1. INTRODUCTION

The initial impetus for this work entailed constructing regional indicators of competitiveness in Mexico, specifically, in 59 metropolitan zones in which, pursuant to the latest census data, around 70% of the gross domestic product (GDP) is generated, and where 57% of the population lives. Analyzing the competitiveness of cities and regions has become an in-vogue topic in the field of regional studies, giving rise to numerous indices of local or regional competitiveness, which are then used to conduct draw comparisons and make rankings. ^{Krugman (1994)} called the affair a "dangerous obsession."

Despite the wide range of available indices -^{Berger (2011)} came up with a list as of 2009 of at least 217 different competitiveness indices- it is unclear what they measure or how these measurements are bound up in a region's prosperity (^{Martin et al., 2004}).

The idea of regional competitiveness has run up against criticism, considering that regions themselves cannot compete, at least not in the same way companies do (^{Krugman, 1994}; ^{Martin et al., 2004}). Nevertheless, competitiveness is simply another way to speak of productivity, ^{Krugman (1994)} claimed; in our view, it makes sense to the extent that productivity can still be approached within the framework of economic theory, while competitiveness is a more open, one might venture multidisciplinary, concept. Accordingly, efforts ought to be channeled into measuring productivity and the sources or drivers of its growth.

This is a recurring problem, or at least it has been since ^{Solow's (1957) 2} paper was published on the appearance of new methodologies revising aggregate productivity or total factor productivity (TFP) measurements and other structural aspects of an economy, such as technological change and, more recently, changes in productive efficiency. The downside of using the Solow approach is that it fails to truly identify the sources of TFP growth. It is just an accounting breakdown (^{Barro and Sala-i-Martin, 2003}). It is unable to pinpoint whether TFP growth is coming about via technical change or improvements in efficiency.

Luckily, in the production (or cost) frontiers field, many alternative methodological possibilities have emerged to measure TFP (Table 1 summarizes a brief taxonomy). Of this wide range, only those stochastic frontier models taking into account an estimate of inefficiency were considered, to the extent that if inefficiency is not reflected, the estimated measure of productivity growth could be biased, without any notion of the precision involved (^{Grosskop, 1993}, sec. 4.3.2, p. 173).

Table 1 Summary of Methodologies 

Source: ^{Del Gatto et al. (2011)}, modified.

As such, this study is interested in why these models make it possible to construct relationships between productivity and technical efficiency, which are economic concepts frequently employed to analyze the economic performance of observed economic units (states, regions), and both are directly tied to the same production theory framework (^{Nishimizu and Page, 1982}; ^{Kumbhakar et al., 2000}; ^{Lobo et al., 2013}). With these stochastic production frontier models, it becomes possible to decompose TFP growth into its sources ("causes"): technological change, changes in technical efficiency, and change of scale. In the context of production theory, it is therefore possible to establish an analytical bridge between competiveness, productivity, and technical efficiency.

The strategy to estimate TFP requires a prior estimate of the level of efficiency and how it has changed over time, as it is one of the three components mentioned. This study makes an initial approach with this sort of methodology with a scope restricted, initially, to exploring the role played y the creative sector in driving technical efficiency in metropolitan zones.

This is an economic sector that is at present at the heart of TFP growth in several urban hubs or dynamic regions in both Mexico and across the globe. The scope of this application is also constrained by the information available. We are working with a short panel in time, and it has to restrict the specification of the basic model implemented.

As a result, this study sets out primarily to find empirical evidence for the following working hypothesis: the creative sector plays an important (significant) role in reducing productive inefficiency in metropolitan zones, as part of broader mechanisms that capture the effects of economies of agglomeration, spillover effects, or positive externalities favorable to endogenous growth in Mexico’s urban hubs. The evidence from European cities reveals that creative activities tend to have a significant impact on discrepancies in productivity, by raising the number of innovations via the creation of new products and varieties (^{Boix and Soler, 2014}).

With that in mind, this paper conducted an analysis of technical efficiency in the 59 metropolitan regions throughout the Mexican republic, quantifying their technical efficiency levels (average), ranking them hierarchically, and estimating the effect of the creative sector on driving efficiency.

This paper is composed of six sections. The second offers an overview of fundamental contributions to the topic; the third and fourth discuss the measurement methodology and introduce the empirical model underpinning the analysis; the fifth shows the descriptive statistics and interprets the results. Finally, section six presents some final considerations.

2. LITERATURE REVIEW

Traditionally, productivity in cities has been directly tied to some type of economy of agglomeration (^{Fujita et al., 1999}; ^{Fujita and Thisse, 2002}). Companies try to set up shop where there are already other companies. ^{Marshall (1981, 2006)} already noted that advantages of that location are to be had, via access to concentrations of inputs and specialized labor and the "spillover" of knowledge and innovation. ^{Melo et al. (2009)} contains a broad meta-analysis of 24 papers published on the relationship between economies of agglomeration and productivity, from which it emerges that the effects on productivity depend on characteristic effects (belonging to) the region, its industrial coverage, and, in general, the way economies of agglomeration are structured. In a context like that, what has come to be known as human capital, which includes aspects pertaining to the quality of the workforce, is undoubtedly a vehicle or part of a mechanism to transmit the (non-observable) impact of technological capture, location, and more (^{Ghosh and Mastromarco, 2013}). The idea consists of building a bridge between productivity and the performance of sectors characteristic to a regional economy, as is the case of the creative sectors.

Since the nineteen-nineties, the literature on the role of the creative economy has taken off. Analysis has focused on studying creative cities (Yenken, 1988; ^{Landry and Bianchini, 1995}; ^{Landry, 2000}), the creative industries (^{Pratt, 1997}; ^{Higgs et al., 2008}; ^{UNCTAD, 2010}; ^{DCMS, 2015}) and the creative classes (^{Florida, 2002}, ²⁰⁰⁴, and ²⁰⁰⁸). One aspect common to these different studies and outlooks is that they agree on the fact that creative activities have gained a great deal of relevance in understanding the forces that detonate growth and economic and social development in the most dynamic regions in the world.

There is as of yet no clear and precise conceptualization as to how a creative economy or creative activities should be understand, in large part as a result of the very breadth of how creativity is understood: “a process to generate something new based on the combination of already-existing elements” (Candance et al., 2015, p. 3). Originally, the idea of the creative industries was tied to culture (^{DCA, 1994}) and the first alternative measurement methodologies were developed for the United Kingdom, focusing on activities characterized by talent, skills, and individual creativity (^{DCMS, 1998} and ²⁰⁰¹).

At present, the most significant proposal for defining and recording (measuring) creative industry activities is the formula used by the United Nations in its report on the creative economy, where these industries are defined as generators of symbolic products (^{UNCTAD, 2008}). Table 2 summarizes the activities that UNCTAD considers to be an integral part of the creative activities or industries.

Table 2 Classification of Creative Industries 

Source: Based on ^{UNCTAD, 2008}.

In its most recent report, ^{UNCTAD (2015)} measures the high economic impact of the creative industries at present: around the world, the cultural and creative goods and services market as of 2012 was on the order of 547 billion dollars, with a sustained annual growth rate of 8.6% between 2002 and 2012.

Analyses of the creative industries have focused on evaluating their impact on the provision of some sort of urban amenity (^{Florida, 2004}; ^{Glaeser, 2012}), the development of new technologies, innovation, and technological change (^{Cunningham, 2008}; ^{Jaaniste, 2009}; ^{Lee and Rodriguez-Pose, 2014}), the level and type of employment (^{DCMS, 2016}), and productivity (^{Chapain et al., 2010}).

Despite the diversity of the analyses piling up about the creative industries, little headway has been made to understand their role in the unequal development of cities in terms of more efficient usage of available resources by a society. Although it has been acknowledged that the concentration of creative activities drives productivity and has a differential impact on city growth, few studies address this phenomenon in the framework of a production frontier model or seek to quantify the effect of the creative sector on the level of technical efficiency (Mandula and Auci, 2013). At the urban scale, these concepts, fundamental to public policy, implicitly contain the requirement that cities need to be efficient in using resources as a whole. One way to understand this can be the production theory framework, but with the entity of analysis being the region or city.

Accordingly, it is appropriate to delve into the exploration with a sample of 59 Mexican cities in an attempt to quantify the effect of the creative sector on driving levels of technical efficiency; it is a conventional exercise just as if it were any other economic sector (for example, manufacturing). It is therefore necessary to specify that the purpose of the study is not the same as the ^{Mundula and Auci (2013}, ²⁰¹⁶⁾ study. To analyze creative activities and in this study, the more common classification system proposed by UNCTAD was used, adapted to the North American Industrial Classification System (NAICS). The sectors considered are listed in Table A1 (see Statistical Annex).

3. METHODOLOGY

Although the neoclassical paradigm in production theory supposes that the producers in an economy always operate efficiently (maximum possible product), in reality, they are inefficient. As similar as two companies may be, they never produce the same product, and their costs and benefits are never equal. These discrepancies can be explained in terms of efficiency and several unpredictable exogenous shocks. This is the basic idea that can be conceptually extrapolated for this case to explain differences across Mexican cities in terms of efficiency levels determined by the presence of sectors with creative activities.

Although a wide range of parametric and econometric methods have been developed to measure (in)efficiency, this paper employs the stochastic production frontier model with panel data, the technique originally developed for cross-sectional data by ^{Aigner, Lovell, and Schmidt (1977)} and ^{Meeusen and van den Broeck (1977)}, which have evolved into applications with panel data. For details on the evolution of this methodology, see ^{Kumbhakar et al. (2015)}, ^{Greene (2008)}, ^{Kumbhakar and Lovell (2000)}, and for non-parametric approaches, see ^{Daraio and Simar (2007)}. In the panel data model framework, drivers of changes in efficiency are initially considered, subsequently leading to families of models, from the basic (fixed and random effects) to the more recent, which better separate the heterogeneity of persistent (or structural) inefficiency and variant inefficiency over time (^{Kumbhakar et al., 2015}).

Generally speaking, production frontier and efficiency models are built as follows. Briefly, given a vector of variables for the input of the producer-i,³ there is a production function f (x _i ;β) , which defines the maximum product possible, meaning a technical or potential maximum, known as the production frontier. What is interesting here is that even when the input vector x _i is exactly the same for different producers, nothing guarantees that they reach the maximum product. In other words, it is very possible for there to be a difference between the observed product y _i and the potential product, y _i ≤ f (x _i ;β), and the quotient yif(xi;β) , it is consistent to define as technical efficiency (0 ≤ ET ≤ 1) . As such, it is usual to define technical inefficiency as IT = 1 - ET , or equivalently, IT = ( f (x _i ;β) - y _i )/ f (x _i ;β) ≥ 0, which measures that deficit or what is missing to reach the maximum product. This is salient to the methodological implementation, because inequality, y _i ≤ f (x _i ;β) can be expressed also as inequality ln y _i = ln f (x _i ;β) - u _i , with the addition of the u _i ≥ 0 term, which is interpreted as technical inefficiency. This inequality ignores the role of uncontrollable or unpredictable factors, even when in reality these factors are numerous and it is inevitable that they will end up “accounted for” as randomness via a second error term v _i or random noise; neither u _i nor v _i are observable. That is why it can be justified to estimate the production function as a stochastic relationship specified by:

As an initial approach to the topic, the choice was made to use the ^{Battese and Coelli (1995)} panel data model, the first of its kind and in extremely widespread use still, which enables an estimate of the exogenous variables that alter the efficiency level, for example, those pertaining to the creative sector. The notation is direct to the case of panel data and, in practice, it is frequent to use a logarithmic transformation of the variables, so y _it is the log of the product for each metropolitan zone ZM-I and time t, x _it is a vector (k x 1) of producer-i input variables measured at time t, and there is a vector β of unknown parameters to estimate. A linear form is therefore assumed for f (·) as follows:

The non-observable global error has thus been decomposed into a first component v _it , which is a random variable that is distributed pursuant to [iid N(0, σv2)] and a second component u _it , which is a random variable as well (non-negative), which supposedly captures the effects of technical inefficiency in the generation of the product and is independently distributed pursuant to a truncated normal distribution N ( m _it , σu2) The expected or average inefficiency, E(u _it ) = m _it is a function of the z _it variables that may affect the technical efficiency of the metropolitan zones and is expressed as follows:

Where z _it is a vector (1xp) of explanatory variables that could have an effect on the production function of a metropolitan zone and δ is a vector (px1) of parameters to estimate.

Looking at the explanatory variables in z in the inefficiency model, any variable could be included that explains the degree to which observed production falls below the stochastic frontier values.⁴ The estimate of the parameters defined by equations (2) and (3) is done using the maximum likelihood method. The derivation of the likelihood function expressed in terms of the variance parameters σ2=σv2+σu2 and γ=σu2 ∕(σv2+σu2) can be found in ^{Battese and Coelli (1993, pp. 19-22)}.⁵ Given that the variables in (2) are in log terms, it is direct to express technical efficiency (ET) via:

The ^{Battese and Coelli (1995)} model, still in widespread use, does suffer from major weaknesses, one of which is that it is not possible to correct for heteroscedasticity. In the stochastic frontier models and, in particular, maximum likelihood estimates, the presence of heteroscedasticity biases the coefficients by overestimating the intercept and underestimating their slope. That is why ^{Caudill, Ford, and Gropper (1995)} extended the model by assuming a functional form for heteroscedasticity (multiplicative type) in estimating the variance, expressed as: σuit=exp⁡(zitγ) , now dependent on a vector z _it (1Xm) with control variables that explain the variance of this error component and a vector γ containing the coefficients associated with the z _it to estimate; u _it is distributed pursuant to a semi-normal, u _it ~ N + (0,σit2 ) Later on, ^{Hadri (1999)} added a similar specification to the idiosyncratic error term: σvit=exp⁡(zitθ), with v _it ~ N (0, σit2) . Although the range of models has grown and become more complex (see ^{Kumbhakar et al., 2015}), given the empirical scope of this research, the ^{Battese and Coelli (1995)} model was considered sufficient with the controls for heteroscedasticity mentioned before.

4. EMPIRICAL MODEL

This study analyzed economic performance in terms of efficiency in 59 metropolitan zones throughout Mexico⁶ (see Map 1) inspired by the smart cities application in ^{Mundula and Auci (2013)}. Both follow the model specified by ^{Battese and Coelli (1995)}, using panel data (see Section 5).

Source: INEGI, digital map.

Map 1 Metropolitan Zones of the Mexican Republic 

The difference between this study and the ^{Mundula and Auci (2013)} study resides in the variables used, as the present study drew on conventional variables to measure capital stock and the labor factor as compared to houses per number of residents and length of the public transport network (km) as a measure of the capital factor, the number of employees for the labor factor, as is usual, and moreover added in human capital.

To quantify the effects of the inefficiency of smart cities, ^{Mundula and Auci (2013)} employed a set of six indicators in which they add in different observable variables. In this case, as this is a first approach, the variables of employed personnel and number of creative-sector economic units were used as variables indicative of size and concentration.

Equation (2), relativized by a scale variable as a labor factor,⁷ is thus estimated as an equation in terms of productivity, which is specified via a Cobb-Douglas function, linear in logs, and for our stochastic frontier model, is as follows:

Where the dependent variable is the value of the product ZM-I at time t measured by the log of the quotient between the real gross census added value (VACB) and employed people (PO) in each metropolitan zone in the years 2003, 2008, and 2013. The input variable, also in relation to labor and in logs, was calculated as the quotient of gross fixed capital stock (ABKF) relative to employed people in each metropolitan zone in the same years.

Where EC _it is the number of creative economic units in the metropolitan zone i in year t; OC _it is the people employed in the creative activities, pEC _it is the concentration of creative activities measured by the participation of the creative units in the total productive units (as a percentage), and pOC _it is the concentration of creative employment with respect to total employment (as a percentage), both for metropolitan zone i in time period t.

One sensitive aspect in these models is the incorporation of external influences driving the efficiency level. These variables are not under full control of the observed unit (firm, state, region, etc.), but do impact its performance. It is usual in practice to distinguish two types of influences of this sort: i) the characteristics of the observed unit (regional heterogeneity), which affect its potential for individual production; and ii) the factors driving efficiency, such as: characteristics of the population, geographic traits, and other institutional aspects (^{Kalb, 2010}). For each study in particular, underpinned by the economic and statistical theory available, these variables were selected.⁸ Given the limited scope of this study, it is necessary to explore in this direction.

5. DESCRIPTIVE STATISTICS AND INTERPRETATION OF THE RESULTS

Table 3 provides the basic descriptive statistics for the census variables used in the analysis. At the detailed level, this is a (balanced) panel database consisting of 10 variables measured for each of the 59 metropolitan zones in Mexico in the years 2003, 2008, and 2013.

Table 3 Statistical Description of the Variables Used (N=177) 

Source: Created by the authors

The estimated production frontier results are summarized in Table 4.⁹ As is to be expected, capital density (capital per employed man) contributes positively to increasing the product per employed man (equivalent to general labor productivity) in the metropolitan zones, and does so inelastically given that its value is less than 1. This coefficient, which is statistically significant, is interpreted as an increase of 10% in the capital density in the metropolitan zones increases the product pertaining to labor by 4.95%. Because this is a simple model (one input and one output), the sum of the elasticities implies decreasing scale yields.

Table 4 Results of the Productive Efficiency Model in Mexican Cities, 2003-2013 

Source: Created by the authors

The coefficients of the four factors driving the technical efficiency level in the metropolitan zones, associated to variables indicating the size (measured by employed people and number of creative economic units) and concentration (measured by their relative shares in the total of the creative activity sector) are statistically significant. The OC and pOC coefficients show negative signs, indicating that both variables have a positive effect on reducing the inefficiency level (or raising efficiency). The other two variables (EC and pEC) display an effect contrary to what was expected, driving up inefficiency (or, on the flipside, diminishing efficiency). This basic, exploratory exercise does come with the inconvenience that it is a short-panel data model,¹⁰ which may make it difficult to fully capture the behavior of several variables, such as the number of companies that over time tend to change more slowly than the employed people. Nevertheless, with the information available, it is the best approximation that can be had to the problem under study. Even so, it does contribute empirical evidence to go deeper into the topic.

With these same results from estimating the model (see Table 4), it is shown that the average technical efficiency level at which production is generated in Mexican metropolitan zones is barely 69.3%, which empirically documents the existence of a margin still to be explored in order to improve efficiency in the use of production factors.

Table 5 shows the ranking of the average (in)efficiency levels over the three years for each metropolitan zone, revealing that the highest levels appear in cities along the northern border of the country; the top two are: Reynosa-Río Bravo and Monterrey; of the ten metropolitan zones with the highest productive efficiency, eight are northern cities, with the exception of Valle de México, in third place, and Guadalajara, in sixth.

Table 5 Technical Efficiency and Inefficiency by Metropolitan Zone, 2003-2013. 

Source: Created by the authors

Table A2 presents the ranking of the technical inefficiency values in greater detail for each year in the sample, reinforcing the congruence of the result: the top ten lowest-inefficiency places include the metropolitan zones in the north in all three years, although their rankings among each other did change; Table A3 supplements these results, showing which metropolitan regions rose in the ranking (with negative signs) or got worse in the national ranking (see Statistical Annex).

Looking at the values in this ranking, the map in Figure 1 shows the geographic location of the metropolitan zones by percentile. It emerges clearly that the efficiency levels are not randomly distributed across the national territory, and in effect, the improvement in efficiency (reduced inefficiency) responds to a pattern associated with the most dynamic economic spaces concentrating the metropolitan zones in the meso-regions: center-north with the highest levels of efficiency and center-south with the poorest performance. Dark gray tones point to efficiency above the median. The lighter tones are those below the median. It thus appears that four border cities, Valle de México, and Guadalajara have the highest efficiency percentile (see Figure 1).

Source: Created by the authors.

Figure 1 Technical Efficiency by Percentile in the Metropolitan Zones, Average 2003-2013 

They are followed in importance by a set of 25 cities located in the northern region, Bajío, and the Yucatan Peninsula. Gray tones reveal the cities with the lowest efficiency levels, where of the 28 cities in this category, most are in the southeast and in the Pacific region of the country, notably, Ríoverde, with the lowest observation in the entire sample of metropolitan zones.

The technical efficiency determined by the variables listed above in the creative sector displays a clear pattern of spatial dependence. Figure 2 shows the scatter plot of the Moran index, which resulted in a spatial dependency coefficient with a positive value of 0.32, which is evidence that there is a positive association across technical efficiency levels in the metropolitan zones.¹¹ This situation is confirmed in the map in Figure 2 showing the values for the local Moran index, clearly revealing the formation of a cluster of cities with high levels of efficiency in the north of the country and in Cuernavaca, Morelos, another of the cities with low efficiency levels in the state of Michoacán, and a cluster of high-efficiency cities surrounded by low-efficiency cities in the Pacific zone, Guadalajara, and in Cuautla, Morelos.

Source: Created by the authors.

Figure 2 Spatial Dependency on Efficiency Levels in the Metropolitan Zones 2003-2013 

Finally, it also is clear that the efficiency levels are positively tied to the location of creative activities in Mexican metropolitan zones. Figure 3 shows a graphic panel in which technical efficiencies are positively tied with the weight of the creative economic units (UECR) in cities, with the weight of creative employment (POCR), and with regional specialization in creative activities (ESPCR).¹²

Source: Created by the authors.

Figure 3 Association Between Technical Efficiency and Creative Activities in the Metropolitan Zones of Mexico, 2003-2013 

6. FINAL CONSIDERATIONS

Mexican metropolitan zones represent the primary spatial concentrations of economic and population activity in the country. According to the latest census data from 2010, they generate around 70% of the national GDP and are home to 57% of the population. As part of the stochastic frontier analysis, 59 delimited metropolitan zones in Mexico were sampled to determine their economic behavior measured in terms of technical efficiency levels. An initial approach to the problem explored four descriptive variables in the creative sector as drivers of inefficiency levels and estimated the effect or impact on the rise in the product.

Pursuant to the results of this work, in Mexico, the metropolitan zones generate a product with an average overall efficiency level of just 69.3%, equivalent to inefficiency of 31.7%. Nevertheless, there is considerable variation between the top performer (88.4%) in the border metropolitan zone of Reynosa-Río Bravo and the lowest performer (53%) in the Ríoverde-Ciudad Fernández zone, so the range is 21%. This is further evidence of how heterogeneity in regional development is expressed.

Strikingly, technical efficiency was higher in the northern border countries and in Valle de México in the central area of the country. By contrast, the lower values clustered in southeastern Mexico. The exploratory analysis revealed that the border-area metropolitan zones in the north of the country constitute a cluster of highly technically-efficient cities, which in turn neighbor cities that are also highly efficient. This points to the conjecture that in some way, the location of companies that are very oriented toward exporting in these zones since the early nineteen-nineties has fueled the rise in technical efficiency and, therefore, in productivity in this region of the country. Finally, although it is just a basic model with a very restricted scope, the outcome furnishes initial empirical evidence as to the need for deeper comparisons with various models, in an endeavor to find more robust results.