Supply restrictions: where employment falls, and why

Version 1.1. Recalibrated. The price elasticity of food demand is now 0.24, the USDA Economic Research Service's compensated estimate for the United States, in place of a round 0.5 chosen by hand. The cost shares are now derived from the published USDA food dollar industry shares and the specialty-crop labour share, so the chain reproduces the food dollar it is matched to; the earlier set implied a farm gate worth 30 cents against the measured 11.8. The motivating policy is now a proposed cap on the H-2A agricultural visa, H.R. 7541, which has never been capped; the behavioural evidence still comes from the H-2B lottery and the note says so. The section on an input used throughout the economy is removed, as is wage indexation from the calibration.Restricting the supply of one input at the top of a production chain reduces output at every stage of it, and reduces employment at the stages nearest the restriction. This note sets out a chain of S producing stages and a household, with the cost share, the elasticity of substitution and the elasticity of supply of own inputs all free to differ between stages, and reduces it to S linear equations in S unknowns. Employment at each stage then splits into three terms: employment per unit of output rises, output falls because the stages downstream buy less, and output falls because households buy less. Calibrated to the USDA food dollar and to a proposed cap on the American H-2A agricultural visa, a 20 percent rise in the price of seasonal farm labour cuts output by 2.40, 0.57 and 0.22 percent along the chain, and cuts employment by 1.23 percent at harvesting and 0.06 percent at processing while raising it by 0.19 percent at retail and food service. Whether the last stage gains or loses employment turns on whether it substitutes away from what it buys faster than households substitute away from what it sells.Every number printed in the note is computed rather than typed. The deposit includes the model, a script that recomputes all 61 printed figures and fails if any moves, an independently written JavaScript port that reproduces 41 of them, and a cross-check showing the two agree to about 1e-15 over 4,000 randomly generated chains.