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Quantitative Method Final Report

Question 6.31 requires the use of the Dataset of oecd.wkf to analyze and compare the figures of Japan and Canada.
Requirement: Report is confined to 10 pages no more than 10 pages. Include introduction, no literature review. Index as follows:

Introduction
Description of your data
Estimation result
Answer each question
Compare result of 2 country
Conclusion
With the help of ChatGPT, that’s the basic answer. Waiting to be reorganized into report.

Final Report (Question 6.31 compare Japan and Canada)

Question 6.31 Everaert and Pozzi20 develop a model to examine the predictability of consumption growth in 15 OECD countries. Their data is stored in the file oecd. The variables used are growth in real per capita private consumption (CSUMPTN), growth in real per capita government consumption (GOV), growth in per capita HOURS worked (HOURS), growth in per capita real disposable labor income (INC), and the real interest rate (R). Using only the data for Japan, answer the following questions:

  • a. Estimate the following model and report the results

    CSUMPTN = β1 + β2 HOURS + β3 GOV + β4 R + β5 INC + e
    Are there any coefficient estimates that are not significantly different from zero at a 5% level?

  • b. The coefficient β2 could be positive or negative depending on whether HOURS worked and private consumption are complements or substitutes. Similarly, β3 could be positive or negative depending on whether government consumption and private consumption are complements or substitutes. What have you discovered? What does a test of the hypothesis H0∶β2 = 0, β3 = 0 reveal?
  • c. Re-estimate the equation with GOV omitted and, for the coefficients of the remaining variables, comment on any changes in the estimates and their significance.
    • I will analyze the dataset in the provided file to estimate the required models for Japan and address the specified questions. Please hold on while I process the data.
    Variables
    CSUMPTN growth in real per capita private consumption.實際人均私人消費成長。
    GOV growth in real per capita government consumption.實質人均政府消費成長。
    HOURS growth in per capita HOURS worked.人均工作小時數成長。
    INC growth in per capita real disposable labor income.人均實際可支配勞動所得的成長。
    R the real interest rate.實際利率。
    Analysis of Results for Question (a):
    The model estimates the coefficients for Japan's data with the following findings:

  • HOURS: Coefficient = 0.4246, p-value = 0.028 (significant at 5% level).
  • GOV: Coefficient = 0.1641, p-value = 0.256 (not significant at 5% level).
  • R (Real interest rate): Coefficient = 0.2434, p-value = 0.003 (significant at 5% level).
  • INC (Disposable income): Coefficient = 0.6083, p-value = 0.000 (significant at 5% level).


    Conclusion: The coefficients for HOURS, R, and INC are significantly different from zero at the 5% level, while GOV is not.

    Next, I will address question (b), focusing on the hypotheses H0:β2=0 and β3=0. ​​

  • Results for Question (b):
  • For β2​ (HOURS):
  • For β3​ (GOV):
  • The hypothesis H0:β2=0 is rejected, indicating that HOURS significantly affects consumption growth. Whether HOURS and private consumption are complements or substitutes depends on the context; here, the positive coefficient suggests a complementary relationship.
  • The hypothesis H0:β3=0 is not rejected, indicating that GOV does not have a statistically significant impact on consumption growth.


    Next, I will re-estimate the model without GOV and evaluate changes in the estimates and their significance for the remaining variables. ​​

    • Results for Question (c):

    Re-estimating the model without the variable GOV produced the following changes in the coefficients:

  • HOURS: Coefficient = 0.3080, p-value = 0.055 (marginally insignificant at the 5% level).
  • The coefficient decreased from 0.4246 to 0.3080, and its significance weakened slightly.
  • R (Real interest rate): Coefficient = 0.2599, p-value = 0.001 (still significant at the 5% level).
  • The coefficient increased slightly from 0.2434 to 0.2599, with consistent significance.
  • INC (Disposable income): Coefficient = 0.7470, p-value = 0.000 (still highly significant).
  • The coefficient increased from 0.6083 to 0.7470, and its significance remains robust.
    Conclusion:
  • Removing GOV slightly alters the magnitude and significance of the remaining coefficients.
  • The positive relationship between HOURS and consumption growth is weakened, while the impact of INC becomes more pronounced.
  • The robustness of R and INC underscores their critical role in explaining consumption growth in Japan. ​
    • 接下來，請再回答以下三個問題：(Next, please answer the following three questions:)
    d. Estimate the equation
    GOV = α1 + α2 HOURS + α3 R + α4 INC + v
    and use these estimates to reconcile the estimates in part (a) with those in part (c).
    e. Re-estimate the models in parts (a) and (c) with the year 2007 omitted and use each of the estimated models to find point and 95% interval forecasts for consumption growth in 2007.
    f. Which of the two models, (a) or (c), produced the more accurate forecast for 2007?
    Results for Question (d):
    The model estimates for GOV based on HOURS, R, and INC are as follows:

  • Constant: Coefficient = 0.0132, p<0.001 (significant at 1% level).
  • HOURS: Coefficient = -0.7106, p=0.001 (significant at 1% level).
  • R (Real interest rate): Coefficient = 0.1004, p=0.273 (not significant).
  • INC (Disposable income): Coefficient = 0.8455, p<0.001 (significant at 1% level).


    Reconciliation between (a) and (c):

  • The negative relationship between HOURS and GOV suggests that HOURS indirectly affects consumption growth through its influence on GOV. Removing GOV in part (c) reduces the direct impact of HOURS on CSUMPTN.
  • The strong relationship between INC and GOV supports the observed increase in the coefficient of INC when GOV is omitted in part (c).


    Next, I will handle part (e) by re-estimating the models excluding 2007 and generating forecasts for that year. ​​

    The error indicates a mismatch in the number of predictors when attempting to forecast for 2007 using the re-estimated models. This is likely due to differences in the variables included in the models.

    To address this, I will carefully adjust the inputs for each model and ensure compatibility with the variable sets used in their estimation. Let me fix this. ​​

    It appears there is a persistent issue with the variable alignment between the prediction inputs and the models. To resolve this, I will double-check the variable alignment in both the model estimation and the data for prediction, then recalculate. ​​

    The issue lies in ensuring the predictors match the number of parameters used during model estimation. For:

  • Model (a): Requires the predictors HOURS,GOV,R,INC along with a constant term (5 total).
  • Model (c): Requires HOURS,R,INC and a constant term (4 total).


    The forecasts will now be recalculated with strict alignment to the predictors used during model estimation. ​​

    • Results for Question (e):

    Forecasts for consumption growth in 2007 based on the re-estimated models:

  • Model (a):
  • Model (c):
    • Next Steps:

    For part (f), I will compare these forecasts to the actual 2007 consumption growth to determine which model is more accurate. ​​

    Results for Question (f):

    The actual consumption growth in 2007 was 0.0036.

    Conclusion:
    Model (c) produced a more accurate forecast for 2007, with a smaller absolute error compared to Model (a). This suggests that the simplified model without GOV may better capture the dynamics of consumption growth for this specific year. ​
    接下來同樣問題，但分析對象是Canada (The next question is the same, but the analysis object is Canada.)

    Analysis for Question (a) for Canada:


    The regression results for the model CSUMPTN=β1 + β2 HOURS + β3 GOV + β4 R + β5 INC + e are as follows:

  • Constant: β1=0.0082, p=0.045 (significant at 5% level).
  • HOURS: β2=0.4125, p=0.001 (significant at 5% level).
  • GOV: β3=−0.0827, p=0.472 (not significant at 5% level).
  • R (Real interest rate): β4=−0.0091, p=0.916 (not significant at 5% level).
  • INC (Disposable income): β5=0.5459, p=0.001 (significant at 5% level).


    Conclusion:

  • Coefficients for HOURS and INC are significantly different from zero at the 5% level.
  • Coefficients for GOV and R are not significantly different from zero.



    Next, I will test the hypotheses H0:β2=0 and H0:β3=0. ​​

  • Results for Question (b) for Canada:
  • For β2​ (HOURS):
  • For β3​ (GOV):
  • Results for Question (c) for Canada:


    After omitting GOV , the coefficients are as follows:

  • Constant: 0.0078, p=0.052 (marginally significant).
  • HOURS: Coefficient increased from 0.4125 to 0.4525, p=0.000 (highly significant).
  • R (Real interest rate): Coefficient slightly changed from −0.0091 to −0.0025, p=0.976 (not significant).
  • INC (Disposable income): Coefficient decreased from 0.5459 to 0.4637, p=0.000 (highly significant).


    Conclusions:

  • Excluding GOV increases the importance of HOURS and reduces the influence of INC slightly.
  • Rtext{R}R remains insignificant and has minimal impact on the model.



    Next, I will estimate GOV based on HOURS, R, and INC for Question (d). ​​

  • Results for Question (d) for Canada:


    The model GOV = α1 + α2 HOURS + α3 R + α4 INC + v yielded the following estimates:

  • Constant: α1=0.0050, p=0.405 (not significant).
  • HOURS: α2=−0.4838, p=0.003 (significant at the 1% level, negative relationship).
  • R (Real interest rate): α3=−0.0790, p=0.547 (not significant).
  • INC (Disposable income): α4=0.9953, p=0.000 (highly significant).


    Reconciliation of (a) and (c):

  • The significant negative relationship between HOURS and GOV indicates that omitting GOV in part (c) amplifies the direct impact of HOURS on CSUMPTN .
  • The strong positive relationship between INC and GOV accounts for the reduced coefficient of INC when GOV is omitted in part (c).



    Next, I will re-estimate the models from parts (a) and (c) without the year 2007 and forecast consumption growth for that year for Question (e). ​​

    The error suggests a mismatch in the input dimensions for the 2007 forecasts. Let me adjust the predictors for each model to ensure they align with the parameter structures used during estimation. ​​

    • Results for Question (e) for Canada:

    Forecasts for consumption growth in 2007 based on the re-estimated models:

  • Model (a):
  • Model (c):
  • Results for Question (f) for Canada:


    The actual consumption growth in 2007 was 0.0295.

  • Model (a):
  • Model (c):
    • You analyzed the data of Japan and Canada and got the answers to these 6 questions. Next, please compare these two countries in your major and tell me what you found? What conclusion was reached?

    Comparative Analysis and Conclusions for Japan and Canada
    Based on the analyses of Japan and Canada regarding the six questions, the results reveal both similarities and differences in the determinants of private consumption growth between these two OECD countries. Here's a comparative summary:

  • 1. Determinants of Consumption Growth:
  • Japan:
  • Canada:
  • In both countries, INC (real disposable income) is a key driver of consumption growth, highlighting the critical role of income in sustaining private consumption.
  • GOV (government consumption) has limited direct influence in both contexts, indicating that public spending does not significantly complement or substitute private consumption.
  • Japan's sensitivity to R (real interest rate) suggests that monetary policy has a more noticeable impact compared to Canada.


  • 2. The Relationship Between Consumption and HOURS Worked (β2​):
  • Japan:
  • Canada:
  • The complementary relationship between HOURS worked and consumption implies that increased labor activity supports higher consumption levels in both economies. This reflects shared dynamics where employment and disposable income are tightly linked.


  • 3. The Role of Government Consumption (β3​):
  • Japan:
  • Canada:
  • In both countries, public sector activities appear to have an indirect rather than direct effect on private consumption.


  • 4. Model Re-Estimation Without GOV:
  • Japan:
  • Canada:
  • Removing GOV clarifies the direct relationships of other variables, particularly HOURS and INC, with private consumption.


  • 5. The Determinants of Government Consumption:
  • Japan:
  • Canada:
  • In both countries, higher disposable income supports increased government consumption, likely through taxation and spending policies. Conversely, increased labor activity may reduce reliance on government-provided services.


  • 6. Forecasting Accuracy for 2007:
  • Japan:
  • Canada:
  • In both countries, simpler models excluding GOV outperform more complex models, suggesting that government consumption's indirect role introduces noise rather than predictive power.


    Key Takeaways and Conclusions:
  • Income as the Dominant Factor:
  • Government Consumption's Limited Role:
  • Monetary Sensitivity Differences:
  • Work-Consumption Dynamics:
  • Model Simplicity for Forecasting:
  • Policy Implications:
  • Japan: Focus on monetary policy adjustments to influence consumption, and maintain stable income growth to support consumption.
  • Canada: Prioritize policies that enhance disposable income to drive private consumption, as monetary policy seems less effective than in Japan.
    This comparison highlights shared economic dynamics while identifying unique country-specific characteristics that can guide tailored policy-making.

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