Concepts Our model Using Stata Constraints
Introducing Maximum Likelihood in Stata
M.S C IN D EVELOPMENT E CONOMICS Q UANTITATIVE M ETHODS COURSE
M
ICHAELMAS2009 26 O
CTOBERSimon Quinn Introducing Maximum Likelihood in Stata University of Oxford
Department of International Development
Product space revisited: What governs the evolution of export structure?
Thesis submitted in partial fulfilment of the requirements of the Degree of Master of Science in Economics for Development
by
Matej Bajgar
St Edmund Hall, Oxford
3 June 2010
I would like to thank Diego Sanchez-Ancochea for his support and advice throughout my work on the essay. I am grateful to Adrian Wood for initial inspiration and valuable comments. I am also grateful for help provided by Francis Teal and Markus Eberhardt.
Abstract
This essay asks what influences the probability that a country starts and continues exporting a given product. Using a large panel of export data, it shows that countries tend to develop exports similar to their overall export structure, but there is no evidence that the probability of exporting a certain product is affected by the existence of a few similar already exported products. It seems that underlying characteristics of a country, rather than product-specific factors accu- mulated through existing exports, are what determines evolution of export structure over time. The underlying characteristics are only partially captured by broad factor endowments. The findings suggest that “islands of excellence” such as export processing zones may not be the best way to promote structural change.
Contents
1 Introduction 4
2 Underlying characteristics and product-specific factors 10
3 Data and stylized facts 11
4 Estimation and main results 17
5 Explaining proxav 26
6 Conclusion 29
1 Introduction
This essay explores the evolution of export structure in countries across the world. It asks what influences the probability that a country starts and continues exporting a given product. More specifically, it asks whether the probability depends on broad underlying characteristics of the economy or rather on possession of factors specific to a narrow group of products.
A distinguishing feature of what is called ‘underlying characteristics’ here is that they have implications for the whole economy or at least a large part of it. What a country exports has traditionally been explained by factor endow- ments (Ohlin, 1933) and technologies (Romer, 1986) available in the country.
But in addition to these, the underlying characteristics of an economy that determine what it exports may also include infrastructure, various kinds of institutions, economic policies and many subtler features1. The characteris- tics develop through factor accumulation, government policies and complex social and economic changes. While some of them can change fast (policies), other evolve only slowly over time (human capital). According to theories that view underlying characteristics of an economy as the only significant determinant of what it exports, the only impact of past exports of some products on present exports of other products should be through resources raised from past exports, which can be used to finance improvements in the underlying characteristics that subsequently lead to shifts in the export structure.
The competing group of determinants of export structure is called ‘product- specific factors’, but it includes factors specific to whole groups of products — mainly product-specific capital, skills and know-how. Their specificity would be best treated in a continuous way, so that each factor is highly conducive to exporting of some products, less suitable for exporting of other products and useless for exporting yet another set of products. These factors will be accumulated primarily through learning by doing2 when the corresponding
1For example language (India exporting services of call centres).
2The learning by doing as suggested here is closest in spirit to the endogenous growth
products are exported. This accumulation, together with the fact that the factors are usually suitable for multiple products, mean that past exports of certain products should increase the probability of exporting products which are similar in the sense that their exporting requires the same or similar product-specific factors.
The question whether underlying characteristics of an economy or product- specific factors determine which products a country exports has profound consequences. If product-specific factors are important, there will be a strong path dependency in the types of products that a country exports. Once it establishes exports in a certain product, it starts accumulating factors spe- cific to this product through learning by doing and as a result it further intensifies exports of the product and/or develops exports in products which are similar.
The path dependency might impose severe constraints on development prospects of the country. If exporting some products leads to higher in- come levels or higher growth than exporting other products, as suggested by Hausmann et al. (2007), and if the country traditionally exports and there- fore has developed product-specific factors in low-growth products, then the country could be caught in a poverty trap. It finds it difficult to develop ex- ports in high-growth products because it lacks the required product-specific factors, and it cannot accumulate the factors since they can only be accumu- lated through exports of the corresponding products.
The case of product-specific factors nevertheless offers a possible solution.
If the government could use active industrial policy in order to establish exports in some high-growth products, firms could start accumulating the factors required for production of these and similar products, the exports would gradually become sustainable even without government support and the country could progressively develop exports in a larger number of similar high-growth products. This is one of arguments behind export-processing zones and other “islands of excellence” exporting products substantially more
model by Young (1991). See also Grossman and Helpman (1991).
advanced than those characteristic for the rest of the economy.3
If, on the other hand, underlying characteristics of an economy are the only important determinant of evolution of its export structure, establish- ment of such islands of excellence will be a costly and ineffective way of promoting structural change. Resources would then be better invested into improvement of the underlying characteristics, for example through accumu- lation of human capital, adoption of technology or improvement of institu- tions.
The discussion above resonates with the debate on whether countries should follow their comparative advantages or defy it. One side of the de- bate is well represented by Justin Lin, according to whom “the key is to make use of the country’s current comparative advantage - not in the factors of production it may have someday, but in the factors of production that it has now” (Lin and Chang, 2009, p. 484). An opposing opinion is expressed for instance by Ha-Joon Chang, who responds to Lin that “given the nature of the process of factor accumulation and technological capability-building, it is simply not possible for a backward economy to accumulate capabilities in new industries without defying comparative advantage and actually enter- ing the industry before it has the right factor endowments” (Lin and Chang, 2009, p. 491).
The discussion above suggests that if the export structure of a country is fully determined by the underlying characteristics of its economy, there should be no direct effect of past exports of some products on present exports of products that are similar. If, on the contrary, product-specific factors accumulated through learning by doing are important, such an effect should be observed.
3A range of types of platforms for promotion of exports is discussed by Radelet (1999).
Milberg (2007) provides an up-to-date survey of literature on export-processing zones.
Johansson and Nilsson (1997) specifically discuss the possibility that the zones might serve as catalysts in promotion of exports by “showing [local firms] how to produce, market, sell and distribute manufactured goods on the world market” (p. 2115).
An important contribution in this area has been made by Hausmann and Klinger (2007) and Hidalgo et al. (2007) who have introduced the notion of product
space — a hypothetical space where similar products lie close to each other, while different products have large distances between them. A crucial concern when defining such a space is what is meant by similarity. In the theoreti- cal framework introduced above two products are similar if their exporting requires similar product-specific factors. Unfortunately, this definition is not suitable for empirical investigation using macro data, because the product- specific factors are generally not measured, at least not for a wide range of products. Hausmann and Klinger (2007) use an outcome-based measure of similarity between two products instead. They call it proximity, and the intuition behind it is straightforward. If two products require similar factors to be successfully exported, they will typically be exported by the same coun- tries — those that own the required factors. To set an example, assume that machines, skills, technology and know-how needed to produce cars are only marginally different from those needed to produce motorcycles. If a country exports cars, it probably also has the factors needed for the production of mo- torcycles and is likely to export motorcycles as well4. Hausmann and Klinger (2007) therefore define proximityas conditional probability of exporting one product given that the other product is exported. Thus proximity is high for pairs of products which are often exported by the same countries and low for pairs of products where few or no countries export both products at the same time.
Hidalgo et al. (2007) and Hidalgo and Hausmann (2009) use theproximity measure in order to analyse the product space. They show that products typically exported by more developed and more diversified countries are sit- uated in the core of the product space with many high-proximity links to other products while products exported by less developed and less diversified
4The relationship between countries, the products they export and the factors or ‘ca- pabilities’ needed to export them is well analysed in terms of the theory of networks by Hidalgo and Hausmann (2009).
countries, mostly primary commodities, are located in the periphery with few links to other products. The authors suggest that movement in the product space, particularly towards its core, is at the heart of the process of economic development. They emphasize that the product space may not be continuous and if firms indeed move only between similar products, some countries may find it difficult to move their exports to new parts of the product space. If exporting some products is more profitable and leads to higher income levels than exporting other products, a wrong position in the product space may become a serious impediment to economic growth.
Hidalgo et al. (2007) compare an economy to a forest with trees as in- dividual products and firms as monkeys living on the trees and consuming their fruit. The process of structural transformation is then like the monkeys jumping from one tree to another. According to the authors the problem is that the monkeys can only jump over certain distance and thus they cannot jump to trees that are too distant. If all monkeys of a particular tribe live in a part of the forest which is not connected with other parts (for example due to a glade separating it from the rest of the forest), the monkeys will not be able to reach trees in the other part of the forest, possibly bearing more fruit. The tribe may get stuck in a poverty trap. The authors conclude that if this happens, there may be a case for a government intervention5 that would carry some monkeys to a new and better-connected part of the forest from which the monkeys would be able to further populate more fruitful niches of the woods.
Hausmann and Klinger (2007) and Hidalgo et al. (2007) provide empir- ical support for the claim that countries tend to develop new exports and keep past exports in products with high proximity to an average product they already export. Unfortunately, their result does not address the key question of this essay, nor does it test the hypothesis about monkeys that would like to move into more fruitful parts of the forest but cannot do so because they can only jump over a limited distance. The problem is that the
5Intervention by Greenpeace would be more appropriate in the monkey metaphor.
result will be obtained whether structure of country’s exports is determined by the underlying characteristics of its economy or by product-specific fac- tors. In the former case, countries exporting certain products will be likely to have characteristics conducive to exporting of these products, and there- fore they will also be likely to start exporting products which are similar, i.e.
exports of which benefit from the same characteristics. In the latter case, countries exporting certain products will probably possess the corresponding product-specific factors, and as a result they will be likely to start exporting products which require the same product-specific factors, and therefore again have high proximity to the already exported products.
What the authors measure corresponds to a distance between the tree where a monkey wants to get and the centre of the area inhabited by its tribe. Their results are then equivalent to saying that monkeys tend to move to trees that are near to the part of the forest where most members of their tribe live. This may be true but it is hardly surprising. What a tribe wishing to send its member to a new tree cares about is not distance of the tree from the centre of the area inhabited by the tribe but its distance from the near- est trees already inhabited by the tribe. Similarly, if product-specific factors developed through learning by doing are important, probability of exporting a certain product should not depend only on proximity of the product to coutry’s average product, but on its proximity to one or several most similar products already exported by the country. Whether this is the case is the question that this essay tries to address.
The rest of the paper is organised as follows. Section 2 restates the distinc- tion between underlying characteristics and product-specific factors using a more formal notation. Section 3 presents data, introduces main indices used for the estimation, and presents summary statistics. Section 4 shows the equations to be estimated, discusses econometric issues and presents estima- tion results. Section 5 examines whether the index found the most econom- ically significant in the previous section can be explained by simple factor
endowments. Finally, the last section summarizes the main findings and dis- cusses limitations of the paper.
2 Underlying characteristics and product-specific factors
This brief section aims to illustrate the distinction between underlying char- acteristics and product-specific factors more formally. Let xict be a dummy for whether product i is exported by country c in period t; Uuct a vector of underlying characteristics ukct of country c in period t; Sct a vector of product-specific factors slct, in country c and period t; ict residual noise;
and Fi a product-specific function of how Uct and Sct impact on probability P(xict = 1). Leti= 1,2, . . .; k= 1,2, . . .; and l= 1,2, . . .. Then
P(xict = 1) =Fi(Uict, Pict, ict).
Assume for illustrative purposes that the impact of ukct and slct on xict is additive and linear, with parameters γki andδli respectively. Define matrices Γ and ∆ as
Γ=
γ11 γ12 . . . γ21 γ22 . . . ... ... . ..
,∆=
δ11 δ12 . . . δ21 δ22 . . . ... ... . ..
.
Let further Uct and Sct depend on past exports. For simplicity assume that the relationship is again additive and linear and that they depend only on exports in the previous period. Let the parameters of howxic,t−1 impacts on Uct and Sct beθki and λli respectively. Define matrices Θ and Λ as
Θ=
θ11 θ12 . . . θ21 θ22 . . . ... ... . ..
,Λ=
λ11 λ12 . . . λ21 λ22 . . . ... ... . ..
.
The ‘specificity’ of product-specific factors means that most elements of ∆ should be zero or economically insignificant. On the contrary, many elements of Γ can be expected to be non-zero and economically significant, either positively or negatively6. The statement that the underlying characteristics do not directly depend on the past exports of the country is equivalent to all elements of Θ being zero. On the other hand, many elements of Λ should be positive. Finally, if exporting of product i depends heavily on factor k, factor k is likely to be best accumulated by exporting of product i. This is equivalent to saying that λki and δki should be correlated.
3 Data and stylized facts
This study uses revised UN export data prepared by Feenstra et al. (2005).
They contain exports decomposed into 1620 products according to the 4- digit Standard International Trade Classification (SITC), Revision 2, and cover 132 countries for years 1962–2000. Many products are not exported by any country in some years. This may be because these products did not exist in the beginning of the period covered, or because of a revision in classification. When these products start being traded, many countries develop new comparative advantages in them at the same time. This might strongly affect results of the analysis, which aims to examine gradual changes in export structures. Moreover, for reasons explained below proximity is calculated using only years 1968–1970; if some products were not exported by any country in this period, proximity could not be calculated for them.
The products which are not exported in some years are therefore dropped for all years, which substantially reduces the number of products to 5087. In
6The non-zero elements of ∆ should be positive. It is difficult to imagine product- specific factors developed through exports of a certain product that would have negative impact on future exports of this or similar products.
7As products which appear only after the beginning of the period are dropped, the remaining dataset may lack products at the technological frontier. This should nevertheless not be a serious problem, as the focus of the essay is more on countries trying to catch up
addition, 28 countries from the former Soviet block have data available only after 1990. These countries are dropped, too.
Another set of data used at several points in this essay was composed by Caselli et al. (2010). Its coverage overlaps with coverage of the export dataset for period 1970–2000 and 92 countries. Out of variables in the dataset, this essay uses average years of schooling of adult population by Barro and Lee (2001), UN data on adult population and data on surface areas of countries from World Bank’s World Development Indicators. Caselli et al.
have imputed missing values in the schooling data using other sources and own estimations. GDP numbers are available for each year but popula- tion and years of schooling are only offered in five-year intervals. Since the main estimations in this essay are run on yearly data, the missing years are filled in using the method of linear interpolation as described for instance in Dezhbakhsh and Levy (1994). Such interpolation is clearly highly problem- atic, especially given that some of the base values used for the interpolation were themselves imputed. On the other hand, education and population are variables that develop only slowly over time and do not fluctuate, so that the interpolation should not be overly misleading, provided that the base values are reasonably correct.
In order to examine country’s movement between various products in the product space, it makes sense to focus onwhether the country exports a given product or not, rather than how much of it the country exports. Then the question is how to define exporting of a product. The most straightforward approach would take a product as exported for any amount of exports larger than zero. The drawback of this approach is that the results might be driven by products exported in negligible amounts, not really saying anything about the structure of exports. A way of addressing this issue would be setting a certain threshold that exports would have to exceed in order to be considered in the analysis. This approach is not without flaws either, because a threshold that is still negligible in the United States may be very high for Nepal. Setting
and climb up the product ladder and less on countries at the world technological frontier.
the threshold in terms of a share of country’s exports rather than in terms of an absolute amount would be a solution but for the sake of comparability of results, this essay adopts the approach of Hausmann and Klinger (2007) who consider a product to be exported by a certain country (in the sense of substantial exports) if its share in the country’s exports is higher than its share in the total world trade. Technically, they define revealed comparative advantage as
RCAi,c,t =
Xi,c,t
P
iXi,c,t
P
cXi,c,t
P
i
P
cXi,c,t
,
where Xi,c,t is the value of exports of product i by country c in year t, and they define a dummy for whether a product is exported as
xi,c,t =
( 1 if RCAi,c,t >1 0 otherwise.
The notion of the product space is built on the idea that some products are more similar to each other than other products. There are many dimen- sions along which two products can be related: factor intensity, technological complexity, a product classification such as SITC, common specific inputs, common markets, visual ressemblance etc.
The measure of similarity used in this essay is called proximity and it comes from Hausmann and Klinger (2007). The idea behind the measure is that if two products are similar to each other along any of the dimensions listed above, they will tend to be exported by the same countries. Proximity of two products is therefore defined in terms of the conditional probabil- ity that one product will be exported by a country, given that the country exports the other product, i.e.
P(xi,t = 1|xj,t = 1) = P
cxi,txj,t P
cxj,t .
This gives two different values depending on the direction in which the con- ditional probability is computed. The values will differ substantially if one of the products is exported by many more countries than the other one.
For example, it may be that almost all countries exporting cars also export canned food, but only a few of the many countries exporting canned food export cars. If this is the case, canned food will not be particularly strongly related to cars. That is why proximity is defined as the smaller one of the two conditional probabilities,
ϕi,j,t = min{P(xi,t = 1|xj,t = 1), P(xj,t = 1|xi,t = 1)}.
Once proximity is defined, it is necessary to find a measure of average similarity of country’s exports to, say, product i. The measure used by Hausmann and Klinger (2007) is called density and it is constructed as the sum of the dummies for exporting all other products weighted by each prod- uct’s proximity to product i,
densityi,c,t = P
jϕi,j,txj,c,t
P
jϕi,j,t , j 6=i.
A disadvantage of this measure is that it is driven by two distinct effects.
First, it reflects the (unweighted) number of products that a country exports, and second, it reflects the average proximity of the country’s exports to product i. This essay overcomes the problem by splitting the index into two distinct indices. The first one is called diversif ication and equals the number of products that a country exports in a given year.
diversif icationc,t =X
j
xj,c,t.
Diversif ication is later used as an explanatory variable in regressions
withxi,c,t as a dependent variable. As the above definition ofdiversif ication
itself contains xi,c,t, its use in the regressions would introduce endogeneity which would be particularly significant in less diversified countries. In order to prevent this problem, a slightly modified version ofdiversif icationis used when running regressions:
diversif icationi,c,t =X
j
xj,c,t, j 6=i.
The second new index defined here is the average proximity of country’s exports to product i. It is called proxav and it is normalized by the sum of proximities of all the other products to product i. Note that it holds that proxav∗diversif ication=density.8
proxavi,c,t = P
jϕi,j,txj,c,t
P
jxj,c,tP
jϕi,j,t, j 6=i.
P roxavmeasures average proximity of a product toall exports of a coun- try. In the monkey forest,proxav would be equivalent to a distance between the centre of an area inhabited by a tribe of monkeys and a tree where the tribe would like to send some of its members. It captures how well certain features of a country fit exporting of a certain product, but it does not say whether the features include primarily underlying characteristics of the econ- omy, or whether product-specific factors are important. As argued in Section 1, in both cases proxav can be expected to have a positive impact on the probability that the product will be exported.
In order to disentangle the effect of product-specific factors from the effect of underlying characteristics of a country, prox5 is defined as the average of 5 highest proximities of products that a country exports to product i. It is again normalized by the sum of proximities of all the other products to product i. If the proximities were ordered by their size, prox5 could be defined as
prox5i,c,t = P5
j=1ϕi,j,txj,c,t 5P
jϕi,j,t , j 6=i.
In approximately 1% of observations countries export less than 5 products in a given year. If uncorrected, this would lead to prox5 lower than proxav, whereprox5 would be artificially low because of lowdiversif ication. P rox5 is therefore set equal to proxav in these cases. P rox10 is constructed in an analogous way with 10 most similar product instead of 5.
8The normalisation byP
jϕi,j,tis done so that the new indices correspond directly to thedensityindex from Hausmann and Klinger (2007). Estimates not presented here show that the normalization does not significantly affect the results.
Theprox5 index does not measure similarity of country’s export structure as a whole to product i, instead it measures presence of a small number of exported products which are very similar to product i, disregarding the rest of the export structure. In the forest,prox5 is the distance between the tree where monkeys would like to jump and the nearest trees already inhabited by their tribe. If product-specific factors are important,a high value of this measure should mean that the relevant product-specific factors are present in the country, and it should therefore lead to a higher probability that product i will be exported. On the contrary, if only underlying characteristics of the country play role in determining what the country exports, prox5 will not have any impact.
The idea of the product space is built on the assumption that the de- terminants of proximity between pairs of products and consequently of the shape of the product space change more slowly than positions of individ- ual countries in the product space. Evolution of the product space itself is certainly an interesting topic, but this essay aims at exploring movements within a given product space. P roximity is therefore calculated separately for years 1968, 1969 and 1970, and the mean of these three proximities is then held fixed and used for construction of the other indices for the whole examined period. Years 1968–1970 are chosen for two reasons. First, in order to avoid endogeneity,proximityshould be calculated using export structures preceding those that indices constructed with proximity will try to explain.
Second, the additional data from Caselli et al. (2010) are only available from 1970 onwards and the period used in the estimations thus starts in 1970. The years for calculating proximity were chosen as the latest years preceding the estimation period.
Table 1 contains summary statistics for the indices of export structure.
Unsurprisingly, proxav is correlated withprox5 and prox10, but almost half of variation in prox5 and prox10 cannot be explained by proxav alone. Af- ter controlling for diversification and its interaction with proxav, the unex- plained proportion of variation in prox5 and prox10 drops to one third and
one quarter respectively. Multicollinearity should not be a serious problem when using proxav, diversif ication and prox5 or prox10 simultaneously as regressors, especially given the size of the dataset. It is weaker for prox5 and that is why prox5 is used in the rest of the paper rather than prox10.
Control regressions not reported here show that choice of prox5 or prox10 does not alter the results in any significant way.
Table 1: Measures of export structure — summary statistics
Variable Mean (Std. Dev.) Min. Max. N
density 0.144 (0.125) 0 0.830 1448816
diversif ication 71.3 (53.3) 2 256 1448816
proxav 0.0019 (0.0008) 0 0.0169 1448816
prox5 0.0043 (0.0019) 0 0.0239 1448816
prox10 0.0038 (0.0017) 0 0.0184 1448816
prox5−proxav 0.0024 (0.0014) 0 0.0209 1448816
prox10−proxav 0.0019 (0.0012) 0 0.0143 1448816
R2from regression ofprox5 on proxav 0.55
R2from regression ofprox5 on proxav,diversif icationand their interaction 0.67
R2from regression ofprox10 onproxav 0.58
R2from regression ofprox10 onproxav,diversif ication and their interaction 0.75 Covers period 1970–2000.
4 Estimation and main results
The aim of this empirical investigation is to see whether the probability that a country starts or keeps exporting a certain product depends on proximity of the product to the most similar products that the country already exports conditional on average proximity of the product to the country’s exports and on the level of diversification of the country. The conditioning is emphasized since without it prox5 would simply capture the effect of proxav — it would probably be significant but severely biased due to the omitted variable.
Panels used in empirical research normally have two dimensions: cross- section and time. This allows researchers to control for country and time fixed effects. The data explored in this essay are different because they are
three-dimensional. They do not only cover a cross-section of countries over time, but for each country and point in time they also contain a wide range of products. There are theoretically several basic ways of exploring such data, differing by the degree of homogeneity imposed on regression coefficients.
One would involve running separate panel regressions for each product and then aggregating information on the estimated coefficients in some way. An- other would run the regressions separately not for each product but for each country. This essay follows the most straightforward route. Regressions are run using all three dimensions of the data at the same time. The advantage of this approach is that it allows controling simultaneously for (i) fixed ef- fects of each product separately in each year, (ii) fixed effects of each country separately in each year and (iii) a time invariant effect of each combination of a product and a country. Disadvantage of this approach is that it im- poses homogeneity on all regression coefficients except intercepts. This is clearly a very strong assumption, and most importantly it precludes direct examination of export determinants that have different impact on different products, for example factor endowments. The three types of fixed effects control for determinants that affect probability that a country starts export- ing some new product. If a higher level of human capital in a country tends to increase the total number of products that a country exports, the country- year fixed effects control for it. But a higher level of human capital should primarily increase the probability of exporting products that are intensive in human capital and reduce the probability of exporting those that are not intensive in human capital. The three-dimensional approach fails to capture this effect.
Ignoring richer dynamics for a moment, the model can be written as P(xict = 1) =F(xic,t−1, diversif icationict, proxavict, prox5ict).
The Linear Probability Model is used here to model probability. It appears to be the least problematic model among the available options, although it carries with it several problems. First, and maybe most importantly, it imposes the same marginal effects on all the observations. This is less of
an issues around middle of the distribution of an explanatory variable, but it may severely affect results in the tails of the distribution. Second, by construction it leads to a heteroskedastic and non-normally distributed error term. This can be overcome by calculation of robust standard errors and a large enough sample. Third, it is not a proper probability model and therefore may sometimes give predicted values smaller than zero or larger than one, for which probability is not defined. Probit and logit would be possible alternatives, but their application in a dynamic equation with fixed effects would be complicated and maximum likelihood estimation with 1.5 million observations would be excessively computationally demanding.
The general functional form used for the estimation is xict =α+
P
X
p=1
ρpxic,t−p +
V
X
v=1 P
X
p=1
βpvvaric,t−pv +Act+Bit+Cic+ict, (1) wherevarv are the explanatory variables other than lagged dependent (num- ber of which isV),Act is a product-invariant country-year-specific effect,Bit is a country-invariant product-year-specific effect andCic is time-invariant ef- fect for each combination of product and country. P is the maximum number of lags to be included.
The regressors include diversif ication, proxav and prox5, which are all devided by their standard deviations so that the estimated coefficients di- rectly show the effect of a one-standard-deviation change in the indices. Trial regressions have revealed that the density index has a stronger explanatory power than any of the other three indices. Sincedensityis equal to a product of proxav and diversif ication, this suggests that the effects ofproxav and prox5 may vary with the range of products a country exports. Interaction terms of proxav with diversif ication and prox10 with diversif ication are constructed using demeaned versions of the indices and are also included in the regressions.
A reparametrization, as used for example by Bond et al. (2004), deals with collinearity of the lagged variables and also enables easier interpretation of results. Writing dvart = vart−vart−1 and ignoring the fixed effects, it
gives
xict =α+
P−1
X
p=1
θpdxic,t−p+θPxic,t−P
+
S
X
v=1
(
P−1
X
p=1
πpvvaric,t−pv +πPvarvic,t−P) +ict. (2) For coefficients on the lagged dependent variables it holds that
θP =−1 +
P
X
p=1
ρp,
and for coefficients on the other regressors it holds that πvP =
P
X
p=1
βpv.
The long-term effect of varv on probability that country c exports product i can be calculated as
πPv
−θP. (3)
In order to control for country-year and product-year specific effects (Act and Bit respectively), ideally dummies for each combination of product-year and country-year would be included. Unfortunately, this is not possible given the size of the dataset. Two different approaches are adopted here. The first one, which is reported throughout the essay, runs a regression with fixed effect for each combination of a product and a country, and includes simple year dummies. This controls for time-invariant components of Act and Bit but relies on the assumption that their time-variant component is not correlated with the regressors. To check robustness of the results, another approach is also adopted, according to which country-year and product-year specific means are substracted from all variables, and the fixed-effects regression is then run without year dummies. These estimates are precisely equivalent to those gained with country-year and product-year dummies included, but their standard errors are slightly different.
Testing with panel unit root tests set up by Maddala and Wu (1999) and Im et al. (2003) (not reported here) suggests that diversif ication, proxav and prox5 are integrated of degree one. Under classical time-series assump- tion, using them as regressors with a dummy as a dependent variable would be inconsistent and would give spurious results. However, Phillips and Moon (1999) show that the wide cross-section dimension of the data, together with its long time-dimension, allow the regression to be interpreted in terms of the long-run average relation parameter. Intuitively, the order of integration does not matter because all the information from potentially spurious regres- sions is gathered. If they were spurious then there would be a zero average effect.
Experimentation with various numbers of lags shows that coefficients change with the addition of the first lags but remain stable from the third lag onwards. Consequently P = 3 in the reported results. Another concern is whether contemporaneous information should be included, i.e. whether minimum of p should be 0 or 1. The first regression results are reported both with and without contemporaneous information, the subsequent results only without it. An exception is diversif ication, for which contemporane- ous information is always included since it controls for changes in the total number of products that a country exports in each year and assures that the results are not driven by drops or surges in exports of the main export commodity in a given country, which would make exports of other products look larger (or smaller) as a share of total exports.
Equation (2) is estimated on yearly data with fixed effects for each com- bination of a country and a product. Hausmann and Klinger (2007) estimate an equation which is similar to (1) but they do so on a panel with five-year averages in six periods. This is problematic in the context of a dynamic equation, since if there are country-product specific time-invariant factors affecting probability that a country exports product i, coefficients on lagged dependent variables will be inevitably biased and inconsistent, and if these fixed effects are correlated with other explanatory variables, other coefficients
will be biased and inconsistent as well. The problem is that controlling for the fixed effects in a dynamic equation will lead to a bias as well. Using yearly data instead of averages allows controlling for the fixed effects, because the bias from using fixed effects in a dynamic panel converges to zero for long T, and the estimates with yearly data should therefore be consistent.
Table 2: Predictors of what countries export — first approach
POLS FE POLS (incl. cont.) FE (incl. cont.)
(1) (2) (3) (4)
x (lagged) -0.137*** -0.388*** -0.137*** -0.389***
(0.001) (0.002) (0.001) (0.002)
diversification 0.009*** 0.025*** 0.008*** 0.022***
(0.000) (0.001) (0.000) (0.001)
proxav 0.022*** 0.042*** 0.023*** 0.054***
(0.000) (0.002) (0.000) (0.002)
proxav*diversification 0.016*** 0.034*** 0.018*** 0.044***
(0.000) (0.001) (0.000) (0.001)
prox5 -0.001*** 0.000 -0.001* 0.002
(0.000) (0.001) (0.000) (0.001)
prox5*diversification -0.002*** -0.004*** -0.002*** -0.005***
(0.000) (0.001) (0.000) (0.001)
Constant -0.044*** -0.084*** -0.049*** -0.113***
(0.001) (0.004) (0.001) (0.004)
Observations 1308608 1308608 1308608 1308608
R2 0.194 0.265 0.196 0.266
Number of cpcode 46736 46736
*** p<0.01, ** p<0.05, * p<0.1
The table contains estimates of equation (2). Only estimates ofθP,πvP andαare reported. Columns (1) and (3) show estimates from pooled ordinary least squares, columns (2) and (4) estimates with
product-country fixed effects. Columns (3) and (4) include contemporaneous information, columns (1) and (2) include it only fordiversif ication. Year dummies were included in all cases. Clustered standard errors are in parentheses.
Result tables only display coefficients on the third lags of explanatory variables because after the reparametrisation only those are relevant and
because it saves space and improves clarity. Pooled ordinary least squares estimates are also reported for comparison. Standard errors are clustered to correct for heteroskedasticity and autocorrelation.
Table 3: Predictors of what countries export — second approach
POLS FE POLS (incl. cont) FE (incl. cont)
(1) (2) (3) (4)
x (lagged) -0.141*** -0.390*** -0.141*** -0.391***
(0.001) (0.002) (0.001) (0.002)
proxav 0.024*** 0.046*** 0.025*** 0.061***
(0.001) (0.002) (0.001) (0.002)
proxav*diversification 0.016*** 0.037*** 0.018*** 0.047***
(0.000) (0.001) (0.000) (0.001)
prox5 0.003*** 0.000 0.003*** -0.004***
(0.001) (0.001) (0.001) (0.002)
prox5*diversification -0.001*** -0.006*** -0.001*** -0.006***
(0.000) (0.001) (0.000) (0.001)
Constant 0.000*** -0.000 -0.000*** -0.000
(0.000) (0.000) (0.000) (0.000)
Observations 1308608 1308608 1308608 1308608
Number of cpcode 46736 46736
R2 0.194 0.264 0.196 0.266
*** p<0.01, ** p<0.05, * p<0.1
The table contains estimates of equation (2). Only estimates ofθP,πvP andαare reported. Columns (1) and (3) show estimates from pooled ordinary least squares, columns (2) and (4) estimates with
product-country fixed effects. Columns (3) and (4) include contemporaneous information,columns (1) and (2) include it only fordiversif ication. Product-year specific and country-year specific means were substracted from all variables. Clustered standard errors are in parentheses.
Table 2 shows basic regression results both with and without contempo- raneous information. Estimated coefficients on measures of export structure with and without fixed effects are qualitatively similar to each other but larger with fixed effects. As could be expected in a dynamic equation, con- trolling for fixed effects leads to substantially more negative θ3, suggesting a bias in the pooled OLS. Since the formula for long-term effect as shown
in (3) has θ3 in its denominator, the long-term effect would be substantially overestimated if pooled OLS was used. The estimates vary only marginally depending on whether contemporaneous information is included. The sub- sequent regressions always report results with fixed effects and without con- temporaneous information.
Table 3 contains results of taking the latter approach described above, where country-year and product-year product year specific means are sub- stracted from all the variables, controlling forAct and Bit. The estimates are almost the same as those in 2. In the rest of the essay the former approach without demeaning and with time dummies is adopted. Table 4 demonstrates that the findings are highly consistent across regions.
There is a statistically and economically significant effect ofproxav. One standard deviation increase in proxav is in the long run on average related to an increases in probability that a product is exported by more than 11 percentage points. The effect of proxav is higher where diversif ication is high. For example, in highly diversified countries with diversif ication one standard deviation above its mean, the marginal effect of proxav goes up to 20 percentage points. However, since the estimates come from a linear prob- ability model, caution is needed with respect to interpreting marginal effects in the tails of the distribution of explanatory variables. On the contrary, the effect of proxav is smaller in less diversified countries. However, the fact that proxav has larger effect in more diversified countries probably does not carry any important economic interpretation. Instead it reflects the fact that more diversified countries have by definition on average higher probabilities of exporting individual products and changes in these probabilities due to changes in proxav have therefore larger magnitudes. Average proportional effect of proxav on probability that a certain product is exported is quite stable across different levels of diversif ication.
Table4:Predictorsofwhatcountriesexport—decompositionaccordingtomainregions WorldDevelopedEAPECALACMENASASSA x(lagged)-0.388***-0.352***-0.318***-0.403***-0.392***-0.449***-0.430***-0.467*** (0.002)(0.004)(0.006)(0.007)(0.005)(0.009)(0.012)(0.008) diversification0.025***0.023***0.019***0.031***0.026***0.035***0.024***0.036*** (0.001)(0.003)(0.003)(0.006)(0.002)(0.004)(0.007)(0.004) proxav0.042***0.025***0.045***0.056***0.041***0.042***0.052***0.046*** (0.002)(0.006)(0.005)(0.007)(0.004)(0.005)(0.009)(0.005) proxav*diversification0.034***0.035***0.028***0.043***0.031***0.035***0.021**0.037*** (0.001)(0.003)(0.004)(0.006)(0.003)(0.004)(0.009)(0.004) prox50.0000.007-0.0030.0060.003-0.008**0.0090.000 (0.001)(0.005)(0.004)(0.005)(0.003)(0.004)(0.006)(0.005) prox5*diversification-0.004***-0.009***0.001-0.004-0.002-0.010***0.001-0.002 (0.001)(0.002)(0.004)(0.003)(0.002)(0.002)(0.005)(0.004) Constant-0.084***-0.058***-0.082***-0.155***-0.086***-0.075***-0.130***-0.099*** (0.004)(0.013)(0.010)(0.017)(0.008)(0.012)(0.023)(0.010) Observations13086082560321280168534429870414224056896341376 R2 0.2650.2440.2080.2610.2690.3080.2790.312 Numberofcpcode46736914445723048106685080203212192 ***p<0.01,**p<0.05,*p<0.1 Thetablecontainsfixed-effectestimatesofequation(2).Nocontemporaneousinformation(exceptfordiversification).Yeardummiesincluded.Only estimatesofθP,πv Pandαarereported.EAP=EastAsiaandPacific;ECA=EasternEuropeandCentralAsia;LAC=LatinAmerica;MENA=Middle EastandNorthernAfrica;SA=SouthAsia;SSA=Sub-SaharanAfrica.Clusteredstandarderrorsareinparentheses.
Diversification includes the contemporaneous effect. The estimated coef- ficient on it is positive and economically significant with fixed effects. This captures the intuition that the probability that a certain product starts being exported in a certain year increases if many other products also begin to be exported in the same year. The role of diversification here is one of a control variable rather than of an interesting regressor per se.
A more striking result is that prox5 does not matter at all, whether on its own or in interaction withdiversif ication. It is statistically significant in some specifications, but its economic effect is completely negligible and ten to twenty times smaller than the one of proxav. Conditional on how similar productiis to an average export article of a country, there is no evidence that the probability of exporting productiwould depend on whether the country already exports some very similar products. If 90% of a country’s exports consist of tropical fruit, the fact that it also exports motorcycles does not at all make it more likely to start exporting cars. This suggests that underlying characteristics of a country are what determines its export structure, while product-specific factors accumulated through exporting of the corresponding products are not very important.
5 Explaining proxav
The proxav index is a significant predictor of probability that a country ex- ports a certain product. The index captures how well characteristics of the country fit the characteristics required for exporting of the product. So far the essay has been agnostic on what these characteristics are. The remaining part of this section asks whether these characteristics can be explained by simple factor endowments, factors traditionally considered as important de- terminants of export structure. In order to answer the question, the following
equation is estimated:
proxavict =β0 +β1diversif icationict+β2schoolingict (4) +β3loglandict+β4logpopict+ict. (5) Schoolingstands for average years of schooling of adult population,logland for logarithm of the land area of a country and logpop for logarithm of the number of adults living in the country. Since the explanatory variables im- pact on exports of each product differently, the equation is estimated sepa- rately for each product.
Table 5 shows percentage shares of estimates that are significantly pos- itive or negative when the equation is estimated on a cross-section in 2000.
More diversified countries have on average higher proximity. This supports a hypothesis of Hidalgo et al. (2007) that some parts of the product space are much denser than its other parts in the sense that products there have more high-proximity links to other products. If the product space was equally dense in all its parts,proxav could not be correlated with any variable which varies only over time and across countries, but not across products. In the light of findings of Hidalgo and Hausmann (2009), the positive relationship betweenproxavanddiversif icationcan also be interpreted so that countries with more complex economies will have more diversified exports and at the same time will be located closer to the centre of the product space, with a lot of connections to other products.
Approximately three quarters of estimates on schooling and land are ei- ther significantly positive or significantly negative. Majority of estimates on schooling are positive while majority of those on land are negative. 9 Popu- lation is significant for slightly more than half of the products. On average these basic endowments explain approximately half of the variance inproxav.
The findings are generally consistent with predictions of the Heckscher-Ohlin
9The reason for this is probably that more than half of products in the sample are manufactures (about 60% of the sample falls into SITC one-digit categories 5-8), and the export of manufactures is typically higher relative to primary products by countries with high skill/land ratio (see Wood, 2009).
Table 5: Exlaining proxav (cross-section in 2000)
share of significant estimates (%) average p o s i t i v e n e g a t i v e estimate
1% 5% 10% 10% 5% 1% βˆ |β|ˆ
diversification 45 56 61 11 9 5 .158 .234
schooling 52 57 60 21 20 16 .123 .298
logland 9 12 15 58 55 47 -.150 .265
logpop 17 29 37 15 12 9 .081 .216
AverageR2 0.46
Columns two to seven contain shares of significant estimates on individual regressors when equation (5) is estimated separately for each product on a cross-section for year 2000 using ordinary least squares.
Numbers for three significance levels are reported. Shares corresponding to lower significance levels also include shares corresponding to higher significance levels. The last two columns report average estimates and average absolute values of the estimates.
theory stating that what country exports depend on are their factor endow- ments. However, it is important to be aware of the fact that the estimated equation is very simple and does not control for any other factors. It is thus possible that the estimates capture effects of other variables. In particular, years of schooling are likely to be correlated with technological sophistica- tion, quality of institutions in a country and other important variables, so that the estimates may be severely biased. The equation should therefore be rather understood as a preliminary look at how much variation inproxav can be explained by a few general characteristics of an economy.
Table 6 shows an overview of significance of estimates for the case where equation (5) is run as a dynamic equation with fixed effects. The estimation technique is analogous to the one used above for explanation of probability that a product is exported. Land had to be dropped because it does not vary with time. The explained fraction of variation in proxav is substan- tially smaller than in the previous case. P roxav is again positively related to diversif ication. Buiding on the interpretation from the previous para- graph, this suggests that even over time as economies diversify, they move to denser parts of the product space. Schooling is completely insignificant. This
Table 6: Exlaining proxav (fixed effects in 1970-2000)
share of significant estimates (%) average p o s i t i v e n e g a t i v e estimate
1% 5% 10% 10% 5% 1% βˆ |β|ˆ
proxav (lagged) 0 0 0 100 100 100 -.340 .340
diversification 67 70 71 17 15 13 .094 .134
schooling 0 2 6 4 2 0 .006 .044
logpop 15 31 38 1 1 0 .186 .215
AverageR2 0.32
Columns two to seven contain shares of significant estimates on individual regressors when equation (5) is estimated separately for each product as a dynamic equation for period 1970-2000. The dynamics are specified analogously to those described in equation (2), the relevant estimates are those on third lags of variables in levels, analogous toθP,πvP from equation (2). Country fixed effects and year dummies are included. No contemporaneous information (except fordiversif ication). Numbers for three significance levels are reported. Shares corresponding to lower significance levels also include shares corresponding to higher significance levels. The last two columns report average estimates and average absolute values of the estimates.
may be partly due to the double intrapolation with which the schooling data was constructed, but it still suggests that development in average years of schooling and factors correlated with it is probably not the most important determinant of changes in export structure. Finally, countries with growing population typically saw an increase in average proxav of their exports. The reason for this may be that population boom is often part of more com- plex social processes which may also include changes in the structure of the economy.
6 Conclusion
An intensly discussed topic in the field of development economics is whether governments should actively promote the development of exports in products that differ substantially from their countries’ present export structures10. An
10Active industrial policy promoting particular products has been advocated by Evans (1995), Amsden (2001) and Chang (2002) among many others.
important aspect of this general issue is the question of whether a country that develops such exports would be able to use the new exports as an outpost in which it acquires product-specific knowledge and endowments and which will help it to develop even more new exports in the remote, and possibly more fruitful, niches of the “product space”.
This essay suggests that the answer to the question is no. The essay confirms the finding of Hausmann and Klinger (2007) that the likelihood of developing or keeping exports of a certain product by a country is higher if the product is similar to the overall export structure of the country. It nevertheless does not find that the likelihood would depend in any significant way on whether the country already exports some very similar products, conditional on its overall export structure. The results are robust across regions and to controlling for fixed effects.
It seems that what countries export is not determined by product-specific factors accumulated through exporting of the corresponding products but rather by underlying characteristics of their economies. It is not clear what these characteristics are, but on the level of disaggregation presented here they can be only partially captured by measures of basic factor endowments
— labour, land and skills – although more so when looking at a cross- section11.
Even if taken on their face value, the results do not imply that active economic policies for promotion of structural change should not be under- taken. They instead suggest that policies that focus on supporting lively discovery activity around country’s specific strengths12 may be more effec- tive than costly promotion of long jumps that by themselves do not secure further development within the new groups of products. To go back to the monkey metaphore, even if the government carries several monkeys to a new
11These findings are in line with Mayer and Wood (2001), Wood and Mayer (2001) and Wood (2003) who argue that relative export structures in South and East Asia and in Africa are to a large extent predetermined by the relative abundance of skills, labour and land and change only slowly over time.
12See Rodrik (2004) and Justin Lin’s view in Lin and Chang (2009).
