## 5.  BGWR Negative Parameter Estimates With a Contiguity Prior

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### I. INTRODUCTION
- Research question: relative importance of institutions and geography for economic growth at a subnational level (central Appalachia).
- Main empirical approach: examine impact of geography (mountainousness) and institutions (percent of farmland under local control) on poverty rates in a homogeneous subnational region to avoid the need for instrumental variables.
- Key tentative finding: initial conditions matter greatly and can have effects lasting hundreds of years; evidence suggests institutional factors may play a dominant role over geographical isolation in Appalachia’s lagging development.

### II. DATA AND SAMPLE
- Region and sample:
  - Central Appalachia includes Appalachian counties of Kentucky, Maryland, Virginia, West Virginia, northwest Tennessee, and northeast North Carolina.
  - Nonmetropolitan U.S. counties sample: 1,887 observations (123 counties deleted mainly due to lack of land-ownership data).
  - Central Appalachian counties sample: 115 observations (nonmetropolitan counties above the 36th parallel).
- Variables:
  - Geography: mountainousness measured as standard deviation of altitude within a county divided by total county land area (Rappaport and Sachs (2003)).
  - Institutions: percent of acres in farm operation by owners divided by total acres in farms (1910 U.S. Census data).
  - Poverty: percent of people of all ages from Small Area Income and Poverty Estimates (1989) by the U.S. Census Bureau.
- Regional context statistics:
  - Area: about 200,000 square miles.
  - Population: some 23 million people.
  - Total personal income: almost US$600 billion.
  - Central Appalachia poverty rate: some 27 percent.

### III. EVIDENCE — OLS BENCHMARKS
- Nonmetropolitan U.S. Counties (Table 1)
  - Dependent variable: Poverty rate
  - Number of observations: 1887
  - R-squared: 0.283
  - Adjusted R-squared: 0.073
  - Coefficients:
    - Geography: Coefficient = -12.858; Standard Error = 4.319; t Statistic = -2.98; P>t = 0.003; [95% Confidence Interval] = -21.328, -4.387
    - Institutions: Coefficient = -7.02; Standard Error = 1.13; t Statistic = -6.20; P>t = 0.000; [95% Confidence Interval] = -9.24, -4.80
    - Constant: 22.52; Standard Error = 0.812; t Statistic = 7.84; P>t = 0.000; [95% Confidence Interval] = 20.93, 24.11
  - Note: 123 counties deleted mainly due to lack of land-ownership data.
- Nonmetropolitan Central Appalachian Counties (Table 2)
  - Dependent variable: Poverty rate
  - Number of observations: 115
  - R-squared: 0.102
  - Adjusted R-squared: 0.086
  - Coefficients:
    - Geography: Coefficient = -52.488; Standard Error = 17.459; t Statistic = -3.01; P>t = 0.003; [95% Confidence Interval] = -87.081, -17.896
    - Institutions: Coefficient = -16.027; Standard Error = 7.994; t Statistic = -2.00; P>t = 0.047; [95% Confidence Interval] = -31.865, -0.188
    - Constant: 40.853; Standard Error = 6.720; t Statistic = 6.08; P>t = 0.000; [95% Confidence Interval] = 27.537, 54.168
- Diagnostics:
  - Cook-Weisberg test: reject null of constant variance at the 1% level (heteroskedasticity present).
  - White’s test: confirms nonconstant variance.
  - Outliers: standardized and studentized residuals showed no influential outliers except a single observation.

### IV. SPATIAL ECONOMETRICS — BGWR APPROACH
- Motivation: OLS cannot capture locational aspects, spatial dependence, and spatial heterogeneity.
- Method: Bayesian Geographically Weighted Regression (BGWR) per LeSage (1999, 2004) to model spatial dependence, parameter smoothing, and heteroskedasticity via observation-level variance weights vi.
- Model components and priors:
  - Spatial weight matrix W uses GWR distance weighting: wij ∝ exp(-θ dij) with normalization.
  - Parameter smoothing: county-specific parameter βi is a convex combination of other βj weighted by wij; prior uncertainty ui.
  - Heteroskedasticity: observation-specific variance parameters vi with prior rr/)2χ distribution; hyperparameter r = 1 (strict belief in heteroskedasticity).
  - δ prior: diffuse value 0.01524 used; resulting estimated δ reported as 27.25 in text (distance-decay prior case); Table 3 lists delta value = 25.27 for the distance prior specification.
  - Gibbs sampling: 5000 draws with first 500 discarded.

### V. SPATIAL ESTIMATIONS — BGWR RESULTS AND CONTIGUITY PRIOR ROBUSTNESS
- Distance-decay prior (exponential weighting) — Table 3 summary:
  - r value: 1
  - Number of observations: 115
  - delta value: 25.27
  - Number of variables: 3
  - Bandwidth: 1.00
  - R-squared: 0.382
  - Number of iterations: 13
  - Number of draws: 5000
  - Decay type: Exponential
  - Discarded observations: 500
  - Prior type: Distance
- Distance-decay BGWR findings:
  - For 101 observations a negative relationship between poverty rates, geography and institutions is confirmed.
  - Sixty-one observations have significant parameter estimates with 95% probability (most in Virginia and West Virginia).
  - 4 observations: significant estimates for geography with 95% probability and for institutions with 90% probability.
  - 2 observations show reverse outcome.
  - Imposing a tight smoothing prior generated 10 new outliers in addition to the single deviant observation initially identified.
- Contiguity smoothing prior (robustness test):
  - Contiguity prior assumes neighboring observations affected exclusively by adjacent counties.
  - With a diffuse prior of 20.42 set, estimation produced δ = 5, indicating some inconsistency between smoothing specification and the data.
  - Despite this, parameter estimates are:
    - Very similar to distance-decay estimates.
    - Not systematically biased.
    - Smoother and exhibit higher precision than GWR estimates.
  - Contiguity-prior BGWR results:
    - 105 observations have negative coefficients for both explanatory variables.
    - 71 observations have statistically significant estimates for geography and institutions with 95% probability.
    - 10 observations: significant estimates with 95% probability for institutions and 90% for geography.
    - 2 observations have the opposite outcome.
- Spatial pattern:
  - Vast majority of counties have significant and negative coefficients.
  - Thirty-eight out of the 48 counties where this is not true are in the western part of the sample (eastern Kentucky and the Cumberland Plateau of middle Tennessee).
  - The western region (region 3) was settled somewhat later than the rest of the sample, possibly diminishing the impact of original colonial land-owning structure.

### VI. CONCLUSIONS AND POLICY-RELEVANT INSIGHTS
- Core conclusions:
  - Both institutions and geography matter for development; they are not mutually exclusive explanations.
  - Measures used are direct measurements linked to regional development (not instrumental variables).
  - Evidence suggests initial institutional arrangements (landownership patterns) have had long-lasting effects on poverty in central Appalachia.
  - While mountainousness remains a plausible contributor to poverty, evidence supports a stronger role for institutional factors in explaining Appalachia’s persistent poverty patterns.
- Policy implication (implicit):
  - Targeting institutional legacies (e.g., increasing local land control or addressing constraints rooted in historical land policies and elite rent-seeking) may be as important, or more important, than addressing geographic isolation alone.

### ADDITIONAL NOTES FROM CONCLUSION AND HISTORICAL CONTEXT
- Highways and tourism:
  - "The enormous expenditures on highways in Appalachia by the federal government have not ended poverty more than 40 years after the antipoverty program began."
  - One possible explanation: "the most mountainous areas of Appalachia are also the most scenic and that this has created job opportunities not available in less mountainous areas."
  - Historical note: "Tourism had already become an important industry in Appalachia by the 1840s."
- Historical settlement phases (Dunaway summary):
  - First phase: before the 1763 Proclamation Line; western Maryland, the Valley of Virginia, northwestern North Carolina, and West Virginia’s eastern and Ohio River edges.
  - Second phase: between 1770 and 1789; upper-east Tennessee, northwestern North Carolina and the area around Madison County, Kentucky.
  - Third phase: post-Revolutionary expansion; eastern Kentucky, the Cumberland Plateau of middle Tennessee, southwestern North Carolina and central West Virginia.
  - Final phase: late 1830s after forced removal of remaining Native Americans.
- Theoretical framing:
  - Paper is "not an attempt to develop an overall theory of economic growth in Appalachia."
  - Aim: "to find why Appalachia did not advance to the production frontier, perhaps as represented by the eastern seaboard of the United States."
  - Analysis consistent with growth models such as Galor (2005) and Parente and Prescott (2000) regarding traps inside the production frontier.
- Evidence on land policy:
  - Land policies before settlement tended to create an elite that, through rent-seeking behavior, retarded growth and contributed to poverty.

*Source: 5.  BGWR Negative Parameter Estimates With a Contiguity Prior — _wp06169 - 5.  BGWR Negative Parameter Estimates With a Contiguity Prior*

### References..............................................................................................................

### _wp06169 - References..............................................................................................................

### Tables
- 1.  Ordinary Least Squares Estimates (Nonmetropolitan U.S. Counties) ................................10
- 2.  Ordinary Least Squares Estimates (Nonmetropolitan Central Appalachian Counties) ......10
- 3.  Bayesian Geographically Weighted Regression Model .....................................................15

### Figures
- 1.  The Repeopling of Southern Appalachia, 1740–1840 ..........................................................8
- 2.  Percent of Total Population in Poverty by Country: 2003..................................................11
- 3.  BGWR and GWR Parameter Estimates..............................................................................16
- 4.  BGWR Negative Parameter Estimates With a Distance Decay Prior ................................17

*https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06169.pdf*

### 5.  BGWR Negative Parameter Estimates With a Contiguity Prior ........................................18

### 5.  BGWR Negative Parameter Estimates With a Contiguity Prior

### I. INTRODUCTION
- Literature debated the relative importance of institutions and geography for economic growth; no consensus exists.
- Subnational study focus: Appalachia (central Appalachia includes Appalachian counties of Kentucky, Maryland, Virginia, West Virginia, northwest Tennessee, and northeast North Carolina).
- Main empirical approach: examine impact of geography (mountainousness) and institutions (percent of farmland under local control) on poverty rates in a homogeneous subnational region to avoid need for instrumental variables.
- Key tentative finding: initial conditions matter greatly and can have effects lasting hundreds of years; evidence suggests institutional factors may play a dominant role over geographical isolation in Appalachia’s lagging development.

### II. INSTITUTIONS AND GEOGRAPHY — Background
- Two broad empirical approaches discussed: explaining relative growth rates vs. relative income/poverty levels; author uses point-in-time relative poverty rates (percent of people of all ages).
- Geography: many interacting biogeographic factors; study focuses on mountainousness (standard deviation of altitude within a county divided by total county land area, from Rappaport and Sachs (2003)).
- Institutions: critique of common institutional measures; the paper uses an institutional measure tied to long-lasting landownership patterns consistent with North’s (1981) concept of institutions.
- Hypotheses:
  - Mountainousness positively related to poverty (via transport costs).
  - Higher percent of farmland under local control negatively related to poverty.

### III. APPALACHIA (context)
- Region characteristics:
  - Covers about 200,000 square miles.
  - Population: some 23 million people.
  - Total personal income: almost US$600 billion.
  - Central Appalachia poverty rate: some 27 percent (more than twice the national average).
- Historical institutional note:
  - By 1800, three-quarters of the region’s acreage was absentee-owned.
  - Early land policies favored large land speculators; landed property concentrated in local elites and absentee owners.
- Institutional measure chosen: number of acres of land in farm operation by owners divided by total number of acres of land in farms (improved and unimproved); interpreted as percent of farmland under local control.

### IV. DATA
- Sample:
  - Nonmetropolitan U.S. counties sample: 1,887 observations (123 counties deleted mainly due to lack of land-ownership data).
  - Central Appalachian counties sample: 115 observations (nonmetropolitan counties of Kentucky, Maryland, North Carolina, Tennessee, Virginia and West Virginia above the 36th parallel).
- Variables:
  - Geography: mountainousness variable from Rappaport and Sachs (2003) — standard deviation of altitude within a county divided by total county land area.
  - Institutions: percent of acres in farm operation by owners divided by total acres in farms (1910 U.S. Census data used as earliest consistent county-level land-holdings).
  - Poverty rates: percent of people of all ages from Small Area Income and Poverty Estimates (1989) by the U.S. Census Bureau.
- Rationale: sample chosen to have relatively uniform geography and climate while allowing variation in mountainousness and landownership patterns.

### V. EVIDENCE
#### A. Ordinary Least Squares (OLS) benchmarks
- Nonmetropolitan U.S. Counties (Table 1)
  - Dependent variable: Poverty rate
  - Number of observations: 1887
  - R-squared: 0.283
  - Adjusted R-squared: 0.073
  - Coefficients (sign convention: negative coefficient means an increase in mountainousness or local land control is associated with a decline in poverty):
    - Geography: Coefficient = -12.858; Standard Error = 4.319; t Statistic = -2.98; P>t = 0.003; [95% Confidence Interval] = -21.328, -4.387
    - Institutions: Coefficient = -7.02; Standard Error = 1.13; t Statistic = -6.20; P>t = 0.000; [95% Confidence Interval] = -9.24, -4.80
    - Constant: 22.52; Standard Error = 0.812; t Statistic = 7.84; P>t = 0.000; [95% Confidence Interval] = 20.93, 24.11
  - Note: A total of 123 counties were deleted from the sample mainly due to lack of land-ownership data.
- Nonmetropolitan Central Appalachian Counties (Table 2)
  - Dependent variable: Poverty rate
  - Number of observations: 115
  - R-squared: 0.102
  - Adjusted R-squared: 0.086
  - Coefficients:
    - Geography: Coefficient = -52.488; Standard Error = 17.459; t Statistic = -3.01; P>t = 0.003; [95% Confidence Interval] = -87.081, -17.896
    - Institutions: Coefficient = -16.027; Standard Error = 7.994; t Statistic = -2.00; P>t = 0.047; [95% Confidence Interval] = -31.865, -0.188
    - Constant: 40.853; Standard Error = 6.720; t Statistic = 6.08; P>t = 0.000; [95% Confidence Interval] = 27.537, 54.168
- Diagnostic tests:
  - Cook-Weisberg test: reject null of constant variance at the 1% level (heteroskedasticity present).
  - White’s test: confirms nonconstant variance.
  - Outliers: standardized and studentized residuals showed no influential outliers except a single observation.

#### B. Spatial Econometrics — BGWR approach
- Motivation: OLS lacks ability to capture locational aspects and spatial dependence/heterogeneity.
- Method: Bayesian Geographically Weighted Regression (BGWR) following LeSage (1999, 2004) to model spatial dependence, parameter smoothing over space, and heteroskedasticity via observation-level variance weights vi.
- Model specification (as described):
  - Spatial weight matrix W defined using GWR distance weighting function: wij ∝ exp(-θ dij) with normalization.
  - Parameter smoothing: each county-specific parameter estimate βi is a convex combination of other βj weighted by wij, with prior uncertainty ui.
  - Heteroskedasticity accommodated via observation-specific variance parameters vi with prior rr/)2χ distribution (hyperparameter r).
  - Hyperparameters and priors used:
    - r value = 1 (strict belief in heteroskedasticity).
    - δ prior: diffuse value 0.01524 used; resulting estimated δ = 27.25 (distance-decay prior case), indicating consistency between prior and data.
    - Gibbs sampling: 5000 draws with first 500 discarded.

#### C. Spatial Estimations — BGWR results and contiguity prior robustness
- Distance-decay prior (exponential weighting) — Table 3 summary:
  - r value: 1
  - Number of observations: 115
  - delta value: 25.27 (Table 3 lists delta value = 25.27; earlier text reports estimation result δ = 27.25 when using a diffuse 0.01524 prior — both values are presented in source)
  - Number of variables: 3
  - Bandwidth: 1.00
  - R-squared: 0.382
  - Number of iterations: 13
  - Number of draws: 5000
  - Decay type: Exponential
  - Discarded observations: 500
  - Prior type: Distance
- Distance-decay BGWR findings:
  - For 101 observations a negative relationship between poverty rates, geography and institutions is confirmed.
  - Sixty-one observations have significant parameter estimates with 95% probability (most in Virginia and West Virginia).
  - 4 observations: significant estimates for geography with 95% probability and for institutions with 90% probability.
  - 2 observations show reverse outcome.
  - Imposing a tight smoothing prior generated 10 new outliers in addition to the single deviant observation initially identified.
- Contiguity smoothing prior (robustness test):
  - Contiguity prior assumes neighboring observations affected exclusively by adjacent counties.
  - With a diffuse prior of 20.42 set, estimation produced δ = 5, indicating some inconsistency between smoothing specification and the data.
  - Despite that, parameter estimates are:
    - Very similar to distance-decay estimates.
    - Not systematically biased.
    - Smoother and exhibit higher precision than GWR estimates.
  - Contiguity-prior BGWR results:
    - 105 observations have negative coefficients for both explanatory variables.
    - 71 observations have statistically significant estimates for geography and institutions with 95% probability.
    - 10 observations: significant estimates with 95% probability for institutions and 90% for geography.
    - 2 observations have the opposite outcome.
- Spatial pattern notes:
  - Vast majority of counties have significant and negative coefficients.
  - Thirty-eight out of the 48 counties where this is not true are in the western part of the sample (eastern Kentucky and the Cumberland Plateau of middle Tennessee).
  - The western region (region 3) was settled somewhat later than the rest of the sample, possibly diminishing the impact of original colonial land-owning structure.

### VI. CONCLUSIONS
- Study supports importance of both institutions and geography in development; both explanations can be relevant and are not mutually exclusive.
- Key takeaways:
  - Measures of geography and institutions used are not instrumental variables but direct measurements of factors linked to regional development.
  - Evidence suggests initial institutional arrangements (landownership patterns) have had long-lasting effects on poverty in central Appalachia.
  - While mountainousness remains a plausible contributor to poverty, the presented evidence supports a stronger role for institutional factors in explaining Appalachia’s persistent poverty patterns.
- Policy implication (implicit from findings): targeting institutional legacies (e.g., local land control and related constraints) may be as important, or more important, than addressing geographic isolation alone.

*Source: 5.  BGWR Negative Parameter Estimates With a Contiguity Prior — _wp06169 - 5.  BGWR Negative Parameter Estimates With a Contiguity Prior*

### conclusion. It is also interesting that the enormous expenditures on highways in Appalachia

### Conclusion

### Highways, tourism, and persistent poverty
- The paper notes that "the enormous expenditures on highways in Appalachia by the federal government have not ended poverty more than 40 years after the antipoverty program began."
- One possible explanation offered is that "the most mountainous areas of Appalachia are also the most scenic and that this has created job opportunities not available in less mountainous areas."
- Historical context: "Tourism had already become an important industry in Appalachia by the 1840s."

### Historical settlement phases (Dunaway summary)
- Four historical resettlement phases in Appalachia are summarized from Dunaway (1995):
  - First phase: before the 1763 Proclamation Line; covered western Maryland, the Valley of Virginia, northwestern North Carolina, and West Virginia’s eastern and Ohio River edges.
  - Second phase: between 1770 and 1789; included upper-east Tennessee, northwestern North Carolina and the area around Madison County, Kentucky.
  - Third phase: post-Revolutionary expansion; covered eastern Kentucky, the Cumberland Plateau of middle Tennessee, southwestern North Carolina and central West Virginia.
  - Final phase: occurred during the late 1830s after the forced removal of the remaining Native Americans.

### Purpose and theoretical framing
- The paper explicitly states it is "not an attempt to develop an overall theory of economic growth in Appalachia."
- The stated aim is "to find why Appalachia did not advance to the production frontier, perhaps as represented by the eastern seaboard of the United States."
- The analysis is positioned as consistent with growth models such as:
  - Galor (2005) for describing overall growth processes.
  - Parente and Prescott (2000) for "reasons why regions might be trapped inside the production frontier."

### Evidence on land policy and elite behavior
- The evidence examined indicates that "land policies in the period immediately before settlement by Euro-Americans tended to create an elite that, through its rent-seeking behavior, retarded growth and contributed to poverty."

*Source: _wp06169 - conclusion. It is also interesting that the enormous expenditures on highways in Appalachia*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06169.pdf_