Income inequality and consumption inequality over time.

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“Income inequality and consumption inequality over time.”

Bachelors Thesis

BSc Economics and Business Economics Specialisation Economics

Faculty of Economics and Business

Author: Deniz Postoğlu Student Number: 11664851

Email: deniz.postoglu@student.uva.nl

Supervisor: Stefan Wöhrmüller Second Reader:

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STATEMENT OF ORIGINALITY

This document is written by Student Deniz Postoğlu who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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ABSTRACT

By means of literature review, this thesis aims to answer the question of how the models and conclusions changed in research about income and consumption inequality. The aim of this paper is to see if and how older and newer articles addressed the measurement errors associated with the Consumer Expenditure Survey data. This paper focuses the measurement errors associated with the Consumer Expenditure Survey data, and how Krueger and Perri (2006) do not acknowledge it while Aguiar and Bils (2015) do. From this, it is concluded that when measurement errors are addressed, consumption inequality is observed to be increasing but if they are not addressed, consumption inequality is observed to be flat. Furthermore, this paper also states Blundell et al.’s (2008) framework about how the trends in income and consumption inequality can be characterised by income shocks and self-insurance. From this model, it is concluded that transitionary income shocks have no effect on consumption and thus in presence of transitionary income shocks, consumption inequality remains flat whereas in the presence of permanent income shocks consumption inequality increases.

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1. Introduction

It is well documented that income inequality in the United States has been increasing since the 1980s (Attanasio, Hurst and Pistaferri, 2012). Increased income inequality has concerning welfare implications depending on how it affects the consumption of the households (Lansing and Markiewicx, 2016). Therefore, studying inequality is an important part of providing policy solutions to some issues such as globalization or income tax policy (Meyer and Sullivan, 2017). Almost always, inequality is expressed in terms of income, but economists are interested in utility functions of individuals which consists of consumption and these utility functions with consumption make up the welfare (Attanasio and Pistaferri, 2016).

Consumption is thought to be a better estimate for economic well-being for several reasons. For instance, it measures the accumulated assets and credits in the long-run better than income because consumption will directly show the changes in asset ownership (Meyer and Sullivan, 2017). Secondly, consumption is found to be a better estimate for the bottom of the distribution by Meyer and Sullivan (2003, 2011, as cited in Meyer and Sullivan, 2017) because they show that economic hardship is worse for low consumption households instead of low-income households. Thirdly, income has fluctuations due to saving or borrowing patterns whereas, consumption is assumed to be smoothed out, so it can be a better indicator for an individual’s economic well-being. Lastly, income indicators exclude unemployment, retirement, health, taxes, transfers, etc., and therefore they are not the best-fitted estimate for the economic well-being (Meyer and Sullivan, 2017). Thus, studying income and consumption inequality together can give broader information about the welfare of both the individuals and the state.

Although, examining consumption inequality has its many advantages, the reason why it is not as available as income studies are, because of measurement errors associated with consumption data. The biggest database for consumption in the U.S. is the Consumer Expenditure Survey (CES) and all the previous research done on consumption, report that the CES might be subject to measurement errors which bias the results. Therefore, researchers try to get rid of measurement errors by using different models to measure consumption, and some of them use better models to get rid of this error than others. Over time, the way consumption is measured changed and researchers tried to improve the previous studies. That being so, this paper aims to discuss the research done about the relationship between income and consumption inequality and how the models and conclusions changed over time by focusing on the articles by Krueger and Perri (2006) and Aguiar and Bils (2015).

The presence of measurement errors and how different researchers deal with make up the main discussion when looking at different studies. On one hand, Krueger and Perri (2006), do

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not account for the measurement error and they conclude that even though an increase in income inequality was observed, consumption inequality remained flat. On the other hand, Aguiar and Bils (2015) control for both classical and non-classical measurement errors with their econometric model and thus report a complementary increase in both income and consumption inequality. This shows the importance of acknowledging the measurement error. Furthermore, Blundell et al. (2008) provide a framework of how income shocks insurance markets determine the link between income and consumption inequality. This is a detailed and useful framework, but they also fail to control for measurement error which leads them to conclude similar results to Krueger and Perri (2006).

Attanasio and Pistaferri (2016) give a summary of the consumption inequality over time in different studies that used different data. They report that Heathcote, Perri, and Violante (2010), who used CE Interview survey concluded an almost flat consumption inequality; whereas Attanasio, Battistin and Ichimura (2007), who merged both Interview and Diary surveys of CE have concluded an increase in the consumption inequality (Attanasio and Pistaferri, 2016). Attanasio and Pistaferri (2014) used PSID also reported an increase in consumption inequality.

In conclusion, this paper consists of four parts. The first section will discuss the paper by Krueger and Perri (2006) by focusing on the Consumer Expenditure Survey data they use, then their methodology to measure the consumption and finally on their results. The second section will examine measurements errors by discussing the ignorance of measurement errors in Krueger and Perri (2006) and later by providing a framework for the classical and non-classical (systematic) measurement errors. The third section will focus on the newer literature by Aguiar and Bils (2015). Firstly, how they measured consumption and the trends they observed will be observed. Secondly, their robustness check using savings rate and their conclusion of a possibility of measurement errors will be stated. Thirdly, the econometric model they used to get rid of these measurement errors and lastly the results from that will be discussed. Finally, the possible theoretical reasons for income and consumption inequality with regards to income shocks and insurance markets and Blundell et al.’s (2008) framework about this theory will be discussed. The last section concludes the findings.

2. Krueger and Perri (2006)

This section will discuss the Consumer Expenditure Survey (CES) used by researchers studying consumption such as Krueger and Perri (2006), and the measurement errors associated with it as discussed in Attanasio and Pistaferri (2016). Later, the methodology Krueger and Perri (2006) used to measure consumption is discussed. Finally, their findings for

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income and consumption inequality using the Gini coefficient, variable of logs, the 90/10 ratio and the 50/10 ratio are stated as well as the interpretation of these results.

2.1. Consumer Expenditure Survey (CES)

In contrast to commonly available and consistent income data, consumption data is usually rare and is not consistent (Attanasio and Pistaferri, 2016). The Consumer Expenditure Survey (CES) is the only available data set for consumption measures for the United States. The Consumer Expenditure Survey (CES) is collected by the United States Census Bureau to calculate the Consumer Price Index (CPI). The CES shows the buying behaviour of American consumers consistently from 1980 (Blundell et al., 2008). It has a large sample size of over 5000 households, and it consists of two parts; the Diary survey and the Interview survey (Aguiar and Bils, 2015). For the Diary survey, individuals report their two-week expenditures once in a year whereas, for the Interview survey, individuals report their expenditures four times each year with three-month intervals (Attanasio and Pistaferri, 2016).

Various papers about consumption inequality agree on the measurement errors associated with the CES expenditure data. For instance, Attanasio and Pistaferri (2016) give reasons to why expenditure reported on the CES may not be an accurate measure for the actual consumption. The CES does not provide information about how much the current durables are worth, which might lead consumption to either be overreported in the case of durable purchases done in the present and underreported in the case of durable purchases done in the past (Attanasio and Pistaferri, 2016). Additionally, to use expenditure for consumption, one needs to know the prices paid by each individual and researchers usually assume the same prices for everyone to get rid of this condition (Attanasio and Pistaferri, 2016). However, for tradable goods assuming same prices will lead to the inaccurate measurement for consumption, because of the presence of arbitrage, not everyone will spend the same price on tradeable goods. Therefore, assuming spending equals consumption in every case might lead to over- or under-reporting economic welfare of individuals (Attanasio and Pistaferri, 2016).

Many other researchers acknowledge that the CES measurements do not estimate the actual consumption and that it has measurement errors that result in biased results (Attanasio, Hurst and Pistaferri, 2012). For instance, Bee, Meyer, and Sullivan (2015, as cited in Attanasio and Pistaferri 2016) report that even though the CES generally illustrates the actual consumption trends well, there is an understatement of income and consumption at the top of the distribution. Thus, it is well documented by researchers that CES is subject to measurement errors and recent studies about consumption inequality such as Aguiar and Bils (2015) try to get rid of these measurement errors with the different ways they measure consumption and with their

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econometric models. However, older studies such as Krueger and Perri (2006) fail to address this measurement error, which leads to different findings for the relationship between income and consumption inequality than the recent studies.

2.2. Methodology

The CES also provides information about income dynamics. Therefore, Krueger and Perri (2006) use CES to measure income by adding after-tax labour earnings and government transfers. For measuring consumption, they recognise that expenditures are a good estimate for the flow of consumption for non- and small- durable goods and services, but the relation is not as direct for durable goods like cars and houses, which is why they calculate service flows of houses and cars from the value of their stock (Krueger and Perri, 2006).

In line with this, service flows from housing is measured by the rent paid by the households; and service flows of cars are measured by the 1/32 times the value of the vehicles owned by the household (Krueger and Perri, 2006). All of these combined, Krueger and Perri (2006) measure household consumption as the total of expenditures nondurables, services, small durables and imputed services from housing and vehicle and it is deflated by CPI. To get to most stable data, their sample only includes the households who have provided complete information.

2.3. Results

Krueger and Perri (2006) plot the inequality trends with four measures; the Gini coefficient, variance of logs, 90/10 ratio and 50/10 ratio. The Gini coefficient measures inequality by looking at all parts of the distribution, which includes extreme cases of rich and poor. The 90/10 ratio looks at the difference between the 90th percentile (top) and the 10th percentile (bottom), and thus excludes the extreme cases. Whereas, the 50/10 ratio measures the difference between 50th percentile (median) and the 10th percentile (bottom). The Gini coefficient and the 90/10 ratio underline the top of the distribution, while the 50/10 ratio and the variable of logs underline the bottom of the distribution (Heathcote, Perri and Violante, 2010).

Krueger and Perri (2006) conclude that income inequality in the United States has increased sharply, which could be seen from the significant increase in the Gini coefficient from 0.3 to 0.37 in the 1980-2004 time period, or 20% increase in the variance of logs. The 90/10 ratio increases from 4.2 to 6, but the 50/10 ratio only increases from 2.2. to 2.7. The different results from the 90/10 ratio and 50/10 ratio means that the inequality is mostly associated with the large divergence between the top and the bottom instead of the median and the bottom.

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However, they do nott observe the same amount of increase in consumption inequality. Gini coefficient for the consumption inequality increased 0.23 to 0.26, and only 5% for the variance of logs, which is less than the increase in income inequality (Krueger and Perri, 2006). The 90/10 ratio increased from 2.9 to 3.4 and 50/10 ratio increased from 1.7 to 1.9. This implies that the consumption distribution between the top and bottom is more equal than the income distribution. From the above measures, Krueger and Perri (2006) conclude that while income inequality increased, consumption inequality remained flat.

3. Measurement Error

This section will firstly discuss the crucial missing element in Krueger and Perri’s (2006) study, which is them not acknowledging the measurement errors in the CES data. Secondly, the discussion will continue with explaining the model for the measurement error and the assumptions for two types of measurement errors: classical and non-classical (systematic).

3.1. Discussion of Krueger and Perri (2006)

Krueger and Perri (2006) measure consumption in a very straightforward way, by adding the expenditures of nondurables, services, small durables and imputed services from housing vehicle. However, they never acknowledge that the CES is subject to measurement errors, which is discussed and addressed in various recent papers. The fact that Krueger and Perri (2006) did not address the measurement error is the main reason for the different results between the older and newer papers because the presence of measurement errors makes the estimates fail to describe the real-world trends.

3.2. Measurement Errors

Measurement errors occur when there is an error while measuring the dependent or the independent variable. The error exists due to mismeasurement, and therefore even in large samples, the error will remain (Stock and Watson, 2015). Measurement error might arise due to the way data is collected. For instance, survey data might be subject to measurement error due to the possibility of respondents giving wrong answers (Stock and Watson, 2015). The OLS estimator will be biased in the presence of measurement error because the estimation will be based on the biased value instead of the true value. Say, 𝑋_𝑖 is the actual value and 𝑋̃ is the _𝑖 stated value of 𝑋_𝑖.

𝑌𝑖 = 𝛽0 + 𝛽1𝑋̃ + 𝑢𝑖 𝑖

Because the regression estimates the stated value with measurement error instead of the actual value, the equation will include an error term for the measurement error and the difference between the actual and stated values.

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𝑌_𝑖 = 𝛽₀+ 𝛽₁𝑋̃ + 𝛽_𝑖 ₁(𝑋_𝑖− 𝑋̃ ) + 𝑢_𝑖 _𝑖

From this equation, if the stated value is correlated with (𝑋_𝑖 − 𝑋̃ ), then the regressor will be _𝑖 correlated with 𝑢_𝑖 (Stock and Watson, 2015). If measurement error did not exist, the difference between the actual and the stated value would be zero, and thus the stated measure would not be correlated with it and the error term. This correlation results in estimated value of 𝛽₁ to be inconsistent and biased.

3.2.1. Classical Measurement Error

For classical measurement error, suppose that; 𝑋̃ = 𝑋_𝑖 _𝑖+ 𝑤_𝑖

Where 𝑋_𝑖 is the actual and unmeasured value, and 𝑤_𝑖 is the random part with a mean zero and because it is random, 𝑤_𝑖 is uncorrelated with 𝑋_𝑖 and 𝑢_𝑖 (Stock and Watson, 2015). Therefore, in a classical measurement error; 𝑐𝑜𝑟𝑟(𝑤_𝑖, 𝑋_𝑖) = 0 and 𝑐𝑜𝑟𝑟(𝑤_𝑖, 𝑢_𝑖) = 0. The probability limit of the parameter estimator is the following,

𝛽₁→𝑝 𝜎𝑥 2 𝜎_𝑥2_{+ 𝜎}

𝑤2 ∗ 𝛽₁

Because the ratio part is smaller than 1, 𝛽̂ will be inconsistent and biased towards zero (Stock ₁ and Watson, 2015).

3.2.2. Non-Classical (Systematic) Measurement Error

Non-classical, also known as systematic, measurement errors carry one opposite assumption of classical measurement error, that is 𝑐𝑜𝑟𝑟(𝑤_𝑖, 𝑋_𝑖) ≠ 0. This means that the error in measuring the dependent variable varies systematically with the regressor, leading to a systematic measurement error. The correlation between the random component and the regressor also means that, as the regressor increases so will the measurement error, because of the direct correlation.

4. Aguiar and Bils (2015)

This section focuses on the newer literature by Aguiar and Bils (2015) about the consumption inequality where the researchers acknowledge and address the measurement error. In line with this, the first section will discuss how the how they measure income and consumption as well the trends they observe in the inequality with their measurements. The second part will examine the robustness check Aguiar and Bils (2015) do with savings rate to check on the CES data, which result them to consider the measurement error associated with the CES data. Later, the econometric model they used to address the measurement errors will be discussed. Finally, the results of their regressions will be stated.

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4.1. Measuring Consumption and Trends in Inequality

The first section focuses on which parts of the Consumer Expenditure Survey use and how they select the sample. Additionally, the approach in which income and consumption are measured with this data is discussed.

4.1.1. Data and Measuring Consumption

Aguiar and Bils (2015) use Interview survey from the Consumer Expenditure Survey for their data. To get more consistent data, they use urban households since the CES only collected their data and they only include the households who provided complete information to surveys (Aguiar and Bils, 2015). Furthermore, they only include households between the age of 25 to 64 and they exclude the top 5% and the bottom 5% from the before-tax income distribution to get rid of outliers (Aguiar and Bils, 2015). Finally, both household expenditure and income are deflated by CPI, so everything is stated in the same unit. To measure income, from the CES, they take total household labour earnings, before-tax total household income and after-tax household income (Aguiar and Bils, 2015).

On the other hand, for consumption, they divide the reported expenditure into 20 groups. Similar to Krueger and Perri (2006), Aguiar and Perri (2015) calculate service flows of housing from rent paid for renters and rent received for landlords. However, for the other durable goods, they directly use the expenditure. Lastly, they correct for the large decrease in food expenditure from 1982 to 1987 due to a wrong wording in the survey by adjusting food expenditure upwards for that period of time (Aguiar and Bils, 2015).

Instead of measuring consumption by adding up expenditures like Krueger and Perri, they measure consumption by looking at how high- and low-income households spend their income on luxuries over necessities (Aguiar and Bils, 2015). This means that high-income households will gravitate towards luxuries at a rate which is much higher than low-income households during an increase in consumption inequality (Aguiar and Bils, 2015). Their estimation is a well-fitted estimate for several reasons. Firstly, it is robust to household-specific and good-specific measurement errors. Additionally, because it is a relative measurement, it is not necessary to have exactly the right measurements for household expenditures (Aguiar and Bils, 2015).

4.1.2. Trends in Income and Consumption Inequality

Aguiar and Bils (2015) look at the trends in income and consumption inequality by graphing several measures from the CES survey, such as labour earning, before-tax income, after-tax income and non-durable expenditures. To define inequality, they divide all households into 5 groups according to their before-tax income; 5th-20th, 20th-40th, 60th-80th and

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80th-95th percentile and as mentioned before the top and bottom 5th percentiles are not used to get rid of outliers (Aguiar and Bils, 2015). Then they take the average of total expenditure and income for each group. From this, they define inequality as the ratio of the average of the top of the distribution and ratio of the average of the bottom of the distribution (Aguiar and Bils, 2015).

For labour earnings, they found a sharp rise of 28 % in inequality between the top- and bottom- income groups. For before-income tax, which is a more extensive measure for income, they found inequality to be lower than in labour earnings for each time, but they observed an overall increase over time of 32 % (Aguiar and Bils, 2015). Furthermore, for after-tax income, income inequality also increased over time with 30 %. Finally, for consumption inequality they found the increase to be lower than that of income, however, the compared to Krueger and Perri (2006) the rate of increase in consumption inequality is found to be larger in Aguiar and Bils (2015).

Furthermore, to investigate if the dispersions resulted from a loss from the bottom of the distribution, they looked at 90/10 and 50/10 ratios just as Krueger and Perri (2006) did. They observed that the total of 32 percent increase in inequality in before-tax income was due to 21% increase in the 90/10 ratio and 11% increase in the 50/10 ratio. For after-tax income it was similar; 21% increase in the 90/10 ratio while 13% increase in the 50/10 ratio (Aguiar and Bils, 2015). Almost twofold of the increase in before- and after- tax income is attributed to the top of the distribution but there is still an increase in income inequality attributed to the bottom of the distribution. However, for consumption, there is almost no observed increase in consumption inequality at the bottom of the distribution which can be interpreted from an increase of 13% in the 90/10 ratio and only an increase of 1% in the 50/10 ratio (Aguiar and Bils, 2015).

4.2. Evidence for the Measurement Error

The Consumer Expenditure Survey also provides information about the savings behaviour of Americans such as net flows to savings account, asset purchases, mortgages and loans (Aguiar and Bils, 2015). Using this information, Aguiar and Bils (2015) apply the savings rate to show evidence measurement error in the CES. To calculate the saving rate, they use the following formula:

𝑆𝑎𝑣𝑖𝑛𝑔𝑠

𝐼𝑛𝑐𝑜𝑚𝑒 = 1 −

𝐶𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 𝐴𝑓𝑡𝑒𝑟 − 𝑡𝑎𝑥 𝑖𝑛𝑐𝑜𝑚𝑒

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Aguiar and Bils (2015) report savings rate increased from 13% (1980-1982) to 23% (2005-2007) and to 25% (2008-2010). They state that this increase is opposite to what is reported in national income accounts (Aguiar and Bils, 2015).

Furthermore, they divide savings by the average after-tax income to report unadjusted savings rates and find that the savings rate has decreased from 3% in 1980 to −12% percent in 2010 (Aguiar and Bils, 2015). They find this be too extreme, because this decrease contradicts with the above savings findings from using the CES. Thus, they conclude that the consumption inequality observed from savings is inconsistent with the expenditure data, and this means that the expenditure data from CE might have a systematic measurement error, which is what they try to solve with their econometric model (Aguiar and Bils, 2015).

4.3. Methodology

This section will discuss their econometric methodology and how they address the measurement errors. Their notations are, ℎ = 1, … , 𝐻 for households, 𝑖 = 1, … , 𝐼 for income groups and 𝑗 = 1, … , 𝐽 for goods. Furthermore, 𝑥_ℎ𝑗𝑡 is the reported expenditure on good 𝑗, and 𝑥 ∗_ℎ𝑗𝑡 is the true expenditure.

𝑥_ℎ𝑗𝑡 = 𝑥 ∗_ℎ𝑗𝑡𝑒𝜁ℎ𝑗𝑡

𝜁_ℎ𝑗𝑡 is the error part and ideally it would be zero so that the estimate would give exactly the true value. However this is not case instead, 𝜁_ℎ𝑗𝑡 it consists of three parts; 𝜓_𝑡𝑗 is the mismeasurement for consumption good, 𝑗, that is underreported, 𝜙_𝑡𝑖 is the mismeasurement that occurs in a particular income group, 𝑖, for common goods and 𝑣_ℎ𝑗𝑡 is the good-household specific measurement error which is normalised to be zero (Aguiar and Bils, 2015).

𝜁_ℎ𝑗𝑡 = 𝜓_𝑡𝑗+ 𝜙_𝑡𝑖 + 𝑣_ℎ𝑗𝑡

In this case, 𝜓_𝑡𝑗 and 𝜙_𝑡𝑖 are systematic errors, meanwhile 𝑣_ℎ𝑗𝑡 is a classical measurement. Their identifying assumption which states that is not correlated to any parts of good 𝑗 and household ℎ at the time 𝑡, and thus 𝑣_ℎ𝑗𝑡 is a classical measurement error (Aguiar and Bils, 2015). From the above discussion, this means that 𝑣_ℎ𝑗𝑡 is a random error with a mean zero which is uncorrelated with both the independent variable and the error term. With their econometric model, they try to get rid of all three of the measurement errors.

For the first part of the estimation, they measure the total expenditure elasticises of all goods, then they do a log-log approximation to Engel curves (Aguiar and Bils, 2015). With a log-log specification, the coefficient of the independent variable equals to the elasticity meaning; 1% change in the independent variable will result in a 𝛽₁% change in the dependent

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variable. This elasticity shows how much the expenditure of goods change when income changes, and this is the same description of the Engel curve.

Aguiar and Bils (2015) measure the true expenditure in first-order expansion, where 𝑋_ℎ𝑡 is the total expenditure at time t by household h, Ζ_ℎis the vector for demographic dummies and the residual 𝑢_ℎ𝑗𝑡 includes income-specific measurement error, idiosyncratic shocks and mismeasurement.

ln 𝑥_ℎ𝑗𝑡− ln x̅ ℎ𝑗𝑡 = 𝛼_𝑗𝑡+ 𝛽_𝑗ln 𝑋_ℎ𝑡+ Γ_𝑗Ζ_ℎ+ 𝑢_ℎ𝑗𝑡

This equation is the first step of their estimation. From this, they get the 𝛽𝑗 value which is used in the second stage of the estimation later. With using this estimation equation, they come up with several problems. For instance, in the case of a zero expenditure on a particular good, log specification would not be appropriate to use because ln 0 would be minus infinity which would make the left side of the equation minus infinity. Therefore, they use “percentage deviation from average expenditure of a good” (Aguiar and Bils, 2015, p. 2739) instead of ln 𝑥_ℎ𝑗𝑡 − ln x̅ ℎ𝑗𝑡. Another problem would arise because mismeasurement of goods in the expenditure would be correlated with the measurement error in the residual (Aguiar and Bils, 2015). To get rid of this endogeneity problem, they use two different IV regressions. The first one uses dummies for income groups and log after-tax income to instrument for total expenditure and for the second one Engel elasticities of the expenditures in the first two total expenditure to instrument for the final two quarters’ total expenditure (Aguiar and Bils, 2015).

For the second part of the estimation, they invert the demand system to get an estimate of how consumption inequality changed over the years and they use 𝛽_𝑗 from the first stage (Aguiar and Bils, 2015).

𝑥̂ = 𝛼𝑖𝑗𝑡 𝑗𝑡+ 𝜙𝑗𝑖+ 𝛽𝑗ln 𝑋ℎ𝑡∗ + 𝜑ℎ𝑗𝑡 + 𝜈ℎ𝑗𝑡 Then they add and subtract 𝑋_𝑖𝑡∗, so there is no actual change in the equation.

𝑥̂ = 𝛼_𝑖𝑗𝑡 _𝑗𝑡+ 𝜙_𝑗𝑖+ 𝛽_𝑗ln 𝑋_𝑖𝑡∗ + 𝛽_𝑗ln(𝑋_ℎ𝑡∗ − 𝑋_𝑖𝑡∗) + 𝜑_ℎ𝑗𝑡+ 𝜈_ℎ𝑗𝑡

From this equation the residual term is defined as: 𝜀_ℎ𝑗𝑡 = 𝛽_𝑗ln(𝑋_ℎ𝑡∗ − 𝑋_𝑖𝑡∗) + 𝜑_ℎ𝑗𝑡 + 𝜈_ℎ𝑗𝑡. This gives the final equation,

𝑥̂ = 𝛼_𝑖𝑗𝑡 _𝑗𝑡+ 𝜙_𝑗𝑖 + 𝛽_𝑗ln 𝑋_𝑖𝑡∗ + 𝜀_ℎ𝑗𝑡

From the model specification above, Aguiar and Bils (2015) regress 𝑥̂ on good-time _𝑖𝑗𝑡 dummies (which have 𝛼𝑗𝑡 as its coefficient), income-time dummies (which have 𝜙𝑗𝑖 as its dummies), the interaction between them and the first stage estimates. This regression will give the coefficient of ln 𝑋_𝑖𝑡∗.

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4.4. Results

Two of the goods that make a big part of the consumption are food at home and non-durable entertainment, which respectively have elasticities of 0.37 and 1.33. Aguiar and Bils (2015) make a graph of 𝑁𝑜𝑛−𝑑𝑢𝑟𝑎𝑏𝑙𝑒 𝐸𝑛𝑡𝑎𝑟𝑡𝑎𝑖𝑛𝑚𝑒𝑛𝑡

𝐹𝑜𝑜𝑑 𝑎𝑡 𝐻𝑜𝑚𝑒 for high-income and low-income households, and find that high-income households shift from food to non-durable entertainment while the reverse is true for low-income households. This shift of high-income households to a luxury good mean that there is an increase in expenditure inequality because low-income households’ consumption on entertainment decreased 16 percent while for high-income households it increased 48 percent (Aguiar and Bils, 2015).

Furthermore, the second-stage regression shows a more precise estimate of consumption inequality, since it shows the change in consumption inequality and compares it to the 1980-1982 period. First regression they do is an OLS regression and find the estimated log consumption inequality to be 0.85 and for the first stage this was 0.90 which shows that consumption inequality in the two-step estimation is almost the same as the first-stage one (Aguiar and Bils, 2015). However, they mention that OLS “weights all goods equally”, which may cause the goods that have small shares in the total expenditure to affect the results (Aguiar and Bils, 2015). This is why they use Weighted Least Squares (WLS) in the remaining regressions where they measure the share of each good from national income accounts’ personal consumption expenditures (PCE) part. WLS regressions suggest that between 1980-2010, after-tax income ratio increased by 21 points, while consumption ratio increased by 13 points (Aguiar and Bils, 2015).

Additionally, they provide an estimation for the income-specific measurement error, 𝜙_𝑗𝑖, and it shows that it very small and positive which means that consumption inequality is overstated in the first years because a positive 𝜙_𝑗𝑖 indicates high-income groups overstating their expenditures while low-income ones understating which results in an overall overreporting (Aguiar and Bils, 2015). Furthermore, they do a robustness check with relaxing the assumption of having a log-linear demand system by using a weighted non-linear specification. However, this does not significantly change the conclusion of a systematic measurement of error that results in an understatement of consumption inequality because of the reporting differences in high- and low-income groups (Aguiar and Bils, 2015). The second assumption they relax as a part of robustness is the assumption of expenditure elasticises being stable over time. In line with this, they re-measure each time period’s expenditure elasticity and as a result of different elasticities, consumption inequality is found to be lower (Aguiar and Bils, 2015).

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In conclusion, they find that consumption inequality tracks income inequality with a larger degree than found in other papers such as Krueger and Perri (2006), because Aguiar and Bils (2015) observed that high-income households consumed more luxuries than necessities relative to low-income households. The main difference between Krueger and Perri (2006) and them is that Aguiar and Bils (2015) correct for two non-classical (systematic) errors which are the mismeasurement for consumption good and income group, and for classical good-household specific measurement error.

5. Income and Consumption Inequality

This section focuses on the theoretical reasons to the relationship between income and consumption inequality with regards to permanent and transitionary income shocks and the presence of insurance. After a general discussion of the theory, the framework provided by Blundell et al. (2008) about the partial insurance model and permanent and transitionary income shocks will be discussed

5.1. Theoretical Reasons for Income and Consumption Inequality

The link between income and consumption inequality is characterised by the income shocks and consumption insurance (Blundell et al, 2008). Friedman (1957, as cited in Krueger and Perri, 2006) showed that transitionary income shocks are easier to self-insure than persistent permanent income shocks. The fact that permanent income shocks are harder to absorb or insure means that their impact is more visible in consumption inequality. Therefore, the persistence of income shocks has a direct link to consumption. For instance, Krueger and Perri (2006) find that in the case of transitionary (low persistence) income shocks, the rise in consumption inequality is lower because households are able to insure themselves by accumulating capital.

In short, if the income shocks are transitionary, there would be no change in the consumption inequality, but if they are permanent, an increase in consumption inequality will observed (Attanasio and Pistaferri, 2016). Finally, making a distinction between transitionary and permanent income shocks are important because there can be better policy solutions to income inequality if the policy-makers know which type of income shock cause it (Attanasio and Pistaferri, 2016).

5.2. Blundell, Pistaferri and Preston (2008)

In line with this theory, Blundell et al. (2008) use a partial insurance model, which is they describe as the degree of income shocks transferring to consumption, to study the link between consumption and income inequality (Blundell et al., 2008). They first measure the partial insurance, then they estimate their model with panel data (Blundell et al., 2008). Furthermore,

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they make two assumptions before they start their empirical research. The first assumption is that the only idiosyncratic uncertainty consumers face is the net income and the second assumption is that consumption and leisure can be separated, which in together implies that all insurance will go through income (Blundell et al., 2008). In their model, variance of permanent and variance of transitionary parts of income are allowed change with time (Blundell et al., 2008).

Their equation for income growth is the following: Δ𝑦𝑖,𝑡 = 𝜁𝑖,𝑡+ Δ𝑣𝑖,𝑡

𝑣𝑖,𝑡 denotes the transitionary component whereas 𝜁𝑖,𝑡 denotes the permanent component of the income. Furthermore, for the consumption growth, they use the following equation to study the degree of transmission of income shocks to consumption.

Δ𝑐_𝑖,𝑡 = 𝜙_𝑖,𝑡𝜁_𝑖,𝑡 + 𝜓_𝑖,𝑡𝜀_𝑖,𝑡+ 𝜉_𝑖,𝑡

Where 𝑐_𝑖,𝑡 is the log of consumption; 𝜁_𝑖,𝑡 is the permanent income shocks that can have an impact on consumption with the factor of 𝜙_𝑖,𝑡; 𝜀_𝑖,𝑡 is the transitory income shocks that is calculated by the factor 𝜓_𝑖,𝑡; and finally 𝜉_𝑖,𝑡 is the random term that shows the innovations in consumption that are independent from income (Blundell et al., 2008). The insurance parameters which are 𝜙 and 𝜓 are the parameters that the researchers are interested in, and in the case of full insurance the following will equation would hold true; 𝜙_𝑖,𝑡 = 𝜓_𝑖,𝑡 = 0, and in the case of no insurance, it would look like this; 𝜙_𝑖,𝑡 = 𝜓_𝑖,𝑡 = 1. The model they used allows for self-insurance through savings which results in smoothing idiosyncratic shocks.

If the model is considered to be with constant relative risk aversion (CRRA) preferences, then it can be interpreted that for the individuals whose current assets are lower than future income, the transitionary shocks are insured through savings but the permanent shocks transfer to consumption (Blundell et al., 2008). This means that saving as a precaution acts as a self-insurance to permanent shocks only when the current assets are higher than the future income and thus this model shows that the link between income shocks and consumption depend on whether the income shock is permanent or transitionary (Blundell et al., 2008).

Furthermore, Blundell et al., 2008 uses mentioned income and consumption growth equations to give the covariance restrictions on both income and consumption growth. They look at variance and covariance of income and consumption to observe the inequality. Particularly, covariance is used to investigate the correlation. From these restriction equations, it is interpreted that; for income inequality to increase, it should be from an increase in either the variance of permanent shocks or the variance of income growth due to transitory shocks; and an increase in consumption inequality should be, either from a decrease in the degree of

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insurance or from an increase in the variances of permanent income shocks (Blundell et al., 2008).

Blundell et al.’s (2008) study focuses on the insurance parameters 𝜙 and 𝜓 and what kind of trend inequality followed in permanent and transitionary parts of income (Blundell et al., 2008). In separate tables for consumption and income, they report the variance of income growth, first-order autocovariances and second-order autocovariances. First and second in this case number of lag values used in the regression and second-order autocovariances give valuable information about the whether or not a correlation exists in the transitionary income. For income, the results show that the variance of income growth increased, and second-order coefficients were insignificant which means transitionary income is uncorrelated (Blundell et al., 2008). For consumption, a very high increase in variation of consumption growth is observed but this high increase is partly due to measurement error and similar to income, first and second-order autocovariances are insignificant (Blundell et al., 2008). Therefore, they do not find significant evidence to the effect of transitionary shocks on consumption growth.

With their combined panel data of PSID and CE, Blundell et al. (2008) plot the variance of log income and variance of log consumption from both the CE and the PSID data in a graph. This graph shows that the variance of log income has a steeper slope than variance of log consumption. Additionally, they observe that consumption inequality becomes flat after the mid 1980s, meanwhile income inequality continues to grow but slower (Blundell et al., 2008). They report an increase in the Gini coefficient for consumption inequality only from 0.25 to 0.28. This increase is almost similar to the one done by Krueger and Perri (2006). However, Blundell et al. (2008) acknowledge that the slight difference is due to Krueger and Perri (2006) not using panel data and therefore not allowing for the endurance of income shocks to change. However, Blundell et al. (2008) also do not control for measurement error, resulting in them finding a flat consumption inequality compared to the findings of an increasing consumption inequality in newer papers.

6. Conclusion

The increase in income inequality in the United States has been observed and researched by studies. However, there aren’t many studies available for consumption inequality and how it moved relative to income inequality. The reason for this is the unavailability of consistent data on consumption. The only big data set containing information about the consumption in the United States is the Consumer Expenditure Survey. However, many papers are stating that the CES might be subject to measurement error. The reason why conclusions about

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consumption inequality and its link with income inequality change are because of how researchers treat these measurement errors.

Krueger and Perri (2006), a relatively older study, calculate consumption directly by adding expenditures of nondurables, services, small durables and service flows from housing and vehicle. They do not acknowledge the presence of measurement errors and therefore do not control for it. Therefore, they conclude is that income inequality increased while consumption inequality remained flat.

On the contrary, Aguiar and Bils (2015) follow an improved model in terms of controlling for measurement errors and measuring consumption inequality. Instead of simply adding total expenditures, they follow an Engel curve approach and measure consumption by looking at relative spending on luxuries versus necessities for high- and low-income groups. The most important part is, in their two-stage regression, they control for two non-classical (systematic) and one classical measurement errors. With this model, they conclude a complementary increase in both income and consumption inequality.

Furthermore, Blundell et al. (2008) provide a framework for how income and consumption inequality is characterised by the persistence of the income shocks and the presence of insurance. By using a partial insurance model, they only find the effect of transitionary income shocks on consumption, and because transitionary shocks do not change the consumption, they observe the consumption inequality to be flat. If the income shocks were in permanent nature, then they would expect the consumption inequality to rise. This framework is useful in real life because, if policy-makers know the nature of the income shocks, they can implement the right policies to increase welfare (Attanasio and Pistaferri, 2016). However, Blundell et al. (2008) also fail to account for measurement errors, making their results biased.

In conclusion, it is well-documented that the CES data might be subject to mismeasurements and therefore those errors need to be addressed to get an unbiased estimate. Krueger and Perri (2006) do not acknowledge this, but newer literature such as Aguiar and Bils (2015) do acknowledge and correct for the measurement errors. This is why Krueger and Perri (2006) find consumption to be flat and yet Aguiar and Bils (2015) find it to be increasing. Attanasio and Pistaferri (2016) mention that Aguiar and Bils’ measure of consumption is a relatively credible one because their estimates are robust to measurement errors. Furthermore, Blundell et al. (2008) provides a detailed model for by including income shocks and insurance markets into the research, which might give more advanced information about the real-world solutions to income and consumption inequality. Therefore, future research can focus on the income shocks and insurance markets model provided by Blundell et al. (2008) and improve it

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by controlling for measurement errors associated with the CES data to get more accurate and robust results that explain the real-world trends better.

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