A variable threshold band approach to measuring market linkages

Abstract

Uncertain and changing economic conditions can have substantial effects on price relationships in spatially separated, linked markets. Although numerous studies have analysed price relationships to characterize market linkage structures, most assume that the relationships and associated linkages are time invariant. This study extends the literature by modelling and estimating time-dependent market linkages that are conditional on changes in exogenous factors. The methodology is used to investigate price relationships in North Carolina (NC) corn and soya bean markets. Empirical results indicate that generalized market-linkage models provide a better representation of price relationships over time, improving the understanding of price discovery dynamics and marketing strategies.

Keywords:

• thresholds
• error-correction
• transaction costs
• integration

JEL Classificarion:

• Q11
• Q13
• D23

Notes

¹ For example, see Obstfeld and Taylor (1997); Goodwin and Holt (1999); Goodwin and Piggott (2001); Lo and Zivot (2001); Sephton (2003); Baghli (2004); Enders and Chumrusphonlert (2004).

² It is also necessary to specify some portion of the data as the initial sample. Typically, this can be 1% or 2% of the sample.

³ The minimization of the SSEs follows Balke and Fomby (1997).

⁴ This is an intuitive, heuristic approach to approximate the standard errors (SEs) in variable threshold estimation. Further research is to be focused on testing bootstrapped SE validity in variable threshold models.

⁵ The test described by Hansen (1982) assumes constant threshold bands. A rigorous theoretical and empirical analysis of the test's applicability to variable thresholds is beyond the scope of this study, but is an avenue for future research.

⁶ Although a higher degree of the Fourier approximation may be desirable, the computational complexity of the estimation procedure increases exponentially. Due to this limitation, we restrict the seasonality modelling to a single-order Fourier approximation.

⁷ Investigating linkages across commodities can be of value, but may not fit the ‘law of one price’ concept.

⁸ Less than 7% of observations were missing in any price series. Interpolated values were verified not to have created outliers or exhibit other unexpected behaviours.

⁹ Results of the ADF tests and OLS estimates of the cointegrating relationships are omitted to conserve space. These are available upon request from the authors.

¹⁰ Individual states may provide some exemptions to these rules for agricultural vehicles; however, these exemptions are typically relatively minor and do not apply to interstate transport.

¹¹ Shocking a sample's last observation is consistent with the literature; for example, see Goodwin and Piggott (2001) and Balagtas and Holt (2009). Other approaches have been implemented by Gallant et al. (1993); Potter (1995); Koop et al. (1996), in which response behaviour is estimated for all possible starting points. However, the difficulty with this approach is appropriately summarizing the response information from shocks to different historical data points. Typically, averaging is applied to the responses; however, this may result in a loss of important information. For example, averaging can smooth out discrepancies existing in various impulse responses or weaken the effects of asymmetric shocks.

¹² A one-half SD to prices is typically much larger than any shocks observed in agricultural markets, but it guarantees that a regime-switch is triggered.

¹³ Due to nonstationarity of prices as well as the error correction properties, shocks can lead to either temporary price response with a return to the price's initial time path or permanent changes to the time path. A permanent shift is likely an indication of price nonstationarity.

¹⁴ In most cases, post-shock price differences are larger. However, in instances when the initial price shock occurred in an auxiliary (not the central) market (not shown, but available upon request), these differences were smaller in the variable threshold model than in the constant band specification. This is likely due to the asymmetric response dynamics between market pairs.