechanisms it contains (see Figure \textcolor{blue}{\ref{fig1}}). The number of trade agreements has risen sharply from the early 1990s, exhibiting a trend towards covering more policy areas, suggesting a deepening of these agreements. Such a shift highlights the evolving dynamics of trade agreements from the simpler, tariff-focused models of the past. Prevailing research investigating the impact of PTAs often presupposes that these agreements represent homogeneous policies. This assumption is manifested in the methodological approach of many empirical studies, which categorize the existence of a PTA merely through the binary variable as ``1'' for presence and ``0'' for absence (\citealp{Magee2008}; \citealp{Egger2015}; \citealp{Egger2022}). However, the binary simplification may obscure the nuanced effects and variations among different PTAs, potentially glossing over their unique characteristics and impacts on international trade dynamics. \cite{DíazMora2024} also confirm that the average effect of trade agreements, based on the homogeneity assumption, is not applicable to specific practices, and that DTAs exhibit significant differences. \\

\begin{figure}[H] 
    \centering 
    \includegraphics[width=0.9\textwidth]{figure1.eps} 
    \caption{Number and depth of DTAs notified and in force over time \\
    Source: Authors' caculations based on the Content of Deep Trade Agreements database. \\
    Note: Our approach to categorizing the depth of trade provisions is inspired by \cite{Hofmann2017}. And we focus on quantifying the provisions that are either mentioned or are legally enforceable (i.e. ``WTO+AC'', ``WTO+LE'', ``WTO-X AC'', ``WTO-X LE''). In the classification, trade agreements are categorized based on the number of covered policy areas: those with fewer than 10 policy areas are labeled as ``less than 10''; those with 10 to 20 policy areas are labeled as ``Between 10 and 20''; and those with more than 20 policy areas are labeled as ``More than 20''.} 
    \label{fig1} 
\end{figure} 

This paper mainly contributes to two strands of literature. First, the paper is connected to the literature on the role of DTAs. Quantitative analysis of deep provisions has been initiated by \cite{Horn2010}, who have examined the specific content of PTAs involving the European Community and the United States. They categorize the areas covered by these agreements into ``WTO Plus (WTO+)'' and ``WTO Extra (WTO-X)''. The depth of DTA integration generally shows in the expansion of provisions from border policies to behind-the-border policies \citep{Osnago2019}. A body of research has reassessed the trade effects of DTAs, revealing positive outcomes (\citealp{Laget2020}; \citealp{Borchert2021}; \citealp{Mattoo2022}; \citealp{Wang2023}). However, most empirical studies substantially overlook the agriculture and food sectors, with only limited research emphasizing the use of machine learning algorithms to identify DTAs affecting the agricultural trade (\citealp{Kim2023}; \citealp{Gordeev2024}). The distinction between our paper and the other two is in our examination of how the vertical depth in DTAs impacts agricultural trade, rather than concentrating on the horizontal depth. This vertical analysis provides a clearer understanding of the commitments' depth and breadth in the specific chapters or disciplines of DTAs \citep{WB2023}. Given the limitations of focusing solely on the policy area (horizontal analysis) in the quantitative assessment of trade agreements, we explore more details by examining clauses related to agriculture from specific chapters and their corresponding sub-provisions. This approach allows us to more directly identify the impact of DTA depth on agricultural trade. \\
Second, it adds to the literature on global agricultural integration in the context of PTA development. The agricultural gravity research has been devoted to analyzing the relationship between PTAs and agricultural trade, particularly in areas such as trade creation and diversion (\citealp{Sun2010}; \citealp{Grant2016}), extensive and intensive margins \citep{Scoppola2018}, economic sanctions \citep{Larch2021} and network perspective (\citealp{Torreggiani2018}; \citealp{Jafari2023}). \cite{Jean2016} evaluate the effects of PTAs, considering cross-product heterogeneity, but they assume the impacts of non-tariff provisions are homogeneous. Since non-tariff provisions in PTAs are not sector-specific, evaluating them at the policy area level may dilute their actual effect on agricultural trade. In contrast, our paper complements this literature by isolating specific agricultural clauses to examine the influence of PTAs on agricultural trade, while accounting for the heterogeneity of agreement provisions. \\
From a methodological perspective, we extend the gravity model commonly used in studies to evaluate the impact of DTAs on agricultural trade flows. Our empirical analysis utilizes two datasets: the Deep Trade Agreements database 2.0 (Vertical Depth) and the UN Comtrade database. In the empirical model, we introduce three types of fixed effects: exporter-time fixed effects and importer-time fixed effects to account for the inward and outward multilateral resistance terms, country-pair fixed effects to control for the time-invariant bilateral trade costs and to mitigate endogeneity in policy variables. During the analysis period (2003-2022), our fingdings show that the deepening of agricultural provisions in trade agreements significantly promotes bilateral agricultural trade flows. The positive impact remains consistent even when accounting for dynamic effects, asymmetric bilateral trade costs, lag effects of agreement, and internal trade (domestic sales) within member countries. Additionally, we conduct further analysis from three perspectives: types of trade agreements, product clustering, and uncertainty shocks. The results indicate that agricultural provisions play a crucial role in South-South PTAs, high value-added products, and the pre-pandemic period. \\
The rest of the paper is organized as follows. Section \ref{sec2} provides the empirical strategy and describes the data used in the analysis. Section \ref{sec3} shows the econometric results. Conclusions are presented in Section \ref{sec4}. 

\section{Empirical strategy and data description}\label{sec2}

\subsection{Empirical strategy}\label{subsec2.1}
In this section, we introduce the empirical methodology to analyze the influence of DTAs on agricultural trade. Gravity models have been widely used to assess the impact of PTAs on trade flows (\citealp{Bergstrand2015}; \citealp{Weidner2021}; \citealp{Jadhav2024}). The empirical analysis builds on the latest advancements in theoretical and empirical gravity literature, with its main features are sketched out below. The typical form of structural gravity equation can be described by 
\begin{equation}\label{eq1}
X_{ij,t} = \pi_{ij,t}Y_{j,t} = \frac{\chi_{ij,t} N_{i,t} (w_{i,t} \tau_{ij,t})^{-\epsilon}}
                {\sum_{m=1}^{M} \chi_{mj,t} N_{m,t} (w_{m,t} \tau_{mj,t})^{-\epsilon}}Y_{j,t}
\end{equation} 
Where $X_{ij,t}$ represents trade flow from exporter $i$ to importer $j$ in the year $t$. $\pi_{ij,t}$ signifies the portion of country $j$'s expenditure on imports from country $i$, which is primarily influenced by production technology $N_{i,t}$, wage levels $w_{i,t}$, and the trade cost $\tau_{ij,t}$ between the two countries. The trade elasticity $\epsilon = \frac{\partial \ln(X_{ij,t} / X_{jj,t})}{\partial \ln(\tau_{ij,t})}$, which reflects the comparative advantage. $\chi_{ij,t}$ captures all structural parameters except $\tau_{ij,t}$. After converting to logarithmic form, the Equation (\ref{eq1}) is described as follows.
\begin{equation}\label{eq2}
ln X_{ij,t} = \ln \chi_{ij,t}N_{i,t}w_{i,t}^{-\epsilon} + \ln\frac{Y_{j,t}}{\sum_{m=1}^M\chi_{mj,t}N_{m,t}w_{m,t}^{-\epsilon}\tau_{mj,t}^{-\epsilon}}+\ln \tau_{ij,t}^{-\epsilon}+\xi_{ij,t}
\end{equation} 
$\ln \chi_{ij,t}N_{i,t}w_{i,t}^{-\epsilon}$ and $\ln\frac{Y_{j,t}}{\sum_{m=1}^M\chi_{mj,t}N_{m,t}w_{m,t}^{-\epsilon}\tau_{mj,t}^{-\epsilon}}$ denote the factors that change over time and influence the bilateral trade flow in countries $i$ and $j$, respectively. $\ln \tau_{ij,t}^{-\epsilon}$ signifies the overall resistance to trade, encompassing both dynamic (such as tariffs and non-tariff barriers) and static factors (such as geography). Given that deep clauses in PTAs have the potential to reduce trade obstacles, we expand the term $\ln \tau_{ij,t}^{-\epsilon}$ by including the depth of PTA between countries $i$ and $j$: 
\begin{equation}\label{eq3}
\ln \tau_{ij,t} = \rho F_{ij}+\alpha_1 Depth_{ij,t}+\alpha_2 PTA_{ij,t}+\sigma_{ij,t}
\end{equation}
Where $F_{ij}$ is the time-invariant general trade cost item \citep{Yang2024}. $Depth_{ij,t}$ denotes the measure of the PTA depth \citep{Hofmann2017}, which is defined in section \ref{subsec2.2} below. $PTA_{ij,t}$ is a binary variable that assumes the value of 1 in cases where a PTA exists between countries $i$ and $j$ at the year $t$ \citep{Limão2016}. Following \cite{Laget2020}, we assess the impact of deep PTAs on the agricultural trade by extending the gravity model. This involves substituting Equation (\ref{eq3}) into Equation (\ref{eq2}):
\begin{equation}\label{eq4}
ln X_{ij,t} = \alpha_1 Depth_{ij,t} + \alpha_2 PTA_{ij,t} + \theta_{i,t} + \Omega_{j,t} + \mu_{ij} + \upsilon_{ij,t}
\end{equation}
We proceed in steps, starting with the traditional OLS specification, and then, incorporating contributions from the literature, each phase introduces a new feature to our specification. In order to address the issue of heteroskedasticity and take into account the presence of zero trade values, we apply the methods of \cite{Santos2006, Santos2011} with PPML estimation. Furthermore, \cite{Santos2006} illustrate that biases are inherent in the logarithmic estimation of these models, and recommend that gravity equations be calculated using a multiplicative approach. After the final adjustment, our preferred empirical model estimates the impact of DTAs on agricultural trade to be:
\begin{equation}\label{eq5}
X_{ij,t} = exp\{\alpha_1 Depth_{ij,t} + \alpha_2 PTA_{ij,t} + \theta_{i,t} + \Omega_{j,t} + \mu_{ij}\} + \delta_{ij,t}
\end{equation}
$X_{ij,t}$ is the international trade flows from source $i$ to destination $j$ at time $t$\footnote{In the robustness checks, $X_{ij,t}$ also includes internal trade flows, as discussed in Section \ref{subsec3.3}.}. $\theta_{i,t}$ and $\Omega_{j,t}$ denote the groups of dynamic dummy variables linked to the source-country and destination-country. The directional fixed effects are designed to adjust for invisible multilateral resistances and any other time-varying characteristics associated with $i$ and $j$ that might affect trade between two countries, including GDP, real exchange rate fluctuations, tariff barriers, and other economic policies (\citealp{Anderson2003}; \citealp{Olivero2012}). $\mu_{ij}$ denotes the set of country-pair ﬁxed eﬀects, which provide the ﬂexible and comprehensive measure of the eﬀects of all time-invariant bilateral trade costs, such as geographical distance and cultural distance. Moreover, it can be used to account for endogeneity of policy variables by capturing all unobservable effects of country-specific characteristics, like contiguity, colonial ties, and common spoken language \citep{Baier2007}. $\delta_{ij,t}$ denotes the clustered standard error calculated at the country-pair \citep{Egger2015}. Following \cite{Egger2022}, we derive main results from consecutive-year data and experiment with interval data in the robustness analysis.

\subsection{Data Description}\label{subsec2.2}
The method presented above requires panel data on the depth of DTAs and bilateral trade at the country level. Information on the depth of DTAs is derived from World Bank Deep Trade Agreements database 2.0 -Vertical Depth\footnote{The Deep Trade Agreements database is freely accessible at the \href{https://datacatalog.worldbank.org/search/dataset/0065624/Content-Of-Deep-Trade-Agreements--Version-2-}{\textcolor{blue}{website}}.}. This vertical analysis of DTAs encompasses specific chapters or disciplines, spanning 18 policy areas. Each area includes various sub-clauses, which are further divided into detailed provisions. In this paper, we specifically focus on provisions that impact agriculture, excluding those that do not significantly pertain to this sector. To quantitatively assess the agricultural integration within DTAs and capture the heterogeneity of provisions, we use the count of 72 provisions as a metric to gauge the depth. These provisions are distributed across six policy areas. The details for agriculture-related provisions outlined in Table \textcolor{blue} {\ref{tabA1}}.These categories are developed to generate quantitative indicators based on binary yes/no questions and counts. \\
The data on agricultural trade flows primarily originates from the UN Comtrade database, which provides global bilateral product-level trade data using 6-digit HS codes. We classify chapters 1-24 in the HS96 version as agricultural products.\\
The data clean proceeds in three stages. First, We focus exclusively on DTAs that involve ``goods'' and ``goods and services'', excluding those limited to services, as noted by \cite{Jafari2023}. We identify provisions within DTAs that contain the term ``agriculture'' or related keywords, assigning each provision a value of 0 or 1, where 1 indicates the presence of the provision in the agreement. The $Depth$ variable is defined as the logarithm of the total number of deep provisions related to agriculture. Additionally, when converting multilateral trade agreements into bilateral ones between pairs of countries, there are cases where two countries are simultaneously involved in multiple trade agreements. In such instances, we use the union of the deep provisions from all these agreements to reflect the trade depth between the two countries. Second, We exclude observations from the trade flow dataset that lack corresponding information on DTAs. Third, we merge the two datasets using a unique identifier based on exporter-by-importer-by-year. The sample includes 225 countries, covering all major economies over the period from 2003 to 2022. 

\section{Results}\label{sec3}
\subsection{Baseline results}\label{subsec3.1}
This subsection discusses the results from estimating the gravity model outlined in Section \ref{subsec2.1}. Table \textcolor{blue} {\ref{tab1}} presents the OLS estimation results for the Equation (\ref{eq4}) and the PPML estimation results for Equation (\ref{eq5}) separately. Several findings stand out. First, all coefficients of depth are positive and significant, indicating that deep agricultural provisions has a positive impact on trade between countries. The PPML estimate implies that the depth of the agricultural provisions boosts agricultural trade flow by 3.75 percent\footnote{The following formula provides the percentage in agricultural trade flows: \( (e^{\alpha_{\textit{depth}}} - 1) \times 100 \)}. Second, the estimates in columns (2) and (4) are similar to the corresponding values in columns (1) and (3), which do not include the PTA covariate. This distinction allows us to identify country pairs with PTAs at some point in time and those that have never had PTAs, where the depth is zero (\citealp{Mattoo2022}). In addition, it indicates that the omission of the PTA covariate does not introduce bias into our model's estimates. As outlined in Table \textcolor{blue} {\ref{tabA1}} within Appendix {\ref{secA}}, deep trade provisions typically encompass a broader range of issues, including intellectual property protection, environmental laws, export subsidies in the agricultural sector, and sanitary and phytosanitary measures (SPS), among others. These provisions not only enhance productivity and efficiency but also facilitate market access for agricultural products, thereby increasing trade volumes. In contrast, the effects of shallow agreements are relatively limited. Some PTAs may offer preferences only for specific product categories and fail to cover all agricultural products, which partially explains their insignificant overall impact on agricultural trade flows. Additionally, the effectiveness of PTAs implementation may vary depending on the enforcement and regulatory capacities of member countries, further limiting their positive impact on trade. \\
\subsection{Robustness checks}\label{subsec3.2}
To ensure the reliability of our baseline model, we undertake a series of robustness checks. In our regression analysis, the anticipated effects of deep trade provisions may serve as a complicating factor. If trade flows rise in expectation of an agreement before it officially comes into force, using current variables will not allow us to accurately attribute these changes to the agreement itself. Evidence of expected impacts also raises concerns regarding our identification strategy and causality. In order to address reverse causality and elucidate the dynamic adjustments in agricultural trade over time, we conduct regressions on our comprehensive sample, incorporating both lead and lag variables. Figure \textcolor{blue} {\ref{fig2}} shows the values of the coefficients of $Depth$ between $t$ - 3 and $t$ + 4. The previous and future levels of PTA depth are not statistically correlated with current trade flows. It takes at least two years for a deep PTA to boost agricultural trade. The result indicates that the impacts of deep PTAs accumulates over time. \\

\begin{table}[htbp]
\caption{OLS and PPML Regressions: Gravity model results}\label{tab1}
\begin{tabular*}{\textwidth}{@{\extracolsep\fill}lcccc}
\toprule%
& \multicolumn{2}{@{}c@{}}{OLS} & \multicolumn{2}{@{}c@{}}{PPML} \\\cmidrule{2-3}\cmidrule{4-5}%
Variables & (1) & (2) & (3) & (4) \\
\midrule
Depth & 0.1162\textsuperscript{***} & 0.1506\textsuperscript{***} & 0.0487\textsuperscript{***} & 0.0368\textsuperscript{**} \\
& (0.014) & (0.027) & (0.010) & (0.016) \\
PTA   & {} & -0.1239  & {} & 0.0431 \\
          & {} & (0.077) & {} & (0.038) \\
Exp.-Year FE & Yes & Yes & Yes & Yes \\
Imp.-Year FE & Yes & Yes & Yes & Yes \\
Exp.-Imp. FE & Yes & Yes & Yes & Yes \\
N & 242720 & 242720 & 219298 & 219298 \\
\botrule
\end{tabular*}
\footnotetext{Note: All specifications incorporate time-varying exporter and importer fixed effects, along with bilateral fixed effects. Robust standard errors, clustered at the country-pair level, are indicated in parentheses. *** \(p<0.01\), ** \(p<0.05\), * \(p<0.1\). The sample includes annual data for consecutive yeras and covers agricultural data for 225 countries over the period 2003-2022.}
\end{table}

\noindent The country-pair fixed effects in Equation (\ref{eq5}) are based on the assumption of symmetrical bilateral trade costs. However, empirical evidence suggests that bilateral trade costs are often asymmetrical. For instance, geographical distance and topographical features may create disparities in bilateral trade costs. A country with more convenient port facilities or superior transportation infrastructure may experience reduced export costs, while another country may face higher import costs. Furthermore, disparities in technological advancements and production efficiency can also contribute to asymmetrical bilateral trade costs. In the estimation presented in columns (1) and (2) of Table \textcolor{blue} {\ref{tab2}}, we employ directional pair fixed effects $(\overrightarrow{\mu_{ij}})$ in place of country-pair fixed effects $(\mu_{ij})$ to model asymmetric time-invariant trade costs\footnote{See \cite{Larch2024} for a similar discussion on the impact of RTAs.}. Comparing these results with those in Table \textcolor{blue} {\ref{tab1}} reveals that they are analogous. Consequently, accounting for asymmetric time-invariant trade costs appears to provide no significant benefit. \\

\begin{table}[htbp]
\caption{PPML Regression: robustness checks}\label{tab2}
\begin{tabular*}{\textwidth}{@{\extracolsep\fill}lcccccc}
\toprule%
& \multicolumn{2}{@{}c@{}}{$\overrightarrow{\mu_{ij}}$} & \multicolumn{2}{@{}c@{}}{3-year intervals} & \multicolumn{2}{@{}c@{}}{internal trade flows} \\\cmidrule{2-3}\cmidrule{4-5}\cmidrule{6-7}%
Variables & (1) & (2) & (3) & (4) & (5) & (6) \\
\midrule
Depth & 0.0250\textsuperscript{***} & 0.0271\textsuperscript{**} & 0.0467\textsuperscript{***} & 0.0291\textsuperscript{*} & 0.0951\textsuperscript{***} & 0.0910\textsuperscript{***} \\
& (0.007) & (0.011) & (0.011) & (0.017) & (0.023) & (0.026) \\
PTA & {} & -0.0076 & {} & 0.0639 & {} & 0.0146 \\
    & {} & (0.032) & {} & (0.045) & {} & (0.053) \\
Exp.-Year FE & Yes & Yes & Yes & Yes & Yes & Yes \\
Imp.-Year FE & Yes & Yes & Yes & Yes & Yes & Yes \\
Exp.-Imp. & No & No & Yes & Yes & Yes & Yes \\
Directional Exp.-Imp. FE & Yes & Yes & No & No & No & No\\
N & 218333 & 218333 & 75881 & 75881 & 74761 & 74761 \\
\botrule
\end{tabular*}
\footnotetext{Note: All specifications feature time-varying exporter and importer fixed effects. Columns (1) and (2) incorporate directional pair fixed effects ($\overrightarrow{\mu_{ij}}$). Columns (3) and (4) use 3-year intervals, so in this sample $t \in \{2003, 2006, 2009, 2012, 2015, 2018, 2021\}$. Columns (5) and (6) include internal trade flows. Robust standard errors, clustered at the country-pair level, are indicated in parentheses. *** \(p<0.01\), ** \(p<0.05\), * \(p<0.1\).}
\end{table}

\noindent An additional consideration is that trade flows don not immediately respond to shifts in trade policy. This delay happens as markets need time to react to new regulations, alter their operations, and for the full effects of these changes to be reflected in trade statistics. Consequently, estimating this adjustment using data from consecutive years may not provide sufficient time for the dependent variable to fully respond. To mitigate this bias, estimations are conducted at 3-year intervals as a set of a robustness analysis\footnote{Consistent with standard practices in related literature, we opt for using data at 3-year intervals, a method commonly employed in gravity model studies.}. Columns (3) and (4) of Table \textcolor{blue} {\ref{tab2}} present the estimation results relevant to this application, replicating the specifications from columns (3) and (4) of Table \textcolor{blue} {\ref{tab1}}, but using data at 3-year intervals. The gravity estimates remain consistent and robust. \\
Another issue we primarily address is that the lack of intra-national trade flows restricts the identification to comparisons solely between PTA members and countries that are not part of a PTA. The inclusion of domestic trade flows aligns with the theoretical foundations of the gravity model\footnote{\cite{Dai2014}, \cite{Donaldson2018} and \cite{Yotov2022}, among others.}. It enables us to quantify the trade diversion effects of trade policies on domestic sales. We construct internal trade flows as the difference between gross production value data and total exports\footnote{Agricultural production data is sourced from the Food and Agriculture Organization of the United Nations (FAOSTAT), available for free on the \href{https://www.fao.org/faostat}{\textcolor{blue}{website}}.}. Columns (5) and (6) of Table \textcolor{blue} {\ref{tab2}} show that introducing domestic trade flows results in a larger estimate of the $Depth$ effect. This outcome provides indicative evidence that internal trade flows may be particularly vulnerable to trade diversion effects. In other words, deep agricultural trade provisions indeed create trade between members at the cost of domestic sales. Similarly, the impact of the PTA dummy variable on trade is not captured in the regression of domestic flows. 

\begin{figure}[H] 
    \centering 
    \includegraphics[width=0.9\textwidth]{figure2.eps} 
    \caption{Dynamic effects \\
    Note: The figure is based on the Column (4) in Table \textcolor{blue} {\ref{tab1}} and uses 95 percent confidence interval, which is adjusted to incorporate lags of $Depth$ up to $t$ - 3 and leads of $Depth$ up to $t$ + 4.} 
    \label{fig2} 
\end{figure}

\subsection{Further discussion}\label{subsec3.3}
\subsubsection{Partners' income levels}\label{Section 3.3.1}
Different sets of provisions may be more critical in DTAs among countries with different development stages. Logically, this variation stems from the diverse motivations for signing trade agreements, which are shaped by the countries involved and their current levels of liberalization.
To examine whether the impact is influenced by the income levels of members, we group the DTAs according to partner countries from the North and South. Using the World Bank's country income classification, we categorize DTAs into three types based on the income levels of the member countries at the time the agreement took effect. When all member countries are classified as high-income, the DTA is classified as a North-North DTA. When all member countries belong to the low-income, lower-middle-income, or upper-middle-income groups, the DTA is classified as a South-South DTA. When both high-income and non-high-income countries are members, it is classified as a North-South DTA. Based on Equation (\ref{eq5}), we add interaction terms between the $depth$ variable and three dummy variables that identify mutually exclusive groups of countries: North-North, South-South, and North-South. \\
Column (1) in Table \textcolor{blue} {\ref{tab3}} demonstrates that the effects of DTAs on agricultural trade differ depending on the income groups of the participating countries. Under equal conditions, North-North DTAs or North-South DTAs show no notable effect, and South-South DTAs significantly enhance trade. An intuitive explanation is that trade liberalization among developed countries is already high, and with relatively robust institutions, DTAs have a smaller impact on them. Additionally, the differing goals and interests between developed and developing countries can diminish the trade-promoting effects of deep provisions. In contrast, through reform commitments that effectively reduce trade barriers, DTAs are more likely to improve institutions between developing countries, thus impacting global trade primarily through trade liberalization in South-South relationships. \\
\subsubsection{Aggregated products levels}\label{Section 3.3.2}
Due to the difficulties associated with the disaggregated data, we classify the 24 chapters into four more aggregated categories. Chapters 01-05 are labeled as animal and live animal products, chapters 06-14 as plant products, chapter 15 as animal and plant oil products, and chapters 16-24 as food, beverages, and tobacco products. Table \textcolor{blue} {\ref{tab3}} lists the estimated coefficients for the four aggregated groups. The depth coefficients of columns 4 and 5 are statistically significant, which may be attributed to the fact that agricultural clauses that improve product quality standards and safety regulations. This enhancement takes an important role in high value-added categories such as animal and plant oil products, as well as food, beverages, and tobacco products. Furthermore, these improvements boost market competitiveness and add value to these products, thereby driving the growth of trade flows. \\
\subsubsection{Impact of COVID-19}\label{Section 3.3.3}
In our study, the dataset spanning 2003 to 2022 (includes) overlaps with the COVID-19 pandemic, and we do not exclude the possibility that some of the research findings may be negatively affected by the persistent of the pandemic. Consequently, we decouple the pandemic period by dividing it into pre-pandemic and post-pandemic phases to assess whether it affects the overall results. Columns (6) and (7) of Table \textcolor{blue} {\ref{tab3}} show that the depth of trade terms in DTA has a significant positive impact on agricultural trade only in the pre-pandemic period. Interestingly, the promotion effect of ``shallow'' PTA becomes apparent in the post-pandemic period. The PTA dummy variable primarily captures whether a framework exists to safeguard trade relations, a role that becomes increasingly critical under heightened uncertainty. Priority supply and safeguard mechanisms among PTA members help maintain smooth trade flows during global supply chain disruptions. However, the effectiveness of deep provisions may not be fully realized in the post-pandemic period due to challenges in implementation and coordination, weakened policy synergies, and conflicts between pandemic control measures and the execution of these clauses.

\begin{sidewaystable}[htbp]
\caption{PPML Regression: further discussion}\label{tab3}
\begin{tabular*}{\textwidth}{@{\extracolsep\fill}lccccccc}
\toprule%
& \multicolumn{1}{@{}c@{}}{Income level groups} & \multicolumn{4}{@{}c@{}}{Product heterogeneity} & \multicolumn{2}{@{}c@{}}{Impact of COVID-19} \\\cmidrule{2-2}\cmidrule{3-6}\cmidrule{7-8}%
{Variables} & {(1)} & {(2)} & {(3)} & {(4)} & {(5)} & {(6)} & {(7)}\\
\midrule
Depth & 0.0624\textsuperscript{**} & 0.0205 & 0.0155 & 0.0816\textsuperscript{*} & 0.0342\textsuperscript{**} & 0.0624\textsuperscript{***} & 0.0337 \\
          & (0.026) & (0.018) & (0.015) & (0.043) & (0.014) & (0.023) & (0.029)\\
PTA   & -0.0074 & 0.0157 & 0.0307 & 0.0423 & 0.0203 & -0.0167 & 0.1487\textsuperscript{***}\\
          & (0.039) & (0.052) & (0.044) & (0.118) & (0.038) & (0.058) & (0.040)\\
Depth*North\_North\ & -0.0452 & {} & {} & {} & {} & {} & 
             {}\\
             & (0.029) & {} & {} & {} & {} & {} & {}\\
Depth*North\_South\ & -0.0210 & {} & {} & {} & {} & {} & {}\\
             & (0.030) & {} & {} & {} & {} & {} & {}\\       
             
Exp.-Year FE & Yes & Yes & Yes & Yes & Yes & Yes & Yes\\
Imp.-Year FE & Yes & Yes & Yes & Yes & Yes & Yes & Yes\\
Exp.-Imp. FE & Yes & Yes & Yes & Yes & Yes & Yes & Yes\\
N & 109882 & 138762 & 156311 & 94615 & 186621 & 186746 & 31258\\
\botrule
\end{tabular*}
\footnotetext{Note: All specifications incorporate time-varying exporter and importer fixed effects, along with bilateral fixed effects. Robust standard errors, clustered at the country-pair level, are indicated in parentheses. Columns (2) to (5) represent Animal,live animal products, Plant products, Animal and plant oil products, etc., and Food, beverage and tobacco products, etc., respectively. Columns (6) and (7) represent Pre COVID-19 and Post COVID-19, respectively. *** \(p<0.01\), ** \(p<0.05\), * \(p<0.1\).}
\end{sidewaystable}

\section{Conclusion}\label{sec4}
As the number of agreements increases and their content becomes more detailed, many PTAs include complex and interrelated clauses that could impact agriculture. The aim of this paper is to examine how the broader framework of economic integration policies affects agricultural trade. In doing so, we first build on others developed in existing studies by drawing key agriculture-relevant information from provisions. Subsequently, we construct vertical depth while considering the heterogeneity of DTAs. The paper presents the empirical study by using extended three-way structural gravity model. \\
Our main finding is that the provisions in DTAs can create more agricultural trade than shallow agreements, with consistent results whether using panel datasets with OLS or PPML estimators. The estimations are also robust when considering dynamic effects, adjusting the country-pair fixed effects, and using 3-year intervals data. Furthermore, internal trade flows may be susceptible to trade diversion effects. The research results further confirm that DTAs have varying impacts on developed and developing economies, primarily due to their different levels of trade liberalization. The added value of agricultural products also affects the efficacy of agricultural provisions. In the context of global trade uncertainty induced by the COVID-19, deep provisions are difficult to implement effectively in practice. \\
As a focus for future research, there remains limited knowledge about the relationship between specific provisions in DTAs and the GVCs in agriculture. This is the area we aim to explore in our upcoming work.

\backmatter
\newpage
\bmhead{Funding}{This research was conducted as part of the project 2024M753602 financed by China Postdoctoral Science Foundation. It is also part of the project GZC20233091 financed by Postdoctoral Fellowship Program of CPSF.}

\bmhead{Conflict of interest}{Authors state no conflict of interest.}

\bmhead{Data availability}{All of the data used in our study comes from openly available databases.}


\begin{appendices}
\section{}\label{secA}

\newcommand{\tabitem}{\textbullet}
\noindent 
\begin{longtable}{|>{\centering\arraybackslash}p{3cm}|>{\centering\arraybackslash}p{2cm}|>{\centering\arraybackslash}p{5cm}|c|}
\caption{Number of agricultural provisions by policy area in all PTAs notified to the WTO} \label{tabA1} \\
\hline
\textbf{Policy area} & \textbf{Type} & \textbf{Provision description} & \textbf{Number} \\
\hline
\endhead

\hline
\multicolumn{4}{|r|}{Continued on next page} \\
\hline
\endfoot

\hline
\endlastfoot

\footnotesize \multirow{2}{*}{Export Restrictions} &  \footnotesize Agriculture-specific 
        & \begin{itemize}\footnotesize 
         \item Requires advance notification of export restrictions related to food security under certain conditions 
         \item Prescribes the use of certain forms of export certification as attestation for SPS requirements, unless Parties decide otherwise 
         \end{itemize} 
         & \footnotesize \multirow{2}{*}{2} \\
\hline

\footnotesize Intellectual Property Rights (IPR) & \footnotesize Data protection / protection of undisclosed information
         & \begin{itemize}\footnotesize
             \item Provides minimum term of protection for undisclosed test or other data for a new agricultural chemical
         \end{itemize}
         & \footnotesize 1 \\
\hline

\footnotesize Countervailing Duties & \footnotesize Subsidies
         & \begin{itemize}\footnotesize
             \item Prohibit export subsidies on agriculture
           \end{itemize}
         & \footnotesize 1 \\
\hline

\footnotesize Sanitary and Phytosanitary Measures (SPS) & \footnotesize All & \footnotesize All & \footnotesize 58 \\
\hline

\footnotesize \multirow{4}{*}{Subsidies} & \footnotesize Definition and coverage (including exclusions) / Substantive disciplines 
         & \begin{itemize}\footnotesize
           \item Does the agreement cover support in the agriculture sector? 
           \item Does the agreement cover support in the fisheries sector? 
           \item Does the agreement include any specific regulation of agricultural subsidies? 
           \item Does the agreement include any specific regulation of fisheries subsidies? 
           \end{itemize} 
         & \footnotesize\multirow{4}{*}{4} \\
\hline

\footnotesize\multirow{5}{*}{Environmental Laws} & \footnotesize General Environmental Protection Areas / MEA Compliance 
        & \begin{itemize}\footnotesize
        \item Does the agreement require states to implement fisheries management? 
        \item Does the agreement provide for differential restriction of fishing subsidies? \item Does the agreement require measures to prevent deforestation and/or require sustainable trade practices in forest products? 
        \item Does the agreement require states to comply with the UN Fish Stocks Agreement, the FAO Code of Conduct for Responsible Fisheries, the 1993 FAO Agreement to Promote Compliance with International Conservation and Management Measures by Fishing Vessels on the High Seas (Compliance Agreement) and the 2001 IUU Fishing Plan of Action/IUU measures in general? 
        \item Does the agreement require states to comply with the 2005 Rome Declaration on IUU Fishing, the Agreement on Port State Measures to Prevent, Deter and Eliminate Illegal, Unreported and Unregulated Fishing, 2009, as well as instruments establishing and adopted by Regional Fisheries Management Organisations? 
        \end{itemize} 
        & \footnotesize\multirow{5}{*}{5} \\
\hline

\footnotesize State Owned Enterprises & \footnotesize Coverage (including exclusions) & \begin{itemize}\footnotesize
              \item Does the agreement regulate state enterprises in agriculture?
              \end{itemize} 
            & \footnotesize 1 \\
\hline
\end{longtable}
\begin{tablenotes}[flushleft]\footnotesize
    \resizebox{\textwidth}{!}{
    \begin{minipage}{\textwidth}
        \item Source: Created by authors.
        \item Note: Considering that most of the reviewed PTAs lack specific provisions related to food or agriculture in the policy area of Technical Barriers to Trade (TBT), we excluded it from the calculation.
    \end{minipage}
    }
\end{tablenotes}



\end{appendices}

\bibliography{sn-bibliography}

\end{document}