8/9/2019 PRUS11_SI_2008

1/11

Common Dynamics Between The US and Puerto Rico

Economies

Csar R. Sobrino

School of Business & EntrepreneurshipUniversity of Turabo

PO BOX 3030

Gurabo, PR 00778Email: sobrinoc1@suagm.edu

ABSTRACT

In this paper, I examine the comovements between US real GDP and Puerto Rico real GDP. To

accomplish it, I employ a cointegration test and the Vahid&Engle (1993)s common feature test.From 1947 to 2009, the findings indicate there are common movements between Puerto Rico and

the US in the long and short run. Likewise, the evidence also shows that Puerto Rico has been

more sensible to US permanent shocks than US transitory shocks.

Keywords: Time Series Models,Macroeconomics, Business Cycles,JEL Classification: C32, E20, E32

8/9/2019 PRUS11_SI_2008

2/11

2

1. Introduction

Puerto Rico is a self-governing non-incorporated territory of the United States and its

economy works under the legal US frame. In other words, there is a common free trade

area, a common custom union, a common currency union. free labor and capital

mobility. According to the economic theory, this circumstance implies common

movements between both economies. In this, Alameda (2000) finds that Puerto Rico

economy is less responsive to US transitory shock in the second period.

In this paper, I employ a different approach to analyze the comovements between the US

and Puerto Rico. First, find a long term relationship between US real GDP and Puerto

Rico real GDP by a cointegration test. Second, conditional to cointegration, find a short

run relationship between both real GDPs using the Vahid and Engle (1993)s test.

Using annual data (1947-2009), the evidence indicates that, consistent with , from 1950-

2007, the real GDP per capita of Puerto Rico has grown almost 8 times while the US real

GDP per capita has grown 3.3 times, PR RGDP has positively responded for almost 4%

to a 1% increase in US permanent shocks. In contrast, in the short run, PR RGDP

positively responds for almost 1.6% to a 1% increase in US transitory shocks.

This paper is organized as follows: Section 2 presents the cointegration and common

cycles tests, and data; Section 3 reports the outcomes of the tests; and, Section 4

concludes.

8/9/2019 PRUS11_SI_2008

3/11

3

2. Cointegration and Cofeature Tests and Data

Consider n variables of integration order I(1) which can be represented in the next VAR

in reduced form of orderp+1:

..(1)

Where x is an (n*1) column vector of time processes; is (n*1) column vector of

deterministic variables; is an (n*n) matrix of coefficients of;Ai is an (n*n) matrix of

coefficients with elements Ajk(i); is the (n*1) matrix of disturbance terms (

where is the (n*n) variance-covariance matrix). Suffix tstands for time.

After some operations of adding and subtraction about (1), it is obtained the following

VECM of orderp:

(2)

Where (

) ,

(

) , and is the first difference

operator.

The Johansen (1991)s cointegration test focuses on the rank(r)of. If 0 < r< n, there are

r linear combinations of the series which are I(0). In other words, r is the number of

cointegrating vectors. When 0 < r< n, the series respond to deviations returning to their

steady state. Likewise, it is used a VAR in first differences when r= 0. Moreover, ifr=

n, it means thatxtisI(0).

To find r, Johansen (1991) suggests two tests statistics: (

) and () . T is the number of usable

8/9/2019 PRUS11_SI_2008

4/11

4

observations and the lambdas are the eigenvalues of . In the first one, the null

hypothesis is number of cointegrating vectors r, and in the second one, the null

hypothesis is number of cointegrating vectors = r.

In addition, to test the restrictions in the cointegrating vector, Johansen (1991)

decomposes into two matrices, and (). is the (n*r) matrix of

cointegrating parameters and is the (n*r) matrix of speed of adjustment parameters.

Once found a long term relationship among the series, the cointegrating vector is used to

find the Vahid and Engle (1993)s statistics for common cycles test. In this approach, the

canonical correlations between {xt} and {xt-1, xt-1,,xt-p} have to be estimated. The

null hypothesis that the dimension of the cofeature space is at least s (the quantity of the

smallest squared canonical correlations) is tested with this statistics. The statistics

is , where

s (i=1,2,3,..,s) are the smallest

squared canonical correlations. This statistics has a Chi-square distribution with s(np+r)-

s(n-s) degrees of freedom.

2.1. Data and Modeling

For the period 1947- 2008 (yearly data), the US real GDP, hereafter QUS, is provided by

the Fed of St. Louis web page (http://research.stlouisfed.org/fred2/) and the Puerto Rico

Planning Board provides the real GDP of Puerto Rico1, hereafter QPR. So, n=2. In Figure

1, both series in logs are shown. At first glance, it looks like they share common

movements: Over 60 years, there is a common tendency and, specifically in the 70s,

1 I thank Dr. Ervin Martinez, Director of the Puerto Rico Planning Board, for making available Puerto

Rican data. Regrettably, quarterly data is not accounted. Quarterly data describes more accurate short runfluctuations than annual data, moreover, in the analysis, degrees of freedom are lost.

http://research.stlouisfed.org/fred2/http://research.stlouisfed.org/fred2/http://research.stlouisfed.org/fred2/http://research.stlouisfed.org/fred2/

8/9/2019 PRUS11_SI_2008

5/11

5

there are similar period recessions and expansions (marked with NBER recessions dates),

although, it is also observed that, after 2001 US recession, Puerto Rico got a small growth

up to 2005 and, later on, negative growth rates. It seems that both processes meander

from each other.

In order to know the integration order of the series, Augmented Dickey-Fuller

tests outcomes are shown in Table 1. They indicate that both processes are no stationary

because the null hypothesis cannot be rejected. In first differences, the null hypothesis

that the process has a unit root is rejected at 5% of significance for both series. This

indicates that both real GDPs areI(1).

For testing the optimal lag order of the VAR, I employ the Akaike Information Criterion

(AIC) which is reported in Table 2:. It indicates the optimal lag order at levels is 3 which

mean in first differences the optimal lag order is 2. So, whenp=2, (2) has the next form:

Including into the former, the model employed in this paper is:

(3)

Where L is a matrix of lag operators and and the number of

usable observations is 62 (=T)

In this form, the matrix of deterministic variables allows changes regarding to include

unrestricted and restricted constants, and, unrestricted and restricted linear trends. If there

are a restricted constant or a restricted linear trend, is part of their coefficients. In other

words, they are included in the cointegrating vector.

http://economics.about.com/cs/economicsglossary/g/augmented.htmhttp://economics.about.com/cs/economicsglossary/g/augmented.htm

8/9/2019 PRUS11_SI_2008

6/11

6

Once established a cointegrating relationship, given p=2, it has to be computed the

canonical correlations between {xt} and {xt-1, xt-1}. The statistics is

, where i=1,2, and thereare s(2+r)-s(2-s) degrees of freedom for

all s>0.

3. Outcomes

Including a drift and a restricted linear trend, the outcomes of trace test are shown in

Table 3. The null hypothesis that r1 cannot be rejected at 5% of significance which

indicates that there is at most one cointegrating relationship between QUS and QPR over

the long run. The null hypothesis that r=0, is rejected at 5% of significance2. This means

that both processes share a common trend.

When it is not included a restricted trend, in both lambda tests, the null hypothesis that

r=0 cannot be rejected. The restricted linear trend is consistent with after 2001 US

recession data shows that both RGDPs veer apart. Likewise, QPR does not show breaks,

for that reason, I have included no dummy. However, to be accurate, I run (1) including a

time dummy (1991-2009=1, otherwise, zero). This dummy is not significant at 5%3.

is (1, -0.22, -0.02), normalized with respect to coefficient ofQUS. The second one is the

cointegrating coefficient ofQPR and the last one is the coefficient of the linear trend. The

restricted is (-0.56,-0.36) which means that when both (or one of them) series deviate

2 In max test, the null hypothesis that r=0 is rejected at 10% and the null hypothesis that r=1 cannot be

rejected at 5% of significance.

3For Puerto Rico, Alameda (2000) divides his analysis into two periods: 1967:01-1991:03 and 1991:03-

1998:06. Using a Chow test and the Economic Activity Index as a proxy variable of real GDP, He findsthat there is a break in 1991:03.

8/9/2019 PRUS11_SI_2008

7/11

7

from their long run equilibrium, the adjustment ofQUS is faster than the adjustment of

QPR.

On the other hand, in order to get the canonical correlations, I use the cointegrating

restriction () to test common cycles. Reported in Table 4, this test indicates that there is

a common feature between QUS and QPR. The null hypothesis that s>0 cannot be rejected

at 5% of significance and the null hypothesis that s>1 is rejected at 5% of significance.

Both, the cointegrating and cofeature vectors are shown in Table 5. Puerto Rico is more

sensible to US permanent shocks than US temporary shocks. Specifically, QPR positively

responds for almost 4% to a 1% change in US permanent shocks in the long run. In the

short run, QPR positively responds for almost 1.6% to a 1% change in US transitory

shocks. The long run outcome is consistent with that, from 1950 to 2007 the real GDP

per capita of Puerto Rico has grown almost 8 times while the US real GDP per capita has

grown 3.3 times4.

In contrast, after 1993 (NAFTA adoption), as reported by Herrera (2004), Mexico real

GDP is less sensible to US permanent shocks than US transitory shocks. In the first case,

the real output increases by less than 1% to 1% rise in US permanent shock. In the second

case, the real output increases by almost 4% to 1% change in transitory shock.

3.1. Robustness

4. Conclusions

4The Puerto Rico real GDP per capita was in 1950, $3,327.01 and in 2007, $26,212.98; and, The US real

GDP per capita was in 1950, 12,989.94 and in 2007, 42,886.92. (Penn Tables 6.3)

8/9/2019 PRUS11_SI_2008

8/11

8

References

Alameda, J. (2000) Globalizacin, Ciclos Econmicos y Respuesta Cclica de la

Economa de Puerto Rico: Evidencia Emprica entre 1967 a 1998, Unidad de

Investigaciones Econmicas, Departamento de Economa, Universidad de Puerto Rico,

Ro Piedras, Feb, #3.

Bram, J., F. Martinez and C. Steindel (2008) Trends and Developments in The Economy

of Puerto Rico New York Federal Reserve, Current Issues 14(2).

Herrera, J. (2004). Business Cycles in Mexico and The United States: Do they share

common movements?Journal of Applied Economics, 7(2), pp. 303-323.

Johansen, S. (1991) Estimation and Hypothesis Testing of Cointegration Vectors in

Gaussian Vector Autoregressive ModelsEconometrica 59:,pp 1551-1580.

Vahid, F. and R. Engle (1993), Common Trends and Common Cycles Journal ofApplied Econometrics, 8, pp. 341-360.

8/9/2019 PRUS11_SI_2008

9/11

9

Figure 1: US RGDP vs. Puerto Rico RGDP

20

21

22

23

24

28.0

28.5

29.0

29.5

30.0

30.5

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

US RGDP in logs (right-hand side)PR RGDP in logs (left-hand side)

8/9/2019 PRUS11_SI_2008

10/11

10

Table 1: Unit Root Test (ADF)

Null Hypothesis P-value

Log ofQUS has a unit root 0.5211

Log ofQPR has a unit root 0.9836

QUS growth rate has a unit root 0.0413

QPR growth rate has a unit root 0.0376

At levels: 10 lags, including intercept and trend.In first differences, 5 lags without intercept and trend.

Table 2: Optimal Lag Order-VAR

lags AIC

1 -9.50551

2 -9.6399

3 -9.64575*

4 -9.55505

5 -9.46928

* indicates the minimal value.

8/9/2019 PRUS11_SI_2008

11/11

11

Table 3: Johansen's Trace Test (restricted trend)

Null Hypothesis: # of

cointegrating vectorsEigenvalue

Trace

Statistic

Critical Value at

5%P-value

r=0 0.31006 26.84242 25.87211 0.0378

r1 0.08039 4.944535 12.51798 0.6044

Table 4: Johansen's Max Test (restricted trend)

Null Hypothesis: # of

cointegrating vectorsEigenvalue

Max-Eigen

Statistic

Critical Value

at 5%P-value

r=0 0.31006 21.89788 19.38704 0.0212

r=1 0.08039 4.944535 12.51798 0.6044

Table 5: Test of Common Cycles

Null Hypothesis: #

of common

features

Canonical

Correlations

Vahid and Engle's

(1993) Statistics (DF)

Critical Value

at 5% (P-value)

s >1 0.6025 16.38 (8) 15.51 (0.0181)

s >0 0.4468 5.42 (2) 5.99 (0.0665)

Table 6: US Real GDP and Puerto Rico Real GDP Common Dynamics

Long Run

Normalized cointegrating vector()

log(QUS) log(QPR) TREND

1 -0.22 -0.02

(-0.03027) (-0.00149)

Short Run

Normalized common feature vector( )log(QUS) log(QPR)

1 -0.53

(-0.1985)

Standard deviations in parentheses