Currency Area SCHE EE

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Currency area and short-run persistence:Puerto Rico is not converging to the US

Csar R. SobrinoSchool of Business & Entrepreneurship

Universidad del TuraboP.O. Box 3030

Gurabo, PR [email protected]

Phone: 001-787-743-7979, ext. (9) 4682Fax: 001-787-704-2732

Ellis HeathHarley Langdale, Jr. College of Business Administration

Valdosta State UniversityValdosta, GA [email protected]

Abstract

Long-run economic convergence in optimum currency areas requires free factormobility, fiscal transfers across regions, openness, and high correlation of shocks.In this paper we examine long-term convergence between the United States ofAmerica and Puerto Rico. We focus on per capita outputs, per capita incomes,outputs and incomes and we use unit root tests and cointegration tests to analyze

these series. From these tests we do not find support for the hypothesis ofconvergence. In other words, while optimum currency literature would suggestthat incomes and outputs for Puerto Rico and the United States should convergein the long run, our results indicate that they do not. In addition, when weaddress short-run persistence in gaps between respective time series, the dataexhibits a common pattern: a systematic widening--Puerto Rico lagging behind--at small, but statistically-significant, rates. All evidence from our study rejects thehypothesis that currency areas provide long-term convergence.

Keywords: Time-series models, Long-term capital movements, International monetary

arrangements, and Institutions, Measurement of Economic Growth; AggregateProductivity; Cross-Country Output Convergence

JEL classification: C32, F21, F33, O47


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1. Introduction

According to Mundell (1961) and Frankel and Rose (1998), the requisites for optimum

currency areas (OCA) are: free factor mobility, fiscal federalism, trade and financial

openness, and high correlation of shocks among member countries. Related literature

suggests that those conditions should assure long-term convergence. The US and its

territories fulfill those conditions. Lefort (1997) finds diversion between the per capita

incomes of the US and PR. Furthermore, the economic stagnation, which started in 2005,

raises the issue of per capita output divergence.1 This fact begs the question of whether

fiscal federalism and economic monetary areas lead to convergence. Recent wisdom

suggests that fiscal federalism is necessary to guarantee long-term convergence in the

Eurozone.2

In this study we examine long-term convergence between the US and PR, but

unlike in Lefort (1997), we use time-series analysis. From this analysis, we detect a long-

term common pattern across series. According to Bernard and Durlauf (1995, 1996), for

convergence (time-series convergence or -convergence) to exist deviations, or gaps,

between respective time series for the US and PR must not contain unit roots and time

series in levels should be cointegrated. Unlike Lefort (1997), we use unit root and

cointegration tests on per capita outputs, per capita incomes, outputs and incomes.

Furthermore, the Dickey-Fuller (DF) and cointegration tests are used to detect a

common long-term pattern. In addition, according to Quah (1992) and Yau and Hueng

1This can be seen in Figure 1, where, over recent years, the persistent decline of the GNP-GDP ratio hasstopped.2 See Bordo et al (2011).


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(2000), dissimilarities in income persistence prevent convergence from occurring. With

this in mind and consistent with CEPAL (2004) on divergent/convergent phases

between the US and PR, we address persistence.

Based on unit root tests on gaps between respective time series the hypothesis of

convergence of outputs and income between the US and PR cannot be accepted.

Likewise, cointegration tests do not support the convergence hypothesis either. The

previous tests and DF test do not show a common pattern across time series. Only

when short-run persistence is addressed does a common pattern arise in the data. This

pattern indicates that there is a systematic widening of the gap with the PR lagging

behind the US at small, but statistically significant, rates. Specifically, the speed at

which the gaps between US and PR per capita outputs and per capita incomes widen

are 0.03% and 0.055% per year, respectively. All evidence rejects the hypothesis that

currency areas lead to long-term convergence.

Section 2 of this paper briefly gives an account of the Puerto Rican relationship

with the US Commonwealth and of the related literature concerning convergence.

Section 3 presents the data, as well as the outcomes from long-term convergence tests.

Section 4 examines the data when for short-run persistence is accounted for. In Section 4

we also conduct sensitivity analysis with PR and specific states from the US such as

New York, Florida and Mississippi. Section 5 concludes.

2. Puerto Rican Economic Model and Literature on Convergence


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Puerto Rico basically operates like one of the 50 states from the US. It shares a common

currency (the US dollar) with the US; it shares a free-trade zone with the US; and they

both share a common customs union. Furthermore, Puerto Ricans are US citizens. They

can get jobs in the US without restrictions. Moreover, PR can ask the US for federal

funds. However, there are some differences that should be noted. PR is under the

jurisdiction of the courts of Massachusetts and the New York Federal Reserve District.

Puerto Ricans do not vote in the US national elections nor do they pay federal income

taxes.

In Dietz (2001), an analysis and a description of the Puerto Rican economic

model is given. For almost fifty years, Puerto Rico encouraged industrial development

by inviting US firms using IRS Section 936 (S936). S936 included tax exemptions for US

corporations in the US territories. In the 1950s and 1960s, this policy was successful in

bringing highly labor-intensive industries to Puerto Rico. Nevertheless, after changes in

the tax policy in the 1970s, highly capital-intensive US firms moved to the island.

Twenty years later, the resulting low impact on employment3, lack of economic linkages

with other domestic sectors and low tax revenues prompted Puerto Ricans to ask for an

end to S936.4

The convergence hypothesis states that countries with similar structural

parameters should converge in living standards to the same steady state levels and

growth rates, provided, according to Solow (1956), that the economies exhibit

diminishing returns to capital. Here, economic integration should improve the

3 The unemployment rate has been permanently above 10% (Bureau of Labor Statistics).4 Unrestricted emigration to the US and US federal transfers are two safety valves for the island.


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allocation of resources and hence achieve convergence. However, the Puerto Rican

economic growth process seems to imply an endogenous technological change where

policy measures have an important impact on the long-run growth rate of an economy.

According to Romer (1986), investment in human capital, innovation and knowledge

leads to convergence. In the economic literature on currency areas and trading zones,

countries should convergent in the long run.5 Hence, Puerto Rico should converge

towards the US in the long run.

There are three principal approaches for examining the convergence hypothesis:

cross-section analysis, panel data and time series. 6 Convergence in approaches that use

either cross-section or panel analysis is referred to as -convergence or -convergence.7

In the former, the type of convergence that is measured is that which occurs when a

poorer economy experiences faster growth than a richer one, because the poorer one is

catching up to the richer one. Specifically, in -convergence studies the sign of the

partial correlation between actual per capita real income growth and its initial level is

important. A negative sign indicates convergence of this type. In the latter, the

convergence being investigated is the type that occurs when the dispersion of the per

capita real income decreases over time. Important cross-section analysis studies include

Barro and Sala-i-Martin (1991, 1992), Ben-David (1993, 1996), Sachs and Warner (1995),

Sala-i-Martin (1996), and Lefort (1997) and Kim (1998). Lefort (1997)extends Barro and

Sala-i-Martin (1991) by including Puerto Rico and does not find support for long-term

5 See Barro and Sala-i-Martin (1991, 1992), Ben-David (1993, 1996), Sachs and Warner (1995), Sala-i-Martin(1996), and Kim (1998).6 Islam (2003) summarizes in detail all techniques used in this approach.7 See Islam (2003) and Young et al (2008).


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convergence. Choi (2004) conducts a panel data study on the US states and finds little

evidence of convergence within this area. According to Bernard and Durlauf(1995,

1996), a stronger form of convergence is time-series convergence ( convergence). This

type of convergence is measured using time-series analysis. An important distinction

associated with -convergence is that it measures whether complete convergence will

occur, not simply whether divergence will be reduced. In the time-series study done by

Bernard and Durlauf (1995) convergence is rejected as well.

3. Data and Long-term Convergence Tests

For the period 1947-2009, the Federal Reserve of St. Louis and the Puerto Rico Planning

Board provide annual data on real GDP, real GNP and the population for the US and

PR.8 Dividing outputs and incomes over populations, we get the per capita income and

output series. Next, we take the natural logarithm of the per capita real GDP, the per

capita real GNP, the real GDP and the real GNP series. These series are shown in

Figures 2a, 2b, 2c, and 2d. In addition, as shown in Table 1, the augmented Dickey-

Fuller and Phillip-Perron tests indicate that all series are I(1).

To accept the long-term convergence hypothesis, according to Bernard and

Durlauf (1995, 1996), differences between per capita outputs, per capita incomes,

incomes, and outputs must not contain unit roots or time trends and times series should

be cointegrated in levels and the cointegrating vector should be (1,-1).9 Table 1 shows

8 NOTE: The 2002 real GDP is calculated from July 2001 to June 2002.9 Even though, Islam (2003) notes that, for all a 1, (1,-a) indicates conditional convergence.


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that a unit root is present in the gaps between the series; hence, we cannot accept the

hypothesis of long-term convergence.

To run a cointegration test, we set up a reduced VAR(p) with n series I(1) which

is converted into the following VECM:

+ !!

!!!!!

!!!

!!!!! = + !!! + ! (1)

where ! is the vector of the time series data; is a vector of deterministic variables; is

the matrix of coefficients of ; = !!

!!!;Ai is the matrix of the VAR

coefficients for all i=1,2,...,p; L is the lag operator; is the first-difference operator; is

the matrix of disturbance terms (~ 0, ); and, is the variance-covariance matrix.

According to Johansen (1991), if the rank of is r( (0, n)), there are rlinear

combinations of !, that are I(0).Then, = !, where and are the (n*r) matrices of

adjustment coefficients and co-integrating vectors, respectively.

In Table 2 the results from the Johansen test are given. When drift is added to

equation (1), at the 5% level of significance, only the per capita real GNP series shows a

common trend. However, the cointegrating vector is not (1, -1). In addition, when a

restricted trend is added to equation (1), at the 5% level of significance, both the per

capita real GNP series and real GDP series are cointegrated. However, the restricted

trend assumption means that those series are not converging. All results reject the

convergence hypothesis.

Now, we run the DF test to examine the behavior across gaps. Equation (2) is the

simple representation of the Dickey-Fuller test:

! = + + !!! + ! (2)


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where !~(0,!!), Tis the time trend, and ! are the subtractions times 100, reported in

Table 1, and is the first-differences operator. The interpretation of the parameters is as

follows: when = 0 and = 0, there is divergence; when < 0 and = 0, there is

convergence; when < 0 and < 0, there is catching up; when < 0 and > 0, there is

lagging-behind; when = 0 and < 0, there is loose catching-up; and when = 0 and

> 0, there is loose lagging-behind.10

Table 3 reports all outcomes of this test. Panel (A) indicates that divergence is

present in per capita outputs. Panel (B) shows that lagging-behind is present in per

capita incomes. Panel (C) indicates that divergence is present in outputs. And, Panel

(D), shows that lagging-behind is present in incomes. Neither cointegration nor DF tests

indicates a common pattern across series.

4. Convergence hypothesis and short-run persistence

None of the test presented addresses short-run persistence given that dissimilarities in

persistence are an important source of non-convergence. According to Quah(1992), and

Yau and Hueng (2000), persistence is a source of income disparities. Also, Stengos and

Yangaz (2011) found evidence of persistence for output gaps in Europe, which leads to

divergence. In CEPAL (2004) it is noted that there are differences in persistence for PR

and the US. We account for short-run persistence using equation (2). From

! !!! = + + !!! + !

we solve for ! and get

10Literature concerning the use of the DF test in this manner can be found in Carlino and Mills (1993),

Oxley and Greasley (1995); Li and Papell (1999); Lee, Lim, and Azali (2005); and, Gmez-Zaldvar, andVentosa-Santaulria (2010).


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! = + + !!! + ! (3)

where = 1+ and equation (3) is a nesting model for both trend stationary and

differences stationary models. Here, if < 1, is the persistence coefficient and

equation (3) is a stationary AR(1) with a deterministic trend.11 Interpreting the Dickey-

Fuller test, when = 1 and = 0, there is divergence; when < 1 and = 0, there isconvergence; when < 1 and < 0, there is catching-up; when < 1 and > 0, there

is lagging-behind; when = 1 and < 0, there is loose catching-up; and when = 1

and > 0, there is loose lagging-behind.

Setting = 1 , equation 2 becomes a partial adjustment equation enabling

us to weigh the short-run persistence with the long-term time trend. Also, this

restriction assures that if 1 and 0+, then equation (3) is a random walk with

drift.12 Then, using two specifications, we regress equation (2) with = 1 , 0,

0 (S1) and 0, 0, and 0 (S2).

Table 4 shows the results. For all panels, there is strong and significant short-run

persistence, close to 1. In addition, in Panel (A) for the S1 specification, the trend

coefficient is positive and significant at the 1% level of significance. This indicates that

lagging-behind is present at about 0.03% per year. In the S2 specification, the trend

coefficient is positive but not statistically significant. From the LR test in both the

restricted case (S1 specification) and the unrestricted case (S2 specification), we cannot

reject the null that b=(1-).

11 Hamilton (1994) and Heij et al (2004).12According to Andrews (1999), this restriction is needed in order to avoid the possibility of an explosive

series and/or series with negative growth.


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Likewise, in Panel (B) under the S1 specification, the trend coefficient is positive

and significant at the 1% level of significance. This indicates that lagging-behind is

present at around 0.055% per year. Under the S2 specification, the trend coefficient

indicates lagging-behind at about 0.054% per year and it is significant at the 1% level of

significance. Again, from the LR test, we cannot reject the null that b=(1-), as well.In addition, in Panel (C) under the S1 specification, the trend coefficient is

positive and significant at the 1% level of significance indicating that lagging-behind is

present at around 0.029% per year. In the S2 specification, the trend coefficient is

positive but not statistically significant. From the LR test, we cannot reject the null that

b=(1-).In Panel (D), under the S1 specification, the trend coefficient is positive and

significant at the 1% level of significance. This indicates that lagging-behind is present

at around 0.057% per year. Under the S2 specification, the trend coefficient indicates

lagging-behind at around 0.065% per year and it is significant at the 1% level of

significance. From the LR test, we still cannot reject the null that b=(1-).When short-run persistence is addressed for gaps between respective time series,

a common pattern emerges in the data. This pattern indicates a lagging-behind outcome

where PR lags behind the US at small, but statistically significant, rates. For all cases,

short-run persistence is so strong that all gaps tend toward random walks. This can be

seen by looking at the S1 specification in all panels where 1, 0+ and 0.

The values of those parameters indicate that there is a tendency towards long-term


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divergence between both economies. All evidence rejects the hypothesis that the

currency areas lead to long-term convergence.

Finally, strong significant short-run persistence is consistent with the outcomes

from CEPAL (2004). Puerto Rican policy actions led to dissimilarities in persistence

across countries. As noted by Quah (1992), Yau and Wen (2000) and Stengos and

Yangaz (2011), short-run persistence may prevent long-term convergence from

happening. A source of policy actions leading to short-run persistence might be

political status (i.e., no statehood), which impeded the full management of tax

exemptions like S936. According to Lefort (1997), political status is the main cause of no

convergence between the US and PR.

4.1. Sensitivity Analysis

It is possible that while PR and the US do not converge in the long run, PR could

converge with particular states in the US. To further examine this we ran the same

analysis as before but instead of using the US, we used New York (NY) and Florida

(FL), because PR is under the NY Fed jurisdiction and FL is the closest state to the

island. We also included Mississippi (MS), which is the lowest performing state in the

US. In Tables 5 and 6, the results are given.

In Table 4 we use the Coincident Economic Index (CEI). This index is mainly a

business cycle gauge, but since it includes employment data it allows us to look at the

trend in the economy. Of course, employment tends to grow more slowly than real

GDP. In Table 5 we compare real per capita personal incomes.


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In Panel (A) of Table 5, we compare PR with the US again, but using the CEI. We

do this as baseline result and to show how the overall results from our previous results

are not sensitive to using the CEI instead of real GDP. Under the S1 specification, the

trend coefficient is positive and significant at the 1% level of significance. The indication

is that lagging-behind is present as before. Using the S2 specification, the trend

coefficient is positive but not statistically significant.

In Panel (B) of Table 5, we compare MS with PR. Under both specifications, the

trend coefficient is not statistically significant. For Panel (C), we compare PR with NY.

Here, the same is true. For Panel (D), under the S1 specification, the gap between FL

and PR is a random walk. Again for all specifications, there is strong and statistically

significant short-run persistence. Specifically, the gaps are near random walks.13

In Table 6, we use the real per capita personal income of both countries. In Panel

(A), we compare PR with NY. Under the S1 specification, lagging-behind is present. In

Panel (B) of Table 6, looking at MS and PR, for the S1 specification, the gap is a random

walk, which indicates divergence. Finally, in Panel (C) of Table 6, the results for FL and

PR are shown. Under the S1 specification, lagging-behind is present. For all panels,

strong short-run persistence is displayed.

Again, as in the previous results we find no evidence of long-run convergence,

and some evidence of strong short-run persistence. This is true even when we compare

PR to individual states.

13 It is important to note that if autocorrelation is present, then should decrease when more lagged

variables are included in equation 3. West (1988) labels series with a root near, but less than, unity "nearrandom" walks.


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5. Conclusions

In this study we examine long-term convergence between the US and Puerto Rico, and

through this analysis, we detect a long-term common pattern across series. To test the

hypothesis convergence ( -convergence), we use unit root and cointegration tests on

output, income, output per capita and income per capita. The findings indicate that

gaps in all series show unit roots indicating that long-run convergence is not taking

place. Those outcomes are corroborated using cointegration tests. Moreover, the

economies only share common trends in per capita real GNP and real GDP. The

Dickey-Fuller tests do not display a common pattern, either. The lack of a common

pattern between the US and PR is addressed by accounting for short-run persistence in

gaps of all series. When short-run persistence is addressed for gaps in all of the time

series, a common pattern arises in the data. This pattern indicates that PR is lagging

behind the USat small, but statistically significant, rates. Standard of living and

productivity are lagging behind. Overall, short-run persistence is so strong that it might

lead to divergence between both economies. Like Leforts outcomes, all evidence rejects

the hypothesis that the currency areas lead to long-term convergence.

PR policy actions led to dissimilarities in persistence between itself and the US

causing a low correlation in short-run persistence shocks, which violates one of the

conditions of OCA. A source of policy actions leading to short-run persistence might be

political status; an example of political status for PR would be its "no statehood" status.

This would have impeded the full management of tax exemptions like S936. Puerto

Rican policy was successful at times, but long-term convergence was never obtained.


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The long-term process involves FDI firms creating economic growth without spillover

effects into the economy and a low impact on employment. This formed a persistent

divergence between output and income in spite of Puerto Rico being a recipient of US

federal funds. The changes in tax policy in the 1990s encouraged the shutdowns of

many US firms without any strong increase in private domestic investment, negatively

affecting output, job creation and income, and making the unemployment rate

persistently high.

Finally, the US federal transfers never balanced the FDIs profit outflows;

however, fiscal federalism has prevented social turmoil in PR like those happening in

Greece, Spain, and Portugal. Overall, unemployed and discouraged workers receive

federal funds for a living. The US finances part of the island's consumption.


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Hamilton, J. (1994) Time Series Analysis. Princeton University Press, Princeton, NewJersey.

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Johansen, S. (1991) Estimation and Hypothesis Testing of Cointegration Vectors inGaussian Vector Autoregressive Models. Econometrica, 59(6), 1551-1580.

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Figure 1

Figure 1 shows the GNP-GDP ratios for the US and PR.

60

70

80

90

100

110

120

50 55 60 65 70 75 80 85 90 95 00 05

US Puerto Rico


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Figure 2

Figure 2a Figure 2b

Figure 2c Figure 2d

In Figure 2, all series are in natural logarithm form. The vertical axis on the right-hand side of each graphmeasures the US series and on the left-hand side the PR series are measured. Figure 2a compares the percapita real GDP series for the US and PR; figure 2b does the same with the per capita real GNP series;figure 2c shows the real GDP series; figure 2d exhibits the real GNP series.Shadow bars indicate US recessions.


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TABLE 1: UNIT ROOT TESTS

Levels First differences

ADF PP KPSS ADF PP

(i) US real GDP per capita -1.86 -13.09 -2.16** -31.43**

(ii) PR real GDP per capita -0.32 -1.15 -2.41** -10.90**

(iii) US real GNP per capita -1.59 -11.6 -2.15** -31.29**

(iv) PR real GNP per capita -1.00 -2.21 -1.67* -9.57**

(v) US real GDP -0.89 -5.6 -2.92** -50.87**

(vi) PR real GDP 0.30 0.72 -2.07** -7.19**

(vii) US real GNP -0.70 -4.68 -2.66** -16.26**

(viii) PR real GNP -0.45 -0.68 -2.66* -49.83**

(i) minus (ii) -0.78 -0.33 0.79** -1.81* -50.85**

(iii) minus (iv) 0.05 -0.14 0.37* -2.07** -50.99**

(v) minus (vi) -0.45 -0.11 0.79** -1.46 -53.37**

(vii) minus (viii) 0.07 -0.04 0.47** -2.55** -51.00**

Critical values

zero-mean stationary stationary trend stationary

ADF PP ADF PP ADF PP KPSS

5% -1.93 -8.29 -2.89 -14.51 -3.4 -21.78 0.463

10% -1.6 -5.88 -2.58 -11.65 -3.13 -18.42 0.347Table 1 shows the unit root tests where ADF indicates the augmented Dickey-Fuller test; PPindicates the Phillips-Perron test. At levels, individual series are assumed trend stationary.Subtractions are assumed zero-mean stationary. Likewise, in first differences, all series but (v), (vii),and (viii) are assumed zero-mean stationary. For (v), (vii), and (viii), stationary is assumed. For the

KPSS tests, the null hypothesis is that the serie is stationary and the alternative hypothesis is thatthe series has a unit root. For all tests, the optimal lag order was set using the Hannan-Quinncriterion. According to Khim and Liew (2004), the Hannan-Quinn criterion neither underestimatesthe lag order for small samples nor overestimates the lag order for large samples. Significancelevels are as follows: * = 10%; ** = 5%.


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TABLE 2: JOHANSEN TEST

H0 Trace Statistic

(A) (B)(a) Real GDP per capita r=0 16.70 25.32

r1 4.22 12.37

(b) Real GNP per capita r=0 21.25 30.04

r1 2.87 11.64

(c) Real GDP r=0 11.97 27.20

r1 1.66 9.09

(d) Real GNP r=0 14.68 30.56

r1 1.41 12.68

Critical values at 5% 15.41 25.733.76 12.45

Normalized vectors (!s)US PR Trend

(A) Real GNP per capita 1 -1.94 (0.3)

(B) Real GNP per capita 1 -0.981 (0.34) -0.01 (0.01)

(B) Real GDP 1 -0.26 (0.04) -0.021 (0.002)

Table 2 shows the Johansen Trace test results. Standard errors are given in

parenthesis. Column (A) is equation (1) with drift. Column (B) is equation (1)with a restricted trend. Using the Hannan-Quinn criterion, the optimal lag orderin equation (1) is one. Results on real GNP series are not reported since PR realGNP is not I(1).


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TABLE 3: DICKEY-FULLER TEST

(A) (B) (C) (D)

a 10.41 15.54 -3.18 15.94

(13.579) (12.017) (26.526) (24.444)

b 0.01 0.05*** 0.07 0.065***

(0.051) (0.017) (0.044) (0.016)

-0.04 -0.06 0.00 -0.02

(0.040) (0.038) (0.035) (0.033)

R2 0.20 0.27 0.17 0.23

Durbin H 0.77 0.67 0.78 0.78

Table 3 shows the DF test following equation (2). The dependent variables in firstdifferences for each column are as follows: Panel (A) per capita output of US inlogs minus per capita output of PR in logs, multiplied by 100; Panel (B) - per capitaincome of US in logs minus per capita income of PR in logs, multiplied by 100; Panel

(C) - output of US in logs minus output of PR in logs, multiplied by 100; and Panel(D) - income of US in logs minus income of PR in logs, multiplied by 100. For theDurbin H test, the p-values are reported. The null hypothesis of this test states thatthere is no autocorrelation. Robust standard errors are given in parenthesis.Significance level is as follows: *** = 1%.


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TABLE 4: CONVERGENCE & SHORT-RUN PERSISTENCE

S1 S2 S1 S2

(A) (B)

a 6.22*** 10.412 15.016*** 15.538(2.279) (13.58) (3.757 (12.017)

b 0.03*** 0.013 0.055*** 0.054***(0.009) (0.051) (0.014 (0.017)

0.97*** 0.96*** 0.945*** 0.94***(0.009) (0.04) (0.014) (0.038)

R2 0.98 0.99 0.97 0.97

Durbin H 0.84 0.99 0.68 0.99

LR Test 0.75 0.96

(C) (D)

a 19.21*** -3.18 40.59*** 15.944(6.315) (26.53) (9.841) (24.444)

b 0.029*** 0.067 0.057*** 0.065***(0.009) (0.044) (0.014) (0.016)

0.971*** 0.99*** 0.943*** 0.975***(0.009) (0.035) (0.014) (0.033)

R2 0.99 0.99 0.97 0.97

Durbin H 0.56 0.78 0.47 0.78LR Test 0.38 0.27

Table 4 shows both specifications for equation(3). The dependent variables for each columnare as follows: Panel (A) per capita output of US in logs minus per capita output of PR inlogs, multiplied by 100; Panel (B) - per capita income of US in logs minus per capita income ofPR in logs, multiplied by 100; Panel (C) - output of US in logs minus output of PR in logs,multiplied by 100; and Panel (D) - income of US in logs minus income of PR in logs, multiplied

by 100. S1: b=(1- ) and a 0 and S2: a 0, b0, 0. For the Durbin H test, the p-values arereported. The null hypothesis of this test states that there is no autocorrelation. For the LR

Test, the p-values are reported. The null hypothesis of this test states that b =(1- ). Forregressions on all gaps where =0, the trend coefficient is negative and significant, however,in contrast to the outcomes shown in Table 4, the p-values from the Durbin H test, are close tozero. Hence, we reject the null that there is no autocorrelation. Robust standard errors aregiven in parenthesis. Significance level is as follows: *** = 1%.


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TABLE 5: SENSITIVITY ANALYSES CEIS

S1 S2 S1 S2

(A) (B)

a -0.350*** -0.34 -0.264 -0.166(0.133) (0.328) (0.225) (0.284)

b 0.003*** 0.003 0.003 0.002(0.001) (0.003) (0.002) (0.003)

0.997*** 0.996*** 0.997*** 0.986***(0.001) (0.017) (0.002) (0.020)

R2 0.99 0.99 0.96 0.96

Durbin H 0.00 0.00 0.00 0.00

LR Test 0.97 0.57

(C) (D)a -0.15 -0.124 0.349 0.311

(0.220) (0.562) (0.241) (0.242)

b 0.001 0.001 0.000 0.002(0.002) (0.005) (0.002) (0.003)

0.998*** 0.998*** 1.000*** 0.948***(0.002) (0.014) (0.002) (0.012)

R2 0.99 0.99 0.98 0.99

Durbin H 0.00 0.00 0.00 0.00

LR Test 0.96 0.00Table 5 shows both specifications for equation(3). The dependent variables for eachcolumn are as follows: Column (A) - Coincident Economic Index (CEI) of the US inlogs minus PR in logs times 100; column (B) - CEI of MS in logs minus PR in logstimes 100; column (C) - CEI of NY in logs minus PR in logs times 100; and column (D)

- CEI of FL in logs minus PR in logs times 100. S1: b=(1- ) and a 0 and S2: a 0,b0,0. For the Durbin H test, the p-values are reported. The null hypothesis of this teststates that there is no autocorrelation. For the LR Test, the p-values are reported. The

null hypothesis of this test states that b=(1- ). Robust standard errors are given inparenthesis. Significance level is as follows: *** = 1%. Data on the US and PR series isfrom 1970q1 to 2007q4. Data on states is from 1979q1 to 2007q2.


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TABLE 6: SENSITIVITY ANALYSIS- REAL PER CAPITA PERSONAL INCOME

(A) (B) (C)

S1 S2 S1 S2 S1 S2

a -7.15*** -10.83*** 0.342 -38.546 -6.59*** -15.68***(2.061) (4.079) (5.558) (29.343) (2.529) (5.203)

b 0.031*** -0.013 -0.002 -0.04 0.027** -0.036(0.011) (0.043) (0.022) (0.036) (0.012) (0.034)

0.969*** 0.935*** 1.002*** 0.815*** 0.973*** 0.910***(0.011) (0.034) (0.022) (0.141) (0.012) (0.034)

R2 0.98 0.98 0.82 0.84 0.97 0.97

Durbin H 0.01 0.01 0.05 0.11 0.11 0.09

LR Test 0.29 0.18 0.05Table 6 shows both specifications for equation (3). The dependent variables for each column are asfollows: Column (a) - real per capita personal income of NY in logs versus PR in logs times 100;column (b) - real per capita personal income of MS in logs versus PR in logs times 100; column (c) -

real per capita personal income of FL in logs versus PR in logs times 100. S1: b=(1- ) and a 0 and S2:a 0,b0, 0. For the Durbin H test, the p-values are reported. The null hypothesis of this test statesthat there is no autocorrelation. For the LR test, the p-values are reported. The null hypothesis of this

test states that b =(1- ). Robust standard errors are given in parenthesis. Significance levels are asfollows: ** = 5%; *** = 1%.

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