MSMEs in Mexico

The “Business Practices in Small Firms in Developing Countries” survey of the World Bank was conducted in Mexico between 2008 and 2014. It has data for slightly more than 10,000 companies with less than 10 employees, distributed in three main sectors of economic activity: manufacturing, services, and commerce. It gathers information on age and years of education of the owner, age of the company, capital stock, gross profits, income, inventory value, adoption of marketing practices, purchase and inventory control, registration of cost and maintenance and financial planning, among others. Of the total information provided by the survey, only the 7690 consistent observations are used.²

The survey collects adoption information on 4 business practices, primarily accounting and financial practices. Each practice is made up of a set of questions, aimed at knowing whether the organization performs specific tasks or not. Table 1 shows the set of tasks that make up each specific practice.

Given that each organizational practice is made up of a different number of tasks, the data were standardized by dividing the number of tasks performed by each company for each practice by the total number of tasks available in that practice, in order to make the information available for each practice comparable; as a result, values ranging from 0 to 1 in each practice are obtained.

Table 2 shows some of the main characteristics of the companies interviewed; on average, they are organizations that sell $16,960 dollars a month, with owners who are 45 years old and who have completed only junior high school education; they are organizations that have an average of 3.4 years in the market and a capital stock equivalent to 1.2 months of sales. Their gross profit margin is just over a third of their sales.

By comparison, companies in the services sector have the highest average sales, capital stock and education levels, while those in the commerce sector (65% of the total number of companies in the sample) have the highest profit margins, even though their sales are on average 25% lower than those in the manufacturing and services sectors. The manufacturing companies (4.9% of the sample) are the oldest.

Regression model with cross-section data

The regression model consists of specifying and estimating a relationship model between the variables related to a given theoretical matter (^{Novales, 1993}); it has one (or more) dependent variables and a set of independent or explanatory variables and establishes a relationship between them, of the form:

When the type of relationship established between the variables is a linear relationship, the general model acquires the following form:

Where:

The βi parameters transfer the effects or impacts of the set of independent variables xi on the dependent variable y. The aim is for the set of explanatory variables to be closely related to the dependent variable; to the extent that this occurs, the error term u_i will tend to be smaller.

The procedure of Ordinary Least Squares (OLS) minimizes the quadratic error of function 14, through the process:

Where SCR represents the sum of residues squared.

Minimizing function (3) provides an unbiased linear estimator of minimum variance, which “is efficient when the error term follows a normal distribution, i.e., has the least possible variance among all the unbiased estimators, whether linear or non-linear”, ^{Novales (1993}), pp. 67.

This result, on the one hand, allows analyzing the degree in which the independent variables are capable of explaining the behavior of the dependent variable; on the other hand, when the regression βi coefficients are analyzed, it allows measuring the individual impact of each of the x _i independent variables on the dependent y _i variable.³

Artificial Neural Network

An Artificial Neural Network (ANN) is a parallel distribution processor that works with a large quantity of data, which posses a natural propensity to store experimental knowledge and turn it into information available for its use (^{Haykin, 1999}). It resembles the brain in two aspects:

An ANN can be defined as a guided graph (^{Larrañaga, Inza and Moujahid, 2003}) that complies with the following properties:

In this way, ANNs can define both linear and nonlinear parameters mapped from an input to an output of the Y=Y(X;W,A) type, which is a continuous function of both the inputs and the W parameters and of the network architecture (A).

A typical ANN architecture is divided into three segments (^{Bishop, 1995}); the first is the input layer, which receives information from the outside; the second is the hidden layer, which establishes the relationship between the input variables (input layer) and the output variables (output layer), defined by:

Hidden layer:

And the third is the output layer, comprised of the sets of neurons that provide the response of the network, of the form:

An important difference between the types of ANN that exist is the number of layers that integrate the learning processes (hidden layers); a larger number of layers allows the approximation of more complex processes. Here, we use a hidden-layer ANN, known as multi-layer perceptron.

The process by which the hidden layers model store information and try to represent the functional forms of the data received in the input layer is known as neuron training. In this process, a subset of data D=X(n),t(n) is used by adjusting the W of Function (5), minimizing the error of the function by means of the gradient descent method, expressed in the Function (6):

The minimization is based on continually evaluating the E_D gradient through the chain rule to find the derivatives, following the steps below:

Additionally, for each of the hidden and output layers, an activation function is estimated, which is determined by the estimation algorithm. The activation function relates the weighted sum of units in a layer to the values of units in the correct layer. This activation function is different for the hidden layers and the output layer.

Econometric application

Through the model developed in section 3.1, the following function is estimated:

Where: ED is the age of the owner; EduD are the years of education of the owner; Ant is the age of the company on the market; Stock is the capital stock; PracMark are the marketing practices; PracCont are the accounting practices; PracReg are the registration of cost and maintenance practices; PracPlan represents the financial planning practices; and β1, ..., β8 are the coefficients estimated for each of the variables.

The econometric analysis shows a differentiated importance of the adoption of administrative practices for the companies under study. Although, overall, they show to be important to explain the growth of sales, the practice that turns out to be more important is financial planning.

The variables of age and education of the owner are statistically significant at a level of 5% and show the expected signs. According to the coefficients, the age of the owner allows them to accumulate certain types of experience and knowledge that impact sales; however, the coefficients are low, indicating that the impact, although positive, is small.

On the other hand, the age of the company, although statistically significant, does not show the expected sign. Theoretically, a positive sign would indicate that the longer the organization is in the market, the more it tends to accumulate experience that allows it to know its customers and competitors and increase sales and, consequently, revenue. The fact that seniority shows a negative sign may be a result of the high mortality of micro organizations in Mexico; given that the average age of the companies in the sample is of only 3 years, as they accumulate years, sales tend to be lower, and by the third year they become so low that they are forced to close.

The capital stock is statistically solid for the explanation of variations in sales, and its impact is the second highest of the set of variables analyzed. It shows the expected sign and is congruent with the idea that the greater the physical capital available to workers, the higher their productivity, and this is reflected in sales.

The most important variable to explain sales behavior is the adoption of financial planning practices, which include timely reviews of budgets, expenses, and profits and losses of organizations, as well as future sales planning. The coefficient is statistically significant and positive, a fact that reinforces the idea that the adoption of certain types of organizational practices can influence the performance of companies.

The practices of purchase and maintenance registering, and purchase and inventory control do not show the expected sign; the latter is not statistically significant at the 5% level. The model as a whole is statistically significant (F=0.00) and has a goodness of fit coefficient, measured by the determination coefficient R² of 0.521.

ANN model

Once the econometric model has been estimated, an Artificial Neuronal Network model was done. Of the 7,464 observations considered valid, 61.1% were used for neuron training, 29.9% for correct training tests, and the remaining 8.9% were used to validate how close the values predicted by the Network are to the actual values.

The type of ANN used is a multi-layered perceptron; the input layer receives information on the following variables or factors: age of the owner, years of education of the owner, age of the business, capital stock, and degree of adoption of 4 administrative practices (marketing, purchase and inventory control, registration of cost and maintenance, and financial planning).

The results show a hidden layer comprised of 4 units-shown in Table 4-whose activation function is the hyperbolic tangent,⁴ and the output layer, which has an activation function for the revenue per employee that relates the weighted sum of units of a layer with the values of units in the correct layer, returned unchanged (identity function) using the function γ(c)=c. The results are shown in Table 3.

The analysis of the reserve sample indicates that ANN results are robust for estimating monthly sales performance. Figure 1 shows the actual and estimated values for the reserve sample. For 90% of the observations (companies with monthly sales of less than $40,500 dollars), the ANN estimates the behavior of sales by company to have errors of less than 3%; however, for those organizations with monthly sales of more than $40,500 dollars (10% of the reserve sample), the value of sales is systematically overestimated by the neural network. This could be an indicator that the higher the sales, the more complex the factors influencing their determination.

Source: Own elaboration of ANN, based on data from the World Bank.

Figure 1 Graphical representation of the results of the estimation 

Regarding the variables introduced in the input layer, Graph 2 shows the analysis of the importance of the variables; the results are relatively coincidental with those obtained using econometric methods. The most important organizational practice to explain sales performance is financial planning. This result indicates that as companies keep an accounting record of their sales and costs, analyze their budgets, and make estimates about future costs and sales, they are able to more efficiently manage their business, allowing them to increase sales.

Figure 2 Standardized importance of each factor 

The second variable in terms of importance is capital stock; this indicates that if organizations have more physical capital, they are able to respond more quickly to increases in demand. This result is consistent with the neoclassical growth theory, which states that a larger capital stock per worker increases work productivity.

At the same time, marketing practices, which could be defined as market intelligence strategies (which not only include advertising, but primarily competitive analysis and the launch of special deals to attract customers), play an important role in determining monthly revenue.

On the other hand, the age of the organization on the market takes 4th place in terms of importance to explain sales. Given the characteristics of the analyzed segment (microenterprises), the average age of the sample is relatively low (just over 3 years), which suggests that companies are located in early stages of the learning curve, so that small differences in time on the market can represent important learning distances, as is also validated by the econometric analysis.

Variables such as the age and education of the owner are not relevant to explain the sales performance, mainly because education barely reaches basic (junior high school).

Finally, there are two accounting practices, which on average have the least influence on the level of sales. On the one hand, the registration of cost control and maintenance and, on the other, inventory control practices. Given the characteristics of the analyzed segment of companies (companies with an average of 3 employees, mainly from the commercial sector), the probability of a high proportion being family businesses tends to increase. The results indicate that, for this type of organization, the development of practices that allow differentiation of personal and organizational assets and a systematic record of costs are, at best, scarce.

The results obtained coincide, in a certain sense, with those obtained by ^{Fajnzylber, Maloney and Montes-Rojas (2009}), given that in order for the activities that these authors indicated (participation in the credit market, payment of taxes, access to training, and membership of business associations) to be carried out, it is necessary to have certain practices within the organizations. Fajnzylber et al. refer to the fact that the characteristics of organizations persist over time as they are correlated with unobserved entrepreneurial skills and capabilities. Some of the unobserved characteristics could be the lack of training in financial and accounting practices, derived from the educational deficiency of Mexican entrepreneurs.