Use of spatial econometrics to analyze convergence in Puerto Rico

1. Regional Convergence of the
Unemployment Rates Among 76
Municipalities of Puerto Rico Using
Spatial Econometrics
by César R. Sobrino
Universidad Ana G. Méndez, Gurabo Campus
March 6, 2020
by César R. Sobrino
Regional Convergence of

2. Motivation
Robert Solow (1956) “Capital should flow from
countries with a high capital-to-output ratio to
countries with a low capital-to-output ratio ”
Convergence occurs when poor country/regions/states
grow faster than the richer regions, thus catching up
with the rich ones
When regions are used, Regional Convergence.
Barro & Sala-i-Martin (1991, 1992) (US states)
Rey & Montouri (1998) use spatial econometrics (US
states)
by César R. Sobrino
Regional Convergence of

3. Motivation
Assumption: closed economy
Unclear if Regional Convergence holds during an
specific trade policy regime
Pernia & Lazatin (2015) regions gain from an open
economy, but, the positive effect is uneven across
regions.
Sanguinetti & Volpe (2009) when tariffs are low
(high), industrial firms disperse across country (move
closer to the main city).
Puerto Rico, presence of the Merchant Act (Section 27:
Jones Act)
by César R. Sobrino
Regional Convergence of

4. Objective
Determine whether there is unemployment rate
convergence across the municipalities of Puerto Rico.
Control for spatial dependence
From 1984 to 2013, unemployment rates of 76
municipalities excluding Culebra and Vieques (Source:
Planning Board of Puerto Rico)
Data range: 1984 & 2013. Sub samples: 1984 & 1996,
and 1997 & 2013
Simionescu (2017) unemployment rate divergence
across counties in Romania
Presman & Klepfish (2008), Israel - all regional
unemployment rates converge in the long run, except
that in the Southern district
by César R. Sobrino
Regional Convergence of

5. Descriptive Statistics
Descriptive Statistics
Mean Median SD CV Moran’s I
LUrate84 3.16 3.22 0.32 0.1 0.52
LUrate96 2.75 2.80 0.29 0.11 0.57
LUrate13 2.78 2.77 0.23 0.08 0.49
CV: Coefficient of variation
According to Moran’s I, data shows spatial
dependence.
Unemployment rates in logs
by César R. Sobrino
Regional Convergence of

6. β- convergence- OLS regression model
LUrate1i − LUrate0i = a + βLUrate0i + ε0i
Where:
LUrate1i is the final(1) unemployment rate for region
i in logs.
LINC0i is the initial(0) unemployment rate for region
i in logs.
LUrate1i − LUrate0i is the growth rate between the
final year and the initial year.
ε0i is an error term
Convergence Divergence
β ∈] − 1, 0[ β > 0
by César R. Sobrino
Regional Convergence of

7. Exploring unconditional β- convergence
1984-2013 1984-1996 1997 - 2013
X : Initial unemployment rate in logs & Y : Growth
rate.
At first glance, β- convergence holds.
by César R. Sobrino
Regional Convergence of

8. Spatial Dependence
When dealing with spatial data you must give special
attention to the possibility that the errors or the
variables in the model show spatial dependence.
Spatial Lag (SAR): if it occurs and we ignore it, we
may encounter an omitted variable problem. The OLS
would then produce biased and inconsistent estimates.
The neighbouring regions are expected to be more
alike (spillover effects)
Spatial Error (SEM) in this case the error terms
across different spatial units are correlated. If there is
spatial error and we ignore it, the OLS estimates
would be unbiased but inefficient. Related to the
measurement error problem
by César R. Sobrino
Regional Convergence of

9. Exploring Spatial Dependence (Quintile Maps)
1984 U. Rate in logs 1996 U. Rate in logs
2013 U. Rate in logs
by César R. Sobrino
Regional Convergence of

10. Moran scatterplot (Moran’s Test)
1984 1996 2013
X: Spatial units; Y: the weighted average or spatial lag
of the corresponding observation on the X axis.
They show spatial dependence because there is a
positive correlation
by César R. Sobrino
Regional Convergence of

11. Outcomes
Range OLS SAR SEM
1984-2013 β -0.61 ∗∗∗
-0.55∗∗∗
-0.723∗∗∗
R2
0.51
AIC -33.57 -36.39 -50.36
λ, ρ - p − value 0.03 0.00
Speed of convergence 0.033 0.044
1984-1996 β -0.37∗∗∗
-0.33∗∗∗
-0.53∗∗∗
R2
0.24
AIC -17.58 -22.47 -34.1
λ, ρ - p − value 0.01 0.00
Speed of convergence 0.04 0.062
1997-2013 β -0.49∗∗∗
-0.41∗∗∗
-0.51∗∗∗
R2
0.49
AIC -62.19 -64.31 -69.27
λ, ρ - p − value 0.06 0.01
Speed of convergence 0.042 0.045
Observations 76 76 76
∗∗∗
significant at 1%
AIC: Akaike Information Criterion
by César R. Sobrino
Regional Convergence of

12. Robustness: SEM Panel Data including Fixed
Effects(FE)
FE(1) FE(2) FE(3)
β -0.70 ∗∗∗
-0.70 ∗∗∗
-0.70 ∗∗∗
(p-value) (0.0000) (0.0000) (0.0000)
λ 0.72 ∗∗∗
0.72 ∗∗∗
0.68 ∗∗∗
(p-value) (0.0000) (0.0000) (0.0000)
Observations 456 456 456
Speed of 0.041 0.041 0.041
convergence
∗∗∗
significant at 1%
Six periods: 1984-1989, 1989-1994, 1994-1999, 1999-2004,
2004-2009, and, 2009-2013
(1): Baltagi et al. (2007); (2) Kapoor et al. 2007 ; and, (3)
Generalised moments method estimation
by César R. Sobrino
Regional Convergence of

13. Conclusions
Regional convergence of the unemployment rates holds
for Puerto Rico, an economy with high freight costs
Convergence rate over entire sample, 4.4% yearly but
first sub sample, 6.2%, second sub sample 4.5%
The Section 936 period with the higher speed of
convergence
Further research should involve the use of per capita
income and/or per capita electricity consumption
by César R. Sobrino
Regional Convergence of

14. References
Simionescu, M. (2017) “Regional convergence of
unemployment rate in Romania”, International
Economics Letters, 6, 7-16
Pernia, E. & J.E. Lazatin (2016) “Do Regions Gain
from an Open Economy?” DP, School of Economics,
University of the Philippines, # 2016-02.
Sanguinetti, P. & C. Volpe (2009) “Tariffs and
manufacturing location in Argentina” Regional
Science and Urban Economics, 39, 155-167
Pressman M & V Klepfish (2008) “Regional
Unemployment Rate Convergence in Israel” ECOMOD
conference, Berlin
Rey SJ & BD Montouri (1999) “US Regional Income
Convergence: a Spatial Econometric Perspective”,
Regional Studies 33 , 143-156.
by César R. Sobrino
Regional Convergence of

15. References
Barro, RJ & X Sala-i-Martin (1992) “Convergence”,
Journal of Political Economy, 100, 223-51.
Baltagi, BH, Song, SH, Jung, BC, &, W Koh (2007)
“Testing for Serial Correlation, Spatial Autocorrelation
and Random Effects using Panel Data”, Journal of
Econometrics 140,5–51.
Kapoor, M, Kelejian, HH, & IR Prucha (2007) “Panel
Data Models with Spatially Correlated Error
Components” Journal of Econometrics 140, 97–130.
Barro, RJ & X Sala-i-Martin (1991) “Convergence
across States and Nations”, Brookings Papers on
Economic Activity, 22, 107-82.
Solow, RM (1956). “A Contribution to the Theory of
Economic Growth” The Quarterly Journal of
Economics, 70, 65-94.
by César R. Sobrino
Regional Convergence of