sources are spliced. We use the series measured in current and constant U.S. dollars to derive the implicit price indices for the quantities. The base year is 2015, and WDI uses that year to calculate the world totals.<sup>12</sup> Using uniform dollar units affords two innovations in the estimation. First, it provides consistent units across countries to estimate trade elasticities. Second, having the world's aggregate GDP and its components in comparable dollar units yields global demand variables for a country's exports, potentially correcting an identification issue in the CET estimation for some cases (see below).

Where available, we obtain time series for 1970-2018, potentially having 49 data points for each country. We avoid the 1950s and 1960s because many developing countries had just become independent, which is a reason why the sample size was small for many countries in the previous estimation of Devarajan, Go, and Li (1999). Seventeen or more Sub-Saharan African countries became independent only in 1960 and after (e.g., Cameroon, Kenya, Madagascar, Senegal, Tanzania, Uganda, Zambia, etc.). Nascent developing countries often have limited statistical capacity in the early years after independence, with issues of measurement reliability. Moreover, we exclude the years after 2018 because of the coronavirus of 2019 (COVID-19) and the disruptive effects of the pandemic on supply chains and global trade.

In cases where the series is shorter, we flag them. For example, for countries belonging to the former Soviet Union, data can only begin from about 1990. As a general rule, we omit countries with fewer than 20 observations.

## _Nonstationarity_

Macroeconomic series and aggregate price indices (such as E, M, D, P<sup>e</sup> , P<sup>d</sup> ) are known to be nonstationary. It typically takes differencing twice to make the series stationary, implying an integration order of two, i.e., I(2). Without further transformation, the significant time trend present in the data could lead to spurious relationships and estimates.

Fortunately, the log ratios of the variables in the estimating equations above reduce the order of integration. Using the Augmented Dickey-Fuller (ADF) unit root test of each transformed variable (ln[MDtt] , ln[DEtt ~~]~~ , ln[PPttmd ~~]~~ , ln[PPttde]), we cannot reject nonstationarity in the null hypothesis. However, differencing the series just once makes each case stationary, implying an integration order of one, I(1). We confirm this finding to be true for each variable for each country.

# _Cointegration_

The presence of the same level of integration at I(1) suggests a possible cointegrating relationship between ln[DEtt ~~]~~ and ln[PPttde] in one set and ln[MDtt] and ln[PPttmd ] in the other. We employ the Johansen cointegration test, including its alternative assumptions and specifications about the presence of a deterministic trend (linear or quadratic) and intercept in the cointegration equation (CE) or the VAR. We add exogenous variables such as global demand conditions for some CET cases (see identification below) or the appropriate trade share in GDP if there are unusual fluctuations in the dependent variable.

> 12The WDI methods and ratios to impute missing observations are described in the link <u>here.</u>

9