Maman ; Setiawan
email: maman.setiawan@wur.nl

Grigorios Emvalomatis

Alfons Oude Lansink

Industrial concentration and price-cost margin in the Indonesian food and beverages sector

Keywords: Industrial Concentration, Price-Cost Margin, Food and Beverages Industry, Competition Law industrial concentration, price-cost margin, competition law, food and beverages sector

come

I. Introduction

It is well known that the industrial concentration in almost all of the economic sectors of Indonesia is relatively high (see [START_REF] Bird | Concentration in Indonesia manufacturing 1975-93[END_REF]. Some sectors in the industry may have a stable and high industrial concentration because of the barriers to entry for new potential firms. The barriers may be caused by natural conditions, such as economies of scale moulded by incumbents, or formal regulations, such as exclusive monopolies, or business strategy.

One of the industry sectors with a high concentration is the food and beverages sector. Data presented by [START_REF] Bird | Concentration in Indonesia manufacturing 1975-93[END_REF] showed that almost all of the subsectors of the food and beverages sector are highly concentrated. Furthermore, Bird concluded that for some of them, high concentration is particularly persistent.

The food and beverages sector contributes significantly to the Indonesian GDP. Since 2004, the output of this sector accounted for about 7% of the GDP and about 23% of the total industrial manufacturing output. This sector plays a vital role in the Indonesian economy and is a public concern, especially in fulfilling basic food needs. Furthermore, the total Indonesian population of about 206 million in 2000 indicates that this industry is an important sector. Additionally, the food and beverages sector absorbed about 23% of total employment in the Indonesian Naturally, policy makers and researchers pay considerable attention to the relationship between the degree of competition and the price markup in the food and beverages sector, mainly because high industrial concentration in the sector will lead to the extraction of consumer surplus by the firms, with consequences for the entire population, but especially for lower income households. The higher industrial concentration may induce a few dominant firms with market power to behave collusively and to generate excess profits by keeping food prices higher than in a more competitive market.

In 1999, the Indonesian Competition Law No. 5 1999 was established. This law was designed to increase effectiveness and efficiency in economic activities through the creation of fair business competition and, subsequently, to improve the people's welfare. The Commission for the Supervision of Business Competition (KPPU) has been the body responsible for enforcing the law in Indonesia. Although the KPPU has limited the anti-competitive behavior of firms, the high concentration in the food and beverages sector continues to exist. Furthermore, a study investigating the competition law in Indonesia that was conducted after the competition law had been established [START_REF] Pangestu | The evaluation of competition policy in Indonesia[END_REF] found ambiguities that are still subject to interpretation in the competition law. The ambiguities may make the investigation and the law enforcement on anti-competitive behavior ineffective. Some previous studies, such as [START_REF] Hill | Concentration in Indonesian manufacturing[END_REF] and [START_REF] Bird | Concentration in Indonesia manufacturing 1975-93[END_REF], focused on the industrial concentration before the Indonesian Competition Law was implemented. [START_REF] Hill | Concentration in Indonesian manufacturing[END_REF][START_REF] Bird | Concentration in Indonesia manufacturing 1975-93[END_REF] observed the industrial manufacturing concentration in Indonesia and found that the seller concentration was remarkably high. Similar research about the trend of the industrial concentration in another Asian country, Malaysia, was conducted by Bhattacharya (2002).

However, a thorough study of the trend of industrial concentration in the food and beverages sector has never been conducted in Indonesia.

As briefly explained in the structure-conduct-performance (SCP) paradigm, the firms in the concentrated industry will have a better industrial performance (usually measured by profitability or price-cost margin). Some research related to the relationship between the industrial concentration and the price-cost margin has been conducted, but mostly in the U.S. and some European countries (Collins and Preston, 1966;Sizrazi, 1974;[START_REF] Ghosal | Market structures, price-cost margins, and unionism : an empirical note[END_REF]and Thurik, 1992;[START_REF] Dickson | Price-cost margins, prices, and concentration in US manufacturing: a panel study[END_REF]. A few studies have focused on the relationship between industrial concentration and price markup in Asian countries. [START_REF] Gan | The relationship between market concentration and profitability in Malaysian manufacturing industries, April, Malayan Economic Review Gan Wee Beng and Yen, Tham Siew[END_REF] and [START_REF] Kalirajan | On the simultaneity between market concentration and profitability : the case of a small-open developing country[END_REF], for example, observed that there was a positive and significant influence of industrial concentration on the price-cost margin in Malaysian manufacturing. [START_REF] Go | Market structure and price-cost margin in Phillipine manufacturing industries[END_REF] also found a positive relationship between the seller's concentration and the price-cost margin in Filipino manufacturing industries. Most of the research conducted to date investigated all subsectors of the manufacturing industry. Additionally, the research connecting the relationship between industrial concentration and the price-cost margin in the Indonesian food and beverages sector is hardly found in the published literature, nationally or internationally. The information about the relationship between the industrial concentration and the price-cost margin will provide further insight for the policy makers on whether the firms in the industry gain more producer surplus through the lessening of the competition and anti-competitive behavior in the industry.

Therefore, the investigation of the effect of industrial concentration on industrial performance has a high relevance for policy makers.

The objectives of this paper are twofold. First, this paper analyzes the trend of industrial concentration in the Indonesian food and beverages sector in the period before and after the establishment of Indonesian Competition Law. The analysis of the trend includes a test for the convergence of industrial concentration in the long run. Second, this paper analyzes the relationship between industrial concentration and the price-cost margin in the Indonesian food and beverages industry. Additionally, the effect of the competition law establishment on the price-cost margin is measured.

II. Industrial Concentration and the Price-Cost Margin

Industrial concentration is a common measure of market structure 1 . It reflects both the number and size distribution of firms in an industry. The industrial concentration may represent the market power and the probability of anti-competitive behavior among firms in the market.

The most commonly used measures of industrial concentration are the concentration ratio for n firms (CR n ) and the Herfindahl-Hirshman Index (HHI), which is based on [START_REF] Pepall | ) Eviews 6 User Guide II, Quantitative Micro Software, LLC Sala-I-Martin, Xavier[END_REF]. 1 We define industrial concentration as in [START_REF] Bain | Relation of profit rate to industry concentration : American manufacturing, 1936-1940[END_REF] Page (1)

2 n 1 i i j ) (MS HHI ∑ = =
(2) where j = 1,2,…, m indexes the subsector, i = 1,2,…n indexes firm i in a subsector, and MS i is the market share of firm i in its respective subsector. CR4 considers the collective share of the four largest firms in a subsector, while HHI j considers the inequality of distribution of market shares among all firms in subsector j.

Both the CR4 and the Herfindahl-Hirschman Index (HHI) measures have a limitation in the calculation, but they complement each other. 3 Hence, it is necessary to use both concentration measures to clearly picture the market structure in the industry.

Additionally, there are some shortcomings related to the calculation of the concentration ratio (CR4 and HHI). The calculation of the concentration ratio will underestimate or overestimate the "true concentration" for a series of reasons [START_REF] Bird | Concentration in Indonesia manufacturing 1975-93[END_REF]. First, the survey of industrial manufacturing in Indonesia includes only the firms classified into large and medium firms. 4 This may overestimate the industrial concentration because small firms are not reported in the survey.

Second, BPS reports firm data based on establishment. The industrial concentration may be underestimated because the calculation may include leading firms that have more than one establishment. Third, the unavailability of information on merger activity in the data, especially about horizontal mergers, is likely to lead to an underestimation of the industrial concentration.

Fourth, because the industrial concentration may be higher in the regional than in the national level, the calculation of industrial concentration in the national level will be underestimated.

2 Considering stocks, this paper calculates industrial concentration based on sales data because sales seem to explain more about the market share than the output. 3 CR4 is commonly used to classify the market into some categories of oligopoly (see [START_REF] Shepherd | The Economics of Industrial Organization[END_REF], but it cannot capture the distribution of the market share for all firms in the market. However, HHI can capture the distribution of the a firm's market share in a market, but it is rather difficult to classify the oligopoly categories from the HHI. In spite of this, [START_REF] Besanko | Economics of strategy 3rd Ed[END_REF] gave a classification of market structure based on HHI. Furthermore, [START_REF] Liebenberg | Structure, conduct, and performance analysis of the south African auto insurance market: 1980-2000[END_REF] also discusses the importance of using both HHI and concentration ratio. 4 BPS defines medium-sized firms as those firms employing more than 20 workers. Finally, it is noted that the industries examined may not be "markets" (see Kamerschen, 1994 for details).

The degree of the biases induced for the reasons mentioned above may not be substantial. [START_REF] Bird | Concentration in Indonesia manufacturing 1975-93[END_REF] gives some arguments in this regard. First, Hill (1990) argued that, in the aggregate, the exclusion of small firms is not a serious problem because small firms contribute no more than 15% of the total manufacturing value added in 1985. Second, different results may exist in the industrial concentration calculation between the method that uses the calculation from BPS establishment data and the one that uses the primary firm data. Although there will be differences, the industrial concentration trend may still be captured quite accurately. Third, vertical, rather than horizontal mergers, are more frequent in Indonesian economy. Therefore, the unavailability of information on merger activity will not have a great impact on the industrial concentration calculation. Finally, all factors underestimating or overestimating the concentration appear not to undermine the trend of the concentration, if their net effects remain constant over time [START_REF] Bird | Concentration in Indonesia manufacturing 1975-93[END_REF]. This paper also estimates the effect of industrial concentration on industrial performance measured by the price-cost margin. The relationship arises because higher industrial concentration may lead to higher industrial performance [START_REF] Bain | Relation of profit rate to industry concentration : American manufacturing, 1936-1940[END_REF][START_REF] Gupta | A simultaneous determination of structure, conduct, and performance in Canadian manufacturing[END_REF]. A mathematical derivation of the effect of industrial concentration on the price-cost margin can be found in [START_REF] Saving | Concentration ratios and the degree of monopoly[END_REF], [START_REF] Cowling | Price-cost margin and market structure[END_REF], Fischer andKamerschen (2003a, 2003b), and [START_REF] Kamerschen | Market structure in the US electricity industry : a long term perspective[END_REF].

Industrial performance is measured by price-cost margin (Sizrazi, 1974;[START_REF] Domowitz | Business cycles and the relationship between concentration and price-cost margins[END_REF]Prince and Thurik, 1992). The price-cost margin (PCM) is calculated according to the formula proposed by Domowitz, Hubbard, and Petersen 5 (1986) and Prince and Thurik (1992). This formula allows for changes in inventories (∆Inventories), considering that changes in inventories are important with regard to the fluctuation in the business cycle in the Indonesian economy from 1995-2006: 5 Their (1988) article which has a connection to this article has been challenged by [START_REF] Kamerschen | Testing for antitrust market definition under the Federal Government Guidelines[END_REF]Park (1993a, 1993b). In the same year, [START_REF] Domowitz | Market structure and cyclical fluctuations in U.S. manufacturing : Reply[END_REF] replied that they did not view the Comment by [START_REF] Kamerschen | Testing for antitrust market definition under the Federal Government Guidelines[END_REF]Park (1993a, 1993b)

III. Data

The CR4 and HHI for the food and beverages industry are calculated using firm-level data from the Annual Manufacturing Survey provided by the Indonesian Bureau of Central Statistics (BPS). The dataset covers the period from 1995 to 2006. This paper uses that period because of the tractable and comparable data for all subsectors among the years. Furthermore, data beyond

have not yet been published.

There are 59 subsectors of International Standard Industrial Classification (ISIC) Level6 in the food and beverages industry, 55 of which are related to food processing, with the remaining to the beverages industry. This paper excludes five subsectors from the analysis because they contain less than four firms in each period. Therefore, this paper uses only 54 of the subsectors in the industry. During the period covered by the data, there were, on average, 5488 firms in the market. About 7.6 percent of them, on average, were involved in exporting activities. In 1995 the food and beverages sector had 5335 firms. This number increased significantly to 7897 in 2006.

Despite this, the number of firms had decreased significantly from 5495 to 4850 (a drop of 12%) in 1998, the year that coincided with a major economic crisis in Indonesia. Table 1 shows that the data are relatively heterogeneous, with relatively high standard deviations and coefficients of variation for all variables. In the period covered by the data, it is observed that the average of CR4 is 0.6328, which characterizes the food and beverages sector as a tight oligopoly, according to the criteria of [START_REF] Shepherd | The Economics of Industrial Organization[END_REF]. It is also seen that the average HHI is 2,266, which according to [START_REF] Besanko | Economics of strategy 3rd Ed[END_REF], this classifies the food and beverages sector as an oligopoly. The average PCM of 0.181 also indicates that the firms in the sector have a positive price markup. Regarding all variables, the data on demand growth (Growth) and capital output ratio (COR) are very heterogeneous. 7 The heterogeneous condition of the demand growth and capital output ratio are related to the economic condition and capital-output applied by the firms, respectively.8

IV. Empirical Model and Estimation

This paper uses two econometric models to investigate the trend of industrial concentration and the relationship between industrial concentration and the price-cost margin. The first model examines the trend of industrial concentration in the industry. It measures whether there is a trend for the industrial concentration to move to a certain value. To confirm the movement of the trend of industrial concentration for all subsectors in the food and beverages sector, this paper uses the theory of absolute convergence 9 [START_REF] Barro | Convergence[END_REF]Sala-i-Martin, 1996;[START_REF] Sorensen | Introducing Advanced Macroeconomics : Growth and Business Cycles[END_REF]. The model can indicate whether there is a tendency for the convergence of the industrial concentration in the long run to one and the same point for all subsectors. In other words, the model assumes that all subsectors have the same steady state in the long run. The assumption is relevant because all subsectors face the same business characteristics in the Indonesian economy. The absolute convergence model 10 is defined as:

j t 1 0 j t j t 0 0 n MS Ln T MS Ln MS Ln β β - ≅ - (4)
where j = 1,2,…,54 indexes subsector, t 0 is the initial year for which data are available (1995), and t n is the final year (2006). j t MS is the market structure in period t and subsector j, captured by the CR4 and HHI. The model is estimated using cross section regression. The food and beverages sector exhibits convergence in market structure if the estimated coefficient of β 1 is significantly positive.

The second model estimates the effect of industrial concentration on the price-cost margin in the industry. Higher industrial concentration, followed by higher market power, increases the ability of the firms or an industry to influence the market equilibrium price. Thus, higher concentration is expected to lead to higher price-cost margins. Moreover, based on [START_REF] Konings | The dynamics of industrial mark-ups in two small open economies: does national competition policy matter[END_REF], [START_REF] Mccloughan | The effectiveness of competition policy and the price-cost margin: evidence from panel data[END_REF], and Looi Kee and Hoekman (2003), the effect of the competition law on the price-cost margin is also investigated. The competition law is represented by the dummy variable of the competition law establishment in Indonesia as used by Looi Kee and Hoekman (2003). This paper also interacts the competition law dummy variable with the industrial concentration. This interaction variable can capture in the way industrial concentration affects the price-cost margin after the competition law establishment. The effect of the industrial concentration on the price cost margin may be lower after the establishment of the competition law because the law can break the cartel and other anti-competitive behavior. As a result, the competition law is also hypothesized to affect the price-cost margin indirectly through its influence on the industrial concentration. In addition, this paper also introduces trend variables and their interaction with the competition law dummy variable to see the trend of the price-cost where j and t index subsector and time, respectively. Law is a dummy variable that assumes the value 1 for the years after the establishment of the competition law (1999), Trend = 0,1,2,…,T, and PCM is the price-cost margin.

F
Regarding the relationship between industrial concentration and the price-cost margin, there is an endogeneity problem in the variable of industrial concentration (Clarke and Davis, 1982;[START_REF] Kalirajan | On the simultaneity between market concentration and profitability : the case of a small-open developing country[END_REF]. This endogeneity may arise because of the argument that the derivation of the price-cost margin comes from an equilibrium condition for profit maximization [START_REF] Jacquemin | Concentration and profitability in a small open economy[END_REF][START_REF] Kalirajan | On the simultaneity between market concentration and profitability : the case of a small-open developing country[END_REF]. Additionally, Clarke and Davis (1982) established the endogeneity problem through underlying cost and demand conditions. Therefore, this paper uses some instrumental variables for the industrial concentration. The instrumental variables chosen are based on the works of Muller andHam (1974), Sizrazi (1974), [START_REF] Gupta | A simultaneous determination of structure, conduct, and performance in Canadian manufacturing[END_REF], Prince and Turik (1992), [START_REF] Kalirajan | On the simultaneity between market concentration and profitability : the case of a small-open developing country[END_REF], [START_REF] Go | Market structure and price-cost margin in Phillipine manufacturing industries[END_REF], and Delorme, [START_REF] Delorme | Structure, conduct, and performance : a simultaneous equations approach[END_REF]. The main instrumental variables estimating the industrial concentration are industry size (Size), growth of demand (Growth), and capital output ratio (COR). Besides the three main instrumental variables, this paper also uses a competition law dummy variable and trend variables as exogenous in the equation that determines PCM.

Equation ( 5) is estimated using unbalanced panel data techniques. 12 This method uses either a fixed effects or random effects model based on the Hausman test (1978). The fixed-effects model is chosen if the Hausman test shows that there is correlation between individual effects and other regressors. Otherwise, the random effects model will be used. In addition, the fixed-effects model uses dummy variables of the subsectors as the source of the heterogeneity, whereas the random effects model uses the intercept deviation of each subsector across the intercept for all subsectors.

11 The derivation of the relationship between industrial concentration and price-cost margin can be found in [START_REF] Cowling | Price-cost margin and market structure[END_REF] and Clarke and Davis (1982).

12 Some subsectors, such as 15145 and 15149, are not reported in 2006.

Trends of Average Industrial Concentration

Table 2 describes the industrial characteristics such as concentration for the CR4 (4 firms), the Herfindahl-Hirschman Index (HHI), the distribution of the number of firms, and the average price-cost margin. The table shows that the industrial concentration was high from 1995 to 2006, but there was a slightly declining trend, especially after the year 2000. This finding suggests that industrial concentration increased steadily before the establishment of Indonesian Competition Law No. 5 1999. After the establishment of the law, the industrial concentration decreased slightly over time. Furthermore, the CR4 and HHI decreased on average by 0.7% and 0.8%, respectively, every year from 1995-2006. The average increasing number of the firms in the industry every year may also be the reason for which the concentration is decreasing.

The price-cost margin is always positive and exhibits a significant increase by on average Based on the estimation of Eq. 4, Table 3 shows that the parameter estimate for the initial industrial concentration is negative (implying that β 1 >0), which means that there is absolute (according to CR4) tend to change slowly over times and some of them experienced concentration reduction, such as the milk, food and wheat flour subsectors. The five least concentrated (CR4) subsectors experienced a significant increase in concentration. For three of them, the increase was larger than 15%, on average.

The Effect of Industrial Concentration on Price-Cost Margin

Table 5 shows the results of the estimation of Equation ( 5), which is estimated using a fixedeffects model with stationary level-form data. The fixed-effects model is used because the Hausman test (1978) rejected the random effects specification. Furthermore, based on the stationarity test of Levin, Lin, Chu (LLC) test ( 2002), the null hypothesis of non-stationary data of the CR4 and PCM is rejected at the 1% critical level, which indicates that the data at the level form are valid for use in the model.

The White test for heteroscedasticity [START_REF] Castilla | Heteroscedasticity in fixed-effects one-way error components models : evaluating the performance of standard tests[END_REF] rejects the null hypothesis of the absence of heteroscedasticity at the 1% critical level. To address the problem of heteroscedasticity, this paper applies the generalized least square (GLS) method to estimate the model. The results in Table 5 suggest that industrial concentration has a significant effect on the price-cost margin, both for the CR4 and HHI measures. As expected, higher industrial concentration yields a higher price-cost margin for the firms. The CR4 coefficient of 0.824 indicates that the price-cost margin will increase by 0.824% following a 1% rise in industrial concentration. Additionally, the HHI coefficient of 0.091 shows that the price-cost margin will increase by 0.091 units for every 1-unit (1000) increase in HHI. Therefore, results show that firms in the food and beverages sector benefit from the oligopolistic market structure. This result is also supported by the data, given that every year, on average, the industry experienced about 18.1% of price-cost margin from 1995-2006 (see Table 1). The results presented here also support the findings of other studies, such as [START_REF] Shirazi | Market structure and price-cost margin in United Kingdom manufacturing industries[END_REF], Prince and Turik (1992), [START_REF] Kalirajan | On the simultaneity between market concentration and profitability : the case of a small-open developing country[END_REF], [START_REF] Go | Market structure and price-cost margin in Phillipine manufacturing industries[END_REF][START_REF] Go | Market structure and price-cost margin in Phillipine manufacturing industries[END_REF][START_REF] Delorme | Structure, conduct, and performance : a simultaneous equations approach[END_REF][START_REF] Delorme | Structure, conduct, and performance : a simultaneous equations approach[END_REF], which found a positive impact of industrial concentration on the price-cost margin.

Furthermore, based on the estimated fixed effects of both models with CR4 and HHI, it is observed that without any influences of the industrial concentration and other variables in the model (ceteris paribus), the subsectors of the food and beverages sector have a heterogeneous price-cost margin. 13 It is also found that the subsectors that are among the least concentrated have a high price-cost margin, indicating that for these subsectors, the degree of concentration is not a very good predictor of PCM. Instead, the high price-cost margin is captured in the model by the fixed-effects, 14 which is not surprising because fixed effects parameters do not take into account some unobserved heterogeneities, such as different characteristics of the industry and scale effect. 13 In the CR4 model, the lowest and the highest fixed effects parameters are -0.248 and 0.333, respectively. Almost similar to the CR4 model, in the HHI model, the lowest and the highest fixed effects parameters are -0.253 and 0.200, respectively.

14 Based on the parameters of the fixed effects of the model with CR4, some subsectors, such as 15492 (ice cubes and other ice products), 15421 (granulated sugar), 15141 (crude cooking oil), 15540 (soft drinks), and 15496 (crackers and other chips), have the highest price-cost margin in the period of estimation. However, some subsectors, such as 15329 (other starch nec), 15321 (wheat flour), 15530 (beer), 15134 (dried food, vegetables), and 15312 (other grain milling), have the lowest price-cost margin in the period of estimation. Also, based on the parameters of the fixed effects of the model with HHI, some subsectors, such as 15421 (granulated sugar), 15510 (liquors), 15540 (soft drinks), 15139 (other fruit and vegetables), and 15141 (crude cooking oil), have the highest price-cost margin in the period of estimation. However, some subsectors, such as 15329 (other starch nec), 15134 (dried food, vegetables), 15125 (processed fish), 15321 (wheat flour), and 15423 (other sugars), have the lowest price-cost margin in the period of estimation. The parameter associated with the trend suggests a positive movement of the price-cost margin during the period. The trend variable coefficient shows that the price-cost margin increases by 0.036 and 0.049 each year for the CR4 and HHI models, respectively.

To examine the effect of the competition law on the price-cost margin, the first order derivatives are calculated for the CR4 and HHI models. We obtain:15 The averages for CR4 and HHI are 0.633 and 2,266, respectively, and the average trend is 5.5.

The net effects of the law on PCM are calculated as -0.014 and -0.075 for the CR4 and HHI models, respectively. The results regarding the Law variable suggest that the Competition law has affected price-cost margin in various ways. First, the parameters associated with the interaction term of Law and the concentration ratios (CR4 and HHI) show that the policy has had a more negative effect on the price cost margins of subsectors that were characterized by higher concentration ratios, which implies that the policy has been targeted more toward sectors with a high price cost margin. Second, the parameters of the interaction terms of Law and trend (-0.031 and -0.049) (almost) offset the positive single trend term, which suggests that the policy was successful in stopping the upward trend in price cost margins before 1999.

Regarding the results on the relationship between the law establishment and the price-cost margin, a number of comments are in order. First, the competition policy may not have been applied effectively to reduce market power. [START_REF] Mccloughan | The effectiveness of competition policy and the price-cost margin: evidence from panel data[END_REF] argues that only an effective competition policy would decrease the price-cost margin. Additionally, [START_REF] Pangestu | The evaluation of competition policy in Indonesia[END_REF] found ambiguities that are still subject to interpretation in the Indonesian competition law, which may make the investigation and the law enforcement on anti-competitive behavior ineffective. Second, the political stability and improved economic environment in 2004-2006 may have resulted in higher profits, thereby confounding the effects of the competition law.

Better stability and economic environment during 2004-2006 may come as a result of successful parliamentary and presidential elections in 2004. Indeed, the data in Table 2 show that the price- firms to innovate and produce differentiated products that may sustain higher prices (Looi Kee and Hoekman, 2003), which may result in higher price cost margins. Indeed, since 1999, the variety of products has been significantly increasing in Indonesia. Fourth, the increase of the industrial concentration for subsectors with low industrial concentration in the initial year may cause the increase of the price-cost margin, on average (as predicted by the model of absolute convergence in Equation ( 4)). This finding is in line with the finding that the competition law affected the subsectors with high industrial concentration ratios more seriously. Finally, although there are some factors that may cause the elevation of the price-cost margin, this result may give a further recommendation for an improvement in the competition law in the industry.

VI. Conclusions

This paper has investigated the trend and convergence of industrial concentration in the Indonesian food and beverages sector. Moreover, it has analyzed the relationship between the industrial concentration and the price-cost margin. This paper contributes to the literature by applying the concept of convergence to the analysis of the trend in industrial concentration. Furthermore, this paper contributes an analysis of the relationship between market structure and industrial performance in the food and beverages sector in Indonesia.

The results show that the industrial concentration of the subsectors in the food and beverages sector tend to be slightly lower in the long run, but the subsectors of the industry still have a high industrial concentration (tight oligopoly structure) in the period covered by the data. In addition, results show that the industrial concentration converges to the same value for all subsectors.

Finally, as expected, the industrial concentration is found to have a positive effect on the pricecost margin.

The competition law has been relatively more successful in reducing the price-cost margin in subsectors that are characterized by a relatively high industrial concentration. Furthermore, the law has almost stopped the upward trend in price-cost margins that existed before the implementation of the law. Nevertheless, the price-cost margin is still higher after the competition law establishment than before, which suggests that a further improvement of the competition law is warranted. The results of this paper demonstrate that higher concentration in a subsector leads to a higher price-cost margin. One way to lower anti-competitive behavior is to eliminate barriers to entry, which effectively lowers concentration. However, the results presented here suggest that the effect of the competition law on the price-cost margin is through the concentration. More precisely, the competition law lowers the effect of concentration on the price-cost margin by breaking cartels.

  2006, and employment in the industry grew significantly (about 19%) in 2006 compared to 2005.

  Both indicators of industrial concentration are based on the market share of the firms and calculated by the following formulas: 2

  as a substantive criticism of their (1988) paper, and the issue remains open. calculated by sales minus intermediate inputs except labor cost.

  100.47% from1995-1999, which coincided with hyperinflation in 1997-1998 (firms sold the old stock at a new price) and the increase in the industrial concentration. The increase in the average industrial concentration from 1995-1999 may also have been caused by firms exiting the industry, especially from 1997-1999 because of the economic crisis. From 1998-1999 there was a 12% reduction in the number of firms in the industry. The reduction in the growth of the pricecost margin occurred simultaneously with the decline of the growth of the concentration from2000-2006.

  steadily from 2004 until 2006. Third, the law establishment may induce

Table 1 . Descriptive statistics of the variables from 1995-2006 Variable Mean Standard Deviation Coefficient of Variation

 1

	Minimum	Maximum

  margin in the whole period as well as the competition law effect on the trend of the price cost margin. The final model of the industrial performance-concentration model 11 is:PCM jt = γ i + θ 1 MS jt + θ 2 Law t +θ 3 Law t *MS jt + θ 4 Trend t + θ 5 Trend t *Law t + v it (5)

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Table 2 . Industrial characteristics 1995-2006

 2

	Year	CR4	HHI	Number of Firms	Average PCM
	1995-1997	0.645	2572	5495	0.069
	1998-2000	0.713	3142	4850	0.225
	2001-2003	0.650	2381	5299	0.197
	2004-2006	0.626	2345	6308	0.235
	Average % Change	-0.693	-0.796	5.133	38.593
	1995-2006
	Average % Change	3.442	8.019	-5.982	100.470
	1995-1999
	Average % Change	-3.056	-5.833	11.485	3.234
	2000-2006

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  convergence in the industrial concentration in the long run. Therefore, in the long run, industrial concentration tends to converge to one and the same value for all subsectors. It can be concluded that the subsectors with a relatively low industrial concentration in 1995 grew relatively fast after the year 1995.

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Table 3 . Absolute convergence of industrial concentration

 3

		Dependent Variable:	Dependent Variable:
	Independent Variable	Ln	CR4	T 2006 -j	Ln	CR4	j 1995	Ln	HHI	T 2006 -j	Ln	HHI	j 1995
			Coefficients			Coefficients
	Intercept		-0.025***			0.270***
				(0.008)					(0.073)
	LnCR4 j,1995 (-β 1 )		-0.029***
				(0.007)
	LnHHI j,1995 (-β 1 )								-0.039***
										(0.010)
	R 2			0.231					0.222
	F-statistics		15.606***			14.806***

Table 4 . Average % change of industrial concentration (CR4)

 4

	The Five Largest	Average %	The Five Lowest Industrial	Average %
	Industrial	Change	Concentrations	Change
	Concentrations
	15212 (Milk Food)	-1.015	15492 (Ice Cubes, other ices)	6.73
	15530 (Beer)	0.055	15311 (Rice Milling)	19.41
	15321 (Wheat Flour)	-1.827	15141 (Crude Cooking Oil)	17.64
	15131 (Canned Fruit, Vegetables)	1.043	15496 (Crackers and Other Chips)	17.08
	15329 (Other Starch Nec)	1.401	15323 (Tapioca)	1.17

Table 4

 4 also supports this finding. It shows that the five most concentrated industries

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	P
	e e r
	R e v i e w

Table 5 . Regression of industrial concentration and other variables on the price-cost margin

 5

	Independent	Dependent Variable : AVERAGE PCM
	Variable	Coefficients	Coefficients
	Intercept	-0.499***	-0.189***
		(0.110)	(0.043)
	CR4	0.824***
		(0.196)
	HHI		0.091***
			(0.025)
	Law	0.373***	0.339***
		(0.043)	(0.033)
	Law*CR4	-0.342***
		(0.088)
	Law*HHI		-0.064
			(0.019)
	Trend	0.036***	0.049***
		(0.012)	(0.011)
	Trend*Law	-0.031**	-0.049***
		(0.013)	(0.011)
	R 2	0.273	0.338
	F-statistics	9.690***	10.651***
	Notes: * denotes test statistic significance at the 10% level
	** denotes test statistic significance at the 10% level
	*** denotes test statistic significance at the 10% level
	Standard error in the parentheses

Page 14 of 20 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Actual codes used are not the ISIC codes, but comparable, coming from Klasifikasi Baku Lapangan Usaha Indonesia (KBLI)

Although the data on demand growth and capital output ratio are too heterogeneous, this may not undermine the accuracy of the estimation given that these two variables appear only as instruments in the model.

The lowest demand growth is found on subsector 15316 (Nuts), which droppedabout -94.21% in 2002 compared to 2001. According to the data survey, this may be caused by firms exiting the market, as well as the decrease in the demand for this product in 2002. The highest demand growth was experienced by subsector 15134 (Dried Fruit and Vegetables), which increased about 696% in 1998 compared to 1997. The significant increase of the demand growth in 1998 is caused by the considerable increase of sales in 1998, after the sales drop caused by the crisis, starting in mid-1997. The high variation of the capital output ratio seems obvious because of the different capital used in each subsector. The subsector with the highest capital output ratio is 15143 (coconut oil), with a value of 3.937, whereas the subsector with the lowest capital output ratio is 15510 (liquors), with capital a output ratio of 5.27*10 -6 .

We slightly abuse notation here. Although we use the partial derivative sign, we evaluate the effect of the competition law as the dummy variable changes from zero to one.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript


Miguel Gómez-Antonio

Bernard Fingleton

Sir William Duncan

Quantitative Methods, R11 -Regional Economic Activity: Growth, Development, and Changes < R1 -General Regional Economics < R -Urban, Rural, and Regional Economics, R12 -Size and Spatial Distributions of Regional Economic Activity < R1 -General

Keywords: C23, R11, R12 Public capital, urban economics, spatial econometrics

Regional productivity variation and the impact of public capital stock: an analysis with spatial interaction, with reference to Spain

Miguel Gomez-Antonio, Bernard Fingleton

INTRODUCTION

One way that the World's current economic malaise can be addressed is by an enhanced level of investment by Governments that is focussed on the public infrastructure. Of course, the impact of such a policy needs to be evaluated in order to see whether it is cost effective. This paper contributes the literature on policy impact evaluation by examining the extent to which public infrastructure investment can potentially enhance productivity, using the recent history of investment in the Spanish regions as a guide to likely impacts elsewhere. There is no single approach to evaluating the impact of public infrastructure on productivity growth, and four main approaches have appeared in the literature, namely the cost function or dual approach, autoregressive vectors (VAR) models, frontier analysis and the production function approach. As will become evident, our approach comes closest to a production function approach, but is sufficiently different to be considered to be a fifth approach to the problem.

Under the dual approach most of the analyses show that public investment reduces entrepreneur costs 1 . However, evidence using VAR models is more ambiguous. For instance the papers by Flores de Frutos (1998) and Batina (1999) show a positive effect, whereas Otto and Voss (1996) and Voss (2002) find a negative impact. Application of frontier analysis to the Spanish case suggests a positive effect 2 . But the most frequently applied approach is based on the neoclassical production functions, commencing with Ratner's (1983) analysis of the relation between infrastructure and private productivity in the US economy. Ratner introduced public capital stock as an input in the aggregate production function, and found that it had a small but significant effect on the level of production. Subsequently Aschauer (1989a) also found a similar (albeit larger) effect, and by breaking public capital stock down into its constituent parts, he was able to show that the components with the biggest impact on productivity were transport infrastructure, energy and water supply. Subsequently, Aschauer (1989b) estimated a panel data model for seven industrialized countries, obtaining similar results under a first differences specification. However Evans and Karras (1994), again using panel data for seven countries, found that the effect of infrastructure on economic growth differed according to the set-up of their model. From a regional perspective, much of the analysis has been carried out for the American states and for the Spanish regions3 . In the case of the US, Munell (1990a) estimated an amplified production function, with panel data for the American states. When the model was specified with the variables in levels and without fixed effects, the impact of public capital on productivity was positive and significant, but smaller than the Aschauer (1989a) estimate.

Building on this, Munell (1990b) broke down public capital stock into its different types, showing that the biggest impacts were attributable to road and water supply infrastructures. In contrast, García-Milá et al (1996), who data for the 48 American states, found no relation between public capital stock and productivity given the presence of region fixed effects. Likewise Holtz-Eakin (1994) concluded that, once fixed regional effects are introduced, public capital stock is not significant.

With regard to the Spanish regions, most papers suggest a positive effect, for example, Marquez et al (2009), De la Fuente (2008), Cantos et al (2005), Ezcurra et al (2005), Moreno et al (2002), Boscá et al (2002), Mas et al (1996), Bajo-Rubio and Sosvilla-Rivero (1993), Flores de Frutos et al (1998) and Gómez-Antonio and Fingleton (2010). However some papers, such as Gorostiaga (1999) and Gonzalez-Páramo and Martinez (2003) do not find a significant effect of public capital stock on economic growth. One of the reasons suggested in the literature for the inconclusiveness of the results is that many analyses do not take into account the existence of spillover effects.

Negative as well as positive inter-regional spatial spillovers may occur, for instance Mas et al (1996), using the production function approach, and Avilés et al (2003), based on duality theory, find positive spillovers. Pereira and Roca-Sagales (2003), applying a vector autoregressive model, show similar results. Moreno and López-Bazo ( 2007) interestingly obtain a negative spillover effect due to transport infrastructure that counterbalances its positive effect on manufacturing productivity within each region. The existence of negative spillovers suggests that a region's public capital raises its comparative advantage, thereby attracting production factors from other regions. Holtz-Eakin and Schwartz (1995) provide no evidence of spatial infrastructure spillovers in the US context. However, Owyong and Thangavelu (2001) find that US public capital positively affects Canadian productivity. Cohen and Morrison (2004) and Bronzini and Piselli (2009), also find significant positive spatial spillovers for the US, and Italy, respectively. However, Boarnet (1998) using data for California's counties, finds that the output of counties is negatively affected by neighbouring counties' infrastructure, likewise Sloboda and Yao (2008) for the US, and Pereira and Andraz (2006) for Portuguese regions.

To summarise the above, the literature on the effects of public infrastructure is inconclusive, although there is a general consensus on the need for a certain level of public infrastructural provision, the results obtained differ substantially once this level is achieved. More recent studies have partially discredited the results obtained in early research. Many researchers agree that the apparently positive impact of public capital stock might be due to inadequate model specifications which cause spurious relations or fail to appropriately control for region or country heterogeneity.

The period analysed in this paper is the decade from 1996 to 2005. We avoid analysing earlier data because of the substantial transformation of the Spanish economy over the longer period, which makes model specification particularly difficult. For instance, in a fixed effects panel, the fixed effects may not capture some variables that vary over time given a longer time period, leading to omitted variable bias. We thus restrict our period of analysis to a As mentioned above, our approach differs from the four approaches that can be found in the literature, and can be seen as a fifth approach that extends the public capital literature by basing the evaluation of public infrastructure on a different theoretical paradigm to that which dominates the literature, namely neoclassical constant returns to scale technology. Our model is rooted in contemporary Urban Economics theory, which provides formal general equilibrium solutions with each agent solving a clearly defined economic problem within the context of a monopolistic competition market structure. One of the most distinctive aspects of this theory is the possibility of increasing returns to scale. By incorporating imperfect competition, increasing returns and externalities in the form of market interdependence, there is an added realism in these models, without compromising rigour and the logic of a closed general equilibrium approach. To our knowledge this theory has not previously underpinned attempts to test the impact of public capital.

In addition to the direct effect on productivity of the mechanisms embodied in our urban economics theory, we also allow for the direct withinprovince effects of variations in worker efficiency, and also for spillovers in efficiency levels across provinces, with efficiency depending on the level of public capital and also the level of human capital. Spillover effects operating across provinces are technological externalities that could also play a key role in regional economic performance, since changes in one region may affect over regions, cascading across the whole country and rebounding back to the F o r P e e r R e v i e w initial province. These impacts might be positive or negative. For example, changes in one region could affect production in other regions by raising the comparative advantage of that region compared with others, and could therefore attract production factors from other locations where output or productivity might as a consequence diminish. On the other hand there are reasons to believe that capital investment in neighbouring provinces might have a positive impact on productivity within a given province as it might enhance connections such as roads, railways or airports.

Although our approach differs somewhat from that of the previous literature, nevertheless our main conclusions are in line with what has been found previously for the Spanish economy. We find that, controlling for interprovince heterogeneity, human capital and spillover between provinces, public capital, in our case working via labour efficiency, has a significant positive direct impact on the level of GDP per worker. The presence of the spillover effect enables us to avoid model misspecification which would otherwise occur if we chose to ignore spatial interaction, and therefore we are able to obtain unbiased estimates and also take into account the total impact effect. Within the positive spillover of labour efficiency, there may be a negative spillover effect of public capital, as has been detected in some other papers, but our model set-up does not allow us to identify this specifically and it is not a focus for our investigation in this paper. The positive spillover effect we identify is the net effect of the spillover of public and human capital spillover and of other unmodelled factors captured by model disturbances.

The paper is divided into the following sections. Section 2 specify the theoretical background of the model and derive the specific reduced form that 9 is going to be estimated. Section 3 details the data set and the data sources utilised for the estimation procedure. Section 4 comments on the main results obtained in the estimation and section 5 concludes.

THE MODEL: THEORETICAL BACKGROUND

At the core of this model is the concept of increasing returns to scale, which has become popular in recent years within both urban and geographical economics (Rivera-Batiz, 1988;Abdel-Rahman and Fujita, 1990;Quigley, 1998;Fujita et al 1999). All of this literature allows increasing returns in the region or city while at the same time the decision problem for each actor is explicitly stated as one of profit or utility maximization. Due to the increase in diversity or variety in producer inputs, increasing density of economic activity can yield external scale economies, even though firms are just earning normal profits. The monopolistic competition model developed by Dixit-Stiglitz allows an equilibrium solution in the context of competitive producers but with increasing returns to the economy as a whole. The approach adopted differs from pro-competitive effects leading to agglomeration. Porter (1990Porter ( , 1998) ) suggests that competition causes firms to be better innovators or faster adopters of others' innovations than they otherwise would be, which enhances the growth rate. To ensure full access to competitors' spillovers, an optimal strategy is for firms in the same sector to cluster together. A similar competitive stimulus is provided by Jacobs (1969) externalities, but based on spillovers between sectors. The model in this paper, following Rivera-Batiz (1988) and Abdel-Rahman andFujita (1990), andCiccone andHall (1996), considers two sectors, industry (including manufacturing and traded services) and producer services and follows the arguments of some of the urban economics literature.

The non-traded producer service sector (hereafter 'services') comprises local services that are not traded in national or international markets and are identified as the array of input requirements that industry demands, such as repair and maintenance of all kinds, transportation and communication services, advertising, engineering and legal support, etc. We assume a monopolistic competition market structure for services4 , which is a direct result of the fact that the market for services are generally highly competitive, and face relatively minor barriers to entry and exit, while at the same time consumers and producers have highly specialized demands making each service sector firm differentiated with respect to the others. So firms in the service sector are assumed to be typically numerous, small, independent and heterogeneous. Industry on the other hand is assumed to have a competitive In order to get to an empirically tractable reduced form we follow closely the presentation of the model given in Fingleton (2001Fingleton ( , 2003Fingleton ( , 2004)).

First we derive the reduced form linking output (Q) to the intensity of activity in a unit area given by the total labour force (N) and land (L). Capital, in the form of public capital or human capital comes through via its impact on labour efficiency. By substituting the level of composite services I into the Cobb-Douglas production function we obtain the industry production technology. In this the level of industry output (Q) is a function of the input of industry labour M, I and L. Note that industry is competitive, with constant returns to scale.

1 1 ( ) Q M I L β β α α - - = (1)
For simplicity the level of composite services is determined by the CES production function. This is what determines the level of composite services I.

It is not simply the sum of each firm's output; it is more, depending on the number of separate varieties. The assumption is that there is a 'love of variety', which means that the varieties produced by differentiated firms results in a higher level of composite services than would otherwise be the case from firms with identical, perfectly substitutable, products.

I i d d d D =         = ∫ ( ) 1 1 µ µ ∂ (2)
In ( 2) i(d) is the "typical" output of a service variety, and there are D varieties.

The level of monopoly power in the service sector is given by the exogenous 12 parameter µ5 . The higher µ is the less one service substitutes for others and the more monopoly power the producer of that service has. As µ increases, we see rising monopoly power and falling elasticity of substitution. More monopoly power enhances the level of composite services providing an input to industry output. As µ falls back towards 1, the level of composite services approaches the number of firms times the equilibrium level of output per firm.

Since we assume a very large number of varieties we approximate the continuous integral by the discrete summation. At equilibrium i(d) is a constant across all varieties and therefore we can reduce the summation to a product as follows:

I i d Di d D i d d D =         =         = = ∑ ( ) ( ) ( ) 1 1 1 µ µ µ µ µ (3)
Broadly speaking, services are relatively labour intensive. We thus assume, for simplicity that each firm producing composite service uses only labour as an input whose requirements are given by

( ) i L ai d s = + % (4)
In ( 4), s represent the fixed labour input requirement and a the marginal input requirement. Following the Chamberlinian framework, the technology used by all firms is considered identical, implying that a and s are the same for all the composite service sector firms. Given the simplified form in equation ( 3), we substitute for I and use the equilibrium values for the number of varieties D and M to obtain the relationship between Q, N and L. We will write the equation in terms of production per unit area, so we restrict L = 1, eliminating land as an input since

1 1 1 α - =
: By doing this we are implicitly including the effect of congestion in the equation, since by eliminating land production will be less than it would otherwise be.

1 ( ) Q M I β β α - = I D i d = µ ( ) ( ) 1 ( ) Q M D i d α β β µ -   =    
If we assume that the economy is at a competitive equilibrium and workers are paid the value of their marginal product, at equilibrium the wage rate (w) equal to the marginal product of M labour is given by

dQ Q w dM M αβ = = (5)
If we assume also that the share of Q going to all labour (N, equal to industry plus services) is given byα , from standard Cobb-Douglas theory, we have wages (considered to be the same as for industry) times number of workers as

a share of Q is wN Q α = (6)
The assumption here is that the inputs are (all types of) labour (coefficient α ), capital and land and the marginal product of each input (wages, returns on capital and land rents) are given by the respective derivatives, and the shares are the marginal products times the amounts (of labour, capital, land) as a proportion of total output Q. The marginal product of all types of labour is

Q w N α = (7)
From this it follows that

wM Q wN Q M N αβ α β = = (8)
Hence service workers (N-M) as a share of total workers is1 β -.

At equilibrium all firms are the same size so the number of firms D is the total services workforce, (1 )N β -, divided by the workers per service firm.

( )

D N ai d s = - + 1 β ( ) (9)
So utilising equilibrium values we have:

( ) ( ) ( ) ( ) 1 (1 ) (1 ) (1 ) (1 ) 1 ( ) ( ) ( ) ( ) 1 N Q N i d ai d s Q N i d ai d s N α β µ β µα β µα β β µα β βα α β γ β β β β - - - - + - -     -       =     +         = + - = Φ (10)
Where: Increasing returns to scale are implied by 1 γ > , so from equation ( 11) it is apparent that this will occur if β < 1 and µ > 1 provided α is not too small. This means that assuming that the loss of production as a result of restricting land is not too severe, then we also need differentiated intermediate goods to be relevant to the output of the competitive sector (β < 1) and for them to be imperfect substitutes for each other (µ > 1) with a degree of monopoly power.

( ) ( ) (1 ) (1 ) (1 ) (1 ) [1 (1 )( 1)] ( ) ( ) 1 i d ai d s µα β µα β βα α β γ βα µα β α β µ β β - - - - = + -= + - - Φ = + - (11)
With a higher enough µ and a low enough β, the production function could have increasing returns, where the favourable effect of density outweighs the congestion effects.

In order to move closer to a convenient reduced form, we log-linearize equation ( 7) by taking natural logarithms, hence

ln ln ln ln w Q N α = + - (12)
And substituting for Q gives

ln ln ln ln ln w N N γ α = + Φ + - 1 ln ( 1) ln w k N γ = + - (13)
Assuming the number of labour efficiency units (N) is equal to the total employment (E) times the level of efficiency (A), we have

1 ln ( 1) ln ( 1) ln w k E A γ γ = + - + - (14)
The Level of Efficiency

In line with Fingleton (2003b) we assume that the level of efficiency depends on 'within region' effects and effects that spillover from provide the basis for a more efficient labour force. We will utilise as indicator of human capital the number of people with high degree level qualifications in the region. Public capital measures will be outlined below. The spillover effect is determined by the scalar parameter ρ and by a so-called weights matrix, W, which is a square n by n matrix for n regions with cell values denoting the strength of interregional interaction, and zeros on the main diagonal. This idea of capturing spillovers by means of a weight matrix has been widely used in the literature, since the appearance of spatial econometrics techniques, for instance under a neoclassical production function approach in Moreno and López-Bazo (2007).

Combining the factors outlined above produces the following specification:

0 1 1 1 ln ln ln ln R i i Pi ir r r A b b H b K W A ρ ε = = + + + + ∑ (15)
Rearranging, and assuming ( ) I W ρ is non-singular, we obtain the equivalent matrix expression

1 1 1 ln ( ) ( ) ( ) ( ) A I W Xb I W Xb I W ρ ε ρ ρ ε - - - = - + = - + - (16)
i i i I W W ρ ρ ∞ - = - = ∑
, with W 0 equal to the identity matrix I, W 2 equal to the matrix product of W and W, and in general W i equal to the matrix product of W i-1 and W. This means that 15), so that a high (low) efficiency level in Province i causes, and is a response to, high (low) efficiency in 'nearby' Provinces.

i i i i i A Xb WXb W W Xb W W Xb W A W Xb ε ρ ρ ε ρ ρ ε ρ ρ ε ρ ε ∞ = = + + + + + + + + = + ∑

The W Matrix

We considered several alternatives candidates as our preferred weights matrix 7 W. A first order binary geographical contiguity matrix, in which the elements are one when regions share a common border, and zero otherwise 8 , is one option considered. However, while this may prove informative in helping to detect localised cross-border spillovers, the main aim of this paper is simply to explore the existence of a direct causal effect using a more general approach to modelling spatial interaction effects, via W, that would otherwise not be present in our specification 9 . Thus we adopt a W matrix in which the value allotted to cell (i,j) is a function 10 of the road distances ij d between the 7 See Fingleton (2003a) for further discussion of alternative assumptions about W.

8 The elements of the main diagonal are set to zero by convention. 9 If the basic theoretical model was New Economic Geography rather than our urban economics specification, then that would automatically capture spatial dependencies based on the size of economies, similar to those embodied in our W matrix as defined below.

10 This way of capturing interactions weighted by distance is used very often in spatial econometrics literature. Fingleton (2003b) hypothesized that the efficiency of the labour force employed within an area will be in part determined by commuting, the frequency of which falls as distance increases. The rate at which this fall-off in commuting frequency occurs is capitals of the provinces and the GDP of the region11 . Since we subsequently standardise the W matrix so that the total in each row sums to 1, the resulting standardised matrix will be the same irrespective of whether we include both origin and destination provinces in our equation, or whether we just include the destination.

0 1; 2 j ij ij ij GDP W i j d W i j α β α β = ≠ = = = = % % % %
Thus we also take into account the (economic) size of the (remote) province in order to measure the interaction between regions. Economic size (GDP) is considered relevant because of the extensive trade and labor market that a large and diverse local economy naturally generates. 12The Reduced Form

Combining equations 14 and 16 gives embodied within the matrix W, which is determined by the varying rate of decline-withdistance of commuting in each individual area. So a scalar that reflects the commuting of people between different regions is selected to weight distances. As this information is not available for the Spanish provinces we weighted using the square to make relation more intense as the distance becomes shorter. Additionally, controlling for distance, we assume that commuting between provinces will be greater the larger the provincial economies. obtained using 2; 2 ( 1)ln ( 1)( ) ( )

α β = = % % and 1; 3 α β = = % % .
( )ln ( ) ( )( 1)ln ( 1)( ) w k E I W Xb I W w I W k I W E Xb γ γ ρ ε ρ ρ ρ γ γ ε - = + - + - - + - = - + - - + - + (17)
On rearranging, making the exogenous variables explicit, and introducing a time subscript, we then have

1 0 1 1 2 1 2 2 ln ln ( ) ( 1)(ln ln ) ln ln ~ (0, ( 1) ) t t t t t t w W w I W k E W E c c H c K N ρ ρ γ ρ ψ ψ γ - - = + - + - - + + + + -Ω (18)
Consistent estimation of the model is not possible via OLS because of the presence of the endogenous variable ln W w on the right hand side of equation 18. Moreover we also may have two-way causation involving employment density and our dependent variable, with employment density increasing (due to migration and enhanced participation rates) as wage rates increase. Consequently the composite variable (ln ln ) E W E ρ is likely to be endogenous also. Note that this composite variable entails a parameter restriction because of the presence of ρ . In order to guard against any potential inconsistency, our model is estimated using instrumental variables 13 .

We assume that human capital and public capital stocks are exogenous, in the case of human capital (H) this is because we assume complex determinants of educational attainment levels, so that any direct feedback from wage levels will be relatively weak. We note that in Spain inter-province migration in response to wage differentials is not strong. In the case of Public capital stock (K), the assumption is that this is mainly controlled by government policy and 13 Specifically we use the xtivreg available in Stata for estimating panel data models with endogenous variables. this is not driven by wage levels. However we also decide to lag these variables by one year, guaranteeing exogeneity, since they pre-date the year of analysis.

These assumptions are supported by model diagnostics, as explained subsequently. Over-identification is achieved by additional instrumental variables, namely the spatial lags of our exogenous variables together with three other measures of public capital, namely social, local and transport infrastructure, each again lagged by one year. We subsequently test for the legitimate exclusion and validity of these instruments.

The restriction in equation ( 18) relating to ρ is caused by the spillover of labour efficiency levels between provinces. To take into account this constraint we use iterated 2SLS, in which each iteration provides an updated value for ρ from the ln W w term which is then used to update

(ln ln ) E W E ρ -
for the subsequent iteration, until ρ reaches a steady state as in Fingleton (2003b). At the first iteration, with no initial estimate for ρ, we assume an arbitrary value for ρ = 0. In order to avoid an explosive model, the estimated value of ρ should be in the interval Confederadas (FUNCAS) 18 as documented in their "Balance Económico

Regional".

The employment density variable (E) is constructed by dividing the total employment, taken from "La Renta Nacional de España y su Distribución Provincial", by the provincial area in square kilometres. Data on the geographic area of each province and on population were provided by the

Office of National Statistics (INE).

Our human capital variable (H) is the proportion of people in each province with higher education, data published in "Human Capital in Spain and its distribution by provinces " by Instituto Valenciano de Investigaciones Económicas (IVIE).

17 Eurostat reported for the period 1995-2005 an average rate of growth of public investment in Spain of 3.37% while in the euro area it was of 2.5%. This higher rate has been sustained throughout the decade even though public expenditure has reduced as a proportion of GDP. At the same time provincial differences have also been reduced during the period thanks to the Structural and Cohesion funds. Most of the Spanish regions were Objective 1 regions and received European funds to finance infrastructure projects. 18 In order to make the Gross Value Added and employment series homogeneous we took the rates of growth of the variable in FUNCAS database and applied it to the variable produced by FBBVA. Previously we had to transform the valued added into constant euros of 1995 using the Implicit Index Prices facilitated by both organisations.

ECONOMETRIC RESULTS

The results in Table 1 show the estimates 20 of the panel model with fixed province effects, estimated with endogenous variables ln W w 19 To satisfy the diagnostic tests described below, the matrix product ln W K has been dichotomised, being equal to 1 for values exceeding the median value, and 0 otherwise. 20 After having eliminated the spatial lag of log total capital as an instrument, as is necessary in order to pass the test of over-identifying restrictions. While our instruments appear to be valid, they could still be weak and therefore lead to biased estimates and inference. However we find that our instruments are strong. Our test statistic is the Cragg-Donald Wald F statistic which is referred to the critical values given by Stock and Yogo (2005). The critical values are determined by the number of instruments and by the number of included endogenous variables, and also by the maximum amount of bias that is acceptable, where bias is relative to bias under OLS. The value of 13.889 lies between the 10% and 5% maximal instrumental variables relative bias critical values of 8.78 and 13.97, being close to the 5% value. We conclude that the maximum bias in our estimator is less than 10% of the bias that would be incurred by OLS estimation. The second element of our test of weak instruments relates to the size of the test. If the true size of the conventional Wald test, with nominal size of 5%, exceeds this by a certain amount, in our case by a maximum of 10%, so that the true size is up to 15%, then we would also conclude that we had weak instruments. The test statistic lies between the critical values for 15% and 10% maximal size (nominal size plus size distortion), equal to 11.22 and 19.45 respectively. With size distortion of no more than 10%, and our earlier evidence of small relative bias, we conclude that our instruments are not weak.

F

To summarize, our main result given in Table 1 is that public capital has a significant positive effect on productivity, with an elasticity equal to approximately 0.14, having controlled for employment density, human capital, labour efficiency spillovers, and for the significant effects of province heterogeneity captured by the fixed effects. There are several channels through which public investment is usually considered to affect regional per capita income. Macroeconomists typically emphasize three "conventional" channels. Public investment is considered to have a direct productivity effect on private production inputs and to have a complementarily effect on private investment. In the short term, however, it is hypothesised that public investment might crowd out private spending, and adversely affect growth if it persists. In this paper we hypothesise that the effect of public capital operates through its effect on worker efficiency, in the same way as human capital. However we acknowledge that the effects of public infrastructure may work through diverse channels and may be indirect, sector-specific and time-specific. For instance while Holtz-Eakin and Lovely (1996) find that infrastructure has no significant direct effects, they do find evidence that public capital may alter productivity through its effect on the number and variety of manufacturing establishments in the local manufacturing base. Likewise Moreno and López-Bazo (2007) demonstrate that public capital has a greater effect on Spain's industrial productivity than on any other economic sector, particularly during the period when Spain experienced rapid economic growth, and increased openness to trade and greater economic liberalization. Also, as we have indicated above, Moreno and López-Bazo ( 2007) and others suggest a more complex relationship between public capital and productivity which involves a negative spillover effect.

Effects of public capital stock

However we are unable to identify this in our model set-up which simply captures the net effect of public and human capital and unmodelled spillovers as part of the labour efficiency spillover. In this paper we focus on the direct effect of public capital, which we find is significant and positive. This leads to one additional consideration, the evaluation of true total effects in models involving spatial processes, as highlighted by LeSage and Pace (2009). Assuming that our parameter estimates apply equally to a single cross-section, when we take account of the spillover effects on account of the presence of the spatial lag ln W w with 0 ρ ≠ in the model, then the derivative 1 ln ln

t t w K - ∂ ∂ 2 0.1386 c ≠ =
as implied by Table 1. It can be shown that the total effect is given by

1 2 1 ln ( ) ln t t w I W Ic K ρ - - ∂ = - ∂
, and since this is a matrix, it is recommended that we consider the mean total effect given by 1

1 1 2 1 ln '( ) ln it ij jt w N N I W Ic K ι ρ ι - - - - ∂ = - ∂ ∑
, in which N = 47, ι is an N by 1 vector of ones, I is an N by N identity matrix and 0.1806355 ρ = as given by Table 1.

Evaluating this quantity gives an implied mean total effect equal to 0.1692, compared with 0.1386 given 0.

ρ = These results are broadly within the range of variation of the elasticities obtained in other papers. Mas et al (1994Mas et al ( , 1996) ) obtained an elasticity associated with productive public infrastructures of 0.23 and 0.08, respectively. However in other papers the reported elasticity is lower, as in Goerlich and Mas (2001) which reported an elasticity of 0.02 or Boscá et al (1999) who obtained an output elasticity of 0.026 for public infrastructures (0.035 in the long run).

CONCLUSIONS

In this paper we have examined the effect of public capital on the variation in wage (productivity) levels across the Spanish Provinces, over the form, so that there does appear to be increasing returns to scale. There are also significant positive effects due to educational attainment which support the thesis that labour efficiency is highly relevant to wage variations across Provinces. The model estimates also indicate that there is a significant relationship between wage levels and 'nearby' wage levels, supporting the hypothesis of positive spatial spillovers and the necessity for a spatial econometric approach.

Although the theoretical provenance of our paper is somewhat different, Ashauer`s hypothesis has not been rejected for the Spanish economy during the period analyzed. However we remain cautious in our conclusion that public capital is relevant, for we are conscious that the estimates may be affected by a more complex relationship between public capital and productivity, involving both positive and negative impacts of public capital stock, which are concealed when we simply observe is the net effect of the spillover of labour efficiency, which embodies the effect of public capital.

Further work is needed to detangle the spillover effects of the variables affecting the labour efficiency level, either based on new data or new methodology, or both. Therefore in terms of policy involvement at a national -Abdel-Rahman, H., Fujita, M., (1990), Product variety, Marshallian externalities, and city size, Journal of Regional Science, 30, 165-183.

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-Salinas-Jiménez, M. M., (2004)

  the period 1970-1983, a Cobb-Douglas production function with

  the results obtained in countries other than Spain,

  span during which we have greater confidence that our model will be appropriate.

  and demands a wide array of different types of services performing highly specialized tasks.

  In which X is the n by k matrix of right hand side variables (the constant, lnH and ln K ) and ε is an independent and identically distributed disturbance term representing measurement error and exogenous shocks to the level of efficiency, hence, contribution to area i´s efficiency level is given by row i of vector Wln(A) which contains the sum of the weighted efficiency levels of other provinces. Note that by making ln(A) depend on Wln(A) and not simply on the constant, ln H and ln K , we capture the totality of the effects influencing the efficiency level, including those represented by the random shocks. Assuming that 1 ρ < , given our preferred (standardised) W matrix (see below) it then follows that

  ( K ) was taken from the publication "Series Históricas de Capital Publico en España y su distribución territorial 1900-2005" which detailed work done by FBBVA in collaboration with IVIE. Our excluded instruments comprise three separate elements of public capital stock, namely the transportation infrastructure, the social infrastructure stock and the local public capital stock. Transportation includes airports, ports, road and railways infrastructures, the social infrastructure includes public capital stock in education and health facilities and local public capital stock comprises local government infrastructures of various kinds, infrastructure relating to water supply and management, plus other residual investments. Our assumption is that these have an indirect effect working via urbanisation, overall public capital and human capital, but they have no direct individual effect on wage levels. We test this exclusion assumption below. Our additional instruments are obtained by the matrix product of matrix W and the vectors of log public 19 and log human capital. As with the exogenous variables, all instruments are lagged by one year.

  2005. The analysis is underpinned by contemporary urban economics theory and the methodology of spatial econometrics, which leads to a reduced form in which wage levels depend on 'nearby' wage levels, employment density, educational attainment and public capital. Endogeneity and constraints on parameter values lead to an iterative 2SLS panel estimation routine. The model supports the theory motivating the reduced

  the absence of more detailed information on how the spillover effects of public investment balance out, we still have to be prudent about the global effects on economic activity. In the presence of negative spillovers, provinces might be competing with each other attempting to obtain more infrastructures than would otherwise be provided. By altering infrastructure investment relative to that of neighbouring regions, each region has the ability to modify the size of its infrastructure stock at the expense of its neighbour. If some regions follow a "beggar-thy-neighbour" policy, all regions will be dragged into fiscal competition. This can lead to gaming behaviour among regions in a national economy. If local and national governments ignore the possible existence of negative spillovers and overestimate the positive effects of public policies, this can lead to inefficiency.The comparisons of the return to different types of infrastructure are on our research agenda for the future.

-

  Boarnet, M.G., (1998), Spillovers and the locational effects of public infrastructures, Journal of RegionalScience, 38,[381][382][383][384][385][386][387][388][389][390][391][392][393][394][395][396][397][398][399][400]

-

  Munell, A.H., (1990b), Why has Productivity Growth declined? Productivity and Public investment, New England Economic Review (Federal Reserve Bank of Boston), January, 3-22. -Office of National Statistics (INE) http://www.ine.es -Otto, G.D., Voss, G. M., (1996), Public capital and private sector productivity, The Economic Record, 70, 209,121-132.-Owyong, D. T., Thangavelu, S.M., (2001), An empirical study on public capital spillovers from the USA to Canada, Applied Economics, 33, 1493-99.-Pedraja, F., Salinas M. M., Salinas J.,(2002), Efectos del capital público y del capital humano sobre la productividad de las regiones españolas, Papeles de EconomíaEspañola, 93, 135-147. Pereira, A. M., Andraz, J. M., (2006), Public investment in transportation infrastructures and regional asymmetries in Portugal, Annals of Regional Science, 40, 803-817.-Pereira, A. M.,Roca-Sagalés, O., (2003), Spillover effects of public capital formation: Evidence from the Spanish regions, Journal of UrbanEconomics, 53,

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	Submitted Manuscript
	'neighbouring' regions. Within regions, assume that what is important is the
	level of human capital (H), the level of public capital ( K ), plus an
	autonomous rate reflecting "learning by doing" which proceeds regardless of
	the other factors. Regions with relatively better-developed human capital are
	expected to make faster technical progress since human capital facilitates
	research, development and the spillover of knowledge. Likewise superior
	infrastructures (communications, urban facilities, health facilities, etc.) will
	F o r
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Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  A in Province i depends on levels of ln H and ln K and on shocks The actual mechanism causing evidently remote interactions is the direct mutual interaction between Province i and its 'neighbours' as defined by W, as indicated by the presence of

		1 R = ∑ r	ir W	ln	r A	in
	equation (
		F o r
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		e
		e r
		R
		e
		v i e
	This shows that ln i A is equal to the weighted sum of the matrix products 6 of w
	the matrices	( 0,..., )

i W i = ∞ and exogenous variables X and ε . The log level of efficiency ln i ε in regions i,j,k,l,…

TABLE 1 :

 1 HEREThe test of the overall validity of the instruments is related to the C statistic described above. In fact the test statistic, the Sargan-Hansen statistic, Also obtained by the Stata command xtoverid, seeSchaffer and Stillman (2010).

	is calculated twice in order to obtain the C statistic. The C statistic is the
	difference between the Sargan-Hansen test statistic calculated for the full set
	of instruments and the Sargan-Hansen test statistic calculated for the reduced
	set of instruments (that is excluding those that are suspected of being
	endogenous). The Sargan-Hansen test statistic for the reduced set is equal to
	0.221 (p-value equals 0.6384 in 2 1 χ ) and the Sargan-Hansen test statistic for
	the full set of instruments is equal to 2.639, which has a p-value of 0.4507 in
	the appropriate 2

3

χ reference distribution (five excluded instruments minus two endogenous variables). The latter provides our test of over-identifying restrictions

23

, with the null being a hypothesis of valid instruments, which is not rejected thus indicating that the instruments are appropriate. We would reject if instruments are correlated with the disturbances, or if excluded instruments should be included in the set of regressors, so that the model is misspecified. This provides justification for our exclusion of the instruments transportation infrastructure, the social infrastructure stock and the local public capital stock from the model specification.

23

  , Capital público y productividad de las Regiones Españolas, Moneda y Crédito, 198, 163-Maudos, J., Pastor, J. M., Serrano, L., (1998), Convergencia en las regiones españolas: cambio técnico, eficiencia y productividad, Revista Española de Economía, 15, (2), 235-264.

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	192.
	-Matmazakis, E. C., (2007), EU infrastructure investment and
	productivity in Greek manufacturing, Journal of Policy Modelling, 29,
	335-344.

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  , Public infrastructure and private productivity in the Spanish regions, Journal of Policy Modelling, 26, 47-64. -Schaffer, Mark, (2010), Xtivreg2: Stata module to perform extended IV/2SLS, GMM and AC/HAC, LIML and k-class regression for panel data models, Statistical Software Components, Boston College

	Submitted Manuscript
	F o r F o r
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Table 1 :

 1 Fixed effects panel estimates with endogenous regressors (T=10, n=47) Between fixed effects and covariates Time sub-indices have been omitted from the table and from the comments to simplify notation.

	Page
	REGRESSORS	Parameter Estimates #
						Standard error
	Productivity Spatial	0.1806355 **	0.0421943
			Lag
					(4.28)
		ln W w
	Employment Density	0.1055751 **	0.0310767
	(ln	E	-	ln ) W E ρ	(3.40)
	Public Capital	0.1386397 **	0.0190934
			lnK	(7.26)
	Human Capital	0.0180546**	0.0084188
			lnH	(2.14)
		R squared	0.5265
	Estimation Method	Instrumental variables
	Instruments	ln_Kh, ln_Ktot,
					WX_ln_Ktot, WX_ln_Kh, ln_Ktpte, ln_Ksoc,
					ln_Kloc
	Notes:

# z-ratios given in brackets beneath the estimates **,* Significant at 5% and 10% level, respectively 2

41 of 40 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

There are very few countries where regional public investment data are available, one exception are Germany and Italy, where recently Marrocu and Paci (2010) obtained a positive and significant but variable public investment effect on production.

The Dixit-Stiglitz theory of monopolistic competition provides the reason why an increase in service labour maps to an increase in service variety, rather than more of the same variety. Monopolistic competition envisages a large number of services firms producing differentiated services and firms freely entering the sector until profits go to zero. The existence of fixed costs means that firms prefer to concentrate on a single variety and reap internal economies of scale; there is no advantage in a variety's production being split between two or more firms. On the other hand if there were no fixed costs, average costs would not decrease with increasing output so no internal economies of scale would be realized. Since each firm is the producer of its own differentiated services, the ensuing monopoly power allows prices to be a mark up on marginal cost. The number of firms supplying services is an endogenous variable in the model instead of being an ad-hoc restriction. There is an equilibrium level of output and therefore equilibrium labour requirement per service firm that is a constant, and as will be stated later we have an equilibrium number of firms. These equilibrium values depend on exogenous parameters.

This is the substitution parameter of the CES production function, which determines the elasticity of substitution, the price elasticity of demand, and the internal returns to scale given by the average cost to marginal cost for producer services in equilibrium.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Note that as i becomes large, W i tends to a matrix in which each cell in a column contains the same value, columns differ, and each row of W i is identical. This means that the matrix products tend to constant vectors.

We use, somewhat arbitrarily, the GDP in 1971, but other years could have been used with very little impact on the outcome. Using a previous year ensures that the resulting W matrix comprises fixed exogenous quantities with no possibility of feedback from the level of productivity.

The estimation results were similar when we used different W matrices, the coefficient varied slightly and all the signs were as expected from theory. The alternative Ws were

This is an option (endog) available within Stata's xtivreg2 command (Schaffer, 2010), and under conditional homoscedasticity, the test statistic is equal to that provided by a Hausman test.

Option orthog in xtivreg2.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

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