Statistical power of intervention analyses: simulation and empirical application to treated lumber prices

Timber product markets are subject to large shocks deriving from natural disturbances and policy shifts. Statistical modeling of shocks is often done to assess their economic importance. In this article, I simulate the statistical power of univariate and bivariate methods of shock detection using time series intervention models. Simulations show that bivariate methods are several times more statistically powerful than univariate methods when underlying series are nonstationary and potentially involved in cointegrating relationships. In an empirical application to detect the long-run price impacts of the voluntary phase-out of chromated copper arsenate in pressure-treating southern pine lumber for residential applications, I find the multivariate methods to be more powerful as well. I identify highly significant long-run price increases of 11% for two of three treated southern pine dimension lumber price series evaluated using multivariate approaches. The univariate method detected a long-run increase only for the third product, and the statistical significance was weak, although comparable, in magnitude to the first two products. FOR . S CI. 55(1):48-63. C OMMODITY MARKETS are regularly affected by changes in regulations and technology shifts, which result in alterations of production and consumption. Resulting supply and demand movements affect prices, profits, and consumer welfare. An example of a demand shift in the building sector is the movement away from traditional solidwood products because of their increasing prices relative to available substitutes, a result of technology advances and government timber harvest policy changes (Eastin et al. 2001, Shook and Eastin 2001). A recent example of a regulatory shift in the US forest product sector is the voluntary phase-out of the wood preservative chro- mated copper arsenate (CCA) and its replacement by alter- native treatments (especially alkaline copper quaternary (ACQ)) by treated lumber processors as a result of an agreement with the Environmental Protection Agency. Although regulatory changes may have large economic impacts, the temporal dynamics of the resulting price and production shifts are not as well understood. Accurate as- sessments of the price and quantity effects of regulatory changes may help lawmakers and agency administrators more accurately compare the costs and benefits of the changes. Such assessments can provide all parties with a scientific benchmark for negotiations regarding economic injuries suffered after such a policy change. Identification of the effects of market shocks can proceed using alternative approaches, but the statistical power (rates of correct hypothesis rejections) of competing approaches has not been subject to systematic evaluation. Intervention models (e.g., Enders 1995) exploit the time series properties of a variable or variables and intuition about the timing of changes in their data generation processes to quantify the effects of shocks. Univariate intervention modeling ap- proaches include those by Holmes (1991), who examined the timber market effects of a southern pine beetle outbreak in Louisiana and Texas, and Yin and Newman (1999), who modeled timber prices in South Carolina after Hurricane Hugo. A bivariate example is Prestemon and Holmes (2000), who also modeled the timber price impacts of Hur- ricane Hugo. In the bivariate example, positive long-run price effects were identified, whereas none were identified in the univariate example. In identifying the existence of a relatively small shock in a time series process, modeling the difference of two vari- ables that share a common trend but not the hypothesized shock could be statistically more powerful than other meth- ods. The added power available from the paired time series, compared with the power of a univariate method, could emanate from a co-relation that is "less noisy" than the process of the shocked individual series alone. The contrast- ing findings regarding timber prices after Hurricane Hugo, for example, might be related to power differences of the intervention models used. In this article, I evaluate the relative statistical power and size of competing univariate and bivariate intervention methods to identify a permanent shift in level in a data generation process. I use simulation methods to measure the power of the univariate method and the bivariate method and compare them. The primary objective of the Monte Carlo simulations is to identify the circumstances in which a permanent shock to a simulated time series is best detected using a bivariate approach and under which circumstances it is best detected using a univariate approach. In an empirical application, I compare the results of univariate, bivariate, and trivariate intervention methods in detecting long-run price shifts for three treated southern pine (especially Pinus