The Effect of Labor’s Bargaining Power on Wealth Inequality in the UK, USA, and France

Introduction

• This paper analyzes the determinants of wealth inequality, focusing on the causal role of labor's bargaining power.
• The study examines the UK, USA, and France, noting similar trajectories in the top 1% share of wealth, with the USA experiencing the sharpest increase in inequality since the 1980s.
• Institutional and structural changes have impacted labor's bargaining power, with union density decreasing substantially since the 1980s in all three countries, except France.

Literature Review and Gaps

• Existing literature analyzes labor's bargaining power and its impact on personal income inequality, wage inequality, and the labor share of income.
• This paper addresses two main gaps in the literature concerning wealth inequality:
  • Underdeveloped econometric analysis on the determinants of wealth inequality.
  • Lack of exploration of the link between labor's bargaining power and wealth inequality.

Theoretical Framework

• The paper presents a theoretical analysis of the channels through which labor's bargaining power impacts wealth inequality.
• It uses a semi-structural vector autoregression analysis with data from the UK, the USA, and France for the period 1970–2019.
• The study identifies the effects of shocks to labor's bargaining on the top 1% share of wealth across the three countries.
• A short-run restrictions are used, assuming that indicators capturing bargaining power are contemporaneously exogenous to wealth inequality.
  • The justifaction is that the political influence of the top 1% on labor institutions takes time to materialize.

Findings

• A positive shock to the bargaining power of labor significantly reduces top 1% wealth shares across all three countries.
  • Shocks to labor's bargaining power explain 32% of the variation in top wealth shares in the UK, 8% in the USA, and 32% in France.
  • The smaller proportion of variation explained in the USA is attributed to the higher volatility of wealth inequality.
• The theoretical overview of the components of wealth inequality and how they are impacted by labor's bargaining power are presented in Section 2.
• Data and estimation methodology in Sections 3 and 4.
• Estimation results and conclusions in Sections 5 and 6.

Components of Wealth Inequality

• Wealth $W_{t}^{f}$ of fractile $f$ (e.g., top 1% wealthiest households) in period $t$ is given by:

  • $(1) \ W<em>{t}^{f} = W</em>{t-1}^{f}(1 + q<em>{t}^{f}) + s</em>{t}^{f}Y<em>{t}^{f} + h</em>{t}^{f}$
  • $q_{t}^{f}$: return on wealth due to capital gains.
  • $Y_{t}^{f}$: pre-tax personal income.
  • $s_{t}^{f}$: saving rate.
  • $h_{t}^{f}$: net inheritances, gifts, and inter vivos transfers.

• The capital gains component ($q_{t}^{f}$) is a weighted change in the price of assets in a portfolio:

  • $(2) \ q<em>{t}^{f} = \sum</em>{j=1}^{J} (\frac{P<em>{j,t} - P</em>{j,t-1}}{P<em>{j,t-1}}) \frac{A</em>{j,t-1}^{f}}{W_{t-1}^{f}}$
  • $A_{j,t}^{f}$: asset $j$ held by fractile $f$ in period $t$.

• Simplifying assumptions:

  • There are only two assets: equities and housing.
  • The composition of assets held by fractile $f$ changes in line with the population.
  • Top 1% capital gains approximate capital gains of stocks; aggregate capital gains approximate capital gains on housing.

• From these assumptions:

  • $(3) \ q<em>{t}^{f} \approx (\frac{P</em>{\text{stocks},t} - P<em>{\text{stocks},t-1}}{P</em>{\text{stocks},t-1}})$
  • $(4) \ q<em>{t} \approx (\frac{P</em>{\text{housing},t} - P<em>{\text{housing},t-1}}{P</em>{\text{housing},t-1}})$

• Integrating inheritance and income taxes:

  • $(5) \ s<em>{t}^{f} = s</em>{\text{post},t}^{f} - T_{y}^{f}$
  • $s_{\text{post},t}^{f}$: saving rate out of post-tax income.
  • $T_{y}^{f}$: average income tax rate.
  • $(6) \ h<em>{t}^{f} = h</em>{\text{post},t}^{f}(1 - T_{h}^{f})$
  • $h_{\text{post},t}^{f}$: post-tax net transfers.
  • $T_{h}^{f}$: average inheritance tax rate.

• The law of motion for top wealth shares:

  • $(7) \ \frac{W<em>{t}^{f}}{W</em>{t}} = \frac{(1 + q<em>{t}^{f}) \frac{W</em>{t-1}^{f}}{W<em>{t-1}} + s</em>{t}^{f} \frac{Y<em>{t}^{f}}{Y</em>{t}} \frac{Y<em>{t}}{W</em>{t-1}} + \frac{h<em>{t}^{f}}{W</em>{t-1}}}{1 + q<em>{t} + s</em>{t}\frac{Y<em>{t}}{W</em>{t-1}} + \frac{h<em>{t}}{W</em>{t-1}}}$

• Focus on four main factors:

  • Differential capital gains ($q<em>{t}^{f} - q</em>{t}$).
  • Share of personal income going to the top 1% ($\frac{Y<em>{t}^{f}}{Y</em>{t}}$).
  • Differential saving rates ($s<em>{t}^{f} - s</em>{t}$).
  • Top 1% net inheritance, transfer and inter vivos flows as a ratio to aggregate wealth ($\frac{h<em>{t}^{f}}{W</em>{t-1}}$).

Impact of Labor Bargaining Power

• A positive shock to labor's bargaining power impacts the top 1% share of income via:

  • Wage inequality and top managerial pay: higher trade union density reduces top managerial pay.
  • Decreasing the capital share of income: redistributes income from capital to labor.

• A positive labor bargaining shock impacts differential capital gains via:

  • Negative impact on stock prices: unionization negatively impacts stock prices.
  • Increase in house prices: labor market insecurity impacts homeownership.

• Impact of a positive labor bargaining shock on differential saving rates is ambiguous due to:

  • Change in relative precautionary saving motives between the top 1% and the bottom 99%.
  • Change in the distribution of income between the two groups.

• A positive labor bargaining shock reduces inheritance flows to the top 1% via a political channel.

• Technological change and globalization also influence these components of wealth inequality.

Data

• Data sources:
  • World Inequality Database (WID) for top 1% of individuals and the share of pre-tax national income of the top 1% of the income distribution.
  • Macro History Database (Jordà et al. 2019) for differential capital gains.
  • EU KLEMS for technological change.
  • KOF de jure measures of financial and trade globalization.
  • WID for progressive taxation.
• Measures of labor’s bargaining power:
  • Trade union density in the UK and USA.
  • Collective bargaining coverage in France.

Estimation Methodology

• Empirical methodology estimates the impact of a labor bargaining shock on wealth inequality using a semi-structural VAR model for each country.

• Short-run restrictions are imposed via a Cholesky Decomposition.

• Key assumption: trade union density and collective bargaining coverage are contemporaneously exogenous to wealth inequality and its components.

  • The justification is that the reverse causality happens with a lag.

• The data generating process is defined according to the following structural equation:

  • $(8) \ B<em>{0}y</em>{t} = B<em>{1} + B</em>{2}y<em>{t-1} + B</em>{3}y<em>{t-2} + u</em>{t}$
  • $y_{t}$ is a $K \times 1$ vector of a set of determinants;
  • $B_{i}$ are the model coefficients, $i = 0, \dots, p$
  • $u_{t}$ is a $K \times 1$ vector of structural shocks.

• Testing for non-fundamentalness and ensuring informational sufficiency of the labor bargaining shock.

• Structural impulse response functions (IRF) and forecast error variance decompositions (FEVD) are presented.

• Estimating the SVAR models in levels with an intercept.

• Confidence interval bands are used to determine the significance, using conventional residual-based bootstrap confidence intervals

Estimation Results

• Labor bargaining shocks are significant across all three countries after 11 years: it explains 32% and 32% of variation in UK and France.
• The magnitude of the effects in the UK and France are almost identical.
• In the USA, labor bargaining shocks explain only 8% of the variation in top wealth shares after 11 years.
• A 1 percent-point increase in union density leads to a 0.29 percent-point and 0.32 percent-point decline in top wealth shares after 8 years in the UK and the USA, respectively.
• In France, a 1 percent-point increase in collective bargaining coverage leads to a 0.38 percent decline by the 8th year, and a bigger drop in the short run.
• Difference in the US due to higher volatility of wealth inequality.
• FEVD in Table 2 shows that bargaining shocks explain the same amount of variation in income inequality across all three countries.

Robustness Tests

• Reordering union density/collective bargaining coverage with respect to the control variables.
• Reducing the size of the system, dropping the least significant variable first.
• Replacing the de jure measure of financial globalization with a de jure measure of trade globalization.
• Replacing top inheritance tax rates with top income tax rates.
• Extending the dataset to estimate the model for the period of 1970–2019 rather than 1970 to 2015.
• Results are robust to alternative orderings, system sizes, and control variables.

Conclusion

• The bargaining power of labor is a significant and robust determinant of the top 1% wealth share across all the countries.
• A positive bargaining shock associated with a 1 percent-point increase in union density in the UK and USA leads to a 0.25 percent-point and 0.36 percent-point decline in top wealth shares after 10 years.
• A positive shock associated with a 1 percent-point increase in collective bargaining coverage in France leads to a much bigger drop in top wealth shares in the short run.
• After 11 years, labor’s bargaining power explains 32%, 8%, and 32% of the variation in top wealth shares in the UK, the USA, and France, respectively.