Patents, Technological Spillovers at the Firm Level, Business and Default Cycles for Credit Risk - Assignment Example

Applied Economics Name: Institution: Applied Economics ECON 1116 2013 Part A QUESTION 4 (a) The use of statistical tests in econometrics is not a straightforward concept therefore not resulting to a clear-cut interpretation. This is mostly applicable in areas where test statistics are used not only for checking the adequacy of a certain model but also to model construction. In solving econometric problems, less reliance should be placed on the indices of model adequacy that are used to develop the model; and on the other hand the emphasis should be placed on the performance of models over other sets of data and against rival models. One of the used methods by econometricians in solving economic and financial problems is Maximum Likelihood Estimation Method. Maximum Likelihood Estimation is a fully parametric estimation. That is, the likelihood function=the joint density of the observed random variable. It involves the process of finding the value of one or more parameters in relation to a given statistic which makes maximizes the known likelihood distribution. An economic or financial problem can take different distribution hence different methods are applied to solve them. For instance, an economic or financial problem characterized by normal distribution can be solved as shown below: For a normal distribution 1 (2) so (3) and (4) giving (5) Similarly, (6) Gives Where; the standard deviation for maximum likelihood is the same for the sample. b) The t-test and similar non-parametric methods are only used to ascertain the difference between two groups. However, where three or more groups are concerned, then ANOVA takes control. If ANOVA testing indicates a difference within groups, then the main area of interest is the knowing the specific groups that exhibit the difference. Considering a three study groups X, Y and Z with different means, is X different from Y, X different from Z, Z different from Y? One of the several post hoc tests can be of help in determining the significant difference between the groups. It is worth noting that if the samples are paired then repeated-measures one-way ANOVA/Friedman’s test is used while unpaired samples utilizes one-way ANOVA or Kruskal-Wallis test. c) Autocorrelation is the cross-correlation with itself over successive time intervals. Autocorrelation occurs when the assumption of independent of the errors is violated and the errors become dependent on one another. That is, the dependency between the errors affects one another in some way. It is worth noting that autocorrelation is a common concept in time-series data as compared to cross-section data. This is because an error in period can have a significant error in the subsequent periods hence the correlation of errors between these two periods. The formula below shows an autocorrelation between times s and t. d) Vector autoregression (VAR) is an econometric model used to demonstrate the linear interdependence among multiple time series. It generalizes bivariate models through allowing for more than one evolving variables (k variables) over the same period (t=1,……T). The components of VAR includes variables that are collected in a k × 1 vector yt, which is coupled with the i th element, yi,t, the time t observation of the variable i . For instance, consider a GDP at a certain period. The value of GDP at period t is given below using a VAR: d) Main criticisms of Dickey-Fuller and Phillips-Perron-type tests Phillips-Person test is a unit root test used in time series analysis to test the null hypothesis that a time series is integrated of order 1. On the other hand, is a statistics test that measures if a unit root is present in an autoregressive model. Main criticism of main criticisms of Dickey-Fuller and Phillips-Perron-type tests is that; the tests are characterized by low power if the process is stationary nevertheless with a root close to the non-stationary boundary. For instance, Dickey-Fuller and Phillips-Perron-type tests are not well developed in determining if =1 or =0.95, especially whenever small samples are involved. QUESTION 5 a) Volatility clustering in finance is basically an observation that large changes tend to be followed by large changes while small changes are followed by small changes. In consideration to quantitative argument, while returns are not correlated, absolute returns or the square of the returns display a positive, slowly but significant decaying autocorrelation function: corr(|rt|, |rt+τ |) > 0 Where T ranges from a few minutes to several weeks. The interrelation between various agents change randomly in time with the obtained time series of price returns demonstrating chaotic bursts that results from on-off intermittency or emergence of attractor bubbling, just like in the financial time series with volatility clustering. These types of financial time series have resulted to the use of Autoregressive Conditional Heteroskedasticity (ARCH model) in financial forecasting and derivatives pricing. This model is developed with an aim of describing the concept of volatility clustering accurately and related effects such as kurtosis. The main argument for ARCH model is that volatility depends on past experiences of the assets process and related volatility process. It is therefore a more precise way of developing an argument that asset volatility tends to revert to some mean as opposed to remaining constant or following a monotonic path over a given period in time. b) Higher order ARCH models are rarely used in practice because it makes it difficult to produce the standard error band for the confidence intervals specifically for conditional variance forecast. This is because forecasting conditional forecast requires the variance of the variance. In addition, high order ARCH models allow negative shocks to have higher conditional variance as compared to positive shocks through the use of dummy variables. EWMA is an alternative model to ARCH modelling because it has some attractive properties like greater weight upon more recent observations. c) Standard GARCH models make an assumption that positive and negative error terms have a symmetric effect in consideration to volatility. That is, both good and bad news have similar effects on the volatility in Standard GARCH models. However, the assumption often undergoes violation, especially in stock returns where volatility increases more following bad news than after good news. Taking empirical arguments, volatility reacts asymmetrically to the sign of the shocks and hence several parameterized extension of Standard GARCH models in the recent times. Some of the extensions are the Exponential GARCH and Threshold ARCH Models . Exponential GARCH Exponential GARCH is given by the formula below: Where  ,   Represents the conditional variance , , , ,  and  are coefficients, And  is the standard normal variable One of the reason as to why EGARCH is preferred to GARCH is because the volatility of the EGARCH model is measured by the conditional variance which is an explicit multiplicative function of lagged innovations as compared to additive function of the lagged error terms in GARCH. EGARCH are characterized by limited instabilities of optimization routines because of no parameter restrictions. However, one limitation of EGARCH is that it allows for unconditional variance with large existence of extreme shocks. Further advantage of EGARCH is that the dependent variable associated with it is in logs hence there is no breaching of the non-negativity constraint. Threshold ARCH Models This is given by the formula below: The main aim of TARCH model is to undertake the division of the distribution of the innovations into disjoint intervals followed by approximation of a piecewise linear function for the conditional standard deviation and the conditional variance respectively. PART B B1. Which of the following is an ARDL (1,3) model? a.) yt = + 1yt-1+2yt-2 +3yt-3 + 0xt + 1xt-1+2xt-2+ 3xt-3 + vt B2. When autocorrelation is present, which assumption of the linear regression model is incorrect? b.) var (et)=2 B3. c.) biased, changing the denominator to N-2 B4. When performing a LM test for serial correlation, how is the test statistic distributed when the null hypothesis is true? a.) 2 B5. What is second order sample autocorrelation? c.) correlation between observations that are two time periods apart B6. How are AR and exponential smoothing models similar? b.) both incorporate past information in the form of moving averages of multiple Variables over time B7. What does it mean for a panel data set to be balanced? c.) the number of observations in the treatment and control group are equal B8. What are the consequences of ignoring or failing to recognize serial correlation? d.) biased, but with minimum variance B9. How do you interpret the estimated va 1 in the following equation: Ln (ENT_EXP) =γ1 + γ2 (INCOME) + e where INCOME is annual household income (in thousands) and ENT_EXP is annual entertainment expenses? c.) the increase in entertain expenses associated with a 1% increase in income B10. Which of the following is not a component of a hypothesis test? b.) goodness-of-fit B11. How do you reduce the probability of committing a Type I error? a.) reduce  B12. When should a left-tailed significance test be used? a.) When economic theory suggests the coefficient should be positive B13. If you are performing a left-tailed significance test and find the area to the left of |tc| is .99, what is the p-value? a.) .01 B14. If Z is a random variable generated by adding together X and Y which are also random variables, what do we know about var(Z) if X and Y are positively correlated? d.) var(Z) = var(X) * var(Y) B15. When estimating a VEC model using a two-step least squares process, what is the second step? a.) use least squares to estimate the cointegrating relationship B16. What type of model shows how series react dynamically to shocks? b.) an impulse response function B17. If you reject the null hypothesis when testing for Autoregressive Conditional Heteroskedasticity (ARCH) effects, what should you conclude? a.) the variance changes over time B18. A model with the following conditional variance function is what type of model? ht= e2 t-1 + e2 t-2 + e2 t-3 a.) ARCH (3) B19. What does it mean for a model to be GARCH-in-mean? d.) the mean increases with the variance B20. Which of the following assumptions must be made in order to use the pooled least squares estimator, but is relaxed in the cluster robust model? a.) E(eit) = 0 B21. Suppose you have a long, narrow panel of data and estimate a single equation with indicator variables and interaction terms for the individuals. In doing this what assumption from the pooled model have you relaxed? b.) errors are uncorrelated with any x’s B22 what is the difference between balanced and unbalanced panels? a.) unbalanced panels have some observations missing, balanced do not B23 what is the difference between a VEC and a VAR? c.) The VEC model is a special form of the VAR and should be used with cointegrated series. B24 If you have a times series data set with 100 years’ worth of data that you use to estimate a distributed lag model of order 3, how many degrees of freedom will you have for hypothesis testing on estimated coefficients? c.) 99 B25. Impulse response functions can be difficult to identify as a result of a.) interdependent dynamics and unobserved data ECON 1116 2012 Paper One Patents, R&D and Technological Spillovers at the Firm Level Main research question addressed The paper is pegged at determining the relationship between research and development and the patent application. A brief critique for patent as a measure of R&D Patent application is not the best measure for the R&D as the generation of a non-linearity by the discrete non-negative feature of the dependent patent variable renders the linear regression model upon which this measure is based inappropriate. To add on this, there are dissenting arguments on how to treat the firm-specific unobservable as they lead to what is termed as fixed and random effects models this further complicates the conventional random effects models which becomes inconsistent (Cincera, 1997, p.267). To this end, it is hard to maintain the assumption of strong exogeneity resulting from the fixed effects approach practically in ascertaining the vivid linkage between patent application and research and development. It is further tiresome to measure the spillovers benefits of a given firm from the R&D done by another firm as claimed by this paper. Independent variable with significant impact in at least two estimated models Spill overs over remains the independent variables with significant impact since it has two effects with the negative effect felt in the first two models arising from the completive spillovers and the positive effect resulting from diffusion spillovers based summing the coefficients attached resulting to 0.26 as the elasticity which is favorable to patenting activities. Serial correlation This refers to the relationship between a particular variable and itself over a given spread of time interval. For example financers users the security previous price to determine its possible future price. When the level variable affects its future level serial correlation tends to be in a repeating patterns. Evidence of serial correlation There is no evidence identified on the knowledge-production function as the GMM-MFEM estimate reveals that a greater part of activities that could lead to serial correlations are performed two years far much before patent application and there is a one year lagged effects of research and development as well as a significant contemporaneous. Paper two Business and Default Cycles for Credit Risk Strength of using data from more than one source This is attached to comparison and contrast of various sources which leads to a sound conclusion on the measurements defaulters and credit spread. One limitation of using data from more than one source It is subjected to time constraints which affects the proper time-series analysis for the various data collected. . Comparing model with and without lags The test reveals a reduced as a difference in 5.6 and 10.4 cycles have a their ranks declined indicated by the elements of shrink DΨ and Dϒ are approximated to be zero with their magnitudes being higher in models with no lags but higher in models with lags as indicated by the increased diagonal of Ƹe .There is a strong negative correlation between GDP and defaults cycles and there is insignificant between credit spreads and GDP and defaults which differ from previous analysis. To get the previous results we lag GDP and spread by one based on the short sample (Koopma & Lucas, 2005, p. 311). This results into a much higher p-value revealing the correlation between default cycle and the short GDP. I.I.D as representation of the error terms It is an abbreviation of independent and identically distributed, in this context, it is follows that defaulters and credit spread be mutually independent and identically distributed to the mean. Evidence validating the assumption of i.i.d The presence of a co-cyclicality relationship between real GDP and the credit spread revealed by a significant loading of negative 14.5 on the GDP cycle resulting from the equation of the credit spread. With the significant loading of 6.12 on the default cycles, this also validates this assumption as there is positive co-relation between the credit spread and default. Insights of paper to finance firms offering credit to small businesses in the UK The paper offers the financial bank a benchmark through the i.i.d to be used in accessing the credit worthiness of the creditors before loans are issued which help reduce the cases of loan defaulters which may severely affects bank reserves which subsequently leads to bankruptcy and hence closure of such banks. Through the negative co-relation between the bank spread and real GDP, the bank spread will thus be increased during declining periods of economic activities as this is associated with higher risk making it possible for increased rates of defaults. This may as well make financial banks to refrain from loaning during periods of declining economics activities which is a proactive strategy to reduce probability of defaults. Paper three Alcohol Abuse and Employment A critique to measurement of alcohol The problem is presented where the binary variable is endogenous and hence the possibility of similar variables that are correlated to both employment and alcohol abuse like the case of emotional problems. Another daunting challenge is the assumption of the non-linearity by M&S. Leading to loss of the significant correlation between alcohol abuse and employment. The previous paper uses model IV as a measure for the alcohol effect based on endogeinity and finds that alcohol reduces employment but increases unemployment but presents a contradiction on the value of statistic which is suggested to bare no significant (Terza, 2002, p. 399). On the other hand, the current paper justifies the earlier finding but has a statistic having a significant. The previous paper did not appreciate the heterogeneity and the subsequent application of conventional multinomial logit which is of much significant as the greater differential figure indicates the impact of alcohols on the two different people. An improvement that Terza claims to have made to the previous work The incorporation of the inherent non-linearity of the mentioned regression structure and further affirms that alcohol abuse impacts in regard to individual observed and unobserved features, are heterogeneous. This is a major area of deviation from the former which only used the model IV estimates and did not find any significant statistic found the Terza. This paper unlike the M&S, goes a notch higher to determine the effect of binary variable on the probability that employment status will be one. Determinants of alcohol abuse and interpretation of the results Where biological dad is alcoholic or was problem drinker, it is found that an individual will be alcoholic and an individual will be non-alcoholic if the biological father is not an alcoholic. Another significant effect is an individual lived with alcoholic he will be alcoholic and if not then one will not be alcoholic. Key factors found to be linked to alcohol abuse Abuse of alcohol is linked to lower rates of acquiring employment and also retention of the employment. As those who are not alcoholic are seen to have difficulty in securing their jobs as. Alcohol abuse is also linked to distress of the people leading with the alcoholic. Policy for reducing alcohol abuse within the UK Labor market is very key to any sound economic development of a country. To this end, the previous researches do not stand the test to ensure effective labor productivity since the potential endogeinity of the abuse variable aspect has not been targeted. Adopting a policy which counts for both heterogeneity and endogeinity will see this issue brought to the least impact. Reference Cincera, M. (1997) “Patents, R&D and Technological Spillovers at the Firm Level: Some evidence from Econometric Count Models for Panel Data” Journal of Applied Econometrics Koopman, S. J. and Lucas, A. (2005) “Business and Default Cycles for Credit Risk” Journal of applied Econometrics. Terza, J. V, (2002) “Alcohol Abuse and Employment: A Second Look” Journal of Applied Econometrics Read More