Linear Regression For Impact Analysis: Energy Bars And Tariffs

Linear Regression and Energy Bar Demand

An effective tool to analyze relationship between two or more variables is linear regression. The regression offers a linear relationship between the dependent and independent variable (Schroeder, Sjoquist & Stephan, 2016). The Board of Schmeckt Gut wanted to know the possible impact of offering energy bar to another store on the demand for energy bars. This depends on the relation between demand of energy bars and number of stores offering energy bars. The dependent variable here is annual average demand of energy bars per person and independent variable is number of stores where energy bars are offered. The demand of energy bars that needs to be estimated is 

Result of the linear regression is given below

The estimated demand equation is 

From the regression result, the multiple R square is obtained as 0.85. The multiple R square shows strength of the estimate linear relationship. The value of multiple R square is closer to 1. This implies a strong positive relation between demand of energy bars and number of stores. The value of R square is estimated as 0.72. R square represents the coefficient of determination. It tells that number stores can explain 72 percent variation in the energy bar demand. The estimated coefficient for number of stores is 7.2169. The positive coefficient implies positive influence of number of stores on demand for energy bars. That is, as the number of stores increase, the energy demand is likely to be increase. In order to have a statistically significant relation coefficient of the dependent variable needs to be statistically significant. The statistical significance of the variable can be examined by the use of p value (Darlington & Hayes, 2016). The p value of number of stores is 0.0000. The p value less than the significant level of 0.05 implies there exists a statistically significant relation between the two variables

The positive significant relation between number of stores and energy demand per person implies that offering energy bars to another store would benefit the company by increasing demand.

As like the impact of number of stores on energy bar demand, the potential effect of tariff on energy bar demand needs to be evaluated on the basis of linear relationship between demand and tariff rate. The dependent variable in the regression analysis again annul average demand of energy bars per person and the independent variable is imposed tariff rate on import. 

Impact of Tariffs on Energy Bar Demand

The result of estimated linear regression between energy bars is given below

The estimated demand equation is

From the regression output, the value of multiple R square is 0.0067. The value is zero implying a weak relationship between tariff and annual average demand of energy bar. The R square value is also low. The estimated value of R square is 0.000045. Therefore, the tariff rate alone cannot explain much of the variation in demand for energy bars. The estimated coefficient of tariff rate is -0.07643.  A negative regression coefficient indicates presence of negative influence of the independent variable on the dependent variable. Therefore, as the tariff rate increases, faced with a high price of imported energy bars people reduces the demand for energy bars. Finally, the statistical significance of tariff rate is tested using p value. The associated p value of the tariff rate is 0.9769. As the o value is greater than the significant value of 0.05 therefore the null hypothesis if no significant relation between rate of tariff and annual average demand for energy bars is accepted.

On the basis of market survey and result of regression is can be said that tariff has a potential adverse impact on energy demand. Tariff by raising effective price of energy bars reduces its demand. The relation though not seem to be statistically significant but the potential distortionary effect of tariff in the long run cannot be ignored.

The impact of an import tariff is not limited to the importing country but it also has severe implication on consumers and particularly producers of the exporting nation. Under free trade, goods are exchanged between the two trading nations. People in the importing countries have demand excess of the domestic supply. The exporting countries on the other hand have supply excess of their domestic demand.  The nations therefore engage in trade in their own interest. The imposition of tariff on a product increases price of the product in the importing country. Unlike autarky, now a price difference exists between exporting and importing nations (Beshkar, Bond & Rho, 2015). The high domestic price of the imported good lead to a significant reduction in demand. This hurts the producer surplus of exporter. The figure below shows the potential impact of tariff on Schmeckt Gut’s energy bars.

The demand and supply curve of energy bar in the Industria market are presented by D₁D₁ and S₁S₁ curve respectively. P* is the world price if free trade is allowed between the two nation. At world price, the supply of energy bar exceeds its demand in the domestic market with the difference is being exported. The volume of export without any trade barriers is (Q_S – Q_D). With tariff the company faces a relatively low price in its domestic market with the price reduces to P₁. The low price in the domestic market though helps to increase domestic demand to Q_D1 (Fan, Li & Yeaple, 2015). The company however suffers a loss in the producer surplus shown by the area A+B+C+D+E.

Potential Welfare Effects of Tariffs

Free trade generally represents a mutually beneficial relation among different nations. Countries by specialization in a particular line of production gain a greater efficiency on the production of the product. Other countries benefitted from importing the good as free trade enables the goods at a cheaper price than otherwise it would be. Any barriers to free trade thus creates a distortion resulted from a misallocation of resources (Feenstra, 2015). The figure shows potential gain and loss of an interventionist policy like tariff on different economic agents.

Demand and supply curve in the domestic market is shown by the respective curve of DD and SS. At the domestic equilibrium price of P_1, Q₁ amount of goods are sold. Allowing foreign producers to enter the market makes the supply curve perfectly elastic. MM represent the domestic and foreign supply together. Free trade lowers the price to P_2. At the world price of P_2, a domestic supply shortage exits showing the volume of import (Hazari, 2016). The import volume with free trade is represented as (QD₁-QS₁). Imposition of a tariff of amount t, increase price to P_3. In response to tariff the import demand is Atolia reduces to (Q_D2-Q_S2). Following a high price, the consumer surplus is reduced by the area a+b+c+d+e.  As against this, the gain in producer surplus is a+f. Tariff though gives government an additional source of revenue, the revenue gains and producer surplus is smaller than the loss of consumer surplus. The tariff thus leads to a net welfare loss of b+e.

The theory of free trade is further supported by the result of regression analysis. The regression analysis also predicts an inverse relation between demand for energy bars and corresponding tariff rate. A free trade therefore is beneficial for both the nation especially for energy bar companies in Industria. Free trade makes it easy for the company to enter smoothly in the Atolia market and expand business there.

References list 

Beshkar, M., Bond, E. W., & Rho, Y. (2015). Tariff binding and overhang: theory and evidence. Journal of International Economics, 97(1), 1-13.

Darlington, R. B., & Hayes, A. F. (2016). Regression analysis and linear models: Concepts, applications, and implementation. Guilford Publications.

Fan, H., Li, Y. A., & Yeaple, S. R. (2015). Trade liberalization, quality, and export prices. Review of Economics and Statistics, 97(5), 1033-1051.

Feenstra, R. C. (2015). Advanced international trade: theory and evidence. Princeton university press.

Hazari, B. (2016). The pure theory of international trade and distortions. Routledge.

Schroeder, L. D., Sjoquist, D. L., & Stephan, P. E. (2016). Understanding regression analysis: An introductory guide (Vol. 57). Sage Publications.

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