^{♦}

^{1}

^{2}

^{3}

Dante Mendes Aldrighi

This paper analyzes the evolution of income elasticities of imports and verifies the validity original Thirlwall’s Law for eight Latin American countries overs the period 1961-2018. Given the econometric issues inherent to classical time-varying parameter regressions, a Bayesian estimation procedure is implemented in order to provide more robust parameter estimates. A stochastic volatility specification is also included to take into account the potential presence of conditional heteroskedasticity. While some Latin American economies showed a rather stable behavior, the income elasticities of imports for Brazil, Colombia and Mexico presented an upward trend from 1961 to 2018. Regarding the validity of original Thirlwall’s Law, there were evidences of the balance-of-payments (BOP) posing a restriction to the growth performance in all of the eight selected Latin American countries.

O objetivo desse estudo é analisar a evolução das elasticidades de importação e verificar a validade da versão original da Lei de Thirwall para oito países da América Latina durante o período de 1961 a 2018. Dadas as questões econométricas inerentes a regressões com parâmetros variantes no tempo, será utilizada uma abordagem bayesiana para a estimação. A fim de levar em consideração a presença de heterocedasticidade condicional, é incluída a especificação com volatilidade estocástica no modelo. Enquanto algumas economias da América Latina mostraram um comportamento estável, as elasticidades-renda de importação para o Brasil, Colômbia e México apresentaram uma tendência de elevação no período analisado. Em relação à validade da Lei de Thirwall, há evidências de que o balanço de pagamentos (BOP) coloca uma restrição à performance de crescimento em todos os oito países selecionados da América Latina.

As the world economy, Latin America has been the stage of both prosperity and recession periods. According to Lopes e Carvalho(2008), economic growth has been poor in Latin America for about three decades. From its economic collapse in the 1980s and, consequently, the later commitment to Neoliberal macroeconomic reforms, the extensive historical disequilibria in the balance-of-payments (BOP) faced by many developing countries have reinforced the need of evaluating the argument of whether international trade is de facto a constraint to economic performance.

Since the seminal paper by

Moreover, one should notice that the BOP-constrained growth approach has been criticized by disregarding the biases and inconsistent parameter estimates due to structural breaks. Since the study of

Despite some recent attempts on dealing with these issues (

This paper focuses on the evolution of income elasticities of imports in Latin America between 1961 and 2018 and verifies whether the BOP was indeed a constraint to the region’s economic growth. To this end, we first estimate time-varying parameter (TVP) univariate regressions with stochastic volatility for the Latin economies’ import functions, following closely the methodology procedure proposed by

As to the contribution to the debate, to the best of our knowledge, this paper is the first application of a Bayesian approach to deal with potential parametric instability while estimating the income elasticities of imports in Latin America. Therefore, the novelty presented in our research is to verify the original Thirwall’s Law using a time varying parameter model and Bayesian inference. This would allow for more robust estimates and a better description of these elasticities’ movements over time. In fact, the results show that the volatility of imports has, in general, decreased from 1961 to 2018 in Latin America. Also, from the estimates for the time-varying income elasticities of imports, it is possible to divide the Latin American economies into two diﬀerent groups, with the first one presenting a rather stable behavior over time, while the second one showed a clear upward trend. This increase is a repercussion of the region’s commitment to Neoliberal trade reforms. Regarding the validity of Thirlwall’s Law, we found favorable evidence for all the countries analyzed.

Besides this introduction and the concluding remarks, the paper is organized in four sections. First, Section 2 focuses on a historical overview of the trade developments in Latin America. Section 3 introduces the Post Keynesian theory of BOP-constrained growth. Section 4 describes the model structure and the estimation procedure of the TVP regression framework. Last, but not least, Section 5 presents the estimates for the time-varying income elasticities of imports, discussing their repercussions for the validity of Thirlwall’s Law in its seminal version and whether the selected economies were on a catching-up or falling behind trajectory in the period.

From the 1950s, the development strategy in Latin America, mainly based on the adoption of import substitution policies, was responsible for reducing the openness and eﬃciency of the regional economies, increasing their external vulnerability, due to higher dependency on a narrow range of export products, and consequently hampering their ability to absorb external shocks (

Recently, empirical research has provided evidences of a direct correlation between the Latin America’s external vulnerability and its rather volatile economic growth (

Despite the existence of distinct patterns, the overall Latin American trade volume has presented an upward trend since the mid 1970s, with an average growth rate of nearly 3.9% per year (

Period
GDP
Trade
Growth
Std. Dev.
C.V.
Growth
Std. Dev.
C.V.
1961 - 1980
5.73%
1.62
0.28
4.73%
10.85
2.29
1980 - 2000
2.35%
2.06
0.88
5.02%
3.92
0.78
2000 - 2018
2.66%
2.35
0.88
2.73%
4.76
1.75
1961 - 2018
3.05%
2.56
0.73
3.9%
7.17
1.84

In terms of development strategy, the shift from the import substitution paradigm toward the adoption of the export-led growth framework in the late 1970s placed trade integration as the cornerstone of the Latin American industrialization process. Trade had become the catalyst of economic growth. The structural adjustment under the neoclassical prescription essentially relied on liberalization reforms, financial deregulation and dismantling of state intervention. While Latin America benefited from increased trade openness in the mid 1980s and early 1990s, its level remained rather stable thereafter. For instance, the region’s degree of openness increased from 21% in 1983 to 45% in 2007 (

Even though several theoretical and empirical studies have propelled the positive impacts of openness on economic performance (

Unless a country can finance ever-growing current account deficits, the economic performance of a given economy cannot grow faster than the rate consistent with BOP equilibrium (

Let the current account equilibrium condition be given by

where

and

where

After transforming equations (1) to (3) into their respective growth rates and solving the subsequent system of linear equations for the domestic income growth rate (

with lower-case letters corresponding to the growth rates of the variables. The time subscripts were dropped for notational convenience. From the relation depicted by equation 4, an improvement in the real terms of trade,

Following

This last equation has come to be known as

Several empirical studies have been conducted in order to validate the applicability of

For the specific case of Latin America,

Additionally, with a sample of ten Latin American economies,

Similarly, using rolling regressions with panel data for a broad sample of developed and emerging economies,

Moreover, based on a multi-sectoral perspective (see

A basic TVP regression model can be defined as

with

As to the evolution process of

with

The stochastic volatility specification is included by imposing a log-volatility process for the time-varying variance

with

Consider

By splitting up the original problem into a number of smaller steps, the Bayesian inference is able to deal with high-dimensional parameter space and potential nonlinearities in the likelihood function. Under the assumption of a certain prior probability density,

where

Regarding the TVP regression model, after defining the prior density

In this paper, the implementation of the MCMC algorithm to explore this posterior distribution follows the procedure developed by

Following the import function defined by ^{1}, namely, Bolivia, Brazil, Chile, Colombia, Ecuador, Mexico, Peru and Uruguay. In 2015, these countries represented together nearly 81% of Latin America GDP (at constant 2010 prices, in USD) (ECLAC, 2017). Hence, the time-varying econometric model for each country is defined as

where ^{1}

Annual data on Gross Domestic Product (GDP), imports and exports of goods and services were obtained from the World Development Indicators (WDI) database, maintained by the World Bank (2020). These data were extracted at constant 2010 prices, in USD. As to the annual REER index, the data were collected from the database developed by

With respect to the choice of prior distributions, this paper follows closely the default values proposed in

These could be considered rather diffuse priors, which contribute to mitigate potential identification issues. Moreover, in order to compute the posterior estimates, the TVP regression model for each country is estimated by drawing 100,000 samples after the initial 10,000 samples were discarded in the burn-in period.

Autocorrelation and convergence are common issues associated to MCMC sampling methods. However, as shown from figures A.1 to A.7 in Appendix B, the sampling method eﬃciently produces uncorrelated samples, since the sample paths look stable and the sample autocorrelations drop stably for all countries. Also, from tables B.1 to B.8 in Appendix C, the convergence diagnosis (CD) and the ineﬃciency factors (IF) of

As the variance of imports depicts a reasonably pronounced time-varying behavior from 1961 to 2018, one should also expect time-variation on the estimates for the Latin American income elasticities of imports. In fact, as shown in Figure 11, the estimates for all eight countries presented some degree of time-variation. With exception of Chile, it is possible to combine the considered Latin American economies into two different groups based on the evolution pattern of their income elasticities of imports. The first group, consisting of Bolivia, Ecuador, Peru and Uruguay, showed rather stable estimates over time, with small changes in the early 1980s and mid 1990s. These results are close to those found by

Even though these evidences are in favor of the Post Keynesian theory of BOP-constrained growth, the validity of the seminal model developed by

where

The Thirlwall’s Law is validated if the parameter

Thus, according to

mean-reverting process by unit root test. For the Thirlwall’s Law to be supported by the data, the null hypothesis of unit root should be rejected at the usual significance levels.

zero-mean process by modelling

In relation to the unit root tests, we will apply the standard Augmented Dickey-Fuller (ADF), Phillips-Perron and a robust ADF version to structural breaks. (

In order to verify zero mean process, the following autoregressive process will be estimated (

To sum up, the evidence obtained supports that

Brazil
Bolívia
Chile
Colombia
Ecuador
Mexico
Peru
Uruguay
ADF
−8
−7
−4
−6
−6
−7
−5
−5
P-value
0
0
0
0
0
0
0
0
PP
−8
−7
−4
−6
−5
−7
−5
−5
P-value
0
0
0
0
0
0
0
0
Break Point ADF
−9
−9
−6
−8
−7
−8
−7
−6
P-value
0
0
0
0
0
0
0
0
0
−0
−0
−0
0
0
−0
−0
P-value
0
0
0
0
0
0
0
0

One should note that the present approach to the BOP-constrained growth model has only considered the seminal model of

Furthermore, given the long-term nature of the theoretical rates of economic growth with BOP equilibrium, these estimates are also considered a measure for evaluating whether an economy has been in a catching-up trajectory relative to the world economy (

With the exception of Peru, there are no evidences of a catching-up process by all other countries from 1961 to 2018. On the other hand, there are evidences of a catching-up process by Brazil and Mexico from 1970-1985. Yet, between 1985 and 2000, the estimates show that the Bolivian economy embarked on a trajectory of catching up, which continued during the period 2000-2015. When considering the last eighteen years (2000-2018), this catching-up process is only observed in Bolivia, Peru and Uruguay. Following

1961-2018
1970-1985
1985-2000
2000-2018
Bolivia
3
-1
4
3
Brazil
3
6
3
2
Colombia
2
2
3
1
Chile
2
1
4
1
Ecuador
1
1
4
1
Mexico
3
6
2
1
Peru
3
2
3
3
Uruguay
2
2
2
3
World Economy
3
3
3
2

(World Bank, 2020).

Economic growth in Latin America has been an intriguing phenomenon, driving a vast variety of theoretical and empirical research. Given the recurrence of trade imbalances during its economic history, the Post Keynesian theory of BOP-constrained growth has emerged as a robust theoretical alternative regarding the potential limits of the region’s long-term economic performance. Several studies have tried to provide empirical evidences supporting these ideas (see e.g.

In general, however, the Post Keynesian research has overlooked econometric issues related to structural breaks and parameter instability over the sample period, compromising the reliability of the estimates due to biases and inconsistency. Despite some attempts on dealing with those issues (see e.g.

For some Latin American economies, namely, Brazil, Colombia and Mexico, the obtained results showed that there has been an upward trend in their estimates of the income elasticity of imports from 1970 to 2015. On the other, for the second group of countries, consisting of Bolivia, Ecuador, Peru and Uruguay, a rather stable behavior was observed. In the particular case of Chile, even though is estimates were relatively volatile over time, the country has recently presented income elasticity of import demand levels similar to those from beginning of the sample. Moreover, the BOP-constrained model developed by

_{a}rttextpid = S0101 − 31572003000100063nrm = iso

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Brasil (CAPES) - Finance Code 001. All errors remain ours.

I thank the financial support from the National Council for Scientific and Technological Development - CNPq - Brazil.

Would like to thank CNPq for financial support.

C11; E12; F43; O47; O54

In a study on measurement issues in estimating elasticity values, Casler (2015) found that the linear in growth rate regression specification provides more accurate estimates than the commonly used linear, logarithmic, logarithmic-linear and linear-logarithmic specifications. Furthermore, the results obtained by the author also advocates in favor of the natural logarithmic growth rate method in comparison to the standard base, the reverse base and the geometric-mean growth rate methods.

The objective of the accept-reject (AR) sampling, also known as the von Neumann sampling, is to sample from a target density

Given the impossibility of direct sampling from the posterior distribution, the Metropolis-Hastings (MH) algorithm is a MCMC method implemented in order to simulate samples by combining the use of the full joint density function and a proposal distribution. This proposal distribution is usually chosen as to correspond as close as possible to the target conditional posterior distribution. More specifically, define

where

In this paper, the implementation of the MCMC algorithm to explore this posterior distribution follows the procedure developed by

Initialize

Sample

Sample

Sample

Sample

Sample

Sample

Sample

Go back to (2).

The steps of each sampling process are discussed below:

Sample

where

and

where

for

for

One should note that, for the TVP regression model, we have:

where

where

Sample h First, note that equations (6) and (8) consist of a nonlinear and non-Gaussian state space model. Following

with

where

with

In order to sample a block

where

and

One should note that

In order to sample ^{2}^{3}

where

and

for

and

which are obtained from a second-order Taylor expansion of

around a certain point

For

and

with

Then, one must find

Initialize

Compute

Run the moment smoother using the current

Replace

Go back to (2).

These steps are looped several times until

Sample

As discussed by [50], by omitting the term

Regarding the TVP regression model, in order to sample

where

Sample

Since the posterior distribution (29) corresponds to the kernel of the inverse gamma distribution, the samples are simply drawn as

Sample

where

Parameter
Mean
Std. Dev.
95% Interval
CD
IF
^{Σ}110.0128
0.0160
[0.0025 - 0.0522]
0.810
39.54
^{Σ}220.0148
0.0207
[0.0025 - 0.0651]
0.082
39.13
φ
0.8707
0.0987
[0.6175 - 0.9889]
0.433
11.31
σ
_{η}0.1392
0.0659
[0.0642 - 0.3136]
0.770
50.56
γ
0.0099
0.0134
[0.0054 - 0.0187]
0.510
59.30

Parameter
Mean
Std. Dev.
95% Interval
CD
IF
^{Σ}110.0235
0.0336
[0.0030 - 0.1096]
0.806
42.75
^{Σ}220.0092
0.0088
[ 0.0022 -0.0317]
0.329
26.57
φ
0.9029
0.0888
[0.6629 - 0.9940]
0.231
12.74
σ
_{η}0.1454
0.0690
[0.0655 - 0.3291]
0.905
54.15
γ
0.0112
0.0139
[0.0052 - 0.0282]
0.437
48.15

Parameter
Mean
Std. Dev.
95% Interval
CD
IF
^{Σ}110.0141
0.0168
[0.0026 - 0.0565]
0.805
39.32
^{Σ}220.0117
0.0121
[0.0024 - 0.0427]
0.888
35.69
φ
0.8877
0.0970
[0.6327 - 0.9931]
0.224
15.73
σ
_{η}0.1411
0.0711
[0.0635 - 0.3304]
0.444
55.75
γ
0.0077
0.0120
[0.0038 - 0.0195]
0.043
57.01

Parameter
Mean
Std. Dev.
95% Interval
CD
IF
^{Σ}110.0131
0.0162
[0.0025 - 0.0524]
0.846
37.64
^{Σ}220.0087
0.0072
[0.0023 - 0.0274]
0.012
25.90
φ
0.9402
0.0556
[0.7900 - 0.9958]
0.045
20.85
σ
_{η}0.2646
0.1333
[0.0997 - 0.6033]
0.044
55.42
γ
0.0241
0.2611
[0.0049 - 0.0866]
0.581
34.78

Parameter
Mean
Std. Dev.
95% Interval
CD
IF
^{Σ}110.0143
0.0170
[0.0026 - 0.0576]
0.990
35.32
^{Σ}220.0192
0.0204
[0.0031 - 0.0720]
0.169
37.86
φ
0.8807
0.0950
[0.6347 - 0.9902]
0.770
11.84
σ
_{η}0.1360
0.0598
[0.0637 - 0.2920]
0.719
43.28
γ
0.0100
0.0066
[0.0053 - 0.0195]
0.636
25.84

Parameter
Mean
Std. Dev.
95% Interval
CD
IF
^{Σ}110.0203
0.0223
[0.0033 - 0.0769]
0.941
36.67
^{Σ}220.0173
0.0161
[0.0036 - 0.0581]
0.237
26.23
φ
0.9475
0.0501
[0.8189 - 0.9956]
0.626
15.52
σ
_{η}0.3218
0.1688
[0.1039 - 0.7561]
0.753
70.82
γ
0.0084
0.0091
[0.0029 - 0.0256]
0.312
59.51

Parameter
Mean
Std. Dev.
95% Interval
CD
IF
^{Σ}110.0113
0.0117
[0.0024 - 0.0408]
0.534
31.74
^{Σ}220.0165
0.0173
[0.0029 - 0.0629]
0.056
32.81
φ
0.9026
0.0800
[0.6930 - 0.9930]
0.675
13.93
σ
_{η}0.2084
0.1212
[0.0730 - 0.5289]
0.229
70.09
γ
0.0134
0.0551
[0.0042 - 0.0436]
0.183
69.35

Parameter
Mean
Std. Dev.
95% Interval
CD
IF
^{Σ}110.0135
0.0182
[0.0025 - 0.0558]
0.575
36.75
^{Σ}220.0090
0.0080
[0.0023 - 0.0295]
0.050
22.53
φ
00.9455
0.0505
[0.8140 - 0.9954]
0.025
13.58
σ
_{η}.2020
0.0887
[0.0854 - 0.4247]
0.815
46.43
γ
0.0306
0.7113
[0.0048 - 0.0660]
0.404
41.07