To obtain an initial sense of the dispersion of agricultural production across market catchment areas, I use a comprehensive database of the caloric value of food crops in Africa to assign an approximate caloric level per unit weight to all staple carbohydrates and convert production data into calories. The median market catchment area had a 2010 population of 2.37 million and has an average production per capita of 1,863 kcal per day of staple carbohydrates during my study period. Average production ranges from 0 to 10,347 kcal per person per day with 63 markets producing less than 1,000 kcal per person per day and 54 markets producing more than 3,000 kcal per person per day, suggesting significant opportunities for net trade between markets.My model uses the notation and basic framework of the one-commodity, two-market rational expectations storage and trade model of Williams and Wright 1991, chapter 9, which I extend to include the storage and trade of 6 grains across the network of 230 African markets and the world market built in the previous section. I embed this storage and trade model within a simple general equilibrium setting by including a composite outside good. While the six grains are subject to trade costs between locations , the outside good has no trade costs so that its price is the same in all locations, and I choose units so as to normalize its price to 110. Production of the outside good is used either for final consumption or for trade and storage services in the agricultural sector. In my simplest baseline case reflective of the short-term, I abstract away from production decisions by letting production of both the 6 grains and the outside good be an exogenous endowment that is unaffected by price changes. In an extension presented at the end of this section, I explicitly model production in each sector and allow for reallocation of factors of production between sectors in response to price changes.
In each location,dutch bucket for tomatoes a representative consumer chooses monthly consumption of each grain and the outside good to maximize utility and a representative competitive grain trader with rational expectations chooses monthly storage, trade, and local sales of each grain to maximize profits. I proceed by considering each of these agents in turn. Having estimated both the demand parameters and the cost parameters, I proceed to use the estimated parameters to solve the model for equilibrium storage, trade, consumption, and prices of every grain in every market in every month. Before proceeding to my counterfactual analysis in the next section, it is important to verify the goodness of fit of the baseline estimated model. Of the four equilibrium variables, the only one I observe at the monthly, market level is prices, so I focus on comparing the model-generated equilibrium prices to the price data. Figure 1.5 shows the actual maize price series from the 4 markets in Kenya and Tanzania from figure 1.1 together with the model-generated price series for these markets. In general, the correlation of the levels of the actual and model-generated price series is high. The correlation coefficient for the average prices for a given market and crop is 0.787. Within markets for all pairs of two crops, the model correctly predicts which crop has a higher average price 83.3% of the time. The correlation of the model-generated prices and the price data within a particular price series seems lower, although the goodness of fit is more difficult to measure. The median correlation coefficient within price series is 0.385. As is clear from the sample price series in figure 1.5, there are many month-to-month price fluctuations that cannot be explained by the parsimonious data used by the representative traders in my model. It is also the case that the correlation coefficient does not fully reflect the goodness of fit of the price series.
The maize price series from figure 1.5, for instance, have within series correlation coefficients of 0.136 , 0.217 , 0.171 , and 0.174 for this period despite the fact that the overall shapes of the series appear quite similar between the data and the model. In addition to monthly, market-level prices, I also observe annual, country-level trade flows as reported in national trade statistics and compiled by CEPII’s BACI project , which includes 37 of my 42 countries of interest as well as the rest of the world, which I group together into a 38th country. Although these data are much less detailed than my model-generated trade data , I can aggregate up my monthly, market-level equilibrium trade quantities and compare them to the annual, country-level data. In table 1.11, I compare net trade flows in the model and the data at different levels of aggregation. The first four rows compare net trade flows at the country level without distinguishing between specific origins and destinations, while in the bottom four rows I attempt to make this distinction by assigning observed trade with non-contiguous partner countries to the adjacent country through which such trade would have to pass so as to enable comparison with my model-generated trade flows. Correlation coefficients between net trade flows in the model and the data are generally very high, although they are somewhat lower at the lowest levels of aggregation. Despite high correlation coefficients, the model appears to perform only moderately well at predicting whether net trade flows are positive, negative, or zero in the data. However, this is largely due to sign discrepancies for very small or zero net trade flows. Once trade flows below a minimum threshold are dropped, the model predicts the correct sign for net trade flows for well above 80% of observations at all levels of aggregation. Discrepancies between the model and the data — particularly for small trade volumes — are likely due in part to the existence of significant informal grain trade flows across borders in many parts of sub-Saharan Africa, which are not captured by official trade statistics.
Tschirley and Jayne2010, for instance, cite estimates of informal, unrecorded cross-border trade flows of maize between Malawi, Mozambique, Tanzania, Zambia, and Zimbabwe exceeding 100,000 t/year. Having estimated the model and established that it can reproduce both the price data and annual, country-level trade data reasonably well, in the next section I conduct my counterfactual analysis in which I compare equilibrium outcomes under the baseline model to outcomes under counter factuals in which I change some of the demand parameters, cost parameters, or exogenous variables. Standard errors in table 1.12 were obtained using a computationally-intensive bootstrapping procedure with 40 iterations. For each iteration, I re-solved the model for equilibrium storage, trade, consumption, and prices under both high and low trade costs using different demand and cost parameter estimates obtained by re-sampling the data used to estimate each parameter with replacement. Due to the lengthy run-time, I limit my iterations to 40 and do not report standard errors for the later counter factuals in this chapter. In addition to the direct effect on price levels, lowering trade costs also affects local price volatility. In absolute terms, the average standard deviation of prices for the 511 grain price series falls from 0.188 to 0.123 under low trade costs. However, in relative terms, the average coefficient of variation increases from 0.330 to 0.387 due to the fall in the mean prices. In absolute terms,blueberry grow pot the frequency of grain prices over 1 USD/kg falls dramatically from 12.5% to 0.9% when trade costs are lowered. In relative terms, the frequency of grain prices exceeding double the series mean increases slightly from 2.0% to 2.1%. Lowering trade costs does therefore appear to be effective at preventing local prices from far exceeding regional and international levels as they have during events like the Horn of Africa famine , but relative price volatility remains significant as high storage costs and similar agricultural calendars within regions mean that seasonal price fluctuations continue to be substantial . The aggregate results in table 1.12 do not reflect the heterogeneity of the effects of reducing trade costs across African markets and countries. Table 1.13 summarizes this heterogeneity by grouping markets and countries according to the sign of the changes they experience in their average grain price index, their net agricultural revenues, and their overall welfare when trade costs are lowered.
The 181 markets and 37 countries in Group A are primarily net grain importers and experience changes similar to the continent-wide aggregate with falling prices and revenues and increasing welfare. The 14 markets and 2 countries in Group B are primarily net grain exporters who experience price increases, revenue increases, and welfare increases under lower trade costs. This is not the case for all exporting regions: the 24 markets in Group C are net exporters that experience price decreases, revenue decreases, and welfare losses. These are mostly landlocked surplus regions that experience negative terms-of-trade effects when the urban and coastal regions they trade with are able to access cheaper grain imports from the world market. Finally, a small group of 10 markets and 2 countries in Group D experience price decreases, revenue gains, and welfare gains due to their particular crop mix and/or their changing export position over time. The results discussed thus far reflect the effects of reducing trade costs in the short run when factors of production cannot reallocate between sectors. In the longer run, the large price changes that my model predicts under lower trade costs are likely to lead to the reallocation of factors of production. In the majority of markets , the decrease in the relative price of grains would lead to a shift of factors of production out of agriculture and into the outside good sector. Using my production model developed previously, I use the actual harvests and the baseline equilibrium prices to back out the implied productivity shocks Bimt and then re-solve the counterfactual with an endogenous supply response using different values for the price elasticity of supply η. Roberts and Schlenker estimate the year-to-year price elasticity of supply for staple grains at 0.097. In the longer run, η may be larger , while a value of η = 1 would be considered unusually high in the agriculture literature. My model and estimation strategy included several important assumptions. In this section, I explore the effects of relaxing some of these assumptions. When defining market catchment areas, I allocated all agricultural production in my 42 countries of interest to the 230 markets in my network. As an alternative, I define market catchment areas for all 263 markets on my initial ideal list and then drop production in the catchment areas of the 33 markets for which I was unable to obtain price data. Re-solving the model for both baseline and counterfactual scenarios using these revised production data does not change my results substantially. Results for all indicators in table 1.12 are well within 95% confidence intervals constructed using the standard errors reported there. For my baseline estimation, I used the Cobb-Douglas elasticity of substitution and set the price elasticity of demand for grains to match the estimate of Roberts and Schlenker 2013 . Both of these values are at the lower end of elasticity estimates in the literature. In table 1.15, I compare my baseline results to results obtained using larger elasticities in my estimation. Each time I change an elasticity, I re-estimate the other demand parameters using the new elasticities, re-solve the model under both existing high trade costs and counterfactual low trade costs, and report the aggregate effects of lowering trade costs in table 1.15. Increasing the elasticity of substitution σ to 3 has virtually no impact on my aggregate results. Increasing the price elasticity of demand to −0.5 leads to less of a fall in expenditure on grains and net agricultural revenues, as consumers increase expenditure more under lower prices. However, the average fall in the grain price index is nearly the same as before, with net grain imports from the world market increasing by nearly eight times as much to cover increased demand. The overall welfare increase from decreasing trade costs does not change significantly from my baseline case. I next analyse the effects of my assumption about trader expectations, which is necessary for model tractability but is likely to lead to underestimates of equilibrium storage by eliminating the effects of uncertainty.