## Introduction

An economic model is a statistical model that enables the quantification of casual relationships identified in a given scenario. Using this model, one identifies the most important factors that influence the actions taken and analyzes the behaviour of pertinent economic variables. Economic models are explanatory in nature, and they generally characterize average behaviour, identifying the qualitative relationships between variables. To establish if the variation in a dependent variable is statistically dependent to the variation of the independent variable, one uses a hypothesis test (McCarthy, 2001).

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In a simple economic model, for example where shippers demand for transportation services depending on the transportation rate charged, one can identify the cause and effect relationship by analyzing the demand for freight transportation. This is depending on the price and the final impacts (Perle, 1960). The demand for freight transportation is in the nature of economics, where demand can be predicted by analysing the forces of demand and supply. The effect of this demand may result to increased or decreased transportation (Baumol & Vinod, 1970).

The increase in transport rates may lead to reduction in tons per miles of commodity shipped. This ultimately results to reduction in supply shipped, and may eventually trigger the increase in price by the shipper. Decrease in transport rates may trigger increase in tons per miles of commodity shipped, thus increased supply and reduction of price (McCarthy, 2001)

## Qualitative Model

Economic models are qualitative in nature. This is because in this particular scenario, the effects of change in one variable-like the transportation rate-will have an effect on the supply of the commodity. This is categorized as qualitative model, since it only gives the impact of the change but does not quantify it (Hummels & Schaur, 2009).

## Transforming Economic Model into an Econometric Model

Transforming the economic model into an econometric model is to turn it into a quantitative one. Therefore, one is required to quantify the different variables in the economic model-for example in the transportation. The latter is charged by the tons per miles covered and the miles travelled depend on variables like the tons per miles charges and the total income (McCarthy, 2001). Thus, to transform the economic model into an econometric one, the demand for freight transportation is expressed as a function of tons per miles, and the total income per shipment. Hence, one can come up with an expression:

*Demand for freight transportation =∫ (tons per miles, total income per shipment)*

But this expression is not complete because the demand for shipment of commodities has several other factors that affect it. These may not have been mentioned. Thus, to make the mathematical expression complete, one must be able to use a variable expression of other dependant of the miles travelled, termed as variables determining the miles travelled (McCarthy, 2001).

At the end, the mathematical expression that transforms the economic model into an econometric one is as follows:

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Where:

- Demand for freight transportation=x
- Tons per miles=b
- Total income per shipment = q
- The determinant factors affecting x = β

x=*∫ *(b,p)

x= β_{1}+ β_{2}(b)+ β_{3}(p)+ α

α is used to capture the approximation error and also stand in for the omissions of the variables in the first expression.

## Hypothesis

In order to be able to use this model to test the hypothesis that demand of freight transportation depends on transport rates charged, we use the following expression:

- If all factors remain constant, the increase in the charges of tons per mile will result to less demand for freight transportation
- If all factors remain constant, the increase in the charges of tons per mile will not result to decreased demand for freight transportation

## Conclusion

The demands for freight transport are determined by the market forces of demand and supply, but the variables such as the number of miles to be travelled and other factors clearly impact the direction and quantity of supply of commodities. The economic models are only quantitative in nature whereas econometric model is a statistical analysis of the economic model.

## References

Baumol, W. J., & Vinod, H. D. (1970). An inventory theoretic model of freight transport demand. New York: *Management Science Journal*, 16(3), 45.

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Hummels, D. L., & Schaur, G. (2009). *Hedging price volatility using fast transport. *New York: NBER Working Paper No. w15154, p. 39

McCarthy, P. S. (2001). *Transportation economics theory and practice: A case study approach.* Long Beach: Prentice Hall, 17 -20.

Perle, E. D. (1960). *Estimation of transportation demand.* Harvard: Harvard University Press, 173.