Abstract
This paper investigates the polarizing effect of FDI on regional earnings in host nations. A key hypothesis is that the link between FDI and regional inequality is mediated by regional capital–labor ratios. In the absence of regional FDI data, a method for estimating the effects of FDI on regional inequality is proposed in which national FDI is hypothesized to be a common factor for regional capital investment. Empirical analysis of regional panel data for Israel shows that regional capital stocks vary directly and heterogeneously with the stock of national FDI, and that regional earnings vary directly and homogeneously with regional capital–labor ratios. These two relationships are used to calculate the contribution of FDI to regional earnings inequality over time. We find a substantial polarizing effect. Between 1988 and 2010 the variance of log regional earnings increased from about 0.011 to 0.025. More than half of this increase may be attributed to the polarizing effects of FDI. Policy implications of these findings are discussed.
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Notes
 1.
CBS: Local Authorities in Israel 2010 http://www1.cbs.gov.il/webpub/pub/text_page.html?publ=58&CYear=2010&CMonth=1.
 2.
CBS (Time SeriesDataBank): Balance Of PaymentsInternational Investment PositionAssets and Liabilities.
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Appendices
Appendix 1: Gini
The Gini counterparts to Eqs. (2), (3) and (7) are:
where \(G_{j}\) denotes the regional Gini coefficient for variable j and \(\Gamma _{ji}\) is the regional Gini correlation coefficient between variable j and variable i. Equation (1.1) assumes that the Gini correlations between k and X and \(\alpha \) and u are zero. Equation (1.3) assumes for simplicity that the variables are independent, in which case their Gini correlations are zero.
The Gini counterpart to Eq. (8) is:
As in Eq. (8) Gini varies directly with KFDI. There is a direct effect and a mitigating effect. The polarizing effect of FDI on regional wage inequality varies directly with \(\beta \), KFDI and inequality in \(\theta \), and it varies inversely with the elasticity of supply of labor as expressed by the Gini correlations between capital and labor. Equations (8) and (1.4) differ insofar as the polarizing effect of FDI does not depend on the variances of wages in the former but it varies inversely with the Gini coefficient for wages in the latter.
Appendix 2: Data
Regional aggregates are constructed using micro data for 1987–2010. Each variable is created from a different source and all data are aggregated to nine regions which form the basic spatial units of analysis (Fig. 1). Variables and their sources are as follows:

Earnings (w) Average earnings in shekels at constant 2005 prices. Source: National Insurance Institute (NII) ‘Wages and Income from Work by Locality and Various Economic Variables’.

Capital (K) Constructed out of regional data for completed construction for plant, and national data for machinery (Beenstock et al. 2011). The physical data for plant have been converted into 2005 prices. Source: Central Bureau of Statistics (CBS)^{Footnote 1}.

FDI stock (KFDI) Published annually by the CBS ($ million)^{Footnote 2} and converted into shekels at 2005 prices.

Regional demographics Population, years of schooling compiled from micro data. Source: Labor Force Survey (LFS).

Regional investment incentives Value (in constant 2005 prices) of investment grants disbursed under Law for Encouragement of Capital Incentives to firms located in preferential areas, accumulated from 1967. Source: Investment Center (annual reports).
Appendix 3: Bootstrapping
When y and x are difference stationary and cointegrated, bootstrapping is carried out in the following steps (Li and Maddala 1997):

1.
Estimate by OLS:
where the DGPs for xand u are:

2.
Construct
where \(v*\) and \(w*\) are drawn with replacement from the EDFs for w and v.

3.
Construct

4.
Estimate by OLS:

5.
Repeat steps 2–4 10,000 times.

6.
The bootstrap estimate of b is the mean of the 10,000 estimates of \(\beta \).

7.
The bootstrap confidence interval for b is based on the percentiles of the distribution function for \(\beta \).
In the case of panel data step 4 is:
where \(v*\) and \(w*\) are drawn from the pooled EDFs and \(c_{i}\) and \(e_{i}\) are heterogeneous.
Appendix 4: Trend stationarity versus difference stationarity
Time series for \(y_{it }\)are used to estimate:
If \(\gamma _{I}\) is less than one in absolute value y\(_{i}\) is trend stationary. The nested test statistic (Dickey and Fuller 1981) is:
where ESS denotes error sums of squares. If DF \(_{i}\) exceeds its critical value the null hypothesis of difference stationarity for y\(_{i}\) is rejected with p value = pv \(_{i}\). The meta statistic (Hedges and Olkin 1985) is:
If Mexceeds its critical value the null hypothesis of difference stationarity is not rejected.
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Beenstock, M., Felsenstein, D. & Rubin, Z. Does foreign direct investment polarize regional earnings? Some evidence from Israel. Lett Spat Resour Sci 10, 385–409 (2017). https://doi.org/10.1007/s120760170192z
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Keywords
 FDI
 Regional inequality
 Capital–labor ratio
 Common correlated effects estimator
 Regional earnings decomposition
JEL Classification
 C23
 R12
 R53