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Spatial autocorrelation and the sensitivity of RESET: a simulation study

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Abstract

Ramsey’s regression specification error test (RESET) is thought to be robust to spatial correlation. Building on the literature on spurious spatial regression, we show that this is not so in presence of spatial correlation in both the error and the independent variable of an econometric model. Correcting the test for spatial correlation improves its performance, though in large samples this strategy is not completely successful. Once assuming that spatial autocorrelation in both the independent variable and in the error is produced by a spatial moving average model instead of a spatial autoregressive one, RESET displays more robustness.

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Notes

  1. Though it might have low power when omitted variables are linearly connected with those included in the model (see Wooldridge 2001, p. 188).

  2. RESET was used in many empirical studies in regional economics. See, for instance, Green and Hadjimatheou (1990), Bougrine (1994), Poncet (2003), Muhammed (1998), Qing and Kaiyuen (2005), Johnson and Kneebone (1991), Johnes and Hyclak (1995), Byers (1990) and Vaona and Ascari (2007).

  3. For the acronyms of the estimators we follow Le Sage (1999).

  4. Negative spatial correlation is a rather controversial issue. While positive spatial correlation arises due to the tendency of similar values of a variable to cluster together, negative spatial correlation reflects the tendency of dissimilar values to cluster together. Goodchild (1986) and Smith (2004) argue that negative spatial correlation is just the result of poorly devised spatial areal units. On the contrary, Griffith (2006) argues that negative spatial correlation might exist, but it is hidden by global positive spatial correlation and spatial filtering can detect it. Waiting that this debate settles, we focus here only on positive spatial correlation, mirroring similar studies in the time-series context (Thursby, 1979; Porter and Kashyap, 1984; Leung and Yu, 2001).

  5. Using a queen matrix of West Germany would alter marginally the number of contiguous location pairs.

  6. It could be possible to use Wald tests or Lagrange Multiplier tests instead of LR tests. Though they are generally thought to be asymptotically equivalent, in small samples they might differ. It is generally recommended to choose among these alternatives on the basis of computational ease (see for instance Poirier, 1995, p. 372 or Greene, 1993, p. 484), so we stick to LR tests.

  7. It can be showed that the F test is a monotonic transformation of a likelihood ratio test (Hayashi 2000, p. 53).

  8. Detailed results are available from the author upon request.

  9. On these issues see also Bivand (1999).

  10. This intuition is confirmed by the fact that RESET reached a size of 21% for ρ x  = 0, ρ u  = 0.99, and a rook lattice 20 × 20.

  11. Regarding the power of the test, we also checked whether it changes depending on the degree of spatial correlation in the independent variable and in the error. We focused on the SEM model, as we have showed that it is more robust to autocorrelation even in a spatial setting. Following Miles and Mora (2003), who performed a similar analysis for nonparametric misspecification testing, we generated 200 samples from the model \( y_{i} = 0.5x_{i} + cx_{i}^{2} + u_{i} \) with c = [−0.9; −0.7; −0.5; −0.3; 0.3; 0.5; 0.7; 0.9], after generating x i and u i according to Eqs. 3 and 4 first with ρ x  = ρ u  = [0.5; 0.7; 0.9; 0.95] and then with ρ x  = 0 and ρ u  = [0.5; 0.7; 0.9; 0.95]. We chose these values of ρ x and ρ u to see if high spatial correlation either in the error and in the independent variable or only in the error affects the power of the test. Using the spatial correlation matrix of West Germany, our samples had 326 observations. We implemented both RESET and TS-RESET and tested the null hypothesis δ 0 = 0. We always obtained a rejection frequency of 100%.

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Acknowledgments

I would like to thank Lucio Regaiolo, Roberto Patuelli, Eckhardt Bode, Antonio Páez and three anonymous referees for helpful comments. Roberto also provided me with the spatial contiguity matrix of West German NUTS-3 regions.

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  1. Department of Economic Sciences, Palazzina 32 Scienze Economiche-ex Caserma Passalacqua, University of Verona, Viale dell’Università, 4, 37129, Verona, Italy

    Andrea Vaona

  2. Kiel Institute for the World Economy, Kiel, Germany

    Andrea Vaona

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Vaona, A. Spatial autocorrelation and the sensitivity of RESET: a simulation study. J Geogr Syst 12, 89–103 (2010). https://doi.org/10.1007/s10109-009-0093-9

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