Economics 236C, Chad Jones Questions for "Problem Sets", Spring 2007 This file will contain a weekly problem related to the paper(s) under discussion. The problem sets are due at the start of the relevant class. ---------------------------------------------------------- Hsieh and Klenow (2006) "Misallocation and TFP" 1. Define the equilibrium allocation of resources (with distortions) for the model in this paper. 2. What is the biggest concern you have about the approach taken in this paper? ---------------------------------------------------------- Farhi and Werning (2006) "Inequality, Social Discounting, and Taxation" What is the economic intuition for why inequality grows without bound in the Atkeson-Lucas (1992) framework discussed by Farhi and Werning? Why doesn't this occur in the Farhi-Werning model? What is the economic interpretation of the value function k(v)? ---------------------------------------------------------- Hall and Jones (2007) "Value of Life and Health Spending" Set up the social planner's problem for the full model and show how to derive equations (20) and (21) in the paper (the key first-order condition and the law of motion for the value of life). Provide some economic intuition for these equations. ---------------------------------------------------------- Jones (2007) Weak Links: Consider the version of the model with the symmetric allocation. Suppose we make the following additions to the model (one at a time). By what proportion is output reduced in each of these cases: 1. Suppose that weird union-type laws lead the economy to underutilize labor. In particular, half the labor sleeps in cots every day, while the other half works. 2. The government steals half of the output of each activity and throws it in the ocean. You should find that there is a large multiplier in one case but not in the other. What explains the difference? ---------------------------------------------------------- Manuelli and Seshadri (2005): 1. Define the optimal allocation of resources in this model. 2. What mechanism at work in the model allows it to explain quantitatively large differences in Y/L across countries? Is this plausible? ---------------------------------------------------------- AJR/HJ/Albouy/etc: Suppose an economist develops a new theory of economic development and technology transfer: information transmission is the key to modern economic growth. To test this theory, the economist runs regressions like Hall and Jones (1999) and AJR (2001), only this time using the new favorite variables: televisions per capita. Of course this variable is endogenous, so it is instrumented, e.g. with lagged TVs, or even distance from the equator, Western European languages, and/or settler mortality. The economist discovers that this measure outperforms other measures of institutions and human capital in horse-race style regressions, and concludes that the theory is an amazing success. Key question: What does this imply about empirical work in the growth literature? How could one hope to test and reject the TV story? ---------------------------------------------------------- Whelan (2003): Suppose $Y=$C+$I is the nominal income accounting identity for an economy, where the $ indicates nominal. Suppose real consumption C grows at rate gC and real investment I grows at rate gI, where these two growth rates are not equal. If gY is the growth rate of chain-weighted real GDP in this economy, then the following holds as an approximation: gY = $C/$Y*gC + $I/$Y*gI Prove that the above approximation is correct. ---------------------------------------------------------- Greenwood, Hercowitz, and Krusell (1997): Define a competitive equilbrium in this model in which households own the capital and "see" the capital accumulation equation explicitly. Note: do this in the standard "sequential" approach (i.e. with "t") rather than for the recursive approach taken by GHK. What is the relative price of equipment to consumption in equilibrium? ---------------------------------------------------------- Jones (2005) "The Shape of Production Functions..." Consider the technology menu setup in Section II of the paper. In particular, suppose the local production function is CES with curvature parameter $\rho$ and suppose the technology menu takes the form H(a,b)=N, where H(a,b) == a^\alpha b^\beta (as in equation 8). Question: Derive the global production function. ---------------------------------------------------------- Acemoglu (2003) "Capital- and Labor-Augmenting Technical Change" Acemoglu considers an equilibrium allocation for his environment, which is a pain to write down because of the usual Romer-style problems. Write down the social planner problem instead. Solve for the optimal growth rate along a balanced growth path. How sensitive do you think Acemoglu's result is that in the long-run researchers will only do LATC? ---------------------------------------------------------- Kortum (1997): 1. What is the pdf and cdf for a Pareto distribution? Given this, what is the following conditional probability equal to: Prob(x>lambda*x0 | x>x0) = ? where lambda is some number bigger than one. 2. What is the answer to this question if the distribution for x is exponential instead of Pareto? 3. Drawing on your answers to the previous questions, why are Pareto distributions so important to Kortum's paper? What happens if the distribution from which ideas are drawn is an exponential distribution? ---------------------------------------------------------- Barro and Sala-i-Martin (Chapter 7): Set up the social planner version of the Schumpeterian growth model. What is the Hamiltonian for this problem (note: this second part requires some work)? ----------------------------------------------------------