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Data Collectionhard
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A survey estimates the unemployment rate by computing: Rate=Number UnemployedLabor Force=5,20065,000=0.08\text{Rate} = \frac{\text{Number Unemployed}}{\text{Labor Force}} = \frac{5,200}{65,000} = 0.08Rate=Labor ForceNumber Unemployed​=65,0005,200​=0.08

From survey data:

  • Number unemployed: U^=5,200\hat{U} = 5,200U^=5,200 (SE = 180)
  • Labor force: L^=65,000\hat{L} = 65,000L^=65,000 (SE = 600)

Using the delta method (Taylor series) to estimate SE(unemployment rate): SE(p^)≈(∂f∂U)2SE(U)2+(∂f∂L)2SE(L)2SE(\hat{p}) \approx \sqrt{\left(\frac{\partial f}{\partial U}\right)^2 SE(U)^2 + \left(\frac{\partial f}{\partial L}\right)^2 SE(L)^2}SE(p^​)≈(∂U∂f​)2SE(U)2+(∂L∂f​)2SE(L)2​ where f(U,L)=U/Lf(U, L) = U / Lf(U,L)=U/L.

The approximate standard error of the unemployment rate is: