Domestic Market Integration and the Law of One Price in Brazil

Contributor Notes

Author’s E-Mail Address: cgoes@imf.org, tmatheson@imf.org

This paper presents the first assessment domestic market integration in Brazil using the law of one price. The law of one price is tested using two panel unit root methodologies and a unique data set comprising price indices for 51 products across 11 metro-areas. We find that the law of one price holds for most tradable products and, not surprisingly, non-tradable products are found to be less likely to satisfy the law of one price. While these findings are consistent with evidence found for other countries, price convergence occurs very slowly in Brazil, suggesting relatively limited domestic market integration.

Abstract

This paper presents the first assessment domestic market integration in Brazil using the law of one price. The law of one price is tested using two panel unit root methodologies and a unique data set comprising price indices for 51 products across 11 metro-areas. We find that the law of one price holds for most tradable products and, not surprisingly, non-tradable products are found to be less likely to satisfy the law of one price. While these findings are consistent with evidence found for other countries, price convergence occurs very slowly in Brazil, suggesting relatively limited domestic market integration.

1. Introduction

Brazil is the fifth largest country in the world by population and landmass and has the seventh largest economy. Yet little is known about the extent of domestic market integration in Brazil. Recent research has shown that Brazil has relatively poor infrastructure (cf. Garcia-Escribano, Góes, and Karpowicz, 2015) suggesting that there are significant barriers to intra-regional trade and limited domestic market integration.

In this paper, we examine domestic market integration in Brazil using the law of one price for the first time. Since the seminal work by Parsley and Wei (1996), the use of a panel unit root methodology to investigate the prevalence of the law of one (LOOP) on intra-country trade has increased (see, for instance, Li and Huang, 2006, and Fan and Wei, 2006). An overwhelming majority of the literature finds that the LOOP holds within countries. We extend the literature by assessing price convergence within Brazil for 51 products (33 tradables and 19 non-tradables) across 11 metro-areas over 14 years.

Two recent panel unit root testing methodologies (Levin, Lin, and Chu, 2002, and Im, Pesaran, and Shin, 2002) suggest that LOOP holds for most tradable products in Brazil and, not surprisingly, non-tradable products are found to be less likely to satisfy LOOP. While these findings are similar to other studies, we find that price convergence occurs relatively slowly, suggesting limited domestic market integration.

2. Methodology

If goods markets are fully integrated, then the difference between the (log) price levels for a tradable product in different cities should be stationary. This implies that there should be co-integration for all pairs of cities i and j: algebraically, pitpjt) ∼ I(0) ∀ i,j or, equivalently, (pi,tp¯t)I(0)i, with p¯t=N1Σi=1Npi,t. If pi,t*=(pitp¯t)I(0)i, then pi,t* is stationary, pi,t is cointegrated, and the LOOP holds.

Two panel unit root tests that build on the Augmented Dickey-Fuller (ADF) framework are used, Levin and others (2002) and Im and others (2002), henceforth, LLC and IPS, respectively. The most important difference between these two methodologies is that LLC impose the parameter of interest ρ (defined below) to be same for all individuals, while IPS relax this assumption.

Both methods start by estimating individual ADF equations using time-effect-treated price indices pi,m,t*pi,m,tp¯m,t for every city i=[1,2,…,11] and product m=[1,2…,51]. For each product m, the basic model is:1

Δpi,m,t*=c˜i,m+Σk=1Ki,mφi,m,kΔpi,m,tk*+(ρi,m1)pi,m,t1*+ηi,m,t(1)

The LLC framework uses two auxiliary regressions to dissipate individual-specific dynamics:

pi,m,t*=α^1,i,m+Σk=1Ki,mφi,m,kΔpi,m,tk*+e^i,m,t(2)
Δpi,m,t1*=α^2,i+Σk=1Ki,mφi,m,kΔpi,m,tk*+υ^i,m,t1(3)

and takes the averaged residuals of (1) to standardize e^i,m,t and υ^i,m,t, resulting in e˜i,m,t and v˜i,m,t. The panel model is then estimated to calculate an asymptotically-normal Z-statistic, that is:

v˜i,m,t=(ρi,m1)e˜i,m,t1+ξi,m,t,ρi,m=ρmi(4)
tρNT=[(N1Σi=1Nξi,m,t2)Σi=1NΣt=2+Ki,mTe˜i,m,t12]12Σi=1NΣt=2+Ki,mTe˜i,m,t1ξi,m,t(5)
ZLLC=υ12(tρNTμN)(6)

where with μ and ν can be found in LLC.

Similarly, following IPS, (1) is estimated and individual t-statistics for i cross sections are calculated and used to compute an asymptotically-normally-distributed panel Zt-bar statistic. Autoregressive parameters ρi,m are allowed to vary individually. The Zt-bar statistic is:

Ztbar=N(N1Σi=1Nti,mN1Σi=1NE[ti,m|ρi,m=1])N1Σi=1Nvar[ti,m|ρi,m=1],ρi,m(ρ¯,σρi,m2)(7)

where E [ti,m | ρi,m = 1] and Var [ti,m | ρi,m = 1] can be found in Im and others (2002).

For those processes that are not explosive, half lives hi,m are computed from the individual ADF regressions (1) and the pooled (4):

hi,m=In(0.5)In(|ρi,m|),|ρi,m|<1i(8)

3. Data

We constructed a new dataset of price indices for 51 products categories across 11 metro-areas using extended CPI (IPCA) microdata; the original data were seasonally adjusted monthly percent changes, which we transformed into price indexes. We then used CPI weights to construct indices for the 51 product categories we analyze. Our original sample starts in August 1999, when the inflation targeting regime begins. After transforming the data, however, we dropped first 18 months to avoid potential bias from the fact that all price indices arbitrarily have the same value by the beginning of the sample. After such adjustments, the final sample ranges from January 2002 to July 2014.

4. Results

The empirical evidence in support for domestic market integration in Brazil is mixed at best. While LOOP seems to hold for most tradable products, the speed of convergence towards the national long-run trend is very slow.

Figure 1 below summarizes the aggregate results, after categorizing the 51 products as being either tradable or non-tradable. At the 10 percent significance level, using IPS, we reject the null hypothesis of a unit root for almost 70 percent of tradable products, while LLC rejects the null hypothesis for just under half of all tradable products. Despite (expected) divergences in rejection rates due to methodological differences, the results are broadly consistent: both LLC and IPS suggest that non-tradable product prices tend to have unit roots more frequently than tradable product prices. Table 1 details the product-specific p-values for both tests.

Figure 1:
Figure 1:

Panel Unit Root Tests Results

(percent rejection of null hypothesis of a panel unit root under different levels of significance, per methodology)

Citation: IMF Working Papers 2015, 213; 10.5089/9781513509969.001.A001

Table 1.

Panel Unit Root Tests

article image
Null hypotheses: all cities have a unit rootSignificant at the *** 1% level; ** 5% level; * 10% level.

Table 2 compares the simple average of the half-lives calculated from the individual ADF regressions (1) with the half-lives of the pooled LLC coefficients for each product. As expected, prices of tradable products converge faster than prices of non-tradable products. However, price convergence is very slow. Average half lives are about 14–16 months for tradable prices and about 20–27 months for non-tradable prices.

Table 2.

Product Half-Lives

article image

Figure 2 shows the distribution function of ρi,m across tradable and non-tradable products. Tables 1 and 2 provide further evidence that the expected difference between the two groups holds. That is, larger share of non-tradable prices have explosive processes, and amongst those processes that are not explosive, non-tradable prices tend to have higher autoregressive parameters.

Figure 2:
Figure 2:

Distribution of ADF coefficients

(distribution function of product-city pairs ADF coefficients, in percent)

Citation: IMF Working Papers 2015, 213; 10.5089/9781513509969.001.A001

Figure 3 shows how the persistence of price level deviations varies across cities. Tradable price divergences range from a maximum of 17 months in Belo Horizonte to a minimum of 10.8 months in Curitiba. By contrast, non-tradable price divergences vary from 23.8 months in Salvador to 15.5 months in Belem. The standard deviation of half lives averages between cities is and months for tradables and non-tradables, respectively. There seems to be no overarching pattern in the distribution of half lives, suggesting a potential avenue for further research.

Figure 3:
Figure 3:

Metro-Area Half-Lives

(in months)

Citation: IMF Working Papers 2015, 213; 10.5089/9781513509969.001.A001

5. International comparisons

While the literature generally supports LOOP within countries, estimated half lives of domestic price deviations vary significantly due to methodological differences. Our work is perhaps most comparable to that of Li and Huang (2006) and Fan and Wei (2006), who found evidence that LOOP holds domestically in Canada and China with monthly data. Average half-lives estimated for Canada and China are 4.72 and 2.35 months, respectively—much lower than we found for tradable products in Brazil (14–16 months).

Brazil’s relatively slow price convergence is further illustrated in Figure 4, where we display derive the implied autoregressive terms for Canada, China, and Brazil using |ρ| = exp(ln(0.5)/h). For both in Canada and China more than 90% of price deviations are corrected within 18 months, but in Brazil the pace of convergence is much slower.

Figure 4:
Figure 4:

Reaction Functions of Price Dispersion

(shock = 100, x axis in months)

Citation: IMF Working Papers 2015, 213; 10.5089/9781513509969.001.A001

Note: Canada and China calculated from half-lives estimated by Li & Huang (2006) and Fan & Wei (2006).

6. Conclusions

We found mixed evidence for domestic market integration in Brazil. LOOP is found to hold for most tradable products and, non-surprisingly, non-tradable products are found to be less likely to satisfy the law of one price. While consistent with evidence found for other countries, our evidence suggests price convergence occurs very slowly in Brazil. This suggests limited domestic market integration and highlights the need for improvements in infrastructure to improve the efficiency and productivity. We also found divergence in the speed of convergence across metro-areas, which may be a useful avenue for future research.

References

  • Fan, C. Simon, and X. Wei, 2006, “The Law of One Price: Evidence from the Transitional Economy of China,The Review of Economics and Statistics, Vol. 88, No. 4, pp. 68297.

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  • Garcia-Escribano, Mercedes, C. Góes, and I. Karpowicz, 2015, “Filling the Gap: Infrastructure Investment in Brazil,IMF Working Paper 15/180 (Washington: International Monetary Fund).

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  • Im, Kyung So, M. Hashem Pesaran, and Y. Shin, 2003, “Testing for Unit Roots in Heterogeneous Panels,Journal of Econometrics, Vol. 115, Issue 1, July, pp. 537.

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  • Levin, Andrew, Chien-Fu Lin and J. Chu, 2002, “Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties,Journal of Econometrics, Elsevier, Vol. 108 (January), pp. 124.

    • Search Google Scholar
    • Export Citation
  • Li, Na, and J. Huang, 2006, “Price Convergence and Market Integration: Strong Evidence Using Canada Data,Emp. Econ. Lett., Vol. 5 (January), No. 13, pp. 1328.

    • Search Google Scholar
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  • Parsley, David, and Shang-jin Wei, 1996, “Convergence to the Law of One Price Without Trade Barriers or Currency Fluctuations”, Quarterly Journal of Economics, Vol. 111 (April), pp. 121136.

    • Search Google Scholar
    • Export Citation
1

In this paper, the lag length k is determined using the Akaike information criterion separately for each equation.

Domestic Market Integration and the Law of One Price in Brazil
Author: Carlos Góes and Mr. Troy D Matheson
  • View in gallery

    Panel Unit Root Tests Results

    (percent rejection of null hypothesis of a panel unit root under different levels of significance, per methodology)

  • View in gallery

    Distribution of ADF coefficients

    (distribution function of product-city pairs ADF coefficients, in percent)

  • View in gallery

    Metro-Area Half-Lives

    (in months)

  • View in gallery

    Reaction Functions of Price Dispersion

    (shock = 100, x axis in months)