Unemployment rate in Spain
Summer 2020
Please read each question carefully and answer it completely. Please provide STATA output in the Appendix although be aware I will only look at your output if I suspect there are issues with your estimations/STATA commands I will not search through output for answers to questions that should be included in the main body of your exam.
IMPORTANT: I have not “cleaned up” these data sets, although I have, in some cases, renamed them, which means that there are variables that you may not be using to answer these questions. For your “four-step” hypothesis tests, please be sure to include both the critical value and p-value approaches, where possible unless otherwise specified, use α = 0.05.
#1. For this question you will be using the data “Spain Phillips,” i.e., data for the inflation and unemployment rate in Spain
(i) Use the Spain data to estimate the model in equation [11.19] contained in Example 11.5 dealing with the Phillips curve. [“Expectations Augmented Phillips Curve”]. Create any necessary variables.
Report your estimated equation (including R2). Briefly define the “natural rate of unemployment” [using cited outside resources if necessary] and explain how your textbook author uses this estimated model to get an estimate of the natural rate of unemployment from this model. What is the estimated “natural rate of unemployment” based on your model?
Model:
The R-squared is 0.2645, implying that the present model can explain 26.45 percent of the inflation rate variation. The scatter matrix below shows the correlation between the two variables.
The term natural rate implies that there will be no permanent changes to a particular variable above or below its level that is considered natural. From the definition, therefore, the natural rate of unemployment is described as the level at which unemployment remains, the effects of monetary policy notwithstanding, however great they can be. The author uses the model coefficients to estimate the natural rate of unemployment, dividing the constant-coefficient by negative beta 1. Based on the present model, the estimated natural rate of unemployment is 29.99 percent.
(ii) Conduct a four-step Durbin-Watson test for serial correlation for this model. Based on this result, is it reasonable too, as the textbook suggests, estimate this model assuming “TS.1′ through TS.5′ hold”?
| Durbin-Watson test for serial correlation |
| Step 1:
|
| Step 2: The test hypothesis relies on a Durbin-Watson test at t=49, k=1 α = 0.05 Reject the Ho if the DW stat <1.3024; Fail to reject the Ho if DW stat > 1.3868. （Since the table just has the value of t=45 and 50, so the value of 49 is estimated as the following: (1.324-1.288)*(2/5)+1.288=1.3024, (1.403-1.376)*(2/5)+1.376=1.3868 Calculated using the Durbin Watson tables |
| Step 3: Based on the stata output, 0.16443
|
| Step 4 0.16443>1.3868 Therefore, fail to reject the null hypothesis |
(iii) In Chapter 15: C7, the authors suggest an IV estimation for this model. Why might IV estimation be necessary? Test the “appropriateness” of the instrument the question suggests, show/explain. Estimate the model using the IV estimation outlined in this question. Report your estimated model and compare it with the OLS results you obtained in (i). Does the (point) estimate of the “natural rate of unemployment” change with this estimation? Show/ Explain.
FOR THIS QUESTION: you DO NOT have to answer the questions in the textbook for Chapter 15: C7 specifically, just use the question to inform your work. Please use STATA to estimate the IV regression.
IV estimation is necessary since it is possible to make causal inferences with data that is observational. Similarly, IV estimation variables are essential in adjusting for both the observed and unobserved confounding effects in the model. The technique is also employed to mitigate the endogeneity of explanatory variables. In testing the “appropriateness” of the instrument, and should be uncorrelated, and and have either any positive or negative correlation. Therefore, it is vital to use a variable that correlates with but not with . The IV estimation is preferred to OLS estimation when the selected instrument has a moderate to high correlation with the variable.
The IV estimation for the model is:
The model is similar to the OLS model since there are no endogenous and exogenous variables. The natural rate of employment, therefore, is 30 percent. It does not change using the IV estimation analysis.
(iv) Do you suspect that either the inflation rate or the unemployment rate has a unit root? Defend your viewpoint with specific evidence using the two methods from our homework assignment. Formally four-step hypothesis test where appropriate.
I suspect that both the inflation rate and unemployment have a unit test.
| Dickey-Fuller test for unit root (unemployment） |
| Step 1: （θ unemployment = 1） （θ unemployment < 1）
|
| Step 2: This hypothesis test is based on the Dickey-Fuller test. α = 0.05 Reject the Ho if the z-test stat < -1.746 and p-value < 0.05. |
| Step 3: p-value = 0.2993 |
| Step 4: Since AND 0.2993>0.05 Do not Reject Ho.
|
| Dickey-Fuller test for unit root (inflation） |
| Step 1: （θ inflation = 1） （θ inflation < 1） |
| Step 2: This hypothesis test is based on the Dickey-Fuller test. α = 0.05 Reject the Ho if the z-test stat < -1.746 and p-value < 0.05. |
| Step 3: p-value = 0.7606 |
| Step 4: Since AND 0.7606<0.05 Do not Reject the Ho. |
(v) Some economists complain that unit root tests have low power. Explain specifically what that means
in terms of unit root hypothesis testing and why that is not a good characteristic of a hypothesis test.
Low power in unit root hypothesis testing implies that there is a deterministic trend in the regression test model. The low power of a unit test implies that the type II error is higher than 0.05 level of significance. A low power causes an imbalance between the type I error and type II error , implying that there is a bias towards the type II error; hence a false null hypothesis is not rejected. Failing to reject the invalid, null hypothesis means that the overall hypothesis testing procedure is compromised.
Appendix (software output):
Appendix 1. OLS regression
Source SS df MS Number of obs = 50
F( 1, 48) = 17.26
Model 455.255359 1 455.255359 Prob > F = 0.0001
Residual 1266.08659 48 26.3768039 R-squared = 0.2645
Adj R-squared = 0.2492
Total 1721.34195 49 35.1294275 Root MSE = 5.1358
Appendix 2. OLS coefficients
Inflation Coef. Std. Err. t P>t [95% Conf. Interval]
unemployment -.4303649 .1035906 -4.15 0.000 -.6386478 -.222082
_cons 12.90661 1.680561 7.68 0.000 9.527611 16.2856
Appendix 3. Durbin Watson test
Durbin-Watson test with normal pvalue
dw Prob < dw Prob > dw
.16443 0.0000 1.0000
Appendix 4. IV estimation
inflation Coef. Std. Err. z P>z [95% Conf. Interval]
unemployment -.4303649 .1014977 -4.24 0.000 -.6292967 -.2314332
_cons 12.90661 1.646607 7.84 0.000 9.679315 16.1339
Appendix 5. Dick Fuller test for unit root of Unemployment
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
Z(t) -1.971 -3.587 -2.933 -2.601
MacKinnon approximate p-value for Z(t) = 0.2993
Appendix 6. Dick Fuller test for unit root of inflation
Test 1% Critical 5%Critical 10%Critical
Statistic Value Value Value
Z(t) -0.980 -3.587 -2.933 -2.601
MacKinnon approximate p-value for Z(t) = 0.7606