Applied Econometrics - Assignment Example

Question 1 ln (y) = a + bx + cx2 + dz + e.ln (w) Ẏ = β0 + β1x + β2 x2 + β3z + β4 ln(w) Assuming N β0 = ln (y)/N – (β1 + β2) Ẍ + β3Ẑ + β4 ln(w)/N d ln(y)/dx = β1 + β2x d ln(y)/dz = Zβ3 + β4 ln (w) d ln(y)/d ln(w) = β4 The change in each of the variables in the right hand side would have a positive direct effect on the left hand side i.e Y. The resultant relationship between the variables and the regressed is positive hence, an indication of a fixed effect on the data. Question 2 a. In the performance of the regression equation, it is necessary to consider the assumptions of the ordinary least square (OLS). One such key assumption is the assumption of zero conditional mean. In typical situations, the prospect is that a regression would deliver consistent or unbiased estimates if the zero conditional mean assumption holds. However, on the contrary if a biased estimate or relationship is delivered, then the regression would be considered as having not been under the zero conditional mean assumption (Jones, 2008.p.202-208). In a regression equation in which the coefficient of wealth is found to be positive, the reason for getting biased estimates would be due to the failure of the zero conditional mean assumption to hold. As is noted in the case, the expectation of an exogenous rise in the level of wealth (meaning positive), would result in a decrease or decline, in the number of hours that one has to work (Wooldridge, 2011; Asteriou & Hall, 2011.p.105-110). b. The use of instrumental variables estimation is always an important way of trying to remedy the problem of omitted variable bias. Therefore, it can be designated as a good way for satisfying assumptions in the independent variable. In the given case of a dummy variable D having two key independent variable assumptions, it would be necessary to refer to D as good due to the following reasons. First, D as an instrumental variable can be stated fairly simply given that its main ingredients are the two key assumptions which have been applied in the derivation of the independent variable estimators (Fox & Fox, 2008.p.130-135). Considering the identification problem that is always experienced in regression equations, it would be appropriate to consider the dummy variable as a good instrumental variable because it is correlated to the variables wealth and labor supply and uncorrelated to the error term (u) (Fox & Fox, 2008.p.140-143). In an equation form, this can be exemplified as: Wealth = β0 + β1 (Labor supply) + error term (u) Let y = wealth; and X = labor supply y = β0 + β1X + u D satisfies the two key assumptions in the sense that it applies the two in the evaluation of the regression equation without having to render the regression estimation as being biased; thus failing to meet up with the zero conditional mean assumption. In running two reduced form regression forms to obtain causal effects of wealth on labor supply in this case, since wealth had been indicated as exogenously rising, D is endogenous hence, can be excluded from the main equation of interest (Asteriou & Hall, 2011.p.125-135; Fox & Fox, 2008). In the first reduced form, it is the endogenous variable that will be regressed on the instrument. Putting a focus on the covariance of D and y; cov (D, y) = cov (D, β0 + β1X + u) = β1cov (D, X) + cov (D, u) Given that the OLS estimation delivers on consistent estimates of π, and since D is uncorrelated with u, X = π0 + π1D + u. In the second reduced form, y = α0 + α1D + w; in this case, the OLS is noted to have delivered a consistent estimate of α1 in which D is uncorrelated to the w. In establishing the help of the reduced forms, β1 = δy/δx = δy/δD x δD/δx The above equation now provides the indirect form of the least squares. When run together as a result of the independent variables, X = π0 + π1D + u. with π1 > 20. In the second form, y = α0 + α1D + w suggesting that an increase in the labor supply will result in increased wealth for those individuals who have won big in the lottery; thus, α1 > 0 With the estimates from these reduced forms, the instrumental variable effect for wealth on labor supply would be β1 = π1/ α1. PART B a. The Effect of Culture on Economic Outcomes Data on immigrants’ entry is used to reveal their impact on the economic factors with a view linked to the culture the immigrants impose on the taste, preferences and priorities of the economy. The variances in cultures imply different buying and selling of products in the markets (Fernández, 2006). The author categorically seeks to answer the question of the impact of immigrants on the economic results of the country by analyzing the impact of culture on economic outcomes. The problems that the immigrants face in the new countries they move into present further problems and shocks which hamper the economic growth in the new countries. Language barrier, discrimination and the level of unpredictability in the areas of mingling and market prevents them from economic activities. b. Female LFP Figure 4 gives the evidence on the impact and the role played by the country of origin, which affects the tastes and preferences of the people in the understanding of cultures and economic development in the long run. The regression results provide information on different issues associated with cultures as affecting the markets. The individual characteristics in the regressions give room for the consideration of the impact of the traits in the economic development, in the regions (Fernández, 2006). c. Elasticity In table 3.2. the elasticity rate is at 0.056 indicating that the value of education for women increases by a positive rate of the same amount. As such, being that the education variable is a missing variable, it could result in the regression model being biased thus violating the zero conditional mean assumption of unbiasness. There would be an upward biased estimate in the column (i) of the table to indicate that the source of bias be a real case of concern. d. Economic effect of GDP on working hours The effect of GDP in the countries of origin affects the level of work on female LFP in the US because the GDP affects the wages of the workers, which is influenced by macroeconomic developments, and taxation. These changes in the country of residence may have positive or negative changes in the family status, school, pension ages and spousal income. The data on medication is also affected by the GDP and the influence of the country of origin underlines all the potential changes in the working hours of the female immigrants (Fernández, 2006). e. The inclusion of the SMSA The inclusion of the SMSA in the analysis of the data in the regression is used to include the possible effects of the social disorders in the regression analysis. The importance of including the other possible factors is to affect the outcome in the female LFP; thus, create a constant out of the possible effects of these factors to affect the outcomes of the tested variables (Fernández, 2006). The levels of crimes in the city within the given states are factors that influence the level of working hours. This is linked to the possibility that crimes lessen the affluence of the persons in these regions and would motivate females employed to work for longer hours (Fernández, 2006). f. The Weaknesses of the Analysis The evidence provided in the work provides to a little extent the impact of culture on the female LFP. The weaknesses related to work are; the author did not include the possible effects of the external economic factors like the GDP, interest rates, inflation and availability of resources as probable factors to affect female LFP. The conditions, terms of employment and the wages of the females are not included as having possible effects in the female LFP. The author did not include all the possible factors that may affect the female LFP; thus, the analysis is not that perfect for the claims of the impact of culture on female LFP (Fernández, 2006). References List ASTERIOU, D., & HALL, S. G. (2011). Applied econometrics. Basingstoke [England], Palgrave Macmillan. FERNÁNDEZ, R. (2006). Women, Work and Culture. New York City, CEPR, NBER. FOX, J., & FOX, J. (2008). Applied regression analysis and generalized linear models. Los Angeles, Sage. JONES, A. (2008). Applied econometrics for health economists: a practical guide. Abingdon, Radcliffe. WOOLDRIDGE, J. (2011). Introductory econometrics. [S.l.], South-Western. Read More