雜譚點滴
評天下大事小事，抒懷中喜怒哀樂。有聊無聊，即興隨筆。冀望四海知音，或存觀省。
2025年4月3日（星期三）是一個極其值得紀念的日子。這一天，美國總統特朗普正式打響貿易大戰，對全球征收所謂的對等關稅（reciprocal tariffs）。
特朗普宣布對美國貿易夥伴實施普遍關稅，所有進口至美國的商品統一征收10%的基準關稅。此外，對他認定為“不公平貿易行為最嚴重”的60個國家額外征收更高關稅。其中，對歐盟和中國分別征收20%和34%的關稅。對中國的額外關稅是在特朗普此前實施的20%關稅基礎上追加，這樣對中國進口商品的總關稅將為54%。
特朗普稱讚這是美國的“解放日”。這一宣布震驚了全世界，並引發了全球貿易戰的擔憂。股市應聲下跌，關稅的規模和範圍令投資者感到措手不及。中國馬上反擊，次日宣布“對原產於美國的所有進口商品加征34%關稅”。
同時，美國政府公布了額外關稅的計算公式，如下：
這篇小文的目的是解釋一下這個公式。至於這個公式能否行得通，那將是另外一個話題。
這個公式其實並不複雜，不過需要理解裏麵的幾個概念。我把官方網站的原文放在後麵，讀者可以參考對照。
美國政府希望通過提高關稅來提高進口產品的價格，從而降低進口量，最終達到進出口貿易額對等，即零順差或逆差。
?τ_i 是新增加的額外關稅率（change in tariff rate）。
【注：上麵的 ？代表小三角。小三角符號文學城顯示不出來】
ε 是進口產品的需求彈性（elasticity of imports）。需求彈性是經濟學裏的一個基本概念，其定義為：
需求彈性 = 需求量變動百分數/價格變動百分數。
這個參數有實證數據做參考。這裏，美國政府取其值為4。也就是說，如果進口價格上升10%，那麽進口量就會降低 40%。
φ 是所謂的 passthrough，即關稅提高後有多少會反映在進口價格裏。這裏，美國政府取其值為 0.25，即25%。這意味著，如果關稅提高10%，進口價格將增加 2.5%。
理解了這幾個概念後，我們可以按部就班就把因果關係梳理一下：
目的：通過征收額外關稅，把貿易逆差降至為零。
假若額外征收的關稅率為 10%，進口價格就會增加 2.5% （=10%×25%）。
進口價格增加 2.5%，進口量就會減少10% (=4×2.5%)。
進口量減少 10%，進口額就會降低 10%*當前進口額。
所以，隻要選擇一個合適的 ?τ_i ，讓 進口額降低量 = 當前的貿易差額 (x_i - m_i)，
貿易逆差神奇地就消失了。
這樣，我們就可以得出上述那個簡單粗暴的公式。感興趣的讀者不妨自己推演一下。
由於美國政府對 ε 和 φ 這兩個參數的取值分別為 4 和 0.25，兩者相乘恰好為1，所以那個公式就可以簡化成
額外關稅率 = （出口量 - 進口量）/ 進口量
一個簡單粗暴的公式誕生了。
附：Reciprocal Tariff Calculations
Executive Summary
Reciprocal tariffs are calculated as the tariff rate necessary to balance bilateral trade deficits between the U.S. and each of our trading partners. This calculation assumes that persistent trade deficits are due to a combination of tariff and non-tariff factors that prevent trade from balancing. Tariffs work through direct reductions of imports.
Reciprocal tariff rates range from 0 percent to 99 percent, with unweighted and import-weighted averages of 20 percent and 41 percent.
Introduction
To conceptualize reciprocal tariffs, the tariff rates that would drive bilateral trade deficits to zero were computed. While models of international trade generally assume that trade will balance itself over time, the United States has run persistent current account deficits for five decades, indicating that the core premise of most trade models is incorrect.
The failure of trade deficits to balance has many causes, with tariff and non-tariff economic fundamentals as major contributors. Regulatory barriers to American products, environmental reviews, differences in consumption tax rates, compliance hurdles and costs, currency manipulation and undervaluation all serve to deter American goods and keep trade balances distorted. As a result, U.S. consumer demand has been siphoned out of the U.S. economy into the global economy, leading to the closure of more than 90,000 American factories since 1997, and a decline in our manufacturing workforce of more than 6.6 million jobs, more than a third from its peak.
While individually computing the trade deficit effects of tens of thousands of tariff, regulatory, tax and other policies in each country is complex, if not impossible, their combined effects can be proxied by computing the tariff level consistent with driving bilateral trade deficits to zero. If trade deficits are persistent because of tariff and non-tariff policies and fundamentals, then the tariff rate consistent with offsetting these policies and fundamentals is reciprocal and fair.
Basic Approach
Consider an environment in which the U.S. levies a tariff of rate τ_i on country i and ?τ_i reflects the change in the tariff rate. Let ε<0 represent the elasticity of imports with respect to import prices, let φ>0 represent the passthrough from tariffs to import prices, let m_i>0 represent total imports from country i, and let x_i>0 represent total exports. Then the decrease in imports due to a change in tariffs equals ?τ_i*ε*φ*m_i<0. Assuming that offsetting exchange rate and general equilibrium effects are small enough to be ignored, the reciprocal tariff that results in a bilateral trade balance of zero satisfies:
Parameter Selection
To calculate reciprocal tariffs, import and export data from the U.S. Census Bureau for 2024. Parameter values for ε and φ were selected. The price elasticity of import demand, ε, was set at 4.
Recent evidence suggests the elasticity is near 2 in the long run (Boehm et al., 2023), but estimates of the elasticity vary. To be conservative, studies that find higher elasticities near 3-4 (e.g., Broda and Weinstein 2006; Simonovska and Waugh 2014; Soderbery 2018) were drawn on. The elasticity of import prices with respect to tariffs, φ, is 0.25. The recent experience with U.S. tariffs on China has demonstrated that tariff passthrough to retail prices was low (Cavallo et al, 2021).
Findings
The reciprocal tariffs were left-censored at zero. Higher minimum rates might be necessary to limit heterogeneity in rates and reduce transshipment. Tariff rates range from 0 to 99 percent. The unweighted average across deficit countries is 50 percent, and the unweighted average across the entire globe is 20 percent. Weighted by imports, the average across deficit countries is 45 percent, and the average across the entire globe is 41 percent. Standard deviations range from 20.5 to 31.8 percentage points.
References
Boehm, Christoph E., Andrei A. Levchenko, and Nitya Panalai-Nayar (2023), “The long and short of (run) of trade elasticities, American Economic Review, 113(4), 861-905.
Broda, Christian and David E. Weinstein (2006). “Globalization and the gains from variety,” Quarterly Journal of Economics, 121(2), 541-585.
Pujolas, Pau and Jack Rossbach (2024). “Trade deficits with trade wars.” SSRN.
Simonovska, Ina and Michael E. Waugh (2014). “The elasticity of trade: Estimates and evidence,” Journal of International Economics, 92(1), 34-50.
Soderberry, Anson (2018). “Trade elasticities, heterogeneity, and optimal tariffs,” Journal of International Economics, 114, 44-62.
