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- Jack Johnston and John Dinardo(1997)_Econometric Methods
- 1997 [Jack Johnston, John Dinardo] Econometric Methods.pdf
- Johnston Econometric Methods Solution
Jack Johnston and John Dinardo(1997)_Econometric Methods
Further Aspects of Two-variable Relationships 2. Specilkation Error 4. Specification and Testing 8. An Introduction to Monte Carlo Methods Extensions to the Basic Model: Groufe Data Treatment Effects and-rfwo-step Methods Matrices A. This is not to say that economists believe that the world can be analyzed adequately in terms of a collection of bivariate relations.
When they leave the two-dimensional diagrams of the textbooks behind and take on the analysis of real problems, multivariate relationships abound. Nonetheless, some bivariate relationships are signiscant in themselves;. This pattern, however, is not replicated in the middle and later. One might be tempted to conclude from Fig. The time dimension is no longer shown explicitly, but most software programs allow the option of joining successive points on the scatter so that the evolution of the series over time may still association between the variables: be traced.
Both parts of Fig. It is clear that although the association is approimately linear in the early part of the period, it is not so in the second half. Figures 1. The derivations of the series are described in the data disk.
The rationale for the logarithmic transformations is discussed in Chapter 2. Figure 1 gives various time plets of gasoline expenditure, price, and income. The real price series, with as the base year, shows the two dramatic price hikes of the early and late s, which were subsequently eroded by reductions in the nominal price of oil and by U. The income and expenditure series are both shown in per capita form, because U.
The population series used to dellate the expenditure and income series is the civilian noninstitutional population aged l 6 and over, which has increased even faster than the general population. Per capita real expenditure on gasoline increased steadily in the and early s, as real income grew and real price declined. This steady rise endedzwith the price shocks of the s, and per capita gas consumption has never regained the peak levels of the early seventies. The scatter plots in Fig.
The plot for the whole period in Fig. The scatter for This is shattered in the middle period This data set will be analyzed econometrically in this and later chapters. These illustrative scatter diagrams have three main characteristics. One is the sign of the association or covariation-that is, do the valiables move together in strength of the association. A third positive negative fashion?
In Section 1 we discuss the extent to which the correlation coefhcient measures the hrst two characteristics for a linear association, and in later chapters we will show how to deal with the linearity question, but tirst we give an example of a bivariate frequency distribution.
The data underlying Figs. When the sample size n is very large, the usually data are printed as a bivariate frequency distribution; the ranges of X and i' are split into subintervals and each cell of the table shows the number of observatiops. Table 1. S It is not possible to give a simple.
However, insmction of the cell frequencies suggests a positive association between the two measurements. First of all, each of the tivecenlral columns of the table gives a distribution of heights for a given chest mesurement. Similarly, the rows of the table give distributions of chet measurements, conditional on height. The direction and closeness of the linear ssociation between two variables are measured by the correlation coefhcient. Stigler, Fc Histor. Figure 1. The product xiyi is positive for all points in quadrants I and lll and negative for all points in quadrants 11and IV.
Since a msitive relationship will have points lying for the most part in quadrants 1 and ,and a negative relationship will have points lying mostly in the other two quadrants, the sign of X''j l xiyi will indicate whether the scatter slopes upward or downward.
This sum, however, will tend to increase in absolute terms as more data are added to the sample. Thus, it is better to express the sum in average terms, giving the sample covariance, -. The value of te covariance depends on the units in which the variables are measured. Changing one variable from dollars to cents will give a new covariance times te old.
To obtain a measure of association that is invariant with respect to units of measurement, the deviations are expressed in standard deviation units. The covariance of the standardized deviations is the correlation coemcient, r nnmely, y'. Omitting subscripts and the limits of summation sincethere is no ambiguity and performing some algebraic manipulations give three equivalent expressions for the correlation coefkient--two in terms of deviations and one in terms of the raw data: Nr.
If we use a period for a subscript over which summation XJ! In conjurtion with the Xi values these marginal frequencies will yield i 1, the standard deviation of X. The marginal frequencies for i' are n. Finally the covariance is obtained from '. To see this, let c be any arbitrary constant. Then X y c. J x2 Ey2 , that is, r2 ci 1 This expression is one form of the Cauchpschwarz inequality. The equality will only hold if each and every y deviation is a constant multiple of the corresponding deviation.
In such a case the observations a1llie on a single straight line, with a positive slope r 1 or a negative slope r 1. Figure l shows two cases in which r is approximately zero.
Thus, the correlation coefhcient measures the degree of linear association. A low value for r does not rule out the possibility of a strong nonlinear association, and such an association might give positive or negative values for rif the sample observations happen to be located in pnrticular segments of the nonlinear relation. Many coefscients that are both numerically large and also adjudged statistically sign cant by tests to be described later may contain no real infonnation.
That statistical signihcance has been achieved does not necessarily imply that a meaningful and useful relationship has been found. The crucial question is, What has caused the observed covariation? Our favorite spurious, or nonsense, correlation was given in a beautiful pathe statistician G.
Udny Yule. Howconfer ever, no British politician proposed closing down the Church of England to immortality on the electorate. Cumulative sunsmts and cumulative rainfall necessarily trend upward, as do the U. The first differences are simply the changes in the series Thus, between adjacent observations. Many series Iat show very high correlations between X and F the Ievels will show very low correlations between A. Yand AF thehrst dterence. This result usually indicates a spurious relationship.
On the other hand, if there is a causal relationship Ytween the variables, we expect to hnd correlations between levels and also between tirst differences. This point has recently been emphasized in an important pamr by Stigler and Sherwin.
Plosser and G. David F. Hendry, Econometrics-Alchemy or Science? Will it alter its course, through some unforeseen force and come to a premature end? However, since most prices, like many economic series, show trend-like movements over time, Stigler and Sherwin wish to guard against being misled by spurious correlation. Thus, in addition to correlating price levels they correlate price changes. As one example, the prices of December silver futures on the New York Commodity Exchange and te Chicago Board of Trade over a day trading period gave 0.
In Minneapolis, Minnesota, and r Kansas City, Missouri, two centers of the iour-milling industry, the monthly wholesale prices of :our over 1 gave correlations of 0. By the fall of the other majors had responded by continuing their credit cards but introducing two prices, a credit price and a lower cash price.
Subsequently one of the independents sued Arco under the antitrust laws. The essence of the plaintiff case was that there were really two separate markets for gasoline, one in which the majors competed with each other, and a second in which the minors competed. They further alleged, though not in this precise language, that Arco was like a shark that had jumpedout of the big pool into their little pool with the intention of gobbling them al1 up.
No one questioned that there was competition within the majors and competition within the minors: the crucial question was whethe. The Lundberg Survey reports detailed information twice a month on the prices of al1 types and grades of gasoline at a very large sample of stations. These data are also averaged for majors and minors.
Twelve differentiated products were defined for the majors and four for the minors. This step allowed the calculation of 66 correlation coefhcients for a11pairs of products within the majors and 6 correlation coefcients within the minors. Each set of coefficients would be expected to consist of very high numbers, re:ecting the intensity of competition inside each group.
However, it was also possible to calculate 48 correlation coecients for a1lcross-pairs of a major price and a minor price. If the plaintiff argument were correct, these 48 coefficients would be of negligible size. On the other hand, if there were just a single large market for gasoline, the cross correlations should not be markedly less than correlations within each group.
A nice feature of the problem was that the within-group correlations provided a standard of reference for the assessment of the cross correlations.
1997 [Jack Johnston, John Dinardo] Econometric Methods.pdf
Distinguish between econometric methods, which are statistical estimation. Johnston, J. Jack johnston john dinardo. To derive cov a, b Gauss-Markov theorem To derive var eo. Econometric methods [Johnston, J] on Amazon. Generalized Method of Moment methods are presented in Chapter 10 as a reasonable and simple estimation approach that is valid in large samples. Carousel Previous Carousel Next.
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Johnston Econometric Methods Solution
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