Exporting Spatial Externalities

Abstract

Using spatial econometrics, we estimate the effect of externalities generated by neighbors’ exports on place-level exports, explicitly modeling the distance to those neighbors. We find there is a positive effect of neighbors’ exports on exports to the same country but less so for exporting generally. We also find that using a spatial-weights term based on the physical distance between exporters greatly outperforms a dichotomous measure based on exporters in the same region. The results are robust to alternative definitions of the spatial weight.

Appendices

Appendix 1: Robustness to Alternative Distance Decay Functions

The spatial weights matrix depends on the distance decay function as that acts to describe how far away a neighbor is economically. Though there is no standard method for determining which distance decay function is most appropriate, the literature does give ideas about what features a distance decay function should have. Kerr and Kominers (2012) provide a micro-founded theory of information exchange on continuous distances that applies directly to the geographic externalities we are considering. They show how distance and information are related in that there should be more weight on neighbors that are geographically closer than those further away. They go on to show that the distance decay should be increasingly large. Two main classes of distance decay functions satisfy those requirements: exponential and inverse decay.

We follow the approach of Bode et al. (2012) and use the exponential decay function e ^{− τd ℓm} with τ = 0.020 in our main results. Table 6 and 7 show that our results are not sensitive to varying τ. We vary τ to be 0.015 and 0.025. These seemingly small changes to τ represent economically large differences. For τ = 0.020, 36.8 % of exports located 50 km away contribute to the spatial weight whereas it is 47.2 % for τ = 0.015 and only 28.7 % for τ = 0.025.

Table 6 Fixed effects results: inverse exponential distance weights, ${e}^{-0.015\times {d}_{\ell m}}$

Table 7 Fixed effects results: inverse exponential distance weights, ${e}^{-0.025\times {d}_{\ell m}}$

The first two columns in Tables 6 and 7 are unaffected since τ is not used in the construction of the simple lag. Going from small to large τ increases the rate of decay. Importantly, we find the specifications with same country and third country spatial lags outperform the simple lag specification regardless of τ, which is our main point. Also importantly, we find that our coefficient estimates on the same country and third country lag are quantitatively similar and qualitatively the same. It is interesting to see, however, that as the rate of decay increases, the coefficient on the log of distance from the export location to the destination better matches the literature by being statistically significant and negative. This is because as the exports of neighbors receive more weight, their influence on the location decision of exports becomes increasingly important over features about the market such as distance away.

Compared to inverse decay d _ℓm  ^− η exponential decay caps the weight at one for neighbors in the exact same location whereas the inverse decay function gives unlimited weight. Furthermore, the exponential decay function gives more weight to those neighbors that are relatively close and within 100 or so kilometers, depending on the parameters. Conversely, the inverse decay function greatly discounts the information from neighbors that are close in favor for increased relative weight for the very furthest neighbors. It is for these reasons that we prefer an exponential decay specification. Nonetheless we provide results for three specifications of inverse decay, for η: 1, 2, and 0.5.

The results using an inverse decay function qualitatively match those using an exponential decay function. Our result on the economic and statistical significance of the same country lag term over the third country lag term remains, as does the better performance of specifications with lags compared to those without a lag or the simple lag. We replicate our results from the exponential lag that as distance decay increases and the weight given to neighbors’ actions decreases, the distance from the location to the destination regains its economic and statistical importance.

Results in columns in tables 8, 9 and 10 using different distance decay functions and different estimators show robustness: there is very little variation in the size of the coefficients. The one exception is the third country lag in the Poisson model where it becomes insignificant or significant at the ten percent level. The large standard error, however, indicates this is more of an issue of convergence in a nonlinear model with many fixed effects.

Table 8 Inverse distance weights, ${d}_{\ell m}^{-1}$

Table 9 Squad inverse distance weights, ${d}_{\ell m}^{-2}$

Table 10 Inverse square root of distance weights ${d}_{\ell m}^{-{\scriptscriptstyle \frac{1}{2}}}$

Appendix 2: Poisson Results

We repeat our fixed effects regressions using the Poisson estimator and robust standard errors following the set up of Sellner et al. (2013). Results are shown in Table 11. All spatial lag variables continue to have positive and highly statistically significant coefficients. Our estimated coefficients in Table 11 are attenuated compared to those in Table 2 by about one third. As both the spatial lag of exports to the same and to other destinations attenuate, their relative importance remains about the same.

Table 11 Poisson fixed effects results: inverse exponential distance, ${e}^{-0.020\times {d}_{\ell m}}$

To interpret the coefficients, as before we multiply the coefficients by the median lags in Table 1. The estimates from specification (5) imply that a 1 % increase in the median of the sum of distance-weighted neighbors exports to the same country causes a 0.093 % increase on own-exports and a 1 % increase in the median of the sum of distance-weighted neighbors exports to third countries causes a 0.002 % increase. Again, the Akaike and Bayesian information criteria favor the specification with both lags included over any other specification. Thus we continue to find support for export externalities to both same country and generally, and in the same relative strength.