Transcript
  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    1/23

    Ella Lorraine Obra Economics 131

    Charmagne Anne Rimando Introduction to Quantitative Research

    Ma. Monserrat Veloso 12 October 2012

    Mary Joice Zamora

    The Unemployment Condition in the Philippines (1990-2009)

    Introduction

    According to researches, the largest part of the peoples income is coming from paid jobs.

    Thus, it is important to study what factors affect the unemployment rate in a certain country.

    However, variables that may explain unemployment may differ from country to country. In this

    paper, we will use the imports, labor force participation, and GDP as independent variables in

    explaining unemployment rate in the Philippines.

    In this research paper different studies conducted will be presented in Chapter 2; so as to

    show that such relationship between our chosen dependent and independent variables exist. It is

    defined that unemployment is present when those who want to work and are seeking for job

    cannot find one. There are studies that argue that there exists a positive relationship between

    imports and unemployment rate and there are those that do not. The focus of this paper would be

    the positive relationship. The presence of a huge amount of imports in country may affect the

    different sectors which provide jobs for the employment pool. In addition, it is known that as

    GDP increases, the unemployment rate decreases. Labor force participation is also one of the

    important variables that may aggravate the unemployment rate in a certain country (refer to

    Chapter 2).

    In the definition of terms part of the paper, the variables that were defined are the only

    ones that were present in the final model which does not contain any problems of CLRM

    (Classical Linear Regression Model); but the reader will expect to see on the review of the

    literature part the definitions of the other variables that were at first included in the model but

    were found to have problems of CLRM to justify why these particular variables were included

    in the preliminary model in the first place.

    Objective

    Even though we have found literature saying that the variables imports, GDP, and labor

    force are related to unemployment rate, we are still not certain whether these relationships are

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    2/23

    present in the condition of the Philippines. Also, in consideration of the mentality of the people

    that imports are better than the local products, it is then important to show, if it is applicable in

    the Philippines, if there is a positive relationship between imports and labor force and

    unemployment rate and that there is a negative relationship between GDP and unemployment

    rate.

    Research Question

    Are the factors of unemployment stated earlier present in the context of Philippines?

    Do the relationships presented in the literature are also the relationships expected in the

    country?

    Methodology

    In doing this paper, we will use secondary data from the National Statistics Coordination

    Board (NSCB) and World Bank. Furthermore, our group used a time-series data from 1990 to

    2009 in order to see the trends of unemployment rate as a function of the independents variables

    we have stated above. Observations have been increased since we have three explanatory

    variables and we need to subtract it from the numbers of observations in order to get the degree

    of freedom. Degrees of freedom means the total number of observations in the sample (= n) less

    the number of independent (linear) constraints or restrictions put on them. In other words, it is

    the number of independent observations out of a total of n observations (Gujarati, 2004: 77)

    If we will just use little observations, the degree of freedom will be low which can be a source

    of a problem. A regression model will be used, generated by using GRETL (Gnu Regression,

    Econometrics, and Time-Series Library) using the method of Ordinary Least Squares. Also, the

    linear model will be transformed into logarithmic model so as to determine which kind of model

    will better show the relationships that we intend to study.

    Definition of Terms

    1.

    Unemployment Rate- According to Rudiger Dornbusch. et.al (2008: 604), unemploymentrate is the fraction of the labor force that is out of work and looking for a job or

    expecting a recall from a layoff, in terms of percentage.

    2. GDP- or Gross Domestic Product is the value of all final goods and services produced in

    the country within a given period (Dornbusch, et.al, 2008: 23). GDP in the model is

    measured in terms of current US dollars .The logarithm of GDP in the model depicts the

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    3/23

    relative change or percentage change in the unemployment rate when the GDP changes

    by 1%.

    3. Labor Force- are the people who are looking for work and are working (Dornbusch,

    2008: 596). The logarithm of labor force shows the relative change in the unemployment

    rate when the labor force changes by 1%.

    4. Imports- from the perspective of the country that is importing, are the commodities that

    are consumed in that country but produced abroad (Dornbusch, 2008: 280). In the models

    presented in this paper, imports are measured in millions of dollars at constant 1985

    prices. The logarithm of Imports represents the percentage change in the unemployment

    rate as the imports changes by 1%.

    Chapter II

    Review of Related Literature

    Introduction

    The problem of unemployment is one of the many things that the countries are facing

    including our country, the Philippines. Since it is one the major things to consider when one talks

    about development it is crucial that we solve this problem. This chapter presents existing studies

    regarding variables that can explain unemployment rate in a country. It will begin through giving

    a brief definition of unemployment which highlights the Philippine description of those

    individuals who are not employed. The next section will be offering different explanatory

    variables for unemployment. Then, delimitation of indicators of unemployment in the

    Philippines will follow. The last section will be providing a conclusion.

    The total absence of work for a certain period of time defines the broad concept of

    unemployment. It takes place when such individuals cannot get an appropriate job despite theirwanting to have one (Stat Informer 2012). Unemployment rate measures the fraction of the

    workforce that is out of work and looking for a job or expecting a recall from a layoff

    (Dornbusch, Fischer, and Startz 2008:42). A kind of living for an individual without work is

    tough, he is financially incapable of buying the basic goods and services he needs. In this regard,

    with high unemployment rate finding a job is a lot more difficult and thus unemployment rate is

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    4/23

    an essential tool to measure economic progress of a specific nation (Dornbusch, Fischer, and

    Startz 2008).

    In the Philippines, the National Statistical Coordination Board (NSCB) has specifically

    defined those people that are unemployed,

    The unemployed include all persons 15 years old and over as of their last birthday and are reported as:

    1.

    without work, i.e., had no job or business during the basic survey reference period; AND

    2.

    currently available for work, i.e., were available and willing to take up work in paid employment or

    self-employment during the basic survey reference period, and/or would be available and willing to

    take up work in paid employment or self-employment within two weeks after the interview date; AND

    3.

    seeking work, i.e., had taken specific steps to look for a job or establish business during the basic

    survey reference period; OR not seeking work due to the following reasons: (a) tired/believe no work

    available, i.e., the discouraged workers who looked for work within the last six months prior to the

    interview date; (b) awaiting results of previous job application; (c) temporary illness/disability; (d) bad

    weather; and (e) waiting for rehire/job recall (Virola 2005).

    This is the international standard accepted as a new measurement of unemployment.

    International standard is needed aiming to make the unemployment rate of countries comparable.

    Generating a significant assessment of countries labor market would then be possible (Stat

    Informer 2012).

    Unemployment rate of a country is explained by several factors and is seen through

    different perspectives. One of which are Structuralist theory, Non-Accelerating Inflation Rate of

    Unemployment (NAIRU), and the chain reaction theory. Structuralist theory argues that lengthy

    variations in unemployment rate are significantly explained by the financial wealth of thecountry. NAIRU approach says otherwise, it points out the role played by some fundamental

    shocks and a set of unemployment-prone labor market institutions, but it is evolving to a pure

    institutionalist view (Agnese and Sala 2008:2). For instance, merely looking to changes in labor

    market body swings on unemployment can be understood. On the other hand, capital

    accumulation and productivity or working age population as examples of growth variables plays

    a vital role in determining how well the labor market performs. This argument is lifted by the

    chain reaction theory (Agnese and Sala 2008).

    In addition, Foreign Direct Investment (FDI) and government size are able to explain

    unemployment. Industrial countries find the size of the government as an essential factor

    affecting unemployment. Theory says that increased in unemployment rate can be caused by a

    large government. Private sectors will be excluded such as the investment area. This results to a

    decline of technical progress and growth productivity and thus decreasing the global economic

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    5/23

    competitiveness of the country. A large government sector also implies greater government

    expenditures which raises labor taxes. In this regard, a higher real cost of labor is prominently

    seen resulting to falling demands for labor. Accordingly, it gives rise to high unemployment rates

    (Feldmann 2006:452). Conversely, FDI refers to the net inflows of investment to acquire a

    lasting management interest (10 percent or more of voting stock) in an enterprise operating in an

    economy other than that of the investor (World Bank 2012). Based on a comparative study

    conducted by Medina Arango (2010: 6) which involving Colombia and the Philippines, FDI has

    a positive effect in the economy of a country: economic growth and employment generation;

    technology and knowledge; access to goods and services; and filling the savings gap of the

    country. Because we want to know the relationship between FDI and unemployment, we shall

    focus on the effect of FDI in job creation. For employment generation, as a country becomes

    more productive, its competitiveness increases thus creates employment (Arango, M. 2010: 6).

    Indeed indicators for unemployment are many and varied that this paper cannot capture

    them all. Economic researches regarding the unemployment in the Philippines are able to present

    different indicators significantly affecting unemployment rate. This paper will only focus on four

    economic variables explaining variations on the rate of unemployment. These are imports,

    growth rate, and labor force participation rate.

    On the other hand, according to Dornbusch (2008:280), imports, from the perspective of

    the country that is importing, are the commodities that are consumed in that country but

    produced abroad. Although at a first glance, imports as a variable does not affect unemployment

    there are studies conducted that present relationships between them. Here we show a positive

    relationship between these two; positive in a sense that when the imports increase, the

    unemployment increases (Autor 2012). Examples of studies that present this particular

    relationship are done by David H. Autor, et.al (2012) which talked about how imports from

    China affected the level of unemployment in the United States. The authors mainly talked about

    how imports affect the labor market and wages in the United States and concluded that the

    employment in terms of manufacturing industry is decreasing at the presence of imports,

    specifically those coming from China. In addition, studies on the relationship of imports and

    unemployment focusing on the productivity sector of United States has found out that rising

    real imports are responsible for approximately 1.3 million of the jobs lost between 2007 and

    2011, or almost one-third of total private non-construction job loss (Mandel and Carew 2012:

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    6/23

    1). Michael Mandel and Diana Carew focused on the productivity sector of United States. The

    difference of this study on the one just mentioned is that their paper asserts that not only the

    unemployment and imports have relationship but that the latter influences the former greatly

    (Mandel and Carew 2012).

    Okuns law, which was named after Arthur Okun, explains the relationship between

    unemployment and GDP growth rate. This theory assumes that there is a negative relationship

    between these two variables. However, Knotek presented a case in the United States in 2003 to

    the first quarter of 2006 where the real GDP growth rate is increasing and the unemployment rate

    is decreasing; however, it is observed that in the latter part of 2006, the growth rate has been

    decreasing while the unemployment rate is also decreasing. Thus, it is argued that the

    relationship between these two variables is statistical rather than a structural feature of the

    economythe application of Okuns may vary across the country (Knotek 2007: 73). In

    addition, Levine (2012:2) stated that

    If the rate of output exceeds the rate of labor force growth,

    some of the new jobs created by employers to satisfy the growing

    demand for their goods and services will be filled by drawing

    from the pool of unemployed workers.

    Another study was conducted by Andrei, Vasile, and Adrian (2012) to test the

    applicability of Okuns law in Romania. In doing this, they used a quarterly data of

    unemployment rate and GDP growth rate from 2000 to 2008, and deseasonalized it. It was

    presented in models used that high growth rates are accompanied by low unemployment rates.

    Furthermore, it is also observed that there is a high value of R2and the value derived from the

    Durbin-Watson test is around 2 which means that the problem of serial correlation is not lurking

    in the model that they used. However the problem of heteroskedascticity is present in their model

    as found out by the Whites test. Also, Kitov and Kitov (2012) conduc ted the same study

    wherein they replaced unemployment rate by employment per population ratio; since it is argued

    that these two are complementary. Also, they focused on cross-country cases, but delimited it to

    largest economies in the world. Furthermore, the model that they used is a lin-log model (the

    dependent variable is linear, while the independent variables are in the logarithmic form), since

    economic growth is measured through percentage changes. As a result of their study, they proved

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    7/23

    that one of the strong forces that have an impact to the employment per population ration is the

    real GDP growth rate.

    In a study done by Brooks (2002) it is presented that unemployment is high and is

    twice the unemployment rate in the Philippines due to high population growth and increasing

    labor participation. The researcher found out that the labor force participation in the country has

    been increasing from 1982 to 2001. This increase can be attributed to the growing involvement

    of womens participation. Furthermore it is observed that the labor productivity is relatively low

    since it is also accompanied by a slow GDP growth. Another study that presents the relationship

    between was from Hamilton Place Strategies, however in the context of trends of unemployment

    rate during Election Day. This organization presented that the unemployment rate is a function of

    unemployed looking for work and labor force, given the formula:

    Unemployment rate= unemployed looking for work

    Labor force

    Source: Hamilton Place Strategies, (2012),Jobs Preview 2012: The Year of the Missing Worker.

    Two arguments were made in this research, that is: First, unemployment rate is . . . a function of

    those who are actively looking for work and have not found it. Second, those that are

    unemployed are not captured in the unemployment rate, but are reflected in the labor force

    participation rate, which declines as people drop out of the workforce or choose not to pursue

    work at all (Hamilton Place Strategies, 2012:3).

    Summary and Conclusion

    In conclusion, unemployment is a very broad economic concept which is also explained

    by numerous variables. Since unemployment is one of the several economic phenomena

    indicating how rich the economy is, it is then necessary to determine explanatory variables for

    unemployment. With the knowledge of such indicators countries can generate actions that can

    help diminish the rate of unemployment. In studying the unemployment rate in the Philippines

    this paper has only chosen three explanatory variables which are imports, growth rate, and labor

    force participation rate. Employing regression analysis, this paper can identify if these variables

    can significantly explain variations in unemployment.

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    8/23

    Chapter III

    Data Presentation and Analysis

    Model 1 shows that only the p-value of the coefficient of the constant is significant at

    1%. Other variables were found to be insignificant. The adjusted R-squared is equal to -

    0.160337, which means that there is/are a variable/s included in the model which does not help in

    explaining the dependent variable. The sign of the coefficient of GDP growth is not consistent

    with that of the literature, which led us to testing if there is a presence of problems of Classical

    Linear Regression Model (CLRM). The tests conducted were test for multicollinearity (Variance

    Inflation Factor), test for heteroscedasticity (Whites Test for Heteroscedasticity), test for

    normality of residuals, test for serial correlation (Durbin-Watson test and Breusch-Godfrey test

    for first-order autocorrelation), and test for specification error (Ramseys RESET). The testsshowed that the model is clear of problems on multicollinearity, heteroscedasticity, and

    specification error, but there is a problem of serial correlation in the model.

    In Model 2 the variables FDI was dropped to solve the problem in Model 1. FDI was

    chosen to be dropped since in the case of the Philippines it does not really explain

    unemployment. In this model the p-value of the coefficient of the constant is the only variable

    that is significant; it is significant at 1%. The adjusted R-squared is equal to -0.117405, which

    means that there is still a variable that does not help in explaining the dependent variable or the

    current variables present in the model are not enough to explain unemployment rate. The

    negative value of the adjusted R-squared of Model 2 is less than that of Model 1. This means that

    a certain extent some of the variables that need to removed were removed therefore making this

    new model more acceptable than that of the first.

    In Model 3, after FDI was dropped there was still a problem in the model thus another

    variable was dropped which is the GDP growth. Even though we have removed the variable FDI

    and GDP growth this does not necessarily mean that we will let the model to contain just two

    variables for we know for a fact that there are other variables that can explain the unemployment

    rate in the Philippines. According to the literature (see the review of the related literature), labor

    force and GDP can explain unemployment rate. So now we add these two particular variables.

    After adding the variable labor force and GDP, the adjusted R-squared became 0.657184,

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    9/23

    because the adjusted R-squared increased, we have the basis of including labor force and GDP in

    the model. The variables with significant p-values in the model are GDP and labor force, being

    significant at 1%. The test for multicollinearity shows that labor force has a VIF greater than 10

    which indicates that multicollinearity is present in the model.

    Model 4 shows that the p-value of the coefficient of both lnGDP and lnLaborForce are

    significant at 1%. The adjusted R-squared is 0.644902, which means that the model explains

    64.49% of variability in the dependent variable. The problem of multicollinearity has been

    removed when the functional form of the variables was changed. Compared to the other models,

    Model 4 is the best model that has been generated. The following regression model was derived,

    Unemployment rate= -7.55919 + 1.00673 lnImport + 19.4568 lnLF1.87094 lnGDP

    the constant term and the import variable are not significant at any level. For a span of 20 years (1990 to

    2009), if the labor force participation increases by 1% it is expected that the unemployment rate will also

    increase by 19.4568%, ceteris paribus. It is also showed that if the lnGDP decreases by 1%, the

    unemployment rate will decrease by 1.87094% while holding the level of lnimports and lnlabor force

    participation constant. Based on the value of the adjusted R-squared, we argue that it is a good model

    since it explains 64% of the variation in the unemployment rate. Based from the F-statistic of 12.50 and

    the critical value of 3.24 we can conclude that the coefficients in this model are significantly different

    from zero.

    Conclusion

    This study presented some of the variables that can explain unemployment in the

    Philippines but in reality there are more variables that are not included in the final model. Even

    though the literature says that the preliminary variables like FDI and GDP growth explain and/or

    are correlated with unemployment rate, in this particular study these variables are not applicable.

    For further study, increase in observations may be needed for the other variables affecting

    unemployment to be applicable to the Philippine context. Ultimately, the variables included in

    the final model was able to explain at a certain extent the unemployment rate as part of the

    unemployment condition in the country from 1990-2009 and from this we can say that in terms

    of improving the welfare of the country, the independent variables can be manipulated as to

    lessen the unemployment rate in the Philippines.

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    10/23

    Appendix

    Actual Data.

    YEARUNEMPLOYMENTRATE IMPORTS

    LABORFORCE GDP

    1990 8.1 269148 24244 44311595230

    1991 9 266139 25631 45417505303

    1992 8.6 289273 26290 52976363148

    1993 8.9 322548 26879 54368183872

    1994 8.4 369325 27654 64084543195

    1995 8.4 428475 28380 74119868202

    1996 7.4 500194 29733 82848194395

    1995 7.9 567682 28901 82344374414

    1998 9.4 484235 29674 72207022472

    1999 9.4 470673 30759 82995145601

    2000 11.2 490768 30911 81026294681

    2001 11 508044 32809 76261998623

    2002 11.5 536535 33936 81357657790

    2003 11.2 594603 34571 83908205720

    2004 11.9 628911 35862 91371236939

    2005 7.7 643839 35286 1.03066E+11

    2006 8 655706 35464 1.22211E+11

    2007 7.4 628664 36213 1.4936E+11

    2008 7.3 633770 36805 1.73603E+11

    2009 7.5 621543 37892 1.68334E+11

    *The data on unemployment rate and imports were taken from National Statistical Coordination Board

    while the labor force was taken from the Department of Labor and Unemployment (website). The Gross

    Domestic Product was taken from World Bank (website).

    From the data given above, we use the statistical package GRETL to obtain thispreliminary regression output using the method of Ordinary Least Squares.

    Model 1: OLS, using observations 1990-2009 (T = 20)Dependent variable: unemployment_ra

    Coefficien

    tStd. Error t-ratio p-value

    const 9.422 1.67966 5.6095 0.00004 ***

    foreign_direct_

    -0.289015 0.474491 -0.6091 0.55101

    GDP_growth 0.0112176 0.213829 0.0525 0.95881

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    11/23

    imports 2.05965e-08

    3.51303e-06

    0.0059 0.99539

    Mean dependent var 9.010000 S.D. dependent var 1.530703Sum squared resid 43.49969 S.E. of regression 1.648857R-squared 0.022874 Adjusted R-squared -0.160337

    F(3, 16) 0.124851 P-value(F) 0.944039Log-likelihood -36.14899 Akaike criterion 80.29797Schwarz criterion 84.28090 Hannan-Quinn 81.07548Rho 0.635402 Durbin-Watson 0.721617

    White's test for heteroskedasticity -Null hypothesis: heteroskedasticity not presentTest statistic: LM = 7.24865with p-value = P(Chi-square(9) > 7.24865) = 0.611249

    Test for normality of residual -Null hypothesis: error is normally distributed

    Test statistic: Chi-square(2) = 5.73632with p-value = 0.0568035

    LM test for autocorrelation up to order 1 -Null hypothesis: no autocorrelationTest statistic: LMF = 13.3367with p-value = P(F(1,15) > 13.3367) = 0.0023604

    All the variables included in the model are not significant, not even at 10%. The next to do

    would be to test if there are any problems in CLRM present in this current model. We have the

    following GRETL output for the different tests that were made.

    1.

    Test for Multicollinearity

    Variance Inflation FactorsMinimum possible value = 1.0Values > 10.0 may indicate a collinearity problem

    foreign_direct_ 1.002GDP_growth 1.510imports 1.510

    VIF(j) = 1/(1 - R(j)^2), where R(j) is the multiple correlationcoefficient between variable j and the other independentvariables.

    Properties of matrix X'X:1-norm = 5.2431077e+012Determinant = 4.7836727e+015Reciprocal condition number = 1.593951e-013

    2. Test for Heteroscedasticity

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    12/23

    White's test for heteroskedasticityOLS, using observations 1-20Dependent variable: uhat^2

    coefficient std. error t-ratio p-value----------------------------------------------------------------

    const 5.93698 10.6870 0.5555 0.5907foreign_direct_ 0.516710 5.05529 0.1022 0.9206GDP_growth 0.332128 1.90017 0.1748 0.8647imports 3.18533e-05 4.91902e-05 0.6476 0.5319sq_foreign_di 0.580412 1.04745 0.5541 0.5917X2_X3 0.0141654 0.453006 0.03127 0.9757X2_X4 3.78463e-06 9.32261e-06 0.4060 0.6933sq_GDP_growth 0.0217692 0.190176 0.1145 0.9111X3_X4 1.37605e-06 4.07276e-06 0.3379 0.7424sq_imports 2.61907e-011 5.69762e-011 0.4597 0.6556

    Warning: data matrix close to singularity!

    Unadjusted R-squared = 0.362432

    Test statistic: TR^2 = 7.248648,with p-value = P(Chi-square(9) > 7.248648) = 0.611249

    3. Test for Normality of Residual

    Frequency distribution for uhat1, obs 1-20number of bins = 7, mean = 2.13163e-015, sd = 1.64886

    interval midpt frequency rel. cum.

    < -1.5469 -1.9246 3 15.00% 15.00% *****-1.5469 - -0.79154 -1.1692 5 25.00% 40.00% *********-0.79154 - -0.036193 -0.41387 4 20.00% 60.00% *******-0.036193 - 0.71915 0.34148 2 10.00% 70.00% ***0.71915 - 1.4745 1.0968 1 5.00% 75.00% *1.4745 - 2.2298 1.8522 2 10.00% 85.00% ***

    >= 2.2298 2.6075 3 15.00% 100.00% *****

    Test for null hypothesis of normal distribution:Chi-square(2) = 5.736 with p-value 0.05680

    4.

    Test for Serial Correlation

    Durbin-Watson statistic = 0.721617p-value = 0.000105588

    Breusch-Godfrey test for first-order autocorrelationOLS, using observations 1990-2009 (T = 20)Dependent variable: uhat

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    13/23

    coefficient std. error t-ratio p-value----------------------------------------------------------------const 0.496714 1.26945 0.3913 0.7011foreign_direct_ 0.494015 0.381343 1.295 0.2147GDP_growth 0.165103 0.166915 0.9891 0.3383imports 4.79090e-07 2.64303e-06 0.1813 0.8586

    uhat_1 0.787691 0.215691 3.652 0.0024 ***

    Unadjusted R-squared = 0.470652

    Test statistic: LMF = 13.336732,with p-value = P(F(1,15) > 13.3367) = 0.00236

    Alternative statistic: TR^2 = 9.413035,with p-value = P(Chi-square(1) > 9.41303) = 0.00215

    Ljung-Box Q' = 8.26774,with p-value = P(Chi-square(1) > 8.26774) = 0.00404

    5. Test for Specification Error

    RESET test for specification (squares and cubes)Test statistic: F = 3.503171,with p-value = P(F(2,14) > 3.50317) = 0.0584

    RESET test for specification (squares only)Test statistic: F = 6.062699,with p-value = P(F(1,15) > 6.0627) = 0.0264

    RESET test for specification (cubes only)Test statistic: F = 6.117924,with p-value = P(F(1,15) > 6.11792) = 0.0258

    From above, we can see that the problem of multicollinearity does not exist. Also in terms of

    heteroscedasticity, from the GRETL output, we can say that the model is acceptable. In the test

    for normality of residual, since the null hypothesis is normal distribution and the given chi-square is 5.736 with a p-value of 0.05680 we accept the null hypothesis.

    The GDP for the previous model does conform to the literature given above and inaddition to that the variables included in the model are all not significant. The following model is

    more acceptable than the previous model but it is underspecified because there are only two

    variables in this new model.

    Model 2: OLS, using observations 1990-2009 (T = 20)Dependent variable: unemployment_ra

    Coefficien

    tStd. Error t-ratio p-value

    Const 8.94214 1.45575 6.1426 0.00001 ***GDP_growth 0.0059488 0.209664 0.0284 0.97770Imports 9.36904e-

    083.44541e-

    060.0272 0.97862

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    14/23

    Mean dependent var 9.010000 S.D. dependent var 1.530703Sum squared resid 44.50837 S.E. of regression 1.618067R-squared 0.000216 Adjusted R-squared -0.117405F(2, 17) 0.001840 P-value(F) 0.998162Log-likelihood -36.37822 Akaike criterion 78.75644

    Schwarz criterion 81.74364 Hannan-Quinn 79.33957Rho 0.696330 Durbin-Watson 0.609766

    White's test for heteroskedasticity -Null hypothesis: heteroskedasticity not presentTest statistic: LM = 7.59469with p-value = P(Chi-square(5) > 7.59469) = 0.180033

    Test for normality of residual -Null hypothesis: error is normally distributedTest statistic: Chi-square(2) = 7.46847with p-value = 0.0238915

    LM test for autocorrelation up to order 1 -Null hypothesis: no autocorrelationTest statistic: LMF = 15.2515with p-value = P(F(1,16) > 15.2515) = 0.0012596

    1. Test for Multicollinearity

    Variance Inflation FactorsMinimum possible value = 1.0Values > 10.0 may indicate a collinearity problem

    GDP_growth 1.508

    imports 1.508VIF(j) = 1/(1 - R(j)^2), where R(j) is the multiple correlationcoefficient between variable j and the other independentvariables

    Properties of matrix X'X:1-norm = 5.2430918e+012Determinant = 3.9614224e+014Reciprocal condition number = 2.3026665e-013

    2. Test for Heteroscedasticity

    White's test for heteroskedasticityOLS, using observations 1-20Dependent variable: uhat^2

    coefficient std. error t-ratio p-value----------------------------------------------------------------const 6.80678 7.44573 0.9142 0.3761GDP_growth 0.654480 1.22842 0.5328 0.6025

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    15/23

    imports 3.49007e-05 3.78969e-05 0.9209 0.3727sq_GDP_growth 0.0287942 0.143722 0.2003 0.8441X2_X3 2.23527e-06 3.18983e-06 0.7007 0.4949sq_imports 3.71737e-011 4.59478e-011 0.8090 0.4320

    Warning: data matrix close to singularity!

    Unadjusted R-squared = 0.379735

    Test statistic: TR^2 = 7.594694,with p-value = P(Chi-square(5) > 7.594694) = 0.180033

    3. Test for Normality of Residual

    Frequency distribution for uhat5, obs 1-20number of bins = 7, mean = 1.5099e-015, sd = 1.61807

    interval midpt frequency rel. cum.

    < -1.3441 -1.7262 4 20.00% 20.00% *******-1.3441 - -0.57989 -0.96199 6 30.00% 50.00% **********-0.57989 - 0.18433 -0.19778 3 15.00% 65.00% *****0.18433 - 0.94854 0.56643 2 10.00% 75.00% ***0.94854 - 1.7128 1.3306 0 0.00% 75.00%1.7128 - 2.4770 2.0949 3 15.00% 90.00% *****

    >= 2.4770 2.8591 2 10.00% 100.00% ***

    Test for null hypothesis of normal distribution:Chi-square(2) = 7.468 with p-value 0.02389

    4.

    Test for Serial Correlation

    Durbin-Watson statistic = 0.609766p-value = 3.02846e-005

    Breusch-Godfrey test for first-order autocorrelationOLS, using observations 1990-2009 (T = 20)Dependent variable: uhat

    coefficient std. error t-ratio p-value--------------------------------------------------------------const 0.744194 3.34239 0.2227 0.8268

    imports 7.58279e-07 4.62108e-06 0.1641 0.8718labor_force 4.22222e-05 0.000183927 0.2296 0.8215GDP 2.28944e-012 1.18537e-011 0.1931 0.8494uhat_1 0.143257 0.294577 0.4863 0.6338

    Unadjusted R-squared = 0.015522

    Test statistic: LMF = 0.236502,with p-value = P(F(1,15) > 0.236502) = 0.634

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    16/23

    Alternative statistic: TR^2 = 0.310442,with p-value = P(Chi-square(1) > 0.310442) = 0.577

    Ljung-Box Q' = 0.271872,with p-value = P(Chi-square(1) > 0.271872) = 0.602

    5. Test for Specification Error

    RESET test for specification (squares and cubes)Test statistic: F = 0.053155,with p-value = P(F(2,15) > 0.0531552) = 0.948

    RESET test for specification (squares only)Test statistic: F = 0.091955,with p-value = P(F(1,16) > 0.0919549) = 0.766

    RESET test for specification (cubes only)Test statistic: F = 0.091887,with p-value = P(F(1,16) > 0.0918871) = 0.766

    In the following model, the variable labor force is added (see the literature) to try to

    remedy the problem of underspecification in the model 2.

    Model 3: OLS, using observations 1990-2009 (T = 20)Dependent variable: unemployment_ra

    Coefficien

    tStd. Error t-ratio p-value

    Const -4.15938 2.89974 -1.4344 0.17072Imports -5.8416e-

    064.24502e-

    06-1.3761 0.18775

    labor_force 0.000696623

    0.00015823 4.4026 0.00044 ***

    GDP -6.50145e-011

    1.0616e-011

    -6.1242 0.00001 ***

    Mean dependent var 9.010000 S.D. dependent var 1.530703Sum squared resid 12.85177 S.E. of regression 0.896234R-squared 0.711313 Adjusted R-squared 0.657184F(3, 16) 13.14111 P-value(F) 0.000139Log-likelihood -23.95626 Akaike criterion 55.91253Schwarz criterion 59.89546 Hannan-Quinn 56.69004Rho 0.108573 Durbin-Watson 1.778832

    White's test for heteroskedasticity -Null hypothesis: heteroskedasticity not presentTest statistic: LM = 7.54334with p-value = P(Chi-square(9) > 7.54334) = 0.580738

    Test for normality of residual -Null hypothesis: error is normally distributed

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    17/23

    Test statistic: Chi-square(2) = 12.483with p-value = 0.00194689

    LM test for autocorrelation up to order 1 -Null hypothesis: no autocorrelationTest statistic: LMF = 0.236502

    with p-value = P(F(1,15) > 0.236502) = 0.633772

    1. Test for Multicollinearity

    Variance Inflation FactorsMinimum possible value = 1.0Values > 10.0 may indicate a collinearity problem

    imports 7.461labor_force 10.329GDP 3.696

    VIF(j) = 1/(1 - R(j)^2), where R(j) is the multiple correlation

    coefficient between variable j and the other independentvariables

    Properties of matrix X'X:1-norm = 1.8586671e+023Determinant = 2.106367e+042Reciprocal condition number = 5.1392367e-025

    2. Test for Heteroscedasticity

    White's test for heteroskedasticityOLS, using observations 1990-2009 (T = 20)

    Dependent variable: uhat^2

    coefficient std. error t-ratio p-value---------------------------------------------------------------const 143.383 92.3403 1.553 0.1515imports 0.000230709 0.000142004 1.625 0.1353labor_force 0.0146942 0.00888184 1.654 0.1290GDP 6.34895e-010 7.86352e-010 0.8074 0.4382sq_imports 5.28123e-011 1.51496e-010 0.3486 0.7346X2_X3 9.71346e-09 7.25126e-09 1.340 0.2100X2_X4 0.000000 0.000000 1.235 0.2451sq_labor_forc 3.72793e-07 2.18861e-07 1.703 0.1193

    X3_X4 0.000000 0.000000 1.348 0.2074sq_GDP 0.000000 0.000000 0.2087 0.8389

    Warning: data matrix close to singularity!

    Unadjusted R-squared = 0.377167

    Test statistic: TR^2 = 7.543342,with p-value = P(Chi-square(9) > 7.543342) = 0.580738

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    18/23

    3. Test for Normality of Residual

    Frequency distribution for uhat1, obs 1-20number of bins = 7, mean = -9.76996e-016, sd = 0.896234

    interval midpt frequency rel. cum.

    < -1.9081 -2.2598 1 5.00% 5.00% *-1.9081 - -1.2047 -1.5564 0 0.00% 5.00%-1.2047 - -0.50122 -0.85294 2 10.00% 15.00% ***-0.50122 - 0.20222 -0.14950 8 40.00% 55.00%

    **************0.20222 - 0.90566 0.55394 8 40.00% 95.00%

    **************0.90566 - 1.6091 1.2574 0 0.00% 95.00%

    >= 1.6091 1.9608 1 5.00% 100.00% *

    Test for null hypothesis of normal distribution:Chi-square(2) = 12.483 with p-value 0.00195

    4. Test for Serial Correlation

    Durbin-Watson statistic = 1.77883p-value = 0.105984

    Breusch-Godfrey test for first-order autocorrelationOLS, using observations 1990-2009 (T = 20)Dependent variable: uhat

    coefficient std. error t-ratio p-value--------------------------------------------------------------const 0.744194 3.34239 0.2227 0.8268imports 7.58279e-07 4.62108e-06 0.1641 0.8718labor_force 4.22222e-05 0.000183927 0.2296 0.8215GDP 2.28944e-012 1.18537e-011 0.1931 0.8494uhat_1 0.143257 0.294577 0.4863 0.6338

    Unadjusted R-squared = 0.015522

    Test statistic: LMF = 0.236502,

    with p-value = P(F(1,15) > 0.236502) = 0.634

    Alternative statistic: TR^2 = 0.310442,with p-value = P(Chi-square(1) > 0.310442) = 0.577

    Ljung-Box Q' = 0.271872,with p-value = P(Chi-square(1) > 0.271872) = 0.602

    5.Test for Specification Error

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    19/23

    RESET test for specification (squares and cubes)Test statistic: F = 1.531411,with p-value = P(F(2,14) > 1.53141) = 0.25

    RESET test for specification (squares only)Test statistic: F = 3.243041,

    with p-value = P(F(1,15) > 3.24304) = 0.0919

    RESET test for specification (cubes only)Test statistic: F = 3.272001,with p-value = P(F(1,15) > 3.272) = 0.0906

    In the Model 3, the VIF for the variable labor force is greater than 10. If the variable is

    greater than 10 according to Danao ( : 231) there is a serious multicollinearity. Labor force has a

    VIF of 10. 329. In the following and last model presented in this paper, Model 4, the remedy that

    was done is to change the functional form of the variables. The variables now are in thelogarithmic form.

    Model 4: OLS, using observations 1990-2009 (T = 20)Dependent variable: unemployment_ra

    Coefficien

    tStd. Error t-ratio p-value

    Const -7.55919 22.1679 -0.3410 0.73754

    l_imports 1.00673 1.86562 0.5396 0.59689l_labor_force 19.4568 4.79581 4.0570 0.00092 ***l_GDP -7.87094 1.30675 -6.0233 0.00002 ***

    Mean dependent var 9.010000 S.D. dependent var 1.530703Sum squared resid 13.31220 S.E. of regression 0.912147R-squared 0.700970 Adjusted R-squared 0.644902F(3, 16) 12.50214 P-value(F) 0.000183Log-likelihood -24.30826 Akaike criterion 56.61651Schwarz criterion 60.59944 Hannan-Quinn 57.39402Rho 0.187524 Durbin-Watson 1.612281

    White's test for heteroskedasticity -Null hypothesis: heteroskedasticity not presentTest statistic: LM = 7.7552with p-value = P(Chi-square(9) > 7.7552) = 0.558992

    Test for normality of residual -Null hypothesis: error is normally distributedTest statistic: Chi-square(2) = 17.053with p-value = 0.000198144

    LM test for autocorrelation up to order 1 -Null hypothesis: no autocorrelationTest statistic: LMF = 0.655874with p-value = P(F(1,15) > 0.655874) = 0.430681

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    20/23

    1. Test for Multicollinearity

    Variance Inflation FactorsMinimum possible value = 1.0Values > 10.0 may indicate a collinearity problem

    l_imports 7.291l_labor_force 9.580

    l_GDP 5.831VIF(j) = 1/(1 - R(j)^2), where R(j) is the multiple correlationcoefficient between variable j and the other independentvariables

    Properties of matrix X'X:1-norm = 24926.499Determinant = 0.84960181Reciprocal condition number = 5.5585008e-008

    2. Test for Heteroscedasticity

    White's test for heteroskedasticityOLS, using observations 1990-2009 (T = 20)Dependent variable: uhat^2

    coefficient std. error t-ratio p-value------------------------------------------------------------const 4209.73 6273.80 0.6710 0.5174l_imports 380.872 599.310 0.6355 0.5394l_labor_force 2196.74 2282.14 0.9626 0.3585

    l_GDP 371.448 648.031 0.5732 0.5792sq_l_imports 13.0121 37.8395 0.3439 0.7381X2_X3 103.304 119.877 0.8618 0.4090X2_X4 40.6016 66.1751 0.6135 0.5532sq_l_labor_fo 406.722 264.428 1.538 0.1550X3_X4 193.477 134.621 1.437 0.1812sq_l_GDP 21.8963 21.3588 1.025 0.3294

    Warning: data matrix close to singularity!

    Unadjusted R-squared = 0.387760

    Test statistic: TR^2 = 7.755203,with p-value = P(Chi-square(9) > 7.755203) = 0.558992

    3. Test for Normality of Residual

    Frequency distribution for uhat2, obs 1-20number of bins = 7, mean = 2.54019e-014, sd = 0.912147

    interval midpt frequency rel. cum.

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    21/23

    < -1.9749 -2.3462 1 5.00% 5.00% *

    -1.9749 - -1.2324 -1.6037 0 0.00% 5.00%-1.2324 - -0.48988 -0.86114 2 10.00% 15.00% ***-0.48988 - 0.25265 -0.11861 11 55.00% 70.00%

    *******************

    0.25265 - 0.99518 0.62391 5 25.00% 95.00% *********0.99518 - 1.7377 1.3664 0 0.00% 95.00%

    >= 1.7377 2.1090 1 5.00% 100.00% *

    Test for null hypothesis of normal distribution:Chi-square(2) = 17.053 with p-value 0.00020

    4. Test for Serial Correlation

    Durbin-Watson statistic = 1.61228p-value = 0.0463899

    Breusch-Godfrey test for first-order autocorrelationOLS, using observations 1990-2009 (T = 20)Dependent variable: uhat

    coefficient std. error t-ratio p-value-------------------------------------------------------------const 2.33204 22.5944 0.1032 0.9192l_imports 0.0835794 1.88883 0.04425 0.9653l_labor_force 1.38548 5.14121 0.2695 0.7912l_GDP 0.433893 1.42555 0.3044 0.7650

    uhat_1 0.223423 0.275878 0.8099 0.4307

    Unadjusted R-squared = 0.041893

    Test statistic: LMF = 0.655874,with p-value = P(F(1,15) > 0.655874) = 0.431

    Alternative statistic: TR^2 = 0.837864,with p-value = P(Chi-square(1) > 0.837864) = 0.36

    Ljung-Box Q' = 0.814197,with p-value = P(Chi-square(1) > 0.814197) = 0.367

    5.

    Test for Specification Error

    RESET test for specification (squares and cubes)Test statistic: F = 0.659016,with p-value = P(F(2,14) > 0.659016) = 0.533

    RESET test for specification (squares only)Test statistic: F = 1.219366,with p-value = P(F(1,15) > 1.21937) = 0.287

  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    22/23

    RESET test for specification (cubes only)Test statistic: F = 1.266486,with p-value = P(F(1,15) > 1.26649) = 0.278

    In this part of the paper, the different ways on how to remedy the problems on CLRM were

    presented in relation to the explaining unemployment rate. The last model is free of all the

    problems of CLRM but we know that the variables included in the last model are not the only

    variables that explain unemployment. There is no multicollineraity in this model given that the

    Variance Inflation Factors (VIF) is less than 10. Also, the Durbin-Watson p-value shows that we

    should accept the null hypothesis, that there is no serial correlation in this model, at 5% alpha

    level. This finding conforms to the rho value, 0.187, which is not significantly different from

    zero. In connection to the earlier findings, the Durbin-Watson statistic is also near the value of 2.

    Thus, the problem of first order serial correlation is not present or is not severe in this model.

    It can also be further improved or not improved if the number of observations increased

    but that way of trying to improve the model is not part of this paper.

    WORKS CITED

    Agnese, Pable, and Sala, Hector. (2008). Unemployment in Japan: a look at the lost

    decade.October 5, 2012 fromhttp://mpra.ub.uni-muenchen.de/14332/1/MPRA_paper_14332.pdf

    Arango, M. (2010). Importance of FDI in the development of Emerging Countries: Application

    to Colombia and the Philippines. Colombia: EAFIT University. Retrieved on October 5,2012 from http://www.paclas.org.ph/PAPERS/Arango.pdf

    Autor, D., Dorn, D., & Hanson, G. (2012). The China Syndrome: Local Labor Market Effects of

    Imports Competition in the United StatesRetrieved

    October 5, 2012 http://economics.mit.edu/files/6613

    Dornbusch, R., Fischer, S., & Startz, R. (2008).Macroeconomics.New York: McGraw-Hill.

    Feldmann, Horst. (2006). Government Size and Unemployment: evidence from IndustrialCountries. Retrieved October 4, 2012 from http://www.jstor.org/stable/30026599.

    Gujarati, D. (2004).Basic Econometrics. New York: McGraw-Hill. PDF Version

    Kitov, Ivan, and Kitov, Oleg. (2012).Employment, unemployment, and real economic growth.

    http://mpra.ub.uni-muenchen.de/14332/1/MPRA_paper_14332.pdfhttp://mpra.ub.uni-muenchen.de/14332/1/MPRA_paper_14332.pdfhttp://mpra.ub.uni-muenchen.de/14332/1/MPRA_paper_14332.pdfhttp://mpra.ub.uni-muenchen.de/14332/1/MPRA_paper_14332.pdfhttp://economics.mit.edu/files/6613http://economics.mit.edu/files/6613http://www.jstor.org/stable/30026599http://www.jstor.org/stable/30026599http://www.jstor.org/stable/30026599http://economics.mit.edu/files/6613http://mpra.ub.uni-muenchen.de/14332/1/MPRA_paper_14332.pdfhttp://mpra.ub.uni-muenchen.de/14332/1/MPRA_paper_14332.pdf
  • 7/26/2019 Econ131 Research Paper. Topic: Unemployment

    23/23

    Retrieved October 5, 2012 fromhttp://arxiv.org/ftp/arxiv/papers/1109/1109.4399.pdf.

    Knotek, Edward, III. (2012).How useful is Okuns Law. Rterieved October 5, 2012 fromhttp://www.kc.frb.org/publicat/econrev/PDF/4q07Knotek.pdf.

    Levine, Linda. (2012).Economic growth rate and the unemployment rate. Retrieved October 5,2012fromhttp://www.fas.org/sgp/crs/misc/R42063.pdf.

    Mandel, M., & Carew, D. (2012, March).Measuring the Real Impact of Imports on JobsRetrieved October 2012http://progressivepolicy.org/wp-

    content/uploads/2012/03/03.2012_Mandel-Carew_Measuring-the-Real-Impact-of-

    Imports-on-Jobs.pdf

    Stat Informer, (2012) The new Official Philippine Definition of Unemployment. RetrievedOctober 5, 2012 fromhttp://www.nscb.gov.ph/ru6/stat%20informer-

    unemployment%20old%20&%20new%20definition.pdf

    World Bank. (2012). Foreign direct investment, net inflows (% of GDP) Retrieved on October 7,2012 fromhttp://data.worldbank.org/indicator/BX.KLT.DINV.WD.GD.ZS?page=3

    Virola, Romulo. (2005). WHO ARE THE UNEMPLOYED IN THE PHILIPPINES?RetrievedOctober 5, 2012 from

    http://www.nscb.gov.ph/headlines/StatsSpeak/041105_rav_mcp_unemployment.asp

    http://arxiv.org/ftp/arxiv/papers/1109/1109.4399.pdfhttp://arxiv.org/ftp/arxiv/papers/1109/1109.4399.pdfhttp://arxiv.org/ftp/arxiv/papers/1109/1109.4399.pdfhttp://www.kc.frb.org/publicat/econrev/PDF/4q07Knotek.pdfhttp://www.kc.frb.org/publicat/econrev/PDF/4q07Knotek.pdfhttp://www.fas.org/sgp/crs/misc/R42063.pdfhttp://www.fas.org/sgp/crs/misc/R42063.pdfhttp://www.fas.org/sgp/crs/misc/R42063.pdfhttp://progressivepolicy.org/wp-content/uploads/2012/03/03.2012_Mandel-Carew_Measuring-the-Real-Impact-of-Imports-on-Jobs.pdfhttp://progressivepolicy.org/wp-content/uploads/2012/03/03.2012_Mandel-Carew_Measuring-the-Real-Impact-of-Imports-on-Jobs.pdfhttp://progressivepolicy.org/wp-content/uploads/2012/03/03.2012_Mandel-Carew_Measuring-the-Real-Impact-of-Imports-on-Jobs.pdfhttp://progressivepolicy.org/wp-content/uploads/2012/03/03.2012_Mandel-Carew_Measuring-the-Real-Impact-of-Imports-on-Jobs.pdfhttp://progressivepolicy.org/wp-content/uploads/2012/03/03.2012_Mandel-Carew_Measuring-the-Real-Impact-of-Imports-on-Jobs.pdfhttp://www.nscb.gov.ph/ru6/stat%20informer-unemployment%20old%20&%20new%20definition.pdfhttp://www.nscb.gov.ph/ru6/stat%20informer-unemployment%20old%20&%20new%20definition.pdfhttp://www.nscb.gov.ph/ru6/stat%20informer-unemployment%20old%20&%20new%20definition.pdfhttp://www.nscb.gov.ph/ru6/stat%20informer-unemployment%20old%20&%20new%20definition.pdfhttp://data.worldbank.org/indicator/BX.KLT.DINV.WD.GD.ZS?page=3http://data.worldbank.org/indicator/BX.KLT.DINV.WD.GD.ZS?page=3http://data.worldbank.org/indicator/BX.KLT.DINV.WD.GD.ZS?page=3http://www.nscb.gov.ph/headlines/StatsSpeak/041105_rav_mcp_unemployment.asphttp://www.nscb.gov.ph/headlines/StatsSpeak/041105_rav_mcp_unemployment.asphttp://www.nscb.gov.ph/headlines/StatsSpeak/041105_rav_mcp_unemployment.asphttp://data.worldbank.org/indicator/BX.KLT.DINV.WD.GD.ZS?page=3http://www.nscb.gov.ph/ru6/stat%20informer-unemployment%20old%20&%20new%20definition.pdfhttp://www.nscb.gov.ph/ru6/stat%20informer-unemployment%20old%20&%20new%20definition.pdfhttp://progressivepolicy.org/wp-content/uploads/2012/03/03.2012_Mandel-Carew_Measuring-the-Real-Impact-of-Imports-on-Jobs.pdfhttp://progressivepolicy.org/wp-content/uploads/2012/03/03.2012_Mandel-Carew_Measuring-the-Real-Impact-of-Imports-on-Jobs.pdfhttp://progressivepolicy.org/wp-content/uploads/2012/03/03.2012_Mandel-Carew_Measuring-the-Real-Impact-of-Imports-on-Jobs.pdfhttp://www.fas.org/sgp/crs/misc/R42063.pdfhttp://www.kc.frb.org/publicat/econrev/PDF/4q07Knotek.pdfhttp://arxiv.org/ftp/arxiv/papers/1109/1109.4399.pdf

Recommended