Comparison of Simulation Methods Using Historical Data in the U.S. International Price Program M.J. Cho, T-C. Chen, P.A. Bobbitt, J.A. Himelein, S.P. Paben, L.R. Ernst, and J.L. Eltinge U.S. Bureau of Labor Statistics ICES III Session 14 – June 19, 2007 Disclaimer: The views expressed in this paper are those of the authors and do not necessarily reflect the policies of the BLS

2 Outline I.U.S. International Price Program (IPP) II.Bootstrap Variance Estimator III.Adequacy of Approximations in Simulation Studies IV.Simulation Methods Considered V.Numerical Results VI.Conclusions

3 I.U.S. International Price Program (IPP) A.IPP is the nations primary source of information on price trends in the international trade of the U.S. economy Export and Import Price Indexes B.IPP involves population structure, sample design and estimation methods with a high degree of complexity

4 C.IPP Index Aggregation Tree Upper Level Strata Lower Level Strata Classification Groups Weight Groups (Company|CG) Items

5 1.Sample frame provided by U.S. Customs Border Protection, and divided into two biannual panels 2.Stratified multistage sampling within panels a. Within a broad product category (stratum), select establishments proportional to trading dollar value b. Within establishment, select detailed product categories (CGs) using systematic PPS c. Within Company|CG, select items D.IPP Sampling Design (Imported Goods)

6 E.IPP Index Formula (modified Laspeyres index)

7 F.Weights 1.Item weight is weight groups weight divided by number of items 2.Weight groups weight is a trade dollar value divided by selection probability 3.CG weight is based on trade weights from the Census Bureau 4.Stratum weight is aggregation of CG weights

8 1. Draw PSUs (establishments) with replacement from the sampled PSUs in each stratum 2. Define bootstrap weights: II.Bootstrap Variance Estimator A.Based on Rao, Wu and Yue (1992)

9 3. Calculate the price STR using bootstrap weights 4. Repeat steps 1-3 B times 5. Compute the bootstrap variance estimator:

10 B. Properties of Under Realistic Approximations to IPP Population Structure, Sample Design and Estimation Methods 1.Over R replications of the simulation design compute

11 2.Evaluation Criteria Relative Bias = Degrees of Freedom =

12 III.Adequacy of Approximations in Simulation Studies A.Notation Features of population and design ( True, Approximation ) Estimator, with cdf Specific functional of e.g. bias or MSE

B.Adequacy of Simulation & Approximation for true 1. Components to include in a. Population structure b. Sampling steps c. Nonresponse d. Weighting e. Variance estimation 2. Approximations for each component in (1) ?

14 1. Taylor expansion: under conditions

15 2. Four Cases Case 1: Small first derivatives, small Case 2: Small first derivatives, large Case 3: Large first derivative Case 4: Large second derivative

17 IV. Simulation Methods Considered A. Use a Single Method for Selection of Sample Units and Related Weights: Same sample units and weights for each month B. Three Methods to Construct Population of Item-Level STRs 1. Resampling Method 2. Fixed-One-Rate Method 3.CDF Interpolation Method

StratumStratum Description P07Edible vegetables, roots, and tubers P08Edible fruit and nuts; peel of citrus fruit or melons P09Coffee, tea, mate and spices P22Beverages, spirits, and vinegar P61Articles of apparel and clothing accessories P74Copper and articles thereof P90Optical, photographic, measuring and medical instruments V.Numerical Results A.Selected Strata

Item STR1 of Design Strata

Original Variance of STR (P90)

Relative Bias of STR (P90)

Degrees of Freedom of STR (P90)

23 VI.Conclusions A. For Complex Establishment Surveys Like IPP, Simulation-Based Evaluations of Est Properties Require Consideration of 1. Approximations to the true population, design and estimation procedures 2. Adequacy of the resulting approximations to the true properties

24 B. Future Work 1. For IPP: Other features of the pop and design e.g. Independence of STRs from sample units 2. Consider generalized variance estimator to improve stability 3. Explore the surface defined by in neighborhoods of the true