Use of the GEELAST header array file

Chapter 13 of the GTAP book is an example of how the GE demand elasticity information might be used to facilitate analysis. In this chapter, George Frisvold examines the global incidence of technological progress in agriculture and food production. One of his findings is that an increase in total factor productivity in Australian agricultural crops benefits Australian farmers while the reverse is true in North America (Table 13.3). Upon further reflection, he attributes this to the fact that the general equilibrium elasticity of demand for Australian crops is elastic, while this same parameter is inelastic in the case of North America. Thus an increase in output in North America is more than offset by the resulting decline in price and overall revenue falls. This translates into a decline in land rents, which is the measure of farmer welfare used by Frisvold. Hence the importance of the GE demand elasticity in economic analysis.

But why is the demand for crops elastic in Australia, but not in North America? The GEELAST program is designed to permit users to quickly decompose the GE demand elasticity into its component parts, thereby facilitating explanation of the results in terms of fundamentals. The general method is one of beginning with a summary array: O, which simply reports the GE own-price elasticity of demand by commodity and region. From this array we can quickly verify that the Frisvolds assertion is correct: NAMs elasticity is -0.75 versus -1.22 for Australia/New Zealand. (Note that these figures are different from those in Table 13.2 of the GTAP book. This is because the figures in Table 13.2 were based on GTAP version 1 data and parameters, whereas all of the results are based on version 2 data and parameters.)

The subsequent arrays with the prefix O decompose the aggregate own-price elasticity of demand. O1, shows how much is derived from domestic agents versus exports. Here, we see that domestic agents contribute less to the ANZ elasticity than to the NAM elasticity (-.13 vs. -.22), and a further breakdown by firms and households in O11 show this to be true across the board. (O111 breaks the domestic firms demands down by sector.) On the other hand, from O1 we can see that export demands are sufficient to make ANZ crop demand elastic, since the qxm entry is equal to -1.1, vs. -.54 for NAM. O2 breaks the export demand down by destination region. Selecting CROPS and ALL REG destinations, then requesting a row share from VIEWHAR we see that East Asia accounts for 40% of ANZs export demand elasticity. This is followed by ROW and SE Asia.

Having rather exhaustively broken down the sectoral demand elasticity, we now turn to the task of explaining why the export demand elasticitys contribution is larger in the case of ANZ. Is this because exports are more important for ANZ than for NAM? Or is it because the export demand elasticity faced by ANZ exporters is larger? To answer this question we need to decompose each agents contribution into a share and a behavioural response. The next set of headers, with prefix S, do precisely this. Thus selecting S1: ALLCOMP/qxm/CROPS/AllREG, we can compare the export share of total output in NAM (.21) to that in ANZ (0.30). We can also compare the average behavioural response (own-price elasticity) on the part of export markets, to the two regions price changes. Here we see again that the ANZ figure is larger: -2.57 for NAM vs. -3.67 for ANZ. The prod entry simply reports the product of the share and the elasticity, which is what was reported previously in header O1.

Thus we can conclude that the large contribution of exports to the GE elasticity of demand for ANZ crops comes from two factors. First, export demands are generally more elastic than domestic demands, and ANZ has a larger share of exports in total output. Secondly, since ANZ is, on average, smaller in the export markets, the own-price elasticity of demand facing its goods in export markets is larger. (The reader will need to review the Armington equations in the model to fully grasp the second point. Since the elasticity of substitution among imports from different sources is the same for all regions, the import shares are the sole cause of differing import demand elasticities facing different exporters.)

The other headers with the S prefix permit one to decompose the domestic and export demand elasticities into their share and elasticity components. In both cases, the first thing to do is to specialise the last two drop down boxes (which initially are Sum TRAD_COMM/Sum REG) to the commodity/region in question eg., crops/ANZ).

The last set of headers in this file permit one to obtain cross-price elasticities as well. X1 reports the cross-price elasticities ETA(i,r,j,s) = q(i,r,j,s)/p(j,s), ie. the quantity response of the (i,r) pair to a change in the price of good j in s. For example, selecting the drop-down box combinations: crops/AustrNZ/crops/All REG, we can observe the change in demand for AustrNZ crops when crops prices in other regions rise. For example, when NAM crops prices rise by one percent, the model predicts an increase in demand for ANZ crops of 0.27%. If crops prices rise worldwide by 1%, then the model predicts a decline in ANZ crop demand of -0.217%, which is simply the column sum in this array.

Finally, X11 permits us to decompose these cross-price elasticities by domestic and export changes. Selecting: crops/AustrNZ/crops/All REG/All QOCOMP reveals that the -0.217 cross price elasticity of demand for AustrNZ crops with respect to the NAM crops price comes almost entirely from the export market (0.25 of the total 0.27 elasticity).

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