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# Aqt instructor-notes-final

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### Aqt instructor-notes-final

1. 1. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES Lectures & Notes ADVANCED QUANTITATIVE TECHNIQUES (COURSE FOR PHD STUDENTS) By Dr. Anwar F. Chishti ProfessorFaculty of Management & Social Sciences 1
2. 2. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES ADVANCED QUANTITATIVE TECHNIQUES Course Plan Fall Semester 2012Course Instructor Professor Dr. Anwar F. Chishti Contacts: Phone Phone: 0346-9096046 Email anwar@jinnah.edu.pk; chishti_anwar@yahoo.comClass venue Computer Laboratory Course contentsTopic 1: Simple/Two-Variable Regression Analysis: • An introduction of estimated model and its interpretation, • Regression Coefficients and Related Diagnostic Statistics: Computational Formulas • Evaluating the results of regression analysis • Standard assumptions, BLUE properties of the estimator. • Take-home assignment - 1Topic 2: Simple Regression to Multiple Regression Analysis • Shortcomings of simple/two-variables regression analysis • An example of multiple regression analysis • Use of Likert-scale type questionnaire, raw-data entry, reliability test and generation of variables • Estimation of multiple regression model • Evaluation of the estimated model in terms of F-statistic, R2 and t- statistic/p-value • Take-home assignment - 2Topic 3: Multiple Regression: Model specification • 3.1(a) Conceiving research ideas and converting it into research projects: a procedure • 3.1(b) Incorporating theory as the base of your research: econometrics theory & economics/management theory • Take-home assignment – 3(a) • 3.2 (a) Specification of an econometric model: mathematical specification 2
3. 3. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES • 3.2(b) Some practical examples of mathematical specification: production-function specification, cost-function specification, revenue- function specification • Take-home assignment – 3(b) • 3.3(a) Conceptual/econometric modeling: (a) Examples in Finance; (b) Examples in Marketing; (c) Examples in HRM • 3.3(b) Incorporating theory as the base of your research: econometrics theory & economics/management theory • Take-home assignment: adopting, adapting and developing a new questionnaireTopic 4: Analyzing mean values • Analyzing mean value, using one-sample t-test • Comparing mean-differences of two or more groups • Comparing two groups * Independent samples t test * Paired-sample t test • Comparing more-than-two groups * One-Way ANOVA * Repeated ANOVA • Take-home assignment – 4Topic 5: Uses of estimated econometric models • Some examples • Take-home assignment – 5Topic 6: Relaxing of Standard Assumptions: Normality Assumption and its testing • Normality assumption • Its testing • Take-home assignment – 6Topic 7: Problem of Multicollinearity: What Happens if Regressors are Correlated? • Consequences, tests for detection and solutions/remedies • Take-home assignment - 7Topic 8: Problem of Heteroscadasticity: What Happens if the Error Variance is nonconstant? • Consequences, tests for detection and solutions/remedies • Take-home assignment - 8Topic 9: Problem of Autocorrelation: What Happens if the Error terms are correlated? • Consequences, tests for detection and solutions/remedies • Take-home assignment - 9Topic 10: Mediation and moderation analysis - I • Estimating and testing mediation 3
4. 4. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES • Take-home assignment – 10Topic 11: Mediation and moderation analysis - II • Estimating and testing moderation • Take-home assignment – 9Topic 12: Time-series analysis - I • Unit root analysis • Take-home assignment – 10Topic 13: Time-series analysis - II • Unit root, co-integration and error correction modeling (ECM) • Take-home assignment – 11Topic 14 Panel data analysis, Simultaneous equation models/Structural equation models • Panl data analysis • SEM, ILS, 2SLS and 3SLS • Take-home assignment – 12Topic 15 Qualitative response regression models (when dependent variables are binary/dummy) and Optimization • LPM, Logit model and Probit Model • Take-home assignment – 13(a) • * Optimization: minimization and maximization • Take-home assignment – 13(b)Topic 16 Welfare analysis: maximization of producer and consumer surpluses and minimization of social costsRequired Text & Recommended Reading The prescribed textbooks for this course are: Gujarati, Damodar N. Basic Econometrics, 4th Edition. McGraw-Hill. 2007 Stock, J. H. and Watson, M.W. Introduction to Econometrics, 3/E. Pearson Education, 2011Reference Books/Materials Studenmund, A.H. Using Econometrics: A Practical Guide, 6/E, Prentice Hall Asteriou, D. and Hall, S.G. Applied Econometrics – A Modern Approach. Palgrave Macmillan, 2007. 4
5. 5. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES Andren, Thomas. (2007). Econometrics. Bookboon.com Salvatore, D and Reagle, D. Statistics and Econometrics, 2nd Ed. Schaum’s Outlines. Instructor’s class-notes (hard copy at photo-copier shop)Assessment Criteria Details Due Date Weighting 10 best weekly assignments (out of total Individual Assignments 13 - 15, each having 2 marks) will be 20 % counted toward total 20% marks. A group of 2 students will select a topic, Group research on selected carry out research, complete a research 20 % research topics study, and make presentation in during the last classes of the semester Mid-term Examination As per University’s announcement 20 % Final Examination As per University’s announcement 40 % Total marks: 100 5
6. 6. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES Topic 1 Simple/Two-Variable Regression Analysis1.1 Simple regression analysis: an exampleAssuming a survey of 10 families yields the following data on their consumption expenditure (Y)and income (X). Y (Thousands) X (Thousands) 70 80 65 100 90 120 95 140 110 160 115 180 120 200 140 220 155 240 150 260The theory suggests that families’ consumption (Y) depends on their income (X); hence,econometric model may be specified, as follows. Y = f(X) (General form) (1a)Or Y = β0 + β1X + e (Linear form) (1b)The above stated regression analysis model contains two variables (one independent variable Xand one dependent variable Y); this model is therefore called Two-variables or Simpleregression analysis model.Is this type of Simple or Two-variable model justified? We will discuss this question later on;let’s first estimate this model, using the Statistical Package for Social Sciences’ software SPSS.The estimated model & interpretation Y = 24.4530 + 0.5091 X (2a) (6.4140) (0.0357) (Standard Error) (2b) (3.8124) (14.2445) (t-statistic) (2c) (0.005) (0.000) (p-value/sig. level) (2d) R= 0.981 R2 = 0.9621 R2adjusted = 0.957 F = 203.082 (p-value = 0.000) DW = 2.6809 N = 10 (2e)1.2 Regression analysis: computational formulasThe econometric model specified in (1) is estimated in the form of estimated model (2a) alongwith all its diagnostic statistics 2(b – e), using the formulas provided, as follows. 6
7. 7. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESThe coefficients ßs ∧ ∧ β0 = Y − β1 X (3) ∧ β1 = ∑ ( Xi − X ) (Yi −Y ) (4) ∑ ( Xi − X ) 2 ∧ β1 = ∑x y i i (5) ∑x 2 iVariances (σ 2) and Standard Errors (S.E): 2  ∧  ∧ ∑e 2 ∑Y  −Yi   i (6) σ =2 = ( N − 2) ( N − 2) ∧ Var ( β 0 ) = σ ∧ 2 = ∑ X .σ i 2 2 (7) N ∑x β0 2 i ∧ ∧ ∧ S .E ( β0 ) = σ β0 = σ β0 2 (8) ∧ ∧ σ2 Var ( β1 ) = σ β1 = 2 (9) ∑x 2 i ∧ ∧ ∧ S .E ( β1 ) = σ β1 = σ β1 2 (10) T-ratios: ∧ β0 Tβ0 = ∧ (11) σβ 0 ∧ β1 Tβ1 = ∧ σβ 11 (12) The Coefficient of Determination ( R2 ):  ∧  ESS ∑Y   i −Y   R2 = = TSS ( ∑Y i −Y ) (13) RSS = 1− TSS =1 − ∑ e 2 i ∑Y −Y ) ( 2 i F – Statistics: F = ESS df = ( R ) ( K −1)2 RSS df (1 − R ) ( N − K ) 2 (14) 7
8. 8. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES Durban-Watson (D.W) Statistics: 2 ∑(e − et −1 ) N t t =2 d = N ∑e t =1 2 t (15)1.3 Estimation of the model using computational formulasWe now use formula provided in (3) to (15), make computations like Table 3.3 (Gujarati,2007) and resolve the model, as follows. Yi = ßo + ß1 Xi + ℮i …….. Linear model (16)Regression Coefficients ( ß i ): ˆ β1 = ∑ xi . yi = 16800 = 0.5091 (17) ∑ xi2 33000 ∧ ∧ β0 = Y − β1 X = 111 − 0.5091 (170 ) (18) = 24.453Variances (σ 2) and Standard Errors (S.E): ∑e 2 ∧ 337.25 σ = 2 = = 42.15625 (19) ( N − 2) 10 − 2 ∧ Var ( β0 ) = σβ ∧ 2 = ∑X .σ i 2 2 = ( 322,000 ) ( 42.15625) 0 N ∑x 2 i ( 10 ) ( 33,000 ) = 41.13428 (20) ∧ ∧ ∧ S .E ( β0 ) = σ β0 = σ β0 2 = 41.13428 = 6.4140 (21) ∧ ∧ σ2 ˆ 42.15625 Var ( β1 ) = σ β1 = 2 = = 0.001277 ∑x 2 i 33,000 (22) ∧ ∧ ∧ S .E ( β1 ) = σ β1 = σ β1 2 = 0.001277 = 0.03574 (23) T-ratios: 8
9. 9. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES ∧ β0 42.453 Tβ0 = ∧ = = 3.8124 σβ 6.414 0 (24) ∧ β1 0.5091 Tβ1 = ∧ = = 14.2445 σβ 0.03574 11 (25) The Coefficient of Determination ( R2 ): R 2 = 1− ∑e 2 i =1 − 337.25 = 0.9621 ∑(Y −Y ) 2 8890 i (26) F – Statistics: F= ( R ) ( K − 1) 2 = 0.9621 ( 2 − 1 ) (1 − R ) ( N − K ) 2 0.0379 (10 − 2 ) (27) 0.9621 = = 203.082 0.0047375The estimated model: Y = 24.4530 + 0.5091X (6.414) (0.0357)  S.E. (3.812) (14.244)  t-ratio (0.005) (0.0000) (p-valuel) R2 = 0.9621 F = 203.082 N = 10 (28)1.4 Regression analysis: the underlying theoryThe above reported formulas reflect how various needed computations are carried out inregression analysis. Specifically, formula (4) estimates the coefficient (β 1) of explanatoryvariable X: ∧ β1 = ∑ ( Xi − X ) (Yi −Y ) ∑ ( Xi − X ) 2That is: ‘the deviations of individual observation on Xi from its mean, multiplied by deviations ofrespective Yi from its mean (cross-deviation), divided by the squares of the variations of Xi’; soit is the ratio between cross-deviations of X – Y variables and X variable. Theoretically, β1 9
10. 10. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESmeasures ‘total cross deviations/variations per unit of variation in X-variable’. The intercept β0measures ‘mean value of Y minus total contribution of mean of X’. ∧ ∧ β0 = Y − β1 X1.5 Error term: its estimation and importanceWhen an econometric model, like 1(b), is specified: Y = β0 + β1X + e (29a)It contains an error or residual term (e); but when model is estimated like 2(a): Y = 24.4530 + 0.5091X (29b)The error term (e) seems to disappear; where does the error term go?In fact the estimated model like 29(b) is valid only for the mean/average values of X and Y, andequality in 29(b) does not hold when values other-than-mean values are used; we can computevalues of error terms or residuals, using the following formula. Yi – Ŷ = e (30a) Yi – (24.4530 + 0.5091Xi) = e (30b)Putting individual-observation values from the original data, that is: Y X 70 80 65 100 90 120 95 140 110 160 115 180 120 200 140 220 155 240 150 260 Yi – (24.4530 + 0.5091Xi) = e 70 – (24.4530 + 0.5091*80 = 4.8181 (30c) 65 – (24.4530 + 0.5091*100) = -10.3636 (30d) 90 – (24.4530 + 0.5091*120 = 4.4545 (30e) 95 – (24.4530 + 0.5091*140) = -0.7272 (30f) 110 – (24.4530 + 0.5091*160) = 4.0909 (30g) 10
11. 11. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES 115 – (24.4530 + 0.5091*180) = -1.0909 (30i) 120 – (24.4530 + 0.5091*200) = -6.2727 (30j) 140 – (24.4530 + 0.5091*220) = 3.5454 (30k) 155 – (24.4530 + 0.5091*240) = 8.3636 (30l) 150 – (24.4530 + 0.5091*260) = -6.8181 (30m)As reflects from the above computations, error term reflects how much an individual Y deviatesfrom its estimated value. The values of error terms play important role in determining the size ofvariance Ϭ2 (computational formula 6), which further affects a number of other computations.A characteristic of error or residual term is that, once we add or take its mean value, it turns outequal to zero, in both cases.1.6 Evaluating the estimated modelAfter running regression, the results are reported usually reported in the following form. Y = 24.4530 + 0.5091X (31a) (6.4140) (0.0357) (Standard error) (31b) (3.8124) (14.2445) (t-statistic) (31c) (0.005) (0.000) (p-value/sig. level) (31d) R= 0.981 R2 = 0.9621 R2adjusted = 0.957 F = 202.868 (p-value = 0.000) DW = 2.6809 N = 10 (31e)The econometric model is specified in the form of 1 (a or b), estimated in the form of 31 (a) andevaluated, using the diagnostic statistic provided in 31(b – e). The estimated model’s evaluationis carried out, using three distinct criteria, namely: (a) Economic/management theory criteria (expected signs carrying with the coefficients of X-variables) (b) Statistical theory criteria (t statistic or p-value, F statistic, and R2) (c) Econometrics theory criteria (Autocorrelation, Heteroscadasticity & Multicollinearity)Economic theory criteria Questions: a) Are these results in accordance with the economic theory? b) Are they in accordance with our prior expectation? 11
12. 12. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES c) Do the coefficients carry correct sign? Answer: Yes, we expected a positive relationship between the income of a family and itsconsumption expenditure. The coefficient of income variable, X, is positive.Statistical theory criteria Question 1: a) Are the estimated regression coefficients significant? b) Are the estimated regression coefficients ßs individually statistically significant? d) Are the estimated regression coefficients ßs individually statistically different from zero? Answer: Here, we need to test the hypothesis: HO: ß1 = 0 H1 : ß1 ≠ 0 ß− 0 t= S .E = (.5091 – 0) / .0357 = .5091 / .0357 = 14.2605 (32)Our t calculated = 14.2605 > t tabulated = 1.86 at .05 level of significance, with df (N – k) = 8; hence, wereject the null hypothesis; the coefficient ß1 is statistically significant. Another way of checkingthe significance level of ßi coefficients is to check its respective p-value (Sig. level). In case ofthe coefficient of X-variable, the p-value = 0.00, suggesting that coefficient ß 1 is statisticallysignificant at p < 0.01. In this second case, we do not need to check the statistical significancelevel, using the t-distribution table appended at the end of some econometrics book; we candirectly check p-value provided next to the t-value in the output of the solved problem. Question 2: a) Are the estimated regression coefficients collectively significant? b) Do the data support the hypothesis that ß1 = ß2 = ß3 = 0 Here, we need to test the hypothesis: HO: ß1 = ß2 = ß3 = 0 H1: ßi are not equal to 0 Answer: Here, we use F-stattistic, namely: 12
13. 13. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES F = ESS df = ESS / K − 1 = ( R ) ( K −1) 2 RSS df RSS / N − K (1 − R ) ( N − K ) 2 (33) = 202.868Our F statistic (F = 202.868 > F 1, 8; .05 = 5.32) suggests that the overall model is statisticallysignificant. Like in case of t-statistics, the significance level of F-statistic can also be checkedfrom p-value given next to Fcalculated in the output of the solved problem. Question 3: Does the model give a good fit? Answer: Yes; our R2 = 0.9621 suggests that 96.21% variation in the dependent variable(Y) has been explained by variations in explanatory variable (X).Econometrics theory criteria 1) No Autocorrelation Criteria (We will discuss 2) No Heteroscadasticity Criteria (these criteria in detail 3) No Multicollinearity Criteria (later on in the course1.7 Interpreting the results of regression analysis The estimated results suggests that if there is one unit change in explanatory variable X(family’s income), there will be about half unit (.5091) change in dependent variable Y (family’sconsumption expenditure). If X and Y both are in rupees, then it means that there will be 51paisas increase in consumption expenditure if the family’s income increases by one rupee.1.8 Standard assumptions of Least-Square estimation techniquesThe linear regression model is based on certain assumptions; if these assumptions are notfulfilled, then we have certain problems to deal with. These assumptions are:1. Error term μ i is a random variable, and has a mean value of zero. ===> μ i may assume any (+), (-) or zero value in any one observation/ period, and the value it assume depends on chance. The mean value of μ i for some particular period, however, is zero, i.e., ∑ (μ i / xi) = 02. The variance of μ I is constant in each period, i.e., Var (μ i ) = б2 13
14. 14. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES This is normally referred to as homoscedasticity assumption, and if this Assumption is violated, then we face the problem of heteroscedasticity.3. Based on assumption 1 and 2 , we can say that variable μ i has a normal distribution, i.e., μ i ~ N(0, б2)4. Error term for one observation is independent of the error term of other observation, i.e., μ i and μ j are not correlated, or Cov (μ i and μ j ) = 0 This is no-serial-autocorrelation assumption, and if this assumption is violated, then we have autocorrelation problem.5. μ i is independent if the explanatory variables (X), that is, the μ i and μ j are not correlated. Cov (X μ ) = ∑{[Xi - ∑ (Xi)] [ μ i -∑ (μ i)]} = 0 6. The explanatory variable (Xi) are not linearly correlated to each other; they do not affect each other. If this assumption is violated, then we face the multicolinearity problem.7. There is no specification problem, that is, a) Model is specified correctly, mathematically, from the economic theory point of view. b) Functional form of the model ( i.e., linear or log-linear or any other form) is correct. c) Data on dependent and independent variables have correctly collected, i.e., there is no measurement error.1.9 BLUE properties of estimator: Given the aforementioned assumptions of the classical linear regression model, the Least -Square estimator (β) possess some ideal properties. 1. It is linear. 2. It is unbiased, i.e., its average or expected value is equal to its true value. ˆ Ε( βi ) = βi 14
15. 15. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES Biasness can be measured as: Bias ˆ = Ε( βi ) − βi − −−  ˆ Ε( βi ) = βi if Bias = 0 3. It is minimum- variance, i.e. it has minimum variance in the class of all such Linearunbiased estimators. 4. It is efficient. An unbiased estimator with the least variance is known as anEfficient estimator. From properly (2) and (3), our OLS estimator is unbiased and minimumvariance, so it is an efficient estimator. 5. It is BLUE, i.e., Best-linear-unbiased estimator.There is a famous theorem known as “Gaus-Markov Theorem” which tells: “Given the assumptions of the classical linear regression model, the least-squareEstimators, in the class of unbiased linear estimators, have minimum variance, So they arebest-linear unbiased estimators, BLUE”. Assignment 1 (Due in the next class)You have already received Gujarati’s (2007) ‘Basic Econometric’; study its relevant section tosolve the following assignment.. 1. Study sections 1.4 & 1.5: How does regression differ from correlation? 2. Read section 1.6: What are some other names used for dependent and independent variables? 3. Study section 1.7: What are different types of data? Explain each type in one or two sentences. 4. Study example 6.1 (page 168-169): Which of the two estimated model (6.1.12 & 6.1.13) is better and why? What do you learn from this example, in general. 15
16. 16. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES Topic 2 Simple Regression to Multiple Regression Analysis2.1 Shortcomings of two-variable regression analysisIn spite of providing the base for general regression, the simple or two-variable regression hascertain limitations; it gives biased results (of Least-Square Estimators, βs) if specified modelexcludes some relevant explanatory variables (namely X2, X3, …..).Let’s revisit to our first topic’s example of “Families’ Consumption’, wherein model wasspecified and run, as follows. Y = β0 + β1X + e = 24.4530 + 0.5091 X (6.4140) (0.0357) (Standard Error) (3.8124) (14.2445) (t-statistic) (0.005) (0.000) (p-value/sig. level) R= 0.981 R2 = 0.9621 R2adjusted = 0.957 F = 203.082 (p-value = 0.000) DW = 2.6809 N = 10 (2.1)If we recall, the results of this estimated model, while we evaluated in terms of economic theory(sign of the coefficient carrying with X) and statistical theory criteria (t-statistic/p-value, F-statistic and R2), were turned out to be reasonably acceptable. But, while we reconsider thespecification of the model, we will find that we had misspecified the model at the first place;according to the theory, consumption (Y) depends on income (X1), as well as, wealth of thefamilies (X2), prices of consumption items (X3), prices of the relatedproducts/substitutes/complements (X4), and so on. Hence, in spite of the fact that resultsprovided in (2.1) are apparently seem reasonable in light of the diagnostic statistic used, theestimated model provides biased results as it does not include some very important and relevantexplanatory variables.Solution then lies in the Multiple regression analysis, wherein all relevant explanatory variablesneed to be included, like the following one. Y = β0 + β1X1 + β2X2 + β3X3 + …………. + βNXN + e (2.2)Let’s take a practical example of using multiple regression analysis (see next sub-section 2.2). 16
17. 17. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES2.2 An example of multiple regression analysisIn case, research topic is: “Organizational justice and employees’ job satisfaction: a case of Pakistani organizations”Knowing that ‘organizational justice’ has 4 well identified facets, namely: 1. Distributive justice (JS) 2. Procedural justice (PS) 3. Interactive justice (IJ), and 4. Informational justice (INJ)Assuming that, if organizational justice prevails in Pakistani organizations, then employeeswould be satisfied (job satisfaction, JS); hence, respective econometric model may be specified,as follows. JS = f(DJ, PJ, IJ, INJ) (2.3)We may estimate this model in linear and/or log-linear form, that is: JS = α0 + α1DJ + α2PJ + α3IJ + α 4INJ + ei (Linear model) (2.4) lnJB = β0 + β1lnDJ + β2lnPJ + β3lnIJ + β4lnINJ + μi (Log-linear model) (2.5) (Note: ‘ln’ stands for natural log)Steps (to be taken):For estimation of linear model 1. As per requirements of the model specified in (2.3), we need to develop a questionnaire, like the one placed at Annex – I; and then collect the required data. 2. Enter the data collected on the employees’ responses in SPSS, using data editor (spreadsheet like that of EXCEL-spreadsheet). Check how data has been entered in file named: CLASS-EXERCISE-DATA_1. 3. Estimate reliability test (Chronbach’s Alpha) of the raw-data on employees’ responses, separately for each of the constructs used (JS, DJ, PJ, IJ & INJ). 4. Try to understand what reliability, validity and generalizability concepts stand for (see Annex – II). Interpret the results of reliability test (See ANNEX – III) 5. Generate data on variables of interest, namely: JS, DJ, PJ, IJ & INJ. 6. Run regression model specified in (2.4), and report the results. JS = 2.371 + 0.098DJ - 0.021PJ + 0.076IJ + 0.292INJ - 0.005AEE (9.882) (2.199) (-0.509) (1.905) (4.472) (-1.636) (0.000) (0.029) (0.611) (0.058) (0.000) (0.103) 17
18. 18. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES R= 0.506 R2 = 0.2560 R2adjusted = 0.2410 F = 17.71 (p-value = 0.000) DW = 1.5930 N = 264 (2.6) (Figures in the first and second parentheses, respectively, are t-statistics and p-values)Note: AEE stands for the combined figures of age, education and experience of the employees,and have been included to capture the combined effects of these variables.For estimation of log-linear model 7. Convert newly generated data on JS, DJ, PJ, IJ & INJ and AEE into their logs 8. Run model 2.5, and report the results lnJS = 0.943 + 0.156lnDJ - 0.015lnPJ + 0.080lnIJ + 0.308lnINJ - 0.084lnAEE (4.594) (2.829) (-0.308) (1.554) (4.506) (-1.645) (0.000) (0.005) (0.758) (0.122) (0.000) (0.101) R= 0.522 R2 = 0.2720 R2adjusted = 0.2580 F = 19.309 (p-value = 0.000) DW = 1.618 N = 264 (2.7)Evaluation and interpretation of the estimated modelsLinear model 2.6 (a) Model is found statistically significant (F = 17.71, p < 0.01); though all the explanatory variables included in the model seem to have explained around 25 percent variance in the dependent variable (R2 = 0.2560; R2adjusted = 0.2410). (b) Variable PJ appears to be highly statistically insignificant (p = 0.611), compared to variables INJ and DJ with highly statistically significant contribution (p < 0.01 & p < 0.05 ) and variable IJ and AEE with moderately statistically significant contribution (p = 0.058 & p = 0.103). (c) Results suggest that variables INJ, DJ and IJ positively contribute towards determination of employees’ job satisfaction, AEE negatively contributes while PJ does not contribute. The negative relationship of AEE with JB suggests that employees of higher age, with relatively higher education and experience, are less satisfied from their jobs. 18
19. 19. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESLog-linear model 2.7 (a) Since the two formulations of the data (nominal-data and log-data), used in linear and log-linear models, differ from each other, we cannot compare results of one model with that of the other. However, we expect relatively better results from a log-linear model; so we can discuss whether or not the results have been improved. Yes, results are relatively improved, especially in terms of F-statistic and t-statistic/p-values. Model is found statistically significant (F = 19.309, p < 0.01); the explanatory variables explain around 27 percent variance in the dependent variable (R 2 = 0.2720; R2adjusted = 0.2580). (b) Log-linear model reinforces the results regarding signs and significance values of the individual explanatory variables. (c) Results (of the both models) suggest that facets like informational justice, distributive justice and informational justice appear to be positively contributing towards employees job satisfaction, as compared to the procedural justice, which needs to be taken care of for an overall satisfaction of Pakistani organizational employees. In addition, the senior, more educated and more experienced employees also need attention as they appear to be mostly dissatisfied from their jobs. 19
23. 23. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES ANNEX - II Credibility of research findings: important considerations (Reliability? Validity? Generalizability?)Reliability: Reliability can be assessed by posing three questions: 1. Will the measure yield the same results on other occasions? 2. Will similar observations be reached by other observers? 3. Is the measure/instrument stable and consistent across time and space in yielding findings?4-Threats to reliability (i) Subject/participant error (ii) Subject/participant bias (iii) Observer error and (iv) Observer’s biasValidity: Whether the findings are really about what they appear to be about.Validity depends upon: History (same history or not), Testing (if respondents know they are being tested), Mortality (participants’ dropping out), Maturation (tiring up), and Ambiguity (about causal direction).Generalizability: The extent to which research results are generalizable. 23
24. 24. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES ANNEX – III Reliability test and interpretationReliability test resultsResponses on the elements of all five constructs (JS, DJ, PJ, Ij & INJ) were entered on SPSS’sdata editor and reliability tests were conducted; the following Cronbach’s Alphas wereestimated. Table 4.4 Results of reliability test Construct Cronbach’s Alpha Job Satisfaction (JS) 0.739 Distributive Justice (DJ) 0.828 Procedural Justice (PJ) 0.890 Interactional Justice (IJ) 0.920 Informational Justice (INJ) 0.834InterpretationAccording to Uma Sekaran (2003), the closer the reliability coefficient Cronbach’s Alpha gets to1.0, the better is the reliability. In general, reliability less than 0.60 is considered to be poor, thatin the 0.70 range, acceptable, and that over 0.80 and 0.90 are good and very good. The reliabilitytests of our constructs happened to be in the acceptable to good and very good ranges. 24
25. 25. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES ANNEX - IV Formulating and clarifying a research topic1Part – I: Two major questions: 3. What are three major attributes of a good research topic? 4. How we can turn research ideas into research projects Three major attributes of a good research topic are • Is it feasible? • Is it worthwhile? • Is it relevant?Capability: is it feasible? » Are you fascinated by the topic? » Do you have the necessary research skills? » Can you complete the project in the time available? » Will the research still be current when you finish? » Do you have sufficient financial and other resources? » Will you be able to gain access to data?Appropriateness: is it worthwhile? » Will the examining institutes standards be met? » Does the topic contain issues with clear links to theory? » Are the research questions and objectives clearly stated? » Will the proposed research provide fresh insights into the topic? » Are the findings likely to be symmetrical? » Does the research topic match your career goals?Relevancy: is it relevant? » Does the topic relate clearly to an idea you were given - possibly by your organisation? Turning research ideas into research projects • Conceive some research idea • Think about research topic (having attributes stated above) • Write research questions • Develop research objectives1 This discussion is based on materials contained in chapter 2 of Saunders, M., Lewis, P. and Thornhill, A. (2011)Research Methods for Business Students 5th Edition. Pearson Education 25
26. 26. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESPart – II: Research topics proposed by MS-ARM studentsARM (section – 2)Performance appraisal as a tool to motivate employees: a comparison of public-private sectororganizationPerformance appraisal in ……………….. (name of organization)Marketing communication and brand loyaltyImplementation of Integrated Management System (IMS) in Pakistan Civil Aviation AuthorityInformation technology and financial servicesCapital structure and firms profitabilityInterest rates, imports, exports and GDPIntra-Group Conflict and Group PerformanceHR practices across public and private organizationsHR practices across SMEs and large companiesHR practices across manufacturing and services sector companiesCorporate governance practices in banking sector of PakistanCorporate governance practices in textile industryCorporate governance practices in pharmaceutical industryEffects of working capital management on profitabilityWorking capital with relationship to size of firmWorking capital and capital structureOptimizing working capitalDividend policy and stock pricesSales, debt-to-equity ratio and cash flowsRelationship between KSE’s, LSE’s and ISE’s stock pricesGold prices and stock exchange indicesInterest rates, bank deposits and private investmentsSecurity Market Line (SML) & Capital Market Line (CML) at KSERelationship between stock market returns and rate of inflation 26
27. 27. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESRelationship between CPI and Bond pricePakistan’s exchange rates with relation to major global currency regimes: an analysisARM (section – 3)Trade deficit, budget deficit and national incomePerformance appraisal and its outcomesImpact of compensation on employee’s job satisfactionHuman resource management & outsourcingAdvertising and brand imagePerformance management in public sector organizationsImpact of training on employees’ motivation and retentionImpact of performance appraisalFinancial returns, returns on shares, equity returns and share pricesFactors contributing towards employee turnover intentionAntecedents of employees’ retentionEmployees’ retention policies and employees’ turnoverImpact of training and development on employees’ motivation and turnover intentionOutsourcing human resource function in Pakistani organizationsExploring the impact of human resources management on employees’ performanceService orientation, job satisfaction and intention to quitBrand equity and customer loyalty: a case of …….. (name of orhanization)PTCL privatization: effects on employees’ moralePTCL privatization: effects on employees’ efficiencyPTCL privatization: effects in terms of profitabilityElectronic and traditional banking: how do customers’ perceive?FPI and FDI in Pakistan: a comparative analysisStock market indices: KSE, LSE and ISE comparedWork family conflict and employee job satisfaction: moderating role of supervisor’s support 27