«ABSTRACT Over the period 1972-1986, the correlations of GDP, employment and investment between the United States and an aggregate of Europe, Canada ...»
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where λ(st−1 ) denotes the fraction of the domestic ﬁrm held by the domestic agent at the start of period t (these share holdings were chosen at t − 1).
The budget constraint for the domestic agent is now given by
Here P (st ) is the price at st of (ex dividend) shares in the domestic ﬁrm, in units of domestic consumption. P ∗ (st ) is the price of shares in the foreign ﬁrm in units of foreign consumption. Note that there are no trading costs or taxes in this speciﬁcation. Note that we do not assume that λ(st ) = λf ∗ (st ).
The problems solved by households and ﬁrms in the economy with period by period stock trade are exactly as in the benchmark economy described in the paper, except that eq. 23 is replaced by eq. A1 and eq. 13 is replaced by eq. A2.
We will guess that there is an equilibrium in this economy with period by period stock trade
with the following properties:
We need to show three things. First, we need to show that this is in fact an equilibrium.
Second, we need to show that allocations in this economy are identical to those in our benchmark model. Third, we need to show that perfect risk sharing is achieved. The strategy of the proof will be as follows. First we will simply assume that the trading strategy described by eq. A3 solves the households problem when stock prices are given by eq. A4. Given this assumption we will use budget constraints, market clearing conditions, and ﬁrst order conditions for ﬁnal-goods-producing ﬁrms to show that perfect risk sharing is achieved. Finally, we will verify that the trading strategy satisﬁes the household’s ﬁrst order conditions for stock purchases.
For notational concision, we temporarily suppress the history-dependent notation. In addition we appeal to symmetry to focus mostly on the domestic economy.
Given a Cobb-Douglas technology, payments to labor are a ﬁxed fraction of the value of intermediate output
Thus the ﬁrst order condition for the household’s purchases of domestic stocks is satisﬁed.
Similarly, it is straightforward to show that the household’s ﬁrst order condition for purchases of foreign stocks is also satisﬁed.
We have now demonstrated that given our candidate share prices, our candidate share trading rules solve the household’s problem and stock markets clear.29 We have also shown that this equilibrium in the economy with period by period trade has the key hallmark of a complete markets environment; there is perfect risk sharing.30 It remains to point out that restricting the choice set for stock holdings after date zero to a single point (the stock holdings initially chosen) will not impact equilibrium allocations given the trading rule described by eq. A3. Thus equilibrium allocations in the economy with trade only at date zero are identical to allocations in this equilibrium of the economy with period by period trade.
A2. Data Sources The data series for U.S. GDP, consumption, investment are from the OECD Quarterly National Accounts (QNA) and they are Gross Domestic Product, Private plus Government Final Consumption Expenditure, Gross Fixed Capital Formation (all at constant prices). For GDP, consumption and investment in the rest of the world, we constructed an aggregate of Canada, Japan, and Europe 15 (an OECD aggregate of the following countries: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Norway, Netherlands, Portugal, Spain, Sweden and United Kingdom). The original series are from the OECD-QNA, the same source we used for the U.S. We aggregated to create a single ﬁctional non-U.S. country by ﬁrst rebasing each series in 1996 national currency constant prices (using series speciﬁc deﬂators from the OECD, QNA) and then expressing everything in 1996 U.S. dollars using PPP exchange rates (from the OECD). Employment for the U.S., Canada, Japan and Europe 15 is the (deseasonalized) civilian employment index series from the OECD, Main Economic Indicators. Employment for the rest of the world is aggregated using constant weights, from the OECD, that are proportional to the number of employed persons in each area in 1995. Since before 1983 employment series for Europe 15 is not available, for the period 1972.1 1983.4 we use employment (aggregated using OECD weights) for Austria, Finland, France, Germany, Italy, Norway, Spain, Sweden and the United Kingdom, while for the period 1962.1 1971.4 we use employment (aggregated using OECD weights) of Finland, Germany, Italy, Sweden and United Kingdom. These were the only European countries for which we could ﬁnd consistent and comparable employment series.
U.S. holdings of foreign stocks, and foreign holdings of U.S. stocks by country and in aggregate are reported in ‘The International Investment Position of the United States’ published in various By construction, stock market clearing is satisﬁed, since λ∗ = 1 − λ and λf ∗ = 1 − λf.
It would be tedious, but straightforward, to describe an economy with a full set of Arrow securities, and to show that the set of equations characterizing equilibrium in that economy is isomorphic to the set of equations characterizing equilibrium in the economy with two stocks.
issues of the Survey of Current Business (SCB) by the Bureau of Economic Analysis (BEA). The U.S. direct investment position abroad, and the foreign direct investment position in the U.S. by country are reported on a historical-cost basis in ‘Direct Investment Positions for [year]: Country and Industry Detail’ in various issues of the SCB by the BEA. Aggregate measures of foreign direct investment at current cost and at market value are from ‘The International Investment Position of the United States’. The U.S. capital stock is the net stock at current cost of private nonresidential ﬁxed assets as reported by the BEA. We estimate FDI (inward and outward) at current cost (market value) for Europe Canada and Japan by ﬁrst computing the share of total FDI on a historical cost basis accounted for by these countries, and then multiplying this fraction by aggregate FDI at current cost (market value). For the period 1972 to 1975 we take direct investment position ﬁgures at market value from Lane and Milesi-Ferretti (2000), and use ratios of market capitalization to the current-cost replacement value of the capital to stock to estimate FDI at current cost.
The series for U.S. market capitalization is the combined NYSE, AMEX and NASDAQ capitalization series from the Center for Research on Stock Prices (CRSP). A series for foreign market capitalization is created by (i) using International Federation of Stock Exchanges data to weight the relative capitalizations of the stock markets corresponding to the U.S. and the set of countries included in the Morgan Stanley MSCI World (developed economies) excluding USA Price Index series in 2000 and (ii) using the ratio of the MSCI World excluding USA series to the MSCI USA series to estimate a series for foreign market. The series for the U.S. real exchange rate is a trade-weighted measure of the real value of the U.S. dollar reported by the Board of Governors (Major Currencies Index). The series for net exports is constructed by taking the ratio between exports minus imports and GDP, all at current prices, from the OECD, QNA. The current account series is the ratio between the current account from the IMF, International Financial Statistics and GDP, all at current prices. Stock prices indexes for the U.S. are from MSCI USA and for the rest of the world are from MSCI World excluding USA. All indexes are in quarterly averages and in dollars.
The complete dataset is available at www.stern.nyu.edu/~fperri/research.
Figure 1. International correlations (rolling window estimates) 1.
0 Employment 0.8 Investment 0.6 GDP 0.4 Consumption 0.2 0.0
0.12 0.1 0.08 0.06
0.16 0.14 0.12 0.1 0.08 0.06 0.04