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The inconsistency between the estimated coefficient and economic theory

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Please explain and show a detailed calculations.

1. Suppose that the true relationship between y, x, and z is yi = β0 + β1xi + β2zi + ui, where
economic theory predicts β0 > 0, β1 < 0, and β2 < 0. Ui is a random error with an expected
value of zero. The following sample model has been proposed:
Answer the following:
a) Show than (beta one tilda)
is a biased estimator of and that the bias is equal to
(see the attachment for full details)

Note: if you can’t see the equation above. In the numerator it says xi minus x bar times zi and in the denominator it says xi minus x bar squared.

b) Let ( beta one hat) be the multiple regression estimate from y on x and z, would you
expect (standard error beta one tilde) or (standard error beta one hat)
to be smaller? Explain.

c) The following sample model has been estimated: The sign of the
coefficient on xi is the opposite of what economic theory predicts. Can this be explained
by the omission of zi? What is the implied sign for the correlation between xi and zi?
Explain your answer.

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The inconsistency between the estimated coefficient and economic theory is examined.

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The Importance of Purchasing Power Parity

Mini Case: Turkish Lira and the Purchasing Power Parity

Veritas Emerging Market Fund specializes in investing in emerging stock markets of the world. Mr. Henry Mobaus, an experienced hand in international investment and your boss, is currently interested in Turkish stock markets. He thinks that Turkey will eventually be invited to negotiate its membership in the European Union. If this happens, it will boost the stock prices in Turkey. But, at the same time, he is quite concerned with the volatile exchange rates of the Turkish currency. He would like to understand what drives the Turkish exchange rates. Since the inflation rate is much higher in Turkey than in the U.S., he thinks that the purchasing power parity may be holding at least to some extent. As a research assistant for him, you were assigned to check this out. In other words, you have to study and prepare a report on the following question: Does the purchasing power parity hold for the Turkish lira-U.S. dollar exchange rate? Among other things, Mr. Mobaus would like you to do the following:

1. Regress the rate of exchange rate changes (percentage change in the exchange rate) on the inflation rate differential to estimate the intercept and the slope coefficient, and interpret the regression results. Interpreting the regression results means that you will have to test for statistical significance and explain how the results support or are inconsistent with PPP theory. Also, discuss the relation between the percentage change in the exchange rate and the inflation differential. For example, if there is a negative 1% inflation differential, what is the predicted percentage changes in the exchange rate?

Note: You will need to calculate both the inflation rate differential and the percentage change in the exchange rate (a.k.a. rate of exchange rate changes) from the data provided.

Data source: You may download the consumer price index data for the U.S. and Turkey from the following website: http://www.oecd.org, "hot file" (Excel format) . You may download the exchange rate data from the website: http://pacific.commerce.ubc.ca/xr/data.html.

Please see attached file for additional information regarding this question. Please provide supporting material to your answer such as excel calculation as well as any necessary graphical demonstration. Many thanks!

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