Dudley L. Poston, Jr. d-poston@tamu Department of Sociology Texas A&M University

Micro-level and Macro-level Effects of Household Poverty in the Texas Borderland & Lower Mississippi Delta:United States, 2006 Dudley L. Poston, Jr. d-poston@tamu.edu Department of Sociology Texas A&M University College Station, Texas, USA Presented at “Census Microdata: Findings and Futures” Conference, University of Manchester 1-3 September 2008

Introduction • The Texas Borderland and the Lower Mississippi Delta are the two poorest regions in the United States. • Both regions are predominately rural. • The Borderland is characterized by a high concentration of Latinos. • The Delta is characterized by a high concentration of blacks.

How is “Poverty” measured? • The next 2 slides show an example calculation, and the minimum poverty thresholds (in US$ in 2006), according to the size of household, and the number of children in the household. • Each household is assigned a poverty value of between 1 and 501 depending on its household income. If the hh income equals the threshold value, the hh receives a poverty value of 100.

EXAMPLE OF CALCULATION OF POVERTY VALUE FOR A HOUSEHOLD • Household A has five members: • two children, their mother, father, and great-aunt. • Their threshold was $24,662 dollars in 2006. (See poverty thresholds for 2006) • Suppose the members' incomes in 2006 were: THE CALCULATION OF POVERTY VALUE: Compare total family income with the family's threshold. Income / Threshold = $25,000 / $24,662 = 1.01 * 100 = 101

Three Poverty Measures at Level-1:The Dependent Variables 1. Whether household is in deep poverty (poverty score of 50 or less) (yes = 1) 2. Whether household is in poverty (poverty score of 100 or less) (yes = 1) 3. Whether household is near or in poverty (poverty score of 150 or less) (yes = 1)

Data The multi-level analyses reported are based on micro-data (level-1) of household heads living in households in the 10 PUMAs in the Texas Borderland, and in the 34 PUMAs in the Lower Mississippi Delta; we use macro-data (level-2) for the 44 PUMAs. From the 1% PUMS of the 2006 American Community Survey, we have developed a sample of 26,425 households in the Texas Borderland and Mississippi Delta; these are one-family households. These are the level-1 data; the household heads are between the ages of 20 and 79. From other data sources, we developed macro-level data for the 44 Borderland and Delta PUMAs. These are the level-2 units.

American Community Survey We use data from the American Community Survey, 2006 sample • 1-in-100 national random sample of the population. • The data do not include persons in group quarters. • This is a weighted sample. Weights are used to produce accurate statistics, esp. standard errors. • The smallest identifiable geographic unit is the PUMA (Public Use Microdata Area), containing at least 100,000 persons. PUMAs do not cross state boundaries. • Approximately 1,344,000 households and 2,970,000 person records. Our sample data of 26,425 households were extracted from this ACS sample of households in the 44 PUMAs of the Borderland and Delta (Above description taken from: http://usa.ipums.org/usa/)

The Regions The next five slides show the PUMAs (Public Use Microdata Areas) we use in our analysis. Each PUMA contains one or more counties. These PUMAs define the “Borderland” and “Delta” regions we are studying. Each PUMA contains samples of households.

PUMA Counties in Borderland and Delta

■ PUMA 400 ■ Jonesboro ■ West Memphis ■ PUMA 700 ■ PUMA 800 ■ Little Rock ■ Pine Bluff ■ PUMA 1700 ■ PUMA 1800 Arkansas

■ Monroe ■ PUMA 500 t ■ PUMA 600 ■ PUMA 700 t ■ PUMA 1200 ■ PUMA 1300 t ■ PUMA 2500 ■ PUMA 2100 ■ Baton Rouge ■ PUMA 1600 ■ PUMA 1700 ■ PUMA 2400 ■ PUMA 1905 L ■Kenner-Metairie L ■ New Orleans L Louisiana *t= top of map, L= lower part of map

■ PUMA 100 ■ PUMA 200 ■ PUMA 500 ■ PUMA 600 ■ PUMA 700 ■ PUMA 1600 ■ PUMA 800 ■ Jackson ■ PUMA 1300 ■ PUMA 1700 ■ PUMA 200 Mississippi

Multilevel research had its start in the field of education. In education, students are grouped in classes, and both students and the classes have characteristics of interest. In our research, we are looking at households that are grouped (aggregated) in PUMAs. What is Multilevel Analysis?

Households and PUMAs • We hypothesize that when it comes to predicting the log likelihood of a household being in poverty, that characteristics of the household (and/or household head), as well as characteristics of the PUMA in which the household is located, will be important independent variables in the model.

Past Research • Traditionally, multilevel research has been conducted in two ways, both of which are statistically incorrect.

The first technique is to disaggregate all the contextual level variables down to the level of the households, and use OLS to solve the equation. • The problem with this approach is that if we know that households are from the same PUMA, then we also know that those households have the same values on the various PUMA characteristics. • “Thus we cannot use the assumption of independence of observations that is basic for the use of classic statistical techniques” (de Leeuw, 1992: xiv).

An alternate technique is to aggregate the household-level characteristics up to the contextual level, say of the PUMA, and to conduct the analysis at the aggregate (PUMA) level. • The main problem here is that we discard all the within-group (i.e., within-PUMA) variation; as much as 80-90 percent of the variation could be thrown away before the analysis begins.

Multilevel Models and Some Terminology • The approaches known as HLM are also known sometimes by other names, multilevel linear and nonlinear models (sociology), mixed-effects models and random-effects models (biometry), random-coefficient regression models (econometrics), and covariance components models (statistics).

The Logic and Methodology • Here is a 2-level model predicting a level-1 dichotomous outcome (Pij ) for the ith Household in the jth PUMA, with two independent variables, Wj and Xij (Wj is a characteristic of the PUMA and Xijis a characteristic of the Household): Pij = 00 + 01Wj + 10 Xij + 11Wj(Xij ) + u0j+ u1j(Xij - X-bar.j) + rij • In this, the macrolevel variable, Wj, interacts with the microlevel variable, Xij (as in 11), and the error structure contains both microlevel terms and macrolevel terms

We couldn’t estimate the preceding with 1-level logit models because the models require that the errors be independent, normally distributed, and have constant variance. In contrast, the random error in the above equation is of a more complex form, namely u0j+ u1j(Xij-X-bar.j)+rij. Such errors are dependent within each level-2 (PUMA) unit because the components u0jand u1jare common to every Household (or level-1 unit) within each of the j level-2 PUMA units. The errors also have unequal variances; this is because “u0j+u1j(Xij -X-bar.j)” depends upon u0j and u1jwhich vary across the level-2 PUMA units; it also depends on the value of “(Xij),” which varies across the level-1 Household units.

In the Borderland area there are 10 PUMAs containing 49 counties. Five of the PUMAs are metro PUMAs (El Paso, Laredo, Corpus Christi, Brownsville, and McAllen); the other five are nonmetro PUMAs. In the Delta there are 34 PUMAs containing 133 counties/parishes. Our multi-level analyses combine the Delta PUMAs with the Borderland PUMAs.

Our models examine three kinds of effects on the individual outcome of poverty: “b” effects, i.e., level-1 direct effects; “G” effects, i.e., level-2 direct effects; and “g” effects, i.e., cross level interactions of the level-2 variables on the slopes.

Descriptive statistics: three poverty measures, households, Borderland & Delta,2006 • Variable | Obs Mean Std. Dev. • deeppov | 26,425 .0652791 .2470223 • pov100 | 26,425 .1808136 .384871 • nearpov | 26,425 .2977483 .4572769

Correlations: three poverty measures, households, Borderland & Delta,2006 • (obs=26,425) • | deeppov pov100 nearpov • -------------+--------------------------- • deeppov | 1.0000 • pov100 | 0.5625 1.0000 • nearpov | 0.4059 0.7215 1.0000

Is there Variance at level-2? • Multilevel analysis is only appropriate when there is a statistically significant amount of variance in the dependent variable at level-2, i.e., among the 44 PUMAs. • The level-2 variance values, known as τ00, for the three poverty dependent variables are shown on the next slide, along with their respective χ2 values and significance levels. • We see that each τ00 is statistically significant, justifying the multilevel analysis of each of the three poverty dependent variables.

One-way ANOVAs for Non-linear Logistic Regression Multilevel Models

Intra-class Correlation The intra-class correlation is the ratio of level-2 variance (referred to as τ00) to the total variance in the dependent variable, and tells us the proportion of variance that occurs at level 2. In a nonlinear model, however, the variance at level-1 is heteroscedastic so can’t be used per se in the denominator. Statisticians, e.g., Scott Long and others, recommend thinking about the level-1 model and the dependent variable, i.e., being in poverty (yes or no), in terms of a latent (unmeasured) variable, and to consider its variance as Π2/3, i.e., the constant variance of the unmeasured latent variable of 3.29. Thus the intra-class correlation,ρ, is calculated as: ρ = τ00/ (τ00 + Π2/3).

The three poverty dependent variables have statistically significant variances at level-2 Deep poverty = 5.4% of variance occurs at level-2 100% poverty = 5.6% of variance occurs at level-2 Near poverty = 5.6% variance occurs at level-2

Descriptive Statistics:Five Level-1 Independent Variables,26,425 Households, Delta & Borderland, 2006 • Variable | Mean Std. Dev. Min Max • -------------------------------------------------- Sex of Head (+)| 1.45 .50 1 2 m=1, f=2 Educ of Head(-) 10.5 3.1 1 17 Duncan SEI (-) 33.2 28.1 0 96 Age (-) 51.1 15.2 20 79 Black or Hispanic Yes =1 (+) .39 .49 0 1

Descriptive Statistics:Five Level-2 Independent Variables,44 PUMAs, Delta & Borderland, @2000 • Variable | Mean Std. Dev. Min Max • -------------------------------------------------- % FIRE | 4.83 1.50 3.00 9.00 (-) % < 9th grade | 27.37 7.29 10.80 40.00 (+) % in poverty | 12.32 4.00 4.00 22.20 (+) % rural | 39.92 22.80 1.00 84.00 (-) % fem HH,no H | 22.00 6.43 11.00 40.00 (+)

HLM coefficients The (gamma)  coefficients are the major indicators of the effects of level-1 characteristics and level-2 characteristics on the outcome, as well as the effects of level-2 characteristics on the level-1 slopes.

First consider the effects of the level-1 variables on each of the three poverty outcomes, controlling for whether the PUMA is in Texas. Tables 1-3 report these results for deep poverty, 100% poverty, and near poverty. Regarding the odds of being in poverty: the effect of age is negative, sex (being female) is positive, education is negative, Duncan’s SEI is negative, and being a main minority is positive.

Re. the cross-level interactions: • Positive effect of being female on all three poverty outcomes is weaker in Texas than in the Delta. • Age is negative on poverty, and so is education, and so is SEI, in the same ways in both Texas and the Delta. • Positive effect of being a minority is less on all three poverty outcomes in Texas compared to in the Delta.

Now examine level-2 effects of % of PUMA with less than 9th grade education; and % rural (Tables 4-6). The direct effect on poverty of % less than 9th grade is positive on all three poverty outcomes; the direct effect of % rural is negative only for deep poverty. The indirect effects of these two level-2 variables are sometimes significant, and sometimes insignificant.

Now examine level-2 effects of % of PUMA in poverty; and % rural (Tables 7-9). The direct effect on poverty of % of PUMA in poverty is positive on all three poverty outcomes; the direct effect of % rural is negative only for deep poverty. The indirect effects of these two level-2 variables are sometimes significant, and sometimes insignificant.

Dudley L. Poston, Jr. d-poston@tamu Department of Sociology Texas A&M University