##### 4 Improvements in Small-Area Demographic Analysis with DLB Data
We now turn to two brief examples that illustrate how analysis can improve when the researcher uses all of the information in DLB data, as opposed to the usual censored form in {1}. We wish to demonstrate how improving fertility estimates improves demographic analysis, by means of some (simplified) examples of an increasingly common research task: analysis of demographic patterns over a large set of small geographic areas.

In order to illustrate the potential analytical gains from full use of DLB data, we estimated the Coale-Trussell M and m parameters twice for each of the 723 municipalities - first using the standard, BLY form of the data, and next using the full DLB sample back to a limit of five years before the census. In the absence of data on marital duration, we adopted the following simple procedure to convert from total to marital-only fertility rates within each municipality before estimating the Coale-Trussell parameters:

• tabulate Bg and Yg values for all women (either BLY or DLB versions)
• calculate pg, the proportion of women in each age group who were married in 1991
• approximate marital births (Bg') with total births: Bg' = Bg
• approximate marital exposure (Yg') as Yg' = pg Yg
• estimate (k,m) = (ln M, m) by Poisson regression of Bg' on vg* with offset ln(Ng* Yg')

Unlike the procedure for approximating marital fertility in the Monte Carlo simulations, this method uses only aggregate data on marital status. Differences between the two procedures are small. Our exposition again focuses on m, the estimated index of marital fertility control.

4.1 Example 1: Spatial Analysis

Table 6 displays summary information on the distribution of m estimates over municipalities. The BLY and DLB columns correspond to the two sources of data. Both data sources indicate that, overall, marital fertility control in Minas Gerais is high. The mean value of m (weighting all municipalities equally) is 0.94 from BLY data, and 0.84 from DLB data. BLY estimates of m are more variable across municipalities, however, with a higher standard deviation (0.68, versus 0.43 for DLB estimates). BLY estimates are also more prone to extreme, implausible values for m, at both the high and low ends of the distribution.

 Table 6 Distribution of Coale-Trussell m estimates across 723 Municipalities in Minas Gerais, 1991 Census BLY data DLB data Mean 0.94 0.84 Std. Dev. 0.68 0.43 Minimum -1.88 -0.65 5%ile 0.00 0.15 25%ile 0.51 0.56 Median 0.92 0.82 75%ile 1.27 1.08 95%ile 2.05 1.65 Maximum 4.96 2.67

Spatial patterns also emerge more clearly with the more stable DLB estimates. [Figure 2] displays two maps of the m estimates for Minas Gerais. Panels (a) and (b) map the BLY and DLB estimates, respectively. Neither map illustrates a clean, simple spatial structure of fertility control. (This might be too much to expect, since the spatial organization of other relevant variables may not be clean and simple.) Minas Gerais appears to have the highest levels of fertility control in the western "beak", the lowest levels in the north. Broadly speaking, there is a northeast-to-southwest gradient of increasing fertility control. The DLB map in panel (b) shows this pattern more coherently

Visual inspection of the maps tells only part of the story, however, because the eye naturally focuses more on the larger municipalities (e.g., those in the northwest). Many important details in the smaller southern and eastern municipalities may be difficult to see from the full map. Table 7 contains (informal) measures of the maps' global "smoothness".

 Table 7 Informal Measures of "Smoothness" for Minas Gerais maps of m BLY data DLB data Number of Municipalities 723 723 Number of Municipalities with m < 0 38 7 Fraction of Neighboring Municipalities in Identical m Categories* .285 .467 Mean Absolute Difference |mi-mj| between Neighbors .641 .324 Fraction of Neighbors with |mi-mj| £ 0.25 .274 .486 Fraction of Neighbors with |mi-mj| £ 0.50 .505 .783 Fraction of Neighbors with |mi-mj| £ 0.75 .679 .920 * "Neighboring" municipalities are those that share a boundary. Categories of m are defined in the map legends. All fractions in the table are calculated using row-standardized weights, so that municipalities with many neighbors and those with few neighbors receive equal treatment. The implicit question for all of the calculated fractions is "Select a municipality at random, then select one of its neighbors at random. What is the probability that the two selected cells satisfy the stated criterion?".

Data in the table indicate that pairs of neighboring municipalities fall in the same range of m (and therefore have identical map colors) approximately 47% of the time in the DLB map, versus 29% in the BLY map. The mean absolute difference in m estimates between neighboring municipalities is only half as large in the DLB map (0.32) as in the BLY map (0.64). Neighboring municipalities have m values within ±0.25 of one another nearly half of the time (49%) on the DLB map, but only about one fourth of the time (27%) in the BLY map. In short, a series of measures all suggest that the DLB map in panel (b) provides a smoother, more coherent, less mottled-looking picture of fertility control in 1991 than the BLY map. Although the spatial structure of fertility control is still complicated, DLB data filter out enough sampling noise from the BLY data to make the overall picture more sensible and more intelligible.

DLB estimation also improves formal statistical analysis of spatial patterns. [Figure 3] illustrates spatial autocorrelation in the BLY and DLB estimates of m, as measured by a common spatial statistic, Moran's I. The horizontal axis in the figure represents a simple distance measure(neighboring municipalities are at distance 1, neighbors of neighbors are at distance 2, and so forth; for reference, the radius of the main area of Minas Gerais, minus the western `beak', is approximately 12 - that is, municipalities on the northern edge of Minas Gerais are about 12 steps from municipalities at the center of the map). The vertical axis represents Moran's I, which is essentially the average correlation in estimated fertility control m between randomly chosen pairs of municipalities at the specified distance [7]. Positive values of I indicate that municipalities at a given distance from one another tend to have similar levels of fertility control, with higher values indicating stronger associations.

Both the DLB and BLY estimates show positive and declining correlations up to about 10 spatial lags, and negative correlations between more distant municipalities. This autocorrelation pattern is consistent with an overall gradient in m over Minas Gerais, as opposed to a set of locally homogeneous but globally heterogeneous "patches" of low or high fertility control ([7], p. 67). It is also the statistical manifestation of the impression made by the maps (particularly the DLB map in panel b) in [Figure 2], which suggest a fairly clear northeast-to-southwest pattern of increasing fertility control.

Both BLY and DLB data exhibit the same pattern in [Figure 2]. However, this correlation pattern is stronger, clearer, and empirically more convincing when one uses the DLB data. Correlations among adjacent municipalities are +0.46 for the DLB estimates of m, compared to only +0.12 for the BLY estimates. At six spatial lags, correlations are +0.20 (DLB) and +0.07 (BLY). At 16 lags (close to corner-to-corner distances on the state map), correlations are -0.14 (DLB) and -0.05 (BLY). As before, expanding the sample size by using the DLB data clearly eliminates much of the sampling noise in the m estimates, and brings the spatial patterns into much sharper relief.

4.2 Example 2: Regression Analysis

As a second example, we use the Minas Gerais data in a manner more familiar to demographers: regression of municipal fertility control levels (m) on municipal characteristics. Like the spatial example above, the actual analysis that we present here is somewhat simplistic. Our objective is to provide a modest illustration of the value of DLB estimates, not to present a thorough, nuanced analysis of Brazilian fertility patterns.

In this spirit, consider a municipal-level analysis of the impact of growth by evangelical Protestant churches on marital fertility in Minas Gerais. Brazil is officially Catholic, but evangelicals are an increasing minority. In Minas Gerais in 1991, 87% of the population was Catholic, 8% evangelical. As with fertility, there are significant inter-municipal differences. Define EVANG as the fraction of women 20-49 in a municipality who report their religion as evangelical Protestant. Seven municipalities have EVANG=0, while at the other extreme eight have EVANG > 0.25, with a maximum (in the municipality of Itueta, on the eastern edge of the state) of 0.41.

It is unclear a priori whether a high percentage of evangelicals in a region should be correlated positively or negatively with fertility control. On one hand, many evangelical churches are family-oriented and emphasize traditional gender roles, which would suggest a pro-natalist influence and lower levels of control in regions with more evangelicals. On the other hand, areas that are "more evangelical" are by construction "less Catholic", which might mean that women tend to use more effective methods of birth control, making m higher in such regions.

A recent study comparing the family planning practices of evangelicals with Catholics in Rio de Janeiro, a state which borders southeastern Minas Gerais, Machado [5] found that evangelicals were more likely to use modern birth control methods, especially sterilization. Machado also notes that one prominent evangelical denomination (the Universal Church) has openly criticized the Catholic Church's position on birth control, has encouraged its members to pool resources in order to fund one another's sterilizations, and seems to have used female participation in debates on sexuality and family planning as a conscious strategy to recruit new members. These findings support the hypothesis of a positive correlation between a municipality's fraction evangelical and its estimated m value.

The left side of Table 8 reports results from a simple exploratory regression with the BLY data, in which the only independent variable other than EVANG is the fraction of the municipality's population residing in urban areas (URB):

 {15}

These BLY results suggest a positive correlation, but the EVANG coefficient of 0.68 is not significantly different from zero (p=.191), and the overall regression fit is poor (R2=.064). In contrast, using the DLB estimates of m as the dependent variable yields a strongly significant positive correlation between m and EVANG (ß=0.90; p=.004), and a much better overall fit for the regression (R2=.197).

 Table 8OLS Regression Estimates, Dependent Variable = m BLY DATA DLB DATA Coefficient Estimate t-stat P-value Estimate t-stat P-value Intercept 0.43 5.63 0.0000 0.27 6.01 0.0000 URB 0.81 6.63 0.0000 0.90 12.37 0.0000 EVANG 0.68 1.31 0.1911 0.90 2.92 0.0036 R2= 0.064 R2= 0.197

Once again, switching to DLB data rids the data of sample noise that obscures important patterns. The DLB regression in Table 8 is only a beginning in the analysis of the effect of religion on Brazilian fertility, but (contrary to the results from the BLY version) the significant coefficient on EVANG is an important signal to the researcher to investigate further.

 Estimating Parametric Fertility Models with Open Birth Interval Data Carl P. Schmertmann André Junqueira Caetano © 1999 - 2000 Max-Planck-Gesellschaft ISSN 1435-9871 http://www.demographic-research.org/Volumes/Vol1/5