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Basics of the Labor Market

Basics of the Labor Market. Participants are assigned motives: Workers look for the best job Firms look for profits Government uses regulation to achieve goals of public policy Minimum wages Occupational safety. Workers The most important actor; without workers, there is no “labor”

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Basics of the Labor Market

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  1. Basics of the Labor Market • Participants are assigned motives: • Workers look for the best job • Firms look for profits • Government uses regulation to achieve goals of public policy • Minimum wages • Occupational safety • Workers • The most important actor; without workers, there is no “labor” • Desire to optimize (to select the best option from available choices) to maximize well-being • Will want to supply more time and effort for higher payoffs, causing an upward sloping labor supply curve

  2. Basics of the Labor Market • Firms • Decide who to hire and fire • Motivated to maximize profits • Relationship between price of labor and the number of workers a firm is willing to hire generates the labor demand curve • Government • Imposes taxes • Safety/environmental regulations • Set minimum wages • Force firms to shuttle workers from home to work (SF, CA) • Mediate labor union disputes with firms

  3. Why is there a shortage of math teachers? Why study Labor Economics? Mathematics History LS (mathematicians) LS (historians) w*ind wunion w*ind LD LD E*math E*hist shortage surplus

  4. How does increasing the minimum wage affect workers and firms? Why study Labor Economics? Low skilled labor market Low skilled labor market LS (workers) LS (workers) wmin wmin w* LD (firms) LD (firms) LF E LF E E* unemployment unemployment

  5. Is there a cost to immigration? Why study Labor Economics? Low skilled labor market LS (workers) A flood of low skilled workers into an economy… w* w* LD (firms) E* E*

  6. Using data to confirm theory (Scatterplots and simple regression) Rise = .018 – (-.012) = .03 Run = -0.053 – 0.037 = -0.09 b = -.03/0.09 = -.333

  7. Using data to confirm theory (multiple regression) • The equation that describes how the dependent variabley is related to the independent variables and error is called the multipleregression model y = b0 + b1x1 + b2x2+. . . + bkxk + e The equation that describes how the mean value of y is related to theindependent variables is called the multiple regression equation E(y) = 0 + 1x1+ 2x2+ . . . + kxk The equation that describes how the predicted value of y is related to the independent variables is called the estimated multiple regression equation: ^ y = b0 + b1x1+ b2x2+ . . . + bkxk

  8. Using data to confirm theory • Formulate a research question: • How has welfare reform affected employment of low-income mothers? • Issue 1: How should welfare reform be defined? • Since we are talking about aspects of welfare reform that influence the decision to work, we include the following variables: • Welfare payments allow the head of household to work less. • tanfben3= real value (in 1983 $) of the welfare • payment to a family of 3 (x1) • The Republican lead Congress passed welfare reform twice both of which were vetoed by President Clinton. Clinton signed it into law after the Congress passed it a third time in 1996. All states put their TANF programs in place by 2000. • 2000 = 1 if the year is 2000, 0 if it is 1994 (x2)

  9. Using data to confirm theory • Formulate a research question: • How has welfare reform affected employment of low-income mothers? • Issue 1: How should welfare reform be defined?(continued) • Families receive full sanctions if the head of household fails to adhere to a state’s work requirement. • fullsanction = 1 if state adopted policy, 0 otherwise (x3) • Issue 2: How should employment be defined? • One might use the employment-population ratio of Low-Income Single Mothers (LISM):

  10. Using data to confirm theory (Using theory to build testable hypotheses) 2. Use economic theory or intuition to determine what the true regression model might look like. Use economic graphs to derive testable hypotheses: Consumption Economic theory suggests the following is not true: Ho: b1 = 0 550 U1 400 U0 300 Receiving the welfare check 55 40 Leisure increases LISM’s leisure which decreases hours worked

  11. Using data to confirm theory (Using theory to build testable hypotheses) 2. Use economic theory or intuition to determine what the true regression model might look like. Use a mathematical model to derive testable hypotheses: The solution of this problem is: Economic theory suggests the following is not true: Ho: b1 = 0

  12. Using data to confirm theory (Model Specification in regression) 3. Compute means, standard deviations, minimums and maximums for the variables.

  13. Using data to confirm theory (Model Specification in regression) 3. Compute means, standard deviations, minimums and maximums for the variables.

  14. Using data to confirm theory (Model Specification in regression) 4. Construct scatterplots of the variables. (1994, 2000)

  15. Using data to confirm theory (Model Specification in regression) • 5. Compute correlations for all pairs of variables. If | r | > .7 for a pair of independent variables, • multicollinearity may be a problem • it is not possible to determine the separate effect of any particular independent variable on y. • Some say avoid including independent variables that are highly correlated, but it is better to have multicollinearity than omitted variable bias.

  16. Using data to confirm theory (Model Specification in regression) Variable transformation

  17. Using data to confirm theory (Estimation) • Least Squares Criterion: Computation of Coefficient Values: In simple regression: In multiple regression: You can use matrix algebra or computer software packages to compute the coefficients

  18. Using data to confirm theory (Omitting variable bias) r2·100%of the variability in y can be explained by the model. .08% epr of LISM Error

  19. Using data to confirm theory (hypothesis testing) H0: 1 = 0 df = 100 – 1 – 1 = 98 (column) a /2 = .025 (row) a = .05 Reject Do Not Reject Reject .025 .025 t .276 0 -1.984 1.984 We cannot reject H0 at a 5% level of significance.

  20. Using data to confirm theory (interpretation) • If estimated coefficient b1 was statistically significant, we would interpret its value as follows: Increasing monthly benefit levels for a family of three by 10% would result in a .058 percentage pointincrease in the average epr of LISM • However, since estimated coefficient b1 is statistically insignificant, we interpret its value as follows: Increasing monthly benefit levels for a family of three has no effect on the epr of LISM. Our theory suggests that this estimate has the wrong sign and is biased towards zero. This bias is called omitted variable bias.

  21. Using data to confirm theory (Estimation) r2·100%of the variability in y can be explained by the model. 15% epr of LISM Error

  22. Using data to confirm theory (Estimation) r2·100%of the variability in y can be explained by the model. 19% epr of LISM Error

  23. Using data to confirm theory (Estimation) r2·100%of the variability in y can be explained by the model. 49% epr of LISM Error

  24. Using data to confirm theory (Estimation) Error lnx1 x2 x3 + x4 x5 x6

  25. Using data to confirm theory (A1: zero mean) • E(e) is probablyequal to zerosince E(e) = 0

  26. Using data to confirm theory (A2: Constant variance) Heteroscedasticity is likely present if scatterplots of residuals versus t, y, x1, x2 … xk are not a random horizontal band of points. ^ okay okay Non-constant variance in black? okay okay

  27. Using data to confirm theory (A2: Constant variance) To test for heteroscedasticity, perform White’s squared residual test by first squaring the residuals, and then using these as the “y” variable in a secondary regression:

  28. Using data to confirm theory (A2: Constant variance) 25 1.24 F.05 = 1.66 74 If F-stat > F05 , we reject H0: no heteroscedasticity Hence, s2 is probably constant

  29. Using data to confirm theory (A2: Constant variance) • If heteroscedasticity is a problem, • Estimated coefficients aren’t biased • Coefficient standard errors are wrong • Hypothesis testing is unreliable • In our example, heteroscedasticity does not seem to be a problem. • If heteroscedasticity is a problem, do one of the following: • Use Weighted Least Squares with 1/xj or 1/xj0.5 as weights where xjis the variable causing the problem • Compute “Huber-White standard errors”

  30. Using data to confirm theory (A3: Normality) Error  is probablynormally distributed if e is normally distributed -20 -16 -12 -8 -4 0 4 8 12 16 20

  31. Using data to confirm theory (A3: Normality) • There are a number of normality tests one can chose. • The Jarque-Bera test involves using the skew and kurtosis of the residuals. • The test statistic follows a chi-square distribution with 2 degrees of freedom: • kurtosis measures "peakedness" of the probability distribution. • High kurtosis →sharp peak, low kurtosis → flat peak. • involves raising standardized residuals to the 4th power • Excel: =kurt(A1:A100) → 0.0214 • skewness measures asymmetry of the distribution. • 0 skew → symmetric distribution, negative skew → skewed left, positive skew → skewed right • involves raising standardized residuals to the 3rd power • Excel: =skew(A1:A100) → 0.3276

  32. Using data to confirm theory (A3: Normality) df = 2 (row)  = .05 (column) Do Not Reject H0 Reject H0: errors are normal .05  2 5.99 2 There is no reason to doubt the assumption that the errors are normally distributed.

  33. Using data to confirm theory (A3: Normality) • If the errors are normally distributed, • parameter estimates are normally distributed • F and t significance tests are valid • If the errors are not normally distributed but the sample size is large, • parameter estimates are approximately normally distributed (CLT) • F and t significance tests are valid • If the errors are not normally distributed and the sample size is small, • parameter estimates are not normally distributed • F and t significance tests are not reliable

  34. Using data to confirm theory (A4: Independence) • The values of  are probablyindependentif the autocorrelation residual • plot or if the Durbin-Watson statistic (DW-stat) indicate the values of e • are independent • The DW-stat varies when the data’s order is altered • If there are multiple time periods, compute DW-stat after sorting by time periods • If the data is cross-sectional, compute the DW-stat after sorting by geography (e.g., NE, NW, Central, SW, SE …) • If the data is both, compute the DW-stat after sorting by time periods and geography

  35. Using data to confirm theory (A4: Independence) There is no reason to doubt the assumption that the errors are independent.

  36. Using data to confirm theory (A4: Independence) • If autocorrelation (or serial correlation) is a problem, • Estimated coefficients aren’t biased, but • Their standard errors may be inflated • Hypothesis testing is unreliable • In our example, autocorrelation does not seem to be a problem. • If autocorrelation is a problem, do one of the following: • Change the functional form • Include an omitted variable • Use Generalized Least Squares • Compute “Newey-West standard errors” for the estimated coefficients.

  37. Using data to confirm theory (A5: Linearity) ^ • The true model is probablylinearif the scatterplot of e versus y is a horizontal, random band of points okay and its height = 0 1. The simple regression line’s slope = 0 2. There is no pattern in this scatter plot.

  38. Using data to confirm theory (A5: Linearity) • If you fit a linear model to data which are nonlinearly related, • Estimated coefficients are biased • Predictions are likely to be seriously in error • In our example, nonlinearity does not seem to be a problem. • If the data are nonlinearly related, do one of the following: • Rethink the functional form • Transform one or more of the variables All 5 model assumptions appear to be valid. Hence, the t and F tests are reliable provided the “right” regressors are included.

  39. Using data to confirm theory (Testing for Overall Significance) H0: 1 = 2 = . . . = 6= 0 dfN = 6 (column) dfD = 93 and = .05 (row) Hence, we reject H0. There is insufficient evidence to conclude that the coefficients are not all equal to zero simultaneously. Do not Reject H0 Reject H0 .05 ≈ 1 16.623 2.20

  40. Using data to confirm theory (Testing for Coefficient Significance) H0: 1 = 0 df = 100 – 6 – 1 = 93 (column) a /2 = .025 (row) a = .05 Reject Do Not Reject Reject .025 .025 t 0 -2.3 -1.986 1.986 I.e., TANF welfare payments influence the decision to work. Reject H0 at a 5% level of significance.

  41. Using data to confirm theory (Testing for Coefficient Significance) H0: 2 = 0 df = 100 – 6 – 1 = 93 (column) a /2 = .025 (row) a = .05 (row) Reject Do Not Reject Reject .025 .025 t 0 -1.39 -1.986 1.986 I.e., welfare reform in general does not influence the decision to work. We cannot reject H0 at a 5% level of significance.

  42. Using data to confirm theory (Testing for Coefficient Significance) H0: 3 = 0 df = 100 – 6 – 1 = 93 (column) a /2 = .025 (row) a = .05 (row) Reject Do Not Reject Reject .025 .025 t 0 1.96 -1.986 1.986 I.e., full sanctions for failure to comply with work rules influence the decision to work. Although we cannot reject H0 at a 5% level of significance, we can at the 10% level (p-value = .054).

  43. Using data to confirm theory (Testing for Coefficient Significance) H0: 4 = 0 df = 100 – 6 – 1 = 93 (column) a /2 = .025 (row) a = .05 (row) Reject Do Not Reject Reject .025 .025 t 0 -3.26 -1.986 1.986 I.e., the share of the population that is black influences the decision to work. Reject H0 at a 5% level of significance.

  44. Using data to confirm theory (Testing for Coefficient Significance) H0: 5 = 0 df = 100 – 6 – 1 = 93 (column) a /2 = .025 (row) a = .05 (row) Reject Do Not Reject Reject .025 .025 t 0 -1.85 -1.986 1.986 I.e., the share of the population that is high school droput influences the decision to work. Although we cannot reject H0 at a 5% level of significance, we can at the 10% level (p-value = .068).

  45. Using data to confirm theory (Testing for Coefficient Significance) H0: 6 = 0 df = 100 – 6 – 1 = 93 (column) a /2 = .025 (row) a = .05 (row) Reject Do Not Reject Reject .025 .025 t 0 -4.89 -1.986 1.986 I.e., the unemployment rate influences the decision to work. Reject H0 at a 5% level of significance.

  46. Using data to confirm theory (Interpreting Coefficients) • Since estimated coefficient b1 is statistically significant, we interpret its value as follows: Increasing monthly benefit levels for a family of three by 10% would result in a .54 percentage pointreduction in the average epr of LISM • Since estimated coefficient b2 is statistically insignificant (at levels greater than 15%), we interpret its value as follows: Welfare reform in general had no effect on the epr of LISM.

  47. Using data to confirm theory (Interpreting Coefficients) • Since estimated coefficient b3 is statistically significant at the 10% level, we interpret its value as follows: The epr of LISM is 3.768 percentage points higher in states that adopted full sanctions for families that fail to comply with work rules. • Since estimated coefficient b4 is statistically significantat the 5% level, we interpret its value as follows: Each 10 percentage point increase in the share of the black population in states is associated with a 2.91 percentage point decline in the epr of LISM.

  48. Using data to confirm theory (Interpreting Coefficients) • Since estimated coefficient b5 is statistically significantat the 5% level, we interpret its value as follows: Each 10 percentage point increase in the high school droput rate is associated with a 3.74 percentage point decline in the epr of LISM. • Since estimated coefficient b6 is statistically significantat the 5% level, we interpret its value as follows: Each 10 percentage point increase in the unemployment rate is associated with a 30.23 percentage point decline in the epr of LISM.

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