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The relationship between the inflation rate and inequality across U.S. states: a semiparametric approach

Abstract

This paper uses a cross-state panel for the United States over the 1976–2007 period to assess the relationship between income inequality and the inflation rate. Employing a semiparametric instrument variable (IV) estimator, we find that the relationship depends on the level of the inflation rate. A positive relationship occurs only if the states exceed a threshold level of inflation rate. Below this value, inflation rate lowers income inequality. The results suggest that a nonlinear relationship exists between income inequality and the inflation rate.

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Notes

  1. 1.

    For non-linear effect of inflation on economic growth, see Hess and Morris (1996), Barro (1996), Fischer (1993), Sarel (1996), and Kremer et al. (2013).

  2. 2.

    Please see "Appendix 1".

  3. 3.

    Leigh (2007) finds that Top 10 and 1% income shares are useful proxies for inequality across the income distribution.

  4. 4.

    See http://www.shsu.edu/eco_mwf/inequality.html. Professor Frank constructed his dataset based on the Internal Revenue Service (IRS), which has a limitation of omission of some individual earning less than a threshold level of gross income. For this reason, we focus more on top income shares as primary indicators of inequality measures.

  5. 5.

    See http://dvn.iq.harvard.edu/dvn/.

  6. 6.

    Initially, we tested semiparametirc IV regression without accounting a structural break and results showed threshold around 6 percent inflation. However as there is the structural break in the dataset, we created dummy variable. Following years and states with greater than 6 percent inflation:

    (i) From 1977 to 1981 50 states had higher inflation than 6 percent, except in 1980 Mississippi where inflation rate was below 6 percent. (ii) From 1988–1990 to 2004–2005, inflation rate in California and Hawaii were above 6 percent. The inflation rates were mostly high during the oil shock and Volcker's disinflationary periods. Since the semiparametric estimator is sensitive to outliers, we created a dummy variable that equals one when the inflation rate was less than 6 percent and zero otherwise to avoid biasing the results.

  7. 7.

    Given possible endogeneity issues, we also use the first lag of the control variables in the model—the growth rates of real per capita income, of high school attainment, of college attainment, and of the unemployment rate. Our results here are qualitatively similar to the model that does not address possible endogeneity issues.

  8. 8.

    For robustness, we also estimate threshold using the method suggested by Hansen (1999) and the results are presented in "Appendix 2". We find the results are similar to the results from the semiparametric approach.

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Corresponding author

Correspondence to Stephen M. Miller.

Additional information

We would like to thank two anonymous referees for many helpful comments. However, any remaining errors are solely ours.

Appendix

Appendix

Appendix 1

Park (2003) considers a semiparametric regression model in which the error term is correlated with the nonparametric part. Although the model cannot eliminate the nonparametric part in the two-step estimation procedure, the author can still obtain a semiparametric estimator with consistency and asymptotic normality with two existing sets of instrumental variables which meet an orthogonality conditions.

The regression model takes the form

$$g_{t} = \phi x_{t} + f\left( {\pi_{t} } \right) + \varepsilon_{t} , t = 1, \ldots ,T$$

with

$$E[\varepsilon_{t} |\pi_{t} ] \ne 0$$

The author considers a case in which an error term, \(\varepsilon_{t} \in R,\) is correlated with a nonparametric part, say \(f\left( {\pi_{t} } \right)\), where \(f\) is an unknown function from \(R^{1}\) to \(R\).

Appendix 2

See Table 3.

Table 3 Results of Hansen (1999) threshold method

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Balcilar, M., Chang, S., Gupta, R. et al. The relationship between the inflation rate and inequality across U.S. states: a semiparametric approach. Qual Quant 52, 2413–2425 (2018). https://doi.org/10.1007/s11135-017-0676-3

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Keywords

  • Income inequality
  • Inflation rate
  • Semiparametric instrumental variable estimation

JEL Classification

  • E31
  • D31
  • C14