Academic journal article
By Hackert, Ann M.; Tokle, Joanne G.
The Journal of Business Forecasting Methods & Systems , Vol. 12, No. 1
Many firms use forecasting to make better business decisions. The probit model is a variation of the linear regression model and offers business an additional forecasting tool. The probit model differs from linear regression in several ways. Ordinarily, the dependent variable in regression analysis is quantitative. Probit models allow the use of qualitative or categorical information. In probit models, the forecast variable (dependent variable) is binary and can take only two possible values typically denoted as 0 or 1. This study examines whether or not smaller firms accept foreign currency in payment for exports. The survey respondents provided categorical information by answering either "yes" or "no."
The probit model also differs from the regression model because it assumes a different functional form. Probit models are estimated using maximum likelihood techniques. Although linear probability models or regression models with a binary dependent variable are sometimes used, the probit model offers two distinct advantages. First, the linear probability model suffers from heteroskedasticity and is not fully efficient. Heteroskedasticity occurs when error terms from a model have nonconstant variance. Pindyck and Rubinfeld describe a study of family income and expenditures as an example of a model with heteroskedasticity. Low income families would spend at a relatively steady rate, while high income families may have more volatile spending habits. If expenditures are the dependent variable, the error variance for high income families would be greater (more volatile) than the error variance for low income families (more stable). Pindyck and Rubinfeld state: "When heteroskedasticity is present, OLS (Ordinary Least Squares) estimation places more weight on the observations which have large variances than on those with small error variances." This means that the estimators (coefficients) obtained from the linear probability analysis may vary widely from sample to sample and forecasting could be improved by using an alternative such as the probit model. The probit model will provide the forecaster with more consistent and comparable results from sample to sample.
Another reason for using the probit model is that we want to interpret the dependent variable as the probability of making a choice (accepting foreign currency or not), so using a transformation based on probability is logical. The predicted values are the probability of observing the category labeled "1." In our example, it represents the probability of answering "yes" to the question: "Do you accept foreign currency in payment for exports?" The predicted values of the linear probability model can theoretically take values less than 0 or greater than 1. These values are not consistent with the interpretation of probabilities, which must fall between 0 and 1. The probit model assures that all predicted values of the model fall within the limits, that is, between 0 and 1. G. S. Maddala provides a more detailed discussion of probit and other limited-dependent variable models.
THE PROBIT MODEL AN APPLICATION
Many studies examine the export practices and policies of large multinational corporations. The export activity of smaller firms is largely ignored even though it represents a significant contribution to overall export activity. Of the approximately 100,000 United States firms that export, 80% are small companies. Smaller firms are recognizing opportunities in foreign markets. The use of fax, 800-numbers and overnight package shipment allow firms more easily and quickly to respond to potential foreign sales.
Although smaller firms are increasingly internationalized, there are still some barriers to successful exporting. In addition to unique marketing skills, international business can require an understanding of foreign exchange transactions and international financing techniques. Aggressive marketing involves not just the sale of the product, but the exchange rate terms of the sales. …