Research Article
Measuring Total Factor Productivity in General Technical Progress Framework
Issue:
Volume 13, Issue 6, December 2024
Pages:
181-192
Received:
7 October 2024
Accepted:
25 October 2024
Published:
12 November 2024
DOI:
10.11648/j.ajtas.20241306.11
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Abstract: The classical Solow's total factor productivity accounting assumes that technical progress is Hicks neutral, which is a special situation in the reality of world economy. This paper expands the setting of technical progress into general technical progress framework, which can cover Hicks neutral technical progress, Harrod neutral technical progress, Solow-neutral technical progress, and various factor-biased technical changes. According to the principle of statistical index number, this paper decomposes the output index into a total factor input index and a total factor productivity index, and adopts normalized CES production function with factor-augmenting technical progress to derive the calculation formulas of the total factor input index and the total factor productivity index, and constructs a new economic growth accounting system, and finds the counteraction and compensation mechanism for diminishing marginal returns. If the factor substitution elasticity is 1 or there is no technical progress bias and factor allocation bias, then the new accounting equation degenerates into the classic Solow growth accounting equation. The new accounting system can measure the influence of total factor input and total factor productivity to economic growth, but also can measure the influences of factor input intensity and factor allocation bias in the growth rate of total factor input, and the influences of technical progress intensity and technical progress bias in the growth rate of total factor productivity. Therefore it is more precise and accurate than classical method.
Abstract: The classical Solow's total factor productivity accounting assumes that technical progress is Hicks neutral, which is a special situation in the reality of world economy. This paper expands the setting of technical progress into general technical progress framework, which can cover Hicks neutral technical progress, Harrod neutral technical progress...
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Research Article
Assessing the Quality of Ordinary Least Squares in General Lp Spaces
Kevin Hoffman
,
Hugo Moises Montesinos-Yufa*
Issue:
Volume 13, Issue 6, December 2024
Pages:
193-202
Received:
20 September 2024
Accepted:
18 October 2024
Published:
18 November 2024
DOI:
10.11648/j.ajtas.20241306.12
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Abstract: In the context of regression analysis, we propose an estimation method capable of producing estimators that are closer to the true parameters than standard estimators when the residuals are non-normally distributed and when outliers are present. We achieve this improvement by minimizing the norm of the errors in general Lp spaces, as opposed to minimizing the norm of the errors in the typical L2 space, corresponding to Ordinary Least Squares (OLS). The generalized model proposed here—the Ordinary Least Powers (OLP) model—can implicitly adjust its sensitivity to outliers by changing its parameter p, the exponent of the absolute value of the residuals. Especially for residuals of large magnitude, such as those stemming from outliers or heavy-tailed distributions, different values of p will implicitly exert different relative weights on the corresponding residual observation. We fitted OLS and OLP models on simulated data under varying distributions providing outlying observations and compared the mean squared errors relative to the true parameters. We found that OLP models with smaller p's produce estimators closer to the true parameters when the probability distribution of the error term is exponential or Cauchy, and larger p's produce closer estimators to the true parameters when the error terms are distributed uniformly.
Abstract: In the context of regression analysis, we propose an estimation method capable of producing estimators that are closer to the true parameters than standard estimators when the residuals are non-normally distributed and when outliers are present. We achieve this improvement by minimizing the norm of the errors in general Lp spaces, as opposed to min...
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Research Article
Self-Exciting Threshold Autoregressive (SETAR) Modelling of the NSE 20 Share Index Using the Bayesian Approach
Issue:
Volume 13, Issue 6, December 2024
Pages:
203-212
Received:
11 October 2024
Accepted:
4 November 2024
Published:
26 November 2024
DOI:
10.11648/j.ajtas.20241306.13
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Abstract: The analysis and interpretation of time series data is of great importance across different fields, including economics, finance, and engineering, among other fields. This kind of data, characterized by sequential observations over time, sometimes exhibits complex patterns and trends that some commonly used models, such as linear autoregressive (AR) and simple moving average (MA) models, cannot capture. This limitation calls for the development of more sophisticated and flexible models that can effectively capture the complexity of time series data. In this study, a more sophisticated model, the Self-Exciting Threshold Autoregressive (SETAR) model, is used to model the Nairobi Securities Exchange (NSE) 20 Share Index, incorporating a Bayesian parameter estimation approach. The objectives of this study are to analyze the properties of the NSE 20 Share Index data, to determine the estimates of SETAR model parameters using the Bayesian approach, to forecast the NSE 20 Share Index for the next 12 months using the fitted model, and to compare the forecasting performance of the Bayesian SETAR with the frequentist SETAR and ARIMA model. Markov Chain Monte Carlo (MCMC) techniques, that is, Gibbs sampling and the Metropolis-Hastings Algorithm, are used to estimate the model parameters. SETAR (2; 4, 4) model is fitted and used to forecast the NSE 20 Share Index. The study's findings generally reveal an upward trajectory in the NSE 20 Share Index starting September 2024. Even though a slight decline is predicted in November, an upward trend is predicted in the following months. On comparing the performance of the models, the Bayesian SETAR model performed better than the linear ARIMA model for both short and longer forecasting horizons. It also performed better than its counterpart model, which uses the frequentist approach for a longer forecasting horizon. These results show the applicability of SETAR modeling in capturing non-linear dynamics. The Bayesian approach incorporated for parameter estimation advanced the model even further by providing a flexible and robust way of parameter estimation and accommodating uncertainty.
Abstract: The analysis and interpretation of time series data is of great importance across different fields, including economics, finance, and engineering, among other fields. This kind of data, characterized by sequential observations over time, sometimes exhibits complex patterns and trends that some commonly used models, such as linear autoregressive (AR...
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