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2023 | OriginalPaper | Chapter

1. Single-Equation Econometric Model

Author : Jerzy Witold Wiśniewski

Published in: Forecasting from Multi-equation Econometric Micromodels

Publisher: Springer Nature Switzerland

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Abstract

The first chapter is devoted to econometric models in the form of one stochastic equation. Linear, product, and limited dependent variable models were presented. In this chapter all stages of building a single-equation econometric model are discussed. These are: specification, estimation of parameters, verification, and exploitation possibilities. Basic methods of estimation of structural parameters and parameters of the stochastic structure of the model are presented. Basic statistical measures determining the quality of an empirical econometric model are also discussed.

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next chapter Multi-Equation Econometric Models

The nature of the category represented by the dependent variable assigns the model to a specific discipline. A dependent variable representing a demographic category, for instance, makes the model demometric; if the dependent variable is sociological in character—the model is sociometric; when the dependent variable represents a psychological category—the model is psychometric.

Structural parameter αj(j = 1, …, k) indicates an increase in the value of observation x_tj by one unit, which, assuming immutability of other explanatory variables (the ceteris paribus principle), changes the size of y_t by α_j units.

Explanatory variables of discrete nature (discrete variables) should be included in the model only exponentially, as it is difficult, in power series terms, to assign economic interpretation to structural parameters.

The statistical data collected must be of appropriate quality, i.e., it should be comparable, with no gaps in the statistical series, both in the interior and on the edges thereof. Any minor data deficiencies can be filled using statistical techniques (interpolation, extrapolation). The statistical material should be free of any statistical bias.

For models consisting of multiple equations.

The estimator ought to be selected to contain the necessary statistical properties, i.e., consistency, unbiasedness, efficiency, and sufficiency. Details on that are presented in Sect. 1.3.

Global and specific goodness-of-fit measures.

Cf. Wiśniewski (1986), subchapter 1.5. This concept means that an economic variable, which—from research perspective—best reflects the economic category constituting the subject of an empirical verification, is called an equivalent variable. Cf. works Wiśniewski (2013), subchapter 1.3.

Including the amount of tax on goods and services.

The term estimator precision is more appropriate, in terms of estimator properties, than the phrase estimator efficiency. Efficiency is usually associated with effectiveness, whereas this property refers to the estimates’ accuracy.

The Aitken’s method is recommended when the random component variations for different statistical observations are not equal, that is, equality (1.16) does not hold.

Random component autocorrelation is a model specification error, for it can result from: 1) an omission of an important, statistically significant explanatory variable in the empirical model, which results in a positive autocorrelation; 2) a defective analytical form of the empirical model, resulting in a positive random component autocorrelation; 3) an excess of statistically insignificant variables in the empirical model, resulting in a negative random component autocorrelation.

It can be demonstrated that if first-order autocorrelation does not occur in the model, there is no autocorrelation of higher order either. Occurrence of first-order autocorrelation, however, indicates a model specification error, which necessitates model re-specification. Re-specification should be continued until the empirical model lacks first-order random component autocorrelation.

If DW(DW^*) > d_u, there are no grounds for rejection of the null hypothesis (H₀), which means that no random component autocorrelation occurrence can be inferred, with a risk of a first-type error (at significance level γ). If DW(DW^*) < d_l, hypothesis H₀ is rejected in favor of an alternative one, by which first-order random component autocorrelation can be inferred. When d_l ≤ DW(DW^*) ≤ d_u, the test does not determine whether autocorrelation occurs or not. This indicates that the DW statistic has hit a region of test insensitivity, which is synonymous with necessary application of another test of random component autocorrelation, e.g., the Student’s t-test, to examine the autocorrelation coefficient.

The alternative hypothesis implies that the statistical test is a test with the so-called two-sided critical region.

Most commonly, a significance level of γ = 0.01 or γ = 0.05 is selected, which implies acceptance of 1% or 5% risk of Type I error.

Provided that all previous measures of the model’s goodness of fit are at a satisfactory level.

An extensive discussion of econometric model building for bound dependent variable transformation can be found in Wiśniewski (1986).

Cf. Goldberger (1972: 321).

Goldberger AS (1972) Teoria ekonometrii. PWN, Warszawa

Wiśniewski JW (1986) Ekonometryczne badanie zjawisk jakościowych. Studium metodologiczne. UMK, Toruń

Wiśniewski JW (2013) Forecasting staffing decisions. Econometrics 1(39):22–29

Title: Single-Equation Econometric Model
Author: Jerzy Witold Wiśniewski
Publisher: Springer Nature Switzerland
Book: Forecasting from Multi-equation Econometric Micromodels
Print ISBN: 978-3-031-27491-6

Electronic ISBN: 978-3-031-27492-3

Copyright Year: 2023
DOI: https://doi.org/10.1007/978-3-031-27492-3_1