Policy Significance Statement

Trade policy changes have become more frequent in the last few years, unlike their pattern prior to 2016. Predicting trade flows in this highly uncertain policy environment requires high-frequency and on-time data, as well as the appropriate techniques; such as machine learning, to provide critical and timely information to stakeholders. In this article, supervised models and neural networks are applied to forecasting agricultural trade patterns, and to identifying underlying contributors including policies. The impact of tariffs and multiple other economic variables on international trade is evaluated and presented.

1. Introduction and Motivation

Efficient and nimble agriculture and food industries are vital to human survival. In the past three years, global agriculture has been buffeted by many shocks—natural disasters, trade wars, and pandemics. Such unprecedented uncertainties have affected the range of decisions starting at the farm and culminating at the consuming household or ports (trade). Assessing such unconventional trends requires ample amounts of data. Over the past decade, increased availability of big data and breakthroughs in computer hardware have challenged conventional statistical and econometric techniques in modeling complex trends or economic relationships (Varian, Reference Varian2014). The challenges include dealing with the sheer volume of data (evolving from spreadsheets to SQL databases, and recently, toward NoSQL and Hadoop clusters), the lengthy list of variables available to explain such relationships (and associated collinearity issues), and the need to move beyond simple linear models. Machine learning (ML) has been offered as an alternative to address many of these challenges (Bajari et al., Reference Bajari, Nekipelov, Ryan and Yang2015; Batarseh and Yang, Reference Batarseh and Yang2017; Mullainathan and Spiess, Reference Mullainathan and Spiess2017; Athey and Imbens, Reference Athey and Imbens2019). Several authors including Chief Economists of Google and Amazon have strongly advocated the use of big data and ML to uncover increasingly complex relationships even in an analysis as simple as fitting a supply or demand function. The economics community is catching on, but the speed of ML advances, that is, new techniques emerge frequently, can make an academic study stale by the time peer reviews are completed. Nonetheless, the academic community facing seismic shocks from advances in data and ML has been called on to revisit time-tested theories and relationships (Mullainathan and Spiess, Reference Mullainathan and Spiess2017). This study takes on this challenge in the context of international trade and offers an ML application using agricultural trade data spanning several decades.

Many international institutions and government agencies project economic variables including trade flows to inform decisions in national and multilateral contexts (World Economic Outlook—International Monetary Fund, 2019; Trade in Goods and Services Forecast, Organization for Economic Cooperation and Development, 2019; U.S. Department of Agriculture, 2019; World Trade Organization, 2019). Since these projections are based on a combination of model-based analyses and expert judgment, several sources have pointed to their limitations, for example, forecast accuracy under 35% (U.S. Department of Agriculture, 2019) and quantifying the contribution of underlying economic factors (Chapter 4, World Economic Outlook—International Monetary Fund, 2019). With recent trade disruptions such as Brexit, USA–China/Japan–South Korea tariffs, the need for alternative approaches to understanding and forecasting (modeling) trade flows is greater now than ever before. During such disruptions, decisions to plant, maintain crop progress, harvest and market in the near term and to invest in farm assets in the medium term have all been impacted by serious supply-side disruptions (e.g., flooding or drought), significant uncertainty in demand (e.g., soybean purchases by China) and sudden collapse of both supply of inputs and demand for output (e.g., Covid-19). These events, especially in the context of agricultural trade, have created a level of uncertainty and complexity unknown over the past several decades. Compounding the situation is the static nature of most trade models, which often conduct comparative static analysis of trade outcomes from deterministic trade policy changes. Little guidance exists on theoretical modeling of trade policy uncertainty and its implications for producer and consumer preferences or behavior.

In this study, ML techniques are applied to the gravity model of bilateral (aggregate or industry) trade flows. The gravity model is often referred to as the workhorse in international trade due to its popularity and success in quantifying the effects of various determinants of international trade. Originally due to Anderson (Reference Anderson1979) and applied to data in Anderson and van Wincoop (Reference Anderson and van Wincoop2003), the gravity model provides the causal association needed to implement ML algorithms in the predictive domain (Santos Silva and Tenreyro, Reference Santos Silva and Tenreyro2006; Yotov et al., Reference Yotov, Piermartini, Monteiro and Larch2016; Athey and Imbens, Reference Athey and Imbens2019). In doing so, this study offers an alternative to time-series projections and expert judgment analyses by relying on neural networks and boosting approaches that allow for alternative and robust specifications of complex economic relationships (Baxter and Hersh, Reference Baxter and Hersh2017; Storm et al., Reference Storm, Baylis and Heckelei2019). ML models can also provide accurate predictions, a priority of many economists in recent months given the trade disruptions among the major economies of the world.

2. Machine Learning Methods

Machine learning, a set of algorithms for advanced statistical analysis and intelligent problem solving, offers a novel approach (driven by big data sets) to identify patterns and model relationships, that is, quantify Y’s response with or without a set X of possible predictors, either supervised or unsupervised, respectively (James et al., Reference James, Witten, Hastie and Tibshirani2013). Supervised learning (such as regression and classification) relates the response of Y to X for either better understanding of their relationship or predicting the response of Y to a potential/future set of X. In contrast, unsupervised learning (such as clustering) usually does not have a pre-defined response variable (Y) and aims to understand the relationships between/among X or observations. In both settings, often relationships are derived from one or more “training” data sample and applied to a “test” data sample to compute prediction accuracy. The sheer volume of data available in recent times allows such a partition of data for cross-validation, that is, training and testing. However, a major trade-off arises between prediction accuracy and model interpretability between conventional (econometric) analysis and ML. As applicable techniques become non-linear or multi-layered with the repeated feedbacks between training and test data, ML techniques often leave interpretability and inference behind to focus more on data patterns and predictions accuracy. This study applies a variety of ML techniques to the trade setting noted earlier and also presents the inner working and challenges of ML in these settings.

A comprehensive review of all ML techniques available at this time is beyond the scope of this study. Excellent sources for that information include James et al. (Reference James, Witten, Hastie and Tibshirani2013), Batarseh and Yang (Reference Batarseh and Yang2017), and Athey and Imbens (Reference Athey and Imbens2019). In the following, the generic optimization problem as in Athey and Imbens (Reference Athey and Imbens2019) is presented along with an outline of techniques employed in this study. Consider a simple example where the outcome Y depends on a set of features X. Assume:

(1)$$ {Y}_i\mid {X}_i\sim N\left(\alpha +{\beta}^T{X}_i,{\sigma}^2\right), $$

where $ \theta =\left(\alpha, \beta \right) $ are parameters of interest, $ {Y}_i $ has a conditional normal distribution with variance $ {\sigma}^2 $. Conventional econometric estimation, that is, least squares, would suggest:

(2)$$ \left(\hat{\alpha},\hat{\beta}\right)=\arg \underset{\alpha, \beta }{\min}\sum_{i=1}^N{\left({Y}_i-\alpha -{\beta}^T{X}_i\right)}^2. $$

In the ML setting, the goal is usually to make a prediction for the outcome from a new set of values for X that is, predicting $ {Y}_{N+1} $ from $ {X}_{N+1} $. Let that prediction, regardless of the actual specification of the relationship between Y and X be $ {\hat{Y}}_{N+1} $. Then, the squared loss associated with this prediction would be:

(3)$$ {\left({Y}_{N+1}-{\hat{Y}}_{N+1}\right)}^2. $$

While “least squares” is an approach to minimize the loss function, other estimators exist that dominate least squares (Athey and Imbens, Reference Athey and Imbens2019). However, ML-based estimators for Equation (3) have a tendency to over or under-fit, which can be corrected by regularization, sampling, or tuning parameters through out-of-sample cross-validation.Footnote ¹ The following provides a brief overview of ML techniques considered in this study:

• • Ridge regression and elastic nets are some basic extensions to the least squares minimization problem in Equation (2) to impose a penalty for increasing the dimensionality of X (i.e., regularization). A major concern with these approaches is the subjective choice on the penalty, often referred to as $ \lambda $, but big data allow for its potential out-of-sample cross validation.

• • Decision trees and their extensions have become extremely popular in recent years. They are referred to as trees since data are stratified or segmented into branches (splits) and leaves (nodes). The stratification is based on the number of predictors and cut-off values for predictors. For instance, if X contains two column vectors, then stratification will be based on both constituents, sequentially or in random, for all possible cut-off values for each of these two predictors, for example, $ {X}_1<{c}_1 $. To make a prediction for new values of X, trees typically use the mode or median of the outcome Y in the region to which the new X belongs. To illustrate, as in Athey and Imbens (Reference Athey and Imbens2019), the total-sample sum of squared errors for outcome Y is given by:

(4)$$ Q=\sum_{i=1}^N{\left({Y}_i-\overline{Y}\right)}^2\hskip1.72em \overline{Y}=\sum_{i=1}^N{Y}_i. $$

After a split based on one of the predictors ($ {X}_k\Big) $using the threshold $ {X}_k<c, $ the sum of total-sample squared errors is:

(5)$$ Q\left(k,c\right)=\sum_{i={X}_{ik}\le c}{\left({Y}_i-{\overline{Y}}_{k,c,l}\right)}^2+\sum_{i={X}_{ik}>c}{\left({Y}_i-{\overline{Y}}_{k,c,r}\right)}^2, $$

where l and r denote left and right of $ {X}_k $ using the cut-off c and

$$ {\overline{Y}}_{k,c,l}=\frac{\sum_{i={X}_{ik}\le c}{Y}_i}{\sum_{i={X}_{ik}\le c}1},{\overline{Y}}_{1,c,r}=\frac{\sum_{i={X}_{ik}>c}{Y}_i}{\sum_{i={X}_{ik}>c}1}. $$

The objective of decision-tree based learning is to minimize $ Q\left(k,c\right) $ for every $ k $ and every $ c\in \left(-\infty, +\infty \right) $, and the process is repeated for subsamples or leaves. As noted earlier, there is a tendency in this approach to over-fit, which can be corrected by using boosting, adding a penalty for the number of leaves, or by pruning the tree. A single tree is often the preferred outcome from this approach for its interpretability. However, prediction accuracy has been significantly improved (at the expense of interpretation) by procedures such as bagging, random forests, and boosting:

• • Bagging involves repeated sampling of the (single) training data to fit a tree each. Then, averaging across trees chosen independently (like in bootstrapping) improves its prediction by lowering the variance.

• • The random forests approach is similar to bagging in the sense that bootstrapped training samples are used to generate decision trees to average out. However, at each split of the decision tree, the choice on predictors (or a subset) is random.

• • Boosting is also similar to bagging, but the decision tree for each training sample is not independent of previous trees, instead, they are chosen sequentially. Each tree is grown using information from previously grown trees and thus, boosting does not involve bootstrap sampling. Unlike bagging and random forests which are applicable to decision trees only, boosting can be employed for any base learner.

• • Extra trees regression: this method deploys several trees for the same problem, and generates a mean of all the trees that reflects inclusion of all observations, and maximizes quality of the predictive outputs. That is, this method implements a meta-estimator that fits and averages a number of randomized trees to control over-fitting.

In the ML literature, the boosting algorithms are popular as they convert a weak base learner (often a single decision tree) into a strong learner (by re-training weak sub-samples as well as tuning of hyper parameters to provide optimized predictions).

• • Neural networks and other deep learning methods are often employed in situations with large volumes of unexplored data to predict an outcome or analyze a pattern (especially used in image and audio recognition, as well as computer vision). These techniques emulate the human brain’s neural system by recursively building multiple layers of nodes. These deep layers (thus referred to as deep learning) include predictors in linear form, but then translate them into latent variables and use non-linear functional forms to relate to the outcome. To illustrate a single-layer network learning, consider the latent variables $ Z $ defined as follows:

(6a)$$ {Z}_{ik}^{(1)}=\sum_{j=1}^k{\beta}_{kj}^{(1)}{X}_{ij},k=1,\dots, {K}_1. $$

Then, a non-linear function $ g(.) $ relates the outcome $ Y $ to $ Z: $

(6b)$$ {Y}_i=\sum_{k=1}^{K_1}{\beta}_k^{(2)}g\left({Z}_{ik}^{(1)}\right)+\varepsilon . $$

The objective of the estimation again is minimizing squared errors, but the layering allows for millions of functional possibilities and parameters. Note that such unsupervised ML techniques often do not have both outcomes $ Y $ to $ X $. In the context of Equations (6a) and (6b), the $ X $ can be thought of some transformation of $ Y $, for example, lagged values.

In this study, ML methods are considered for the standard specification of the gravity model:

(7)$$ {Y}_{ijt}=g\left({X}_{it},{X}_{jt},i,j,t\right), $$

where $ {Y}_{ijt} $ is bilateral trade between country $ i $ and country $ j $ at time $ t, $(response variable) and $ {X}_{it(jt)} $ is the set of possible predictors from both countries and the set $ \left\{i,j,t\right\} $ refer to a variety of controls on all three dimensions (Anderson and van Wincoop, Reference Anderson and van Wincoop2003; Yotov et al., Reference Yotov, Piermartini, Monteiro and Larch2016). The major ML techniques applied include random forests, extra tree regression, boosting, and neural networks. While it is tempting to compare ML models with econometric approaches, for example, the popular Poisson Pseudo-Maximum Likelihood (PPML) method commonly used to estimate trade flows, a word of caution is in order. ML techniques often encompass four paradigms—descriptive, diagnostic, predictive, and prescriptive—and the focus of this study is in the predictive domain. Nonetheless, we do present results from applying PPML estimates of the gravity model in Appendix I.

3. The Agricultural Trade Setting and Data

References to agricultural trade abundantly appear in literature dating back to 1000 BCE. One of the earliest pathways connecting Mediterranean to Arabia, Indian sub-continent, and Far East was the Incense Route. As the name suggests, incense made of aromatic plants and oils was a major traded commodity, but spices, silk, and precious stones were also major transactions along this route. Then came Spice and Silk Routes and numerous other inter- and intra-continental routes facilitating trade in agricultural products and other goods. The industrial revolution of 18th century favored agricultural industries, but that in late 19th and early 20th century expanded rapidly into transport and energy sectors. Fast forward to the later parts of the 20th century, agriculture still accounted for at least a quarter of exports (or imports) of major trading nations. For instance, the 1960 edition of the State of Food and Agriculture from United Nations’ Food and Agriculture Organization noted the significant share of agriculture in merchandise exports from the new world (North America and Oceania) to the rest of the world.

Anderson (Reference Anderson2016) reviewing the evolution of food trade patterns over the past six decades, notes that agriculture’s share of global merchandise trade was about 27% in 1960. While that share has fallen to 11% in 2014 (due in part to lower prices of agricultural goods relative to industrial goods) the volume of agricultural exports has continued the strong upward trend of the early 20th century. Agricultural products are also unique in many aspects, for example, high volatility of prices, high level of trade protection, and immobility of countries’ endowments such as land and water. More importantly, Anderson (Reference Anderson2016) notes the concentration in both country and commodity shares of global exports of farm products. In particular, less than 10 items made up half of that trade in agricultural products and two-thirds of the world’s exports of farm products are accounted by just a dozen trading economies. Despite that concentration, the set of commodities that stand out for having most countries involved in world trade are shown in Table 1. The seven commodities—wheat, corn, rice, sugar, beef, milk powder, and soybean—have not only been traded for long but also have the most countries engaged on the export or import side. Hence, this study chose to apply ML techniques to understand the patterns of agricultural trade where the longest time series and most country pairings exist, that is, the seven commodities in Table 1.

Table 1.

Number of exporting and importing countries of major agricultural products, 1970–2009.

Source: Liapis (Reference Liapis2012).

Abbreviations: Exp, number of exporters; Imp, number of importers.

In terms of sources of data for the gravity model application, this study employs bilateral trade (import data) from United Nations (UN) Comtrade for the seven commodities noted above.Footnote ² UN Comtrade provides data using several nomenclatures, we use the Standard International Trade Classification Revision 1 classification as this classification features data with the longest possible time-frame, that is, from 1962 for some commodities. Specific codes are: 0111 for beef, 0221 and 0222 for milk powder, 041 for wheat, 042 for rice, 044 for corn, 0611 for sugar, and 2214 for soybean. Tariff data are obtained from the UNCTAD Trade Analysis Information System database. For our purposes, we use the simple average for each bilateral trade pair across each of the seven commodities. To account for missing tariff data (countries often only report a single year across a decade or so), the approach of Jayasinghe et al. (Reference Jayasinghe, Beghin and Moschini2010) is employed to derive implied average tariffs for missing observations. Note that tariff data are only available from 1988.

Data for (35) gravity variables such as GDP, population, contiguity, distance, common language, currency, WTO membership, preferential trade agreements, and colonial ties are from the dynamic gravity dataset constructed by Gurevich and Herman (Reference Gurevich and Herman2018). Their work built a new gravity dataset that improves upon existing resources (e.g., CEPII data) in several ways: first, it was constructed to reflect the dynamic nature of the globe by closely following the ways in which countries and borders have changed between 1948 and 2016. Second, they increased the time and magnitude of variation within several types of variables. All three sources of data are merged to arrive at a data set featuring imports, tariffs, and economic variables from 1988 to 2016.Footnote ³ ML models were trained on various cuts of the data as noted in the next section. The data are in cubical form: country pairs, commodity, and time.

4. Supervised Machine Learning Model Selection and Validation

Recall that multiple ML approaches are employed to predict bilateral trade for each of the seven agricultural commodities. Within decision trees, in addition to random forests and extra tree regression, two types of boosting—LightGBM, XGBoost—are considered (Ke et al., Reference Ke, Meng, Finley, Wang, Chen, Ma, Ye and Liu2017):

• • LightGBM scans all data instances to estimate the Gain, measured in terms of the reduction in the sum of squared errors, from all the possible Split points. Instead of changing the weights for every incorrectly predicted observation at every iteration like other methods, for example, GBoost, LightGBM tries to fit the new predictor to the errors made by the previous predictor.

• • LightGBM splits the tree level-wise with the best fit, whereas XGBoost algorithms split the tree leaf-wise. The leaf-wise algorithm can reduce more loss than the level-wise algorithm, and hence can lead to better prediction accuracy.

Using off the shelf Python libraries, each of these models employed all 35 gravity variables noted earlier along with tariffs in the bilateral trade context. Gurevich and Herman (Reference Gurevich and Herman2018) provided 70 gravity variables, but we chose to employ the 35 variables based on correlation analysis. The first step here was to avoid near perfect collinearity among the 70 variables. Then, the data had alternative representations for the size of the economies, for example, GDP total and per capita, and in current and constant dollars. For this second step, measures of feature importance for each of the seven models under alternative variables representing the same phenomenon, for example, size were obtained. The splits and gains then determined the variables to be included in the model. That is, the high cardinality (correlation) of $ X $ and alternative representations of $ X $ led variable selection by way of information gains from splits (using out-of-the-box python libraries). In most models, only 10–12 features accounted for most of the information gains and they appear consistent with the set of variables employed in traditional econometric analysis. After selecting variables, ML algorithms were deployed. Main parameters tuned for all three boosting methods are maximum depth of the tree, learning rate, number of leaves, and feature fraction. The choice among these supervised models was also dictated by the adjusted R-square, the most commonly used statistical measure in analytics, as shown below (Ke et al., Reference Ke, Meng, Finley, Wang, Chen, Ma, Ye and Liu2017). Both supervised and unsupervised ML methods allow for cross-validation, where predictions can be compared to actuals.

Since data spanned 1962–2016, the training data cut-off point was set at 2010 leaving enough room to compare predictions with actuals starting in 2011.Footnote ⁴ This partitioning of data allowed for a longer time series to learn as well as have enough data to compare predictions to actuals (2011–2016). Major challenges for many of these algorithms were a large number of zeros in bilateral trade matrices, tariffs as well as time invariant variables in the gravity context such as distance, language, and contiguity. To test the sensitivity of predictions to alternative sets of data, three variations of data were considered to implement ML models: without tariffs (1962–2016), with actual tariffs (1988–2016) and with missing tariffs filled in as per Jayasinghe et al. (Reference Jayasinghe, Beghin and Moschini2010). Thus, each commodity’s trade was subjected to four supervised and a non-supervised model for three different data sets for learning and obtaining predictions for 2011–2016.

Table 2 presents the four best-fitting models among the supervised ML approaches and the training and test sample sizes for each of these models.Footnote ⁵ The results presented here are from the data set with missing tariffs filled in (1988–2016). While the fit and predictions including validation statistics were similar for the two data sets with tariffs and with missing tariffs filled in, the models using data from 1962 to 2016 yielded lower adjusted R-squares. Some differences in feature importance between these three variations in data were observed, which are detailed in the next section. Note that milk powder had the most observations for training as well as testing among the seven commodities. As can be seen in Table 2, the extra tree regression had the best performance for beef and milk powder, while Random Forest yielded highest R-square for corn, rice, and soybean. For sugar, LightGBM provided the best fit. Note, however, adjusted R-squares were similar across the models. The adjusted R-square in the best-fitting models ranged between 45 and 83% (boldfaced numbers in Table 2). Lower adjusted R-square values for rice and sugar are likely due to high variance in the inputs used for the models and incomplete data from older years. The staple rice, in particular, is often considered a thinly traded commodity with a low share of trade in production for a large number of countries. Both products (rice and sugar) tend to be highly protected by large Asian countries. Under-fitting was not found for any of the seven commodities and therefore, adjusted R-square metric appears to represent the model’s quality. Moreover, each of the commodity models was deployed on a global scale, which places all countries on the same level of abstraction when using the response variable.Footnote ⁶ An additional cut of the data set was also considered: focus on large trading pairs only. While the fit improved considerably when considering large traders only, those results are not reported here given the arbitrary cut to the sample data.

Table 2.

Supervised models’ validation measures.

5. Deep Neural Networks Model

Neural networks, a form of deep learning, can take several paradigms: recurrent and convolutional neural networks, hybrids, and Multilayer Perceptron (MLP). This study employs MLP given the tabular data context (along with its cardinality) and the goal of obtaining better predictions. MLP is a feed-forward algorithm with the following steps:

• • #1, Forward pass: here, the values of the chosen variable are multiplied with weights and bias is added at every layer to find the calculated output of the model.

• • #2: Calculate the error or the loss: the data instance is passed, the output is called the predicted output; and that is compared with real data called the expected output. Based upon these two outputs, the loss is calculated (using Back-propagation algorithm).

• • #3: Backward pass: the weights of the perceptrons are updated according to the loss.

In Python, the MLP algorithm uses Stochastic Gradient Descent (SGD) for the loss function (Scikit, 2019). SGD is an iterative method for optimizing an objective function with smoothness properties.Footnote ⁷ As noted earlier, neural networks do not have obvious validation statistics, unlike supervised models.

6. Results and Discussion

In addition to employing ML techniques, this study considered traditional approaches to estimating the gravity Equation (7). As noted by Disdier and Head (Reference Disdier and Head2008), many econometric techniques have been used in estimating Equation (7), but the more recent approach that accounts for zeros in $ {Y}_{ijt} $, heteroscedasticity in additive errors to Equation (7) and other issues is PPML estimation (Santos Silva and Tenreyro, Reference Santos Silva and Tenreyro2006). The PPML approach and its variations in the high-dimension context, posed several specification and estimation challenges. In particular, the pair-wise fixed effects, for example, origin-time and destination time, as in Yotov et al. (Reference Yotov, Piermartini, Monteiro and Larch2016) as well as Correia et al. (Reference Correia, Guimaraes and Zylkin2019), created significant collinearity issues and convergence problems. Nonetheless, results from estimating Equation (7) using basic PPML methods and the chosen 35 gravity variables (plus tariffs) for the seven commodities of this study are reported in the Appendix I. Given the limited ability of PPML-based methods to identify the relative importance of explanatory variables (in the presence of thousands of fixed effects) as noted in the World Economic Outlook, IMF (2019), the following section presents results from ML methods only.Footnote ⁸

Figures 1–3 and Tables 3 and 4 present the results from the supervised learning models, while Figure 4 details those from the neural networks application to capturing the gravity trade relationship in Equation (7).

Figure 1.

Supervised model predictions of aggregate trade values, 2011–2016.

Figure 2.

Supervised model predictions of top partners’ trade values, 2011–2016.

Figure 3.

Supervised model predictions of 2nd top partners’ trade values, 2011–2016.

Table 3.

Ranking variables by information gain (normalized values).

Table 4.

Relative importance of variables based on information gain (percent).

Notes. 100 indicates the variable with the highest information gain. All other variables together accounted for another 84–126% of information gains across the seven commodities.

Figure 4.

Neural networks prediction of top country’s aggregate exports, 2014–2020.

6.3. Deep neural networks model results

Turning now to neural networks, Figure 4 presents predictions for the top exporter for each of the seven commodities. Recall from the discussion of Equations (6a) and (6b) that these models do not necessarily have a response variable. In that sense, learning here happens primarily with the bilateral trade data. Python libraries are used to deploy the neural network, namely, scikit-neuralnetwork. The training sample cut-off is set at 2014 and projections are made until 2020. Figure 4 shows that all commodities’ predictions, with the exception of Netherlands’ milk powder exports, closely track respective actuals for 2014–2017. In fact, there is at least one projection that almost mimics actual in all projections except in the case of milk powder.

It is not straightforward to compare ML and deep learning models, but each has its advantages and disadvantages (Storm et al., Reference Storm, Baylis and Heckelei2019). Likewise, comparisons to traditional/econometric approaches are tenuous given causality issues noted earlier. Nonetheless, an attempt is made here to explore the merits of each approach and relevance in specific contexts. The supervised machine learning models, primarily of the decision-tree kind with bagging, random forests, or boosting, have a structure relating a response variable to set of predictors. The estimated structure is often heterogeneous, non-linear, and based on repeated learning, that is, minimizing the total-sample sum of squared errors. The supervised techniques are straight forward to implement particularly in uncovering complex relationships and can be compared among themselves in terms of validation statistics such as error sum of squares. They also provide information on the most relevant predictors including the relative strength of alternative predictors. However, this technique cannot provide standard errors on predictors’ contribution or a coefficient capturing the relationship between Y and X, due in part to the non-linear and repeated learning process noted above. These models are a great fit for problems primarily focused on near- to medium-term predictions, for example, prices, trade flows, especially when a large volume of data are available. Neural networks carry similar advantages in prediction problems, but do not have predictors. As demonstrated using bilateral trade data predictions, they appear most suited to longer-term projections, for example, climate change. Figure 5 confirms this claim using the example of U.S. wheat exports to all countries, that is, actuals and predictions from three models—LightGBM, Extra trees regression, and neural networks—show the better long-term fit of neural networks. Note that supervised techniques with rolling training samples can also generate a sequence of medium-term projections that can be integrated for longer-term projections.Footnote ¹² The pruning and regularization involved in supervised methods may limit the amount of data used in learning (as shown in Table 2 on training and test data), whereas neural network approaches attempt to use all data. In contrast, econometric approaches offer structure and inference with carefully chosen causal relationships, often linear and homogeneous. The later are seldom cross-validated and also suffer from specification or variable selection bias like (unlike) supervised (unsupervised) models.

Figure 5.

Comparison of predictions from supervised models and neural networks.

7. Outlier Events (Future Work) and Conclusions