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Opportunity as a replacement therapy

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Abstract and Figures

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.
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Opportunity as a replacement therapy
Sergey Alexeev
University of New South Wales, Australia
Thomas Mason
University of Manchester, United Kingdom
October, 2021
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
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
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
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
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.
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
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
xsl =γs+θz
sl +w
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
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
1. Estimate ˆ
θby regressing xsl on w
sl and state dummies, obtaining residual bεsl,2=
xsl w
sl ˆ
2. Estimate αs,βand µby with regression of ysl on state dummies and xsl using
sl and (z
sl z
sl)bεsl,2as IVs, where zsl is the sample mean of z
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
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).
Table 2: The effect of immobility on deaths from substances
Dependent variable: Deaths for substances per 100,000
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)
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
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)
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
+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).
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
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
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
4 Discussion
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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I introduce binscatterhist, a command that extends the functionality of the popular binscatter command (Stepner, 2013, Statistical Software Components S457709, Department of Economics, Boston College). binscatter allows researchers to summarize the relationship between two variables in an informative and versatile way by collapsing scattered points into bins. However, information about the variables’ frequencies gets lost in the process. binscatterhist solves this issue by allowing the user to further enrich the graphs by plotting the variables’ underlying distribution. The binscatterhist command includes options for different regression methods, including reghdfe (Correia, 2014, Statistical Software Components S457874, Department of Economics, Boston College) and areg, and robust and clustered standard errors, with automatic reporting of estimation results and sample size.
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This paper provides early evidence of the impacts of the COVID-19 pandemic on minority unemployment in the United States. In the first month following March adoptions of social distancing measures by states, unemployment rose to 14.5 percent but a much higher 24.4 percent when we correct for potential data misclassification noted by the BLS. Using the official definition, unemployment in April 2020 among African-Americans rose by less than what would have been anticipated (to 16.6 percent) based on previous recessions, and the long-term ordering of unemployment across racial/ethnic groups was altered with Latinx unemployment (18.2 percent) rising for the first time to the highest among major groups. Difference-in-difference estimates confirm that the initial gap in unemployment between whites and blacks in April was not different than in periods prior to the pandemic; however, the racial gap expanded as unemployment for whites declined in the next two months but was largely stagnant for blacks. The initially large gap in unemployment between whites and Latinx in April was sustained in May and June as unemployment declined similarly for both groups. Non-linear decompositions show a favorable industry distribution partly protected black employment during the early stages of the pandemic, but that an unfavorable occupational distribution and lower average skills levels placed them at higher risk of job losses. An unfavorable occupational distribution and lower skills contributed to a sharply widened Latinx-white unemployment gap that moderated over time as rehiring occurred. These findings of disproportionate impacts on minority unemployment raise important concerns regarding lost earnings and wealth, and longer-term consequences of the pandemic on racial inequality in the United States.
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This is the first paper that studies the effects of including non-monetary income from housing (imputed rent) in the measure of income on intergenerational income mobility. Using national panel data sets for Australia, the United States and Germany, it is shown that only Australian society becomes 22% less mobile as measured by an intergenerational rank correlation. This decrease is also confirmed using the intergenerational transition matrices. As a result, cross-regional comparisons of intergenerational income mobility may be misleading, especially using tax data as imputed rent is rarely taxed.
We show that a standard linear triangular two equation system can be point identified, without the use of instruments or any other side information. We find that the only case where the model is not point identified is when a latent variable that causes endogeneity is normally distributed. In this non-identified case, we derive the sharp identified set. We apply our results to Acemoglu and Johnson’s (2007) model of life expectancy and GDP, obtaining point identification and comparable estimates to theirs, without using their (or any other) instrument.
This paper provides a synthesis of theoretical and empirical work on the Great Gatsby Curve, the positive empirical relationship between cross-sectional income inequality, and persistence of income across generations. We present statistical models of income dynamics that mechanically give rise to the relationship between inequality and mobility. Five distinct classes of theories are developed, including models on family investments, skills, social influences, political economy, and aspirations, each providing a behavioral mechanism to explain the relationship. Finally, we review empirical studies that provide evidence of the curve for a range of contexts and socioeconomic outcomes as well as explore evidence on mechanisms.
Purpose of the review: To assess the current state of the opioid overdose crisis along three major axes: drug markets and patterns of use, the effectiveness of systems of care, and international developments. Recent findings: Overdose is a major contributor to mortality and disability among people who use drugs. The increasing number of opioid overdoses in North America especially is an indication of changing drug markets and failing regional systems of care. Globally, we see three clusters of overdose prevalence: (1) a group of countries led by the United States with historically high rates of opioid overdose, (2) a group of countries with increasing rates within a concerning range, (3) a group with very low rates. The contamination of street drugs, the quality and accessibility of treatment, and the overall system of care all contribute to the prevalence of overdose. Summary: Drug markets and pattern of consumption in parts of the world are shifting towards contamination and opioids like fentanyl as the drug of choice, which dismantles insufficient and largely ineffective systems of care. Furthermore, outside of North America, more countries like Estonia, Lithuania, Sweden, Finland, and Norway show very concerning numbers. Without a consistent system response, effects will be devastating.
This paper examines the impact of the SARS epidemic in 2003 on intergenerational mobility in China. Using large cross-city variation in SARS cases, our triple difference-in-differences estimates suggest that the SARS epidemic significantly increases the intergenerational transmission of education. Our results show that a one percent increase in the number of SARS cases leads to a 9.3 percent increase in the maternal intergeneration transmission coefficient. The effect of the SARS epidemic is stronger for admission to 4-year bachelor programmes and more concentrated in female students and students in large cities. This paper also investigates the potential mechanisms and finds that more highly educated mothers tend to be more engaged in children’s studies during the epidemic period when teachers are absent. These results convey the warning message that pandemics may reduce intergenerational mobility of education.
Lewbel (2012, Journal of Business and Economic Statistics 30: 67–80) provides a heteroskedasticity-based estimator for linear regression models containing an endogenous regressor when no external instruments or other such information is available. The estimator is implemented in the command ivreg2h by Baum and Schaffer (2012, Statistical Software Components S457555, Department of Economics, Boston College). In this article, we give advice and instructions to researchers who want to use this estimator.