Opportunity as a replacement therapy

Abstract

Deaths from addiction are a pressing issue worldwide that has proven impossible to address with penalties or harm reduction policies. Utilizing Chetty, Hendren, et al. (2014)’s high-quality intergenerational mobility estimates for the US counties and resolving endogeneity with heteroskedasticity-based instruments, we show that a lack of economic opportunity almost fully (!) explains these deaths. We conclude that public spending to improve economic opportunities may have a better chance of reducing addiction than spending on drug law enforcement or harm reduction policies.

Full text

Opportunity as a replacement therapy
Sergey Alexeev
University of New South Wales, Australia
Thomas Mason
University of Manchester, United Kingdom
October, 2021
Abstract
Deaths from addiction are a pressing issue worldwide that has proven impossible
to address with penalties or harm reduction policies. Utilizing Chetty, Hendren,
et al. (2014)’s high-quality intergenerational mobility estimates for the US counties
and resolving endogeneity with heteroskedasticity-based instruments, we show that
a lack of economic opportunity almost fully (!) explains these deaths. We conclude
that public spending to improve economic opportunities may have a better chance of
reducing addiction than spending on drug law enforcement or harm reduction policies.
Keywords: death of despair, intergenerational mobility, addiction.
JEL codes: I1, I12, I14, D6, D63, J62.
1 Introduction
Across a wide spectrum of countries, nearly every year, the media reports the wors-
ening of economic opportunities and record levels of deaths from drug and alcohol
poisoning (e.g., Chetty, Grusky, et al. 2017; Kennedy and Siminski 2022; Krausz,
Westenberg, and Ziafat 2021; Manduca et al. 2020). The COVID-19 pandemic fur-
ther accelerated these trends (e.g., Couch, Fairlie, and Xu 2020; Mulligan 2020).
A causal linkage between these two areas has been speculated by Case and Deaton
(2015,2017,2020). They coined the term ‘death of despair,’ which initially referred
to a marked increase in the overall mortality of middle-aged white non-Hispanic in-
dividuals in the United States (US) attributed to suicide, drug and alcohol poisoning
(both accidental and undetermined intent), and deaths due to chronic liver diseases
and cirrhosis. Their presumed explanation is a lack of economic perspective. Similar
trends are now also evident in other countries (e.g., Australian Institute of Health
and Welfare 2021).
To quantify economic perspective, economists use measures of intergenerational
income mobility, which, in a more narrow sense, is understood as the degree to which
an individual’s position in the income distribution persists or changes from one gen-
eration to the next (J¨antti and Jenkins 2015). For example, a society in which an
individual’s adult income is altogether independent of their parents’ income is a highly
mobile society. A society in which one’s percentile in the income distribution is always
identical to one’s parents’ percentile is completely immobile. In a practical sense, in-
tergenerational income mobility demonstrates how individuals’ economic well-being is
determined by a factor they never had a chance to influence: their parents’ economic
well-being.
Apart from being a potential contributor into the death from dispare, income
mobility plays role the economy’s efficiency. Higher mobility is preferred because it
minimizes losses driven by talented and productive workers from the bottom of income
distribution not fully realizing their potential and contribution to society. Another

2 EVIDENCE FROM THE US COUNTIES 2
role of mobility is the encouragement of human capital accumulation. Individuals
from low-income countries lack incentives to invest in education or hard work if they
sense their prospects are out of their control. Individuals from wealthier households
are additionally discouraged from hard-working and education through reduced com-
petition from the poorer families.
Unfortunately, data on income mobility is scanty. Measuring mobility is a technical
and data-demanding exercise. It requires large, nationally representative longitudinal
surveys containing income information for two generations of earners observed at the
age when their income potential is maximized. This is the reason why a conclusive
empirical causal link between income immobility and death from despair has been hard
to establish.1Our main contribution is a causal quantification of how an inability
to escape one’s economic and social confines contributes to addiction and potential
mortality.
To achieve our goal, we use the various location-level measures of equality of
outcome and opportunity offered by Chetty, Hendren, et al. (2014). Their analysis
uses 40 million child-parent pairs using 17 years of tax data in the US, and, to date,
their work is the largest in the field, thus offering a unique opportunity to investigate
the role of immobility on addiction deaths. We now expand on the data sources.
2 Evidence from the US counties
2.1 Data
Table 1: Descriptive statistics
Variable N Mean Min
Percentiles
Max
1st 5th 10th 25th 50th 75th 90th 95th 99th
Deaths 3056 824.67 241.30 540.20 609.60 651.10 722.65 811.90 914.05 1011.10 1079.90 1228.40 1382.30
Immobility 2769 0.331 0.069 0.163 0.209 0.237 0.284 0.334 0.378 0.420 0.445 0.502 0.660
Inequality 2742 0.381 0.161 0.229 0.263 0.281 0.323 0.374 0.432 0.487 0.527 0.590 0.632
Unemployed 3272 8.9 1.4 3.0 4.0 4.9 6.7 8.6 10.6 12.7 14.9 20.7 29.3
White 3272 76.324 0.200 0.500 28.880 43.910 65.340 85.000 94.010 96.560 97.290 98.210 99.160
Source: Centers for Disease Control and Prevention (2022), Chetty, Hendren, et al. (2014), Economic Research Service (2022).
We construct a cross-sectional county-level dataset from multiple publicly available
sources. Table 1characterises the variable used in the analysis. Our outcome variable
is age-adjusted (to the 2000 US population) death rates (per 100,000) from drug and
alcohol-induced causes for 2011 taken from the WONDER online database run by
Centers for Disease Control and Prevention (2022). These deaths are unambiguously
defined by the CDC and located in a separate category. A known limitation of this
database is that statistics representing fewer than ten deaths are suppressed, but since
we pool together deaths for all genders, races, and age groups, our values are always
well above this threshold.
Although death data is available for any year, 2011 is considered to match the
county-level estimates of mobility that we take from Chetty, Hendren, et al. (2014).
In their paper, the mobility estimates are based on a model where the outcome variable
is respondent income in the fiscal year 2011–2012. In practice, for the country-level
1See Knapp et al. (2019) for a commendable attempt.

2 EVIDENCE FROM THE US COUNTIES 3
estimates, we use the data titled ‘Geography of Mobility: County Intergenerational
Mobility Statistics and Selected Covariates’ provided by the Harvard University Op-
portunity Insights Team. The team aggregates various datasets based on published
papers.
Immobility is defined as the slope from the OLS regression of child rank on parent
rank in their respective income distributions within each county. Inequality is the
Gini coefficient. Both immobility and inequality are analytically bound within a unit
interval, with zero corresponding to the most egalitarian outcome and 1 to the least.
Unexpectedly, in the data, the inequality coefficients for Cherokee County in North
Carolina and New York County in New York were higher than unity, which is not
possible. To address this in the least ad-hoc manner, we considered the top 1% of
inequality estimates as missing data.
Other county-level covariates are taken from the Atlas of Rural and Small-Town
America provided by the US Department of Agriculture (Economic Research Service
2022). These covariates are the unemployment rate and per cent of non-Hispanic
whites in 2010.
2.2 Methods
The primary objective is to estimate the effect of income immobility on death from
addiction using cross-sectional country-level data. To do that, we formulate the fol-
lowing linear model with an endogenous explanatory variable:
ysl =αs+βxsl +w′
slµ+εsl,1(1)
xsl =γs+θz′
sl +w′
slϕ+εsl,2(2)
where Equation (1) is the structural equation of interest, Equation (2) is a linear pro-
jection for the endogenous variable. The variable ysl is the death rate from drug and
alcohol-induced causes in state sand county l. The variable xsl is an intergenerational
income persistence (immobility) in county l. The array of controls is denoted with
w′
sl. Parameters αsand γsare the state fixed effects. Finally, the IVs are represented
by the vector zsl′.
The IVs are constructed exploiting information contained in heteroskedasticity of
εsl,2(Lewbel 2012; Lewbel, Schennach, and Zhang 2022). Here, z′
sl is a generated
from w′
sl under the standard assumption of regressors exogeneity, E(w′
slεsl,i ) = 0,
i= 1,2; and two additional assumptions that z′
sl is uncorrelated with the product of
heteroskedastic errors, Cov(z′
sl, εsl,1εsl,2) = 0 and Cov(z′
sl, εsl,2)= 0.
In practice, the following two-step procedure is performed (Baum and Lewbel
2019):
1. Estimate ˆ
θby regressing xsl on w′
sl and state dummies, obtaining residual bεsl,2=
xsl −w′
sl ˆ
θ−bγs.
2. Estimate αs,βand µby with regression of ysl on state dummies and xsl using
w′
sl and (z′
sl −z′
sl)bεsl,2as IVs, where zsl is the sample mean of z′
sl.

2 EVIDENCE FROM THE US COUNTIES 4
In the second step, we use a feasible, efficient, two-step generalised method of mo-
ments (GMM) estimator with robust variance. GMM is preferred because, when
heteroskedasticity is present, it is more efficient than the simple IV estimator (Baum,
Schaffer, and Stillman 2003).
2.3 Results
2.3.1 Immobility vs inequality
Figure 1: Deaths and immobility vs inequality – graphical association
Notes: Binned scatterplot with the OLS regressions of death on immobility (the left figure) or
inequality (the right figure) with robust errors and state fixed effects; figure also shown marginal
histograms.
Source: Centers for Disease Control and Prevention (2022), Chetty, Hendren, et al. (2014), Eco-
nomic Research Service (2022).
The left side of Figure 1shows a graphical association between deaths and immo-
bility using the binned scatterplot.2The red line corresponds to the OLS estimates
with state fixed effects and robust errors. The OLS coefficient stands at 509 and
is highly statistically significant. It means that a hypothetical move from complete
mobility to complete immobility causes 509 deaths from addiction. In contrast, the
right part of Figure 1shows the association between inequality and deaths. Here, the
coefficient is not statistically significant.
In these two regressions, the state fixed effects play an important role. If they are
not included, not only immobility but also inequality are associated with the deaths.
We believe that the effect should be included to account for state-level characteristics
and, importantly, public policies that are governed at the state level.
The demonstrated graphical links between immobility or inequality and death
are difficult to interpret causally. If we use the prefered heteroscedasticity-based
IV within the Durbin–Wu–Hausman test of endogeneity, we reject the consistency
of the OLS for immobility with Pvalue, χ2(1) <0.0001. That is, while OLS is
efficient, the estimated parameter is not centred around the true effect of immobility
on deaths. Remarkably, for inequality, the consistency can not be rejected with P
value, χ2(1) = 0.3952.
2The scatterplot allows users to visualize the relationship between pairs of variables but can
be difficult to interpret with large sample sizes. Binned scatterplot solves this issue by collapsing
observations into bins and fitting a regression line. Binned scatterplot creates 20 equal-sized bins;
thus, if the scattered points are closer to each other, the underlying number of observations is higher.
The horizontal distance between points, however, is hard to interpret. Therefore, the figure includes
two histograms showing the variables’ distribution (Pinna 2022).

2 EVIDENCE FROM THE US COUNTIES 5
Table 2: The effect of immobility on deaths from substances
Dependent variable: Deaths for substances per 100,000
IV
Immobility 1537.5*** 2099.5*** 873.0*** 965.2*** 1868.4* 887.1**
(401.5) (512.6) (229.0) (289.1) (792.7) (331.5)
Unemployment 13.88*** 14.06
(2.377) (15.41)
Unemployment20.485*** -0.294
(0.122) (0.413)
Share white 0.393 -4.891+
(0.305) (2.594)
Share white20.00601+ 0.0342*
(0.00313) (0.0151)
Unemployment 0.174*** 0.221
×Share (0.0146) (0.207)
OLS
Immobility 396.2*** 440.2*** 520.2*** 536.8*** 525.0*** 402.9***
(44.29) (44.34) (43.65) (44.33) (41.08) (46.60)
Unemployment 19.49*** 14.51
(1.374) (15.45)
Unemployment20.752*** -0.371
(0.0917) (0.397)
Share white 0.0620 -4.276+
(0.192) (2.426)
Share white20.00221 0.0207*
(0.00143) (0.0105)
Unemployment 0.168*** 0.355+
×Share (0.0117) (0.205)
State FE ✓ ✓ ✓ ✓ ✓ ✓
N 2765 2765 2765 2765 2765 2765
Notes: The IV is constructed exploiting information contained in heteroskedasticity of the included
regressors (Lewbel 2012). All variables are centred. Robust errors are reported in the brackets.
+p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001.
Source: Centers for Disease Control and Prevention (2022), Chetty, Hendren, et al. (2014), Eco-
nomic Research Service (2022).
Table 3: The effect of inequality on deaths from substances
Dependent variable: Deaths for substances per 100,000
IV
Inequality -1227.3 -1012.2 -255.6 -301.7 419.1 -187.2
(1104.1) (906.5) (269.4) (296.1) (286.8) (212.4)
Unemployment 24.56*** 41.94***
(3.194) (7.632)
Unemployment20.909*** -1.102***
(0.143) (0.215)
Share white -0.886+ 0.532
(0.492) (1.202)
Share white2-0.00679 -0.00978
(0.00420) (0.00756)
Unemployment 0.190*** 0.0647
×Share (0.0206) (0.0563)
OLS
Inequality 12.39 30.18 33.77 41.45 149.2*** 3.392
(34.91) (35.55) (40.71) (41.25) (37.61) (38.55)
Unemployment 21.28*** 38.37***
(1.425) (7.780)
Unemployment20.814*** -1.044***
(0.0989) (0.214)
Share white -0.441* -0.156
(0.216) (1.281)
Share white2-0.00244 -0.00456
(0.00159) (0.00720)
Unemployment 0.173*** 0.0907
×Share (0.0129) (0.0564)
State FE ✓ ✓ ✓ ✓ ✓ ✓
N 2738 2738 2738 2738 2738 2738
Notes: The IV is constructed exploiting information contained in heteroskedasticity of the
included regressors (Lewbel 2012). All variables are centred. Robust errors are reported in the
brackets.
+p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001.
Source: Centers for Disease Control and Prevention (2022), Chetty, Hendren, et al. (2014),
Economic Research Service (2022).

2 EVIDENCE FROM THE US COUNTIES 6
We now report the estimates when our empirical framework is applied to the data.
Table 2focus on the effect of immobility and Table 3of inequality. The top of the
tables reports the IV results, and the bottom reports the corresponding OLS results.
To generate the IV, we use two regressors and their functions. These regressions were
chosen based on the plausibility of being exogenous and, more importantly, because
they exhibit sufficient heteroskedasticity to satisfy the assumption of the IV relevance.
The second criterion is more restrictive than the first one.
While we report only results using regressors based on unemployment and race
composition, we also tested a number of other regressions that satisfied both criteria.
In all cases, we see that OLS estimates of the effect of immobility are underestimated,
whereas the estimates of the effect of inequality are never precise.
The IV methods that we apply require that the variables be centred. To have
OLS estimates that are directly comparable, they are also computed on the same
centred variables. The usual benefit of centring also applies; that is, the variance
of the included interaction and polynomial terms are improved (Angrist and Pischke
2008, Ch. 6). Centring also improves the interpretation of the intercept and the direct
comparison of the coefficients in the same model, but these are of no substantive value
to us since regressors are chosen for their heteroskedasticity.
In the rightmost column of the tables, we report the results for the full mod-
els; other columns show the results when variables are included individually. In all
columns of Table 2, the immobility estimates are much higher than those reported
in Figure 1. This shows that the OLS underestimates the effect of immobility. The
true effect might be up twice higher. The full model estimated with OLS shows that
nearly all nonfocal coefficients are not statistically significant, indirectly supporting
the assumption of the regressors’ exogeneity. In contrast, the effect of inequity, as
shown in all columns in Table 3, is not present.
2.3.2 Immobility via inequality
Figure 2: The Great Gatsby Curve across the US counties
Notes: OLS regressions with robust errors. The state fixed effects are included in the left figures
but excluded on the right.
Source: Centers for Disease Control and Prevention (2022), Chetty, Hendren, et al. (2014), Eco-
nomic Research Service (2022).
At this point, one should develop a suspicion that inequality is a potential IV
since it is known to correlate closely with immobility (Durlauf, Kourtellos, and Tan

2 EVIDENCE FROM THE US COUNTIES 7
2022); but at the same time, it does not appear to influence deaths from substance
abuse. Figure 2plots the OLS regression line and reports robust standard errors
corresponding to the model where immobility is the outcome and inequality is a
regressor. A strong relationship is present; it holds true whether state fixed effects
are included (the left figure) or not (the right figure).
Table 4: The effect of immobility on deaths from substances – over-identified equation
Dependent variable: Deaths for substances per 100,000
Immobility 386.6+ 465.5* 663.5** 781.5** 1019.5*** 852.6**
(206.6) (213.1) (218.7) (267.9) (209.6) (288.6)
Unemployment 20.36*** 21.26*
(1.644) (9.656)
Unemployment20.869*** -0.518+
(0.0786) (0.279)
Share white 0.162 -4.106*
(0.315) (1.861)
Share white20.00427 0.0315*
(0.00308) (0.0138)
Unemployment 0.169*** 0.103+
×Share (0.0124) (0.0533)
State FE ✓ ✓ ✓ ✓ ✓ ✓
¯
R20.190 0.156 0.0604 0.0508 0.0753 0.164
N 2684 2684 2684 2684 2684 2684
Jval 7.808 7.974 0.508 0.117 1.225 3.138
J df 1 1 1 1 1 5
J P value 0.00520 0.00474 0.476 0.732 0.268 0.679
Notes: The IVs are constructed exploiting information contained in heteroskedasticity of the
included regressors (Lewbel 2012). The second IV is the Gini coefficient. All variables are
centred. Robust errors are reported in the brackets.
+p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001.
Source: Centers for Disease Control and Prevention (2022), Chetty, Hendren, et al. (2014),
Economic Research Service (2022).
Table 4reports the results when the inequality and heteroskedasticity are jointly
treated as the IVs. This allows greater efficiency and permits Sargan–Hansen tests
of the orthogonality conditions. The null hypothesis of this test is that all excluded
instruments are exogenous and valid. Each column of the table reports Hansen’s J.
The Pvalue indicates no problem with any of the IVs (except in the first two columns).
The full model in the right column shows minor differences relative to Table 2in the
point estimates for immobility, but the efficiency (and thus our confidence in our
findings) is markedly improved.
2.3.3 Marginal effects
While the established effect of immobility on deaths appears statistically robust, it is
hard to interpret the effect in an economic or clinical sense. The literal interpretation
of the estimated effect is that a marginal increase in immobility (the usual ∂y/∂x)
produces 852.6 deaths on average, with this effect being constant for any initial value
of immobility. This number of deaths is nearly the same as the mean deaths in the
data – 824.57 This effect is shown on the left side of Figure 3. It shows the predicted
death for 11 values of immobility, which are all the same.
A more appealing interpretation is a change in the deaths for a proportional change
in immobility (semi-elasticity). This effect is shown on the right side of Figure 3. The
semi-elasticity is computed as a numeral derivative of the form ∂y/∂ ln(x) = x×∂y/∂x
as explained in Baum (2010) or Boggess and MacDonald (2013). The figure shows
the results for 11 values of immobility (point semi-elasticities). For example, a small

REFERENCES 8
Figure 3: The effect of immobility on death from substances – marginal effects
Notes: OLS regressions with robust errors. The state fixed effects are included in the left figures
but excluded on the right.
Source: Centers for Disease Control and Prevention (2022), Chetty, Hendren, et al. (2014), Eco-
nomic Research Service (2022).
percentage increase in immobility when immobility is 0.2 causes 170.52 deaths; for
0.5, it is 426.32, and for 0.7, it is 596.846.
3 International evidence
Tom?
4 Discussion
Declarations
Declarations of interest: none
This research did not receive any specific grant from funding agencies in the public,
commercial, or not-for-profit sectors.
The funding sources had no involvement in the conduction of the research and/or
preparation of the article; in the collection, analysis, and interpretation of data; in
the writing of the report; and in the decision to submit the article for publication.
Data used in this work is publicly available.
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