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How internally mobile is capital?


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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  1. 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.

  2. 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.

  3. 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 \(h_{jit} ={\mathop {\sum }\nolimits _{n=0}^\infty } {b_j^n e_{jt-n} -} {\mathop {\sum }\nolimits _{n=0}^\infty } {b_i^n} e_{it-n}\) .

  4. 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.


  • Anselin, J.-L.: Spatial Econometrics: Methods and Models. Kluwer, Boston (1988)

    Book  Google Scholar 

  • Banerjee, A., Carrion-I-Silvestre, J.L.: Testing for panel cointegration using common correlated effects estimators. Dept of Economics, University of Birmingham. (2011, 2014)

  • Beenstock, M., Ben Zeev, N., Felsenstein, D.: Capital deepening and regional inequality: an empirical analysis. Ann. Reg. Sci. 47, 599–617 (2011)

    Article  Google Scholar 

  • Beenstock, M., Felsenstein, D.: Estimating spatial spillover in housing construction using nonstationary panel data. J. Hous. Econ. 28, 42–58 (2015)

    Article  Google Scholar 

  • Beenstock, M., Felsenstein, D.: Econometric Analysis of Nonstationary Spatial Panel Data. Springer, Berlin (2017). (forthcoming)

  • Bernard, A.B., Redding, S.J., Schott, P.K.: Testing for factor price equality with unobserved differences in factor quality and productivity. Am. Econ. J. Microecon. 5, 135–163 (2013)

    Article  Google Scholar 

  • Caliendo, L., Parro, D., Rossi-Hansberg, E., Sarte, P.-D.: The impact of regional and sectoral productivity changes on the US economy. NBER Working Paper 20168 (2014)

  • Chudik, A., Pesaran, M.H., Tosetti, E.: Weak and strong cross-section dependence and estimation of large panels. Econom. J. 14, C45–C90 (2011)

    Article  Google Scholar 

  • Garofalo, G.A., Yamarik, S.: Regional convergence: evidence from a new state-by-state capital stock series. Rev. Econ. Stat. 84, 316–323 (2002)

    Article  Google Scholar 

  • Glaeser, E.L., Gottlieb, J.D.: The wealth of cities: agglomeration economies and spatial equilibrium in the United States. J. Econ. Lit. 47, 983–1028 (2009)

    Article  Google Scholar 

  • Im, K.S., Pesaran, M.H., Shin, Y.: Testing for unit roots in heterogeneous panels. J. Econom. 115, 53–74 (2003)

    Article  Google Scholar 

  • Krugman, P.: Geography and Trade. MIT Press, Cambridge (1991)

    Google Scholar 

  • Nocco, A.: Preference, heterogeneity and economic geography. J. Reg. Sci. 49, 33–56 (2009)

    Article  Google Scholar 

  • Pedroni, P.: Critical values for cointegration tests in heterogeneous panels with multiple regressors. Oxford Bull. Econ. Stat. 61, 653–670 (1999)

    Article  Google Scholar 

  • Pedroni, P.: Panel cointegration: asymptotic and finite sample properties of pooled time series with an application to the PPP hypothesis. Econom. Theory 20, 597–625 (2004)

    Article  Google Scholar 

  • Pesaran, M.H.: A simple panel unit root test in the presence of cross section dependence. J. Appl. Econom. 22, 265–312 (2007)

    Article  Google Scholar 

  • Pesaran, M.H.: Estimation and inference in large heterogeneous panels with a multi-factor error structure. Econometrica 74, 967–1012 (2006)

    Article  Google Scholar 

  • Pesaran, M.H.: Testing weak cross-sectional dependence in large panels. Econom. Rev. 34, 1087–1117 (2015)

  • Roback, J.: Wages, rents and the quality of life. J. Polit. Econ. 90, 1257–1278 (1982)

    Article  Google Scholar 

  • Sarafides, V., Wansbeek, T.: Cross-sectional dependence in panel data analysis. Econom. Rev. 31, 483–531 (2012)

    Article  Google Scholar 

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Beenstock, M. How internally mobile is capital?. Lett Spat Resour Sci 10, 361–374 (2017).

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

JEL Classification

  • R12
  • R32
  • R53