Income Inequality, Household Debt, and Consumption Growth in the United States

Abstract

In this paper, the SV-TVP-VAR model is used to study the relationships between income inequality, household debt, and consumption growth in the US. This is of great significance for studying whether household debt can become a “substitute” for income and whether it is possible to achieve sustainable growth in consumption under the background of worsening income inequality. According to the research results, the main conclusions are as follows: Firstly, the widening of income inequality would increase consumption in the short term but restrain consumption in the medium and long term, as the relationship between them would turn from positive to negative. Secondly, household debt could improve consumption in the short term but reduce consumption in the medium and long term, with long-term effects being greater than medium-term effects, which means that the long-term negative impact of US household debt on household consumption would be persistent. Lastly, widening income inequality has led to rising household debt over different maturities.

1. Introduction

Since the 1980s, with the increasing income gap, the issue of income inequality has become a major contradiction in US society. In September 2011, the “Occupy Wall Street” movement broke out in the US with the slogan “We are the 99%”, highlighting that the issue of income inequality between the “1%” and “99%” has intensified and reached a climax. Prior to this, Stiglitz recognized the seriousness of income inequality. In April 2011, Stiglitz pointed out that “the top 1% earners in US control 40% of the wealth” and argued that the income inequality has also brought about inequality of opportunity. At present, the gap of US income inequality continues to widen, resulting in worse consequences. The income shares of the top 1% and 10% earners in the US expanded from 10.5% and 34.2% in 1980 to 18.8% and 45.5% in 2021, respectively (Source: WID, https://wid.world/country/usa/, accessed on 1 August 2022). At the same time, the shares of the top 1% and 10% earners continued to rise, while the share of the bottom 50% continued to fall. Economic and social inequalities have also continued to rise during the COVID-19 pandemic [1], and the widening income gap has caused more serious social conflict [2,3,4]. The academic literature has attributed the secular rise in income inequality primarily to the contraction of tax policy, the rise of super managers, the effect of financialization, the erosion of union power, etc. [5,6,7].

As income inequality has widened in the US, the distribution of income has tilted toward the rich, but the US economy has performed strongly and is in a good position compared to other economies. However, what is the driving force behind the relatively decent economic growth? Generally speaking, there were two main drivers of economic growth during this period: the continuous boom in consumer spending and the irrationally exuberant nature of the real estate market [8]. Consumption has always played an important role in the US economy. Before the late 1970s, the ratio of consumption to GDP in the US remained around 60%. Since the 1980s, that ratio has continued to rise, reaching 67.2% in 2020 (Source: Bureau of Economic Analysis. Percentage Shares of Gross Domestic Product. https://apps.bea.gov, accessed on 10 August 2022). Robust growth in consumption was one of the major reasons for the US economic boom. At the same time, consumption also provides a huge cushion, especially during a recession of the economy, which can be helpful in mitigating sharp recessions. However, there is a paradox between rising income inequality and rising consumer spending. According to conventional economic theory, the widening of the income gap will lower demand growth and drag down the economy. In fact, the US economy grows well with consumer spending, largely due to the role of household debt.

The life cycle hypothesis and persistent income hypothesis of classic consumption theory prove that debt can smooth household intertemporal consumption. These two theories link household income, borrowing, and consumption, arguing that household consumption depends on lifetime permanent income rather than current income. Therefore, when current income does not match current consumption, rational consumers can make up the gap by borrowing within the controllable range of expected total income, so as to maximize utility for the entire life cycle. According to this view, household debt affects consumption through income and is used as a “substitute” for income [9].

The study of the relationships between income inequality, household debt, and consumption has theoretical and practical significance [10,11]. Theoretically, both life cycle theory and the absolute income hypothesis involve the relationship between income and consumption. This paper extends the research on income level to include income inequality, considering income inequality as an important factor influencing debt, and focuses on evaluating the relationships between income inequality, household debt, and consumption. Practically, due to income inequality in the US becoming increasingly serious, it is necessary to pay more attention to the sustainability of consumption, especially household debt, which can act as a bridge to make up the gap between income and consumption. Therefore, in terms of theoretical significance and practical pertinence, it is of great importance to analyze the relationships between income inequality, household debt, and consumption, and to reveal how these relationships will change in different periods (short, medium, and long term), with the US as the research object.

Existing studies on income inequality, household debt, and consumption have focused on the interaction between two variables. Although a few studies have analyzed the relationships among all three variables, no further analysis has been conducted on their influence across different time periods. Therefore, in this paper, income inequality, household debt, and consumption are put into one analytical framework. In this framework, the short-, medium-, and long-term patterns of the three variables are discussed. This study demonstrates, in the context of rising income inequality, whether household debt can act as a “substitute” for income to benefit consumption growth sustainably. The contributions of this paper are as follows: (1) income inequality, household debt, and consumption are included in an analytical framework to conduct a systematic analysis, which further expands the scope of research from two variables to three variables; (2) the time variance of the relationship among income inequality, household debt, and consumption is explored, examining their interactions at different times; (3) theoretical support is provided for the necessary narrowing of the income gap, proving that an increase in household debt is strongly correlated with a decline in future consumption.

2. Literature Overview and Research Hypothesis

2.1. The Impact of Income Inequality on Consumption

The impact of income inequality on consumption has always been an important topic in economics academia. In 1949, American economist James S. Duesenberry proposed the relative income hypothesis in the “theory of income, savings, and consumer behavior”. This theory emphasizes the “demonstration effect” of consumption behavior. Duesenberry argued that household consumption not only depends on its own income, but is also influenced by the consumption behavior of others from the same income class, which means that consumption has attributes of showiness and comparison. With the increase in income inequality, there are more conspicuous consumers [12,13,14]. Christen et al. (2005) [15] believed that income inequality increases conspicuous consumption. They called it “keeping up with the Joneses”, which plays an important role in understanding relative income in consumption behavior. Charles et al. (2013) [16] and Pybus et al. (2022) [17] also analyzed the relationship between income inequality and conspicuous consumption and proved the existence of the Veblen effect, i.e., the consumption expenditure level of households with low relative income increased. Frank et al. (2014) [18] expanded the research category of conspicuous consumption to different income groups and proposed the expenditure cascade mechanism. According to this theory, the increase in expenditure by some people leads to an increase in expenditure by others whose income is lower than theirs, which in turn results in an increase in expenditure by those whose income is lower than the second group, and so on. In conclusion, the increase in consumption by some individuals or families will lead to an increase in expenditure by other groups whose income is lower than theirs. However, income inequality may also reduce conspicuous consumption. Jin et al. (2011) [19] pointed out that there was a negative correlation between income inequality and consumption deducted by education expenditure in China, according to data from urban households, which may be caused by the precautionary saving motive of seeking status. Shen et al. (2022) [20] analyzed the relationships between income inequality, consumption, and household debt in China; they maintained that income inequality inhibited consumption growth, but that household leverage ratio could promote household consumption to a certain extent. The above studies mainly focused on the relationship between income inequality and consumption, while ignoring the variation of time. The effects of income inequality on consumption may differ in the short, medium, and long term. Therefore, on the basis of this assumption and the theories explained above, we propose the first hypothesis.

Hypothesis H1 (H1).

Income inequality promotes consumption in the short term but restrains consumption in the medium and long term.

2.2. The Impact of Household Debt on Consumption

The analysis of the impact of household debt on consumption growth can be divided into positive and negative effects [21,22,23]. Firstly, household debt acts as fuel for consumption growth. Ludvigson (1999) [24] proved that consumer credit loans play a decisive role in consumption. Specifically, every 1% increase in credit loans improves consumption expenditure of nondurable goods and services by 0.1%. Parker (1999) [25] believed that household debt has significantly promoted the US consumption level since the 1980s. Lombardi et al. (2017) [26] found that the increase in household debt promotes consumption, thus boosting economic growth in the short term. Secondly, household debt may dampen consumption. Mian et al. (2017) [27] maintained that the increase in the household leverage ratio would drag down consumption in 3 years. Lombardi et al. (2017) [26] summarized their finding that the increase in household debt had a reverse effect on economic growth within 1 year. Every 1% increase in the household leverage ratio would drag down GDP growth by 0.1%. At the same time, when the leverage ratio of the household sector exceeds 60%, household debt exerts a greater drag on economic growth.

Furthermore, highly leveraged household debt has a negative impact on consumption. According to an investigation of the influence of excessive household debt on consumption after the subprime crisis in the US, Dynan et al. (2012) [28] found that highly leveraged households decreased their consumption more sharply than other households during the process of deleverage, which led to weak consumption. Laster, Dynan et al. (2013) [29] maintained that there were four reasons why highly leveraged households reduced consumption: restricted consumer credit due to high leverage, reduction in cash flow because of paying off debts, increased uncertainty in the future, and motivation of lowering household leverage ratio. Mian et al. (2013) [30] demonstrated that households with high leverage ratios were more likely to cut consumption expenditure when encountering negative housing price shocks, causing greater macroeconomic fluctuations due to their higher marginal propensity to consume. Bunn et al. (2014) [31] demonstrated that, after the financial crisis, households with high debt reduced consumption expenditure due to tight credit conditions and increased concerns about future solvency. Alter et al. (2018) [32] believed that households with debt have a different marginal propensity to consume. Households with high debt have higher financial leverage, which make them more vulnerable to negative income shocks or more severe credit constraints. From 2010 to 2014, household consumption decreased by 4%, while the debt-to-income ratio increased by 100%. Therefore, it is necessary to analyze the impact of US household debt on consumption over time. We propose the second hypothesis.

Hypothesis H2 (H2).

Household debt boosts consumption in the short term but deters it in the long term.

2.3. The Impact of Income Inequality on Household Debt

Household debt rises when the income gap is widened. Moreover, the correlation between household debt and income inequality is strong [33,34,35,36,37,38,39,40,41]. Christen et al. (2005) [15] put forward that income inequality in the US has greatly exacerbated the increase in household debt, which means that the widening income gap has led to the excessive use of debt by households with slow income growth to maintain their consumption level. Barba et al. (2009) [42] proposed that the increase in household debt in the United States is a result of the worsening income inequality. Kumhof et al. (2015) [43] studied how the change in US income distribution impacted the high leverage of the household sector and the 2008 financial crisis. The results showed that the income share of high-income households increased significantly from 1983 to 2008, resulting in a widening income gap, while the debt leverage of low- and middle-income households grew. Wolff (2010) [44] pointed out that the reason for the sharp rise in US household debt in the 21st century was that middle-class families tried to maintain their consumption status and social status through debt in the face of declining or stagnant real wages. Carr et al. (2015) [45] proved that the increase in household debt in the US could be highly associated with income inequality and pointed out that the “Veblen effect” of relative income could lead to an increase in household debt. Klein (2015) [46] used panel co-integration techniques to test the relationship between income disparity and household debt, revealing a long-term relationship between the two variables. Specifically, a 1% increase in income inequality would lead to an increase in household credit of 2–6%. Cynamon and Fazzari (2016) [47] believed that the widening of income inequality between the bottom 95% and the top 5% has been an important factor driving the continuous expansion of household debt in the United States since the 1980s. Wildauer (2016) [48] analyzed the continuous growth of debt caused by the widening and aggravating income gap in the US. He pointed out that, under the background of the widening income gap, families with lower incomes often mark families with higher incomes as their reference group and tend to borrow and consume more in order to maintain or catch up with the consumption level of those with higher incomes. Belabed et al. (2018) [49] analyzed the relationship between income gap and household debt according to the expenditure transmission mechanism, and they maintained that households below the top income level reduced their savings to try to keep up with the consumption pattern of the top income level households, resulting in an increase in expenditure pressure and debt expansion of the middle- and lower-income households. Bahadir et al. (2020) [50] proved that the worsening of income inequality would lead to an increase in households with credit constraints, which would result in a greater impact of credit shock on consumption and further expansion income inequality. Cheah et al. (2022) [51] argued that the correlation between income inequality and household debt in Malaysia is asymmetrical in the long and short term. Moreover, they also pointed out that only a reduction in income inequality had a significant positive impact on household debt, while an increase in income inequality had no significant impact. Therefore, it is reasonable to evaluate the impact of income inequality on household debt in the US over different time spans. Accordingly, we present the third hypothesis.

Hypothesis H3 (H3).

Income inequality results in higher household debt at different times.

3. Materials and Methods

3.1. Data

The variables in this paper were income inequality, household debt, and consumption.

First, the Theil Index was used as an indicator of income inequality. There are many indicators to explain income inequality in the literature, such as the Gini coefficient, inverted Pareto–Lorentz coefficient, and Theil index. Berisha et al. (2018) [52] analyzed income inequality by looking at the evolution of the shares of the top centile in total income, as represented by the Theil index. The Thiel index measures the difference between the distribution of income and the population distribution among individual groups. If the income share of all groups is equal to the population share, the Thiel index is 0. For example, if the income shares of the top 1% and the bottom 99% are 1% and 99%, respectively, the income distribution is equal. The index for the top 1% income group is constructed as T = Itop1 × |Itop1 − Ntop1| + Ib99 × |Ib99 − Nb99|, where I is the income share of each income quartile and N is the size of each share.

Second, the outstanding US household debt at the end of the year was selected as the index of household debt. The US household debt is made up of mortgages and consumer credit for the purchase of homes, consumer durables, and other consumer goods and services. In this paper, household debt refers to the gross outstanding debt of households. The total US household debt is a better indicator of household debt than any one of its components. Referring to the selection of household debt indicators by Iacoviello (2008) [37], when discussing the relationship between household debt and income inequality in the United States, household debt in this paper is the sum of all household debts.

Third, personal consumption expenditure was used as an indicator of consumption growth. Bahadir et al. (2020) [50] studied the impact of income inequality on the total consumption of household credit shock. Therefore, the total personal consumption expenditure of each year was selected to illustrate the impact of income inequality and household debt on consumption growth.

The three variables were based on data from the WID, Mark W. Frank’s National Income Inequality Database, the Federal Reserve’s Financial Accounts, and the Bureau of Economic Analysis. In addition, the sample range was from 1952 to 2021.

3.2. Variable Description

Table 1 shows the variable settings and their processing methods.

Table 2 displays the descriptive statistical results after first-order difference of the income gap (Theil), household debt (debt), and household consumption (consume) in the United States. Because the first-order differences of the three variables were stable, we constructed the SV-TVP-VAR model.

Table 1 shows the variable settings and their processing methods. Theil, debt, and consume represent income inequality, household debt, and personal consumption expenditures, respectively. These variables were then processed by difference. Table 2 shows the descriptive statistics of the variables. The three core explanatory variables were stationary. The mean of Theil was greater than 1.5%, but the standard deviation was lower than 0.1, indicating that the distribution of Theil’s index was concentrated around 0.017. Moreover, combined with the skewness and kurtosis values, this shows that the distribution of income inequality was more concentrated. The mean debt was around 0.23, indicating a high overall level of household debt. However, at the same time, the standard deviation was as high as 0.917062, which indicates that the distribution of household debt was more volatile. Taking the large difference between the maximum and minimum of the debt and the high skewness into consideration, it can be concluded that there were structural differences in household debt and large internal disparities. The mean consume was 0.05337, indicating that the consumption was at a medium level. However, the standard deviation, the kurtosis, and the skewness were low, indicating little internal difference in consumption.

3.3. Methods

To investigate the short-, medium-, and long-term relationships between income inequality, household debt, and personal consumption expenditures, we constructed an SV-TVP-VAR model for this paper. Firstly, an SVAR model was established:

(1)$A{y}_t=F_1{y}_{t-1}+\cdots +F_s{y}_{t-s}+{\epsilon }_t,t=s+1,\dots ,n,$

where $y_t$ is an (n × 1)-dimensional observed variable, A is a (k × k)-dimensional joint parameter matrix, and $F_1\dots F_s$ s is a (k × k)-dimensional coefficient matrix. The perturbation term ${\epsilon }_t$ is a (k × 1)-dimensional structural shock, with ${\epsilon }_t$ ≈ N(0,∑∑). ∑ is a diagonal array composed of standard deviations of the following form:

(2)${\displaystyle \sum }=\left[\begin{array}{cccc}{\sigma }_1& 0& 0& 0\\ 0& {\sigma }_2& 0& 0\\ 0& 0& {\sigma }_3& 0\\ 0& 0& 0& {\sigma }_4\end{array}\right].$

Furthermore, since the structure shock obeys recursive identification, A is a lower triangular matrix of the following form:

(3)$A=\left[\begin{array}{cccc}1& 0& 0& 0\\ a_{21}& 1& 0& 0\\ a_{31}& a_{32}& 1& 0\\ a_{41}& a_{42}& a_{43}& 1\end{array}\right].$

The model can be rewritten as

(4)$y_t=B_1{y}_{t-1}+\cdots +B_s{y}_{t-s}+A^{-1}{\displaystyle \sum }{\epsilon }_t, {\epsilon }_t~N\left(0, I_k\right),$

where $B_i=A^{-1}{F}_i, i=1,\dots , s$. Straightening each row element of the B matrix to obtain β is defined by $X_t=I_s\left(y_{t-1},\dots ,y_{t-s}\right)$, where ⊗ represents the Kronecker product. It can then be expressed as

(5)$y_t=X_t\beta +A^{-1}{\displaystyle \sum }{\epsilon }_t.$

Furthermore, the time-varying case is introduced into SVAR to obtain SV-TVP-VAR.

(6)$y_t=X_t{\beta }_t+A^{-1}{\displaystyle \sum }{\epsilon }_t,$

$g_t=\left(g_{1t},g_{2t},g_{3t},g_{3t}\right),g_{jt}=log{\sigma }_{jt}^2,$

$j=1,\dots ,4, t=p+1,\dots ,n.$

It is also assumed that all parameters obey a random wandering process:

${\beta }_{t+1}={\beta }_t+u_{\beta t},$

${\alpha }_{t+1}={\alpha }_t+u_{\alpha t},$

$h_{t+1}=h_t+u_{ht},$

(7)$\left(\begin{array}{c}\begin{array}{c}{u}_{\beta t}\\ u_{\alpha t}\end{array}\\ u_{ht}\\ {\epsilon }_t\end{array}\right)~N\left[0,\left[\begin{array}{cccc}I& 0& 0& 0\\ 0& {\displaystyle \sum }\beta & 0& 0\\ 0& 0& {\displaystyle \sum }\alpha & 0\\ 0& 0& 0& {\displaystyle \sum }h\end{array}\right]\right], t=s+1,\dots n,$

${\beta }_{p+1}~N\left({\mu }_{\beta 0},{{\displaystyle \sum }}_{\beta 0}\right),$

${\alpha }_{p+1}~N\left({\mu }_{\alpha 0},{{\displaystyle \sum }}_{\alpha 0}\right),$

$h_{p+1}~N\left({\mu }_{h0},{{\displaystyle \sum }}_{h0}\right).$

The time-varying parameters are shown in Equations (2) and (3). The information disturbance between time-varying parameters is not correlated. ${{\displaystyle \sum }}_{\beta 0}, {{\displaystyle \sum }}_{\alpha 0}, {{\displaystyle \sum }}_{h0}$ are diagonal matrices.

According to the above TVP-VAR model, the first step is to calculate the results of parameter estimation, including the mean, standard deviation, 95% confidence interval, Geweke statistic, and inefficiency factor. The second step is to depict the graph of the interval impulse response function. The responses of income inequality to consumption, of household debt to consumption, and of income inequality to household debt were investigated in the 1, 2, and 4 periods.

4. Results

Using the SV-TVP-VAR model, simulated calculations were performed 10,000 times. The estimated values of the parameters are shown in Table 3. Because invalid values were less than 100, compared with 10,000 simulations, it can be concluded that the SV-TVP-VAR estimates were robust (see Table 3). Furthermore, the results of equally spaced shocks can be used to analyze the time-varying relationships between income inequality, household debt, and consumption, as well as the long-term and short-term effects.

Figure 1a shows the impact effect of income inequality (Theil) on consumption. According to Figure 1a, the short-term shock effect is positive, while the medium- and long-term effects are negative. The results suggest that the widening of income inequality will raise consumption in the short term, but curb consumption in the medium and long term, with negative effects from the former to the latter. The main reason is that, after the short-term widening of income inequality, low-income households will generate extensive conspicuous consumption based on the “keeping up with the Joneses” effect, which will lead to an increase in consumption [12,53,54,55,56], consistent with hypothesis H1.

Figure 1b represents the impact of household debt on consumption. According to Figure 2, household debt leads to a weak improvement in consumption in the short term. After the 40th period (1991), the growth of household debt had a positive impact on the improvement of household consumption, which means that household debt improves consumption in the short term. However, the medium- and long-term impact curves show that the increase in US household debt reduced the level of consumption, with the long-term negative effect being greater than the medium-term negative effect, indicating that the long-term negative impact of US household debt on consumption is sustained. At the same time, from the perspective of time variability, after the 40th period (1991), the long-term negative impact effect of US household debt on consumption gradually increased, supporting hypothesis H2.

Figure 1c represents the impact of the income gap on household debt. According to Figure 2, US household debt would have a positive impact on income inequality in the short, medium, and long term, in line with hypothesis H3. The main reason for this result is that high-income groups and low-income groups have different borrowing purposes due to different credit constraints. The former group has fewer credit constraints; hence, they can obtain more loans from lending institutions and gain high returns through increased leverage speculation. However, the latter has more credit constraints and can only use borrowing to smooth consumption, while being unable to obtain speculative gains. On the whole, widening of the income gap would lead to a rise in household debt. In detail, from 1981 to 2021, the income shares of the top 1% and 10% among income groups increased from 10.7% and 34.3% to 19% and 45.6%, respectively, while the household leverage ratio increased from 47.6% to 78% during the same period (see Figure 2). Accordingly, widening of the income gap in the US is positively correlated with the continuous rise in household debt. Meanwhile, for low-and middle-income households, high household debt is accompanied by a new form of socioeconomic insecurity, a phenomenon that Leichi and Fitzgerald (2014) [57] called “the hidden crisis of the American middle class”.

5. Discussion

Starting from the paradox between income inequality and strong consumer spending in the US, this paper explored whether household debt could replace income and have a lasting impact on consumption growth under the background of increasing income inequality. The results show that widening of the income gap and an increase in household debt would promote consumption in the short term, but restrain consumption in the long term. Moreover, widening of the income gap would lead to an increase in household debt. In detail, the rise in income inequality has intensified the shift of income distribution from low-saving households at the bottom to high-saving households at the top. At the same time, the redistribution from low- to high-saving households would reduce consumer spending. Consequently, low-income groups would aim to increase household debt to meet the consumption standard. Therefore, household debt cannot replace income to bring about a sustainable increase in consumption. We believe that a continuous reduction in income inequality in the US is the key.

The rise in income inequality has forced households with fewer income gains to use debt to keep up with the consumption level of households with larger income gains, which is consistent with the discovery of the “Veblen effect” in consumption by Bertrand and Morse (2012) [58] and Carr et al. (2015) [45], as well as the “expenditure cascades” proposed by Frank et al. (2014) [18]. Specifically, the “Veblen effect” refers to the increase in consumption expenditure by households with low income. “Expenditure cascades” denote that the relative income and expenditure patterns of households of a high income class may affect the expenditure of families with low income. It was not until the 1980s that financial institutions developed a large number of credit products driven by financial innovation, together with the gradual development of credit scoring, securitization, etc. Under this background, the borrowing needs of low-income families were satisfied; thus, their insecurities were compensated. However, this boost is not sustainable. With the increasing gap of income inequality in the US, high-income groups have a lower average propensity to consume, while low-income groups have a higher average propensity to consume. This paradox leads to insufficient consumption in the entire society and limited sustainable ability to improve the consumption.

Household debt influences consumption growth through the income effect and the crowding out effect. Specifically, the income effect of household debt is that households improve payment ability by increasing debt in the short term, which may stimulate consumption. However, in the medium and long term, with the continuous rise of household debt, household debt repayment pressure also increases gradually. Households would reduce expenditures to repay debts with the consequence of an inhibition of consumption growth, which is reflected as the crowding out effect of household debt. In earlier studies, some scholars focused on the income effect of household debt. For example, Bacchetta and Gerlache (1997) [59] and Lombardi et al. (2017) [26] showed that household debt plays a positive role in promoting consumption growth. However, as household debt continues to increase year by year, its long-term crowding out effect gradually replaces the short-term income effect, resulting in a restraining effect on the growth of consumption. The crowding out effect of the household sector is mainly realized in three ways. Firstly, an increase in debt burden will inhibit the increase in consumption expenditure. Secondly, due to credit constraints by financial intermediaries, over-indebted households cannot obtain new loans and will face increasing debt burdens, leading to further reductions in consumer spending. Thirdly, in order to prevent future uncertainties, households aim to increase savings and reduce consumption expenditure. For example, during the COVID-19 pandemic, a large number of households chose to increase savings to cope with the uncertainty of falling income and reduced consumption expenditure.

The research results provide strong support for the view presented above that there is a correlation between income inequality, household debt, and consumption in the United States. At the same time, the results in the short, medium, and long term can contribute to the existing research. Specifically, there are two main differences in terms of research objects and methods compared with the previous literature. Firstly, we considered the interactions between income inequality, household debt, and consumption. Unlike the conclusion drawn by Berisha and Meszaros (2018) [52] that an increase in income inequality and consumption results in an increase in household debt based on the Johansen and Engle–Granger cointegration test, this paper placed income inequality, household debt, and consumption into a framework to discuss their interaction, which is of great significance for analyzing whether household debt can replace income to promote sustainable growth in consumption under the background of the widening income gap. Secondly, we analyzed the time variance among income inequality, household debt, and consumption. Although Bahadir et al. (2020) [50] added time series and used transnational regression data to prove that the short-term rise and long-term decline in consumption in countries with unequal income distribution is greater than that in other countries, they did not analyze the impact of household debt on consumption and of income inequality on household debt over different periods. This paper studied the short-, medium-, and long-term relationships between the three variables in order to examine their interactions during different periods.

From the perspective of practical research, the conclusions of this paper provide theoretical support for narrowing income inequality. In this paper, income inequality, household debt, and consumption were placed into one analytical framework. Their relationships over time were analyzed in a systematic way. The results show that household debt cannot make a long-term contribution to consumption in place of income. The only way to ensure sustainable growth in consumption is to narrow the income gap.

6. Conclusions

This paper examined the relationships between income inequality, household debt, and consumption in the US using the SV-TVP-VAR model. This study is of great significance in determining whether household debt can become a “substitute” for income to ensure sustainable growth in consumption under the background of the widening income gap. According to the research results, three points can be summarized. Firstly, the widening income inequality increases consumption in the short term but restrains consumption in the medium and long term, with the relationship between them turning from positive to negative. As income inequality increases, the growth of consumer spending is hampered. Secondly, household debt can improve consumption in the short term, but a continuous increase in household debt reduces consumption in the medium and long term. Moreover, the negative long-term effect is greater than the negative medium-term effect. It is reasonable to say that a rise in household debt hampers growth in consumption. Lastly, income inequality leads to greater household debt in the US in the short, medium, and long term. Against the background of the rise in income inequality, the only way to achieve sustainable consumption growth is to raise the disposable income of households, especially low-income groups. Although household debt can make up for income shortages to boost consumption growth in the short term, this effect is not sustainable in the long term and brings negative shocks. For example, before the 2008 US financial crisis, the irrational exuberance of consumption resulted in an increase in household debt. When households were unable to repay debts, the boom went bust. Therefore, improving household income and narrowing the income gap are the only way to achieve sustainable consumption growth.

There were three limitations of this paper. The first limitation was the research method. SV-TVP-VAR was used in this paper to analyze the relationships between income inequality, household debt, and consumption in the US. However, the analysis of the mechanism underlying this relationship was insufficient. We can use more abundant empirical methods to conduct in-depth research, such as the dynamic stochastic general equilibrium model, which is based on the real business cycle theory. The second limitation was the choice of data. This paper used macro data of the United States, although micro data of low-income and high-income households may better illustrate the impact of income inequality on consumption. The third limitation was that this study focused on the US; thus, the results are not applicable to other countries. However, income inequality and household debt are becoming prevalent worldwide, which may not only have a great impact on countries’ economies, but also aggravate social and political problems. Therefore, it is reasonable to pay attention to the issues of income inequality and household debt in different countries. Considering the above limitations, future research directions should address three aspects: the use of other empirical methods such as DESG and panel VAR; the addition of new explanatory variables such as economic growth and consumption upgrading; and an increase in the number of countries studied, including OECD countries, emerging economies, and other advanced economies.

Author Contributions

Conceptualization, H.S. and Y.Y.; Methodology, Y.P., H.S. and Y.Y.; Software, M.L.; Validation, M.L.; Formal analysis, Y.P.; Data curation, M.L.; Writing—original draft, Y.Y.; Writing—review & editing, H.S.; Visualization, M.L.; Supervision, Y.P. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

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Figures and Tables

Figure 1. Equally spaced impact results. (a) Theil—Consume; (b) Debt—Consume; (c) Theil—Debt.

Figure 2. The relationship between the income shares of the top 1% and 10% and the household debt-to-GDP ratio. Source: World Inequality Database, BIS. Source: WID, BIS.

Table 1

Variable settings and processing methods.

Variable	Variable Setting	Processing Methods
Income Inequality	Theil	Difference
Household Debt	Debt	Difference
Personal Consumption Expenditures	Consume	Difference

Table 2

Descriptive statistics of variables.

	Theil	Debt	Consume
Mean	0.017237	0.235941	0.05337
Median	0.017821	0.060463	0.049828
Maximum	0.171515	4.624372	0.104617
Minimum	−0.138381	−2.146016	−0.024454
Std. Dev.	0.055457	0.917062	0.026617
Skewness	−0.118047	2.381443	0.04788
Kurtosis	3.737226	12.56041	2.909194
ADF test	Stationary(−7.797500)	Stationary(−9.689600)	Stationary(−8.710366)

Note: T-statistics are shown in parentheses.

Table 3

Parameter estimation results of SV-TVP-VAR model.

Parameter	Mean	Std. Dev.	95%U	95%L	Geweke Statistic	Inefficiency Factor
sb1	0.0094	0.0030	0.0053	0.0170	0.952	23.15
sb2	0.0064	0.0016	0.0040	0.0103	0.556	10.64
sa1	0.0055	0.0016	0.0034	0.0096	0.864	22.53
sa2	0.0055	0.0016	0.0034	0.0097	0.041	19.22
sh1	0.1398	0.0747	0.0346	0.3200	0.823	65.19
sh2	0.0063	0.0042	0.0034	0.0132	0.147	91.66

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