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Semi-parametric models of spatial market integration

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Abstract

We develop fully flexible, semi-parametric models of price linkages in spatially distinct regional US markets for plywood and lumber products. The models are developed within the framework of generalized additive models (GAM) which are estimated using penalized maximum likelihood estimation methods and generalized cross-validation techniques. Such nonlinear models are a natural extension to an extensive literature that has developed increasingly flexible models of the Law of One Price and spatial market integration. The GAM estimates and marginal responses to price changes exhibit substantial nonlinearities. Dynamic impulse responses demonstrate significant asymmetries in price responses to exogenous shocks. The results are largely consistent with efficiently linked regional markets for lumber and plywood products in that price transmission elasticities are generally close to unity and localized market shocks evoke equilibrating adjustments in regional markets.

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Fig. 1

Source: Food and Agriculture Organization Forest Products Production and Trade Database

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Notes

  1. See Fackler and Goodwin (2001) for a comprehensive overview of the methodology applied and markets examined in empirical evaluations of spatial market integration or the law of one price.

  2. Lence and Falk (2005) demonstrated that cointegration—a condition that is sometimes taken to be synonymous with market integration—is actually a distinct concept. That is, cointegration in and of itself does not necessarily confirm market integration.

  3. Sawnwood is wood produced by sawing roundwood (harvested trees) lengthways or by profile chipping. Plywood is a laminate made by gluing wood veneers together, typically with alternating grain patterns. Plywood veneers are usually cut in a continuous circular fashion around the log.

  4. Housing starts are taken from the St. Louis Federal Reserve FRED database.

  5. The specific lumber market definitions are, for Inland West, Idaho, Montana, Utah, Wyoming, Colorado, New Mexico, Arizona, and Eastern Oregon and Washington; West of the Mississippi River corresponds to markets west of the Mississippi River but excluding mills in Spokane and Northern California. For plywood, West of the Mississippi River corresponds to plants in Arkansas, Louisiana, and Texas; and the Southeast US corresponds to plants in Georgia, Florida, South Carolina, and the Carolinas. Note that our characterization of regions into West and South does not apply to the aggregation of lumber markets west of the Mississippi River, which is comprised of a large aggregation of markets that exist across both regions.

  6. It should be noted, however, that exchange rates may be a relevant regressor in comparisons of international markets, even when trade prices are quoted in a common currency. For example, a considerable volume of world trade is conducted in US dollar terms. In such a case, exchange rate distortions and imperfect exchange rate pass-through may be indicated when the relevant \(\beta _2\) parameter is different from zero.

  7. For example, Heckscher (1916) noted the importance of ‘commodity points,’ that resulted from transportation costs, and their similarity to the gold points in species flow mechanisms. See Obstfeld and Taylor (1997) for a discussion of Heckscher’s views on transactions costs and purchasing power parity.

  8. When prices are considered in logarithmic terms, which is usually the case, \(\tau _{12}\) represents transactions costs in price-proportional terms.

  9. Note that wood products used in the construction industry are mainly of softwood varieties. Hardwood lumber products are typically consumed in higher-valued uses, such as furniture and cabinets.

  10. Note that the empirical analysis applies to logarithmic prices throughout. Thus, marginal effects and price differentials can be interpreted in proportional terms.

  11. The unit root testing results are presented in an appendix.

  12. Simulation evidence in Gospodinov et al. (2013) suggests that estimates based on the VAR model in levels are typically more accurate than estimates from models selected based on pretests.

  13. All of the bootstrapping results presented in this paper utilized 500 replications.

  14. Tsay’s test orders the data according to the value of the threshold variable (the lagged price differential in this case) and calculates out-of-sample recursive residuals. An F-test of linearity is given by the regression F statistic derived from regressing the recursive residuals on the ordered threshold variables.

  15. See Hornik et al. (1989) for a detailed discussion of neural networks and activation functions.

  16. A comment on nomenclature is helpful at this point. Our generalized additive vector autoregressive model is semi-parametric in that it includes additive intercept terms and parameters (the model variances) corresponding to the assumed distribution (Gaussian in our case). The remaining portions of the model, which relate the covariates to the dependent variables, are fully nonparametric in that they are represented by nonparametric splines.

  17. We utilize thin plate regression splines with penalized higher-order derivatives of the basis functions applied to a set of 50 equally spaced knot points. Details regarding our specification and estimation of the VGAM models are contained in a supplementary ”Appendix”.

  18. Interpretation of marginal effects and degrees of freedom is entirely analogous to a semi-parametric power-series expansion. Each order of the expansion uses one degree of freedom, such that the entire marginal effect is represented by p parameters (accounting for p degrees of freedom) in a pth-order expansion.

  19. Details regarding the specification and estimation of the GAM models are presented in an ”Appendix”. Yee (2015) notes that this approach is only ‘quasi-maximum likelihood’ as the error term does not have a precise parametric definition in nonparametric models. Estimation methods estimate parameters under the assumption that the likelihood function depends only on the first two moments.

  20. In strict terms, the interpretation of intercepts as average proportional price differences only holds when the price transmission elasticity is 1.0.

  21. We allow for a maximum EDF of 9. The empirical results presented below were not sensitive to allowing a higher dimension basis.

  22. These estimates are provided in an ”Appendix”.

  23. Confidence intervals on the VGAM impulses are calculated using 500 replications of size \(n=1,179\) with replacement. Impulses for each replication are generated and used to define a 90% confidence interval for the responses. Prices with and without a shock are dynamically forecasted 24 weeks into the future, and the impulse is given by the difference in forecasts. Note that the logarithmic nature of prices implies that the shocks and adjustments are equivalent to percentage changes in prices.

  24. These four firms accounted for 58% of US capacity in 2017 (Lang 2017).

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Acknowledgements

We are grateful for the helpful comments and suggestions of two anonymous reviewers and an associate editor. This research was supported through two joint venture research agreements with the US Forest Service.

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  1. North Carolina State University, Box 8109, Raleigh, NC, 27695, USA

    Barry K. Goodwin & Jeffrey P. Prestemon

  2. Virginia Polytechnic Institute, Blacksburg, VA 24061, USA

    Matthew T. Holt

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Correspondence to Barry K. Goodwin.

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Goodwin, B.K., Holt, M.T. & Prestemon, J.P. Semi-parametric models of spatial market integration. Empir Econ 61, 2335–2361 (2021). https://doi.org/10.1007/s00181-020-01985-2

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