Lecture 3:
research process:

• Research questions, motivations and contribution
• Hypotheses
• Data
• Analysis
• Results
• Check whether the results confirm hypothesis

Correlation:

• Correlation coefficient r
• Bounded measure

Regression analysis:

1. simple bivariate regression: one single variable

• x1: explanatory variable; independent variable; regressor; predictor variable …
• y: dependent variable and outcome variable
• B0: intercept/constant
• B1: slope; regression coefficient for the variable x1 (size or magnitude of the effect x1 on y)
• E: error term
• We want to estimate B0, B1 ( you have estimated veriables

How to estimate:

• OLS: technique to best represent the linear relationship between x  and y (minimize the sum of standard deviations form the line) (minimize the sum of the squared residuals)
• How to draw a straight line: Find the one that best fits the data (goes through, or as close to, as many of the data points as possible)
• Minimize sum of the estimated errors

2. Multiple regression: two or more independent variables: we analyze the relation relationship between a single dependent variable and several independent variables

• The coefficient of each independent variable indicates change in dependent variable when the independent variable changes but all other independent variables remain constant (ceteris parisbus)

Dummy variables independent variables:

How many dummies to include:

With intercept include m-1 dummies the omitted one is the base/reference,  However if you have only two categories one dummy is sufficient to represent both. Otherwise, one is perfectly predicted  by the other (exact linear relationship) and the regression coefficients cannot be estimated.

Regression coefficients:

What to look for when interpreting:

1. Sign
2. Significance
3. Size, magnitude
4. Then interpret

• The regression coefficients b1 coefficient measures the amount of change in y due to change x1 while the other regressors are held constant (ceteris paribus)
• It represents the change in the DV for a one-unit increase in the IV while the other regressors are held constant.

Article:

What is about:

• LMEs vs CMEs
• Flexible vs rigid labour markets.
• What does this mean for management bureaucracies: starting point

Hypothesis:

• High shares of flexible workers à high shares of managers
• Labour market flexibility à lack of trust, loyalty, commitment à management and control required
• Labour market flexibility à Lack of learning and knowledge accumulation à bad for innovation and labour productivity growth

Why are we doing this:

• Insignificant or conflicting results in literature
• Sparse empirical work on topic
• Important to test the theory at the firm level
• The Netherlands represent an interesting case to do so: CME but with LME features

What are we looking at:

• Data source: SCP organization-level survey data. For the Netherlands à Data collection: telephone interviews plus a postal survey.
• Information on:

1. Organizations
2. From various sectors
3. Percentage of employees with managerial positions in an organization
4. Shares of flexible workers
5. Industry
6. Firm size

• Survey of 2009-10 is used

Theory à variables à data à model

• The substantial variation in shares of flexible workers (IV à combination of % of temporary workers and %  of manpower agency workers plus freelancers) allows analysing the impact of the latter on management rations (DV), controlling for a number of influential factors ( Fim size, growth, age, dummies for: restructuring operation; competitive market; sensitive to business fluctuations; industry dummies. How am I Supposed to know? à look at literature

A note on the regression equation:

• The hypothesis lead to the regression equation
• Sometimes the regression equation is explicitly presented in the paper
• Here, the regression equation is not presented, but you should be able to infer it from the text and/or regression table
• Choose key IV and then look at regression coefficient. Also look at significant level

Assessing your model:

• Goodness fit
• Coefficient of determination (R-squared):

1. Proportion of the variation in y that is explained by the linear combination of the x variables
2. Between 0 (no prediction) and 1 (perfect prediction)
3. In a bivariate linear regression, it equals the squared correlation coefficient
4. If r2 between 0.21 and .30, 30% of the variation in y is explained by the x’s

• R2 increases as we keep adding variables
• Adjusted coefficient of determination: Adjusted r2:

1. Modified measure of R2 that takes into account the number of independent variables and sample size
2. Some punishment for the inclusion of additional explanatory variables
3. When comparing between models, search for highest r2

• F test: A test for the overall significance of the model, tests whether all parameters are jointly zero b1=b2à compare to critical values of F-distribution or look at corresponding p-value or significance

Estimates and significance:

• Does my main IV have a significant impact on the DV
• How can I determine this: Statistical significantce (Compare to 0 and t-test)
• Note: statistical vs economic significane
• First formulate Null and alternative hypothesis H0 bj=0 h1: bj is not 0
• Choose the significance level
• Option 1:

• Option 2:

•  So if p-value<0.01, the estimate is significantly different from 0