Differential Tariffs and Income Inequality in the United States: Some Evidence from the States

Abstract

This paper explores the macroeconomic and distributional consequences of consumption tariffs and materials tariffs. It highlights the contrasting effects of consumption and raw materials tariffs on the dynamics of key measures of aggregate economic activity and inequality. We perform empirical estimation of these effects using a panel of annual data that spans the U.S. states over the period 1980–2015. We find that consumption tariff increases lead to statistically significant reductions in income inequality, while having contractionary effects on domestic output in the short term. Materials tariff increases also have a negative impact on economic activity while increasing income inequality. Our empirical results are robust to different model specifications and measures of income inequality, consistent with the predictions of the underlying theoretical model. This work shows the importance of disaggregating tariffs when studying the distributional effects of trade policy.

Appendices

Appendix 1 provides some of the details supporting the results reported in the text

1.1 Properties of transitional matrix

The local transitional dynamics of the aggregate economy summarized by Eqs. (12a)-(12c) is of the form:

$$ \left(\begin{array}{c}\dot{K}\\ {}\dot{L}\end{array}\right)=\left(\begin{array}{cc}{a}_{11}& {a}_{12}\\ {}\Omega \left(\kappa {a}_{11}+{b}_1\right)& \Omega \left(\kappa {a}_{21}+{b}_2\right)\end{array}\right)\left(\begin{array}{c}K-\tilde{K}\\ {}L-\tilde{L}\end{array}\right) $$

(35)

where ${\displaystyle \begin{array}{l}{a}_{11}={F}_K-\delta -\lambda {F}_{LK}\left(1-L\right)-\lambda {F}_{Lm}\left(1-L\right){m}_K+\left({F}_m-1\right){m}_K;\\ {}{a}_{12}={F}_L-\lambda \left[{F}_{LL}\left(1-L\right)-{F}_L\right]-\lambda {F}_{Lm}\left(1-L\right){m}_L+\left({F}_m-1\right){m}_L\end{array}}$

$$ {\displaystyle \begin{array}{l}\Omega \equiv {\left\{\frac{\left(1-\gamma \right)}{\left(1-L\right)}\left[\frac{\alpha +\beta L}{\left(\alpha +\beta \right)}\right]-\frac{\gamma \eta L}{1-L}\right\}}^{-1}>0;\kappa =\left(1-\gamma \right)\left(\frac{\alpha }{\alpha +\beta}\right)\frac{1}{K}>0;\kern0.48em \\ {}{b}_1=-{F}_{KK}-{F}_{Km}{m}_K;\kern0.48em {b}_2=-{F}_{KL}-{F}_{Km}{m}_L\end{array}} $$

and for notational convenience, λ ≡ (1 + τ_cθ)/[η(1 + τ_c)]. Using the fact that the underlying production function is Cobb-Douglas, the relevant partial derivatives may be expressed as

$$ {\displaystyle \begin{array}{l}{F}_L=\beta \frac{F}{L},{F}_{KL}=\alpha \beta \frac{F}{LK},{F}_{mK}=\alpha \left(1-\alpha -\beta \right)\frac{F}{mK},{F}_{mL}=\beta \left(1-\alpha -\beta \right)\frac{F}{mL}\\ {}{m}_K=\left(\frac{\alpha }{\alpha +\beta}\right)\frac{m}{K},{m}_L=\left(\frac{\beta }{\alpha +\beta}\right)\frac{m}{L}\end{array}} $$

Substituting these expressions and using the steady-state relationships (15b)-(15d), the expressions may be simplified as follows:

$$ {\displaystyle \begin{array}{c}{a}_{11}=-\frac{\beta }{\alpha +\beta}\delta <0;{a}_{12}=\beta \frac{F}{L}\left(1+\lambda \left(\frac{\alpha +\beta L}{L\left(\alpha +\beta \right)}\right)\right)+{\tau}_m{m}_L>0\\ {}{b}_1=-\alpha \left(\alpha -1\right)\frac{F}{K^2}-\alpha \left(1-\alpha -\beta \right)\frac{F}{K^2}\left(\frac{\alpha }{\alpha +\beta}\right)=\frac{F}{K^2}\left(\frac{\alpha \beta}{\alpha +\beta}\right)>0\\ {}{b}_2=-\alpha \beta \frac{F}{KL}-\alpha \left(1-\alpha -\beta \right)\frac{F}{KL}\left(\frac{\beta }{\alpha +\beta}\right)=-\frac{F}{KL}\left(\frac{\alpha \beta}{\alpha +\beta}\right)<0\end{array}} $$

We immediately see that the determinant of the transitional matrix: Ω(a₁₁b₂ − a₂₁b₁) < 0, implying that the aggregate transitional dynamic path, summarized by the relationship between L(t) and K(t) is a saddlepoint, the stable path of which is described by

$$ L(t)-\tilde{L}=\left(\frac{\mu -{a}_{11}}{a_{12}}\right)\left(K(t)-\tilde{K}\right) $$

(36)

With a₁₂ > 0, the slope of the relationship (36) depends upon sgn(μ − a₁₁). To determine this we first solve for the stable eigenvalue, μ < 0, in terms of its trace, T, and its determinant, Δ: $\mu =\frac{1}{2}\left(T-\sqrt{T^2-4\Delta}\right)$

Using this expression it is straightforward to show that μ − a₁₁ < 0 if and only if (κa₁₁ + b₁) > 0. Using the above to evaluate this expression, we see that

$$ \left(\kappa {a}_{11}+{b}_1\right)>0\kern1em \mathrm{if}\kern0.5mm \mathrm{and}\kern0.5mm \mathrm{only}\kern0.5mm \mathrm{if}\kern1.50em \varepsilon >\left(\frac{\delta }{\delta +\rho}\right)\left(\frac{\alpha }{\alpha +\beta}\right) $$

(37)

where ε ≡ (1 − γ)⁻¹ is the intertemporal elasticity of substitution. Clearly (37) is a very mild restriction.

1.2 Long-run Effects of Tariff Rates

To derive the long-run effects of tariffs rates we take the differentials of (15):

$$ \left(\begin{array}{cccc}1& -\alpha & -\beta & -\left(1-\alpha -\beta \right)\\ {}\frac{m+\delta K}{Y-m-\delta K}& \frac{-\delta K}{Y-m-\delta K}& \frac{1}{1-L}& \frac{-m}{Y-m-\delta K}\\ {}1& -1& 0& 0\\ {}1& 0& 0& -1\end{array}\right)\left(\begin{array}{c}d\hat{Y}\\ {}d\hat{K}\\ {}d\hat{L}\\ {}d\hat{m}\end{array}\right)=\left(\begin{array}{c}0\\ {}\frac{\left(\theta -1\right)}{\left(1+{\tau}_c\right)\left(1+{\theta \tau}_c\right)}d{\tau}_c\\ {}0\\ {}\frac{1}{1+{\tau}_m}d{\tau}_m\end{array}\right) $$

(38)

In the case of the consumption tariff, the following expressions (^ denotes proportionate changes) are obtained:

$$ \frac{d\hat{\tilde{Y}}}{d{\tau}_c}=\frac{d\hat{\tilde{K}}}{d{\tau}_c}=\frac{d\hat{\tilde{L}}}{d{\tau}_c}=\frac{d\hat{\tilde{m}}}{d{\tau}_c}=-\frac{\left(1-\theta \right)\left(1-\tilde{L}\right)}{\left(1+{\tau}_c\right)\left(1+{\theta \tau}_c\right)}<0 $$

(39)

Applying these changes to (16), we show further

$$ \frac{d\hat{\tilde{x}}}{d{\tau}_c}=\frac{d\hat{\tilde{C}}}{d{\tau}_c}=\frac{d\hat{\tilde{l}}}{d{\tau}_c}=\frac{\left(1-\theta \right)\tilde{L}}{\left(1+{\tau}_c\right)\left(1+{\theta \tau}_c\right)}>0 $$

(40)

$$ \frac{d\hat{\tilde{y}}}{d{\tau}_c}=\frac{\left(\hat{L}-1\right)-\theta \left(L+{\tau}_c\right)}{\left(1+{\tau}_c\right)\left(1+{\theta \tau}_c\right)}<0 $$

(41)

The corresponding effects of the tariff on imported inputs are:

$$ \frac{d\hat{\tilde{Y}}}{d{\tau}_m}=\frac{d\hat{\tilde{K}}}{d{\tau}_m}=-\frac{\tilde{m}}{\left(1+{\tau}_m\right)}\left(\frac{\left(1-\tilde{L}\right)}{\tilde{Y}-\tilde{m}-\delta \tilde{K}}+\frac{\left(1+{\tau}_m\right)}{\beta \tilde{Y}}\right)<0 $$

(42)

$$ \frac{d\hat{\tilde{L}}}{d{\tau}_m}=-\frac{\left(1-\tilde{L}\right)}{\left(1+{\tau}_m\right)}\frac{\tilde{m}}{\left(\tilde{Y}-\tilde{m}-\delta \tilde{K}\right)}<0 $$

(43)

$$ \frac{d\hat{\tilde{m}}}{d{\tau}_m}=-\frac{1}{\left(1+{\tau}_m\right)}\left(\frac{\tilde{m}\left(1-\tilde{L}\right)}{\tilde{Y}-\tilde{m}-\delta \tilde{K}}+\frac{1-\alpha }{\beta}\right)<0 $$

(44)

From these one can derive:

$$ \frac{d\hat{\tilde{x}}}{d{\tau}_m}=\frac{d\hat{\tilde{y}}}{d{\tau}_m}=\frac{d\hat{\tilde{C}}}{d{\tau}_m}=-\frac{\tilde{m}}{\left(1+{\tau}_m\right)}\left[-\frac{\tilde{L}}{\tilde{Y}-\tilde{m}-\delta \tilde{K}}+\frac{1+{\tau}_m}{\beta \tilde{Y}}\right] $$

(45)

$$ \frac{d\hat{\tilde{l}}}{d{\tau}_m}=-\frac{\tilde{L}}{1-\tilde{L}}\frac{d\hat{\tilde{L}}}{d{\tau}_m}=\frac{\tilde{L}}{\left(1+{\tau}_m\right)}\frac{\tilde{m}}{\left(\tilde{Y}-\tilde{m}-\delta \tilde{K}\right)}>0 $$

(46)

1.3 Derivation of condition (17)

Recalling steady-state condition (15b) and using the homogeneity of the production function, we obtain

$$ {F}_K\tilde{K}+{F}_L\tilde{L}+{F}_m\tilde{m}-\tilde{m}-\delta \tilde{K}=\left(\frac{1+{\tau}_c\theta }{1+{\tau}_c}\right)\frac{1}{\eta }{F}_L\left(1-\tilde{L}\right) $$

Using the equilibrium optimality conditions (15c) and (15d) then yields

$$ \rho \tilde{K}+{\tau}_m\tilde{m}+{F}_L\tilde{L}-\left(\frac{1+{\tau}_c\theta }{1+{\tau}_c}\right)\frac{1}{\eta }{F}_L\left(1-\tilde{L}\right)=0 $$

Which we may then rewrite as

$$ \rho \tilde{K}+{\tau}_m\tilde{m}+\left(\frac{\tau_c\left(1-\theta \right)}{1+{\tau}_c}\right)\frac{1}{\eta }{F}_L\left(1-\tilde{L}\right)+{F}_L\left(\tilde{L}-\frac{1}{\eta}\left(1-\tilde{L}\right)\right)=0 $$

from which we immediately infer the restrictions

$$ \tilde{L}<\frac{1}{1+\eta}\kern1.25em \mathrm{or}\ \mathrm{equivalently}\kern1em \tilde{l}>\frac{\eta }{1+\eta } $$

(47)

Appendix 2

1.1 Data

Tariffs. The tariff rate data provided by the WDI correspond to the weighted mean applied tariff of effectively applied rates weighted by the product import shares corresponding to each partner country. This estimate is computed using data classified according to the Harmonized System of trade at the six- or eight-digit level. The IMF computes data on tariff by means of the average of the effective rate (ratio of tariff revenue to import value) and of the average unweighted tariff rates. From the USITC, we obtain a tariff rate on consumption that is computed as the ratio of duties collected to total imports.

Inequality. This measure is constructed for the U.S. as well as for each state by Mark W. Frank and extended beyond his own study and is publicly available from his website at: http://www.shsu.edu/eco_mwf/inequality.html Frank constructs the Gini coefficient from tax data reported in Statistics of Income published by the Internal Revenue Service (IRS). For the construction method, see Frank (2009).

Macroeconomic variables. Other variables are retrieved from the Bureau of Economic Analysis (BEA).