To evaluate the extent to which this assumption affects my results, I build 30 individual, small-scale, tractable models of grain storage and trade with full rational expectations in which harvests and world prices are stochastic. For the purposes of these models, I collapse all months, all grains, and all markets in each country into a single annual national harvest for which I calculate a sample mean and variance over my 10 year period of interest. For 20 countries with ports or direct access to Johannesburg, South Africa, I build a model for each country with just that country and the world market. For the remaining 21 countries, I build 10 models each consisting of a landlocked country, a coastal country, and the world market39. I choose a centrally-located major city in each country and use my trade cost estimates to compute a single representative trade cost between each landlocked and coastal country and between each coastal country and the world market. I use my estimated demand parameters for each country as well as my estimated monthly storage cost parameters aggregated up to the annual level. For world prices, I compute a single annual world price index for each coastal country based on its harvest year and demand share parameters and calculate the sample variance of the month to-month change in price of these indices over my 10 year period of interest. Putting all of this information together, I use the RECS solver in MATLAB to solve each of the 30 models and run simulations using actual observed harvest and world price shocks to solve for equilibrium storage, trade, price,hydroponic bucket and consumption in every country in every year under full rational expectations.
I then re-solve each model under counterfactual low trade costs. Despite volatile local harvests and high baseline trade costs, my results from this exercise indicate that inter-annual storage in Africa is limited even under full rational expectations, likely due to high storage costs and the position of most countries as net grain importers. Under existing high trade costs, an average of 2.0% of the grain harvest is stored inter annually, and there is positive inter-annual storage in only 50 of the 400 total country-years in my 30 models. Under counterfactual low trade costs, an average of 0.3% of the grain harvest is stored inter-annually, and there is positive inter-annual storage in only 7 of the 400 total country-years in my 30 models, as cheaper trade serves as a partial substitute for storage. The use of my assumption about trader expectations does appear to lead to underestimates of annual storage, but adjusting for these underestimates does not affect my main results. In my main model, under existing high trade costs, an average of 0.3% of the grain harvest is stored inter-annually, and there is positive inter-annual storage in just 1.5% of total market-crop-years, while under counterfactual low trade costs there is no inter-annual storage in any market-crop-year. To determine how allowing for full rational expectations affects my results, I re-solve my main model under both existing and counterfactual trade costs while restricting traders’ choice of inter-annual storage of each grain in each market to equal the percentage of grain stored inter-annually in equilibrium for that country for that year in the results from my individual full rational expectations models. The percentage changes in net agricultural revenues, the average grain price index, expenditure on grains, and welfare are all within two tenths of a percentage point of my baseline results, and the results for all indicators in table 1.12 are well within 95% confidence intervals constructed using the standard errors reported there.
Thus I conclude that my assumption about trader expectations does not have a statistically significant effect on my results. Given the fact that inter-annual storage is limited, it is reasonable to ask to what extent my results would change if I used a more parsimonious model with no storage at all. In recent trade papers dealing with the agricultural sector , it is common to use annual data on production and farm-gate prices, the prices farmers receive when they sell their produce immediately after harvest. Using annual data, one can avoid having to deal with harvest cycles and intra-annual storage, which is necessary for there to be positive consumption in non-harvest months. To better understand the differences between this approach and the one I have used in this chapter, I use the harvest month price for each crop in each market from my baseline estimated model as the annual farm-gate price and build a new static model with all variables aggregated up to the annual level and no storage. I re-estimate trade costs for this new static annual model using the same approach as for my dynamic monthly model and then solve for equilibrium with both my new trade cost estimates and counterfactual low trade costs. Trade cost estimates converge in 6 iterations for the static annual model, and each iteration takes only 2 minutes . However, my trade cost estimates are 23.4% lower on average using the static annual model, and the overall welfare gain from lowering trade costs is 32.9% smaller than under the dynamic monthly model with storage. These differences can be explained by the pattern of equilibrium storage and trade described in Proposition 1. When production is widespread, trade between markets almost never occurs at the beginning of the harvest cycle when farm-gate prices are measured. During this period, local production and storage is used for consumption, spatial arbitrage conditions do not bind, and equilibrium price gaps are narrower.
Instead, trade occurs primarily at the end of the harvest cycle once local stocks have been depleted,stackable planters which is when equilibrium price gaps are wider and spatial arbitrage conditions bind. Using monthly data and a dynamic model with storage to identify more precisely when agricultural trade occurs thus seems important to avoid underestimating trade costs and their effects on welfare, particularly in developing country contexts with large seasonal price fluctuations. Further details on this exercise with graphical examples are contained in the appendix. Having confirmed the robustness of my main results to the relaxation of several of my key assumptions and explored alternate approaches, I next turn my attention to two extensions in which I run additional counter factuals to further explore the consequences of high trade costs in sub-Saharan Africa and the options for reducing them. Reducing trade costs everywhere in Africa to match transport costs elsewhere in the world is likely not feasible in the short run. However, it may be feasible to reduce trade costs along certain high-priority routes. This section considers the extent to which some routes matter more than others for achieving the welfare effects of the main counterfactual. Even if a long-term goal of reducing trade costs everywhere is maintained, trade cost reduction will not be simultaneous, so the results in this section also shed light on welfare effects during the potentially long transitional period from a high trade cost to a low trade cost regime. I start by looking at the effects of reducing trade costs along the 413 overland links within Africa while holding port-to-world-market sea trade costs constant and of reducing port-to-world-market sea trade costs while holding overland trade costs constant. Results in the second and third columns of table 1.16 indicate that while overland trade cost reduction accounts for over 70% of the overall welfare gain, nearly half of the overall welfare gain is achievable by just reducing sea trade costs between African ports and the world market.Overland trade and sea trade are partial substitutes as both can reduce prices in grain-deficit markets.Since reducing port-to-world-market sea trade costs is likely more feasible than reducing overland trade costs everywhere in Africa, I start with this scenario and then look at whether adding trade cost reductions on a few key overland routes can substantially narrow the gap with my main counterfactual. I select key routes by first identifying the markets with the biggest welfare gaps between the “just sea” scenario in column 3 and the main counterfactual in column 1 and then identifying the most important overland links connecting these markets to their trading partners. In columns 4 and 5 of table 1.16, I show that adding trade cost reductions on just 30 overland links to the “just sea” scenario allows for over 70% of welfare gains to be achieved, and adding trade cost reductions on 75 overland links allows for 86% of welfare gains to be achieved. These results are encouraging for policy-makers and multilateral donors who may have limited resources to invest in trade cost reduction. Generally speaking, the results suggest that investment in “trade corridors” of the type promoted by the African Development Bank and other institutional donors may be worthwhile.
Although it is likely that the specific corridors I identify might not be the most important ones when other goods besides grains are considered, my corridor selection exercise, which is detailed in the appendix, suggests that certain types of corridors may be particularly beneficial. First, reducing trade costs from the world market all the way to “dry ports” in densely-populated inland areas like Addis Ababa, Ethiopia and Kinshasa, D.R. Congo can achieve major welfare gains even if trade costs from the dry ports to further-inland areas remain high. Second, reducing trade costs along inland corridors with imbalances or fluctuations in production and consumption can lead to large gains without significant involvement of the world market. Third, targeting those inland areas isolated by extremely high trade costs can lead to very large welfare improvements for those areas. In 2013, African cereal grain yields averaged 1.4 tonnes per hectare, compared to 3.1 in South Asia, 4.2 in Latin America, and 7.3 in the US. Low productivity in African agriculture is primarily due to the low use of inputs like fertilizer, and institutional donors and organiza adoption to narrow this productivity gap. This section uses my estimated model to look at the effects that widespread technology adoption in Africa would have under existing high trade costs and counterfactual low trade costs. A complete model of technology adoption is beyond the scope of this chapter. Instead, I estimate what would happen if productivity everywhere in Africa doubled, i.e. if African cereal grain yields increased to 2.8 tonnes per hectare, which is much closer though still below levels elsewhere in the world. In the context of my model of production, this is equivalent to a doubling of all Bimt, which would double agricultural production in the short run . Practically speaking, I implement this counterfactual by doubling the harvest in all markets and all time periods while keeping all other exogenous variables and parameters the same40 . Table 1.17 compares results for key aggregate indicators from my main counterfactual , counter factuals with technology adoption under high trade costs and low trade costs , and a combined counterfactual in which trade costs are lowered and technology adoption occurs 41. Under high trade costs, technology adoption leads to a collapse of prices and agricultural revenues, as high trade costs confine much of the increased production to local markets with inelastic demand. Only 39 markets experience an increase in agricultural revenues, 37 of which are net importers for which increased production primarily serves to replace imports so that the price does not fall as much as in other markets42. In contrast, under low trade costs, agricultural revenues increase on aggregate and for 184 individual markets , as much more of the increased production can be exported to deficit areas and the world market. Low trade costs are thus a prerequisite for widespread technology adoption to increase the incomes of African farmers.The net welfare effect of doubling productivity through technology adoption is similar in magnitude to the net welfare effect of lowering trade costs43. Although lower trade costs and productivity improvements are partial substitutes as both lead to lower prices in most markets, the combined welfare effect of both represents 92% of the sum of the effects of each intervention on its own . These findings suggest that agricultural policy in Africa should give as much weight to trade cost reduction as to technology adoption and prioritize comprehensive approaches that include both.