ECON2300代做、代写Python/c++编程

ECON2300: INTRODUCTORY ECONOMETRICS Research Project Coordinator: Professor Alicia N. Rambaldi Due: 4:00 PM on 29 April, 2025. This project weighs 25% of your final overall mark. Total possible points = 100. Background From the seminal work of D. S. Evans (1987), “The Relationship Between Firm Growth, Size, and Age: Estimates for 100 Manufacturing Industries”1, macroeconomists have been interested in the determi- nants of firm growth as well as the role of the size (size of the workforce) and age (years since business start) of the firm. In this project you will be investigating whether changes in owners and managers over the life of the firm have a significant effect on the growth (annual sales) of the firm, and whether the effect depends on the size and age of the firm. The dataset ECON2300 Projectdata.csv contains data on 399 men’s clothing stores, containing the following variables: ? tsales: annual sales in thousand of Euros ? sales: sales per square meter ? margin: gross-profit-margin ? nown: number of owners (managers) ? nfull: number of full-timers ? npart: number of part-timers ? ncaus: number of causal employees (temporary workers) ? hoursw: total number of hours worked ? hourspw: number of hours worked per worker ? inv1: investment in shop-premises ? inv2: investment in automation. ? ssize: sales floor space of the store (in m2). ? age: age of business in years ? Other variables that might be needed for the analyses: – ln tsales = log(tsales), – ln nown = log(nown), – nown2 = nown ? nown, – ln age = log(age), 1https://doi.org/10.2307/2098588 1 – age2 = age ? age, – ln hoursw = log(hoursw), – hoursw2 = hoursw ? hoursw, – ln ssize = log(ssize), – ssize2 = ssize ? ssize, – hourspw age = hourspw ? age, – nown age = nown ? age, – D young = ifelse(age <= 37, 1, 0), – nown Dage = nown ?D young, – nown hoursw = nown ? hoursw, – lnown Dyoung = lnnown ?D young, – lnown lage = ln nown ? ln age, It will be very useful to run a summary of the dataset for further reference when completing the analyses. The key relationship under study will be: E(Annual Sales) = f(Number of Owners(managers), workforce(size of the firm), age of the firm, ..., other controls) You are to explore linear and non-linear relationships between the number of owners (managers), nown, and annual sales, tsales, as well as the roles and interactions of hoursw, a proxy for the size of the workforce, and age, the age of the firm. Presentation of Modelling Results and Submission of Project Report Please read this carefully ? For plots, your axes should be appropriately labelled and the plot should be titled. ? Please present estimated models in a table format, following Lecture 5, slide 30 as a template. Please use the following convention to denote statistical significance of coefficients: significant at the ?5% level, or ??1% level. ? Include the R code and output as an appendix section to the project report. The section should be labelled ”Appendix” and appear at the end of the project report. ? Please submit your project report via the submission link provided in the course’s Blackboard site. The submission must be a single “pdf” file. Projects submitted in any other format will receive a deduction of 5%. 2 Part 1: Visualisation - 10 points 1.(a) Plot the data for tsales againts nown. From the visual evidence, do you expect the relationship to be negative, positive, not significant? Provide a short paragraph explanation of your answer. (3 points) 1.(b) Plot the data for tsales againt hoursw. Provide a short paragraph highlighting the main fea- tures from the visual inspection, addressing the expected sign of the coefficient and evidence of heteroskedasticity. (2 points) 1.(c) Plot the data for tsales againt age. Provide a short paragraph highlighting the main features from the visual inspection, addressing the expected sign of the coefficient and evidence of het- eroskedasticity. (2 points) 1.(d) Provide a short summary paragraph based on the evidence gathered in (a) to (c), addressing the following: Do you expect number of owners (managers), size and age of the firm to be significantly related to total annual sales? and Do you expect any relationship between these variables to be non-linear? (3 points) Part 2: Linear Models - 30 points Please estimate the following models (using robust standard errors “HC1”) and present them in a table, labelled “Table 1: Linear Models”. 2.(a) Running correct models and presenting a complete Table 1: (8 points) – Models (1) - (4) tsalesi = β0 + β1nowni + ui (1) tsalesi = β0 + β1nowni + β2hourswi + ui (2) tsalesi = β0 + β1nowni + β2hourswi + β3agei + ui (3) tsalesi = β0 + β1nowni + β2hourswi + β3agei + β4ssize+ ui (4) – Model (5). Create a dummy variable to denote ”young” firms D young = 1 if age <= 37, D young = 0 otherwise. tsalesi = β0 + β1nowni + β2hourswi + β3D youngi + β4ssize+ ui (5) Considering the models in Table 1, please respond to the following questions: 2.(b) Why are we using 37 as the cut-off point to define D young? (Hint: Descriptive Statistics) (2 points) 2.(c) Comment on the sign of β1 and significance of the variable nown across the five models. Pro- vide a short paragraph to indicate why the observed pattern is consistent with our theoretical understanding. (Hint: Think about omitted variable bias) (3 points) 2.(d) Why are we estimating the models with robust standard errors? Estimate Model (5) assuming homoskedasticity and provide a short paragraph to indicate what differs between the two versions of the model (Hint: estimate using “lm(...)”, instead of “lm robust”(...)” (4.5 points) 3 2.(e) As stated in the Background, it is expected that firm size and age play a key role in firm per- formance. How do Models (4) and (5) provide empirical evidence towards this relationship and whether it is linear? You might also go back and look at Part 1 (c). (Hint: Think about “younger” vs older firms). Write a short paragraph. (4.5 points) 2.(f) Compute 95% Confidence Intervals for β1, the coefficient of our variable of interest, from Models (4) and Model (5). What do these indicate about the robustness of the modelling so far? Write a short paragraph. (4 points) 2.(g) Considering the estimates, Rˉ2 and RMSE, which model(s) from this analysis would you recom- mend as a base or benchmark model? Justify your response. (4 points) Part 3: Non-Linear Models - 25 points In this section we consider alternative functional forms. Please estimate the following models (using robust standard errors “HC1”) and present them in a table, labelled “Table 2: Non-Linear Models and Models with Interactions”. 3.(a) Running correct models and presenting a complete Table 2: (8 points) – Model (1) considers a quadratic form for the regressors, Models (2) and (3) are linear-log in form tsalesi = β0+β1nowni+β2hourswi+β3agei+β4ssizei+β5nown 2 i +β6hoursw 2 i +β7age 2 i +ui (1) tsalesi = β0 + β1ln nowni + β2ln hourswi + β3ln agei + β4ln ssizei + ui (2) tsalesi = β0 + β1ln nowni + β2ln hourswi + β3D youngi + β4ln ssizei + ui (3) – Models (4) - (5). These models have a log-linear form ln tsalesi = β0 + β1nowni + β2hourswi + β3agei + β4ssizei + ei (4) ln tsalesi = β0 + β1nowni + β2hourswi + β3D youngi + β4ssizei + ei (5) – Models (6) - (7). These models have a log-log form ln tsalesi = β0 + β1ln nowni + β2ln hourswi + β3ln agei + β4ln ssizei + ei (6) ln tsalesi = β0 + β1ln nowni + β2ln hourswi + β3D youngi + β4ln ssizei + ei (7) Considering the models in Table 2, please respond to the following questions: 3.(b) Looking at the estimation results from Model 1, would you say that a quadratic functional form is supported by the data? Please use relevant statistical tests to reach your conclusion. Show your work and explain in a short paragraph. (3 points) 3.(c) Looking at the estimation results from Models 2 and 3. Provide an interpretation of the magnitude of the effect of nown on tsales. Compute ?tsales?nown in each case, and compare it to that of your benchmark model. Show your work. (5 points) 3.(d) Can you use Rˉ2 or RMSE to compare the fit of Models 3 and 5? What about amongst Models 4, 5, 6 and 7? Explain in a short paragraph whether these are possible and state why this is the case. (3 points) 4 3.(e) What conclusion do you reach from Models 4-7 about the relationship between the number of owners (managers) and annual sales? Please use the relevant statistical tests to justify your response. Show your work and write a short paragraph with your conclusion. (2 points) 3.(f) Looking at the estimation results for Models 6 and 7, provide (in a short paragraph) the economic interpretation of the effect of hoursw, age, and D young on annual sales. (4 points) Part 4: Non-Linear Interaction Models - 20 points In this section we consider interactions. Specifically, we wish to establish if the effect of the number of owners (managers) on annual sales depends on the size and age of the firm. Please estimate the following models (using robust standard errors “HC1”) and present them in a table, labelled “Table 3: Models with Interactions”. 4.(a) Running correct models and presenting a complete Table 3: (8 points) – Model (1) and (2) are linear with interactions tsalesi = β0 + β1nowni + β2hourswi + β3agei + β4ssizei +β5nowni × agei + β6nown× hourswi + ui (1) tsalesi = β0 + β1nowni + β2hourswi + β3D youngi + β4ssizei +β5nowni ×D young + β6nown× hourswi + ui (2) – Models (3) and (4) are log-log with interactions ln tsalesi = β0 + β1ln nowni + β2ln hourswi + β3ln agei + β4ln ssizei +β5ln nowni × ln hourswi + β6ln nowni × ln agei + ei (3) ln tsalesi = β0 + β1ln nowni + β2ln hourswi + β3D youngi + β4ln ssizei +β5ln nowni × ln hourswi + β6ln nowni ×D youngi + ei (4) Considering the models in Table 3, please respond to the following questions: 4.(b) Looking at the estimation results from Models 1 and 2, test the significance of the effect of number of owners(managers) on annual sales. Show your work and explain in a short paragraph. (4 points) 4.(c) Looking at the estimation results from Models 3 and 4, test the significance of the effect of number of owners(managers) on annual sales. Show your work and explain in a short paragraph. (4 points) 4.(d) Using Model 4 estimates, Estimate the difference in tsales (computed in Euros) between D young =1 and D young = 0, when variables are at their mean value. Show your work. (4 points) Part 5 - Discussion and Conclusions - 15 Points In less than 200 words, please provide an overall conclusion from your analysis addressing the following: ? Is the number of owners(managers) a significant determinant of annual sales? Using your preferred model(s) provide estimates of the slope (one unit change in nown) and elasticity (1% change in nown). 5 ? Are the interactions of nown with the size and age of the firm important in explaining annual sales? Provide some numerical evidence from your analysis to illustrate