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International Trade

CAS EC 391

Spring 2022

Problem Set 1

Note: All data files are provided in STATA and EXCEL. The dataset in STATA contains the variables’ description (type “describe” in the command window). Get familiar with the structure of the data and the content of the dataset. Make sure you understand the information contained in each variable.

QUESTION 1 (Lab Work I). Comparative Advantage and Institutions. 15 POINTS. Use “data-set-PS1-Q1.dta” to examine the role of institutions in the pattern of exports, for your assigned country (see the country-assignment file in http://learn.bu.edu). Attach the LOG file with your work. 

The goal of this question is to construct measures of comparative advantage and use them to support/reject the argument in Nunn (2007). The question will get you familiar with STATA commands to manage data and create simple statistics.

a) First, we will construct the “Revealed Comparative Advantage” (RCA) index using the formula in the class notes,

 

The variable  denotes exports of country c in industry i, denotes world exports in industry i,  are total exports for country c, and  are total world exports. Additionally:

The dataset contains the variable , named “xci”. Use the command “egen” to construct ,, and. Name these variables “xi”, “xc”, and “x”, respectively. Finally, use the command “gen” to generate the RCA index. Name this variable “rca”. 

b) Identify the five industries that have the highest RCA indexes for your country in 1997. Which are they? To do so, use the command “list” after restricting the data to your country and year 1997.

c) Calculate the mean contract intensity (“Ii”) across all goods using the command “egen”. Name that variable “m_Ii”. How many of the top-5 goods in b) are above and below the overall contract intensity mean?

d) Calculate the mean quality of institutions (“Qc”) across all countries using the command “egen”. Name this variable “m_Qc”. Is “Qc” in your country below or above the world mean? Use the command “egen” combined with “if” to construct the mean “Qc” among countries in the OECD and non-OECD group, respectively. Name those variables “m_Qc_oecd” and “m_Qc_no_oecd”.  Is “Qc” in your country below or above the mean among the countries belonging to the same group (OECD/non-OECD)?

e) Using all the data, run an Ordinary Least Square (OLS) regression where the dependent variable is logarithm of RCA and the controls are the measure of institutional quality “Qc”, the measure of contract intensity “Ii”, and the interaction between institutional quality and contract intensity “QcxIi”. First, use the command “gen” to generate the log of RCA, and the interaction variable “QcxIi”; name those variables “log_rca” and “Qc_x_Ii”. Then, use the command “reg” to run the OLS regression.

Interpret the coefficient on the interaction variable: How is the RCA index related to the interaction variable? What does its sign mean? Which other factors seen in class (apart from institutions) may affect the pattern of exports of a country?

 

QUESTION 2 (Lab Work II). The Gravity Equation. 15POINTS. Use “data-set-PS1-Q2.dta” to examine the role of “gravity” in explaining bilateral trade flows. Attach the LOG file with your work.  

The goal of this question is to apply regression analysis to study empirical regularities in international economics. Additionally, the question is aimed at getting you familiar with STATA commands related to OLS.

a) Take the logarithm of “trade_od”, “distance”, “GDP_o”, and “GDP_d”, using the command “gen”. Name each variable “log_name”. 

b) [“Naïve” Gravity.] Estimate the following equation by OLS: 

log (trade_od) = C + b₁ log GDP_d + b₂ log GDP_o + b₃ log distance + b₄ cborder + b₅ clanguage + b₆ ccolony + e_od 

where C denotes a constant and e_od is the error term. The remaining variables are described in the STATA dataset (type “describe” in the command window). 

Interpret the coefficients: Why did we use logs? Is there some coefficient statistically insignificant at 1%? What’s the effect of distance? 

c) Use the “naïve gravity” model in b) to predict the values of trade shares. Use the command “predict” right after running the OLS regression above. Name the predicted variable “log_trade_hat”. Pick the country pair where USA is the exporter and China the importer and compare predicted and data values for the (log of) trade shares.  Is the gravity model good in fitting the data for that country pair? Report the R-squared from the regressions in c): how good is “naïve gravity” overall in fitting the data for trade shares?

d) Construct a scatterplot of predicted versus data values using the command “scatter”. Make sure to put a title and clearly label the axis.

e) [“Fixed Effect” Gravity.] Estimate the equation above by OLS, replacing log GDP_d with one set of country dummies, and log GDP_o with a second set of country dummies. STATA has a few options to construct these dummy variables. For instance, you can use the command “egen” together with “group”. Name the sets of dummies “dummy_d” and “dummy_o”, respectively.

Did the coefficient on log of distance change with respect to the estimates in c)? Name two variables that the country dummies may be capturing.

 

QUESTION 3. U.S. Trade Data. 15 POINTS. This problem will introduce students to one of the most common sources for U.S. economic data and give them an overview of the magnitudes and patterns of trade in the U.S. for the past century.

a) The Bureau of Economic Analysis (BEA) prepares the official economics accounts for the United States, including the international accounts. Go to the BEA website: https://www.bea.gov/. Click on the tab “Tools” and select “Interactive Data”. Select “GDP & Personal Income” under Domestic Data. Click on “Begin using the data…” and download the following table (in Excel or CVS format):

1.  Choose Table 1.1.5 “Gross Domestic Product” in “Section 1-- Domestic Product and Income”.  This table contains the nominal values of the major components of GDP.  

2. “Modify” the table to display all years of data (annually). 

3. “Download” data in CVS or XLS format. Choose a place to save the file in your computer. 

b) Use EXCEL. To visualize how US trade has grown, create two time series: exports/GDP and imports/GDP.  (Why is it useful to divide a trade flow by GDP?)  A quick check: exports/GDP in 1929 is 0.0564.       

c) Use EXCEL. Make a chart of the two series you created in part b) with years on the x-axis and share of GDP on the y-axis.  Be sure to label the series.

Answer the following questions:

d) How much did exports, as a fraction of GDP, grow from 1950-1972?  How much did exports grow from 1972-94?

e) How much did exports, as a fraction of GDP, grow from 2000-2020?  How much did imports grow from 2000-2020?

f) As you found in part e., U.S. imports have been growing more quickly than exports in the last 20 years.  When a country is importing more than it is exporting, that country is said to be running a trade deficit.  In what other period did the United States run a large trade deficit?

QUESTION 4. Ricardian Model of Trade. 25 POINTS. Consider a Ricardian economy with 2 countries, home and foreign (a foreign variable is denoted with a *) and two goods, bicycles, , and mopeds, .  The home country has  and the foreign country is smaller, .  The representative consumer in each country has preferences of the form .  The production functions for the countries are:

where  and are, respectively, the amounts of labor used in producing good  in the home country and foreign country.

Home Country in the Closed Economy.

a) Write out the home consumer’s maximization problem.  Hint: the consumer maximizes utility subject to a budget constraint.  Use  for the home wage,  as the price of mopeds and use the normalization that the price of a bike is equal to 1.

b) Solve the home consumer’s problem for the demand functions for bikes and mopeds.  Hint: the functions should be of the form , where the ’s are combinations of . Show all your work.

c) 
Write out the maximization problem for the home firm that produces bikes.  Take the first order condition and solve for the wage, .  Remember, .  Show all your work.

d) Write out the maximization problem for the home firm that produces mopeds, given .  Take the first order condition and solve for the price of mopeds.  Show all your work.

e) What is home country consumption of bikes and mopeds in the closed economy?

The Open Economy.

Now consider an open economy in which the home and foreign country trade freely. The production functions, utility functions and labor endowments are the same as they are in question 1.  Under free trade, prices will be the same in each country.  Denote this world price of mopeds .  The (world) price of bikes is still 1.

f) What is the opportunity cost in terms of bikes (number of bikes given up to get one moped) in each country?  Which country specializes in which good?

g) Write out the maximization problem for the home-country firm that is in operation. (the other firm produces zero).  Use the first order condition to find . 

h) Write out the maximization problem for the foreign-country firm that is in operation. (the other firm produces zero).  Use the first order condition to get an expression for .

i) Write out the foreign consumer’s maximization problem.  Hint: consumers maximize utility subject to a budget constraint.  Use  for the foreign wage,  as the price of mopeds and use the normalization that the price of a bike is equal to 1.

j) Write out the demand functions for bikes and mopeds in the foreign country,  and .  You do not need to show the maximization problem. Hint: Refer to questions a) and b).

k) The balanced trade condition requires that the value of home country imports be equal to the value of foreign country imports, .  Substitute the demand functions into this relation.  Use the expressions from g) and h) to solve for the value of  and .

l) 
Graph the relative world supply curve on the figure provided below.  Label the opportunity costs of the home and foreign country.  Hint: this should look like a step function.  Label this curve .

m) Using the demand functions that you solved for above, solve for the relative demand curve, .  Hint: this should only be a function of . 

n) Add the relative demand curve to the graph and label it .

o) What is the equilibrium price of mopeds?

 

QUESTION 5. Heckscher-Ohlin Model of Trade. 15 POINTS. Suppose that there are two countries, Home and Foreign, two factors of production, capital and labor, and two products, food and cloth. Suppose that the production functions in both industries are such that payments to capital are a constant share of output: 20% in the cloth industry and 80% in the food industry.

a) Which good is capital-intensive?  Which good is labor intensive? 

b) Suppose that the home country has 100 units of labor and 200 units of capital, while the foreign country has 300 units of labor and 150 units of capital.  Under free trade, which country would export cloth?  Which country would export food?

c) What happens to the income of capital owners and laborers in each country when the countries open to trade?

d) Generalize the results from b) and c).  How do endowments determine the pattern of trade and the effect on income in the Heckscher-Ohlin model?

QUESTION 6. Increasing Returns to Scale and Monopolistic Competition. 15 POINTS. A country produces manufactured goods, whose industry is characterized by increasing returns to scale, monopolistic competition, and firms that differentiate their products.  Firms are symmetric: all firms have identical cost functions and demand functions given below. 

 

where  is the quantity demanded when the total industry demand is , the number of firms in the industry is , the average price in the industry is  and the price charged by the firm is , is the total cost of producing   units, is the fixed cost of production, and  is the marginal cost of production. Assume that does not change with the price in the industry.

a)  Derive an equation that relates average cost  to , , , and .  That is, derive an equation with  on the left-hand side and , ,  and  on the other. Hint: firm symmetry implies that each firm charges the same price.

b) Derive an equation that relates marginal revenue  to ,  and .  Hint: use demand to get P in terms of Q then multiply by Q to get total revenue.

c) To maximize profits, firms set marginal revenue equal to ___________________. 

d)  Given your answers to b) and c) derive an equation that relates  to ,  and . 

e) Sketch the equations from a. and d. below.  Label the equilibrium number of firms  and the equilibrium price .

f) Suppose the country opens to trade, which leads to a larger market size, .  Show the effect of this on your graph from e., labeling the new price  and the new number of firms .  Clearly label any curves that shift, and in which direction they shift.