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Aqt instructor-notes-final

  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; 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. 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
  20. 20. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES Assignment 2 (Due in the Next Class)1. Briefly explain (in bullet-points) what the major contribution is that of simple/two- variables regression model, and why we have to resort to multiple regression analysis.2. Go through the steps suggested for estimation of a linear-regression model; what is the difference between a linear and log-linear model? (a) How do the steps of estimation of a log-linear model differ from that of linear model? (b) How do the interpretations of the two model differ?3. What is reliability? How is reliability test run in SPSS? Why is the running of reliability test important?4. What is the procedure of generating data on variables of interest? How is a Likert-scale questionnaire used for generation of data on variables of interest?5. How are and for what purposes, F-statistic, R2 and t-statistic/p-values used for the evaluation and interpretation of estimated models?6. Study material (entitled “Formulating and clarifying a research topic”) provided in Annex – IV: (a) In Part – I (of Annex – IV), the answers of the following two questions have been provided: 1. What are three major attributes of a good research topic? 2. How can we turn research ideas into research projects? (b) In Part – II, you have been provided two lengthy lists of research topics proposed by my MS ARM’s class students of section 2 & 3. You please select one topic of your choice (select topic in light of what you have learnt from materials provided in Part – I), develop 2 – 3 research questions and 4 – 5 research objectives, and submit me through email ( &, latest by 12.00 (Noon) Monday; please note: we will discuss your selected topic along with research questions and objectives in Monday’s evening class (along with the remaining/leftover part of previous Lecture – 2). Please also note: you may suggest a topic of your own (not already enlisted), along with research questions and objectives. Whether you select a topic from our list or suggest the one from your own side, two students of my ARM class will assist you to carry out research on that topic, as part of your AQT class requirements, for a 20% marks. 20
  21. 21. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES ANNEX – I (Questionnaire) Section IYour Organization (Tick 1 or zero): Government = 1 2. Private = 0Your gender (Tick 1 or zero): Male = 1 2. Female = 0Your age (in years like 25 years, 29 years,)Your education (actual total years of schooling, like 14 years; 18 years)Your area of specialization:Your job title in this organization:Experience: Working years in this organization: Section IIStrongly disagree – 1 Disagree = 2 Not disagree/neither agreed = 3 Agreed = 4 Strongly agreed = 5JS: Job satisfaction (Agho et al. 1993; Aryee, Fields & Luk (1999)) 1 2 3 4 51 I am often bored with my job (R)2 I am fairly well satisfied with my present job3 I am satisfied with my job for the time being4 Most of the day, I am enthusiastic about my job5 I like my job better than the average worker does6 I find real enjoyment in my work Organizational Justice (Niehoff and Moorman (1993)) Strongly disagreed = 1 Slightly disagree = 2 Disagree = 3 Neutral (Not disagree/neither agreed) = 4 Agreed = 5 Slightly more agreed = 6 Strongly agreed = 7 Distributive justice items (DJ) 1 2 3 4 5 6 71 My work schedule is fair2 I think that my level of pay is fair3 I consider my workload to be quite fair4 Overall, the rewards I receive here are quite fair5 I feel that my job responsibilities are fair Procedural justice items (PJ) 1 2 3 4 5 6 71 Job decisions are made by my supervisor in an unbiased manner2 My supervisor makes sure that all employee concerns are heard before job decisions are made3 To make formal job decisions, supervisor collects accurate & complete information4 My supervisor clarifies decisions and provides additional information when requested by employees5 All job decisions are applied consistently across all affected employees6 Employees are allowed to challenge or appeal job decisions made by the supervisor Interactive justice items (IJ)1 When decisions are made about my job, the supervisor treats me with kindness and consideration2 When decisions are made about my job, the supervisor treats me with respect & dignity3 When decisions are made about my job, supervisor is sensitive to my own needs4 When decisions are made about my job, the supervisor deals with me in truthful manner 21
  22. 22. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES5 When decisions are made about my job, the supervisor shows concern for my rights as an employee6 Concerning decisions about my job, the supervisor discusses the implications of the decisions with me7 My supervisor offers adequate justification for decisions made about my job8 When decisions are made about my job, the supervisor offers explanations that make sense to me9 My supervisor explains very clearly any decision made about my job Strongly disagree – 1 Disagree = 2 Not disagree/neither agreed = 3 Agreed = 4 Strongly agreed = 5 Informational justice items (INJ) 1 2 3 4 51 Your supervisor has been open in his/her communications with you2 Your supervisor has explained the procedures thoroughly3 Your supervisor explanations regarding the procedures are reasonable4 Your supervisor has communicated details in a timely manner5 Your supervisor has seemed to tailor (his/her) communications to individuals’ specific needs. 22
  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
  28. 28. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES Topic 3 Multiple regression: model specification3.1(a) Conceiving research ideas and converting it into research projects: a Procedure Procedure: Research ideas à research topic à research questions à research Objectives à research hypothesesYour Take-home Assignment 2’s question 6 has set the example how research ideas and topicsare converted in to research projects, adopting the procedure detailed above. Students have alsoprovided details of their chosen topics; let’s discuss those topics and clarify them further,judging them in light of the relevant theories (section 3.1b).3.1(b) Incorporating theory as the base of your researchEconometrics theoryPlease study section 7.2 and 7.3 of Andren (2007)2 and try to understand what difference itcreates when we omit a relevant explanatory variable or include an irrelevant one in aneconometrics model.Economics/management theoryLet us evaluate whether the research projects you have proposed are based on the relevanteconomic/management theory, and if not, then how you can incorporate the relevant theory intoyour projects. Discussion on your proposed research projects (You need to take notes on suggestions for improvements, and submit the improved version of your research project as part of your next assignment 3 (a). (See Annexure – I for topics for discussion Assignment 3 (a)1. You must have taken the notes on suggestions made during our class discussion on your respective research projects; you please refine your topics and research questions and objectives, in light of the discussions as well as what the following research articles suggest2 Andren, Thomas. (2007). Econometrics., pp.74-77 28
  29. 29. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESregarding basing your research on relevant theory (soft copies of papers are provided onAQT-Class Yahoo Group). Article/Note: ‘Formulating a Research Question’ Rogelberg, Adelman & Askay (2009). Crafting a Successful Manuscript: Lessons from 131 Reviews. J Bus Psychol (2009) 24:117–121 (Study only 8-points given under heading ‘Conceptual and/or theoretical rationale’.) Thomas, Cuervo-Cazurra & Brannen (2009). From the Editors: Explaining theoretical relationships in international business research: Focusing on the arrows, NOT the boxes. Journal of International Business Studies (2011) 42, 1073–1078 (Read only ‘Abstract’ and ‘Introduction’ sections, and try to understand Figure 1 (Typical conceptual diagram). Andren, Thomas. (2007). Econometrics. (Read only sections 72 & 73, pp.74-77) 29
  30. 30. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES Topic 3 Multiple regression: model specification….continuesIn sub-section 3.1(a), we carried out an exercise on how a conceived research idea can beconverted in to a research projects (Research ideas à research topic à research questions àresearch objectives). In sub-section 3.1(b), we tried to learn how much important theeconometrics (omission and inclusion of relevant and irrelevant explanatory variables) andeconomics/management theories are for specification of an econometrics model. In this newsubsection 3.2, we will try to learn what role different mathematical formulations can play ineconometrics modeling 3.2 Specifying an Econometric Model: Mathematical SpecificationThis section further consists of two subsections, namely: 3.2(a) Specification of an econometric model: mathematical formulation in general 3.2(b) Some practical examples of mathematical formulations/specifications: production function, cost-function and revenue function3.2(a) Specification of an econometric model: mathematical formulation in generalOur discussion in earlier sections on simple regression and multiple regression analysis clarifiestwo major points, namely: 1. The simple and multiple regression analysis assumes that variable Y depends on variable X, but for this phenomenon of dependence or causation, the researcher takes insights from the basic theory (economics/management). 2. Previous discussion further emphasizes that it is the researcher’s responsibility to specify an econometric model such that it contains all major relevant explanatory variables as independent variables; otherwise, empirical results obtained in terms of estimated coefficients would be biased.While specifying a model, the researcher has to take the above points in to consideration.Additionally, the researcher has to decide which mathematical formulation of the model he/sheshould use so that the true relationship between dependent and independent variables is capturedto the maximum extent. This is how an econometric model is/should be specified. 30
  31. 31. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESLet’s proceed further, taking some practical examples of mathematical formulations of themodel. In case, we have the following type of relationship between Y – X variables: Y Y Y X X X Case 1 (a) Case 1 (b) Case 1 (c)Case 1a is a general linear relationship, and can be measured, as follows. Y = β0 + β1X1 + e (3.1)In 3.1, we expect β1to carry positive sign.The case 1(b) represents an exponential case, and can be measured, as follows: 2 Y = β0 + β1X1 + β2X 1 + e (3.2)Specially, the parameters β1and β2 will carry positive signs.In case of a cubic-type of relationship like 1(c), the following mathematical formulation will have to beadopted. 2 3 Y = β0 + β1X1 + β2X 1 + β3X 1 + e (3.3)The coefficients β1and β2 will carry positive but β3 negative sign.In other words, it means that if we have to measure the stated type of relationships betweenour Y – X variables, we need to use the relevant type of mathematical formulations whilespecifying our econometrics model.In certain other cases/on certain occasions, we have to adopt some other mathematicalformulations like the following ones: Y = β0 + β1X1 + β2X1X2 + β3X2 + e (3.4) 2 2 Y = β0 + β1X1 + β2X 1 + β3X1X2 + β4X2 + β5X 2 + e (3.5) 31
  32. 32. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESEquation 3.4 measures linear relationship, but includes an interaction term (X1X2). β2 can takeany sign (+, - or 0); a positive sign would show positive effect of the interaction of X 1 and X2 on Y, anegative sign would mean negative effect of interaction of these two variables and zero effectwould mean zero effect on dependent variable Y. Let’s visit some practical examples where wecan use some of the above stated mathematical formulations (next section).3.2(b) Some practical examples: production, cost and revenue functionsProduction functionIn case, we have data on production of product Y, wherein two major inputs used are X 1 and X2: Y X1 X2 2500 1 150 2525 2 152 2555 3 155 2592 4 159 2635 5 161 2677 6 169 2718 7 174 2745 8 178 2766 9 181 2781 10 182Let’s check relationship between Y – X1, and Y – X2 (separately), using mathematical formulation givenin (3.3), using data provided in above table. Do this as Take-home Assignment 3b (Question 1); show the estimated relationship through hand-drawn graphLet’s check relationship between Y and X1 & X2, using mathematical formulation given in (3.4), usingdata provided in the above table. Do this as Take-home Assignment 3b (Question 2); interpret the results, including that of the interaction term 32
  33. 33. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESCost FunctionCost function can be developed when you have data like the following one: Y TC 1 193 2 226 3 240 4 244 5 257 6 260 7 274 8 297 9 350 10 420Mathematical formulation of a typical cost-function is: 2 3 TC = β0 + β1Y - β1Y + β1Y + e (3.6)Did you notice the signs of a typical cost-function are opposite to that of a typical production-function(given in 3.3). Estimate cost-function 3.6 as Take-home Assignment 3b (Question 3); show the estimated relationship through hand-drawn graph Assignment 3b: Question 4 Download 8 – 10 published research articles on the area of research/topic you have chosen for your class research project, study the conceptual models tried in these research articles, and develop your own model, including the mathematical one as part of your Take-home Assignment 3(b), due in next class; be ready for a class presentation also. 33
  34. 34. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES Topic 3 Multiple regression: model specification….continues 3.3 Conceptual/econometric modeling 3.3 (a) Examples in Finance 3.3 (b) Examples in Marketing 3.3 (c) Examples in HRM3.3 (a) Examples in Finance: summaryExample 1: Interest rates and GDP: a case of PakistanExample 2: Capturing effects of interest rates on Pakistani economyExample 3: Exchange rates and Pakistan’s trade: an analysisExample 4: Exchange rates and Pakistan’s economy: an analysisExample 5: Research on Working Capital (WC) Proposal 1: “Relationship between Profitability and Working Capital Management”, using econometric technique Proposal 2: “Liquidity-profitability trade-off”, using Goal programming (ofOperations Research) 34
  35. 35. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES3.3 (a) Examples in FinanceExample 1: Interest rates and GDP: a case of Pakistan3Though we are interested in analyzing the effect of interest rates on Pakistan’s national income,but we know that interest rates do not affect GDP directly, rather these affect saving (bankdeposits) and private investments, and as a consequence GDP is affected; so we conceptualizethe path of the effect, as follows: Interest rates (↑↓) à bank deposits (↑↓) & private investments (↓↑) à GDP (↓↑)The above path of the effect (of interest rates) can be captured, through econometrics model,postulated, as follows. Private investment = ƒ(Interest rates) (3.7a) GDP = ƒ(Private investments_predicted in equation 7a) (3.7b)Theory tells us that private investment (PI) is influenced not only by the interest rate (R) but isalso affected by openness of the economy (OE) and, especially the costs and taxes (C&T).Hence, equation 3.7a would change to: PI = ƒ(R, OE, C&T) (3.8a) ̂The private investment predicted on the basis of equation 3.8a (PI) is not the only determinant ofGDP, government expenditure (GE) or budget spending is another determining variable; while inPakistani context, Foreign Direct Investment (FDI) and Pakistan’s productive population, that is,the active labor force (LF) are two other factors should be considered as determinants ofPakistan’s national income (GDP). Hence, model 3.7b would change, as follows. ̂ GDP = ƒ(PI, GE, FDI, LF) (3.8b)The model postulated in 3.8 (a – b) still needs improvement; government expenditure (GE) andFDI are not autonomous in nature, the former depends on government revenues (GR) andgovernment borrowing from foreign (FB) and domestic (DB) sources, and the latter depends3 Students are urged to think over the difference between topic of this Example 1 and that of Example 2, and then tryto understand how conceptual/econometric modeling can be differently developed to take care of the differenceswhich the two topics necessitate. 35
  36. 36. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTES upon economy’s openness (OE) and cost of production and taxes (C&P). To incorporate theseeffects, the model would therefore adopt the following form. PI = ƒ(R, OE, C&P) (3.9a) GE = ƒ(GR, FB, DB) (3.9b) FDI = ƒ(OE, C&P) (3.9c) ̂ ̂ ̂ GDP = ƒ(PI, GE, FDI, LF) (3.9d)Model 3.9 (a – d) represents what we need to do for a piece of research conducted under title“Interest rates and GDP: a case of Pakistan”. In case we extend the scope of our research to whatis needed under title “Capturing effects of interest rates on Pakistani economy”, we will thenhave to adopt the model specified in the following Example 2.Example 2: Capturing effects of interest rates on Pakistani economyNotice the difference between the two topics (Example 1 and 2); the first topic requiresanalyzing the effect of exchange rates on GDP, while the second topic asks for looking in to thesame thing from a little broader perspective, that is, from the point of view of whole economy.Since the model specified for the first topic covers largely the methodology needed for thesecond topic, we can use the same first example model 3.9 (a – d), with an additional equationfor analyzing the effect of interest rates on bank deposits, which can be assumed to bedetermined by money supply in the country (M), in addition to the interest rates (R). Bank deposit = ƒ(R, M) (3.9e)Hence, model 3.9 (a – e) will be used for the piece of research identified in example 2.Example 3: Exchange rates and Pakistan’s trade: an analysis4According to the theory, the appreciation or depreciation of exchange rates (ER) affects thecountry’s trade; appreciation of a country’s currency makes exports expensive and importscheap, and depreciation makes exports cheap and imports expensive. This stated phenomenon istrue for the two trade partners, but is also affected by certain other situations prevailing in thetwo trading countries. The foreign country’s exchange rates with respect to her other major trade4 Students are urged to think over the difference between topic of this Example 3 and that of Example 4, and then tryto understand how conceptual/econometric modeling can be differently developed to take in to account thedifferences which the two topics necessitate. 36
  37. 37. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESpartners, availability and prices of the substitutes in foreign country and world over, consumers’income, trade openness and political situations are some other important factors affecting exportand import trade. Tracing and finding out the effects of the determinants of export and import trade might be easywhen trade of certain known commodities between two specific countries is analyzed; but thecase becomes cumbersome, and needs extra care when analysis of trade is required at aggregatelevel, for instance the topic of this piece of research - Exchange rates and Pakistan’s trade: ananalysis.We can think primarily about some very simple questions like what the exchange rates are(definition), how these are determined (or are autonomous in nature), they affect what and how,and specifically what relationship they have with trade – its two components, imports andexports. And since we are analyzing the exchange rates of Pakistan and her trade, we shouldthink over the answers of such questions in the context of Pakistan’s economy.Exchange rates (ER) are not autonomous in nature, these are determined by the forces of demandfor and supply of major medium of currency (US dollar in Pakistan) used in imports and exportstrade. Value of imports seems to be the major factor to determine demand for US dollar inPakistan, and while value of exports, workers’ remittances (WR), foreign direct investment(FDI) and foreign borrowings (FB) appear to be the major determinants of supply of dollar.Hence, these demand and supply factors determine exchange rates in Pakistan, which in turnaffect volumes of import and export. ER = ƒ(IM, EX, WR, FDI, FB) (3.10) ̂ IM = ƒ(ER) (3.11) ̂ EX = ƒ(ER) (3.12)But ER̂ is not the only determinant of import (IM). Imports in Pakistan have historically beenlargely composed of capital goods (28% in 1980-81 and 24% in 2010-11) and industrial rawmaterials (58% in 1980-81 and 60% in 2010-11)5; the value of the share of Pakistan GDP’smanufacturing sector (GDPM) may therefore be included in equation 3.11 as proxy to representthe demand for imports, in addition to the population or its growth rate (POP) as proxy for thesize of the market. Hence, equation 3.11 adopts new form, namely: ̂ IM = ƒ(ER, GDPM, POP) (3.13)5 Government of Pakistan (2012). Pakistan Economic Survey 2011-12. Statistical Appendix Table 8.5B 37
  38. 38. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESIn case of exports, primary commodities and semi-manufactured and manufactured productshave been the major components, with share of 44% in 1980-81 and 18% in 2010-11, 11% in1980-81 and 13% in 2010-11 and 45% in 1980-81 and 69% in 2010-11, respectively 6. The valuesof the primary (GDPP) and secondary/manufacturing sectors’ contributions to GDP (GDPM)may therefore be included in equation 3.12 as proxies to represent major supplying sectors ofexports. The demand for Pakistani exports has come from both developed (60.8% in 1990-91 and44.5% in 2010-11) and developing (39.2% in 190-91 and 55.5% in 2010-11) countries 7, theworld’s GDP can be taken as proxy to represent demand from the whole world (GDPW). Hence,equation 3.12 adopts the new form, namely: ̂ EX = ƒ(ER, GDPP, GDPM, GDPW) (3.14)Summarizing the model, ER = ƒ(IM, EX, WR, FDI, FB) (3.15a) ̂ IM = ƒ(ER, GDPM, POP) (3.15b) ̂ EX = ƒ(ER, GDPP, GDPM, GDPW) (3.15c)We can add even some other relevant variables and improve the model (model 3.15), andreviewing the relevant literature on respective topics and sub-topics, with special reference toPakistan, would help us in this regards.Please note that model 15 (a – c) will restrict research to the analysis of the effects of exchangerates on Pakistan’s trade; in case, if someone is interested to analyze the exchange rates’ effectson Pakistan economy (or GDP), then model specified in following Example 4 should be used.Example 4: Exchange rates and Pakistan’s economy: an analysisModel specified in 3.15 (a – c) will work as the base to analyze the effect of exchange rates onimport and export trade, and incorporation of an additional equation (3.15d), which transfers the ̂ ̂effects of imports (IM) and exports (EX) to GDP will help complete a model for the analysisnecessary for new topic. ̂ ̂ GDP = ƒ (IM, EX, POP) (3.15d)The effect of the size of population (POP) has been included as a proxy for the effect of domesticconsumption on country’s GDP.6 Government of Pakistan (2012). Pakistan Economic Survey 2011-12. Table 8.5A7 Government of Pakistan (2012). Pakistan Economic Survey 2011-12. Table 8.7 38
  39. 39. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESExample 5: Research on Working Capital (WC)Working capital: in generalWorking capital is defined as8: Working Capital (WC) = current assets (CA) - current liabilities (CL) (3.16a) Where Current assets are cash and other assets that can be converted to cashwithin a year, and Current liabilities are obligations that the company plans to pay off within the year.Working capital indicates the assets the company has at its disposal for current expenses. Theprocess of managing the WC efficiently is called Working capital Management. An excess ofworking capital many mean that the company is not managing its assets efficiently. Its not using itsassets to get a bigger return or better profit. An aggressive company may keep its working capitalsmaller. But a very low working capital may mean the company may not be suited well enough topayoff its short term obligations.This decision of how to manage the working capital of the company depends on the Workingcapital policy of the company. An important factor that determines the policy is the industry in whichthe company operates. For Example, an IT service company may not have a lot of shot-debt interms of inventory but it still needs to pay wages, insurances and other expenses like rent. Thecompany needs to have a policy that makes sure it sets targets were it gets paid as the projectprogresses so it can keep paying its staff in time. The company has to manage its accountreceivables according to this policy. Some industries operate in a high profit margin that they canafford to have a longer term on the account receivables because the higher cash balance part of thecurrent assets. The Collection Ratio helps project this aspect of a company; The collection ratio isdefined as: Collection Ratio = Accounts Receivable / (Revenue/ 365) 3.16b)Collection ratio tells us the average number of days it takes a company to collect unpaid invoices. Aratio which is very near to 30 days is very good since it means that the company is getting paid on amonthly basis.Sales is another attribute that strongly impacts working capital. It is the ability of a company to sell itsproducts fast enough to get the money back to put back into operations or supplies for producingmore materials. Moving inventory fast is always a good plan for a company. It also helps in reducingcosts associated with holding and moving inventory. A good ratio that helps put the attribute inperspective is inventory turnover ratio, which is defined as: Inventory turnover ratio = sales / inventoryOr Inventory turnover ratio = Cost of goods sold / inventory (3.16c)8 The following material is based on; downloaded on October 12, 2012. 39
  40. 40. LECTURES & ADVANCED QUANTITATIVE TECHNIQUES NOTESThis ratio shows the efficiency the company has in selling its products. The higher the ratio the betterthe company is able to move the products. Again this could be dictated by the industry, for example,a daily products company is usually forced to sell its products fast enough or lose it. The ratio alsoprovides a good insight into how a company is doing within an industry. The direct ratio ofcompanies can be compared to see how well the company is able to sell the products in comparisonto its competitors.Financing is another attribute of Working Capital management. Debt - Asset ratio provides a goodinsight into how much of the companys assets are being financed though debt. The debt – assetratio is defuned as: Debt-asset ratio = Total liabilities / Total assets (3.16d)Working capital management becomes a very important aspect for a company since it is the first lineof defense against market downturn cycles and recession. A company with cash is usually in a goodposition to make better use of the opportunities the markets provide. Its can spend the money onR&D for coming up with better products. Increase in current assets, especially, increase in accountreceivables due to growth is sales have to be managed efficiently. Ability to control working capitalplays a significant role in the survival of the company.Research on Working CapitalLet us see how the above information on working capital (WC) and working capital management(WCM) has been used by different researchers to carry out research on the topic under study.Lazaridis and Tryfonidis’s (2006)9 and Gill, Biger and Mathur (2010)10 analyzed the relationshipbetween profitability and working capital management, using about the same model, andmeasuring and generating the dependent and independent variables in the following way: No. of Days A/R = (Accounts Receivables/Sales) x 365 No. of Days A/P = (Accounts Payables/Cost of Goods Sold) x 365 No. of Days Inventory = (Inventory/Cost of Goods Sold) x 365 Cash Conversion Cycle = (No. of Days A/R + No. of Days Inventory) – No. of Days A/P Firm Size = Natural Logarithm of Sales Financial Debt Ratio = (Short-Term Loans + Long-Term Loans)/Total Assets Fixed Financial Asset Ratio = Fixed Financial Assets/Total assets Profit = (Sales - Cost of Goods Sold) / (Total Assets - Financial Assets)9 Lazaridis I, and Tryfonidis D, (2006). Relationship between working capital management and profitability of listedcompanies in the Athens stock exchange. Journal of Financial Management and Analysis, 19: 26-25.10 Gill, A., Biger, N. and Mathur, N. (2010). The Relationship Between Working Capital Management AndProfitability: Evidence From The United States. Business and Economics Journal, Volume 2010: BEJ-10 40