TI153 Applied Macroeconometrics (Part 3): Homework
October 5th, 2023
The homework on macro panel data methods accounts for 73 th of the final grade. The homework should be handed in individually. The deadline for handing in the complete homework is Sunday October 29th at one minute before midnight (23.59h). Please, email the homework as one pdf file to [email protected] .
Guidelines
1. Read and study the econometric techniques discussed during the lectures. Read the relevant literature if you think this is necessary to improve your understanding of these methods.
2. To address the questions below, you can use a ready-to-go package like Eviews (or an alternative). The estimation options in Eviews are limited, however. Moreover, Eviews is not always the most efficient way of obtaining results. Therefore, you should also use an additional (preferably, matrix-based) programming language such as Matlab or Gauss to obtain your results. The code discussed during the lectures can serve as the basis to write your own code. You can report your own code as an appendix to your pdf file (do not include code in your main text and replies, though).
3. All questions below must be answered with the use of the entire dataset provided in the Excel file Dataset.xlsx (see Canvas). This dataset contains data on aggregate consumption and some of its determinants. The dataset is a typical macro dataset containing data for 18 advanced economies (N=18) over the period 1970−2018 (T=49). The panel is balanced. The variables included in the dataset are the log of the private consumption to GDP ratio (lcy), the growth rate of real GDP (gy), the real short-term interest rate (rsr), the unemployment rate (ur), and a bank crisis dummy (cris). The source of the data is the Jord`a-Schularick-Taylor macro-history database (version 6, July 2022) for which details can be found at
4. Answer each question concisely and to the point. Put your estimation results in tables with necessary clarifications in footnotes. Do not just report the numbers, but also discuss them briefly. Note that you should not apply a degrees of freedom correction when calculating standard errors (hence, when calculating standard errors in Eviews, always choose the option ’no degrees of freedom correction’).
1. Static panel
To start, regress the log consumption to income ratio (lcy) on the real short-term interest rate (rsr) and on the unemployemt rate (ur) variables. The first regressor allows for substitution and/or income effects of the real interest rate on saving (and therefore consumption), while the second regressor, the unemployment rate, can be considered a proxy for macro-economic uncertainty. It can also capture potential cyclicality in the consumption ratio. You should allow for country-fixed effects but, for now, you can assume that there is no endogeneity and no cross-sectional dependence in the error term and no heterogeneity in the slope parameters. Answer the following questions:
a. Under the assumptions made, which estimator can you use? Why?
b. Report the coefficient estimates for both regressors. What can you conclude?
c. Use a White correction on your standard errors that allows for heteroskedasticity both in time and in space (White diagonal standard errors). Report the estimated standard errors. Remember that you should not apply a degrees of freedom correction when you calculate standard errors.
d. Calculate and report the coefficients and standard errors as obtained from Eviews but also as obtained from code that you have written yourself (for instance in Matlab or Gauss). You should obtain identical results in both cases.
e. Report the value of the panel Durbin-Watson statistic. What can you conclude from this statistic?
2. Dynamic panel
It is well known that the consumption ratio is rather persistent. To capture this persistence and to (hopefully) get rid of autocorrelation in the regression error, a lagged value of the log consumption- income ratio can be added to the regression equation. Regress the log consumption-income ratio (lcy) on its own first lag and on the variables considered also in Exercise 1, namely the current real short-term interest rate (rsr) and the unemployment rate (ur). You should again allow for country-fixed effects, and you can again assume that there is no endogeneity nor cross-sectional dependence in the error term and no heterogeneity in the slope parameters. Answer the following questions:
a. Which estimator do you use? Why should you be careful when using this estimator in the present context? Give a justification for using this estimator given your dataset.
b. Report the coefficient estimates and White diagonal standard errors for the lagged consumption ratio, and for the regressors rsr and ur. You should again make sure that you obtain identical coefficient estimates in Eviews and in your own code (e.g., Matlab or Gauss). How have your estimates changed compared to the static panel case?
c. Report the panel Durbin-Watson statistic. What does it suggest compared to the static panel case? Is this statistic appropriate in the present context?
d. Given the possibility that there still is autocorrelation in the residuals, you can use cross-section cluster- robust standard errors that take into account time-dependencies in the data. Report these standard errors for all the coefficient estimates reported in part b) of this question. Report both the standard errors obtained from Eviews and standard errors that you obtain from your own code and check that they are identical (Note: calculate these standard errors without a degrees of freedom correction)
e. Is a correction of the standard errors sufficient to deal with autocorrelation in a dynamic panel data model that includes a lagged dependent variable? Explain why/why not. How could you tackle autocorrelation of the AR type? How could you tackle autocorrelation of the MA type?
3. Endogeneity
In the regression of the consumption ratio on its own lag, on the real short-term interest rate (rsr) and on the unemployemt rate (ur) variables, there can be endogeneity problems - even in the absence of autocorrelation in the residuals - if these regressors are correlated with the error term. To correct for biases stemming from endogeneity, an instrumental variables approach is necessary. One possibility is to use lagged values of the dependent variable and regressors as instruments (i.e., internal instruments). In what follows, make sure that you always use two lags of the dependent variable and each regressor as instruments. Assume homogeneity of the slope coefficients and cross-sectional independence in the error term. You should allow for country-fixed effects. Answer the following questions:
a. Calculate the IV (1st step) estimates of the homogeneous dynamic panel regression where lcy is regressed on its own first lag and on rsr and ur. Assume that there is no autocorrelation in the residuals when deciding on your instrument set, i.e., you can use lags one and two of lcy, rsr and ur as instruments. Report the three coefficient estimates. Also report the estimated White diagonal standard errors for the three coefficients. Make sure to obtain the results from both Eviews and from your own written code. b. With the same instrument set, calculate the GMM (2nd step) estimates with the use of a White correction (Note: make sure to use the White diagonal GMM weights in the panel options in Eviews). Report the three coefficient estimates and the White diagonal standard errors. Again, provide results from both Eviews and from your own written code.
c. What is the value of the test for overidentifying restrictions (Hansen/Sargan or J test) in the GMM case considered in part b)? What are the degrees of freedom for this test? What do you conclude from the test result? In Eviews, the instrument rank is reported to be 24. Where does this number come from?
d. Assume now that there is first-order autocorrelation of the moving average (MA) form in the residuals. Adjust your instrument set accordingly. Apply IV estimation. Use two-way cluster-robust standard errors. Report the instrument set used, the IV coefficient estimates for all three coefficients and the estimated standard errors.
4. Cross-sectional dependence
Again, regress the log consumption-income ratio (lcy) on its own first lag, on the real short-term interest rate (rsr) and on the unemployemt rate (ur) variables and on a set of country dummies. You may ignore endogeneity concerns and possible slope heterogeneity, so you are back in the case of Question 2. You suspect that there is cross-sectional dependence in the residuals of the estimation results obtained in Question 2b. Answer the following questions:
a. From your results obtained in Question 2b, calculate the estimated residuals for each country in the panel. Based on country pairs of residuals, calculate the cross-sectional dependence statistic CDp by Pesaran (2004). Make sure to obtain the results from both Eviews and from your own written code. Report the test statistic and its p-value. What can you conclude?
b. A first way to incorporate cross-sectional dependence is to add time dummies to the regression equation which allows for homogeneous cross-sectional dependence. This can easily be done in Eviews with the option ’period fixed effects’. Report the parameter estimates for the coefficients on the three regressors and the corresponding White diagonal standard errors.
(An alternative approach is to add the cross-sectional means of the dependent variable and the three regressors to the regression equation under the assumption that they enter the regression with identical parameters across countries. This approach is probably easier to implement when working with your own code. Try this out and check that you obtain the same result as with time dummies.)
c. A second way to incorporate cross-sectional dependence is with the CCEP estimator which allows for heterogeneous cross-sectional dependence. In this case the cross-sectional means of the dependent variable and the three regressors should be added to the regression equation under the assumption that they enter the regression with different parameters across countries. As with country fixed effects, they are then factored out of the regression. Write your own code (in Matlab or Gauss, for instance) to implement the CCEP estimator. Report the CCEP estimates for the coefficients on the three regressors and the corresponding White diagonal standard errors.
5. Heterogeneity
Investigate the cyclicality of the private consumption ratio by regressing the log consumption to GDP ratio (lcy) on its own first lag and on the growth rate of real GDP (gy). It is often suggested that private consumption decreases during recessions (e.g., because of tighter credit constraints) implying that the private consumption ratio is procyclical. To investigate this cyclicality, there is no need to deal with endogeneity. However, it is probable that the impact of the business cycle on consumption differs across countries, for instance because of differences in institutions. Hence, a mean-group (MG) approach should be implemented that is based on country-by-country estimation. Make sure to always include a constant in the country-specific regressions (i.e., country fixed effects). Answer the following questions:
a. Report the MG estimate of the coefficient on real GDP growth in the regression of lcy on lagged lcy and gy. Also report the (non-parametric) standard error for this estimate (see lecture slides). What can you conclude?
b. How can you calculate the estimated mean-group long-run impact of real GDP growth on the private consumption ratio? Report the estimate that you obtain by only considering the countries for which you obtain dynamically stable results.
c. Report the CCEMG estimate of the coefficient on real GDP growth in the regression of lcy on lagged lcy and gy. Again, report the (non-parametric) standard error for this estimate. What can you conclude?
6. Panel local projections
An important implication of bank crises is that they may negatively affect credit supply, implying more binding credit constraints and depressed consumption-income ratios in the years after a crisis. Investigate what happens to the log consumption to income ratio in the aftermath of a bank crisis. To this end, calculate impulse responses by estimating fixed effects panel local projections (FE-LP’s). More specifi- cally, regress the log consumption to income ratio lcy at t + h on the current period t bank crisis dummy (cris) and on two control variables: the once lagged log consumption to income ratio (i.e., for year t − 1) and the current period t real GDP growth variable (gy). Don’t forget to include country-fixed effects. Estimate the LP’s over the horizon h = 0, ..., 5. Make sure to also write your own code to estimate LP’s in a quick and efficient manner. Answer the following questions:
a. Provide the estimates for the coefficient on the cris regressor in the LP’s for h = 0, ..., 5
b. For each of these coefficients, also report the two-way cluster-robust standard error
c. Using the reported estimates, make a figure of the IRF of the impact of cris on lcy at h = 0, ..., 5 that also shows the 90% confidence interval of the IRF
