## Abstract

If capital is perfectly mobile between regions within countries, and regional TFPs share a common stochastic trend, the ratio of regional capital–labor ratios should remain constant over time. Spatial panel data on regional capital–labor ratios in Israel are used to test this hypothesis. Since the data are nonstationary, pairwise panel cointegration tests are applied. These tests are complicated by cross-section dependence between the spatial panel units. Although the null hypothesis of perfect capital mobility is overwhelmingly rejected, rejection of long-term perfect internal capital mobility is not overwhelming.

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## Notes

By contrast, there is an empirical literature on internal labor mobility. For example, Bernard et al. (2013) find that wages are not equated within the US. However, evidence of internal labor mobility does not necessarily presage the same for internal capital mobility.

Measures of regional TFP for e.g. US states are based on regional allocations of the national capital stock as in Garofalo and Yamarik (2002), or capital is ignored as in Caliendo et al. (2014). Bernard et al. (2013) used wage bill data to overcome unobserved differences in regional labor productivity. In the absence of “capital bill” data, we rely on Eq. (6) to account for unobserved differences in capital productivity.

If TFP is trend stationary \(\hbox {lnA}_{\mathrm{it}} = \hbox {a}_{\mathrm{j}} + \hbox {b}_{\mathrm{j}}\hbox {lnA}_{{\mathrm{jt-1}}} + \hbox {c}_{\mathrm{j}}\hbox {t} + \hbox {e}_{\mathrm{it}}\) where \(0 \le \hbox {b}_{\mathrm{i}} < 1\) and \(\hbox {e}_{\mathrm{i}}\) is stationary. Hence, \(\hbox {lnA}_{\mathrm{jt}}\) – \(\hbox {lnA}_{\mathrm{it}}\) tends to \(\hbox {f}_{\mathrm{ji}}+\uptau _{\mathrm{ji}}\hbox {t} +\hbox {h}_{{\mathrm{jit}}}\) where \(f_{ji} =\frac{a_j }{1-b_j }-\frac{a_i }{1-b_i }\), \(\tau _{ji} =\frac{c_j }{1-b_j }-\frac{c_i }{1-b_i }\), and \(h_{jit} ={\mathop {\sum }\nolimits _{n=0}^\infty } {b_j^n e_{jt-n} -} {\mathop {\sum }\nolimits _{n=0}^\infty } {b_i^n} e_{it-n}\) .

Hence \(\hbox {K}_{\mathrm{it}} = [1 +(\hbox {K}_{\mathrm{Mt}}/\hbox {K}_{\mathrm{pt}})]\hbox {K}_{{\mathrm{pit}}}\) where \(\hbox {K}_{\mathrm{M}}\) and \(\hbox {K}_{\mathrm{P}}\) denote the national stocks of machinery and plant respectively. The allocation rule rescales regional capital stock data for plant. Consequently, the allocation rule has no effect on tests for \(\upmu = 1\) since \(\hbox {K}_{\mathrm{i}}\) and \(\hbox {K}_{\mathrm{j}}\) are rescaled identically.

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Beenstock, M. How internally mobile is capital?.
*Lett Spat Resour Sci* **10**, 361–374 (2017). https://doi.org/10.1007/s12076-017-0190-1

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DOI: https://doi.org/10.1007/s12076-017-0190-1

### Keywords

- Internal capital mobility
- Pairwise panel cointegration
- Cross-section dependence

### JEL Classification

- R12
- R32
- R53