Keynesian Consumption Theory and UK Interest Rates: A Statistical Analysis Case Study

Evaluating UK Energy Consumption and Interest Rates Using MLRM

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Introduction: Keynesian Consumption Theory and UK Interest Rates: A Statistical Analysis

In general, Econometrics relies on some conceptual theories, which consist of some fruitful aspects. For understanding the summary of the findings of this report, the “Keynesian Consumption theory” has been undertaken here. The summary of “Keynesian Consumption theory”, declares that the class of consumption is impacted by disposable income. Keynesians argued that the stage of consumption is defined by the group of disposable income, rather than the level of earnings. According to Keynes, when income rises, people tend to expend more, thus leading to increased consumption and improved aggregate demand. He also suggested that when payment reduces, savings rise, leading to more inferior consumption and diminished aggregate demand. This theory is broadly acknowledged and has been utilized as the base for many economic approaches, including fiscal and monetary procedures.

Understandings through equation

As the undertaken theory, “Keynesian Consumption theory” specifies a suitable equation. It denotes the movement of the variables and the role of that variables as Independent and dependent variables. Keynesians state that many notable factors consisting of the rate of interest and energy consumption provide a wider contribution to a country’s current level of income.

The Keynesian consumption theory expresses that consumption is forced by disposable income (Cömert, 2019). This indicates that consumption is specified by the amount of income that is vacated for households after taxes are spent. The equation undertakes this theory.

“C = a + bY_d”

Where C denotes autonomous consumption, b stands for the marginal tendency to consume, and Y denotes disposable income. Through this consumption, “Autonomous consumption” is the lowest class of consumption that is independent of earnings, while the marginal tendency to consume is the balance of an additional unit of earnings that is consumed. Therefore, an expansion in disposable income will guide to an accumulation in consumption, while a reduction in disposable income will show a reduction in consumption.

Objective of report

This report has stated a framework on which the interest rate movements and energy of the UK have been analyzed. The OLS method has been elaborated on in this report. As the core methodology selection, it highlighted a broad description of the “Multiple Linear Regression Model”. The result has also been formed by a periodic MLRM analysis through Pre-estimation, Regression estimation, and post-estimation analysis. The forecasting analysis is also a vital component of this report.

Methodology and Data Section (MLRM)

The “Multiple Linear Regression Model” has been chosen as an effective methodology for elaborating the dataset in this report. It is also a comfortable method to define the independent and dependent variables significantly. It is a state of linear regression that models the connection between a dependent variable and two or more independent variables. The independent variables can be straight or categorical, and the dependent variable can also be constant or categorical. This is done by equipping a linear equation to the data and evaluating the coefficients for the separately independent variables, which are considered comfortable parameters of the regression equations (Paul, et al. 2019). These coefficients are then utilized to indicate the value of the dependent variable, given the values of the independent variables.

It can also be utilized to construct assumptions based on data. As an example, it can be utilized to predict the future revenue of a product or the success of an advertising movement. “Multiple linear Regression” can also be employed to determine the most influential factors and describe the variation in the dependent variable (Malone, et al. 2020).

In this analysis, the data has been collected from the UK’s energy and interest rate 34 years average movements and its impacts on the UK’s gross national profit. Here the “years” has been used as the prime dependent variable and “Interest rate” used as the prime independent variable.

Equation explanation

This analysis has particularly symbolized the OLS (Ordinary Least Square), which indicated the linear regression analysis. The equation has been expressed here.

Y = β0 + β1x + ε

Where β0 has been utilized in form of the Intercept

β1 acted as the slope, which is the energy rate (Constant)

ε stands for the component random error in this analysis.

During the implementation of the OLS method, the β0 and β1 have been utilized as the estimation. This method strives to undervalue the sum of the squared residuals (Burton, 2021). The regression will demonstrate the distance from each data point to the line of regression.

Results and Discussion

Pre-estimation analysis (Correlation analysis)

Figure 1: Pre-estimation analysis through Correlation analysis

As pre-estimation analysis, at first, it has been stated the correlation analysis, where two separate dependent (X) and Independent variables (Y) have been selected. It is containing the interest and energy rates. Through this analysis, the T-statistics profitability was measured for the dependent variable at 1.0000, while the independent variable has been measured at -0.075571, -1.637797, and 0.1021 respectively. It is significantly demonstrated the profitability standard of the coretaion analysis.

Figure 2: Pre-Estimation through Johansen Cointegration Test

The second form has been utilized for this Pre-estimation analysis, which is Johansen Cointegration Test. Through this analysis, the unrestricted cointegration rank test has been measured at 0.180958 and 0.002327 for the Eigenvalue, while the Trace statistics have been measured at 93.704436 and 1.080892 respectively for both of the variables (Ivascu, et al. 2021). The critical value at 0.05 level has been evaluated at 11.22480 and 4.129906 respectively for both of the variables. It has also demonstrated the probability test, which is measured at 0.0001 and 0.3472 respectively. The maximum Eigenvalue has also been evaluated, where the measurement has been calculated at 0.180958 and 0.002327. On the other hand, its core value has been measured at 92.62347 and 1.080892 for the two variables.,

Figure 3: Unit Root Test for the analysis of Pre-estimation analysis

The Unit root test has also been formed in this Pre-estimation analysis. Through this analysis, t-statistic have been measured at some different levels. At first, the Augmented Dickey-Fuller test statistic has been measured at -6.016064. At the 1% level, the critic value has been measured at -3.978266. At the 5% level, the critic value has been estimated at -3.419686. At the 10% level, the critical value has been measured at -3.132458.

Regression estimation

Figure 4: Pre-estimation analysis

As the evaluation of the regression estimation, the co-efficient values of the two variables have been determined at 23.75891 and -3.18 for both of the variables in this test. The std. error has been measured at 14.19802 and 1.94 for both of the variables, where the t-static value has been demonstrated at 1.673396 and -1.637797. The probability test has been found 0.0949 and 0.1021 for both variables. Through this analysis, the R-squared value has been measured at 0.005711, while the S.E regression has been demonstrated at 14.597981 (Dawoud, et al. 2022). The sum squared resid has been measured at 11192.505. The Log-Likelihood standard has been evaluated at -884.3196. The F-statistic has been measured at 2.682379.

Figure 5: Periodic estimation through Breusch-Godfrey Serial Correlation LM test

Post estimation

Figure 6: Post-Estimation Test through Multicollinearity test

Post estimation phase has been measured on the basis of the Multicollinearity test. The analysis has also specifically evaluated both of the variables. The co-efficient variable has been measured at 201.5836 and 3.76 (Apprx) for both of the variables. The uncentered VIF standard has been compared same for both of the variables at 37024.13 and the Centered VIF has been evaluated at 1.00.

Figure 7: Heteroskedasticity Test

According to the analysis of the Heteroskedasticity test, the F-statics standard has been analyzed at 0.332166. The observation R-squared has been identified at 0.333351 and the scaled explained SS has been evaluated at 2.228405. The probability test for the F-standard (1467) has been evaluated at 0.5647 and both of the probability Chi-square have been identified at 0.5637 and 0.1355, respectively.

Figure 8: Normality Test as Post-Estimation

The normality test has been valued through the series analysis of the interest and energy data. Through the normality test, the mean standard has been valued at -7.24 (Approx). The median standard has been evaluated at -0.317362. The skewness and kurtosis analysis have been analyzed at 2.619566 and 14.48447 respectively as per the sample of both of the variables.

Forecasting Analysis

In terms of the evaluation of the forecasting, it has been used several methods RMSE, MAE, and MAPE, consisting from the static forecast. In this analysis, RMSE estimates the difference between the expected values and the real values. MAE calculates the average volume of the errors in a set of forecasts, without regarding their direction (Singla, et al. 2021). MAPE calculates the percentage of error in the forecast by taking into understanding both the volume and direction of the errors. All three measurements provide an indication of the precision of a forecasting method and can be utilized to compare different methods.

Figure 9: Forecasting Evaluation

Figure 10: Energy rate forecasting

Figure 11: Periodic Forecast

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Conclusion

According to the report, there has been clearly stated some statistical analysis. A broad description of the economic theory and its equation expression have been highlighted. Several statistical analysis have been shown in this report, on which the distribution of the variable has been relied. Forecasting analysis and suitable graphical representation have also been stated in this report. That is why this report played a crucial role in the statistical analysis.

References

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Article

Senthilnathan, S., 2019. Usefulness of correlation analysis.Available at SSRN 3416918. Retrieved from: https://pubmed.ncbi.nlm.nih.gov/34300085/ [Retrieved on: 20.04.23]