Banking crises in the US: the response of top income shares in a historical perspective

Abstract

This paper examines the response of income concentration in the US to the occurrence of major systemic banking crises since the beginning of the twentieth century. In doing so, the paper analyzes the shape of the upper income tail as well as the national income shares accruing to different groups within the richest decile. The findings suggest that systemic banking crises reduce income concentration within the top decile of the US pre–tax and transfers income distribution, and more generally, that the effect is highly heterogeneous across different top income groups. While the richest income group loses ground, the lower half of the top decile appears to gain in relative terms. However, evidence suggests that the estimated short-term effect of market forces stemming from banking crises can be relatively small in magnitude and even temporary in nature, as it may be quickly reabsorbed. These findings lend indirect support to the idea that only substantial changes in government policies and institutional frameworks can bring about radical changes in income distribution.

Appendices

Appendix A: Methods and data

1.1 Detailed derivation of the impulse response functions

As described in the text, for every income group i under investigation, I define the information set at time t as $\boldsymbol {\digamma }_{T}=\{{g^{i}_{t}}, X_{t}, BC_{t}\}$ for every t = (T, T − 1, T − 2, ...). I also define the set of ‘crisis off’ values as $\boldsymbol {{\Theta }}^{0}_{T+s}=\{B{C^{0}_{T}}= 0,BC^{0}_{T + 1}= 0,..., BC^{0}_{T+s}= 0\}$, assuming that the banking crisis lasts for s + 1 years and begins at year T, where s = (0, 1, ... , S). I recall that the total impact of crisis on the inequality indicator under investigation ($I_{T+h}^{G}$) can be written as follows:

$$ I_{T+h}^{G}=g^{i}_{T+h} - E\{g^{i}_{T+h}/\boldsymbol{\digamma}_{T},\boldsymbol{{\Theta}}^{0}_{T+h}\} \text{,} $$

(5)

where $g^{i}_{T+h}$ is the actual growth rate of the inequality indicator¹ under analysis and $E\{g^{i}_{T+h}/\boldsymbol {\digamma }_{T},\boldsymbol {{\Theta }}^{0}_{T+h}\}$ represents the objective of the estimation, namely the value of the growth rate of the inequality index under the condition of no crisis, which depends on the empirical specification. One can rewrite model (1) as follows:²

$$ g^{i}_{i,t}=\left( 1-\theta_{i} L\right)^{-1}\left[\sum\limits_{k = 0}^{4}\phi_{i,k}BC_{t-k} + \rho_{i}^{\prime}X_{i,t} + u_{i,t}\right] \text{.} $$

(6)

and

$$ g^{i}_{i,t}=\sum\limits_{k = 0}^{4}\sum\limits_{j = 0}^{\infty}\phi_{i,k}\theta^{j}_{i,1} BC_{t-k-j} + \sum\limits_{j = 0}^{\infty}{\theta^{j}_{i}}\rho_{i}^{\prime}X_{i,t-j} + \sum\limits_{j = 0}^{\infty}{\theta^{j}_{i}} u_{i,t-j} \text{.} $$

(7)

The counterfactual can now be subtracted from $g^{i}_{i,t}$ in order to obtain the realization of the IRF at the h’th period following the shock.

$$\begin{array}{@{}rcl@{}} \displaystyle I^{G}_{T+h}&=& \sum\limits_{k = 0}^{4}\sum\limits_{j=k}^{h+k}\phi_{i,k}\theta^{j-k}_{i,1} + \displaystyle \sum\limits_{j = 0}^{h}\theta^{j}_{i,1}\rho_{i}^{\prime}X_{i,T+h-j} - {E^{0}_{T}}\left\{\sum\limits_{j = 0}^{h}{\theta^{j}_{i}}\rho_{i}^{\prime}X_{i,T+h-j} \right\} \\ &&+\displaystyle \sum\limits_{j = 0}^{h}{\theta^{j}_{i}}u_{i,T+h-j} - {E^{0}_{T}}\left\{\sum\limits_{j = 0}^{h}{\theta^{j}_{i}}u_{i,T+h-j}\right\} \text{.} \end{array} $$

(8)

It is clear that one can ignore the last two terms only by assuming that the error term, the convariates and the whole set of parameters do not change with the occurrence of the crisis. Under these strict invariance assumptions, one obtains the following formula:

$$I^{G}_{T+h}= \sum\limits_{k = 0}^{4}\sum\limits_{j=k}^{h+k}\phi_{i,k}\theta^{j-k}_{i,1} $$

Under the invariance assumptions described above, the derivation of the realizations of the impulse response functions (IRFs) is straightforward.

As an illustration, I derive the first three realizations for the growth rate (this justifies the superscript G) of the inequality index under investigation for a specific income group i:

$$ I^{G}_{i,0}=\phi_{i,0} $$

(9)

$$ I^{G}_{i,1}=\phi_{i,0}\theta_{i} +\phi_{i,1} $$

(10)

$$ I^{G}_{i,2}=\phi_{i,2}+ \theta_{i}(\phi_{i,0}\theta_{i} +\phi_{i,1}) $$

(11)

By cumulating those responses over time (for every year j > 0) one obtains the dynamic cumulated impact on the level of the index for every income group i, indicated as $I^{L}_{i,j}$.

$$ I^{L}_{i,0}=I^{G}_{i,0} $$

(12)

$$ I^{L}_{i,1}=I^{L}_{i,0} + I^{G}_{i,1} $$

(13)

$$ I^{L}_{i,2}=I^{L}_{i,1} + I^{G}_{i,2} $$

(14)

1.2 Data on stock market crashes, economic recessions, and currency crises

Data on currency crises are taken from Bordo et al. (2001) up to 1970 and from Laeven and Valencia (2010) thereafter. The currency crises identified occur in 1933, 1960, 1971, and 1985.

I further reconstructed information about stock market crashes based on the dates listed in Mishkin and White (2003) where the two authors, taking 1929 and 1987 as benchmarks, identify stock market crashes when an overall nominal decline of minimum 20% in the stock market index is recorded. The recent 2007 crash also fully qualifies as a market crash according to this criteria. Crash identification varies depending on the index used (Dow Jones, S&P500 or NASDAQ) and depending on the time window used to record a decline in share price. Using weekly data for the Dow Jones, only 1929 and 1987 are identified as crashes. Using a three-month window, crashes are identified in 1907, 1930–1932 and 1987 with Dow Jones, while S&P500 also identifies 1929 and NASDAQ 1987, among others. Using a one-year window and the Dow Jones, one could identify, among others, 1904, 1914, 1915, 1930–33 and 1988. S&P500 identifies 1907, 1917, and 1930–33. With the use of NASDAQ, one can also add 1984 as a crash year. Even though the analysis of Mishkin and White stops in early 2000, it is easy to check that the 12-month window would certainly list the year 2008 as a ‘crash’ year; Dow Jones went down more than 20% from the peak of October 2007 to July 2008 and by more than 50% to March 2009. In the end, and taking the work of Mishkin and White (2003) as a benchmark, I have identified the onset of 12 stock market crashes episodes: 1917, 1920, 1929, 1937, 1940, 1946, 1962, 1969, 1973, 1990, 2000, and 2007.

Finally, based on the official recording of the US economic cycles by the National Bureau of Economic Research (NBER), I record 17 contraction episodes.³ More precisely, I record the following years as the onset year of an economic contraction: 1913, 1918, 1923, 1926, 1929, 1937, 1945, 1948, 1953, 1957, 1960, 1970, 1974, 1980, 1990, 2001, 2008.

1.3 Data on top marginal tax rates

Data on top marginal tax rates are taken from Sialm (2009) up to 2008. The top marginal tax rate is associated with the richest fractile (the Top 0.01%). Instead, for the income group at the bottom of the top decile (the Top 10–Top 5%) I make use of the marginal tax rate for income ranging from $100,000 to $250,000 (US 2008 dollars) always reported in Sialm (2009). The marginal tax rate for income higher than $250,000 is associated with the top decile (the Top 10%) as a whole.⁴ In 2013, the top marginal tax rate increased back to its 1993 level (39.6%) for incomes above $400,000 (US 2012 dollars) and I use this information to update the series on marginal tax rates up to 2015 (no changes occur between 2008 and 2012 or between 2013 and 2015). In particular, I assume that the 2013 proportional change of marginal tax rates associated with the Top 10% and the Top 10–Top 5% is the same as that for the top marginal tax rate.

Appendix B: Tables and graphs

Table 5 Descriptive statistics of the main distributional variables

Fig. 7

The impulse response to US banking crises on the levels of the Top 0.01% share. Models with no time trend and with additional regressors. Notes: The figure shows the impact of systemic banking crises on top 0.01% income share. The estimates of the dynamic effects are obtained from the estimation of ADL model using the growth rate of the top income share coefficient and general crisis dummy variables. Both panels use an empirical specification which is different from the baseline model (1). Panel a excludes the time trend from the model (1). Panel b, instead, augments model (1) with two additional regressors: the percentage change of the marginal net-of-tax rates and the average real world GDP per capita growth rate (excluding the US). The estimated parameters of the model served to calculate the Impulse Response Functions. The standard errors are derived using bootstrapping with 100 replications

Fig. 8

The impulse response to different macroeconomic crises on the levels of the US Top 0.01% Share. Notes: The figure shows the impact of a variety of macroeconomic crises on the Top 0.01% income share. Macroeconomic crises include systemic banking crises (the baseline), stock market crashes, currency crises, and economic recessions. The estimates of the dynamic effects are obtained from the estimation of ADL model (1) using the growth rate of the top income share coefficient and general crisis dummy variables and time trend. The estimated parameters of the model served to calculate the Impulse Response Functions. The standard errors are derived using bootstrapping with 100 replications. We do not include stock market crashes episodes which coincide with the systemic banking crises or a world war (e.g., 1917, 1929, and 2007 crashes are excluded). Similarly, we do not include economic recessions episodes which coincide with the systemic banking crises or a world war (e.g., 1918, 1929, 1945, and 2008 recessions are excluded)

Fig. 9

The impulse response to different macroeconomic crises on the levels of the US Top 1% wealth share. Notes: The figure shows the impact of systemic banking shocks, stock market crashes, currency crises, and economic recessions on the US Top 1% of nation net personal wealth. The estimates of the dynamic effects are obtained from the estimation of ADL model (1) using the growth rate of the top income share coefficient and general crisis dummy variables and time trend. The estimated parameters of the model served to calculate the Impulse Response Functions. The standard errors are derived using bootstrapping with 100 replications. The source of the data on the Top 1% wealth share is Saez and Zucman (2016). We do not include stock market crashes episodes which coincide with the systemic banking crises or a world war (e.g., 1917, 1929, and 2007 crashes are excluded). Similarly, we do not include economic recessions episodes which coincide with the systemic banking crises or a world war (e.g., 1918, 1929, 1945, and 2008 recessions are excluded)